JP6072317B2 - Eccentricity measuring method and eccentricity measuring device - Google Patents

Description

  The present invention relates to an eccentricity measuring method and an eccentricity measuring device.

  In a lens, various errors may occur during the manufacture of the lens. In addition, the optical system includes one lens or a plurality of lenses, but in the optical system, various errors may occur during assembly.

  An error in the manufacture of the lens is the decentering of the lens surface. An error in assembling the optical system includes decentration of the lens itself. When the lens or the optical system is decentered, the optical performance of the lens or the optical system is deteriorated. Also, the greater the amount of eccentricity, the greater the degradation of optical performance.

  If the amount of decentration can be known, the amount of decentration can be used for the pass / fail judgment of the completed lens or optical system. Here, the pass / fail determination is to determine whether or not the completed lens or optical system has a desired optical performance. When the amount of eccentricity is smaller than the specified value, it is acceptable, and when it is large, it is unacceptable.

  If the determination result is unacceptable, the information on the amount of eccentricity can be used for adjustment of a lens manufacturing apparatus (a polishing apparatus or a molding apparatus) or adjustment during assembly of an optical system. For this reason, there is a great demand for measuring the amount of eccentricity.

  As a technique for measuring the amount of eccentricity, there are a measurement technique described in Patent Document 1 and a measurement technique described in Patent Document 2.

Japanese Patent No. 837190 Japanese Patent No. 4260180

  The measurement technique described in Patent Document 1 uses an autocollimation method. In the autocollimation method, even when the optical system is composed of a plurality of lenses, the amount of eccentricity can be measured for each lens surface.

  In the measurement technique described in Patent Document 2, a stylus type probe is used. In this method, the shape of the lens surface is measured by bringing the probe into contact with the lens surface. Further, the shape of the reference member prepared in advance is measured with the probe. Then, the amount of eccentricity is measured by obtaining a relative positional deviation between the reference member and the lens surface. In the measurement technique described in Patent Document 2, the amount of eccentricity can be measured for two lens surfaces.

  The autocollimation method assumes that the lens surface is a spherical surface. That is, the autocollimation method does not support aspherical measurement in principle. Therefore, the measurement technique described in Patent Document 1 cannot measure the amount of eccentricity for an aspheric lens or an optical system including an aspheric lens.

  In this case, it is conceivable that the vicinity of the top of the aspheric surface is regarded as a spherical surface and the same measurement as that of the spherical surface is performed. However, in such measurement, if the aspheric surface is greatly decentered, a state in which reflected light from the aspheric surface cannot be received occurs. Therefore, the amount of eccentricity cannot be measured for an aspheric lens.

  In the measurement technique described in Patent Document 1, an image of an index is observed. In this case, even if the reflected light can be received, if the amount of aspheric surface is large, the index image is greatly blurred. Therefore, the amount of eccentricity cannot be measured for an aspheric lens.

  In the measurement technique disclosed in Patent Document 2, it is necessary to bring a probe into contact with the lens surface. For this reason, an optical system composed of a plurality of lenses cannot measure the eccentricity of all the lenses.

  For example, when the optical system is composed of three lenses, there are lenses on both sides of the central lens. In this case, the probe cannot be brought into contact with the lens surface of the central lens. Therefore, the shape of the lens surface cannot be measured with the central lens. Further, with the lenses on both sides, the shape of the lens surface facing the lens surface of the central lens cannot be measured.

  In measurement, the probe and the lens surface are moved relative to each other. Since the moving speed at this time is low, the measurement time becomes long. Further, since the shape of the reference member has to be measured, the measurement time also becomes longer in this respect.

  The present invention has been made in view of such problems, and an eccentricity measuring method and an eccentricity capable of measuring the eccentricity in a short time regardless of the shape of the lens surface and the number of lenses constituting the optical system. It aims at providing a measuring device.

In order to solve the above-described problems and achieve the object, the eccentricity measuring method of the present invention is:
A method of measuring the amount of eccentricity by irradiating a test optical system arranged on a measurement axis with a light beam from a plurality of object height coordinates outside the measurement axis ,
An acquisition step of acquiring wavefront data for each of the plurality of object height coordinates based on the light beam emitted from the test optical system;
A first extraction step of extracting a predetermined aberration component from the wavefront data;
A second extraction step of extracting a first aberration component from a predetermined aberration component using a relationship between predetermined aberration components of a plurality of object high coordinates ;
An analysis step of analyzing simultaneous linear equations for the first aberration component, the decentration aberration sensitivity, and the decentering amount,
The predetermined aberration component is an aberration component including an aberration component caused by decentration,
The first aberration component is an aberration component that is proportional to the first power of the decentration amount among the predetermined aberration components,
The decentration aberration sensitivity is an aberration sensitivity proportional to the first power of the decentering amount.

