DE112015002718T5 - Method for measuring an amount of eccentricity and device for measuring an amount of eccentricity - Google Patents

Abstract

A method of applying a light beam to an objective optical system disposed on a measuring axis and measuring the amount of eccentricity is provided. The method includes a detection step of detecting wavefront data based on the light beam emitted from the subject optical system, a first extraction step in which a predetermined aberration component is extracted from the wavefront data, a second extracting step in which a first aberration component of the predetermined aberration component and an analyzing step of simultaneously analyzing linear equations for the first aberration component, an eccentric aberration sensitivity and the amount of eccentricity, wherein the predetermined aberration component is an aberration component containing an aberration component caused by eccentricity, the first aberration component being a first power of the eccentricity amount in the is predetermined aberration component proportional aberration component and the eccentric aberration sensitivity one to the 1. Potency of the eccentricity amount is proportional aberration sensitivity.

Description

Technical area

The present invention relates to a method of measuring an amount of eccentricity and means for measuring an amount of eccentricity.

State of the art

When manufacturing lenses, various errors can occur in the lenses. In addition, an optical system is formed of one lens or a plurality of lenses. In an optical system, various errors can occur during assembly.

Examples of defects in lens fabrication include eccentricity of a lens surface. Moreover, examples of errors in the mounting of the optical system include eccentricity of the lens itself. Occurrence of eccentricity in the lens or the optical system results in decrease of optical power of the lens and optical power of the optical system. In addition, the more the amount of eccentricity increases, the more the optical power decreases.

Detecting the amount of eccentricity allows use of the amount of eccentricity to determine the acceptance of the finished lens or optical system. The term "determination of acceptance" means a determination of whether the finished lens or optical system has the desired optical performance. The lens or the optical system having an eccentricity amount smaller than a prescribed value is assumed, and the lens or optical system having an eccentricity amount larger than the prescribed value is scrapped.

Moreover, when the determination result is "retired," information about the amount of eccentricity can be used to adjust the manufacturing apparatus (a polishing apparatus and a molding apparatus) and to adjust the mounting of the optical system. For this reason, there is a strong demand for measuring the amount of eccentricity.

Examples of techniques for measuring the amount of eccentricity include a measuring technique disclosed in Patent Literature 1 and a measuring technique disclosed in Patent Literature 2.

Citation List

patent literature

• PTL 1: Japanese Patent Publication No. 837190
• PTL 2: Japanese Patent Publication No. 4260180

The measurement technique disclosed in Patent Literature 1 uses the autocollimation method. The autocollimating method enables measurement of the amount of eccentricity for each of the lens surfaces even if the optical system is formed of a plurality of lenses.

In the measuring technique disclosed in Patent Literature 2, a pen-type probe is used. In the method, the probe is brought into contact with a lens surface and thereby the shape of the lens surface is measured. In addition, the surface of a pre-prepared reference element is measured with the probe. Thereafter, the amount of eccentricity is measured by determining a relative positional displacement between the reference element and the lens surface. The measurement technique disclosed in Patent Literature 2 enables the measurement of amounts of eccentricity for two lens surfaces.

PRESENTATION OF THE INVENTION

Technical task

The autocollimation method is based on the precondition that the lens surface is a spherical surface. More specifically, the autocollimation method is theoretically inconsistent with the measurement of an aspherical surface. For this reason, the amount of eccentricity for an aspherical lens and an optical system containing an aspherical lens can not be measured with the measuring technique disclosed in Patent Literature 1.

In this case, there is a method to perform measurement in the same manner as that for a spherical surface, the part near the aspherical surface top being considered to be a spherical surface. However, in such a measurement, an aspherical surface, which is largely eccentric, causes a state in which reflected light from the aspherical surface can not be received. For this reason, the amount of eccentricity for an aspherical lens can not be measured.

Moreover, in the measurement technique disclosed in Patent Literature 1, an index image is observed. In this case, the index image is very distorted when the aspherical surface amount is large, even if the reflection light can be received. For this reason, the amount of eccentricity for an aspherical lens can not be measured.

Moreover, the measuring technique disclosed in Patent Literature 2 requires contact of the probe with the lens surface. For this reason, amounts of eccentricity of not all lenses can be measured in an optical system formed of a plurality of lenses.

For example, in the case where the optical system is formed of three lenses, there are lenses on both sides of the middle lens. In this case, the probe can not be brought into contact with the lens surfaces of the middle lens. For this reason, the shapes of the lens surfaces in the center lens can not be measured. In addition, in the lenses disposed on both sides, the shapes of the lens surfaces on both lenses facing the lens surfaces of the center lens can not be measured.

In addition, the sensor and the lens surface are relatively moved during the measurement. Since the movement speed is low during this process, the measuring time is increased. In addition, since the measurement technique requires a measurement of the shape of the reference element, the measurement time is also increased in this regard.

The present invention has been made in view of these problems. It is an object of the present invention to provide a method for measuring an amount of eccentricity and a device for measuring an amount of eccentricity which allow the measurement of the amount of eccentricity in a short time irrespective of the shape of the lens surface and the number of lenses constituting the optical system ,

Solution of the task

In order to achieve the above objects and achieve the object, a method of measuring the amount of eccentricity according to the present invention is a method in which a light beam is applied to an objective optical system disposed on a measuring axis to measure the amount of eccentricity wherein the method of measuring the amount of eccentricity comprises:
a detecting step of detecting wavefront data based on the light beam emitted from the subject optical system;
a first extracting step in which a predetermined aberration component is extracted from the wavefront data;
a second extracting step in which a first aberration component is extracted from the predetermined aberration component; and
an analysis step in which linear equations for the first aberration component, an eccentric aberration sensitivity and the amount of eccentricity are simultaneously analyzed,
in which
the predetermined aberration component is an aberration component containing an aberration component caused by eccentricity,
the first aberration component is an aberration component proportional to the 1st power of the amount of eccentricity in the predetermined aberration component; and
the eccentric aberration sensitivity is an aberration sensitivity proportional to the 1st power of the amount of eccentricity.

A device for measuring the amount of eccentricity according to the present invention comprises the following:
a light projection system disposed at one end of a measuring axis;
a light receiving system disposed at the other end of the measuring axis;
a holding member holding an objective optical system; and
a processing device connected to a wavefront measuring device,
in which
the holding element is arranged between the light projection system and the light receiving system,
the light projection system is provided in a position to apply a light beam to the objective optical system,
a detection step, a first extraction step, a second extraction step, and an analysis step are performed in the processing means,
Wavefront data is detected in the detection step on the basis of the light beam emitted from the objective optical system,
in the first extraction step, extracting a predetermined aberration component from the wavefront data,
in the second extracting step, extracting a first aberration component from the predetermined aberration component,
linear equations for the first aberration component, an eccentric aberration sensitivity and the amount of eccentricity are simultaneously analyzed in the analysis step,
the predetermined aberration component is an aberration component containing an aberration component caused by eccentricity,
the first aberration component is an aberration component proportional to the 1st power of the amount of eccentricity in the predetermined aberration component; and
the eccentric aberration sensitivity is an aberration sensitivity proportional to the 1st power of the amount of eccentricity.

Advantageous effect of the invention

According to the present invention, it is possible to provide a method for measuring an amount of eccentricity and a device for measuring an amount of eccentricity which enables measurement of the amount of eccentricity in a short time irrespective of the shape of the lens surface and the number of lenses constituting the optical system ,

BRIEF DESCRIPTION OF THE DRAWINGS

1 Fig. 11 is a conceptual diagram illustrating a state where aberration is caused by eccentricity;

2A . 2 B and 2C are diagrams for explaining a degree of freedom of eccentricity, 2A illustrates the degree of freedom of eccentricity on a spherical surface and 2 B and 2C illustrate the degree of freedom of eccentricity on an aspherical surface;

3A and 3B are diagrams illustrating coordinates in a measuring system and eccentricity of an objective optical system, wherein 3A the eccentricity illustrated by lens surfaces and 3B illustrating the eccentricity through sphere centers;

4 FIG. 15 is a diagram illustrating a flowchart of a measuring method according to the present embodiment; FIG.

5 Fig. 15 is a diagram illustrating a flowchart of the measuring method according to the present embodiment;

6A and 6B Fig. 15 are diagrams illustrating states in which a light beam is applied to the objective optical system, wherein 6A Radiation from the radiation position P illustrated and 6B Radiation from the radiation position P 'illustrated;

7 Fig. 15 is a diagram illustrating a flowchart of the measuring method according to the present embodiment;

8th Fig. 15 is a diagram illustrating a flowchart of the measuring method according to the present embodiment;

9A and 9B FIGs. are diagrams for explaining system aberration in a light projection system, wherein FIG 9A illustrates a state in which no system aberration occurs and 9B illustrates a condition in which a system aberration occurs in the light projection system;

10A and 10B FIG. 15 are diagrams illustrating a system aberration in a light receiving system, wherein FIG 10A illustrates the system aberration in a sensor component forming unit and 10B illustrates the system aberration in a wavefront data acquisition unit;

11 Fig. 10 is a diagram illustrating a method of previously determining a system aberration component;

12A and 12B are diagrams illustrating a first turn wherein 12A illustrates a state before the first rotation is performed, and 12B illustrate a state after the first rotation has been performed;

13A . 13B and 13C FIG. 15 are diagrams illustrating a state in which the ball centers are changed by the first rotation, wherein FIG 13A illustrates the positions of the centers of the sphere before the first rotation, 13B illustrates the positions of the ball centers after the first rotation and 13C illustrates the amounts of movement of the ball centers caused by the first rotation;

14 Fig. 15 is a diagram illustrating a state in which an optical light receiving system is interposed between the subject optical system and the light receiving system;

15 Fig. 12 is a diagram illustrating a state in which a first rotation axis is eccentric to the measurement axis;

16A and 16B are diagrams illustrating relative relationships between the first axis of rotation and the measuring axis, wherein 16A illustrates a state in which the measuring axis coincides with the first axis of rotation, and 16B illustrates a state in which the first rotation axis is inclined relative to the measurement axis;

17 Fig. 12 is a diagram illustrating a state in which the first rotation axis is offset from the measurement axis;

18 Fig. 10 is a diagram illustrating a flowchart of Example 1;

19 Fig. 10 is a diagram illustrating a flowchart of Example 2;

20 FIG. 15 is a diagram illustrating a flowchart of a measuring method according to the present embodiment; FIG.

21A . 21B . 21C and 21D are diagrams illustrating a motion state of the radiation position, wherein 21A illustrates a position of a radiation position before the movement, 21B a position illustrating a radiation position after the movement, 21C illustrates a position of the other radiation position before the movement and 21D illustrates a position of the other radiation position after the movement;

22 Fig. 15 is a diagram illustrating a flowchart of the measuring method according to the present embodiment;

23A . 23B . 23C and 23D are diagrams illustrating a motion state of the radiation position, wherein 23A a position illustrating a radiation position before the movement, 23B illustrates a position of the other radiation position before the movement, 23C a position of a radiation position after the movement illustrated and 23D illustrates a position of the other radiation position after the movement;

24A and 24B illustrate a motion state of the radiation position, wherein 24A illustrates the case where the direction of movement of the radiation position is unidirectional, and 24B illustrates the case where the moving direction of the radiation position is bidirectional;

25A . 25B and 25C are diagrams illustrating patterns of radiation position, where 25A illustrates a state in which the radiation positions are bi-directional, 25B illustrates a state in which the radiation positions are concentric and 25C illustrates a state in which the radiation positions are lattice-shaped;

26A and 26B illustrate a state in which the light beam is applied to the subject optical system, wherein 26A illustrates radiation at an angle θ and 26B illustrates radiation at an angle θ ';

27 Fig. 15 is a diagram illustrating a flowchart of the measuring method according to the present embodiment;

28A and 28B are diagrams illustrating a second rotation wherein 28A illustrates a state before the second rotation is performed, and 28B illustrate a state after the second rotation has been performed;

29A and 29B Fig. 10 are diagrams for explaining a change of the coordinate axes caused by the second rotation, wherein 29A illustrates a state before the second rotation is performed, and 29B illustrate a state after the second rotation has been performed;

30A and 30B are diagrams illustrating a movement of the ball center point caused by the first rotation, wherein 30A illustrates the movement of the ball center in a forward measurement and 30B illustrates the movement of the sphere center in a backward measurement;

31A . 31B . 31C and 31D are diagrams illustrating a movement of the ball center point caused by the first rotation and the second rotation, wherein 31A illustrates the position of the center of the sphere before the first rotation in a forward measurement, 31B illustrates the position of the sphere center after the first rotation in the forward measurement, 31C illustrates the position of the center of the sphere before the first rotation in a backward measurement and 31D illustrates the position of the sphere center after the first rotation in the backward measurement;

32A . 32B and 32C _{Fig. 15} are diagrams illustrating an object height _{function occurring} in the eccentric aberration _{sensitivities} B _2jl (Ox, Oy) and B _3jl (Ox, Oy), wherein 32A illustrates the case where the subject optical system is not eccentric and 32B and 32C illustrate the case where the subject optical system is eccentric;

33A . 33B and 33C _{Fig. 11} are diagrams illustrating an object height function occurring in the eccentric aberration _sensitivity B _4jl (Ox, Oy), wherein 33A illustrates the case where the subject optical system is not eccentric and 33B and 33C illustrate the case where the subject optical system is eccentric;

34A . 34B and 34C _{Fig. 11} are diagrams illustrating an object height _{function occurring} in the eccentric aberration _{sensitivities} B _5jl (Ox, Oy) and B _6jl (Ox, Oy), wherein 34A illustrates the case where the subject optical system is not eccentric and 34B and 34C illustrate the case where the subject optical system is eccentric;

35A . 35B and 35C _{Fig. 11} are diagrams illustrating an object height _{function occurring} in the eccentric aberration _{sensitivities} B _7jl (Ox, Oy) and B _8jl (Ox, Oy), wherein 35A illustrates the case where the subject optical system is not eccentric and 35B and 35C illustrate the case where the subject optical system is eccentric;

36 Fig. 10 is a diagram illustrating an eccentricity amount measuring apparatus according to the embodiment;

37A and 37B are diagrams illustrating a structure and a function of an SH sensor, wherein 37A illustrates a state in which one can think of a plane wave on the SH sensor, and 37B illustrates a condition where a non-planar wave is incident on the SH sensor;

38A . 38B . 38C and 38D are diagrams illustrating a system aberration in the SH sensor, wherein 38A illustrates the case where the substrate is curved, 38B illustrates the case in to which the substrate is inclined, 38C illustrates the case where an error occurs in the lens pitch, and 38D illustrates the case where the focal length differs between the lenses;

39A and 39B illustrate modifications of the light projection system, wherein 39A illustrates a first modification and 39A illustrates a second modification;

40A and 40B FIG. 15 are diagrams illustrating a positional relationship between a holding member and the measuring axis, wherein FIG 40A illustrates the case where the first axis of rotation coincides with the measuring axis, and 40B illustrates the case where the first axis of rotation does not coincide with the measuring axis;

41A and 41B FIG. 12 are diagrams illustrating modifications of the holding member, wherein FIG 41A illustrates a first modification and 41B illustrates a second modification;

42A and 42B FIG. 15 are diagrams illustrating a state in which the second rotation is performed, wherein FIG 42A illustrates a state before the movement of the holding member and 42B illustrates a state after the movement of the holding member;

43 Fig. 12 is a diagram illustrating the light projection system in the case where the subject optical system has a negative refractive power;

44 Fig. 12 is a diagram illustrating a modification of the light receiving system;

45 Fig. 15 is a diagram illustrating a first modification of the eccentricity amount measuring apparatus;

46 Fig. 12 is a diagram illustrating a second modification of the eccentricity amount measuring apparatus; and

47 FIG. 15 is a diagram illustrating a third modification of the eccentricity amount measuring apparatus. FIG.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Before explaining the examples, the effect and effect of the embodiments according to certain aspects of the present invention will be described below. In explaining the effect and the effect of the embodiments, the explanation will be made by concrete examples. However, similar to the examples to be described later, aspects exemplified herein are but a few of the aspects included in the present invention, and there are a large number of variations in these aspects. Thus, the present invention is not limited to the aspects set forth as an example.

• (I) Durch die Exzentrizität verursachte Aberration wird hier nachfolgendend erläutert. 1 ist ein konzeptuelles Diagramm, das einen Zustand illustriert, in dem ein Abbildungsfehler durch Exzentrizität verursacht wird. Da 1 ein konzeptuelles Diagramm ist, sind Positionen, Größen und Formen der Bilder von Bild IM1, Bild IM2 und Bild IM3 nicht exakt.

Before explaining the method of measuring the amount of eccentricity according to the present embodiment, explanation will be given on the following: (1) an aberration caused by the eccentricity; (II) a degree of freedom of eccentricity; (III) coordinates in the measuring system; and (IV) a wavefront after transmission through an eccentric lens surface.

• (I) Aberration caused by the eccentricity will be explained below. 1 Fig. 11 is a conceptual diagram illustrating a state where an aberration is caused by eccentricity. There 1 is a conceptual diagram, positions, sizes and shapes of the images of image IM1, image IM2 and image IM3 are not exact.

When the optical system is eccentric, eccentricity causes aberration. When the optical system is formed of a plurality of lenses, the aberration caused by the eccentricity of a lens surface is successively relayed to other lens surfaces.

As in 1 As illustrated, with respect to an image of an object point OB, an image IM1 is formed by a lens surface LS1, an image IM2 is formed by a lens surface LS2, and an image IM3 is formed by a lens surface LS3. In this way, the image of the object point OB is formed by the lens surface LS1 and the image formed is passed through the lens surface LS2 and the lens surface LS3.

In 1 For example, the lens surface LS1, the lens surface LS2 and the lens surface LS3 are eccentric to the optical axis. In this case, the image IM1, the image IM2 and the image IM3 are formed in positions removed from respective positions on the optical axis.

In addition, with the eccentricity of the lens surface LS1, an aberration occurs in the image IM1. The image IM1 corresponds to the object point of the lens surface LS2. Since the lens surface LS2 is also eccentric, aberration also occurs in image IM2. The aberration in the image IM2 is an aberration obtained by adding the aberration caused by the eccentricity of the lens surface LS2 to the aberration in the image IM1. The aberration in the image IM3 is an aberration obtained by adding the aberration caused by the eccentricity of the lens surface LS3 to the aberration in the image IM2.

• (II) Der Freiheitsgrad der Exzentrizität wird hier nachfolgend erläutert. Der Freiheitsgrad der Exzentrizität gibt die Art der Exzentrizität an. Der Freiheitsgrad der Exzentrizität wird grob in Verschiebung und Neigung eingeteilt. 2A, 2B und 2C sind Diagramme zur Erläuterung eines Freiheitsgrads der Exzentrizität, 2A illustriert den Freiheitsgrad der Exzentrizität auf einer sphärischen Oberfläche und 2B und 2C illustrieren den Freiheitsgrad der Exzentrizität auf einer asphärischen Oberfläche.

In this way, the image in the state in which the lens surfaces are eccentric is relayed, while the aberration occurring in the lens surface LS1, the lens surface LS2, and the lens surface LS3 is added, respectively.

• (II) The degree of freedom of eccentricity is explained below. The degree of freedom of eccentricity indicates the type of eccentricity. The degree of freedom of eccentricity is roughly divided into displacement and inclination. 2A . 2 B and 2C are diagrams for explaining a degree of freedom of eccentricity, 2A illustrates the degree of freedom of eccentricity on a spherical surface and 2 B and 2C illustrate the degree of freedom of eccentricity on an aspherical surface.

As in 2A illustrated, the eccentricity may be given in a spherical surface by a position of the ball center. The degree of freedom of eccentricity in a spherical surface is geometrically only a shift in an X direction and a shift in a Y direction.

Moreover, in a spherical surface, the inclination may be regarded as a displacement in the X direction, a displacement in the Y direction, and a displacement in a Z direction even if the spherical surface is inclined, with a certain point in a distance serves as a center. Accordingly, the degree of freedom of eccentricity in a spherical surface can be regarded as only a shift in the X direction and a shift in the Y direction.

In the production also occurs a distance shift. Spacing displacements in fabrication are, for example, an error in a thickness of a lens and an error in a distance between lenses in a system of two lenses. In fact, the offset displacement caused by a manufacturing defect can not be distinguished from a distance shift caused when the spherical surface is tilted.

In contrast, as in 2 B and 2C Illustrated, an aspheric surface includes an aspheric surface top surface and an aspheric surface axis. The aspheric surface axis is a rotationally symmetric axis. Since an aspheric surface includes an aspheric surface axis, an aspheric surface includes inclination in a direction A and inclination in a direction B as a degree of freedom of eccentricity in addition to a displacement in the X direction and a displacement in the Y direction. The displacement in the X direction and the displacement in the Y direction serve as degrees of freedom of eccentricity with respect to the surface aspherical surface. In addition, the inclination in the direction A and the inclination in the direction B serve as degrees of freedom of eccentricity with respect to the aspherical surface axis.

• (III) Die Koordinaten im Messsystem werden hier nachfolgend erläutert. 3A und 3B sind Diagramme, die Koordinaten im Messsystem und eine Exzentrizität eines gegenständlichen optischen Systems illustrieren, wobei 3A die Exzentrizität durch Linsenoberflächen illustriert und 3B die Exzentrizität durch Kugelmittelpunkte illustriert.

In this way, a spherical surface and an aspherical surface differ in the number of degrees of freedom of eccentricity. Accordingly, the number of degrees of freedom of eccentricity is, for example, at most 6 when a first surface of a lens is a spherical surface and a second surface thereof is an aspheric surface.

• (III) The coordinates in the measuring system are explained below. 3A and 3B are diagrams illustrating coordinates in the measuring system and an eccentricity of an objective optical system, wherein 3A the eccentricity illustrated by lens surfaces and 3B the eccentricity illustrated by ball centers.

The measuring system includes a light projection system and a light receiving system. In 3A and 3B For example, the light projection system is illustrated with an Ox axis, an Oy axis and an Oz axis, and the light receiving system is illustrated with a ρx axis and a ρy axis. In addition, are the coordinates of the light projection system are given by the object height coordinates (Ox, Oy, Oz), and the coordinates of the light receiving system are given by the pupil coordinates (ρx, ρy).

As in 3A As illustrated, the subject optical system is formed of lens surfaces from a first lens surface LS ₁ to a j-th lens surface LS _j . It is assumed that the lens surfaces are shifted from the Oz axis in the Y direction. In addition, it is assumed that all lens surfaces are spherical surfaces.

• (IV) Eine Wellenfront nach einer Übertragung durch eine exzentrische Linsenoberfläche wird hier nachfolgend erläutert. Dies wird hier nachfolgend unter Verwendung eines numerischen Ausdrucks erläutert.

As in 2A illustrated, the eccentricity of the lens surface may be indicated by its spherical center when the lens surface is a spherical surface. Illustrated for this reason 3B the displacements of the lens surfaces using the ball centers. In 3B SC ₁ , SC ₂ , ... and SC _j indicate the ball centers of the respective lens surfaces. Moreover, δ ₁ , δ ₂ , ... and δ _j indicate the shift amounts of the respective lens surfaces in the Y direction.

• (IV) A wavefront after transmission through an eccentric lens surface will be explained hereinafter. This will be explained below using a numerical expression.

As in 3A illustrated, a light beam LB is radiated from the object height coordinates (Ox, Oy) in the light projection system to the subject optical system. The light beam LB is emitted from a plane OxOy. Accordingly, the exact object height coordinates are (Ox, Oy, 0), but are expressed as (Ox, Oy) to simplify the explanation.

A light beam LB 'transmitted through the subject optical system is made incident on the light receiving system. The light beam LB indicates a part of the light beam which should originally be applied to the objective optical system. In the same way, the light beam LB 'indicates a part of the light beam that should originally be incident on the light receiving system.

In the light receiving system, wavefront data are detected based on the light beam LB '. Since the lens surfaces in the subject optical system are eccentric, the wavefront of the light beam LB 'includes wavefront aberration caused by the eccentricity. For this reason, analysis of the wavefront data enables detection of the wavefront aberration caused by the eccentricity.

Here, the aberration that occurs in a rotationally symmetric optical system can be developed using a polynomial expression such as a term that does not depend on the amount of eccentricity, a term that is proportional to the 1st power of the amount of eccentricity, a term that is square to the square Eccentricity amount, a term proportional to the cube of the amount of eccentricity and a term proportional to the fourth power of the amount of eccentricity ... (see: Third-order Aberration Theory for Optical System with Eccentricity, Third-order Aberration Theory of Eccentric Optical System, both published by the Japan Optomechatronics Association, Image field distribution model of wavefront aberration and models of distortion and field curvature [T. Matsuzawa: J. Opt. Soc. Am. A, 28, No. 2 (2011)] 96-110]).

wobei
Δ_j der Exzentrizitätsbetrag in Bezug auf die Oz-Achse in der j-ten Oberfläche ist,
B_j1(Ox,Oy,ρx,ρy) eine zur 1. Potenz des Exzentrizitätsbetrags in der j-ten Oberfläche proportionale exzentrische Aberrationsempfindlichkeit ist und
B_j2(Ox,Oy,ρx,ρy) eine zum Quadrat des Exzentrizitätsbetrags in der j-ten Oberfläche proportionale exzentrische Aberrationsempfindlichkeit ist.Here, only the terms that depend on the amount of eccentricity are used to develop the wavefront aberration. In this case, the wavefront aberration W can be expressed, for example, by the following expression (1). However, the wavefront aberration W is explained here as a deviation from the wavefront if the objective optical system is not eccentric.

in which
Δj is the _amount of eccentricity with respect to the Oz axis in the jth surface,
_Bj1 (Ox, Oy, ρx, ρy) is an eccentric aberration sensitivity proportional to the 1st power of the amount of eccentricity in the jth surface, and
B _j2 (Ox, Oy, ρx, ρy) is an eccentric aberration sensitivity proportional to the square of the amount of eccentricity in the jth surface.

As expressed by the expression (1), each term of the polynomial expression is given by the product of the amount of eccentricity and the eccentric aberration sensitivity. In Expression (1), the amount of eccentricity is not limited to the shift amount in the Y direction. Accordingly, the amount of eccentricity is given by Δ, not δ, meaning a general amount of eccentricity.

Moreover, the wavefront aberration W in the expression (1) is developed on the basis of the aberration theory, and the development is performed until the term proportional to the square of the amount of eccentricity (to the term proportional to Δ ² ). Since the amount of eccentricity caused by a manufacturing error is small, the amount of aberration in each term is generally regarded as minute for the terms proportional to the third and fourth and higher powers of the amount of eccentricity and can be ignored. For this reason, the expression (1) does not include terms proportional to the third and fourth and higher powers of the amount of eccentricity.

Each of the terms on the right side of the expression (1) is referred to as an "aberration component". In addition, each of the terms multiplied by the amount of eccentricity Δ is referred to as an "eccentric aberration component". Each of the terms on the right side of the expression (1) is multiplied by the amount of eccentricity Δ. Accordingly, all terms on the right side of the expression (1) are eccentric aberration components.

Table 1 explains all the terms of expression (1). [Table 1] term Explanation of the term Δ ₁ B ₁₁ (Ox, O y, ρ x, ρ y) eccentric aberration component proportional to the 1st power of the amount of eccentricity in the first surface Δ ₁ ² B ₁₂ (Ox, O y, ρ x, ρ y) eccentric aberration component proportional to the square of the amount of eccentricity in the first surface Δ ₂ B ₂₁ (Ox, O y, ρ x, ρ y) eccentric aberration component proportional to the 1st power of the amount of eccentricity in the second surface Δ ₂ ² B ₂₂ (Ox, O y, ρ x, ρ y) eccentric aberration component proportional to the square of the amount of eccentricity in the second surface ... ... Δ _j B _j1 (Ox, Oy, ρx, ρy) eccentric aberration component proportional to the 1st power of the amount of eccentricity in the jth surface Δ _j ² B _j2 (Ox, Oy, ρx, ρy) eccentric aberration component proportional to the square of the amount of eccentricity in the jth surface

As illustrated in Table 1, the eccentric aberration components included in the expression (1) eccentric aberration components (proportional to Δ Terme), which are proportional to the first power of the eccentricity and eccentric aberration components (Δ ² to proportional terms), which the square of the eccentricity are proportional. Moreover, _Bj1 (Ox, Oy, ρx, ρy) is an eccentric aberration _sensitivity proportional to the 1st power of the amount of eccentricity in the j-th surface, and _Bj2 (Ox, Oy, ρx, ρy) is a square of the amount of eccentricity in the j-th surface proportional eccentric aberration sensitivity.

As described above, the wavefront aberration is obtained by analyzing the wavefront data. The wavefront aberration can be developed by a polynomial expression of aberration components.

wobei
B_1j1(Ox,Oy) bis B_9j1(Ox,Oy) exzentrische Aberrationsempfindlichkeiten sind. In addition, the eccentric aberration sensitivity in each aberration component can be developed with a polynomial expression based on the aberration theory. For example, when developed by a Zernike polynomial, the eccentric aberration _sensitivity B _jl (Ox, Oy, ρx, ρy) can be expressed by the following expression (2).

in which
B _1j1 (Ox, Oy) to B _9j1 (Ox, Oy) are eccentric aberration _{sensitivities} .

If the eccentric aberration _sensitivity is given by B _zjl (Ox, Oy), B _zjl (Ox, Oy) is the eccentric aberration _{sensitivity of} the term multiplied by the _Zth term of the Zernike terms, and that to the 1st power of the Zernike term Eccentricity amount in the j-th surface proportional eccentric aberration sensitivity.

Table 2 illustrates a correlation between each of the terms of the Zernike terms and the function and aberration that indicate each term. Table 2 illustrates the correlation thereof for the first through ninth terms of the Zernike terms. [Table 2] Zernike Terme function aberration 1st term 1 Spherical aberration (Piston) 2nd term ρx Coma (tilt) 3rd term ρy Coma (tilt) 4th term 2 (ρx ² + ρy ² ) - 1 Spherical aberration (focal point) 5th term ρx ² - ρy ² astigmatism 6th term 2ρxρy astigmatism 7. Term 3 (ρx ² + ρy ² ) ρx - 2ρx coma 8. Term 3 (ρx ² + ρy ² ) ρy - 2ρy coma 9th term 6 (ρx ² + ρy ² ) ² - 6 (ρx ² + ρy ² ) + 1 Spherical aberration ... ... ...

The terms of the Zernike terms are given by the pupil coordinates ρx and ρy. Here the order is determined by the order in ρx and the order in ρy is determined to be the maximum order of the pupil coordinates. If the maximum order is an even order, the order of the function of the term is an even order. If the maximum order is an odd order, the order of the function of the term is an odd order. For example, in the second term of the Zernike terms, the maximum order of the pupil coordinates in the second term of the Zernike terms is the first order and one odd order, since the pupil coordinate is ρx. Accordingly, the function indicating the second term of the Zernike terms is a function in which the maximum order of the pupil coordinates is the first order and an odd order.

In addition, in the sixth term of the Zernike terms, the maximum order of the pupil coordinates in the sixth term of the Zernike terms is the second order and an even order because the pupil coordinates are ρxρy. Accordingly, the function indicating the sixth term of the Zernike terms is a function in which the maximum order of the pupil coordinates is the second order and an even order.

Table 3 illustrates the results of the first term to the ninth term taken together. [Table 3] Zernike Terme function Maximum order of the pupil coordinates Order of the pupil coordinates 1st term 1 0 just 2nd term ρx 1 odd 3rd term ρy 1 odd 4th term 2 (ρx ² + ρy ² ) - 1 2 just 5th term ρx ² - ρy ² 2 just 6th term 2ρxρy 2 just 7. Term 3 (ρx ² + ρy ² ) ρx - 2ρx 3 odd 8. Term 3 (ρx ² + ρy ² ) ρy - 2ρy 3 odd 9th term 6 (ρx ² + ρy ² ) ² - 6 (ρx ² + ρy ² ) + 1 4 just ... ... ... ...

Moreover, the second term in expression (2) is a term obtained by multiplying B _2jl (Ox, Oy) by ρx. Accordingly, the second term of expression (2) is a term obtained by multiplying B _{2j 1} (Ox, _{O y} ) having a function with the pupil _coordinates in an odd order.

Moreover, the sixth term in expression (2) is a term obtained by multiplying B _6jl (Ox, Oy) by ρxρy. Accordingly, the sixth term of expression (2) is a term obtained by multiplying B _{6j 1} (Ox, _{O y} ) with a function having the pupil _coordinates in even order.

Table 4 explains all terms of expression (2). [Table 4] term Explanation of the term 1 · B _1jl (Ox, Oy) Term that is multiplied by a function with the pupil coordinates in even order ρx · B _2jl (Ox, Oy) Term multiplied by a function with the pupil coordinates in odd order ρy · B _3jl (Ox, Oy) Term multiplied by a function with the pupil coordinates in odd order {2 (ρx ² + ρy ² ) - 1} · B _4jl (Ox, Oy) Term that is multiplied by a function with the pupil coordinates in even order {ρx ² -ρy ² } * B _5jl (Ox, Oy) Term that is multiplied by a function with the pupil coordinates in even order 2ρxρy · B _6jl (Ox, Oy) Term that is multiplied by a function with the pupil coordinates in even order {3 (ρx ² + ρy ² ) ρx - 2ρx} · B _7jl (Ox, Oy) Term multiplied by a function with the pupil coordinates in odd order {3 (ρx ² + ρy ² ) ρy - 2ρy} · B _8jl (Ox, Oy) Term multiplied by a function with the pupil coordinates in odd order {6 (ρx ² + ρy ² ) ² - 6 (ρx ² + ρy ² ) + 1} · B _9jl (Ox, Oy) Term that is multiplied by a function with the pupil coordinates in even order ...

When the eccentric aberration _{sensitivity Bjl} (Ox, Oy, ρx, ρy) is developed by means of a Zernike polynomial, in this way the terms of the polynomial expression in terms multiplied by a function with the pupil coordinates in odd order and in terms classified, which are multiplied by a function with the pupil coordinates in even order.

In addition, the eccentric aberration _sensitivity B _zjl (Ox, Oy) can be developed by means of a polynomial. The developed expression differs, however, between the terms multiplied by a function with the pupil coordinates in odd order and the terms multiplied by a function with the pupil coordinates in an even order.

Here, the cases where the index "I" in the eccentric aberration _sensitivity B _zjl (Ox, Oy) is "I = 1" and "I = 2" are explained separately below.

In the case of "I = 1", the eccentric aberration _sensitivity by B _zj1 (Ox, Oy) gives the eccentric aberration _{sensitivity of} the term multiplied by the _Zth term of the Zernike terms and that to the 1st power of the amount of eccentricity in the j-th surface proportional eccentric aberration sensitivity.

The following is an explanation of the eccentric aberration _sensitivity B _zj1 (Ox, Oy) of the term multiplied by a function with the odd-order pupil _coordinates . The eccentric aberration _sensitivity B _zj1 (Ox, Oy) is the eccentric aberration _{sensitivity associated} with the second term, the third term, the seventh term, the eighth term, ... the Zernike terms (hereinafter referred to as "the second term and others the Zernike term ") is multiplied. The eccentric aberration _sensitivity B _zj1 (Ox, Oy) (z = 2, 3, 7, 8, ...) is given by the following expression (3).

As expressed by the expression (3), the eccentric aberration _sensitivity B _zj1 (Ox, Oy) of the term multiplied by the second term and other of the Zernike terms in the eccentric aberration sensitivity, which is proportional to the 1st power of the amount of eccentricity, is even Function for the object height coordinates.

The following is an explanation of the eccentric aberration _sensitivity B _zj1 (Ox, Oy) of the term, which is multiplied by a function with the pupil coordinates in an even order. The eccentric aberration _sensitivity B _zj1 (Ox, Oy) is the eccentric aberration _{sensitivity associated} with the first term, the fourth term, the fifth term, the sixth term, the ninth term ... of the Zernike terms (hereinafter referred to as "the fourth term Term and others of the Zernike terms ") is multiplied. The eccentric aberration _sensitivity B _zj1 (Ox, Oy) (z = 1, 4, 5, 6, 9, ...) is given by the following expression (4).

As expressed by the expression (4), the eccentric aberration _sensitivity B _zj1 (Ox, Oy) of the term multiplied by the fourth term and other of the Zernike terms in the eccentric aberration sensitivity, which is proportional to the 1st power of the amount of eccentricity, is odd Function for the object height coordinates.

In the case of "I = 2", the eccentric aberration _sensitivity by B _zj2 (Ox, Oy) gives the eccentric aberration _{sensitivity of} the term multiplied by the _Zth term of the Zernike terms, and the Square of the eccentricity amount in the j-th surface proportional eccentric aberration sensitivity.

The following is an explanation of the eccentric aberration _sensitivity B _zj1 (Ox, Oy) of the term multiplied by a function with the odd-order pupil _coordinates . The eccentric aberration _sensitivity B _zj2 (Ox, Oy) is the eccentric aberration _{sensitivity of} the term multiplied by the second term and other of the Zernike terms. The eccentric aberration _sensitivity B _zj2 (Ox, Oy) (z = 2, 3, 7, 8, ...) is given by the following expression (5).

As expressed by the expression (5), the eccentric aberration _sensitivity B _zj2 (Ox, Oy) of the term multiplied by the second term and other Zernike terms in the eccentric aberration sensitivity, which is proportional to the square of the amount of eccentricity, is an odd function the object height coordinates.

The following is an explanation of the eccentric aberration _sensitivity B _zj1 (Ox, Oy) of the term, which is multiplied by a function with the pupil coordinates in an even order. The eccentric aberration _sensitivity B _zj2 (Ox, Oy) is the eccentric aberration _{sensitivity of} the term multiplied by the fourth term and others of the Zernike terms. The eccentric aberration _sensitivity B _zj2 (Ox, Oy) (z = 1, 4, 5, 6, 9 ...) is given by the following expression (6).

As expressed by the expression (6), the eccentric aberration _sensitivity B _zj2 (Ox, Oy) of the term multiplied by the fourth term and other of the Zernike terms in the eccentric aberration sensitivity, which is proportional to the square of the amount of eccentricity, is an even function the object height.

C in expressions (3) to (6) is a constant that does not depend on the object height coordinates, the pupil coordinates, and the eccentricity. Moreover, the indexes in C in the order from the left indicate the Zth term of the Zernike terms, the jth surface, the value of I, the order in the object height coordinate Ox, and the order in the object height coordinate Oy.

In this way, the eccentric aberration _sensitivity B _zjl (Ox, Oy) is classified according to conditions in the case where it serves as an odd function for the object height coordinates, and in the case where it serves as an even function for the object height coordinates.

As described above, the aberration is caused by the eccentricity of the lens surface in the subject optical system. The aberration that has occurred shows up as a wavefront aberration. In this way, the eccentricity of the lens surface and the aberration are closely related. The wavefront aberration is given by the amount of eccentricity and the eccentric aberration sensitivity. Accordingly, the amount of eccentricity can be determined based on the wavefront aberration and the eccentric aberration sensitivity.

The following is an explanation of the method of measuring the amount of eccentricity according to the present embodiment (hereinafter referred to as "measuring method according to the present embodiment").

The method for measuring the amount of eccentricity according to the present embodiment is a method in which a light beam is applied to an objective optical system disposed on a measuring axis and in which the amount of eccentricity is measured, the method comprising: a detecting step; wherein wavefront data is detected based on the light beam emitted from the subject optical system, a first extracting step in which a predetermined aberration component is extracted from the wavefront data, a second extracting step in which a first aberration component is extracted from the predetermined aberration component, and a second extracting step An analysis step in which a system of linear equations for the first aberration component, the eccentric aberration sensitivity and the amount of eccentricity is analyzed, and wherein the predetermined aberration component is an aberration k component is one caused by the eccentricity Aberration component, the first aberration component is an aberration component proportional to the 1st power of the amount of eccentricity in the predetermined aberration component, and the eccentric aberration sensitivity is an aberration sensitivity proportional to the 1st power of the amount of eccentricity.

4 11 illustrates a flowchart of the measuring method according to the present embodiment. The measuring method according to the present embodiment is a method in which a light beam is applied to an objective optical system disposed on a measuring axis and in which the amount of eccentricity is measured. For this reason, the measuring method according to the present embodiment includes step S100, step S200, step S300, and step S400.

Step S100 is a detection step. As described above, a light beam is applied to the subject optical system. The light beam applied to the subject optical system is transmitted through the subject optical system and is radiated from the subject optical system. At step S100, wavefront data WFD is detected based on the light beam emitted from the subject optical system.

Step S200 is a first extraction step. In the first extraction step, a predetermined aberration component is extracted from the wavefront data WFD. The predetermined aberration component is an aberration component containing an aberration component caused by eccentricity.

In a state where the lens surface is eccentric in the subject optical system (hereinafter referred to as "eccentric state"), the wavefront of the light beam radiated from the subject optical system includes wavefront aberration caused by the eccentricity. The wavefront data WFD are not data indicating the wavefront aberration itself but contain information about wavefront aberration.

The wavefront aberration is the sum total of aberrations of different types. At step S200, by analyzing the wavefront data WFD, it is possible to obtain aberration amounts in the respective aberrations. The analysis uses a polynomial expression. Examples of the polynomial expression include a Zernike polynomial.

wobei
W₁ bis W₉ Aberrationskomponenten sind und
f₁(ρx,ρy) bis f₉(ρx,ρy) Funktionen sind, die Zernike-Terme angeben.When the wavefront aberration W is developed using a Zernike polynomial, the wavefront aberration W is given by the following expression (7). In this example, the wavefront aberration is developed using the terms of the Zernike terms up to the ninth terms.

in which
W ₁ to W ₉ aberration components are and
f ₁ (ρx, ρy) to f ₉ (ρx, ρy) are functions that specify Zernike terms.

Herein, the wavefront aberration W _M obtained by analyzing the wavefront data WFD is known. For this reason, by varying W ₁ to W ₉ in the expression (7), a combination of W ₁ to W _{9 is} determined, with which a difference between the wavefront aberration W and the wavefront aberration W _M becomes the smallest.

In contrast, the wavefront aberration W may be given by the expression (1) as described above. The expression (1) will be shown again hereunder.

In addition, the eccentric aberration _sensitivity B _j1 (Ox, Oy, ρx, ρy) can be developed as shown in Expression (2 '). In expression (2 '), the Zernike term is given by f _z (ρx, ρy). In addition, the terms from the fifth to the eighth term and the tenth term and the following terms of the Zernike terms are omitted.

When the expression (2 ') is substituted into the expression (1), the following expression (1-1) is obtained.

In expression (1-1), both the index of f and the first index of B indicate the degree of the Zernike term. When the terms are summarized by the degree of the Zernike term, expression (1-2) is obtained.

The following expressions (8-1) to (8-9) are obtained from the expression (7) and the expression (1-2).

The right side of each of the terms of expression (8-1) to expression (8-9) is formed from the terms containing Δ ₁ to Δ _j and the terms containing Δ ₁ ² to Δ _j ² . As described above, W ₁ to W _{9 are given} by using the terms multiplied by the amount of eccentricity Δ. In this way, since the W ₁ to W _{9 are} eccentric aberration components, each term multiplied by the amount of eccentricity Δ is an "eccentric aberration component".

In addition, the predetermined aberration component as described above is an aberration component containing the aberration component caused by the eccentricity. W ₁ to W ₉ are eccentric aberration components, that is, the aberration components caused by the eccentricity. Accordingly, W ₁ to W ₉ serve as the predetermined aberration components.

In this way, the predetermined aberration component can be extracted from the wavefront data WFD by determining the wavefront aberration through the analysis of the wavefront data WFD, that is, by determining a combination of W ₁ to W ₉ .

Step S300 is a second extraction step. In the second extraction step, a first aberration component is extracted from the predetermined aberration component. The first aberration component is a aberration component proportional to the 1st power of the amount of eccentricity.

In the measuring method of the present embodiment, a system of linear equations for the amount of eccentricity is prepared as described later, and the amount of eccentricity is determined by solving the system of linear equations. The first aberration component is used for the system of linear equations.

As described above, W ₁ to W ₉ serve as the predetermined aberration components. However, each of W ₁ to W ₉ is formed of an aberration component that is proportional to the 1st power of the amount of eccentricity and an aberration component that is proportional to the square of the amount of eccentricity. In this case, the amount of eccentricity and the amount of aberration do not have a linear relationship.

For this reason, the aberration component proportional to the 1st power of the amount of eccentricity, that is, the first aberration component, is extracted from the predetermined aberration component.

The first aberration component is obtained by excluding the aberration component proportional to the square of the amount of eccentricity from each of the expressions of Expression (8-1) to Expression (8-9). Accordingly, when the first aberration component is W ₁₁ to W ₉₁ , W ₁₁ to W _{91 are given} by the following expressions (9-1) to (9-9).

When the expressions (9-1) to (9-9) are simplified, they are given by the following expressions (10-1) to (10-9).

Step S400 is an analysis step. In the analysis step, linear equations for the first aberration component, the eccentric aberration sensitivity, and the amount of eccentricity are simultaneously analyzed.

When the first aberration component is extracted, the relationship between the amount of eccentricity and the amount of aberration can be linearly treated. Moreover, if the relationship between the amount of eccentricity and the amount of aberration can be linearly treated, the amount of eccentricity can be determined with high accuracy by solving the system of linear equations described later, even if the amount of eccentricity of the subject optical system is large, as a manufacturing error.

As is clear from the expressions (10-1) to (10-9), a system of linear equations can be worked out by extracting the first aberration component. The left side of each of the expressions (10-1) to (10-9) is an aberration amount. In contrast, the unit of Δ ₁ to Δ _{j is} a length or an angle. Accordingly, for example, to obtain the expressions (10-1) to (10-9), the unit of _{B111 is} "aberration amount / length" or "aberration amount / angle".

The unit "aberration amount / length" indicates the amount of occurrence of aberrations when a single end face in the subject optical system is shifted by one unit of the amount of eccentricity. In addition, the unit "aberration amount / angle" indicates the degree of occurrence of aberrations when a single end face in the subject optical system is one unit of the Eccentricity is inclined. Accordingly, B ₁₁₁ to B _{9j1 indicate} the corresponding eccentric aberration _sensitivity as described above.

The eccentric aberration sensitivity can be calculated based on data in the construction of the subject optical system. In this way, the first aberration component on the left side, that is, the amount of aberration and the eccentric aberration sensitivity on the right side in each of the expressions (10-1) to (10-9) become known. Accordingly, the amounts of eccentricity Δ ₁ to Δ _{j can be} obtained by solving the system of linear equations of expressions (10-1) to (10-9).

The first aberration component is an amount proportional to the 1st power of the amount of eccentricity. Accordingly, the eccentric aberration sensitivity must be the aberration sensitivity proportional to the 1st power of the amount of eccentricity. In this way, the eccentric aberration sensitivity, which is proportional to the 1st power of the amount of eccentricity, is a change in the eccentric aberration per unit of the eccentricity amount of an aberration component which is proportional to the 1st power of the amount of eccentricity.

Here, wavefront data is detected using a light beam radiated from the subject optical system. For this reason, the subject optical system can be formed of one lens or a plurality of lenses. In addition, since the degrees of freedom of the eccentricity that can be measured are displacement and inclination, the lens surface may be a spherical surface or an aspherical surface. In addition, since the eccentricity of each of the lens surfaces is not measured singly, the measurement can be performed in a short time.

In this way, according to the method of measuring the amount of eccentricity of the present embodiment, it is possible to measure the amount of eccentricity in a short time irrespective of the shape of the lens surface and the number of lenses constituting the optical system.

The following is an explanation of a preferred embodiment of the measuring method according to the present embodiment.

In the measuring method according to the present embodiment, it is preferable that the light beam in the detection step is radiated from two radiation positions that are symmetric about two radiation positions with respect to the measurement axis and the first extraction step selects the predetermined aberration component from the respective wavefront data in a radiation direction and the respective wavefront data in the radiation direction extracted in another direction of radiation.

5 11 illustrates a flowchart of the measuring method according to the present embodiment. In the measuring method according to the present embodiment, step S100 includes step S110, step S120, step S130, and step S140. In addition, step S200 includes step S210 and step S220.

Step S100 is a detection step. The detecting step includes step S110, step S120, step S130, and step S140.

In the detection step in the measuring method according to the present embodiment, a light beam is radiated from two radiation positions. The two radiation positions are different from each other. 6A and 6B FIG. 15 are diagrams illustrating a state in which a light beam is applied to the subject optical system, FIG 6A Radiation from the radiation position P illustrated and 6B Radiation from the radiation position P 'illustrated.

At step S110, a light source in the radiation position P in the light projection system 1 arranged. The object height coordinates of the radiation position P are (Ox, Oy, 0). The light beam is transmitted from the light source to the objective optical system 2 created. A spherical wave 4 is emitted by the light source. The spherical wave 4 becomes the objective optical system 2 come in. Because the objective optical system 2 is eccentric to the Oz axis, becomes a non-planar wave 7 from the objective optical system 2 radiated. The Oz axis is the measuring axis.

In step S120, wavefront data WFD is detected. The objective optical system 2 radiated non-level wave 7 will be on the light receiving system 3 come in. Then, the wavefront data WFD from the light receiving system 3 detected.

At step S130, the light source in the radiation position P 'of the light projection system 1 arranged. The object height coordinates of the radiation position P 'are (-Ox, -Oy, 0). The light beam is transmitted from the light source to the objective optical system 2 created. An uneven wave 7 ' becomes of the objective optical system 2 radiated.

At step S140, wavefront data WFD 'is detected. The objective optical system 2 radiated non-level wave 7 ' will be on the light receiving system 3 come in. The wavefront data WFD 'are from the light receiving system 3 detected.

Here, the radiation position P and the radiation position P 'are symmetrical with respect to the measurement axis. However, each lens surface of the subject optical system is eccentric to the measurement axis. For this reason, the beam radiated from the radiation position P and the beam radiated from the radiation position P 'have asymmetric optical paths passing through the objective optical system. In this case, the uneven wave 7 and the not plane wave 7 ' no symmetrical wavefront shapes. For this reason, the wavefront data WFD and the wavefront data WFD 'are not symmetric data.

Step S200 is a first extraction step. Step S200 includes step S210 and step S220. As described above, the wavefront data WFD and the wavefront data WFD 'are not symmetric data.

Thereafter, at step S210, a predetermined aberration component is extracted from the wavefront data WFD at the radiation position P. In addition, at step S220, a predetermined aberration component is extracted from the wavefront data WFD 'in the radiation position P'.

At step S300, a first aberration component is extracted. Step S400 is performed using the extracted first aberration component. The amounts of eccentricity Δ ₁ to Δ _j can be obtained by solving a system of linear equations in step S400.

In this way, according to the method of measuring the amount of eccentricity according to the present embodiment, it is possible to measure the amount of eccentricity in a short time irrespective of the shape of the lens surface and the number of lenses constituting the optical system.

Moreover, in the measuring method of the present embodiment, it is preferable that the predetermined aberration component includes a second aberration component, the second aberration component is an aberration component proportional to the square of the amount of eccentricity in the predetermined aberration component, the object height coordinates are coordinates indicating the irradiation position, the predetermined function is one Function indicating the second aberration component and being a function including the object height coordinates as a variable, the extracting step including a first calculating step and a second calculating step, in the first calculating step, a sum of the predetermined aberration component in the one irradiation position and the predetermined aberration component in the one other radiation position when the predetermined function is an odd function, and a difference between them in the second calculation step and the predetermined aberration component in the one radiation position and the predetermined aberration component in the other radiation position when the predetermined function is an even function.

7 11 illustrates a flowchart of the measuring method according to the present embodiment. In the measuring method according to the present embodiment, step S100 includes step S110, step S120, step S130, and step S140. In addition, step S200 includes step S210 and step S220. In addition, step S300 includes step S310, step S320, and step S330. A detailed explanation of steps S100 and S200 will be omitted.

In the measuring method according to the present embodiment, moreover, a light beam is applied to the objective optical system of two radiation positions symmetrical with respect to the measuring axis. Thereby, it is possible to detect the wavefront data WFD and the wavefront data WFD '(step S100).

Thereafter, a predetermined aberration component is respectively extracted from the wavefront data WFD and the wavefront data WFD '(step S200).

If the one radiation position P has object height coordinates (Ox, Oy), the other radiation position P 'here has object height coordinates (-Ox, -Oy). The light beam is emitted within a plane OxOy (Oz = 0). For this reason, only Ox and Oy are used for the object height coordinates.

The wavefront aberration W is detected by analyzing the wavefront data WFD. In this case, since the object height coordinates of the radiation position are P (Ox, Oy), the predetermined aberration components W ₁ to W ₉ extracted from the wavefront aberration are given by the expressions (8-1) to (8-9) described above ,

In addition, the wavefront aberration W is detected by analyzing the wavefront data WFD '. In this case, since the object height coordinates of the radiation position P 'are (- Ox, -Oy), the predetermined aberration components W ₁ to W ₉ extracted from the wavefront aberration are represented by expressions (8-1') to (8-9 ' ) are given as follows.

In this way, according to the measuring method of the present embodiment, two predetermined aberration components are detected. Thereafter, the first aberration component is extracted using the two predetermined aberration components. This extraction is carried out at step S300. Step S300 is the second extraction step.

The following is an explanation of the second extracting step, that is, a step of extracting the first aberration component. The following predetermined aberration components will be used for explanation.

W ₂ (Ox, O y, Δ ₁ , Δ ₂ , ..., Δ _j ) and W ₂ (-O x, -O y, Δ ₁ , Δ ₂ , ..., Δ _j ) are represented by expression (8-2 ) or expression (8-2 ').

As described above, W ₂ contains the aberration component that is proportional to the 1st power of the amount of eccentricity and the aberration component that is proportional to the square of the amount of eccentricity. The aberration component proportional to the 1st power of the amount of eccentricity is the first aberration component, and the aberration component proportional to the square of the amount of eccentricity is the second aberration component. The first aberration component is referred to as W ₂₁ and the second aberration component is referred to as W ₂₂ .

Table 5 illustrates terms in the first aberration component W ₂₁ for the expression (8-2) and the expression (8-2 '). For ease of explanation, W _{21 is given} only with the object height coordinates. [Table 5] (8-2) W ₂₁ (Ox, Oy) Δ ₁ B ₂₁₁ (Ox, O y) Δ ₂ B ₂₂₁ (Ox, Oy) ... Δ _j B _2j1 (Ox, Oy) (8-2 ') W ₂₁ (-Ox, -Oy) Δ ₁ B ₂₁₁ (-Ox, -Oy) Δ ₂ B ₂₂₁ (-Ox, -Oy) ... Δ _j B _2j1 (-Ox, -OY)

In addition, Table 6 illustrates terms in the second aberration component W ₂₂ for the expression (8-2) and the expression (8-2 '). [Table 6] (8-2) W ₂₂ (Ox, Oy) Δ ₁ ² B ₂₁₂ (Ox, O y) Δ ₂ ² B ₂₂₂ (Ox, O y) ... _Δj ² B _2j ² (Ox, _{O y} ) (8-2 ') W ₂₂ (-Ox, -Oy) Δ ₁ ² B ₂₁₂ (-Ox, -Oy) Δ ₂ ² B ₂₂₂ (-Ox, -Oy) ... Δ _j ² B _2J2 (-Ox, -OY)

Each of the terms B _2j1 (Ox, Oy) and B _2j1 (-Ox, -Oy) in Table 5 gives the eccentric aberration sensitivity of the term multiplied by the second term of the Zernike terms and that to the 1st power of the amount of eccentricity in the j-th surface proportional eccentric aberration sensitivity.

In this case, the eccentric aberration _sensitivity B _zj1 (Ox, Oy) (z = 2, 3, 7, 8 ...) of the term multiplied by the second term and other of the Zernike terms is represented by the expression (3 ). Expression (3) is shown below again.

Accordingly, the terms B _2j1 (Ox, Oy) and B _2j1 (-Ox, -Oy) are given by expressions (3 ') and (3''), respectively, from the expression (3).

As a result, "B _2j1 (-Ox, -Oy) = B _2j1 (Ox, Oy)" is satisfied. In this way, the eccentric aberration _sensitivity B _2j1 (Ox, Oy) of the term multiplied by the second term of the Zernike terms in the eccentric aberration sensitivity, which is proportional to the 1st power of the amount of eccentricity, serves as an even function with respect to the object height coordinates.

In contrast, each of the terms B _2j2 (Ox, Oy) and B _2j2 (-Ox, -Oy) in Table 6 gives the eccentric aberration sensitivity of the term multiplied by the second term of the Zernike terms and the square of the Eccentricity amount in the j-th surface proportional eccentric aberration sensitivity.