The eccentricity measuring device of the present invention is
A light projecting system arranged at one end of the measurement axis;
A light receiving system disposed at the other end of the measurement axis;
A holding member for holding the test optical system;
A processing device connected to the wavefront measuring device,
The holding member is disposed between the light projecting system and the light receiving system,
The light projecting system is provided at a position where the test optical system is irradiated with a light beam,
A test optical system arranged on the measurement axis is irradiated with a light beam from a plurality of object height coordinates outside the measurement axis,
In the processing apparatus, an acquisition process, a first extraction process, a second extraction process, and an analysis process are executed,
In the acquisition step, wavefront data for each of the plurality of object height coordinates is acquired based on the light beam emitted from the test optical system,
In the first extraction step, a predetermined aberration component is extracted from the wavefront data,
In the second extraction step, the first aberration component is extracted from the predetermined aberration component using the relationship between the predetermined aberration components of the plurality of object height coordinates ,
In the analysis step, simultaneous linear equations for the first aberration component, the decentration aberration sensitivity, and the decentration amount are analyzed,
The predetermined aberration component is an aberration component including an aberration component caused by decentration,
The first aberration component is an aberration component that is proportional to the first power of the decentration amount among the predetermined aberration components,
The decentration aberration sensitivity is an aberration sensitivity proportional to the first power of the decentering amount.

  According to the present invention, it is possible to provide an eccentricity amount measuring method and an eccentricity amount measuring apparatus capable of measuring an eccentricity amount in a short time regardless of the shape of the lens surface and the number of lenses constituting the optical system.