In this case, the eccentric aberration _{sensitivity is Bzj2} (Ox, Oy) (z = 2, 3, 7, 8, ...) of the term multiplied by the second term and other of the Zernike terms by Expression (5) given. Expression (5) is shown below again.

Accordingly, the terms B _2j2 (Ox, Oy) and B _2j2 (-Ox, -Oy) are given by expressions (5 ') and (5''), respectively, from the expression (5).

As a result, "B _{2j 2} (-O x, -O y) = -B _{2j 2} (Ox, _{O y} )" is satisfied. In this way, the eccentric aberration _sensitivity B _2j2 (Ox, Oy) of the term multiplied by the second term of the Zernike terms in the eccentric aberration sensitivity, which is proportional to the square of the amount of eccentricity, serves as an odd function with respect to the object height coordinates.

Table 7 illustrates the first aberration _component W ₂₁ when "B _2j1 (-Ox, -Oy) = B _2j1 (Ox, Oy)" is reflected. As is clear from Table 7, when the two radiation positions are symmetric, that is, when the object height coordinates are (Ox, Oy) and (-Ox, -Oy), then "W ₂₁ (-Ox, -Oy) = W ₂₁ (Ox, Oy) "fulfilled. In this way, the first aberration component W ₂₁ serves as an even function with respect to the object height coordinates. [Table 7] (8-2) W ₂₁ (Ox, Oy) Δ ₁ B ₂₁₁ (Ox, O y) Δ ₂ B ₂₂₁ (Ox, Oy) ... Δ _j B _2j1 (Ox, Oy) (8-2 ') W ₂₁ (-Ox, -Oy) Δ ₁ B ₂₁₁ (Ox, O y) Δ ₂ B ₂₂₁ (Ox, Oy) ... Δ _j B _2j1 (Ox, Oy)

In addition, Table 8 illustrates the second aberration _component W ₂₂ when "B _{2j 2} (-O x, -O y) = B _{2j 2} (Ox, _{O y} )" is reflected. As is clear from Table 8, when the two radiation positions are symmetric, "W ₂₂ (-Ox, -Oy) = -W ₂₂ (Ox, Oy)" is satisfied. In this way, the second aberration component W ₂₂ serves as an odd function with respect to the object height coordinates. [Table 8] (8-2) W ₂₂ (Ox, Oy) Δ ₁ ² B ₂₁₂ (Ox, O y) Δ ₂ ² B ₂₂₂ (Ox, O y) ... _Δj ² B _2j ² (Ox, _{O y} ) (8-2 ') W ₂₂ (-Ox, -Oy) -Δ ₁ ² B ₂₁₂ (Ox, Oy) -Δ ₂ ² B ₂₂₂ (Ox, Oy) ... -Δ _j ² B _2j ² (Ox, _{O y} )

In contrast, W ₄ (Ox, O y, Δ ₁ , Δ ₂ , ..., Δ _j ) and W ₄ (-O x, -O y, Δ ₁ , Δ ₂ , ..., Δ _j ) are expressed by expression ( 8-4) or expression (8-4 ').

As described above, W ₄ contains the aberration component, which is proportional to the 1st power of the amount of eccentricity, and the aberration component, which is proportional to the square of the amount of eccentricity. The aberration component proportional to the 1st power of the amount of eccentricity is the first aberration component, and the aberration component proportional to the square of the amount of eccentricity is the second aberration component. The first aberration component is referred to as W ₄₁ , and the second aberration component is referred to as W ₄₂ .

Table 9 illustrates terms in the first aberration component W ₄₁ for the expression (8-4) and the expression (8-4 '). For ease of explanation, W _{41 is given} only with the object height coordinates. [Table 9] (8-4) W ₄₁ (Ox, Oy) Δ ₁ B ₄₁₁ (Ox, O y) Δ ₂ B ₄₂₁ (Ox, Oy) ... Δ _j B _4J1 (Ox, Oy) (8-4 ') W ₄₁ (-Ox, -Oy) Δ ₁ B ₄₁₁ (-Ox, -Oy) Δ ₂ B ₄₂₁ (-Ox, -OY) ... Δ _j B _4J1 (-Ox, -OY)

In addition, Table 10 illustrates terms in the second aberration component W ₄₂ for the expression (8-4) and the expression (8-4 '). [Table 10] (8-4) W ₄₂ (Ox, Oy) Δ ₁ ² B ₄₁₂ (Ox, O y) Δ ₂ ² B ₄₂₂ (Ox, O y) ... Δ _j ² B _4J2 (Ox, Oy) (8-4 ') W ₄₂ (-Ox, -Oy) Δ ₁ ² B ₄₁₂ (-Ox, -Oy) Δ ₂ ² B ₄₂₂ (-Ox, -Oy) ... Δ _j ² B _4J2 (-Ox, -OY)

Each of the terms B _4j1 (Ox, Oy) and B _4j1 (-Ox, -Oy) in Table 10 gives the eccentric aberration sensitivity of the term multiplied by the fourth term of the Zernike terms and that to the 1st power of the amount of eccentricity in the j-th surface proportional eccentric aberration sensitivity.

In this case, the eccentric aberration _sensitivity B _zj1 (Ox, Oy) (z = 1, 4, 5, 6, 9 ...) of the term multiplied by the fourth term and other of the Zernike terms is expressed by ( 4). Expression (4) is shown below again.

Accordingly, the terms B _4j1 (Ox, Oy) and B _4j1 (-Ox, -Oy) are given by expressions (4 ') and (4''), respectively, from the expression (4).

As a result, "B _4j1 (-Ox, -Oy) = -B _2j1 (Ox, Oy)" is satisfied. In this way, the eccentric aberration _sensitivity B _4j1 (Ox, Oy) of the term multiplied by the fourth term of the Zernike terms in the eccentric aberration sensitivity, which is proportional to the 1st power of the amount of eccentricity, serves as an odd function with respect to the object height coordinates.

In contrast, each of the terms B _4j2 (Ox, Oy) and B _4j2 (-Ox, -Oy) in Table 11 gives the eccentric aberration sensitivity of the term multiplied by the fourth term of the Zernike terms and the square of the Eccentricity amount in the j-th surface proportional eccentric aberration sensitivity.

In this case, the eccentric aberration _sensitivity B _zj2 (Ox, Oy) (z = 1, 4, 5, 6, 9 ...) of the term multiplied by the fourth term and other of the Zernike terms is expressed by the term (6) as described above. Expression (6) is shown below again.

Accordingly, the terms B _{4j 2} (Ox, _{O y} ) and B _{4j 2} (-O x, -O y) are given by expressions (6 ') and (6''), respectively, from the expression (6).

As a result, "B _4j2 (-Ox, -Oy) = B _4j2 (Ox, Oy)" is satisfied. In this way, the eccentric aberration _sensitivity B _4j2 (Ox, Oy) of the term multiplied by the fourth term of the Zernike terms in the eccentric aberration sensitivity, which is proportional to the square of the amount of eccentricity, serves as an even function with respect to the object height coordinates.

Table 11 illustrates the first aberration _component W ₄₁ when "B _4j1 (-Ox, -Oy) = -B _4j1 (Ox, Oy)" is reflected. As is clear from Table 11, if the two radiation positions are symmetric, then "W ₄₁ (-Ox, -Oy) = -W ₄₁ (Ox, Oy)" is satisfied. In this way, the first aberration component W ₄₁ serves as an odd function with respect to the object height coordinates. [Table 11] (8-4) W ₄₁ (Ox, Oy) Δ ₁ B ₄₁₁ (Ox, O y) Δ ₂ B ₄₂₁ (Ox, Oy) ... Δ _j B _4J1 (Ox, Oy) (8-4 ') W ₄₁ (-Ox, -Oy) -Δ ₁ B ₄₁₁ (Ox, Oy) -Δ ₂ B ₄₂₁ (Ox, Oy) ... -Δ _j B _4J1 (Ox, Oy)

In addition, Table 12 illustrates the second aberration _component W ₄₂ when "B _{4j 2} (-O x, -O y) = B _{4j 2} (Ox, _{O y} )" is reflected. As is clear from Table 12, if the two radiation positions are symmetric, then "W ₄₂ (-Ox, -Oy) = W ₄₂ (Ox, Oy)" is satisfied. In this way, the second aberration component W ₄₂ serves as an even function with respect to the object height coordinates. [Table 12] (8-4) W ₄₂ (Ox, Oy) Δ ₁ ² B ₄₁₂ (Ox, O y) Δ ₂ ² B ₄₂₂ (Ox, O y) ... Δ _j ² B _4J2 (Ox, Oy) (8-4 ') W ₄₂ (-Ox, -Oy) Δ ₁ ² B ₄₁₂ (Ox, O y) Δ ₂ ² B ₄₂₂ (Ox, O y) ... Δ _j ² B _4J2 (Ox, Oy)

As described above, in the predetermined aberration component W _2, the function indicating the first aberration component W _{21 is} an even function, and the function indicating the first aberration component W _{22 is} an odd function. In contrast, in the predetermined aberration component W _4, the function indicating the first aberration component W _{41 is} an even function and the function indicating the first aberration component W _{42 is} an odd function.

Here, assuming that the predetermined function is a function indicating the second aberration component and a function including the object height coordinates as a variable, it is classified into the case of a straight function and the case of an odd function.

For this reason, step S310 is executed to perform different calculations in the case where the predetermined function is an odd function and the case where the predetermined function is an even function.

In the predetermined aberration function W _2, since the function indicating the second aberration function W _{22 is} an odd function, the predetermined function is an odd function. In this case, the determination result in step S310 is "YES". As a result, step S320 is executed. Step S320 is the first calculation step.

In the first calculation step, a sum of the predetermined aberration component in the one radiation position and the predetermined aberration component in the other radiation position is obtained. More specifically, the sum of W ₂ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j ) and W ₂ (-Ox, -Oy, Δ ₁ , Δ ₂ , ..., Δ _j ) is obtained.

Expression (11) indicates the result of the sum of the two predetermined aberration components.

Here, the first aberration component W _{21 is given} by the expression (9-2). The expression (9-2) is shown below again.

Accordingly, expression (11 ') is obtained from the expression (11) and the expression (9-2).

As shown in Expression (11 '), by obtaining the sum of two predetermined aberration components, the first aberration component W ₂₁ remains, but the second aberration component W ₂₂ disappears. Accordingly, the first aberration component W ₂₁ can be extracted from the predetermined aberration component W ₂ .

In contrast, in the predetermined aberration component W ₄ , since the function indicating the second aberration component W _{42 is} an even function, the predetermined function is an even function. In this case, the determination result in step S310 is "NO". As a result, step S330 is executed. Step S330 is the second calculation step.

In the second calculating step, a difference between the predetermined aberration component in the one radiation position and the predetermined aberration component in the other radiation position is obtained. More specifically, the difference between W ₄ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j ) and W ₄ (-Ox, -Oy, Δ ₁ , Δ ₂ , ..., Δ _j ) is obtained. Expression (12) indicates the result of the difference between the two predetermined aberration components.

Here, the first aberration component W _{41 is given} by the expression (9-4). Expression (9-4) is shown below again.

Accordingly, expression (12 ') is obtained from the expression (12) and the expression (9-4).

As shown in Expression (12 '), by obtaining the difference between the aberration components, the first aberration component W ₄₁ and the second aberration component W ₄₂ disappear. Accordingly, the first aberration component W ₄₁ can be extracted from the predetermined aberration component W ₄ .

Table 13 illustrates the result including the case where the aberration component serves as an even function for the object height coordinates, and the case where the aberration component serves as an odd function for the object height coordinates for each of the first aberration _component W _z1 and the second aberration _component W _z2 . In Table 13, the first aberration _{component is} given by W _z1 and the second aberration _{component is} given by W _z2 . [Table 13] z = 2, 3, 7, 8 ... z = 1, 4, 5, 6, 9 ... Predetermined aberration component first aberration component (proportional to the 1st power of the amount of eccentricity) even function with respect to the object height coordinates W _z1 (-Ox, -Oy) = W _z1 (Ox, Oy) Odd function with respect to the object height coordinates W _z1 (-Ox, -Oy) = -W _z1 (Ox, Oy) second aberration component (proportional to the square of the amount of eccentricity) odd function with respect to the object height _coordinates W _z2 (-Ox, -Oy) = -W _z2 (Ox, Oy) even function with respect to the object height _coordinates W _z2 (-Ox, Oy) = W _z2 (Ox, Oy)

As is clear from Table 13, the first aberration component for the following predetermined aberration components can be extracted from the predetermined aberration component by performing the first calculation step.

In this way, W _{z is} the following expression for the aberration component multiplied by a function having the odd-order pupil coordinates, that is, those having a function such as the second term and others of the Zernike terms (z = 2, 3, 7, 8 ...) multiplied aberration component W _z obtained.

In addition, by performing the second calculating step, the first aberration component for the following predetermined aberration components can be extracted from the predetermined aberration component.

In this way, W _{z is} the following expression for the aberration component multiplied by a function with the pupil coordinates in an even order, that is, those having a function such as the fourth term and others of the Zernike terms (z = 1, 4, 5, 6, 9 ...) receive multiplied aberration component W _z .

In this way, the first calculating step is executed when the predetermined function, that is, the function indicating the second aberration component, is an odd function. In the first calculation step, the sum of the predetermined aberration component in the one radiation position and the predetermined aberration component in the other radiation position is obtained. As a result, the first aberration component can be extracted from the predetermined aberration component.

In addition, the second calculation step is executed when the predetermined function is an even function. In the second calculating step, the difference between the predetermined aberration component in the one radiation position and the predetermined aberration component in the other radiation position is obtained. As a result, the first aberration component can be extracted from the predetermined aberration component.

As explained above, the first aberration component is extracted by executing step S300. Step S400 is performed using the extracted first aberration component. The amounts of eccentricity Δ ₁ to Δ _j can be obtained by solving the system of linear equations in step S400.

In this way, according to the method of measuring the amount of eccentricity according to the present embodiment, it is possible to measure the amount of eccentricity in a short time irrespective of the shape of the lens surface and the number of lenses constituting the optical system.

Moreover, the measuring method according to the present embodiment enables extraction of the first aberration component from the predetermined aberration component, even if a design aberration component exists.

In the above-described explanation, the wavefront aberration W is a deviation from the wavefront when the subject optical system is not eccentric. The wavefront aberration W will be explained hereinafter as a deviation from an ideal wavefront such as a plane wave and a spherical wave.

The design aberration component will be explained hereinafter. The subject optical system in measuring the amount of eccentricity is a lens assembly, a single group, and a single lens. The objective optical system is manufactured on the basis of design data. An optical system is constructed to minimize the occurrence of aberration in a combination of a plurality of lenses. However, it is very difficult to reduce the extent of occurrence of all aberrations to zero. In addition, in the design, aberration occurs in a part of such assembled lenses as in each individual group and every single lens.

Accordingly, the subject optical system contains an aberration in the design phase. For this reason, when the aberration is called a design aberration, the design aberration is also included in the wavefront aberration. When the design aberration component is M (Ox, Oy, ρx, ρy), the wavefront aberration W is given by the following expression (1-3).

wobei
M₁(Ox,Oy) bis M₉(Ox,Oy) Funktionen sind, die von den Objekthöhenkoordinaten abhängen.The design aberration component M (Ox, Oy, ρx, ρy) is a predetermined aberration component. The design aberration component M (Ox, Oy, ρx, ρy) can also be developed with a polynomial expression based on the aberration theory, in the same way as the eccentric aberration sensitivity. For example, when a Zernike polynomial is used, the design aberration component M (Ox, Oy, ρx, ρy) may be developed with a polynomial expression as indicated by the following expression (13).

in which
M ₁ (Ox, Oy) to M ₉ (Ox, Oy) are functions that depend on the object height coordinates.

When the function dependent on the object height coordinates is given by M _z (Ox, Oy), M _z (Ox, Oy) is a function dependent on the object height coordinates and a function in the term multiplied by the Zth term of the Zernike terms is. The Zernike terms are functions that depend on the pupil coordinates. Accordingly, M _z (Ox, Oy) may also be regarded as a function dependent on the object height coordinates and a function in the term multiplied by a function dependent on the pupil coordinates.

In this way, when the design aberration coordinates M (Ox, Oy, ρx, ρy) are developed by means of a Zernike polynomial, the terms of the polynomial are classified into terms that are multiplied by the function with the odd-order pupil coordinates and terms , which are multiplied by the function with the pupil coordinates in even order.

In addition, the function M _z (Ox, Oy), which depends on the object height coordinates, can be developed by means of a polynomial. The developed expression differs, however, between the terms multiplied by the function with the pupil coordinates in odd order, and the terms which are multiplied by the function with the pupil coordinates in an even order.

M _z (Ox, Oy) of the term multiplied by the function with the pupil coordinates in odd order is M _Z (Ox, Oy) of the term multiplied by the second term and other of the Zernike terms. In this case, _Mz (Ox, Oy) (z = 2, 3, 7, 8, ...) is given by the following expression (14).

As shown in Expression (14), M _Z (Ox, Oy) of the term multiplied by the second term and other of the Zernike terms serves as an odd function with respect to the object height coordinates.

M _z (Ox, Oy) of the term multiplied by the function with the pupil coordinates in even order is M _Z (Ox, Oy) of the term multiplied by the fourth term and another of the Zernike terms. In this case, _Mz (Ox, Oy) (z = 1, 4, 5, 6, 9 ...) is given by the following expression (15).

As shown in Expression (15), M _Z (Ox, Oy) of the term multiplied by the fourth term and others of the Zernike terms serves as an even function with respect to the object height coordinates.

Table 14 illustrates the results involving the case where the function serves as an even function and the case where the function serves as an odd function for each of the following functions: the function indicating the first aberration component; the function indicating the second aberration component and the function depending on the object height coordinates in the design aberration component (hereinafter referred to as "function indicating the design aberration component"). [Table 14] z = 2, 3, 7, 8 ... z = 1, 4, 5, 6, 9 ... Predetermined aberration component first aberration component (proportional to the 1st power of the amount of eccentricity) even function with respect to the object height coordinates W _z1 (-Ox, -Oy) = W _z1 (Ox, Oy) Odd function with respect to the object height coordinates W _z1 (-Ox, -Oy) = -W _z1 (Ox, Oy) second aberration component (proportional to the square of the amount of eccentricity) odd function with respect to the object height _coordinates W _z2 (-Ox, -Oy) = -W _z2 (Ox, Oy) even function with respect to the object height _coordinates W _z2 (-Ox, -Oy) = W _z2 (Ox, Oy) Construction aberration component (function dependent on object height coordinates) odd function with respect to the object height coordinates M _z (-Ox, -Oy) = -M _z (-Ox, -Oy) even function with respect to the object height coordinates M _z (-Ox, -OY) = M _z (Ox, Oy)

As described above, when the first calculating step is executed, the second aberration component disappears in the case where the predetermined function, that is, the function indicating the second aberration component, is an odd function. As is clear from Table 14, the function indicating the design aberration component is also an odd function when the function indicating the second aberration component is an odd function. For this reason, the design aberration component also disappears when the first calculation step is performed. As a result, the first aberration component can be extracted from the predetermined aberration component.

Moreover, when the second calculating step is executed, the second aberration component disappears in the case where the predetermined function is an even function. As is clear from Table 14, the function indicating the design aberration component is also an even function when the function indicating the second aberration component is an even function. For this reason, the design aberration component also disappears when the second calculation step is executed. As a result, the first aberration component can be extracted from the predetermined aberration component.

Step S400 is performed using the extracted first aberration component. The amounts of eccentricity Δ ₁ to Δ _j can be obtained by solving a system of linear equations in step S400.

In this way, according to the method of measuring the amount of eccentricity according to the present embodiment, it is possible to measure the amount of eccentricity in a short time irrespective of the shape of the lens surface and the number of lenses constituting the optical system, even if the subject optical system includes a design aberration.

Moreover, in the measuring method of the present embodiment, it is preferable that the detecting step includes a first rotation and the subject optical system is rotated about the measuring axis in the first rotation and the wavefront data before the first rotation and the wavefront data after the first rotation in the same irradiation position be recorded.

8th 11 illustrates a flowchart of the measuring method according to the present embodiment. In the measuring method of the present embodiment, step S100 includes step S110, step S121, step S122, and step S150. A detailed explanation of steps S200, S300 and S400 will be omitted.

As described above, wavefront data is data containing information about the wavefront aberration. The wavefront data is captured by the light-receiving system. For example, if the light receiving system is an interferometer, the wavefront data is phase data. In addition, the wavefront data is data of light dot image positions when the light receiving system is a Shack-Hartmann sensor (hereinafter referred to as a "SH sensor"). The details of the SH sensor will be described later.

9A and 9B are diagrams for explaining system aberration in the light projection system, wherein 9A illustrates a state in which no system aberration occurs and 9B illustrates a state in which a system aberration occurs in the light projection system. The system aberration is an aberration that includes the measurement system itself. System aberration occurs in the light projection system and in the light receiving system.

As in 9A illustrated, the light source is in the radiation position P of the light projection system 10 arranged. When in the light projection system 10 no system aberration occurs, becomes a spherical wave 40 emitted from the light source. The spherical wave 40 becomes the objective optical system 20 come in. Because the objective optical system 20 is eccentric to the Oz axis, becomes a non-planar wave 50 from the objective optical system 20 radiated.

For the wavefront of the radiated light beam, the aberration can be removed by using a spatial filter or the like. However, there are cases where the aberration can not be sufficiently removed due to a manufacturing defect. In this case occurs in the light projection system 10 a system aberration.

When the system aberration in the light projection system 10 occurs, the wave front of the optical system 20 applied light beam a distorted wavefront 60 , as in 9B illustrated. In this case, one of the objective optical system differs 20 radiated, non-level wave 51 from the not plane wave 50 in the case where the spherical wave 40 to the objective optical system 20 is created.

10A and 10B are diagrams illustrating a system aberration in the light receiving system, wherein 10A illustrates the system aberration in a sensor component forming unit and 10B illustrates the system aberration in a wavefront data acquisition unit.

The light receiving system 30 For example, a sensor component is a unit 31 forms, and a wavefront data detection unit 32 educated. The not plane wave 50 pointing to the light receiving system 30 is dropped, passes through the sensor component forming unit 31 and then reaches the wavefront data detection unit 32 ,

An optical system is in the sensor component forming unit 31 arranged, if necessary. For example, when the light beam diameter made incident on the light receiving system is required to substantially match the light receiving area in the wavefront data acquiring unit 32 becomes an optical system in the sensor component forming unit 31 arranged. In addition, an optical system is in the sensor component forming unit 31 arranged, that is, in the case where a plurality of light spot images is to be formed.

If the optical system contains a manufacturing error or if there is an error in the mounting of the optical system, then an aberration occurs in the optical system. For this reason, occurs in the sensor component forming unit 31 a system aberration. In this case, the system aberration becomes a non-planar wave 50 added. As a result, it differs, as in 10A illustrated, a non-level wave 52 pointing to the wavefront data acquisition unit 32 of the uneven wave 50 ,

Besides, if the light receiving system 30 As described above, an interferometer becomes an interference fringe in the wavefront data acquiring unit 32 educated. In addition, a plurality of light spot images in the wavefront data detection unit 32 formed when the light receiving system 30 an SH sensor is.

Accordingly, the wavefront data acquiring unit shares 32 the interference fringe into tiny areas to capture information about the wavefront. As another example, the wavefront data acquiring unit recognizes 32 Positions of the light spot images. To perform the operation, the wavefront data acquisition unit instructs 32 a structure in which, for example, tiny, light-receiving elements 33 (hereinafter referred to as "light receiving elements") are arranged in a two-dimensional manner.

For example, if the wavefront data acquisition unit 32 contains a manufacturing error, the light receiving elements 33 not evenly arranged, as in 10B illustrated. This causes system aberration in the wavefront data acquisition unit 32 , In addition, the manufacturing error may vary in the size of the light receiving areas of the light receiving elements 33 cause. In this case, too, system aberration occurs in the wavefront data acquiring unit 32 on.

In this way, the system aberration is also included in the wavefront aberration when the light projection system 10 and / or the light receiving unit 30 contains a system aberration. In this case, they are used by the light receiving system 30 Wavefront data is not captured as data that accurately reflects wavefront aberration due to the eccentricity of the subject optical system 20 is caused.

When the system aberration is Sys (Ox, Oy, ρx, ρy), the wavefront aberration W is given by the following expression (1-4). However, the wavefront aberration W is explained here as a deviation from the wavefront in the case where the subject optical system is not eccentric and system aberration does not exist.

The system aberration component can be determined in advance. 11 is a method of previously determining the system aberration component. In this example, it is assumed that in the sensor component forming unit 31 a system aberration occurs.

In this process becomes an optical system 21 used with a very small aberration. 11 illustrates a state in which that of the optical system 21 radiated light beam with the light beam ( 10A ), that of the subject optical system 20 was radiated at the angle, the position and the light beam diameter, with which the light beam to the light receiving system 30 is thought of. In particular, the radiation position P _p , the radiation angle, the position of the optical system 21 and the tilt of the optical system 21 adjusted with respect to the Oz axis to reach the state.

In 11 is the light source in the radiation position P _p (0x _p , 0y _p , 0) of the light projection system 10 arranged. Because in the light projection system 10 no system aberration occurs, becomes a spherical wave 40 emitted from the light source. The spherical wave 40 is on the optical system 21 come in. The optical system 21 is an optical system with a very small aberration. Accordingly, a plane wave 53 from the optical system 21 radiated. The plane wave 53 becomes on the sensor component forming unit 31 come in.

Here is a system aberration in the sensor component forming unit 31 to the plane wave 53 added. As a result, a non-level wave 54 from the sensor component forming unit 31 radiated. The not plane wave 54 is applied to the wavefront data acquisition unit 32 come in and wavefront data is captured.

The detected wavefront data contains only information about the system aberration in the sensor component forming unit 31 , The wavefront aberration W 'obtained from the wavefront data is given by the following expression (16).

However, as described above, that of the optical system is caused 21 radiated light beam with the light beam ( 10A ), that of the subject optical system 20 was radiated at the angle, the position and the light beam diameter, with which the light beam to the light receiving system 30 is thought of. Accordingly, the radiation position _Pp (Ox _p , Oy _p , 0) corresponds to the light projection system 10 in 11 the radiation position P (Ox, Oy, O) in 10A , For this reason, the object height coordinates of W 'are given by (Ox, Oy).

Sys (Ox, Oy, ρx, ρy) can be removed by a calculation of expression (17).

If the number of radiation positions is one, this process can be easily performed. However, if the number of radiation positions is very large, the number of data sets to be detected becomes huge, and this method can not be easily performed.

For this reason, in the measuring method of the present embodiment, two wavefront data sets in the same radiation position are detected. To accomplish this, step S100 is executed, as in FIG 8th illustrated.

12A and 12B are diagrams illustrating a first turn wherein 12A illustrates a state before the first rotation is performed, and 12B illustrates a state after the first rotation has been performed. It is assumed that both the light projection system and the light receiving system contain an aberration.

At step S110, as in FIG 12A illustrated, a light beam from the radiation position P (Ox, Oy, 0) on the subject optical system 20 radiated. A wavefront 60 becomes the objective optical system 20 come in. An uneven wave 51 becomes of the objective optical system 20 radiated. The not plane wave 51 contains a system aberration of the light projection system 10 and the eccentric aberration of the objective optical system 20 , The not plane wave 51 will be on the light receiving system 30 come in. The light receiving system 30 also contains a system aberration. Accordingly, the finally detected wavefront contains the system aberration of the light projection system 10 , the eccentric aberration of the objective optical system 20 and the system aberration of the light receiving system 30 ,

Thereafter, step S121 is executed. In this way, wavefront data WFDθ1 are detected. The wavefront data WFDθ1 contains information about the system aberration of the light projection system 10 , Information about the eccentric aberration of the objective optical system 20 and information about the system aberration of the light receiving system 30 , The wavefront aberration W is obtained by analyzing the wavefront data WFDθ1. The wavefront aberration W is given by the following expression (1-5). In this example, the eccentricity of the subject optical system is regarded as a shift in the Y direction, therefore the amount of eccentricity is indicated by δ.

Thereafter, step S150 is executed. At step S150, a first rotation is performed. In the first turn, the objective optical system becomes 20 rotated around the measuring axis. The rotation angle is for example 180 °. The position of the light projection system 10 is recorded. Therefore, the radiation position P is not moved. In addition, the position of the light receiving system 30 also recorded.

After completion of step S150, step S110 is executed. At step S110, as in FIG 12B illustrated, a light beam from the radiation position P (Ox, Oy, 0) on the subject optical system 20 radiated. The wavefront 60 becomes the objective optical system 20 come in. An uneven wave 55 becomes of the objective optical system 20 radiated. The not plane wave 55 is different from the non-level wave 51 ,

The not plane wave 55 contains the system aberration of the light projection system 10 and the eccentric aberration of the objective optical system 20 , The not plane wave 55 will be on the light receiving system 30 come in. The light receiving system 30 also contains a system aberration. Accordingly, the finally detected wavefront contains the system aberration of the light projection system 10 , the eccentric aberration of the objective optical system 20 and the system aberration of the light receiving system 30 ,

Thereafter, step S122 is executed. In this way, wavefront data WFDθ2 are detected. The wavefront data WFDθ2 contains information about the system aberration of the light projection system 10 , Information about the eccentric aberration of the objective optical system 20 and information about the system aberration of the light receiving system. The wavefront aberration W is obtained by analyzing the wavefront data WFDθ2. The wavefront aberration W is given by the following expression (1-6).

As described above, the system aberration component Sys (Ox, Oy, ρx, ρy) is an aberration component caused by a manufacturing error of the light projecting system and / or the light receiving system. The system aberration component depends on the coordinates (Ox, Oy, ρx, ρy). When the eccentric state between the eccentric state before the rotation of the objective optical system 20 and the eccentric state after rotation does not change much, the system aberration component Sys (Ox, Oy, ρx, ρy) can be considered substantially non-eccentric dependent.

The system aberration component is the same in Expression (1-5) and Expression (1-6). For this reason, at step S200, calculation of expression (18) is performed. The calculation removes Sys (Ox, Oy, ρx, ρy) and enables extraction of the predetermined aberration component.

Here, as described above, two wavefront data sets are detected in the measuring method according to the present embodiment. For this reason, the wavefront data acquired before the first rotation is referred to as "reference data" and the wavefront data acquired after the first rotation is referred to as "measurement data". In this case, Expression (18) analyzes the measurement data using the reference data as the reference wavefront. More specifically, the wavefront aberration given by expression (18) is a deviation of the wavefront after the first rotation from the wavefront before the first rotation of the subject optical system.

The amount of change of the wavefront data from the reference data to the measured data is determined, for example, by an analysis. In the case of using an SH sensor, a vector is calculated to the light spot image position of the measuring point image on the basis of the light spot image position of the reference point image. The reference light spot image used for the vector calculation corresponds to the measuring light spot image by one-to-one correspondence. The two one-to-one corresponding light spot images are light spot images formed by the same microlens array. In the case of using an interferometer, the amount of phase change of the measurement phase data is calculated based on the reference phase data.

Here, the dot images are images obtained by photographing the light spot images. The reference point image is an image obtained by photographing a light spot image formed when the reference wavefront is incident on the SH sensor. In addition, the measurement point image is an image obtained by photographing a light spot image formed when the measurement wavefront is incident on the SH sensor. When the first rotation is performed, the reference point image is an image obtained by photographing a light spot image in the state before the first rotation is performed, and the measuring point image is an image obtained by photographing the light spot image in the state after the first one Rotation was performed.

This captures final wavefront data from the reference data and the measurement data. For example, when the rotation angle is 180 °, each of the lenses of the subject optical system is displaced by an amount that is -2 times the amount of eccentricity with respect to the measurement axis.

Here, when the lens surface is formed of a spherical surface, the position of the lens surface can be indicated by the sphere center. 13A . 13B and 13C FIG. 15 are diagrams illustrating a state in which the ball centers are changed by the first rotation, wherein FIG 13A illustrates the positions of the centers of the sphere before the first rotation, 13B the Positions of the ball centers after the first rotation illustrated and 13C illustrates the amounts of movement of the ball centers caused by the first rotation. In 13A . 13B and 13C becomes the objective optical system 22 formed from four lens surfaces.

As in 13A illustrated, are the ball centers 70 . 71 . 72 and 73 arranged on a side of the first rotation axis in the state before the first rotation is performed. When the first rotation is made from this state, the ball centers become 70 . 71 . 72 and 73 moved to the other side of the first axis of rotation, as in 13B illustrated. The other side is in a position opposite to the one side with the first rotation axis positioned therebetween.

As in 13C 1, the amount of eccentricity of the ball center with respect to the measuring axis δ1 is the center of the sphere 70 , δ2 in the sphere center 71 , δ3 in the sphere center 72 and δ4 in the sphere center 73 , By rotation of the objective optical system, each of the ball centers becomes 70 . 71 . 72 and 73 relocated. The amount of displacement is -2 times the amount of eccentricity before rotation with respect to the measuring axis.

At step S200, a predetermined aberration component is extracted from the final wavefront data. In this process, the predetermined aberration component is an aberration amount corresponding to an amount that is -2 times the amount of eccentricity with respect to the measurement axis. Thereby, the aberration amount which is -2 times the amount of eccentricity with respect to the measurement axis can be extracted even if there is a system aberration.

After the execution of step S200, step S300 is executed. The first aberration component is extracted by executing step S300. Step S400 is performed using the extracted first aberration component. The amounts of eccentricity Δ ₁ to Δ _j can be obtained by solving a system of linear equations in step S400.

Each of the amounts of eccentricity Δ ₁ to Δ _j is an amount of eccentricity that is -2 times the amount of eccentricity with respect to the measurement axis. The amount of eccentricity obtained by executing step S400 is divided by -2 and the amount of eccentricity with respect to the measuring axis is determined. The amount of eccentricity in this process is the amount of eccentricity in the state before the subject optical system is rotated.

In this way, according to the method of measuring the amount of eccentricity according to the present embodiment, it is possible to measure the amount of eccentricity in a short time irrespective of the shape of the lens surface and the number of lenses constituting the optical system, even if system aberration in the light projection system and / or the light receiving system exists.

When a plurality of lens surfaces exist, the amount of eccentricity between the lens surfaces can be evaluated. In this case, as in 13C illustrated, a new axis 80 set to minimize the amount of eccentricity of a plurality of lens surfaces distributed in the space. Thereafter, the amount of eccentricity of the lens surfaces is based on the new axis 80 evaluated.

To the new axis 80 For example, a temporary axis is set, a distance from the temporary axis to the corresponding sphere center on a surface of each lens is obtained, and the sum of the squares of the distances is obtained. Thereafter, the temporary axis is changed to set a temporary axis, where the minimum sum of squares is the new axis. As another example, an amount is obtained by dividing a distance from the temporary axis to the corresponding sphere center on a surface of each lens by the radius of curvature of the lens, and the sum of the squares of the amounts is obtained. Thereafter, the temporary axis can be changed to set a temporary axis, where the minimum sum of squares is the new axis.

Moreover, in the measuring method of the present embodiment, it is possible to remove the design aberration component even if the design aberration component exists.

The wavefront aberration W of expression (1-4), expression (1-5) and expression (1-6) has been explained as a deviation from the wavefront when the subject optical system is not eccentric and system aberration does not exist. When the wavefront aberration W is a deviation from an ideal wavefront such as a plane wave and a spherical wave, a similar explanation can be given where the term of the design aberration component M (Ox, Oy, ρx, ρy) is added to W.

The design aberration component M (Ox, Oy, ρx, ρy) is an aberration component given only by the object height coordinates and the pupil coordinates and does not depend on the amount of eccentricity. For this reason, the design aberration component can be treated in the same way as the system aberration component Sys (Ox, Oy, ρx, ρy).

For this reason, each of Sys (Ox, Oy, ρx, ρy) in Expression (1-5) and Sys (Ox, Oy, ρx, ρy) in Expression (1-6) is replaced by M (Ox, Oy, ρx, ρy ) replaced. In this case, the design aberration component M (Ox, Oy, ρx, ρy) is the same between the expression (1-5) and the expression (1-6). Therefore, M (Ox, Oy, ρx, ρy) is removed when the calculation of the expression (18) is performed at step S200. As a result, the predetermined aberration component can be extracted.

In addition, a subject optical system generally includes, apart from eccentricity, a rotationally symmetric manufacturing defect such as a radius of curvature error of each surface, a pitch error, and a refractive index error. Accordingly, the actually measured wavefront aberration W also includes an aberration component caused by a manufacturing error. However, the wavefront aberration caused by a rotationally symmetrical manufacturing error is also an aberration component given only by the object height coordinates and the pupil coordinates, and does not depend on the amount of eccentricity. For this reason, it is possible to treat them in the same way as the system aberration component Sys (Ox, Oy, ρx, ρy) and the design aberration component M (Ox, Oy, ρx, ρy). Accordingly, even if the subject optical system includes a rotationally symmetric manufacturing error such as a radius of curvature error of each surface, a pitch error, and an error in the refractive index, the predetermined aberration component can be extracted.

Moreover, in the actual wavefront measurement, it is not necessary to analyze the wavefront aberration W as a deviation from an ideal wavefront such as a plane wave and a spherical wave. As indicated by the expression (18), it is sufficient to analyze a deviation of the wavefront after the first rotation from the wavefront before the first rotation of the subject optical system.

Accordingly, by analyzing the wavefront aberration, the system aberration component can be removed from a deviation between the wavefront data WFDθ1 and the wavefront data WFDθ2, whereby it is possible to extract the predetermined aberration component.

In the following explanation, deviation of the wavefront after the first rotation from the wavefront before the first rotation of the subject optical system is analyzed in the same manner as above. For this reason, an explanation will be omitted in the following explanation of how to obtain a reference wavefront of the wavefront aberration W.

After the execution of step S200, step S300 is executed. The first aberration component is extracted by executing step S300. Step S400 is performed using the extracted first aberration component. The amounts of eccentricity Δ ₁ to Δ _j can be obtained by solving a system of linear equations in step S400.

In this way, according to the method of measuring the amount of eccentricity according to the present embodiment, it is possible to measure the amount of eccentricity in a short time irrespective of the shape of the lens surface and the number of lenses constituting the optical system, even if a design aberration is implied optical system exists.

In addition, in the measuring method of the present embodiment, it is possible to remove an aberration component of the light-receiving optical system even when the optical light-receiving system disposed between the subject optical system and the light-receiving system is eccentric.

The optical light receiving system will be explained hereinafter. As described above, the light beam emitted from the subject optical system is made incident on the light receiving system. Here, an optical light receiving system may be arranged to properly set the diameter of the light beam incident on the light receiving system. 14 FIG. 12 is a diagram illustrating a state in which an optical light receiving system is interposed between the subject optical System and the light receiving system is arranged. In this example, it is assumed that no system aberration or design aberration occurs.

The light receiving optical system is formed of lens surfaces from the (j + 1) th lens surface to the mth lens. Here, when the lens surface of the light-receiving optical system becomes eccentric, an aberration occurs. 14 also illustrates the displacements of the lens surfaces using the ball centers. In 14 SC _{j + 1} , SC _{j + 2} , ... and SC _m indicate the ball centers of the respective lens surfaces. Moreover, δ _{j + 1} , δ _{j + 2} , ... and δ _m indicate the shift amounts of the respective lens surfaces in the Y direction.

When a lens surface of the light-receiving optical system is eccentric, the wavefront aberration of the wavefront incident on the light-receiving system has a value obtained by adding the wavefront aberration caused by the eccentricity of the light-receiving optical system to the wavefront aberration caused by the eccentricity of the subject optical system , Accordingly, the finally detected wavefront includes an eccentric aberration of the subject optical system and an eccentric aberration of the light receiving optical system.

Here, the wavefront data WFDθ1 is detected by executing step S110 and step S121. The wavefront data WFDθ1 contains information about the eccentric aberration of the subject optical system and information about the eccentric aberration of the light receiving optical system. The wavefront aberration W is detected by analyzing the wavefront data WFDθ1. The wavefront aberration W is given by the following expression (1-7). Since it is assumed that the eccentricity is a displacement in the Y direction, the amount of eccentricity is given by δ.

Next, step S150 is executed. The first rotation is performed at step S150. In the first rotation, the objective optical system is rotated about the measuring axis. The rotation angle is for example 180 °. The position of the light projection system is recorded. Accordingly, the radiation position P is not moved. In addition, the positions of the light-receiving optical system and the light-receiving system are also recorded.

Thereafter, the wavefront data WFDθ2 is detected by executing step S110 and step S122. The wavefront data WFDθ2 contains information about the eccentric aberration of the subject optical system and information about the eccentric aberration of the light receiving optical system. The wavefront aberration W is detected by analyzing the wavefront data WFDθ2. The wavefront aberration W is given by the following expression (1-8).

Table 15 illustrates results of comparison of the eccentric aberration components of the light-receiving optical system between the expression (1-7) and the expression (1-8). As is clear from Table 15, the eccentric aberration components of the light-receiving optical system are the same between the expression (1-7) and the expression (1-8). [Table 15] Expression (1-7) Expression (1-8) δj _{+ 1} B _{(j + 1) 1} (Ox, Oy, ρx, ρy) δj _{+ 1} B _{(j + 1) 1} (Ox, Oy, ρx, ρy) δ _{j + 1} ² B _{(j + 1) 2} (Ox, O y, ρ x, ρ y) δ _{j + 1} ² B _{(j + 1) 2} (Ox, O y, ρ x, ρ y) δ _{j + 2} B _{(j + 2) 1} (Ox, O y, ρ x, ρ y) δ _{j + 2} B _{(j + 2) 1} (Ox, O y, ρ x, ρ y) δ _{j + 2} ² B _{(j + 2) 2} (Ox, O y, ρ x, ρ y) δ _{j + 2} ² B _{(j + 2) 2} (Ox, O y, ρ x, ρ y) ... ... δ _m B _m1 (Ox, Oy, ρx, ρy) δ _m B _m1 (Ox, Oy, ρx, ρy) δ _m ² B _m2 (Ox, Oy, ρx, ρy) δ _m ² B _m2 (Ox, Oy, ρx, ρy)

For this reason, at step S200, calculation of the expression (18) is performed. Since the eccentric aberration component of the light-receiving optical system is removed by the calculation, the predetermined aberration component can be extracted.

After the execution of step S200, step S300 is executed. The first aberration component is extracted by executing step S300. Step S400 is performed using the extracted first aberration component. The amounts of eccentricity Δ ₁ to Δ _j can be obtained by solving a system of linear equations in step S400.

In this way, according to the method of measuring the amount of eccentricity according to the present embodiment, it is possible to measure the amount of eccentricity in a short time irrespective of the shape of the lens surface and the number of lenses constituting the optical system, even if an eccentric optical light receiving system exist.

The explanation described above has illustrated the case where the detecting step includes the first rotation. Step S100 in FIG 8th can be performed at a variety of radiation positions. The wavefront of the light beam emitted by the objective optical system becomes, for example measured off-axis and on-axis by the light-receiving system, and wavefront data is recorded. Thereafter, the first rotation is performed by a certain angle. After the first rotation, the wavefront of the light beam emitted from the subject optical system is measured off-axis and on-axis by the light-receiving system, and wavefront data is recorded. Here, the case where the radiation position is on the measurement axis is called "on-axis", and the case where the radiation position is not on the measurement axis is called "off-axis".

Moreover, in the measuring method of the present embodiment, the detecting step includes the first rotation, wherein the objective optical system is rotated in the first rotation about an axis parallel to the measuring axis, and the wavefront data before the first rotation and the wavefront data after the first rotation in the same radiation position.

In the measuring method according to the present embodiment, the first rotation is performed around a first rotation axis. The first axis of rotation is an axis other than the measuring axis and an axis for rotating the objective optical system substantially about the optical axis.

15 FIG. 12 is a diagram illustrating a state in which the first rotation axis is eccentric to the measurement axis. FIG. In 15 is the first axis of rotation AX _R1 in the Y direction of the measuring axis, that is, the Oz axis shifted. The amount of shift is called E.

In the measuring method according to the present embodiment, the flowchart in FIG 8th illustrated step S100 performed. First, step S110 is carried out and thereby a light beam is radiated from the radiation position P (Ox, Oy, O) to the subject optical system. Thereafter, step S121 is executed, thereby detecting wavefront data WFDθ1. The wavefront aberration W is given by the following expression (1-9). Since the eccentricity of the subject optical system is set as a shift in the Y direction in this example, the amount of eccentricity is given by δ.

In addition, since the amounts of E and δ can generally be set to minuscule amounts, the amount of aberration for the terms proportional to the 3rd power or higher of the amount of eccentricity in each term can be considered minute and ignored. For this reason, the expression (1-9) contains no terms proportional to the 3rd power or higher of the amount of eccentricity.

Thereafter, step S150 is executed. The first rotation is performed at step S150. In the first turn, the objective optical system becomes 20 rotated around the measuring axis. The rotation angle is for example 180 °.

After the completion of step S150, step S110 is executed, thereby irradiating a light beam from the radiation position P (Ox, Oy, O) to the objective optical system. Thereafter, step S122 is executed, thereby detecting wavefront data WFDθ2. The wavefront aberration W is given by the following expression (1-10).

Thereafter, step S200 is executed. The wavefront data WFDθ1 detected before the first rotation are reference data, and the wavefront data WFDθ2 detected after the first rotation are measurement data. Accordingly, the final wavefront aberration is determined by analyzing the measurement data using the reference data as the standard for the wavefront.

More specifically, in order to obtain the final wavefront aberration, calculation of Expression (19) is performed using the wavefront aberration given by Expression (1-9) as reference data and the wavefront aberration given by Expression (1-10) as measurement data.

As a result, the final wavefront aberration is given by Expression (1-11).

The wavefront aberration given by the expression (1-11) is a deviation of the wavefront after the first rotation from the wavefront before the first rotation of the subject optical system.

Here, δ ₁ and E indicate the amount of eccentricity respectively. Accordingly, (-4δ ₁ E) to (-4δ _j E) can each be said to indicate the square of the amount of eccentricity. Table 16 explains all the terms in expression (1-11). [Table 16] term Explanation of the term (-2δ ₁ ) B ₁₁ (Ox, Oy, ρx, ρy) eccentric aberration component proportional to the 1st power of the amount of eccentricity in the first surface (-4δ ₁ E) B ₁₂ (Ox, Oy, ρx, ρy) eccentric aberration component proportional to the square of the amount of eccentricity in the first surface (-2δ ₂ ) B ₂₁ (Ox, O y, ρ x, ρ y) eccentric aberration component proportional to the 1st power of the amount of eccentricity in the second surface (-4δ ₂ E) B ₂₂ (Ox, Oy, ρx, ρy) eccentric aberration component proportional to the square of the amount of eccentricity in the second surface ... ... (-2δ _j ) B _j1 (Ox, Oy, ρx, ρy) eccentric aberration component proportional to the 1st power of the amount of eccentricity in the jth surface (-4δ _j E) B _j2 (Ox, Oy, ρx, ρy) eccentric aberration component proportional to the square of the amount of eccentricity in the jth surface

As expressed by the expression (1-11), the final wavefront aberration is formed of the aberration component proportional to the 1st power of the eccentricity amount and the aberration component proportional to the square of the eccentricity amount, that is, the first aberration component and the second aberration component. In this way, the predetermined aberration component is extracted by performing the calculation of the expression (19).

The expression (1-9) and the expression (1-10) contain no design aberration component or eccentric aberration component of the light-receiving optical system. However, the terms may include these aberration components. However, these aberration components are removed by performing a calculation of the expression (19). For this reason, these aberration components are not described in Expression (1-9) or Expression (1-10).

Expression (1-11) contains the second aberration component. The reason for this is because the first rotation axis is shifted by the shift amount E from the measurement axis. For this reason, the amount of eccentricity can not be determined without processing using the equation associated with the first eccentric component.

That is why, as in 7 illustrates the wavefront data before the first rotation and the wavefront data after the first rotation in the radiation position P '. The wavefront data before the first rotation is reference data and the wavefront data after the first rotation is measurement data. The final wavefront aberration in the radiation position P 'is determined by analyzing the measurement data using the reference data as the wavefront standard.

Since the radiation position P 'is symmetrical to the radiation position P, the object height coordinates are (-Ox, -Oy, 0). Accordingly, the final wavefront aberration is given by Expression (1-12).

The wavefront aberration given by the expression (1-12) is a deviation of the wavefront after the first rotation from the wavefront before the first rotation of the subject optical system.

As is clear from the expression (1-11) and the expression (1-12), the final wavefront aberration includes the aberration component proportional to the 1st power of the eccentricity amount and the aberration component proportional to the square of the eccentricity amount, that is, the first aberration component and the second aberration component, as the predetermined aberration components.

Thereafter, step S300 is executed to extract the first aberration component. Here the aberration component is given by Wz. The aberration component Wz multiplied by the function with the odd-order pupil coordinates is an aberration component multiplied by the second term and others of the Zernike terms. The aberration component Wz (z = 2, 3, 7, 8, ...) is obtained by obtaining the sum of the expression (1-11) and the expression (1-12). Expression (20) indicates a result of the sum.

Here, "Bz _j1 (-Ox, -Oy) = Bz _j1 (Ox, Oy)" and "Bz _j2 (-Ox, -Oy) = -Bz _j2 (Ox, Oy)" are satisfied. Accordingly, expression (21) is obtained from expression (20).

As given by the expression (20), by calculating the sum thereof, the first aberration component remains and the second aberration component disappears. Accordingly, the first aberration component Tz (Ox, Oy, δ ₁ , δ ₂ , ..., δ _j ) can be extracted from the predetermined aberration component.

In contrast, the aberration component Wz multiplied by the function with the even-order pupil coordinates is an aberration component multiplied by the fourth term and others of the Zernike terms. The aberration component Wz (z = 1, 4, 5, 6, 9 ...) is obtained by obtaining the difference between the expression (1-11) and the expression (1-12). Expression (22) indicates a result of the sum.

Here, "Bz _j1 (-Ox, -Oy) = Bz _j1 (Ox, Oy)" and "Bz _j2 (-Ox, -Oy) = -Bz _j2 (Ox, Oy)" are satisfied. Accordingly, expression (23) is obtained from expression (22).

As given by the expression (22), by calculating the difference thereof, the first aberration component remains and the second aberration component disappears. Accordingly, the first aberration component Tz (Ox, Oy, δ ₁ , δ ₂ , ..., δ _j ) can be extracted from the predetermined aberration component.

In addition, the coefficient in Expression (21) and Expression (23) is "δ ₁ , δ ₂ , ..., δ _j ". As in 15 illustrated, each of the δ ₁ , δ ₂ , ..., δ _{j is} an amount of eccentricity from the first axis of rotation. This illustrates that the first rotation axis serves as a standard indicating the amount of eccentricity. In particular, the measuring axis does not serve as the standard indicating the amount of eccentricity.

Thereafter, step S400 is performed using the first aberration component Tz (Ox, Oy, δ ₁ , δ ₂ , ..., δ _j ). The system of linear equations is solved in step S400. Thereby, the value that is -2 times the amount of eccentricity based on the first rotation axis is determined as a solution.

In this way, the second aberration component disappears, and the first aberration component is extracted, and it becomes possible to treat the displacement of each surface of the objective optical system and the aberration amount of the first aberration component in a linear manner. As a result, it is possible to detect the amount of displacement of each surface as it rotates about the first rotation axis AX _{R1 of} the subject optical system, even if the measurement axis Oz does not coincide with the first rotation axis AX _R1 . Accordingly, it is possible to accurately determine the amount of eccentricity based on the first rotation axis.

As described above, in the measuring method according to the present embodiment, the subject optical system is rotated by a certain angle about the measurement axis or the first rotation axis, and thereby two wavefront data are detected. Thereafter, by analyzing the wavefront aberration, it is possible to remove the design aberration, the system aberration, and the eccentric aberration of the light-receiving optical system, using the wavefront data before the first rotation as the reference data and using the wavefront data after the first rotation as the measurement data.

Moreover, in the measuring method of the present embodiment, it is preferable that the angle for rotating the objective optical system is 10 ° or more. In addition, it is preferable that the angle for rotating the objective optical system is preferably 180 °.

In the explanation described above, the subject optical system is rotated by 180 ° about the measuring axis or the first rotation axis. However, the angle of rotation can be any angle. A preferred rotation angle is 10 ° or more and a more preferable rotation angle is 180 °.

In addition, the first axis of rotation may be inclined with respect to the measuring axis. This point will be described below.

16A and 16B are diagrams illustrating relative relationships between the first axis of rotation and the measuring axis, wherein 16A illustrates a state in which the measuring axis coincides with the first axis of rotation, and 16B illustrates a state in which the first axis of rotation is inclined relative to the measuring axis.

As described above, when each lens surface is a spherical surface, the amount of displacement of the ball center by the first rotation is -2 times as large as the amount of eccentricity with respect to the measurement axis. In contrast, when every lens surface of the subject optical system 90 is an aspherical surface, the state of the displacement caused by the first rotation is as in 16A illustrated. As in 16A Illustrated is an aspheric surface 91 through an aspherical surface top 92 and an aspherical surface axis 93 given.

When the rotation angle in the first rotation is 180 °, the amount of displacement of the aspherical surface top and the amount of displacement of the aspherical surface axis are -2 times as large as the amount of eccentricity with respect to the first rotation axis AX _R1 before rotation. The aspherical surface top 92 becomes due to the first rotation, for example, to a position of an aspherical surface top 92 ' relocated. In this case, the amount of displacement of the aspherical surface top is 92 -2 × y1. The amount of displacement of the aspherical surface axis 93 is -2 × a1.

As described above, the amount of displacement of each surface can be detected by rotating the subject optical system about the first rotation axis out of the first aberration component. The amount of eccentricity of the subject optical system based on the first rotation axis can be determined from the amount of displacement. Accordingly, the amount of displacement of each surface with rotation of the subject optical system about the first axis of rotation must reflect the amount of eccentricity of the subject optical system.

When the first rotation is performed, the first rotation axis AX _R1 desirably coincides with the measurement axis AX _M. However, the first rotation axis AX _R1 may be shifted or inclined with respect to the measurement axis AX _M. In this case, if the shift amount or the tilt amount is minute, the shift and the tilt cause no problem in actual use. In particular, when the first rotation axis AX _R1 is shifted with respect to the measurement axis AX _M , the displacement has no influence on the amount of displacement caused by the first rotation. Accordingly, in this case, the amount of displacement of each surface accurately reflects the amount of eccentricity of each surface.

In contrast, as in 16B illustrated, when the first axis of rotation AX _R1 is inclined with respect to the measuring axis AX _M , the inclination has an influence on the amount of displacement caused by the first rotation. For example, it is assumed that the first rotation axis AX _R1 is inclined at an angle θ with respect to the measurement axis AX _M. In this case, the amount of displacement Y1 is the surface aspherical surface 92 "Y1 = -2 × y1 × cosθ".

In this way, when the first rotation axis AX _R1 is inclined by θ, a change in the amount of displacement by cosθ times is as large as that in the case where the first rotation axis AX _{R1 is} not inclined. However, even if θ is about 1 °, the change resulting from the amount of displacement in 16A is calculated, 0.02% or less. Accordingly, in this case, the amount of displacement of the aspherical surface top reflects 92 essentially exactly the amount of eccentricity.

In addition, the amount of displacement A1 is the aspheric surface axis 93 "A1 = (-a1 + θ) - (a1-θ) = -2 × a1". This is the same amount as the one in 16A calculated amount of relocation. Accordingly, the amount of displacement of the aspherical surface axis is not affected by the inclination of the first rotation axis AX _R1 . The same applies to the amount of displacement of the aspherical surface axis of each surface. Accordingly, in this case, the amount of displacement of the aspherical surface axis of each surface accurately reflects the amount of eccentricity.

Therefore, the eccentricity of the subject optical system can be detected without any problem even if the first rotation axis AX _{R1 has} a minute inclination with respect to the measurement axis AX _M.

Moreover, when the subject optical system is rotated, it is preferable that no offset occurs in the first rotation axis AX _R1 . Even if a displacement occurs when the amount of displacement occurring in the first rotation axis AX _R1 is minute, no problem occurs in actual use. 17 is a diagram illustrating a state in which the first rotation axis is offset from the measurement axis.