It is a conceptual diagram which shows a mode that an aberration generate | occur | produces by eccentricity. It is a figure explaining eccentric freedom degree, Comprising: (a) shows the eccentric degree of freedom in a spherical surface, (b), (c) shows the eccentric degree of freedom in an aspherical surface. It is a figure which shows the decentration of the coordinate in a measurement system, and a to-be-tested optical system, Comprising: (a) is the figure which showed decentration with the lens surface, (b) is the figure which showed decentration with the spherical center. It is a figure which shows the flowchart of the measuring method of this embodiment. It is a figure which shows the flowchart of the measuring method of this embodiment. It is a figure which shows a mode that the light beam is irradiated to a test optical system, Comprising: (a) shows irradiation from the irradiation position P, (b) has shown irradiation from the irradiation position P '. It is a figure which shows the flowchart of the measuring method of this embodiment. It is a figure which shows the flowchart of the measuring method of this embodiment. It is a figure explaining the system aberration in a light projection system, Comprising: (a) shows the state in which system aberration has not generate | occur | produced, (b) shows the state in which system aberration has generate | occur | produced in the light projection system. It is a figure which shows the system aberration in a light-receiving system, Comprising: (a) shows the system aberration in a sensor component structure part, (b) shows the system aberration in a wavefront data acquisition part. It is a figure which shows the method of calculating | requiring a system aberration component beforehand. It is a figure which shows 1st rotation, Comprising: (a) shows the state before performing 1st rotation, (b) has shown the state after performing 1st rotation. It is a figure which shows a mode that a ball center changes with 1st rotation, Comprising: (a) shows the position of the ball center before the 1st rotation, (b) shows the position of the ball center after the 1st rotation. (C) shows the amount of movement of the ball center by the first rotation. It is a figure which shows a mode that the light reception optical system has been arrange | positioned between the test optical system and the light reception system. It is a figure showing the state where the 1st axis of rotation is eccentric to the measurement axis. It is a figure which shows the relative relationship of a 1st rotating shaft and a measurement axis, Comprising: (a) shows the state in which a measuring axis and a 1st rotating shaft correspond, (b) is 1st with respect to a measuring axis. The rotation axis of FIG. It is a figure showing the state where the 1st axis of rotation has blurred with respect to a measurement axis. It is a figure which shows the flowchart of the example 1 of execution. It is a figure which shows the flowchart of the execution example 2. FIG. It is a figure which shows the flowchart of the measuring method of this embodiment. It is a figure which shows the mode of a movement of an irradiation position, (a) shows the position before the movement of one irradiation position, (b) shows the position after the movement of one irradiation position, (c) is the other The position before the movement of the irradiation position is shown, and (d) shows the position after the movement of the other irradiation position. It is a figure which shows the flowchart of the measuring method of this embodiment. It is a figure which shows the mode of a movement of an irradiation position, (a) shows the position before the movement of one irradiation position, (b) shows the position before the movement of the other irradiation position, (c) shows one side The position after the movement of the irradiation position is shown, and (d) shows the position after the movement of the other irradiation position. It is a figure which shows the mode of a movement of an irradiation position, Comprising: (a) shows the case where the movement direction of an irradiation position is one direction, (b) has shown the case where the movement direction of an irradiation position is two directions. It is a figure which shows the pattern of an irradiation position, Comprising: (a) shows the state of an irradiation position in two directions, (b) shows the state of an irradiation position concentric, and (c) shows the state of an irradiation position in a grid | lattice form. Is shown. It is a figure which shows a mode that the light beam is irradiated to a test optical system, Comprising: (a) shows irradiation by angle (theta), (b) has shown irradiation by angle (theta) '. It is a figure which shows the flowchart of the measuring method of this embodiment. It is a figure which shows 2nd rotation, Comprising: (a) shows the state before performing 2nd rotation, (b) has shown the state after performing 2nd rotation. It is a figure for demonstrating the change of the coordinate axis by 2nd rotation, Comprising: (a) shows the state before performing 2nd rotation, (b) shows the state after performing 2nd rotation. ing. It is a figure which shows the movement of the ball center by 1st rotation, Comprising: (a) shows the movement of the ball center at the time of front side measurement, (b) shows the movement of the ball center at the time of back side measurement. . It is a figure which shows the motion of the ball center by 1st rotation and 2nd rotation, Comprising: (a) is the time of front side measurement, shows the position of the ball center before 1st rotation, (b) At the time of front side measurement , Shows the position of the ball center after the first rotation, (c) shows the position of the ball center before the first rotation, (d) shows the position of the ball center before the first rotation, The position of the ball center after rotation is shown. FIG. 6 is a diagram showing an object height function appearing in decentering aberration sensitivities B _2jl (Ox, Oy) and B _3jl (Ox, Oy), where (a) shows a case where the optical system to be _tested is not decentered, and (b) (C) shows a case where the optical system to be tested is decentered. FIG. 5 is a diagram showing an object height function appearing in decentration aberration sensitivity B _4jl (Ox, Oy), where (a) shows a case where the test optical system is not decentered, and (b) and (c) show the test optics. The case where the system is eccentric is shown. FIG. 6 is a diagram showing an object height function appearing in decentration aberration sensitivities B _5jl (Ox, Oy) and B _6jl (Ox, Oy), where (a) shows a case where the optical system to be _tested is not decentered, and (b) (C) shows a case where the optical system to be tested is decentered. FIG. 6 is a diagram showing an object height function appearing in decentering aberration sensitivities B _7jl (Ox, Oy) and B _8jl (Ox, Oy), where (a) shows a case where the optical system to be _tested is not decentered, and (b) (C) shows a case where the optical system to be tested is decentered. It is a figure which shows the eccentricity measuring device of embodiment. It is a figure which shows the structure and function of SH sensor, Comprising: (a) has shown the mode when a plane wave injects into SH sensor, (b) has shown the mode when a non-plane wave enters into SH sensor. 4A and 4B are diagrams illustrating system aberrations in the SH sensor, where FIG. 5A illustrates a case where the substrate is distorted, FIG. 5B illustrates a case where the substrate is tilted, and FIG. 5C illustrates a case where an error occurs in the lens pitch. , (D) shows a case where the focal lengths of the lenses are different. It is the modification of a light projection system, Comprising: (a) shows the 1st modification, (b) has shown the 2nd modification. It is a figure which shows the positional relationship of a holding member and a measurement axis | shaft, Comprising: (a) shows the case where a 1st rotating shaft corresponds with a measuring axis, (b) shows a 1st rotating shaft and a measuring axis. The case where it did not do is shown. It is a figure which shows the modification of a holding member, Comprising: (a) shows the 1st modification, (b) has shown the 2nd modification. FIGS. 2A and 2B are diagrams illustrating a state in which the second rotation is performed, in which FIG. 2A illustrates a state before the holding member is moved, and FIG. 2B illustrates a state after the holding member is moved. It is a figure which shows a light projection system in case a to-be-tested optical system has negative refractive power. It is a figure which shows the modification of a light-receiving system. It is a figure which shows the 1st modification of an eccentricity measuring device. It is a figure which shows the 2nd modification of an eccentricity measuring device. It is a figure which shows the 3rd modification of an eccentric amount measuring apparatus.