An offset occurring in the first rotation axis AX _R1 may be indicated by a displacement and an inclination with respect to the measurement axis AX _M. It is assumed, for example, that the first rotation axis AX _R1 is displaced by a distance T and inclined at an angle θ with respect to the measurement axis AX _M. In this case, the amount of displacement Y1 is the surface aspherical surface 92 "Y1 = -y1 + T - y1 × cosθ". However, even if θ is about 1 °, as described above, the change resulting from the amount of displacement in 16A is calculated, 0.02% or less. Accordingly, in this case, the amount of displacement of the aspherical surface top reflects 92 essentially exactly the amount of eccentricity.

In addition, the amount of displacement A1 is the aspheric surface axis 93 "A1 = (-a1 + θ) - (a1-θ) = -2 × a1". This is the same amount as the one in 16A calculated amount of relocation. Accordingly, the amount of displacement of the aspherical surface axis is not affected by the inclination of the first rotation axis AX _R1 . The same applies to the amount of displacement of the aspherical surface axis of each surface. Accordingly, in this case, the amount of displacement reflects the aspheric surface axis 93 exactly the amount of eccentricity.

A shift 95 additionally enters from the aspherical surface top 92 different aspherical surface tops. Relocation 95 in an aspherical surface top 94 is, for example, d4sinθ and therefore the amount of displacement in the aspherical surface top is 94 "-Y4 + T - y4 × cosθ + d4sinθ", where d4 is a distance between the aspherical surface top 92 and the aspherical surface top 94 in the direction of the measuring axis AX _M is. Specifically, the amount of displacement is increased by an addition that is sin θ times as large as the distance in the direction of the measurement axis AX _M.

Thus, it may be assumed that an imaginary rotation axis AX _I other than the first rotation axis AX _{R1 is} generated. The imaginary rotation axis AX _I is an axis shifted by a distance T / 2 from the measurement axis AX _M and inclined by an angle θ / 2. It can be assumed that the objective optical system is rotated about the imaginary rotation axis AX _I. Therefore, it is possible to detect the amount of displacement of each surface from the first aberration component caused by rotation about the imaginary rotation axis AX _I. It is possible to determine the amount of eccentricity of the objective optical system based on the imaginary rotation axis AX _I on the basis of the amount of displacement. Accordingly, no problem arises in an actual use even if the first rotation axis is inclined with respect to the measurement axis.

Moreover, the first rotation may be performed even in the case where a light beam is radiated from a pair of radiation positions. Examples of the first rotation will be explained using Example 1 and Example 2.

18 FIG. 15 is a diagram illustrating a flowchart of Example 1. In Example 1, first, the first rotation is performed in a radiation position, and thereby wavefront data before the first rotation and wavefront data after the first rotation are detected. Thereafter, the radiation position is changed and the first rotation is performed in the other radiation position, and thereby wavefront data before the first rotation and wavefront data after the first rotation are detected.

Step S100 includes step S110, step S121, step S122, step S130, step S141, step S142, step S150, and step S151.

At step S100, step S110, step S121, step S150, step S110, and step S122 are performed. Thereby, in the radiation position P, wavefront data WFDθ1 before the first rotation and wavefront data WFDθ2 after the first rotation are detected.

The state in which the execution of step S122 is ended is a state after the first rotation. For this reason, step S151 is executed, and the subject optical system is thereby returned to a state before the first rotation has been performed.

Thereafter, step S130, step S141, step S150, step S130, and step S142 are executed. As a result, wavefront data WFD'θ1 before the first rotation and wavefront data WFD'θ2 after the first rotation are detected in the radiation position P '.

In this way, the light source in Example 1 is located by guiding the light source in the OxOy direction before the first rotation at desired OxOy coordinates and reference data is detected. In particular, reference data is acquired in desired object height coordinates (Ox, Oy). Thereafter, a first rotation is performed, thereby rotating the subject optical system.

Thereafter, measurement data is acquired after the first rotation. In this process, the coordinates of the light source, that is, the object height coordinates (Ox, Oy) are not changed before the first rotation and after the first rotation. Accordingly, measurement data having the same object height coordinates (Ox, Oy) as those before the first rotation are detected.

Thereafter, the subject optical system is returned to the state before the first rotation, and the light source is guided in the OxOy direction and arranged at coordinates other than the first OxOy coordinates, and reference data is detected. Specifically, reference data is detected at object height coordinates (Ox ', Oy') different from the first object height coordinates (Ox, Oy). Thereafter, by performing the first rotation, the first measurement data is acquired.

In this way, in Example 1, detection of reference data and detection of measurement data are alternately repeatedly performed. After the acquisition of the reference data and the acquisition of the measurement data at all object height coordinates are completed, a wavefront analysis is performed thereafter.

Im in 18 In the flowchart illustrated, the rotation state after the execution of step S122 is the state after the first rotation. For this reason, step S130 and step S142 may be performed to detect wavefront data WFD'θ2 without executing step S151. Thereafter, the step S151 is executed and the subject optical system is thereby returned to the state before the first rotation. Thereafter, steps S130 and S141 may be performed, and thereby wavefront data WFD'θ1 is detected.

In this way, in Example 1, it is possible to detect wavefront data before the first rotation and wavefront data after the first rotation in each of the radiation positions even if there are a plurality of radiation positions. By analyzing the wavefront aberration, it is possible to remove the design aberration, the system aberration and the eccentric aberration of the light receiving optical system, using the wavefront data before the first rotation as the reference data and using the wavefront data after the first rotation as the measurement data.

19 FIG. 13 is a diagram illustrating a flowchart of Example 2. FIG. In Example 2, wavefront data in the one radiation position and in the other radiation position are first detected. Thereafter, a first rotation is performed to again detect wavefront data in the one radiation position and the other radiation position.

Step S100 includes step S110, step S121, step S122, step S130, step S141, step S142, and step S150.

In step S100, step S110, step S121, step S130, and step S141 are first executed. Thereby, wavefront data WFDθ1 in the radiation position P and wavefront data WFD'θ1 in the radiation position P 'in a state before the first rotation are detected.

Thereafter, step S150 is executed, thereby rotating the subject optical system. Thereafter, step S110, step S122, step S130, and step S142 are executed. Thereby, wavefront data WFDθ2 in the radiation position P and wavefront data WFD'θ2 in the radiation position P 'in a state after the first rotation are detected.

In this way, in the example 2, before the first rotation, the light source is located by guiding the light source in the OxOy direction at a plurality of object height coordinates, and reference data is detected. In particular, the acquisition of all datasets of the reference data is completed at a plurality of object height coordinates. Thereafter, the first rotation is performed, thereby rotating the subject optical system.

After the first rotation, the light source is again guided in the OxOy direction and measurement data is acquired. When acquiring the measurement data, the light source is at the same OxOy coordinates as those used before the first rotation. In particular, the acquisition of all measurement data sets is completed at the same object height coordinates as those used prior to the first rotation. Upon completion of the acquisition of all measurement data sets, a wavefront analysis is performed.

In this way, in Example 2, first, a rotation is performed after all the reference data sets are acquired.

Thereafter, by obtaining a sum or a difference of predetermined aberration components between symmetrical object height coordinates, it is possible to extract an aberration component proportional to the 1st power of the amount of eccentricity among the eccentric aberrations caused by the eccentricity of the objective optical system, that is, the first aberration component.

Im in 19 The flowchart illustrated is the radiation position after the execution of step S150 P '. For this reason, step S142 may be executed, and thereby wavefront data WFD'θ2 is detected. Thereafter, step S110 and step S122 may be performed, and thereby wavefront data WFDθ2 is detected.

In this way, in Example 2, it is possible to detect wavefront data before the first rotation and wavefront data after the first rotation in each of the radiation positions, even if a plurality of radiation positions exist. By analyzing the wavefront aberration, it is possible to remove the design aberration, the system aberration and the eccentric aberration of the light receiving optical system, using the wavefront data before the first rotation as the reference data and using the wavefront data after the first rotation as the measurement data.

Moreover, in the measuring method of the present embodiment, it is preferable that each of the one radiation position and the other radiation position is moved and the wavefront data in the radiation position after the movement is detected.

The number of lens surfaces in a lens is two. When the two lens surfaces are aspherical surfaces, the number of degrees of freedom of eccentricity is 8 when displacement and inclination occur in each lens surface. In addition, when four lens surfaces are aspheric surfaces in two lenses, the number of degrees of freedom of eccentricity is 16 when displacement and inclination occur in each lens surface. In this way, the number of degrees of freedom of eccentricity increases as the number of eccentric lens surfaces increases.

An increase in the number of degrees of freedom of the eccentricity means that the number of j increases in Δ ₁ to Δ _j in the expressions (9-1) to (9-9). Since Δ ₁ to Δ _{j are} unknown quantities, Δ ₁₀ and above can not be obtained when the number of linear equations is 9 at the maximum, although it is possible to detect Δ ₉ .

For this reason, the one radiation position and the other radiation position are moved, and wavefront data in the moved positions are detected. In this case, the following expressions (9-1 ') to (9-9') are obtained from the radiation positions (Ox1, Oy1) and (-Ox1, -Oy1) before the movement.

In addition, the following expressions (9-1 ") to (9-9") are obtained from the radiation positions (Ox2, Oy2) and (-Ox2, -Oy2) after the movement.

As a result, further degrees of freedom can be determined since the number of linear equations is a maximum of 18.

In this way, the number of linear equations can be increased by increasing the number of radiation positions. Therefore, according to the measuring method of the present embodiment, it is possible to increase the number of measurable degrees of freedom of eccentricity.

Moreover, in the measuring method of the present embodiment, it is preferable that the one radiation position is moved, the wavefront data is detected in a radiation position after the movement, then the other radiation position is moved and the wavefront data is detected in a radiation position after the movement.

20 FIG. 10 illustrates a flowchart of the measuring method of the present embodiment. FIG. In 20 Step S200 and subsequent steps are omitted. 21A . 21B and 21C are diagrams illustrating a motion state of the radiation position, wherein 21A illustrates a position of a radiation position before the movement, 21B illustrates a position of a radiation position after the movement, 21C illustrates a position of the other radiation position before the movement and 21D illustrates a position of the other radiation position after the movement.

In the measuring method of the present embodiment, step S100 includes step S111, step S123, step S131, step S143, step S160, step S161, step S170, and step S171.

At step S100, a light beam is radiated from a radiation position Pn and a radiation position P'n. Here, the radiation position Pn is the one radiation position and the radiation position P'n is the other radiation position. The radiation position Pn and the radiation position P'n are symmetrical with respect to the measurement axis.

N is set by the user before the execution of step S111. N indicates the number of changes in the radiation position. The number of times set in N is a scheduled number of times. The value of n is set to 0. n indicates the number of movements of the radiation position.

Thereafter, the step S111 is executed. At step S111, a light beam is radiated from the radiation position Pn. In particular, as in 21A illustrated, the light source is at the radiation position P0 (Ox0, Oy0,0). Because the objective optical system 2 is eccentric to the measuring axis, becomes a non-planar wave 9 ₀ from the objective optical system 2 radiated. The not plane wave 9 ₀ is from the light receiving system 3 recognized.

After completion of step S111, step S123 is executed. At step S123, wavefront data WFDn are based on the non-plane wave 9 ₀ recorded. Thereafter, step S160 is executed.

At step S160, n and N are compared. If n is not equal to N, the number of movements of the radiation position does not reach the planned number of times. For this reason, 1 is added to the current number of movements, and step S170 is executed. At step S170, the radiation position is moved. The amount of movement can be set in advance by the user.

After the execution of step S170, step S111 is executed again. At the step of moving the radiation position, the light source is at a radiation position P1 (Ox1, Oy1.0) as in FIG 21B illustrated. An uneven wave 9 ₁ is from the objective optical system 2 radiated. The not plane wave 9 ₁ is from the light receiving system 3 recognized.

Here, the radiation position P1 (Ox1, Oy1,0) differs from the radiation position P0 (Ox0, Oy0,0). For this reason, the non-level wave is different 9 ₁ from the non-level wave 9 ₀ .

After completion of step S111, step S123 is executed. At step S123, wavefront data WFDn are based on the non-plane wave 9 ₁ recorded. The movement of the radiation position and the detection of the wavefront data WFDn are performed until n becomes equal to N. All data sets of the acquired wavefront data WFDn are stored.

When n becomes N at step S160, the movement of the radiation position is completed. This completes the movement of the one radiation position and the detection of the wavefront data at the radiation position after the movement. Thereafter, the value of n is set to 0.

Thereafter, step S131 is executed. At step S131, a light beam is radiated from the radiation position P'n. In particular, as in 21C illustrated, the light source is at the radiation position P'0 (-Ox0, -Oy0,0). The radiation position P'0 (-Ox0, -Oy0,0) is located at a position symmetrical to the radiation position P0 (Ox0, Oy0,0) with respect to the measuring axis. An uneven wave 9 ' ₀ becomes from the objective optical system 2 radiated. The not plane wave 9 ' ₀ is from the light receiving system 3 recognized.

Here, the radiation position P'0 (-Ox0, -Oy0,0) differs from the radiation position P0 (Ox0, Oy0,0) and the radiation position P1 (Ox1, Oy1,0). For this reason, the non-level wave is different 9 ' ₀ from the non-level wave 9 ₀ and the non-level wave 9 ₁ .

After completion of step S131, step S143 is executed. At step S143, wavefront data WFD'n based on the non-planar wave 9 ' ₀ recorded. Thereafter, step S161 is executed.

At step S161, n and N are compared. If n is not equal to N, the number of movements of the radiation position does not reach the planned number of times. For this reason, 1 becomes the current one Number of movements is added and step S171 is executed. At step S171, the radiation position is moved. The amount of movement can be set in advance by the user.

After the execution of step S171, step S131 is executed again. At the step of moving the irradiation position, the light source is at a radiation position P'1 (-Ox1, -Oy1,0), as in FIG 21D illustrated. The radiation position P'1 (-Ox1, -Oy1,0) is located at a position symmetrical to the radiation position P1 (Ox1, Oy1,0) with respect to the measurement axis. An uneven wave 9 ' ₁ is from the objective optical system 2 radiated. The not plane wave 9 ' ₁ is from the light receiving system 3 recognized.

Here the radiation position P'1 (-Ox1, -Oy1,0) differs from the radiation positions P'0 (-Ox0, -Oy0,0), P0 (Ox0, Oy0,0) and the radiation position P1 (Ox1, Oy1, 0). For this reason, the non-level wave is different 9 ' ₁ from the non-level wave 9 ' ₀ , the not plane wave 9 ₀ and the non-level wave 9 ₁ .

After completion of step S131, step S143 is executed. At step S143, wavefront data WFD'n based on the non-planar wave 9 ' ₁ recorded. The movement of the radiation position and the detection of the wavefront data WFD'n are performed until n becomes equal to N. All data sets of the acquired wavefront data WFD'n are stored.

When n becomes N at step S161, the movement of the radiation position is completed. This completes the movement of the one radiation position and the detection of the wavefront data at the radiation position after the movement.

After in 21A . 21B . 21C and 21D When the radiation in the radiation position P1 (Ox1, Oy1.0) is completed, the radiation position is moved to the radiation position P'0 (-Ox0, -Oy0.0). However, the radiation position may be moved to the radiation position P'1 (-Ox1, -Oy1,0) and thereafter moved to the radiation position P'0 (-Ox0, -Oy0,0).

In this way, the number of linear equations can be increased by increasing the number of radiation positions. Therefore, according to the measuring method of the present embodiment, it is possible to increase the number of measurable degrees of freedom of eccentricity.

Moreover, in the measuring method of the present embodiment, it is preferable that the wavefront data in each of the one radiation position and the other radiation position be detected, and thereafter the one radiation position and the other radiation position are moved and the wavefront data in each of the radiation positions after the movement is detected.

22 11 illustrates a flowchart of the measuring method according to the present embodiment. The step S200 and subsequent steps are omitted. 23A . 23B . 23C and 23D are diagrams illustrating a motion state of the radiation position, wherein 23A a position illustrating a radiation position before the movement, 23B illustrates a position of the other radiation position before the movement, 23C a position of a radiation position after the movement illustrated and 23D illustrates a position of the other radiation position after the movement.

In the measuring method of the present embodiment, step S100 includes step S111, step S123, step S131, step S143, step S162, and step S172.

First, step S111 is executed. At step S111, a light beam is radiated from the radiation position Pn. In particular, as in 23A illustrated, the light source is at the radiation position P0 (Ox0, Oy0,0).

After completion of step S111, step S123 is executed. At step S123, wavefront data WFDn are based on the non-plane wave 9 ₀ recorded.

Thereafter, step S131 is executed. At step S131, a light beam is radiated from the radiation position P'n. In particular, as in 23B illustrated, the light source is at the radiation position P'0 (-Ox0, -Oy0,0).

After completion of step S131, step S143 is executed. At step S143, wavefront data WFD'n based on the non-planar wave 9 ' ₀ recorded. Thereafter, step S162 is executed.

At step S162, n and N are compared. If n is not equal to N, the number of movements of the radiation position does not reach the planned number of times. For this reason, 1 is added to the current number of movements, and step S172 is executed. At step S172, the radiation position is moved. The amount of movement can be set in advance by the user.

After the execution of step S172, step S111 is executed again. At the step of moving the radiation position, the light source is at a radiation position P1 (Ox1, Oy1.0) as in FIG 23C illustrated.

After completion of step S111, step S123 is executed. At step S123, wavefront data WFDn are based on the non-plane wave 9 ₁ recorded.

Thereafter, the step S131 is executed. At step S131, a light beam is radiated from the radiation position P'n. At this step, since the irradiation position has been moved, the light source is at the irradiation position P'1 (-Ox1, -Oy1,0), as in FIG 23D illustrated.

After completion of step S131, step S143 is executed. At step S143, wavefront data WFD'n based on the non-planar wave 9 ' ₁ recorded. Thereafter, step S162 is executed.

The movement of the radiation position and the detection of the wavefront data WFDn and WFD'n are performed until n becomes equal to N. All data records of the acquired wavefront data WFDn and WFD'n are stored.

When n becomes N at step S162, the movement of the radiation position is completed. Thereby, the movement of the one radiation position and the movement of the other radiation position and the detection of the wavefront data at the radiation position after the movement are completed.

In this way, the number of linear equations can be increased by increasing the number of radiation positions. Therefore, according to the measuring method of the present embodiment, it is possible to increase the number of measurable degrees of freedom of eccentricity.

In 21A . 21B . 21C and 21D and 23A . 23B . 23C and 23D the direction of movement of the radiation position is a direction approaching the Oz axis. However, the direction of movement of the radiation position may be a direction away from the Oz axis. In addition, in 21A . 21B . 21C and 21D and 23A . 23B . 23C and 23D illustrates four radiation positions, but the radiation positions are not limited to four. In addition, the light beam can be radiated from the origin (0,0,0).

24A and 24B are diagrams illustrating a motion state of the radiation position, wherein 24A illustrates the case where the direction of movement of the radiation position is unidirectional, and 24B illustrates the case where the direction of movement of the radiation position is bidirectional.

24A illustrates a unidirectional movement of the radiation direction. In 24A the movement of the radiation direction is started from the maximum negative object height coordinates. The radiation position is moved to the maximum positive object height coordinates. More specifically, the radiation position is moved in the order of a radiation position P'4 (-Ox4,0,0), a radiation position P0 (0,0,0) and a radiation position P4 (Ox4,0,0).

24B illustrates a bidirectional movement of the radiation direction. In 23B the movement of the radiation direction is started from a position on the axis. Thereafter, the radiation position is moved to the maximum positive object height coordinates. Thereafter, the radiation position is returned to the position on the axis (on the Oz axis), and the radiation position is moved to the maximum negative object height coordinates. Specifically, the irradiation position is moved from the irradiation position P0 (0,0,0) to the irradiation position P4 (Ox4,0,0), and thereafter the irradiation position is changed from the irradiation position P0 (0,0,0) to the irradiation position P'4 (-Ox4 , 0,0) moves.

In 24A For example, the radiation position can be moved randomly between the radiation position P4 (Ox4,0,0) and the radiation position P4 '(-Ox4,0,0). In the same way can in 23B the radiation position coincidentally between the radiation position P0 (0,0,0) and the radiation position P4 (Ox4,0,0) or between the radiation position P0 (0,0,0) and the radiation position P'4 (-Ox4,0,0 ) are moved.

In this way, the number of linear equations can be increased by increasing the number of radiation positions. Therefore, it is possible to increase the number of measurable degrees of freedom of eccentricity.

25A . 25B and 25C are diagrams illustrating patterns of radiation position, where 25A illustrates a state in which the radiation positions are bi-directional, 25B illustrates a state in which the radiation positions are concentric and 25C illustrates a state in which the radiation positions are lattice-shaped.

In 25A the radiation positions are in the light projection system 1 only on the ox axis and the oy axis. In 25B and 25C the radiation positions are in the light projection system 1 also between the ox axis and the oy axis. In 25B the radiation positions are concentric or radial. In 25C the radiation positions are arranged in a grid-like manner.

In addition, the criterion of the slope of the movement of the radiation position in the light projection system 1 from about the effective aperture of the subject optical system to about 1/50 the effective aperture size. When the amount of eccentricity is to be measured with high accuracy, the slope of the movement is set to a small value, and thereby more data sets of wavefront data are detected.

Moreover, the first aberration component can be extracted by detecting wavefront data having only the maximum positive object height and the maximum negative object height. For this reason, when the measurement must be completed in a short time, the diameter of the radiated light beam may be substantially equal to the diameter of the subject optical system. In this case, however, the object height is set to a small value to prevent vignetting of the light beam from the effective aperture of the subject optical system.

In this way, the number of linear equations can be increased by increasing the number of radiation positions. Therefore, it is possible to increase the number of measurable degrees of freedom of eccentricity.

Moreover, in the measuring method according to the present embodiment, it is preferable that detection of the wavefront data is performed in a first radiation state and a central light beam of the light beam in the first radiation state is parallel to the measurement axis.

In the first radiation state, the central radiation beam of the light beam is parallel to the measurement axis. As in 6A and 6B in particular, is the central light beam CR of the radiation position P (Ox, Oy, 0) of the light projection system 1 radiated light beam parallel to the Oz axis, that is, to the measuring axis. In this case, if the radiation position P (Ox, Oy, O) in the OxOy plane is changed, that of the subject optical system changes 2 radiated light beam. Although here is the angle of incidence of the light beam on the light receiving system 3 is changed, the incidence position hardly changes. Therefore, the positional adjustment between the light receiving system 3 and the on the light receiving system 3 made light beam made small.

Moreover, in the measuring method according to the present embodiment, it is preferable that detection of the wavefront data is performed in a second radiation state and the central light beam of the light beam crosses the measurement axis at a predetermined angle in the second radiation state.

In the second radiation state, the central radiation beam of the light beam crosses the measurement axis at a predetermined angle. 26A and 26B illustrate a state in which the light beam is applied to the subject optical system, wherein 26A illustrates radiation at an angle θ and 26B illustrates radiation at an angle θ '. As in 26A and 26B illustrated, crosses the central light beam CR of the radiation position P (Ox, Oy, 0) of the light projection system 1 radiated light beam the Oz axis, that is, the measuring axis at an angle θ. "| Θ | = | θ '| "is fulfilled.

In 26A and 26B also becomes a spherical wave 4 emitted from the radiation position P (Ox, Oy, O). However, a light beam is transmitted to the objective optical system 2 created in a position and an angle different from those in 6A and 6B different. For this reason, not even waves differ 8th and 8th' that of the objective optical system 2 be radiated from the non-level waves 7 in 6A and the not even waves 7 ' in 6B ,

When each of the one radiation position and the other radiation position is moved and the detection of the wavefront data is made at the radiation positions after the movement, it is desirable to detect the wavefront data at the radiation positions after the movement while changing the predetermined angle.

Moreover, in the measuring method of the present embodiment, it is preferable that the second extracting step is performed using a predetermined functional system, the predetermined functional system is a functional system indicating the first aberration component and the predetermined aberration component in the one irradiation position and the predetermined aberration component in the other Radiation position are applied to the predetermined functional system.

Thereby, it is possible to extract an amount proportional to the 1st power of the amount of eccentricity Δ, that is, to extract the first aberration component.

Moreover, in the measuring method of the present embodiment, it is preferable that the detecting step includes a second rotation, that the subject optical system is rotated in the second rotation through 180 ° about an axis orthogonal to the measuring axis, and that wavefront data before the second rotation and wavefront data after second rotation are detected.

27 11 illustrates a flowchart of the measuring method according to the present embodiment. In the measuring method of the present embodiment, step S100 includes step S110, step S123, step S124, and step S180. A detailed explanation of steps S200, S300 and S400 will be omitted.

28A and 28B are diagrams that illustrate a second turn. 28A illustrates a state before the second rotation is performed, and 28B illustrates a state after the second rotation has been performed.

Here is the objective optical system 20 for simplicity, with reference terms "front" and "back" provided. If, for example, a ray of light to the objective optical system 20 is applied, the light beam from the side of the lens 23 can be applied and the light beam can from the side of the lens 25 be created. The case of applying a light beam from the side of the lens 23 is referred to as "front" and the case of applying a light beam from the side of the lens 25 is referred to as "behind".

The eccentric aberration sensitivity of each lens varies between the case where a light beam is applied to the subject optical system 20 from the "front" (hereinafter referred to as "forward measurement") and the case where a light beam is applied to the objective optical system 20 from "behind" (hereinafter referred to as "backward measurement").

If the objective optical system 20 is formed of six lens surfaces, the lens surfaces are consecutively referred to as "first surface", "second surface", ... and "sixth surface" when referred to "from the front". In the forward measurement, the surface through which the light beam is first transmitted is the first surface. In the backward measurement, the light beam is transmitted through the surfaces in the order of the sixth surface, the fifth surface ..., and the first surface is the last surface through which the light beam is transmitted.

The object point is through the lens surfaces of the objective optical system 20 forwarded. For this reason, the object point forwarded to the back of the lens surface is laterally shifted from an ideal position thereof when a lens surface is eccentric. This shift is considered to cause aberration in the subsequent posterior lens surfaces. In particular, the aberration caused by eccentricity is related to the order of the lens surfaces. This is the reason why the eccentric aberration sensitivity between the forward measurement and the backward measurement of the subject optical system 20 changes. In the measuring method according to In the present embodiment, this circumstance is used to increase the amount of information related to the first aberration component.

At step S110, a light beam as shown in FIG 28A illustrated, from the radiation position P (Ox, Oy, 0) to the objective optical system 20 created. In this step, the objective optical system 20 arranged so that the light projection system 10 the lens 23 opposite. Accordingly, the light beam from the side of the lens 23 to the objective optical system 20 created. An uneven wave 51 becomes of the objective optical system 20 radiated. The not plane wave 51 will be on the light receiving system 30 come in.

Thereafter, step S123 is executed. As a result, the wavefront data WFDθ3 are detected.

Thereafter, step S180 is executed. At step S180, a second rotation is performed. In the second rotation becomes the objective optical system 20 rotated about an axis orthogonal to the measuring axis. The rotation angle is 180 °. When the second rotation is performed, the subject optical system 20 arranged so that the light projection system 10 the lens 25 opposite. Accordingly, a light beam is emitted from the side of the lens 25 to the objective optical system 20 created. The positions of the light projection system 10 and the light receiving system 30 are not moved.

After completion of step S180, step S110 is executed. At step S110, a light beam as shown in FIG 28B illustrated, from the radiation position P (Ox, Oy, 0) to the objective optical system 20 created. A wavefront 60 becomes the objective optical system 20 come in. An uneven wave 55 becomes of the objective optical system 20 radiated. The not plane wave 56 is different from the non-level wave 51 ,

Thereafter, step S124 is executed. In this way, wavefront data WFDθ4 are detected.

Here, the wavefront data WFDθ3 differs from the wavefront data WFDθ4. Accordingly, at the end, two first aberration components can be obtained.

In this way, the measuring method according to the present embodiment can increase the number of the first aberration components because a light beam that makes it possible to detect different data sets of wavefront data is radiated. Accordingly, it is possible to increase the number of measurable degrees of freedom of eccentricity.

When performing the second rotation, the measurement results should be handled carefully. 29A and 29B Fig. 10 are diagrams for explaining a change of the coordinate axes caused by the second rotation, wherein 29A illustrates a state before the second rotation is performed, and 29B illustrates a state after the second rotation has been performed. In the state, the subject optical system is rotated by 180 ° about the Oy axis.

In the state before the second rotation is performed, a forward measurement is performed. In the forward measurement is, as in 29A illustrated, a lens L1 disposed on the side of the origin (0,0,0) and a lens L2 is arranged to follow the lens L1. Accordingly, the lens surfaces are arranged in the order of the lens surface L1 ₁ , the lens surface L1 ₂ , the lens surface L2 _1, and the lens surface L2 ₂ from the side of origin (0,0,0). The coordinate axis X _L2 is in the same direction as the direction of the Ox axis.

In this state, a light beam is radiated from the radiation position P (Ox, Oy, O) to the objective optical system. The light beam is applied to the lens L1 and the lens L2 in this order.

In contrast, in the state after the second rotation has been performed, a backward measurement is performed. When measuring backwards, as in 29B illustrated, the lens L2 is disposed on the side of origin (0,0,0) and the lens L1 is arranged to follow the lens L2. Accordingly, the lens surfaces are arranged in the order of the lens surface L2 ₂ , the lens surface L2 ₁ , the lens surface L2 _2, and the lens surface L2 ₁ from the side of origin (0,0,0). Coordinate axis X _L2 is in a direction opposite to the direction of the Ox axis.

The direction of the coordinate axis Y _L2 is not changed between the forward measurement and the backward measurement, but the direction of the coordinate axis X _L2 is opposed therebetween. Here, in the forward measurement, it is assumed that the ball center of the lens L2 is on the positive side. In this case, in the backward measurement, the ball center of the lens L5 is on the positive side based on the coordinate axis X _L2 . However, based on the ox axis, the ball center of the lens L2 is on the negative side in the backward measurement.

When the subject optical system is rotated about the axis of Ox, the direction of the coordinate axis X _L2 does not change, but the direction of the coordinate axis Y _L2 differs by 180 °. Accordingly, based on the Oy axis, the sign of the position of the ball center in the backward measurement is negative, for example, when the sign of the position of the ball center in the forward measurement is positive.

In view of the above, the sign of the numerical value for the measurement results obtained in the backward measurement must be reversed in the processing in step S200 and subsequent steps.

Moreover, in the measuring method of the present embodiment, it is preferable that the amount of eccentricity at a time of detecting the wavefront data before the second rotation has an absolute amount equal to the absolute amount of the eccentricity amount at a time of detecting the wavefront data after the second rotation.

As described above, the subject optical system is rotated about the measurement axis in the first rotation. Thereby, the amount of displacement caused by the rotation can be determined for each lens. The second rotation measurement also uses the same measurement system as the first rotation measurement. In the second rotation, the subject optical system is arranged so that the front and the back of the subject optical system are reversed. Thereafter, the processing is performed in the same manner as that in the measurement with the first rotation, and thereby the first aberration component is extracted.

However, the absolute value of the distance between the lens and the rotation axis must be set to the same value between the forward measurement and the backward measurement. For example, it is assumed that the subject optical system includes six lens surfaces. Here, each of the six lens surfaces is a spherical surface. Moreover, it is assumed that the amounts of eccentricity of the first surface, the second surface,... And the sixth surface in the forward measurement are (X1, Y1), (X2, Y2),... And (X6, Y6). The amount of eccentricity of each lens surface is indicated by the XY coordinates based on the first rotation axis.

In the backward measurement, the subject optical system is rotated about the Y axis in the forward measurement. Thereby, the front-and-back direction of the subject optical system is reversed. Thereafter, the backward measurement is performed. In the backward measurement, the objective optical system is arranged such that the amounts of eccentricity of the respective lens surfaces in the backward measurement are (-X1, Y1), (-X2, Y2), ..., and (-X6, Y6).

In the measurement arrangement for performing the backward measurement, the objective optical system must be arranged such that the absolute amounts of the predetermined distances between the backward measurement and the forward measurement are equal. The predetermined distances are distances between the ball centers of the respective lens surfaces of the subject optical system and the first rotation axis in the forward measurement.

The first rotation may also be performed in the measuring method of the present embodiment. In the forward measurement, a plurality of data sets of wavefront data are acquired before and after the first rotation in the forward measurement. Thereafter, the second rotation is performed, thereby generating a state in which the backward measurement can be performed. The second rotation reverses the front and back of the subject optical system.

In the case where the lens surface is a spherical surface, the ball center is moved by the first rotation when the lens surface is eccentric. 30A and 30B are diagrams illustrating a movement of the ball center point caused by the first rotation, wherein 30A illustrates the movement of the ball center in a forward measurement and 30B the movement of the ball center in a backward measurement. 30A and 30B illustrate the lens surface near the center of the sphere with a circle. Accordingly, the two circles indicate a part of the same lens surface.

The movement of the ball center in the forward measurement will be explained with reference to FIG 30A explained. Before the first turn is the center of the sphere 96 in the first quadrant of the OxOy coordinate system. After the first turn, the ball center is located 96 in the third quadrant. The amount of movement of the sphere center 96 is δf, an x-component is δX, and a y-component is δY.

The movement of the ball center in the backward measurement will be explained with reference to FIG 30B explained. Before the first turn is the center of the sphere 96 in the second quadrant of the OxOy coordinate system. After the first turn, the ball center is located 96 in the fourth quadrant. The amount of movement of the sphere center 96 is δr, an x-component is δX, and a y-component is δY.

As described above, in the measurement for performing the second rotation, the subject optical system is arranged such that the absolute value of the predetermined distances between the backward measurement and the forward measurement is the same. Accordingly, "| δf | = | δr | "fulfilled.

In vector, showing the movement of the sphere center 96 indicates the direction of the vector of the Y component between the forward measurement and the backward measurement is the same. In contrast, the direction of the vector of the X component between the forward measurement and the backward measurement is reversed.

In view of the above, the sign of the numerical value for the measurement results obtained in the backward measurement must be reversed in the processing in step S200 and subsequent steps.

31A . 31B . 31C and 31D are diagrams illustrating a movement of the ball center point caused by the first rotation and the second rotation, wherein 31A illustrates the position of the center of the sphere before the first rotation in a forward measurement, 31B illustrates the position of the sphere center after the first rotation in the forward measurement, 31C illustrates the position of the center of the sphere before the first rotation in a backward measurement and 31D illustrates the position of the sphere center after the first rotation in the backward measurement.

The origin of the OxOy coordinates is at the position of the first axis of rotation. In particular, illustrate 31A . 31B . 31C and 31D Positions of the center of the sphere with respect to the first axis of rotation. Moreover, if an aspherical surface is included in the subject lens, the movement of the aspheric surface caused by the first rotation and the second rotation may be affected by the position of the aspherical surface top and the position of the aspherical surface axis with respect to the first rotation axis using the 31A . 31B . 31C and 31D similar diagrams. However, if the position of the aspherical surface axis in 31A . 31B . 31C and 31D is illustrated, the Ox axis indicates the amount of inclination in the B direction, and the Oy axis indicates the amount of inclination in the A direction.

When measuring forward, the center of the sphere is located 96 in the state before the first rotation in the first quadrant of the OxOy coordinate system, as in 31A illustrated. When the first rotation is performed in this state, the state after the first rotation in the forward measurement is obtained. In this state, the ball center is located 96 in the third quadrant of the OxOy coordinate system, as in 31B illustrated.

The subject optical system is returned from this state to the state before the first rotation, and the second rotation is performed. Thereby, the state before the first rotation in the backward measurement is obtained. In this state, the ball center is located 96 in the second quadrant of the OxOy coordinate system, as in 31C illustrated. When the first rotation is performed in this state, the state after the first rotation in the backward measurement is obtained. In this state, the ball center is located 96 in the fourth quadrant of the OxOy coordinate system, as in 31D illustrated.

The absolute amount of the amount of displacement of the ball center caused by the first rotation 96 is between 31B and 31D equal. In addition, will be off 31B and 31D it is understood that the X direction of the motion vector of the sphere center is reversed between the forward measurement and the backward measurement.

For this reason, the solution of the system of linear equations for the eccentricity between the forward measurement and the backward measurement is the same when the sign for the eccentric aberration sensitivity of the displacement in the X direction of the backward measurement is reversed. Accordingly, the system of linear equations for the amount of eccentricity can be solved by simultaneously using the forward measurement, eccentric aberration sensitivity proportional to the 1st power of the amount of eccentricity, and the backward measurement, eccentric aberration sensitivity proportional to the 1st power of the amount of eccentricity. In particular, by using more evidence of the eccentric aberration sensitivity, it is possible to detect the amount of eccentricity of more degrees of freedom with high accuracy. The amount of eccentricity that can be detected is the position of the sphere center in the state of 31A ,

When the subject optical system includes an aspherical surface, with respect to the eccentric aberration sensitivity of the aspherical surface, a system of linear equations for the amount of eccentricity can be solved by reversing the sign of the eccentric aberration sensitivity of the displacement in the X direction and the inclination in the A direction become. The inclination amount in the A direction that can be detected is an inclination amount of an aspherical surface axis based on the first rotation axis before the first rotation in the forward measurement, in the same manner.

After completion of the measurement in the forward measurement, the second rotation is performed. In this process, the backward measurement can be performed without returning the subject optical system to the state before the first rotation. This measurement is the same as the condition in which the sphere center 96 located in the fourth quadrant, as in 31D illustrated.

Moreover, in the measuring method of the present embodiment, it is preferable that the first extraction step is performed using a Zernike polynomial and the predetermined aberration component is a coefficient of the Zernike polynomial.

Wavefront data contains information about the wavefront aberration. For this reason, by applying the wavefront data to the Zernike polynomial, it is possible to resolve the aberration component in the wavefront aberration into a spherical aberration, a coma and an astigmatism, and the like, and to quantify the aberration amount for each of the aberration components.

When wavefront data is detected by performing the first rotation, the coefficient of each term of the Zernike polynomial does not indicate the wavefront aberration of the wavefront radiated from the subject optical system itself. The system aberration component and the design aberration component of the subject optical system were removed from the aberration component indicated by the coefficient of each term. The removal of the system aberration component and the design aberration component has already been explained above.

In addition, as described above, the results given by the expressions (3) to (6) are obtained when the Zernike polynomial is used.

With respect to the eccentric aberration _{sensitivity in the} aberration _component proportional to the 1st power of the _amount of eccentricity, the eccentric aberration _sensitivity B _zj1 (Ox, Oy) (z = 2, 3, 7, 8 ...) of the second term and others of the Zernike Terms as described above are given by the following expression (3).

In addition, the eccentric aberration _sensitivity B _zj1 (Ox, Oy) (z = 1, 4, 5, 6, 9 ...) of the term multiplied by the fourth term and others of the Zernike terms is expressed by the following expression (4).

With respect to the eccentric aberration _{sensitivity in the} aberration _component proportional to the square of the _amount of eccentricity, the eccentric aberration _sensitivity B is _zj1 (Ox, Oy) (z = 2, 3, 7, 8 ...) of the second term and others of the Zernike terms as described above by the following expression (5).

In addition, the eccentric aberration _sensitivity B _zj1 (Ox, Oy) (z = 1, 4, 5, 6, 9 ...) of the term multiplied by the fourth term and others of the Zernike terms is expressed by the following expression (6).

The wavefront aberration caused by the eccentricity of the subject optical system can be resolved into aberration components with the Zernike polynomial. Distributions of the resolved aberration components in the respective object height coordinates are known theoretically (see: Image field distribution model of wavefront aberration and models of distortion and field curvature [T. Matsuzawa: J. Opt. Soc. Am. A, 28, No. 2 (2011 ) 96-110]).

For this reason, on the basis of this theory, the distribution of functions whose object height coordinates are used as variables (hereinafter referred to as "object height functions") is classified for the eccentric aberration _sensitivity B _zjl (Ox, Oy). The classified result is simply shown below. The following tables illustrate the aberration component (I = 1) proportional to the 1st power of the amount of eccentricity, the aberration component proportional to the square of the eccentricity amount (I = 2), and the aberration component (I = 3) proportional to the power of the eccentricity amount. However, the Z1th term of the Zernike terms, which is a piston component of the wavefront aberration, is omitted since it is difficult to accurately measure the component in an actual wavefront measurement.

First, Table 17 illustrates a result of classification of the eccentric aberration _{sensitivities} B _2jl (Ox, Oy) and B _3jl (Ox, Oy). [Table 17] Order of object height function 0 1 2 3 B _2jl (Ox, Oy) I = 1 O O I = 2 O O I = 3 O Order of object height function 0 1 2 3 B _3jl (Ox, Oy) I = 1 O O I = 2 O O I = 3 O

In the eccentric aberration _{sensitivities} B _2jl (Ox, Oy) and B _3jl (Ox, Oy) in the aberration _component proportional to the 1st power of the _amount of eccentricity, the object height function appears in the 0th power and the square of the object height coordinates. Accordingly, the 1st power of the Eccentricity amount proportional aberration component as an even function for the object height coordinates. With respect to the aberration component proportional to the square of the amount of eccentricity, the object height function appears in the 1st power and the 3rd power of the object height coordinates. Accordingly, the aberration component proportional to the square of the amount of eccentricity serves as an odd function for the object height coordinates. With respect to the aberration component proportional to the 3rd power of the amount of eccentricity, the object height function appears in the square of the object height coordinates. Accordingly, the aberration component proportional to the 3rd power of the amount of eccentricity serves as an even function for the object height coordinates.

32A . 32B and 32C _{Fig. 15} are diagrams illustrating an object height _{function occurring} in the eccentric aberration _{sensitivities} B _2jl (Ox, Oy) and B _3jl (Ox, Oy), wherein 32A illustrates the case where the subject optical system is not eccentric and 32B and 32C illustrate the case where the subject optical system is eccentric. In the drawings, the function indicated by "I = 1" indicates an object height function appearing in the aberration component proportional to the 1st power of the amount of eccentricity, the function indicated by "I = 2" indicates an object height function corresponding to the square of the The eccentricity amount proportional aberration component appears, and the function indicated by "I = 3" indicates an object height function appearing in the aberration component proportional to the 3rd power of the amount of eccentricity.

Here, B _2jl (Ox, Oy) indicates an x component of a wavefront _tilt (coma) and B _3jl (Ox, Oy) indicates a y component of the wavefront tilt (coma). As in 32B and 32C 1, the aberration component in the wavefront tilt (x-component) proportional to the 1st power of the amount of eccentricity is given by an even function for the object height coordinates. The aberration component proportional to the square of the amount of eccentricity is given by an odd function of the object height coordinates. The aberration component proportional to the 3rd power of the amount of eccentricity is given by an even function of the object height coordinates.

Therefore, the first aberration component for the wavefront tilt (x-component) can be extracted by obtaining the sum of the predetermined aberration component in the one radiation position and the predetermined aberration in the other radiation position. For example, if the object height coordinates are given by (Ox, Oy), in symmetric object height coordinates of (Ox, Oy) and (-Ox, -Oy), such as (0,4) and (0, -4) and (1,2 ) and (-1, -2), the predetermined aberration component in the one radiation position and the predetermined radiation component in the other radiation position are extracted and the sum of them should be obtained. Since the amount of eccentricity to be treated in the present embodiment is minute, the aberration component proportional to the 3rd power of the amount of eccentricity is very small and therefore can be ignored.

The same processing can be performed for the wavefront tilt (y-component).

Next, Table 18 illustrates a result of a classification of the eccentric aberration _sensitivity B _4jl (Ox, Oy). [Table 18] Order of object height function 0 1 2 3 B _4jl (Ox, Oy) I = 1 O O I = 2 O I = 3 O

In the eccentric aberration _sensitivity B _4jl (Ox, Oy) in the aberration _component proportional to the 1st power of the _amount of eccentricity, the object height function appears in the 1st power and the 3rd power of the object height coordinates. Accordingly, the aberration component proportional to the 1st power of the amount of eccentricity serves as an odd function for the object height coordinates. With respect to the aberration component proportional to the square of the amount of eccentricity, the object height function appears in the square of the object height coordinates. Accordingly, the aberration component proportional to the square of the amount of eccentricity serves as an even function for the object height coordinates. With respect to the aberration component proportional to the 3rd power of the amount of eccentricity, the Object height function in the 3rd power of the object height coordinates. Accordingly, the aberration component proportional to the 3rd power of the amount of eccentricity serves as an odd function for the object height coordinates.

33A . 33B and 33C _{Fig. 11} are diagrams illustrating an object height function occurring in the eccentric aberration _sensitivity B _4jl (Ox, Oy), wherein 33A illustrates the case where the subject optical system is not eccentric and 33B and 33C illustrate the case where the subject optical system is eccentric. In the drawings, the function indicated by "I = 1" indicates an object height function appearing in the aberration component proportional to the 1st power of the amount of eccentricity, the function indicated by "I = 2" indicates an object height function corresponding to the square of the The eccentricity amount proportional aberration component appears, and the function indicated by "I = 3" indicates an object height function appearing in the aberration component proportional to the 3rd power of the amount of eccentricity.

Here B _4jl (Ox, Oy) indicates a spherical aberration (focus). As in 33B and 33C 1, the spherical aberration (focal point) aberration component proportional to the 1st power of the amount of eccentricity is given by an odd function with respect to the object height coordinates. The aberration component proportional to the square of the amount of eccentricity is given by an even function with respect to the object height coordinates. The aberration component proportional to the 3rd power of the amount of eccentricity is given by an odd function with respect to the object height coordinates.

Accordingly, the first aberration component with respect to the spherical aberration (focus) can be extracted by obtaining the difference between the predetermined aberration component in the one radiation position and the predetermined aberration in the other radiation position. For example, if the object height coordinates are given by (Ox, Oy), in symmetric object height coordinates of (Ox, Oy) and (-Ox, -Oy), such as (0,4) and (0, -4) and (1,2 ) and (-1, -2), the predetermined aberration component in the one radiation position and the predetermined radiation component in the other radiation position are extracted and the difference between them should be obtained. Since the amount of eccentricity to be treated in the present embodiment is minute, the aberration component proportional to the 3rd power of the amount of eccentricity is very small and therefore can be ignored.

Table 19 illustrates a result of a classification of the eccentric aberration _{sensitivities} B _5jl (Ox, Oy) and B _6jl (Ox, Oy). [Table 19] Order of object height function 0 1 2 3 B _5jl (Ox, Oy) I = 1 O O I = 2 O O I = 3 O O Order of object height function 0 1 2 3 B _6jl (Ox, Oy) I = 1 O O I = 2 O O I = 3 O O

In the eccentric aberration _{sensitivities} B _5jl (Ox, Oy) and B _6jl (Ox, Oy) in the aberration _component proportional to the 1st power of the _amount of eccentricity, the object height function appears in the 1st power and the 3rd power of the object height coordinates. Accordingly, the aberration component proportional to the 1st power of the amount of eccentricity serves as an odd function for the object height coordinates. In terms of the square of the eccentricity amount proportional aberration component, the object height function appears in the 0th power and in the square of the object height coordinates. Accordingly, the aberration component proportional to the square of the amount of eccentricity serves as an even function for the object height coordinates. With respect to the aberration component proportional to the 3rd power of the amount of eccentricity, the object height function appears in the 1st power and the 3rd power of the object height coordinates. Accordingly, the aberration component proportional to the 3rd power of the amount of eccentricity serves as an odd function for the object height coordinates.

34A . 34B and 34C _{Fig. 11} are diagrams illustrating an object height _{function occurring} in the eccentric aberration _{sensitivities} B _5jl (Ox, Oy) and B _6jl (Ox, Oy), wherein 34A illustrates the case where the subject optical system is not eccentric and 34B and 34C illustrate the case where the subject optical system is eccentric. In the drawings, the function indicated by "I = 1" indicates an object height function appearing in the aberration component proportional to the 1st power of the amount of eccentricity, the function indicated by "I = 2" indicates an object height function corresponding to the square of the The eccentricity amount proportional aberration component appears, and the function indicated by "I = 3" indicates an object height function appearing in the aberration component proportional to the 3rd power of the amount of eccentricity.

Here both B _5jl (Ox, Oy) and B _6jl (Ox, Oy) indicate astigmatism. As in 34B and 34C illustrated, the aberration component in astigmatism proportional to the 1st power of the amount of eccentricity is given by an odd function for the object height coordinates. The aberration component proportional to the square of the amount of eccentricity is given by an even function of the object height coordinates. The aberration component proportional to the 3rd power of the amount of eccentricity is given by an odd function of the object height coordinates.

Accordingly, the first aberration component with respect to the astigmatism can be extracted by obtaining the difference between the predetermined aberration component in the one radiation position and the predetermined aberration in the other radiation position. For example, if the object height coordinates are given by (Ox, Oy), in symmetric object height coordinates of (Ox, Oy) and (-Ox, -Oy), such as (0,4) and (0, -4) and (1,2 ) and (-1, -2), the predetermined aberration component in the one radiation position and the predetermined radiation component in the other radiation position are extracted and the difference between them should be obtained. Since the amount of eccentricity to be treated in the present embodiment is minute, the aberration component proportional to the 3rd power of the amount of eccentricity is very small and therefore can be ignored.

Table 20 illustrates a result of a classification of the eccentric aberration _{sensitivities} B _2jl (Ox, Oy) and B _3jl (Ox, Oy). [Table 20] Order of object height function 0 1 2 3 B _7jl (Ox, Oy) I = 1 O O I = 2 O O I = 3 O Order of object height function 0 1 2 3 B _8jl (Ox, Oy) I = 1 O O I = 2 O O I = 3 O

In the eccentric aberration _{sensitivities} B _7jl (Ox, Oy) and B _8jl (Ox, Oy) in the aberration _component proportional to the 1st power of the _amount of eccentricity, the object height function appears in the 0th power and the square of the object height coordinates. Accordingly, the aberration component proportional to the 1st power of the amount of eccentricity serves as an even function for the object height coordinates. With respect to the aberration component proportional to the square of the amount of eccentricity, the object height function appears in the 1st power and the 3rd power of the object height coordinates. Accordingly, the aberration component proportional to the square of the amount of eccentricity serves as an odd function for the object height coordinates. In relation to the power proportional to the 3rd power of the eccentricity amount Aberrationskomponente appears the object height function in the square of the object height coordinates. Accordingly, the aberration component proportional to the 3rd power of the amount of eccentricity serves as an even function for the object height coordinates.

35A . 35B and 35C _{Fig. 11} are diagrams illustrating an object height _{function occurring} in the eccentric aberration _{sensitivities} B _7jl (Ox, Oy) and B _8jl (Ox, Oy), wherein 35A illustrates the case where the subject optical system is not eccentric and 35B and 35C illustrate the case where the subject optical system is eccentric. In the drawings, the function indicated by "I = 1" indicates an object height function appearing in the aberration component proportional to the 1st power of the amount of eccentricity, the function indicated by "I = 2" indicates an object height function corresponding to the square of the The eccentricity amount proportional aberration component appears, and the function indicated by "I = 3" indicates an object height function appearing in the aberration component proportional to the 3rd power of the amount of eccentricity.

Here both B _7jl (Ox, Oy) and B _8jl (Ox, Oy) indicate a coma. As in 35B and 35C 1, the aberration component in the coma proportional to the 1st power of the amount of eccentricity is given by an even function for the object height coordinates. The aberration component proportional to the square of the amount of eccentricity is given by an odd function of the object height coordinates. The aberration component proportional to the 3rd power of the amount of eccentricity is given by an even function of the object height coordinates.

Therefore, the first aberration component for the coma can be extracted by obtaining the sum of the predetermined aberration component in one radiation position and the predetermined aberration in the other radiation position. For example, if the object height coordinates are given by (Ox, Oy), in symmetric object height coordinates of (Ox, Oy) and (-Ox, -Oy), such as (0,4) and (0, -4) and (1,2 ) and (-1, -2), the predetermined aberration component in the one radiation position and the predetermined radiation component in the other radiation position are extracted and the sum of them should be obtained. Since the amount of eccentricity to be treated in the present embodiment is minute, the aberration component proportional to the 3rd power of the amount of eccentricity is very small and therefore can be ignored.

The second eccentric aberration amount can be extracted by fitting the predetermined aberration component extracted from the wavefront data in the irradiation position P and the predetermined aberration component extracted from the wavefront data in the irradiation position P 'into the predetermined function system for each object height. Examples of the functional system include field terms (image field distribution model of wavefront aberration and models of distortion and field curvature [T.Matsuzawa: J. Opt. Soc. Am. A, 28, No. 2 (2011) 96-110]).

Next, an explanation will be given of a method of calculating the eccentric aberration sensitivity. As described above, there are cases where the subject optical system includes a design aberration. In addition, the eccentricity amount measuring device may include a system aberration. In addition, the optical light receiving system may include an eccentricity. In addition, the first rotation axis may be shifted from the measurement axis when the first rotation is performed.

When such aberration components exist, the wavefront aberration W is given by the following expression (1-13).

In contrast, the eccentric aberration sensitivity is determined using, for example, optical simulation software. In the optical simulation software, a wavefront aberration amount that occurs when the degree of freedom of the eccentricity is eccentric by one unit amount is calculated for each of the lenses of the subject optical system. The wavefront aberration amount is the eccentric aberration sensitivity.

In an optical simulation, an optical system for which a wavefront is actually measured is determined by using the set values of the lenses of the subject optical system, the light projection system, and the light receiving system. The optical system is placed in a position without system aberration or displacement of the first axis of rotation of the measuring axis. The optical system is also placed in a position in which the subject optical system, the light projection system and the light receiving system are not eccentric.

In this case, "δ ₁ = 0, δ ₂ = 0, ..., δ _m = 0, E = 0, Sys (Ox, Oy, ρx, ρy) = 0" are satisfied. Accordingly, the wavefront aberration W at the time when the eccentric aberration sensitivity is detected is given by Expression (1-14). Reference M (Ox, Oy, ρx, ρy) is a design aberration of the subject optical system, the light projection system, and the light receiving system.

First, process 1 is executed. In process 1, a light beam tracking simulation is performed in a state where the amount of eccentricity Δ _{i of} the subject optical system satisfies "Δ _i = δ ₁ = 0", and wavefront data is obtained by calculation.

Thereafter, process 2 is executed. In Process 2, the unit amount of eccentricity in Expression (1-14) (for example, Δ _o = 0.01 mm) is provided only to the first surface of the subject optical system. In this case, the wavefront aberration W is given by Expression (1-15).

Thereafter, in process 2, a light beam tracking simulation is performed in the state where the amount of eccentricity Δ _{o of} the subject optical system satisfies "Δ _o = δ ₁ = 0", and wavefront data is obtained by calculation.

When an SH sensor is used as the wavefront detection device, a light beam tracking simulation is performed and data of the light spot image position is detected. The data of the spot position corresponds to the wavefront aberration of Expression (1-14) and / or the wavefront aberration of Expression (1-15), differentiated by the pupil coordinates.

Process 3 is performed. In process 3, the wavefront data obtained in process 2 with respect to the wavefront data obtained in process 1 is analyzed and the wavefront aberration is determined. In this case, the wavefront aberration is given by Expression (1-16). The wavefront aberration given by the expression (1-16) is a deviation of the wavefront at the time when the single face is eccentric from the wavefront at the time when the subject optical system is not eccentric. Accordingly, it is actually unnecessary to directly calculate the wavefront aberration W of the expression (1-15).

Process 4 is executed. In process 4, process 2 and process 3 are performed for the object height coordinates (-Ox, -Oy) symmetrical to the object height coordinates (Ox, Oy). In this case, the wavefront aberration W is given by expression (1-17).

Process 5 is performed. In process 5, the expression (1-16) and expression (1-17) with the Zernike polynomial are respectively developed. The terms of the Zernike terms are classified into terms that are multiplied by a function with the pupil coordinates in odd order, and terms that are multiplied by a function with the pupil coordinates in an even order.

The aberration component containing the term multiplied by a function with the odd-order pupil coordinates is an aberration component containing the term multiplied by the second term and others of the Zernike terms. With respect to the aberration components (z = 2, 3, 7, 8 ...), the sum is obtained in this case. As a result, expression (24) is obtained.

The aberration component containing the term multiplied by a function with the pupil coordinates in an even order is an aberration component containing the term multiplied by the fourth term and others of the Zernike terms. With respect to the aberration components (z = 1, 4, 5, 6, 9 ...), the difference is obtained in this case. As a result, Expression (25) is obtained.

Expression (25) is converted to Expression (25 ').

Here Δ _{o is} known. In addition, the amounts of the following four wavefront aberrations can be determined from the light beam tracking simulation. Accordingly, Sz ₁ (Ox, Oy) is also known.