  Prior to the description of the examples, effects of the embodiment according to an aspect of the present invention will be described. It should be noted that, when the operational effects of the present embodiment are specifically described, a specific example will be shown and described. However, as in the case of the embodiments to be described later, those exemplified aspects are only a part of the aspects included in the present invention, and there are many variations in the aspects. Therefore, the present invention is not limited to the illustrated embodiment.

  Before explaining the method of measuring the amount of eccentricity of this embodiment, (I) aberrations caused by eccentricity, (II) degrees of freedom of eccentricity, (III) coordinates in the measurement system, (IV) after passing through the decentered lens surface The wavefront will be described.

  (I) The aberration caused by decentration will be described. FIG. 1 is a conceptual diagram showing how aberration occurs due to decentration. Since FIG. 1 is a conceptual diagram, the positions of the image IM1, the image IM2, and the image IM3, and the size and shape of the image are not accurate.

  When the optical system is decentered, aberration occurs due to the decentration. When the optical system is composed of a plurality of lenses, aberrations generated by the decentering of one lens surface are relayed one after another on the other lens surfaces.

  As shown in FIG. 1, for the image of the object point OB, the image IM1 is formed by the lens surface LS1, the image IM2 is formed by the lens surface LS2, and the image IM3 is formed by the lens surface LS3. Thus, the image of the object point OB is formed by the lens surface LS1, and the formed image is relayed by the lens surface LS2 and the lens surface LS3.

  In FIG. 1, the lens surface LS1, the lens surface LS2, and the lens surface LS3 are decentered with respect to the optical axis. In this case, the image IM1, the image IM2, and the image IM3 are formed at positions away from the optical axis.

  In addition, aberration occurs in the image IM1 with the decentering of the lens surface LS1. This image IM1 corresponds to an object point on the lens surface LS2. Here, since the lens surface LS2 is also decentered, aberration also occurs in the image IM2. The aberration in the image IM2 is obtained by adding the aberration generated by the decentering of the lens surface LS2 to the aberration in the image IM1. The aberration in the image IM3 is obtained by adding the aberration generated by the decentering of the lens surface LS3 to the aberration in the image IM2.

  As described above, in the state where the lens surface is decentered, the images are relayed while adding aberrations generated on the lens surface LS1, the lens surface LS2, and the lens surface LS3.

  (II) The eccentric degree of freedom will be described. The degree of eccentricity indicates the type of eccentricity. The degree of freedom in eccentricity is roughly divided into shift and tilt. FIG. 2 is a diagram for explaining the degree of freedom of eccentricity, in which (a) shows the degree of freedom of eccentricity on a spherical surface, and (b) and (c) show the degree of freedom of eccentricity on an aspherical surface.

  As shown in FIG. 2A, the eccentricity on the spherical surface can be expressed by the position of the spherical center. The degree of freedom of eccentricity on the spherical surface is geometrically only a shift in the X direction and a shift in the Y direction.

  In the case of a spherical surface, even if the spherical surface is tilted about a certain point in space, it can be considered that the tilt causes a shift in the X direction, a shift in the Y direction, and a gap in the inter-plane distance in the Z direction. Therefore, the degree of freedom of eccentricity on the spherical surface may be considered as only the shift in the X direction and the shift in the Y direction.

  In addition, the gap | interval of a surface space arises also at the time of manufacture. The deviation of the surface interval at the time of manufacture is, for example, an error in thickness for one lens and an error in lens interval for two lenses. In practice, it is not possible to distinguish the gap between the planes due to manufacturing errors and the gap between the planes when the spherical surface is tilted.

  On the other hand, as shown in FIGS. 2B and 2C, the aspheric surface has an aspheric surface top and an aspheric axis. The aspheric axis is a rotationally symmetric axis. Since an aspherical surface has this aspherical axis, in the case of an aspherical surface, there are a tilt in the A direction and a tilt in the B direction in addition to the shift in the X direction and the shift in the Y direction. The shift in the X direction and the shift in the Y direction are eccentric degrees of freedom with respect to the aspheric surface top. Further, the tilt in the A direction and the tilt in the B direction are degrees of freedom of eccentricity with respect to the aspherical axis.