Accordingly, Bz ₁₁ (Ox, Oy) can be determined from Expression (25 '). The term Bz ₁₁ (Ox, Oy) given in Expression (25 ') serves as an eccentric aberration sensitivity in the first surface of the subject optical system. The eccentric aberration sensitivity is the eccentric aberration sensitivity proportional to the 1st power of the amount of eccentricity and the eccentric aberration sensitivity per unit amount of eccentricity in the Zth term of the Zernike terms and the object height coordinates (Ox, Oy).

Process 6 is performed. In Process 6, Process 1 to Process 5 are performed for all degrees of freedom of eccentricity (δ ₁ ... δ _i ... δ _j ) and all object height coordinates (Ox1, Oy1) ... (Oxq, Oyq) (q-point) , for which a wavefront measurement is performed, and the eccentric aberration sensitivity _Bzil (Ox, Oy) is determined.

The eccentric aberration sensitivity of a slope is calculated for an aspherical surface. The center of rotation of the inclination in this calculation may be an aspherical surface top or other location on an aspherical surface axis. In the case where an arbitrary position other than the aspheric surface top is selected as the center of the inclination, the eccentricity of a displacement must be defined as the eccentricity of the position.

When the execution of Process 6 is completed, a matrix of the eccentric aberration sensitivities is obtained as follows. [Numeric expression 1]

In addition, the system of linear equations using the matrix of eccentric aberration sensitivities is as follows. [Numeric expression 2]

The left side of the system of linear equations given in numerical expression 2 is formed of Tz calculated from data obtained in an actual wavefront measurement. More precisely, it is a matrix of measurement data. A matrix multiplied by the matrix of eccentric aberration sensitivities on the right side is a matrix of magnitudes of displacements with a rotation at the time when the subject optical system is rotated by a certain angle about the first rotation axis. This is used as a matrix of the amounts of relocations.

Here is the number of degrees of freedom of eccentricity j. In the case containing, for example, two spherical surfaces and two aspherical surfaces, the degree of freedom of one spherical surface is X and Y, the degree of freedom of the other spherical surface is X and Y, the degree of freedom of an aspheric surface is X, Y, A and B and The degree of freedom of the other aspherical surface is X, Y, A and B and the degrees of freedom j are 12. The Zernike terms to be used are moreover 2 to n terms. In addition, the object heights are points q of (Ox1, Oy1)... (Oxq, Oyq).

In the system of linear equations, Tz measured for each of the object height coordinates is substituted without any changes in the equations, and the amount of eccentricity is analyzed. Since Tz has a value twice the magnitude of the original first aberration component in the step of removing the second aberration component, the value of Tz in the matrix of the measurement data is divided by 2 in view of the above.

The eccentric aberration sensitivity varies depending on the object height coordinates. For this reason, the eccentric aberration sensitivity is detected in each object height coordinate.

Here, the eccentric aberration sensitivity of the term multiplied by the odd-order function of the pupil coordinates as described above is an eccentric aberration sensitivity multiplied by the second term and others of the Zernike terms. The eccentric aberration _sensitivity B _zj1 (Ox, Oy) (z = 2, 3, 7, 8 ...) in this case is given by the expression (3).

wobei
g₀(Ox,Oy) eine Funktion mit den Objekthöhenkoordinaten mit der maximalen Ordnung von 0 ist,
g₂(Ox,Oy) eine Funktion mit den Objekthöhenkoordinaten mit der maximalen Ordnung von 2 ist und
g₄(Ox,Oy) eine Funktion mit den Objekthöhenkoordinaten mit der maximalen Ordnung von 4 ist.The expression (3) can be expressed as the following expression (26).

in which
g ₀ (Ox, Oy) is a function with the object height coordinates with the maximum order of 0,
g ₂ (Ox, Oy) is a function with the object height coordinates with the maximum order of 2 and
g ₄ (Ox, Oy) is a function with the object height coordinates with the maximum order of 4.

The eccentric aberration sensitivity of the term multiplied by the function with the pupil coordinates in an even order is an eccentric aberration sensitivity multiplied by the fourth term and others of the Zernike terms. The eccentric aberration _sensitivity B _zj1 (Ox, Oy) (z = 1, 4, 5, 6, 9 ...) in this case is given by the expression (4).

wobei
g₁(Ox,Oy) eine Funktion mit den Objekthöhenkoordinaten mit der maximalen Ordnung von 1 ist,
g₃(Ox,Oy) eine Funktion mit den Objekthöhenkoordinaten mit der maximalen Ordnung von 3 ist und
g₅(Ox,Oy) eine Funktion mit den Objekthöhenkoordinaten mit der maximalen Ordnung von 5 ist.The expression (4) can be expressed as the following expression (27).

in which
g ₁ (Ox, Oy) is a function with the object height coordinates with the maximum order of 1,
g ₃ (Ox, Oy) is a function with the object height coordinates with the maximum order of 3 and
g ₅ (Ox, Oy) is a function with the object height coordinates with the maximum order of 5.

D in expressions (26) and (27) is a constant that does not depend on the object height coordinates, the pupil coordinates, and the amount of eccentricity. In addition, the indexes in D consecutively indicate, from the left, the Zth term of the Zernike terms, the jth surface, the value of I, and the order in the object height coordinates.

As function g _k (Ox, Oy) (K = 1, 2, 3 ...) an orthogonal function system or field terms can be used.

wobei
g₀(Ox,Oy) eine Funktion mit der Potenz von (Ox,Oy) mit der maximalen Ordnung von 0 ist,
g₂(Ox,Oy) eine Funktion mit der Potenz von (Ox,Oy) mit der maximalen Ordnung von 2 ist und
g₄(Ox,Oy) eine Funktion mit der Potenz von (Ox,Oy) mit der maximalen Ordnung von 4 ist.The expression (21) can be developed in the same way. The aberration component containing the term multiplied by the odd-order function of the pupil coordinates is the aberration component multiplied by the second term and others of the Zernike terms. In this case, the aberration component T _z (Ox, O y, δ ₁ , δ ₂ , ..., δ _j ) / 2 can be expressed as the following expression (28).

in which
g ₀ (Ox, Oy) is a function with the power of (Ox, Oy) with the maximum order of 0,
g ₂ (Ox, Oy) is a function with the power of (Ox, Oy) with the maximum order of 2, and
g ₄ (Ox, Oy) is a function with the power of (Ox, Oy) with the maximum order of 4.

wobei
g₁(Ox,Oy) eine Funktion mit der Potenz von (Ox,Oy) mit der maximalen Ordnung von 1 ist,
g₃(Ox,Oy) eine Funktion mit der Potenz von (Ox,Oy) mit der maximalen Ordnung von 3 ist und
g₅(Ox,Oy) eine Funktion mit der Potenz von (Ox,Oy) mit der maximalen Ordnung von 5 ist.Moreover, the aberration component containing the term multiplied by the function with the pupil coordinates in even order is the aberration component multiplied by the fourth term and others of the Zernike terms. In this case, the aberration component T _z (Ox, O y, δ ₁ , δ ₂ , ..., δ _j ) / 2 can be expressed as the following expression (29).

in which
g ₁ (Ox, Oy) is a function with the power of (Ox, Oy) with the maximum order of 1,
g ₃ (Ox, Oy) is a function with the power of (Ox, Oy) with the maximum order of 3, and
g ₅ (Ox, Oy) is a function with the power of (Ox, Oy) with the maximum order of 5.

E in expressions (28) and (29) is a constant that does not depend on the object height coordinates, the pupil coordinates, and the amount of eccentricity. In addition, the indexes in E consecutively indicate, from the left, the Zth term of the Zernike terms, the jth surface, the value of I, and the order in the object height coordinates.

A compensation is performed on Tz obtained from wavefront _data measured for each object height _coordinate and _Bzjl determined by calculation, and the aberration is applied to the coefficients E and D.

By adjustment, D can be obtained from the data of the expression (1-16) and the expression (1-17) containing the second aberration component. The second aberration component is removed by the equalization and the aberration can be applied to D.

By adjustment, E can be obtained from the data of the expression (1-11) and the expression (1-12) containing the second aberration component. The second aberration component is removed by the equalization and the aberration can be applied to E.

As a result, the system of linear equations can be expressed as follows. [Numerical Expression 3]

In the system of linear equations, E is determined by equalizing Tz, which is calculated from the wavefront data measured for each object height coordinate and substituted into the equations, and the amount of eccentricity is analyzed.

In the system of linear equations, assuming an orthogonal function system as the object height function, a certain type of filtering is performed on Tz calculated from the wavefront data obtained from an actual wavefront measurement, and thereby it is possible to estimate the influence of error of Tz to reduce. However, it is necessary to take a large number of points of the object height coordinates in the wavefront measurement and for an analysis step to apply Tz to E.

Two types of systems of linear equations were illustrated. Both of the systems of linear equations can be used.

Since the data used is data in which the aberration component proportional to the square of the amount of eccentricity is removed, if the aberration component proportional to the third power or to a higher power of the amount of eccentricity can be ignored, the matrix of the measured data may be equal to the product of the matrix eccentric aberration sensitivity and matrix of eccentricity amount. For this reason, equations are created in which the measurement data matrix equals the product of the eccentric aberration sensitivity matrix and the eccentricity amount matrix. The amount of eccentricity of each degree of freedom of sensitivity can be determined using a balancing algorithm such as the least squares method.

Since the matrix of the measurement data and the matrix of the eccentric aberration sensitivity are formed from the aberration component proportional to the 1st power, the amount of eccentricity can be detected with high accuracy even if the amount of eccentricity is as large as a manufacturing error.

Moreover, for example, the amount of displacement of each lens surface is -2 times as large as the amount of eccentricity of each lens surface based on the rotation axis when the subject optical system is rotated 180 ° about the first rotation axis. In this state, each element (δ ₁ , δ ₂ , ..., δ _j ) of the matrix of the amounts of displacement obtained by analyzing the system of linear equations illustrated in Numerical Expression 2 is -2 times as large as the amount of eccentricity of each lens surface the axis of rotation. For this reason, each detected element (δ ₁ , δ ₂ , ..., δ _j ) of the matrix is divided by displacement amounts by -2, and thereby the amount of eccentricity of each lens is determined on the basis of the rotation axis before the rotation of the objective optical system.

There are cases where the rotation angle in the first rotation is different from 180 °, for example, 90 °. In such a case, the amount of eccentricity for each degree of freedom of eccentricity of each lens surface may be determined on the basis of the rotation axis taking into account the amount of displacement of each lens surface caused by the rotation.

Since the matrix of the measurement data and the matrix of the eccentric aberration sensitivity are formed from aberration components proportional to the 1st power of the amount of eccentricity, the amount of eccentricity can be detected with high accuracy even if the first rotation axis is offset from the measurement axis.

In addition, there are cases where the degree of the measurement error is recognized as a repeatability for each of the Zernike terms. In such a case, the equations are weighted based on the measurement error and the system of linear equations is solved. Thereby, an error of the amount of eccentricity obtained by analysis is also reduced.

In addition, when the second rotation is performed, a system of linear equations can be created as follows. It is assumed that Tz is the data of the first aberration component in the forward measurement, B is the eccentric aberration sensitivity in the forward measurement, T'z is the data of the first aberration component in the backward measurement, and B 'is the eccentric aberration sensitivity in the backward measurement. As given by the numerical expression 4, since the amount of displacement (δ ₁ , δ ₂ , ..., δ _j ) in the forward measurement is the same as the amount of displacement (δ ₁ , δ ₂ , ..., δ _j ) in the backward measurement, the sign of the sensitivity should be considered in view of the way the subject optical system is subjected to the second rotation. In the case where the second rotation of the subject optical system is performed around the Y axis, for example, with respect to the eccentric aberration sensitivity, a shift in the X direction and a tilt in the A direction are both the degree of freedom of the sensitivity are the sign of the eccentric aberration sensitivity of the backward measurement for the forward measurement reversed. [Numeric expression 4]

The following is an explanation of the degree of freedom of the sensitivity that can be measured in the measuring method according to the present embodiment. In the measuring method according to the present embodiment, the amount of eccentricity of each degree of freedom of eccentricity for each lens is measured by using wavefront aberration information in a wavefront transmitted through the subject optical system. For this reason, as the degrees of freedom of the eccentricity increase, it becomes more difficult to distinguish the degrees of eccentricity for the degrees of freedom of eccentricity. For this reason, the coarse standard of the measurable degree of freedom of eccentricity is shown below.

Table 21 illustrates, by circles, the terms proportional to the 1st power of the amount of eccentricity as the wavefront aberration is developed to the power using the pupil coordinates, the object height, and the amount of eccentricity. The terms given by the circles are the first aberration components. The first aberration components multiplied by the function of the Z2 term are, for example, the component proportional to the power of 0 of the object height, the component proportional to the square, .... The first aberration components that multiply by the function of the Z4 term are, are the component proportional to the 1st power of the object height and the component proportional to the 3rd power, .... In Table 21, a hyphen (-) indicates that there is no first aberration component therein.

In addition, the degree of freedom of the eccentricity in the table indicates the first aberration component caused by the degree of freedom of the eccentricity. In the system of linear equations illustrated in numerical expression 2, the number of degrees of eccentricity measurable is considered aggregated to the number of circles in Table 21, even though data of the first aberration component is used at many object heights. In particular, the number of circles may be considered as substantially an amount of information related to the eccentricity. [Table 21]

For the purpose of simplifying the eccentricity degrees of freedom measurable in the present embodiment, it is assumed that third order components (the second to eighth terms of the Zernike terms) or lower order of the pupil coordinates and first power or lower power components of the object height coordinates occur on the first aberration components of the subject optical system.

In such a case, the first aberration components may be indicated by black circles in Table 21. The number of black circles is 8. Since the information amount is regarded as aggregated to 8, the number of degrees of freedom of the eccentricity that can be detected is 8.

For example, in the case of a spherical surface, the number of degrees of freedom of eccentricity is 2. For this reason, the number of degrees of freedom of eccentricity of each lens surface is 8 when the subject optical system is formed of four lens surfaces. Accordingly, in this case, the amount of eccentricity in each lens surface can be measured. Moreover, in the case of an aspheric surface, the number of degrees of freedom of eccentricity is, for example, 4. For this reason, the number of degrees of freedom of eccentricity of each lens surface is 8 when the subject optical system is formed of two lens surfaces. Accordingly, also in this case, the amount of eccentricity in each lens surface can be measured.

However, the order of the pupil coordinates and the order of the object height coordinates that can be measured increase according to the aberration property of the subject optical system and the wavefront measurement conditions. For this reason, Figure 8 is a rough standard when the orders of object height coordinates and pupil coordinates are restricted to low orders.

Moreover, when a forward measurement and a backward measurement are performed using a second rotation, information on the black circles in each of the measurements can be detected in the same manner. However, since the eccentric aberration sensitivity differs between the forward measurement and the backward measurement as described above, the number of black circles, that is, the number of the first aberration components is increased to 16. Accordingly, the eccentricity measurement of 16 degrees of freedom of eccentricity can be performed.

By determining the condition number of the matrix of the eccentric aberration sensitivity in the numerical expressions 2, 3 and 4, it is possible to judge the degree of error propagation to the detected amount of eccentricity when an error in Tz is included, which is the data acquired from an actual wavefront measurement is calculated. The condition number can be calculated using a ratio of the maximum singular value to the minimum singular value of the matrix. The value of the condition number is smaller in the matrix with a smaller degree of error propagation. The minimum value of the condition number is 1. When the wavefront of the subject optical system is measured, countless methods are possible as a method of dropping a beam on the subject optical system. It is possible to improve the accuracy of the amount of eccentricity that can be detected by selecting an incidence method that reduces the condition number.

The measuring method according to the present embodiment enables a simple wavefront measurement in a short time for each of the object heights using an SH sensor as the wavefront sensor. Therefore, the amount of eccentricity can be measured easily and in a short time. Moreover, since it is possible to accurately extract the eccentric aberration amount of the subject optical system by removing the aberration components caused by various manufacturing errors in the measurement system and the design aberration component of the subject optical system, it is possible to accurately measure the amount of eccentricity to reach.

The subject optical system serving as the target of the measurement system of the present embodiment is a rotationally symmetric optical system.

The following is an explanation of the wavefront data in an SH sensor and a wavefront aberration analysis method using the wavefront data. An SH sensor is formed of a microlens array and an imager (such as a CCD and a CMOS). When the focal length of the microlens is f, the microlens array and the imager are fixed at a distance of f between them.

When a wavefront is incident on the SH sensor, the wavefront is split by a microlens array and a plurality of spot images are projected onto the imager. The positions of the light spot images are referred to as the wavefront image.

The measuring device containing the SH sensor generally contains a manufacturing defect and the manufacturing defect serves as a system aberration. The following is an explanation of a common method for removing the system aberration.

A Wavefront Where there is no aberration, the SH sensor is invaded, and light spot image positions formed in this process (Sox (ρx, ρy), Soy (ρx, ρy)) are measured. The light dot image positions are referred to as wavefront data. (ρx, ρy) serve as coordinates (pupil coordinates) of the position of the microlens.

The light spot image position (Sox, Soy) contains an influence of the system aberration sys (ρx, ρy). In this case, (Sox, soy) are given by the following expressions (30) and (31).

Thereafter, a wavefront W having an aberration is made incident, and light spot image positions (Sx, Sy) formed in this process are measured. In this case, (Sx, Sy) are given by the following expressions (32) and (33).

Expression (34) is obtained by obtaining a difference between Expression (30) and Expression (32).

Expression (35) is obtained by obtaining a difference between Expression (31) and Expression (33).

The expression (34) and the expression (35) are data sets each indicating a differential amount of the wavefront. There are two types of methods for determining the wavefront from the data.

The first method is a method in which an equalization of the expression (34) and the expression (35) is performed with the function obtained by differentiating the Zernike polynomial after ρx and the function obtained by differentiating the Zernike polynomial after ρy, and the Zernike coefficient is determined (wavefront analysis 1).

The second method is a method in which the expression (34) and the expression (35) are integrated via ρx and ρy to obtain the wavefront (wavefront analysis 2).

In the ordinary method, one of the two methods is used. However, if the method is used, it is necessary to make the wavefront where incident to the SH sensor without aberration and detect wavefront calibration data. In this case, a wavefront where no aberration is made incident on the SH sensor and thereby wavefront data is detected at a plurality of object height coordinates. However, this method requires high costs.

In contrast, in the measuring method according to the present embodiment, no wavefront Wo without aberration is made incident on the SH sensor. Instead, the objective optical system is rotated about the first rotation axis, the wavefront W1 is measured before the first rotation, and the wavefront W2 is measured after the first rotation.

First, the wavefront W1 is made incident on the SH sensor, and measurement of the light spot image positions (S1x (ρx, ρy), S1y (ρx, ρy)) formed in this process is performed. Thereafter, the first rotation is performed, the wavefront W2 is made incident on the SH sensor, and measurement of the light spot image positions (S2x (ρx, ρy), S2y (ρx, ρy)) formed in this process is performed.

Thereafter, expressions (36) and (37) are obtained by obtaining the difference between the light dot image positions.

To obtain a wavefront from the data, the wavefront is analyzed by one of the following two types of procedures.

The first method is a method in which an equalization of expression (36) and expression (37) is performed with the function obtained by differentiating the Zernike polynomial after ρx and the function obtained by differentiating the Zernike polynomial after ρy, and the Zernike coefficient is determined (wavefront analysis 1).

The second method is a method in which the expression (36) and the expression (37) are integrated via ρx and ρy to detect the wavefront (wavefront analysis 2).

For example, when an SH sensor is used for the light receiving system, the wavefront data used in the explanation of the item (IV) described above is data of the light dot image positions. Moreover, analyzing the wavefront aberration from the wavefront data means performing the processing indicated in Expression (36) and the processing indicated in Expression (37) for the datasets of the light spot image position data obtained in the two states, and thereafter performing wavefront analysis 1 or the wavefront analysis 2 and determining the wavefront aberration.

Moreover, the eccentricity amount measuring apparatus according to the present embodiment includes a light projecting system disposed at one end of a measuring axis, a light receiving system disposed at the other end of the measuring axis, a holding member holding a subject optical system, and processing means connected to a wavefront measuring device, wherein the holding member is disposed between the light projecting system and the light receiving system, the light projection system is provided in a position to apply a light beam to the subject optical system, the processing means comprises a detecting step, a first extracting step second extraction step and performing an analysis step, wavefront data is detected in the detection step based on the light beam emitted from the objective optical system in the first extraction step In the second extracting step, extracting a predetermined aberration component from the wavefront data, extracting a first aberration component from the predetermined aberration component, analyzing, in the analyzing step, a system of linear equations for the first aberration component, eccentric aberration sensitivity and an amount of eccentricity, the predetermined aberration component being an aberration component an aberration component caused by eccentricity, the first aberration component is an aberration component proportional to the 1st power of the amount of eccentricity in the predetermined aberration component, and the eccentric aberration component is an aberration sensitivity proportional to the 1st power of the amount of eccentricity.

36 illustrates a device for measuring the amount of eccentricity according to the present embodiment. A device for measuring the amount of eccentricity 100 contains a light projection system 102 , a light receiving system 103 and a holding element 104 , In addition, the device for measuring the Exzentrizitätsbetrags contains 100 also a main unit 101 , The main unit 101 is with the light projection system 102 , the light receiving system 103 and the holding element 104 Mistake.

The light projection system 102 is disposed on a side of a measuring axis AX _M and the light projection system 103 is arranged on the other side. In addition, the retaining element 104 between the light projection system 102 and the light receiving system 103 arranged. In this way, the light projection system 102 and the light receiving system 103 provided so that they face each other, wherein the retaining element 104 is arranged in between.

The light projection system 102 produces a beam of light which is incident on an objective optical system 105 is to create. To accomplish this, the light projection system includes 102 a light source. Examples of the light source include a laser, an LED, a halogen lamp and a xenon lamp.

In addition, the light projection system 102 contain an optical system. A spherical wave can be generated by condensing the light emitted by the light source through the optical system.

In the device for measuring the amount of eccentricity 100 is the light projection system 102 on a guide frame 107 fixed, with a holding element 106 is arranged in between. The guide frame 107 is on a guide frame 108 fixed. The guide frame 108 is on the bulk unit 101 fixed.

Both guide frames, the guide frame 107 and the guide frame 108 , are a frame that moves in one direction. The direction of movement of the guide frame 107 is orthogonal to the direction of movement of the guide frame 108 , For this reason, the light projection system 102 through the guide frame 107 and the guide frame 108 in a plane orthogonal to the measuring axis AX _M (hereinafter referred to as "in an OxOy plane"). The measuring axis AX _M coincides with the Oz axis.

The objective optical system 105 is on the retaining element 104 placed. Here is the objective optical system 105 in an eccentric state. For this reason, the objective optical system 105 arranged so that the main focus objective optical system 105 coincides with the measuring axis AX _M. For this reason, the position of the subject optical system 105 preferably adjustable in the OxOy plane.

A holding element 109 is for example between the holding element 104 and the subject optical system 105 arranged. The holding element 109 is made up of two guide frames. The two guide racks are in the same way as the guide frame 107 and the guide frame 108 combined. This makes it possible to determine the position of the objective optical system 105 in the OxOy level.

In this way, the holding element 109 an adjustment function in the OxOy plane. The holding element 109 can be provided with other functions. The functions will be described later.

After the objective optical system 105 on the retaining element 109 is placed, a light beam from a position on the measuring axis AX _M to the objective optical system 105 created. Thereafter, a predetermined aberration component is outputted from the light receiving system 103 extracted wavefront data extracted. The position of the objective optical system 105 can be adjusted to minimize the predetermined aberration component.

For example, by using the Zernike polynomial, the amount of aberration associated with the tilt, the amount of aberration of a coma, and the amount of aberration associated with the focus are extracted. The position of the objective optical system 105 can be adjusted so that the amount of aberration associated with the tilt and the amount of aberration of the coma are minimized and that the amount of aberration associated with the focal point is made substantially equal to the aberration in the design.

In addition, there are optical systems with different specifications than the subject optical system 105 , For this reason, differ the front focal position and the rear focal position of the subject optical system 105 depending on the subject optical system 105 , In the device for measuring the amount of eccentricity 100 is the light projection system 102 in the front focus position of the subject optical system 105 arranged and the light receiving system 103 is in the rear focus position of the subject optical system 105 arranged.

To measure the amount of eccentricity for the subject optical system 105 of different types, it is necessary that at least two of the following are movable along the measuring axis AX _M : the light projection system 102 , the retaining element 104 and the light receiving system 103 , In the system for measuring the amount of eccentricity 100 becomes the retaining element 104 from a movement mechanism 110 held. By guiding the guide mechanism 110 is it possible the retaining element 104 that is, the objective optical system 105 to move along the measuring axis AX _M.

The sole movement of the retaining element 104 however, only allows that causes either the light projection system 102 or the light receiving system 103 coincides with the focus position. Out This is why either the light projection system 10 or the light receiving system 103 made movable along the measuring axis AX _M. Otherwise, the light projection system can 102 and the light receiving system 103 be movable instead of no movement mechanism 110 include.

In addition, a retaining element 111 between the light projection system 102 and the holding element 104 be provided. The holding element 111 is provided in a position to the subject optical system 105 to keep. When the total length of the subject optical system 105 is long, the objective optical system 105 stable with the retaining element 111 being held. The holding element 111 can be provided with other functions. The functions will be described later.

The light receiving system 103 contains a wavefront measuring device. The wavefront measuring device is on a rear focal plane of the subject optical system 105 arranged. The wavefront measuring device is, for example, an SH sensor. 37A and 37B are diagrams illustrating a structure and a function of the SH sensor wherein 37A illustrates a condition in the case where a plane wave is incident on the SH sensor, and 37B illustrates a condition in the case where a non-planar wave is incident on the SH sensor.

An SH sensor 120 becomes from a microlens arrangement 121 and an imaging element 122 educated. The picture element 122 is for example a CCD or a CMOS. It is assumed that the microlenses are arranged in the structure at regular intervals and each of the microlenses has no aberration.

In the SH sensor 120 is the on the SH sensor 120 incident light beam through the microlens array 121 compacted. In this time, the same number of light spot images as the number of microlenses through which the light beam was transmitted is formed in the condensing position. The picture element 122 is located at the compacting position. Each of the spot images is from the imaging element 122 receive. In the picture element 122 Tiny light receiving elements are arranged in a two-dimensional manner. Therefore, it is possible to recognize positions of the respective light spot images.

If a plane wave on the SH sensor 120 light spots are formed at regular intervals, as in 37A illustrated. In contrast, light spot images are not formed at regular intervals when a non-planar wave is incident on the SH sensor 120 is thought of as in 37B illustrated. In this way, the positions of the respective light spot images depend on the shape of the SH sensor 120 incident wavefront, that is, the extent of the occurrence of wavefront aberration.

When a wavefront to be measured on the SH sensor 120 is thought to be the wavefront through the microlens array 121 divided up. As a result, the wavefront becomes the imaging surface of the imaging element 122 projected as a plurality of the light spot images. The wavefront aberration can be measured from amounts of offset of the light spot image positions of reference positions.

The reference positions are positions of the spot images formed when a plane reference wave is incident on the SH sensor in advance and the plane wave is projected (see: Data Processing of Shack-Hartmann Mirror Surface Measurement Apparatus, Report of the National Astronomical Observatory of Japan (Vol. 2, No. 2), p. 431-446). These are the positions of the respective light spot images in 37A ,

As described above, when the amount of eccentricity is measured with high accuracy, it is preferable that a larger amount of information is obtained by setting the slope of the movement of the radiation position to a small value. Setting the slope of the movement to a small value increases the number of measurement points. Since the light spot images are imaged only by the imaging element in the SH sensor, it is possible to complete the detection of the wavefront data in a very short time. In this way, by using the SH sensor, it is possible to perform the measurement in a sufficiently practical time.

As described above, there are cases where the light receiving system 103 that is, the wavefront measuring device has a system aberration. 38A . 38B . 38C and 38D are diagrams showing a system aberration in the SH sensor 120 illustrate, where 38A illustrates the case where the substrate is curved, 38B illustrates the case where the substrate is tilted, 38C illustrates the case in which an error in the lens pitch occurs, and 38D illustrates the case where the focal length differs between the lenses.

In the SH sensor 120 becomes the microlens array 121 from a substrate 121 and microlenses 121b educated. In 38A have the microlenses 121b the same focal length on, but the substrate 121 is curved. In this case, the arrangement of the microlenses 121b uneven. For this reason, even if a plane wave is invaded, the intervals between light spot images also become uneven.