  Thus, the number of degrees of freedom of eccentricity differs between spherical and aspherical surfaces. Therefore, for example, when the first surface of one lens is a spherical surface and the second surface is an aspheric surface, the number of degrees of freedom of eccentricity is six at the maximum.

  (III) The coordinates in the measurement system will be described. 3A and 3B are diagrams showing the coordinates in the measurement system and the decentration of the optical system to be tested. FIG. 3A is a diagram showing the decentration with a lens surface, and FIG. 3B is a diagram showing the decentration with a spherical center.

  The measurement system has a light projecting system and a light receiving system. In FIG. 3, the light projecting system is represented by the Ox axis, the Oy axis, and the Oz axis, and the light receiving system is represented by the ρx axis and the ρy axis. The coordinates of the light projecting system are represented by object height coordinates (Ox, Oy, Oz), and the coordinates of the light receiving system are represented by pupil coordinates (ρx, ρy).

As shown in FIG. 3 (a), the optical system to be measured is composed of a lens surface of the first lens surface LS ₁ up to the j lens surface LS _j. Here, a situation is considered in which these lens surfaces are shifted in the Y direction with respect to the Oz axis. The lens surfaces are all spherical.

As described in FIG. 2A, when the lens surface is a spherical surface, the eccentricity of the lens surface can be represented by a spherical center. Therefore, in FIG. 3B, the lens surface shift is represented using a spherical center. In FIG. 3B, SC ₁ , SC ₂ ,..., SC _j represent sphere centers of the lens surfaces. Further, δ ₁ , δ ₂ ,..., Δ _j represent the amount of shift in the Y direction of each lens surface.

  (IV) The wavefront after passing through the decentered lens surface will be described. Here, a description will be given using mathematical expressions.

  As shown in FIG. 3A, a light beam LB is irradiated on the optical system to be measured from the object height coordinates (Ox, Oy) in the light projecting system. The light beam LB is emitted from the OxOy surface. Therefore, the object height coordinate is (Ox, Oy, 0) to be precise, but is (Ox, Oy) for simplicity.

  The light beam LB 'transmitted through the test optical system enters the light receiving system. The light beam LB indicates a part of the light beam originally irradiated on the optical system to be tested. Similarly, the light beam LB 'indicates a part of the light beam that is originally incident on the light receiving system.

  In the light receiving system, wavefront data is acquired based on the light beam LB ′. Here, since the lens surface is decentered in the test optical system, the wavefront of the light beam LB 'has a wavefront aberration caused by the decentering. Therefore, by analyzing the wavefront data, it is possible to obtain wavefront aberration caused by decentration.

  Here, the aberration generated in the rotationally symmetric optical system is a term that does not depend on the amount of eccentricity, a term that is proportional to the first power of the eccentricity amount, a term that is proportional to the square of the eccentricity amount, a term that is proportional to the third power of the eccentricity amount, A term proportional to the fourth power of the amount of decentering can be developed using a polynomial expression (see: third-order aberration theory of an optical system with decentration, third-order aberration theory of an eccentric optical system) Both, Japan Opto-Mechatronics 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]).

  Here, the wavefront aberration is developed using only the term depending on the amount of eccentricity. In this case, the wavefront aberration W can be expressed by, for example, the following formula (1). However, the wavefront aberration W here is described as a deviation from the wavefront when the optical system to be tested is not decentered.

W (Ox, Oy, ρx, ρy, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₁₁ (Ox, Oy, ρx, ρy)
+ Δ ₁ ² B ₁₂ (Ox, Oy, ρx, ρy)
+ Δ ₂ B ₂₁ (Ox, Oy, ρx, ρy)
+ Δ ₂ ² B ₂₂ (Ox, Oy, ρx, ρy)
+ ...
+ Δ _j B _j1 (Ox, Oy, ρx, ρy)
+ Δ _j ² B _j2 (Ox, Oy, ρx, ρy) (1)
here,
Δ _j is the amount of eccentricity with respect to the Oz axis in the j-th plane,
B _j1 (Ox, Oy, ρx, ρy) is the decentration aberration sensitivity proportional to the first power of the decentration amount on the j-th plane,
B _j2 (Ox, Oy, ρx, ρy) is the decentration aberration sensitivity proportional to the square of the decentration amount on the j-th plane,
It is.

  As shown in the equation (1), each term of the polynomial is represented by the product of the amount of decentration and the decentration aberration sensitivity. In equation (1), the amount of eccentricity is not limited to the amount of shift in the Y direction. Therefore, in terms of a general amount of eccentricity, the amount of eccentricity is represented by Δ instead of δ.