In addition, the optical axis of the microlens 121b directed outward when the position of the microlens 121b approximates the periphery. For this reason, the interval between the light spot images successively widens to the peripheral part.

In addition, in 38B the substrate 121 not curved and the microlenses 121b are arranged regularly. In addition, the microlenses exhibit 121b the same focal length. The entire microlens array 121 is, however, in relation to the imaging element 122 inclined. In this case, when a plane wave is incident, spot images are formed at regular intervals. However, the entire light spot images are moved to positions shifted from their original positions.

In addition, in 38C the substrate 121 not curved and the microlenses 121b have the same focal length. The arrangement of the microlenses 121b is however uneven. For this reason, even if a plane wave is incident, the intervals between the light spot images also become uneven.

In addition, in 38D the substrate 121 not curved. The microlenses 121b However, they have different focal lengths. Since there are microlenses with different external shapes, in this case, the arrangement of microlenses 121b uneven. For this reason, even if a plane wave is invaded, the intervals between light spot images also become uneven.

If a manufacturing error in the microlenses 121b occurs, contains the wavefront measuring device 103 in this way a system aberration. In this case, the positions of the respective light spot images on the imaging element 122 are different from the positions of the light spot images formed with the wavefront to be measured.

In this case, there is a method in which a plane wave is applied in advance to the SH sensor 120 is considered to determine the positions of the respective light spot images, and in which the determined positions are used as reference positions. The plane wave used when the reference positions are detected and the wavefront to be measured pass through substantially the same measurement system. For this reason, by previously determining the reference positions, it is possible to accurately measure the wavefront to be measured by canceling the system aberration, even if the system aberration exists.

However, forming a very accurate plane wave requires high costs. Moreover, in the case where the wavefront is measured, when a light beam is radiated from the outside of the axis, it is required that the angles of the light beam incident on the SH sensor be between the wavefront to be measured and that detected correspond to the reference positions wavefront with high accuracy.

Although the two wavefronts can be made coincident with each other with high accuracy, the aberration caused by the eccentricity is difficult from the design aberration of the subject optical system due to a rotationally symmetric manufacturing error such as a radius of curvature error and a distance error of each surface of the subject optical system aberration and the aberration caused by a manufacturing error of the light projection system such as the light projection system.

These problems are solved by performing a first rotation to detect wavefront data, even in the case of using an SH sensor.

In the device for measuring the amount of eccentricity 100 is the light projection system 102 in the front focus position of the subject optical system 105 arranged. When the light source of the Light projection system 102 is a point light source, a spherical wave is radiated from a light-emitting part of the light source. In this case, the light projection system 102 arranged so that the front focal plane of the objective optical system 105 coincides with the light radiating part.

The light source of the light projection system 102 is not limited to a point light source. It is sufficient that the light source of the light projection system 102 includes a light-emitting part that can be considered substantially as a point light source. The light-emitting part does not have to emit light itself. For example, a spherical wave is radiated from a small hole by illuminating the small hole. In this case, the small hole can be regarded as a point light source.

That of the light source of the light projection system 102 radiated light beam is over an off-axis area of the subject optical system 105 transfer. That of the objective optical system 105 radiated light beam is applied to the rear focal plane of the subject optical system 105 projected.

As described above, the light source of the light projection system 102 in the OxOy plane through the guide frame 107 and the guide frame 108 movable. For this reason, by moving the radiation position in the OxOy plane, it is possible to move the position of the light beam that is the objective optical system 105 passes.

Here is the light receiving system 103 , For example, the wavefront measuring device, in the rear focal position of the subject optical system 105 arranged. For this reason, only the angle of incidence of the light receiving system (the wavefront measuring device) changes. 103 incident light beam, even if the position of the subject optical system 105 is changed by passing light beam.

In this way it is in the device for measuring the amount of eccentricity 100 possible by moving the light source (object point) of the light projection system 102 To capture in the OxOy plane off-axis wavefront data and axial wavefront data, without the objective optical system 105 or the light receiving system (wavefront measuring device) 103 to move.

The purpose of detecting the off-axis wavefront data is to detect more types of aberration components caused by eccentricity. In particular, only information about the aberration component proportional to the power of the object height can be acquired from the axial wavefront data. In contrast, information about the aberration component proportional to the 1st power or a higher power of the object height is acquired from the off-axis wavefront data.

In addition, the device for measuring the Exzentrizitätsbetrags 100 a processing device 112 contain. The processing device 112 is over a cable 113 with the light projection system 102 , the light receiving system 103 , the guide frame 107 and the guide frame 108 connected. The light projection 102 is with the processing device 112 over the retaining element 106 connected, but can not over the holding element 106 be connected. The connection with the retaining element 109 can after the function of the holding element 109 be determined.

The processing device 112 performs the acquisition step, the first extraction step, the second extraction step, and the analysis step. In the detection step, wavefront data is detected based on the light beam emitted from the subject optical system. In the first extraction step, a predetermined aberration component is extracted from the wavefront data. In the second extraction step, a first aberration component is extracted from the predetermined aberration step. In the analysis step, a system of linear equations for the first aberration component, eccentric aberration sensitivity, and the amount of eccentricity is analyzed.

Moreover, the predetermined aberration component is an aberration component including an aberration component caused by eccentricity, the first aberration component is an aberration component proportional to the 1st power of the amount of eccentricity in the predetermined aberration component, and the eccentric aberration sensitivity is an aberration sensitivity proportional to the 1st power of the amount of eccentricity.

The steps, the aberration component, the predetermined aberration component, the first aberration component and the eccentric aberration component have already been described with reference to the flowchart of FIG 1 explained. Accordingly, an explanation thereof is omitted here.

In this way, the device for measuring the Exzentrizitätsbetrags 100 capable of carrying out the method of measuring the amount of eccentricity according to the present embodiment. Therefore, according to the eccentricity amount measuring apparatus, it is possible to measure the amount of eccentricity in a short time irrespective of the shape of the lens surface and the number of lenses constituting the optical system.

39A and 39B illustrate modifications of the light projection system. 39A illustrates a first modification and 39B illustrates a second modification.

The first modification will be in 39A illustrated. A light projection system 130 contains a light source 131 , an optical fiber 132 and a radiation unit 133 , One side of the fiber optic cable 132 is with the light source 131 connected and the other side of the optical fiber 132 is with the radiation unit 133 connected.

From the light source 131 radiated light is transmitted to the optical fiber 132 invaded, spreads through the interior of the optical fiber 132 and reaches the radiation unit 133 , In the light projection system 130 is the radiation unit 133 small, even if the light source 131 has a large size. As the radiation unit 133 on the device for measuring the amount of eccentricity 100 is attached, it is possible to increase the size of the device for measuring the amount of eccentricity 100 to prevent. The radiation unit 133 may optionally include an optical system.

In addition, in the light projection system 130 the light source 131 and the radiation unit 133 through the fiber optic cable 132 connected with each other. In this case, it is possible relative positions of the light source 131 and the radiation unit 133 to change as desired. Accordingly, the light source needs 131 not on the device for measuring the amount of eccentricity 100 to be appropriate. As a result, it is possible to enlarge the apparatus for measuring the amount of eccentricity 100 to prevent, even if the light source 131 has a large size.

The second modification is in 39B illustrated. In the second modification, the light projection system includes 140 a substrate 141 and light sources 142 , The light sources 142 are arranged in a grid-like manner. The radiation position may be obtained by radiating a light beam from any of the light sources 142 be changed. Accordingly, the guide frame 107 and the guide frame 108 in the device for measuring the amount of eccentricity 100 not necessary in the second modification.

In the device for measuring the amount of eccentricity 100 a first turn can be made. When the first rotation is performed, the retaining element can 109 be used as a bogie. 40A and 40B are diagrams illustrating a positional relationship between the holding member and the measuring axis, wherein 40A illustrates the case where the first axis of rotation coincides with the measuring axis, and 40B illustrates the case where the first axis of rotation does not coincide with the measuring axis.

When the retaining element 109 as the bogie is used, the first rotation with the holding element 109 be performed. As in 40A illustrated, a rotation axis AX _{R1 of} the holding element is correct 109 that is, the first axis of rotation preferably coincides with the measuring axis AX _M. In this case, the system aberration component and the design aberration components may be removed using expression (18).

However, it is difficult, the axis of rotation AX _{R1 of} the holding element 109 to coincide with the measuring axis AX _M. For this reason, the rotation axis AX _{R1 of} the holding element is correct 109 not coincide with the measuring axis AX _M , as in 40B illustrated. In this case, the system aberration component and the design aberration components may be removed using expression (20).

As described above, the retaining element 109 be provided with the turning function instead of the adjustment function in the OxOy plane or the adjustment function in the direction along the measuring axis AX _M. Otherwise, the retaining element 109 be provided with these three functions.

The following is an explanation of the modifications of the holding member 109 , 41A and 41B FIG. 12 are diagrams illustrating modifications of the holding member, wherein FIG 41A illustrates a first modification and 41B illustrates a second modification.

In the in 36 illustrated device for measuring the Exzentrizitätsbetrags 100 is the device for measuring the amount of eccentricity 100 configured so that the measuring axis AX _M coincides with the vertical direction in the paper. The device for measuring the amount of eccentricity 100 However, it can be rotated by 90 °, whereby the device for measuring the Exzentrizitätsbetrags 100 is configured so that the measuring axis AX _M coincides with the horizontal direction in the paper. In the configuration in which the measuring axis AX _M coincides with the horizontal direction in the paper, the holding element can 109 be configured as follows.

In the first modification, the retaining element 109 from a V block 150 formed as in 41A illustrated. Here is the objective optical system 105 with a cylindrical mounting frame 151 held. The mounting frame 151 is held in a V-shaped recessed part. Two inclined surfaces of the recessed part contact the external peripheral surface of the mounting frame 151 , The first rotation can be performed by rotating the lens barrel while maintaining the contact state.

In the second modification, the retaining element 109 from a rotary motor 152 formed as in 41B illustrated. The objective optical system 105 gets off the rack 151 held. The mounting frame 151 is with the rotary motor 152 connected. The first rotation can be done by turning the motor 152 be performed.

In addition, the retaining element 111 provided with the function while holding the subject optical system 105 to help but the retaining element 111 may be provided with a function for performing the second rotation. 42A and 42B FIG. 15 are diagrams illustrating a state in which the second rotation is performed, wherein FIG 42A illustrates a state before the movement of the holding member and 42B illustrates a state after the movement of the holding member.

When the retaining element 111 is provided with the turning function, the second rotation with the holding element 111 be performed. The holding element 111 is made of an annular part 111 and a rotating mechanism 111b educated. The objective optical system 105 is through the annular part 111 of the holding element 111 held.

The annular part 111 is with the turning mechanism 111b rotatable about a rotation axis AX _R2 . Since the rotation axis AX _{R2 is} orthogonal to the measurement axis AX _M , the rotation axis AX _R2 serves as the second rotation axis. Accordingly, the subject optical system 105 by turning the annular part 111 be rotated about the second axis of rotation AX _R2 .

In the process, as in 42A is a part of the objective optical system 105 inside the retaining element 109 positioned. For this reason, the second rotation can not be performed in this state. Therefore, the holding element 104 a bit to the light receiving system 103 moves, as in 42B illustrated. In this way, a space between the objective optical system 105 and the holding element 109 educated. As a result, the subject optical system 105 be rotated about the second axis of rotation AX _R2 .

The second rotation may also be performed in the first modification of the holding member. In this case, the user lifts the subject optical system 105 and returns to the front and back of the subject optical system 105 around. Then the objective optical system becomes 105 on the V-block 150 arranged. In this case, the external peripheral surface of the mounting frame abuts 151 to the two inclined surfaces of the recessed part also. That's why the absolute amount of the amount of eccentricity with respect to the rotation axis before and after the second rotation has not changed.

In addition, the second rotation can be performed also in the second modification of the holding member. In this case, the user draws the subject optical system 105 from the mounting frame 151 and returns the front and back of the subject optical system 105 around. Then the objective optical system becomes 105 in the mounting frame 151 used. In this state, the mounting frame 151 with the rotary motor 152 kept connected. For this reason, the absolute amount of the amount of eccentricity with respect to the rotation axis before and after the second rotation is not changed.

In this way, the absolute amount of the amount of eccentricity with respect to the rotation axis before and after the second rotation is not changed in both the first modification and the second modification. The absolute value of the amount of eccentricity with respect to the rotation axis means 29A and 29B | .DELTA.R |.

The following is an explanation of the case where the subject optical system has a negative refractive power. 43 Fig. 12 is a diagram illustrating the light projection system in the case where the subject optical system has a negative refractive power.

As in 43 illustrated, becomes a light projection system 160 from a light source 161 and an optical system 162 educated. The optical system 162 gets out of a lens 163 and a lens 164 educated. One from the light projection system 160 radiated light beam is with the lens 163 converted into a parallel light beam. The parallel beam of light is with the lens 164 converted into convergent light. For this reason, an objective optical system 170 arranged so that the rear focal position thereof coincides with the condensing position of the convergent light beam.

Thereby, it is possible to measure the amount of eccentricity in a short time irrespective of the shape of the lens surface and the number of lenses constituting the optical system, even if the subject optical system has a negative refractive power.

The following is an explanation of a modification of the light receiving system 103 , 44 Fig. 10 is a diagram illustrating a modification of the light receiving system.

The light receiving system 180 becomes of an optical system 181 and a wavefront measuring device 184 educated. The optical system 181 is an optical system with variable power and is made of a lens 182 and a lens 183 educated. One of a figurative optical system 190 radiated light beam 185 is with the lens 182 compacted. Then the light beam with the lens 183 in a ray of light 186 transformed. By doing that, the focal length of the lens 182 from the focal length of the lens 183 made different, it is possible here, the diameter of the light beam 185 from the diameter of the light beam 186 to make different.

When the wavefront measuring device 184 is an SH sensor, a parallel beam of light is preferably made incident on many microlens arrays. When the parallel light beam 185 has a small diameter, the parallel light beam can not be incident on many microlens arrays.

For this reason, the diameter of the light beam with the variable power optical system becomes 181 increased. In this way, the light beam 186 which has a large beam diameter to which microlens arrays are incident. In this case, the number of microlens arrays that is the radiation area of the light beam 186 occupy noticeably larger than that in the case with a small beam diameter. In particular, the number of light spot images formed with the microlens arrays is markedly increased. Therefore, it is possible to improve the spatial resolution in the SH sensor.

As a result, wavefront data with high spatial resolution can be detected. This means that it is possible to increase the amount of spatial information in the wavefront data. By performing detection of the wavefront data with high spatial resolution, it is possible to perform adjustment to the Zernike coefficient with high accuracy. As a result, since it is possible to extract the predetermined aberration component and the first aberration component with high accuracy, it is possible to obtain the amount of eccentricity with high accuracy.

The following is an explanation of a first modification of the eccentricity amount measuring apparatus. 45 FIG. 15 is a diagram illustrating a first modification of the eccentricity amount measuring apparatus. FIG. The first modification is explained, wherein the wavefront measuring device 103 is used as the light receiving system.

In the device for measuring the amount of eccentricity 100 becomes a spherical wave to the objective optical system 105 created. The to the objective optical system 105 scale However, light beam can be a plane wave. As in 45 is illustrated in a device for measuring the Exzentrizitätsbetrags 200 a plane wave 210 to an objective optical system 220 created. The object height coordinates in this case may be indicated by an angle of the plane wave with respect to the measurement axis.

The plane wave 210 becomes in the rear focus position of the subject optical system 220 compacted. Even if the wavefront measurement system 103 In the rear focus position, therefore, it is difficult to perform the wavefront measurement because the spatial resolution is insufficient.

For this reason, the device for measuring the amount of eccentricity contains 200 a lens 230 between the objective optical system 220 and the wavefront measuring device 103 , The Lens 230 is arranged so that the front focal position of the lens 230 coincides with the condensing position. In this way, the condensed light with the lens 230 converted into a substantially parallel light beam. As a result, it is possible to project the light beam to the entire light-receiving surface of the wavefront measuring device 103 to come up with.

When in the device for measuring the amount of eccentricity 200 the radiation position is changed becomes the incident angle of the plane wave 210 to the objective optical system 220 changed. In this case, the direction of the objective optical system 220 radiated wavefront changed. Therefore, it is not necessary, the guide frames 107 and 108 in the device for measuring the amount of eccentricity 100 provide.

The following is an explanation of a second modification of the eccentricity amount measuring apparatus. 46 Fig. 10 is a diagram illustrating the second modification of the eccentricity amount measuring apparatus.

As described above, in the eccentricity amount measuring apparatus, it is correct 100 the radiation position with the front focal position of the subject optical system 105 match. However, the radiation position is not necessarily correct with the front focus position of the subject optical system 105 match. As in 46 illustrated, is the radiation position of a spherical wave 250 in a device for measuring the amount of eccentricity 240 a position taken from the front focal position of the subject optical system 220 away and away from the objective optical system 220 is.

The spherical wave 250 becomes with the objective optical system 220 compacted. Accordingly, the lens 230 in the same way as the device for measuring the amount of eccentricity 200 between the objective optical system 220 and the wavefront measuring device 103 arranged.

The functions and operations of the lens 230 and the wavefront measuring device 103 were related to the device for measuring the amount of eccentricity 200 explained and an explanation thereof is omitted here.

An explanation of a third modification follows. 47 Fig. 15 is a diagram illustrating the third modification of the eccentricity amount measuring apparatus.

As described above, in the device for measuring the amount of eccentricity 100 the radiation position moves to detect wavefront data. However, the wavefront data can be detected while the radiation position is held. As in 47 are in a device for measuring the amount of eccentricity 260 the incidence position and the angle of incidence of the plane wave 210 fixed. The objective optical system 220 becomes an axis 270 turned. The object height coordinates in this case can be determined by the rotation angle of the objective optical system 220 in terms of the measuring axis AX _M.

The plane wave 210 becomes with the objective optical system 220 compacted. Accordingly, the lens 230 in the same way as the device for measuring the amount of eccentricity 200 between the objective optical system 220 and the wavefront measuring device 103 arranged.

In the device for measuring the amount of eccentricity 260 becomes the compression position with rotation of the subject optical system 220 moved in the vertical direction in the paper. Accordingly, the on the wavefront measurement system 103 imagined beam in vertical Direction moves. A movement of the wavefront measuring device 103 is not required if the light receiving surface of the wavefront measuring device 103 is sufficiently broad. In addition, by setting the rotational position of the subject optical system 220 on the back main point of the objective optical system 220 the vertical amount of movement of the wavefront measuring device 103 dropped light beam and reduces the size of the light receiving surface of the wavefront measuring device 103 is limited to the minimum size.

Industrial Applicability

As described above, the present invention is suitable for a method of measuring an amount of eccentricity and a device for measuring an amount of eccentricity, which allow measurement of the amount of eccentricity in a short time, irrespective of the shape of the lens surface and the number of lenses, the optical system form.

LIST OF REFERENCE NUMBERS

1, 10

LIGHT PROJECTION SYSTEM

2, 20, 22

PRESENT OPTICAL SYSTEM

3, 30

LIGHT SYSTEM

4

SPHERICAL WAVE

7, 7 ', 8, 8', 9 ₀ , 9 ' ₀ , 9 ₁ , 9' ₁

NOT LEVEL WAVE

21

OPTICAL SYSTEM

23, 24, 25

LENS

31

THE SENSOR COMPONENT FORMING UNIT

32

WAVE FRONT DATA ACQUISITION UNIT

33

LIGHT RECEIVING ELEMENT

40

SPHERICAL WAVE

50, 51, 52, 54, 55, 56

NOT LEVEL WAVE

53

LEVEL WAVE

60

INTERLOCKED WAVE FRONT

70, 71, 72, 73

BALL MIDDLE POINT

80

NEW AXIS

90

PRESENT OPTICAL SYSTEM

91

ASPHEREIC SURFACE

92, 92 ', 94

TOP OF THE ASPHARIC SURFACE

93

AXIS OF ASPHEREIC SURFACE

95

RELOCATION

96

BALL MIDDLE POINT

100

DEVICE FOR MEASURING THE ECCENTRICITY AMOUNT

101

BULK UNIT

102

LIGHT PROJECTION SYSTEM

103

LIGHT RECEPTACLE SYSTEM, WAVE FRONT MEASURING DEVICE

104

RETAINING ELEMENT

105

PRESENT OPTICAL SYSTEM

106

RETAINING ELEMENT

107

MANAGEMENT STRUCTURE

108

MANAGEMENT STRUCTURE

109

RETAINING ELEMENT

110

MOVING MECHANISM

111

RETAINING ELEMENT

111

RINGING PART

111b

ROTARY MECHANISM

112

PROCESSING DEVICE

113

ELECTRIC WIRE

120

SH-SENSOR

121

MICRO LENS ARRANGEMENT

121

Substrate

121b

MICRO LENS

122

FIGURE ELEMENT

130

LIGHT PROJECTION SYSTEM

131

LIGHT SOURCE

132

OPTICAL FIBER

133

RADIATION UNIT

140

LIGHT PROJECTION SYSTEM

141

Substrate

142

LIGHT SOURCE

150

V-BLOCK

151

MOUNTING STRUCTURE

152

ROTARY ENGINE

160

LIGHT PROJECTION SYSTEM

161

LIGHT SOURCE

162

LIGHT PROJECTION SYSTEM

163, 164

LENS

170

PRESENT OPTICAL SYSTEM

180

LIGHT SYSTEM

181

OPTICAL SYSTEM

182, 183

LENS

184

WAVE FRONT-MEASURING DEVICE

185, 186

BEAM

190

PRESENT OPTICAL SYSTEM

200

DEVICE FOR MEASURING THE ECCENTRICITY AMOUNT

210

LEVEL WAVE

220

PRESENT OPTICAL SYSTEM

230

LENS

240, 260

DEVICE FOR MEASURING THE ECCENTRICITY AMOUNT

250

SPHERICAL WAVE

270

AXIS

AX _M

MEASURING AXIS

AX _R1

FIRST ROTARY AXLE

AX _R2

SECOND ROTARY AXLE

CR

CENTRAL RADIATION BUNDLE

e

AMOUNT OF SHIFT

LS1, LS2, LS3

LENS SURFACE

LS ₁ , LS ₂ , LS _j

LENS SURFACE

L1, L2 LENS

L1 ₁ , L1 ₂ , L2 ₁ , L2 ₂

LENS SURFACE

IM1, IM2, IM3

IMAGE

IF

OBJECT

X, Y, A, B

FREEDOM OF EXCENTRICITY

SC ₁ , SC ₂ , ..., SC _j , SC _{j + 1} , SC _{j + 2} , SC _m

BALL MIDDLE POINT

δ ₁ , δ ₂ , ..., δ _j , δ _{j + 1} , δ _{j + 2} , ..., δ _m

AMOUNT OF SHIFT IN Y-DIRECTION

Claims (17)

A method of measuring an amount of eccentricity in which a light beam is applied to an objective optical system disposed on a measurement axis to measure an amount of eccentricity, the method of measuring the amount of eccentricity comprising: a detection step of detecting wavefront data based on the light beam which is radiated from the objective optical system; a first extracting step in which a predetermined aberration component is extracted from the wavefront data; a second extracting step in which a first aberration component is extracted from the predetermined aberration component; and an analyzing step of simultaneously analyzing linear equations for the first aberration component, an eccentric aberration sensitivity and the amount of eccentricity, the predetermined aberration component being an aberration component including an aberration component caused by eccentricity, the first aberration component is an aberration component proportional to the 1st power of the amount of eccentricity in the predetermined aberration component, and the eccentric aberration sensitivity is an aberration sensitivity proportional to the 1st power of the amount of eccentricity. A method of measuring the amount of eccentricity according to claim 1, wherein the light beam is applied in the detection step from two radiation positions, the two radiation positions are symmetrical with respect to the measuring axis and the first extraction step extracts the predetermined aberration component respectively from the wavefront data in one radiation position and the wavefront data in the other radiation position. A method of measuring the amount of eccentricity according to claim 2, wherein the predetermined aberration component includes a second aberration component, the second aberration component is an aberration component proportional to the square of the amount of eccentricity in the predetermined aberration component, the object height coordinates are coordinates that indicate the radiation position, a predetermined function is a function indicating the second aberration component, and is a function containing the object height coordinates as a variable, the second extraction step includes a first calculation step and a second calculation step, in the first calculation step, obtaining a sum of the predetermined aberration component in the one radiation position and the predetermined aberration component in the other radiation position when the predetermined function is an odd function, and in the second calculating step, a difference between the predetermined aberration component in the one radiation position and the predetermined aberration component in the other radiation position is obtained when the predetermined function is an even function. A method of measuring the amount of eccentricity according to claim 2 or 3, wherein the detection step includes a first rotation, the objective optical system is rotated in the first rotation about the measuring axis and Wave front data before the first rotation and wavefront data after the first rotation in the same radiation position are detected. A method of measuring the amount of eccentricity according to claim 2 or 3, wherein the detection step includes a first rotation, the objective optical system is rotated in the first rotation about an axis parallel to the measuring axis and Wave front data before the first rotation and wavefront data after the first rotation in the same radiation position are detected. A method of measuring the amount of eccentricity according to claim 4 or 5, wherein an angle for rotating the objective optical system is 10 ° or more. The method for measuring the amount of eccentricity according to claim 6, wherein the angle for rotating the objective optical system is 180 °. A method of measuring the amount of eccentricity according to any one of claims 2 to 7, wherein both the one radiation position and the other radiation position are moved and the wavefront data in the moving radiation positions are detected. A method of measuring the amount of eccentricity according to claim 8, wherein which is moved to a radiation position, the wavefront data is detected in a radiation position after the movement, then the other radiation position is moved and the wavefront data is detected in a radiation position after the movement. The method of measuring the amount of eccentricity of claim 8, wherein the wavefront data is detected in both the one radiation position and the other radiation position; thereafter moving the one radiation position and the other radiation position and detecting the wavefront data in each of the radiation positions after the movement. A method of measuring the amount of eccentricity according to any one of claims 1 to 10, wherein the detection of the wavefront data is performed in a first radiation position and is a central radiation beam of the light beam in the first radiation state parallel to the measurement axis. A method of measuring the amount of eccentricity according to any one of claims 1 to 10, wherein the detection of the wavefront data is performed in a second radiation position and a central radiation beam of the light beam in the second radiation state crosses the measurement axis at a predetermined angle. A method of measuring the amount of eccentricity according to claim 1, wherein the second extraction step is performed using a predetermined functional system, the predetermined functional system is a functional system indicating the first aberration component and the predetermined aberration component in the one radiation position and the predetermined aberration component in the other radiation position are applied to the predetermined functional system. A method of measuring the amount of eccentricity according to any one of claims 1 to 13, wherein the detection step includes a second rotation, the objective optical system is rotated in the second rotation by 180 ° about an axis orthogonal to the measuring axis and Wavefront data before the second rotation and wavefront data after the second rotation are detected. The method for measuring the amount of eccentricity according to claim 14, wherein the amount of eccentricity at a time of detecting the wavefront data before the second rotation has an absolute amount equal to the absolute amount of the amount of eccentricity at a time of detecting the wavefront data after the second rotation. A method of measuring the amount of eccentricity according to any one of claims 1 to 15, wherein the first extraction step is performed using a Zernike polynomial, and the predetermined aberration component is a coefficient of the Zernike polynomial. Device for measuring the amount of eccentricity, comprising: a light projection system disposed at one end of a measuring axis; a light receiving system disposed at the other end of the measuring axis; a holding member holding an objective optical system; and a processing device connected to a wavefront measuring device, wherein the holding element is arranged between the light projection system and the light receiving system, the light projection system is provided in a position to apply a light beam to the objective optical system, the processing means performs a detecting step, a first extracting step, a second extracting step and an analyzing step, Wavefront data is detected in the detection step on the basis of the light beam emitted from the objective optical system, in the first extraction step, extracting a predetermined aberration component from the wavefront data, in the second extracting step, extracting a first aberration component from the predetermined aberration component, linear equations for the first aberration component, an eccentric aberration sensitivity and the amount of eccentricity are simultaneously analyzed in the analysis step, the predetermined aberration component is an aberration component containing an aberration component caused by eccentricity, the first aberration component is an aberration component proportional to the 1st power of the amount of eccentricity in the predetermined aberration component; and the eccentric aberration sensitivity is an aberration sensitivity proportional to the 1st power of the amount of eccentricity.

Images