Further, in the expression (1), the wavefront aberration W is developed based on the aberration theory, but the expansion is up to a term proportional to the square of the eccentricity (a term proportional to Δ ² ). In general, since the amount of eccentricity caused by a manufacturing error is small, a term that is proportional to the third power or more of the amount of eccentricity can be ignored because the amount of aberration in each term is considered minute. Therefore, the expression (1) does not include a term proportional to the third power of the eccentricity.

  Here, each term on the right side of Equation (1) is referred to as an “aberration component”. A term multiplied by the amount of eccentricity Δ is referred to as “decentration aberration component”. Each term on the right side of Equation (1) is multiplied by an eccentricity amount Δ. Therefore, all the terms on the right side of Equation (1) are decentration aberration components.

Table 1 shows the explanation of each term in the formula (1).

As shown in Table 1, the decentration aberration component in the expression (1) includes an eccentric aberration component proportional to the first power of the decentering amount (a term proportional to Δ) and an eccentric aberration component proportional to the square of the decentering amount (Δ ² )). Further, B _j1 (Ox, Oy, ρx, ρy) is the decentration aberration sensitivity proportional to the first power of the decentering amount on the j-th surface, and B _j2 (Ox, Oy, ρx, ρy) is 2 of the decentering amount on the j-th surface. The decentration aberration sensitivity proportional to the power.

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

Furthermore, the decentration aberration sensitivity in each aberration component can be developed by a polynomial based on the aberration theory. For example, when developed with Zernike polynomials, decentering aberration sensitivity _{B jl (Ox, Oy, ρx} , ρy) is expressed by the following equation (2).

_{B jl (Ox, Oy, ρx} , ρy)
= 1 ・ B _1jl (Ox, Oy)
+ ρx ・ B _2jl (Ox, Oy)
+ ρy ・ B _3jl (Ox, Oy)
+ {2 (ρx ² + ρy ² ) -1} B _4jl (Ox, Oy)
+ {ρx ² -ρy ² } ・ B _5jl (Ox, Oy)
+ 2ρxρy ・ B _6jl (Ox, Oy)
+ {3 (ρx ² + ρy ² ) ρx-2ρx} ・ B _7jl (Ox, Oy)
+ {3 (ρx ² + ρy ² ) ρy-2ρy} B _8jl (Ox, Oy)
+ {6 (ρx ² + ρy ² ) ² -6 (ρx ² + ρy ² ) +1} ・ B _9jl (Ox, Oy)
+ ... (2)
here,
B _1jl (Ox, Oy) to B _9jl (Ox, Oy) are decentration aberration sensitivity,
It is.

Incidentally, to represent the decentering aberration sensitivity _{B zjl (Ox, Oy),} B zjl (Ox, Oy) is a decentering aberration sensitivity of terms first Z term of Zernike term is multiplied by the eccentric in the j surface This is the decentration aberration sensitivity proportional to the first power of the quantity.

Table 2 shows the relationship between each term of the Zernike term, the function representing each term, and the aberration. Table 2 shows the correspondence between the first to ninth terms of the Zernike term.

  Each term of the Zernike term is represented by pupil coordinates ρx and ρy. Here, the order determined by the order at ρx and the order at ρy is the maximum order of the pupil coordinates. If this maximum order is an even order, the order of the function of that 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 term, since the pupil coordinates are ρx, the maximum degree of the pupil coordinates in the second term of the Zernike term is the first order and the odd order. Therefore, the function representing the second term of the Zernike term is a function of which the maximum degree of the pupil coordinates is the first order and the odd order.

  In the sixth term of the Zernike term, since the pupil coordinates are ρxρy, the maximum degree of the pupil coordinates in the sixth term of the Zernike term is second order and even order. Therefore, the function representing the sixth term of the Zernike term is a function in which the maximum degree of pupil coordinates is second order and even order.

Table 3 shows a summary of the first to ninth terms.

The second term of Equation (2) is a term obtained by multiplying B _2jl (Ox, Oy) by ρx. Therefore, the second term of Equation (2) is a term obtained by multiplying B _2jl (Ox, Oy) by a function having an odd-order pupil coordinate.

The sixth term of Equation (2) is a term obtained by multiplying B _6jl (Ox, Oy) by ρxρy. Therefore, the sixth term of Equation (2) is a term obtained by multiplying B _6jl (Ox, Oy) by a function having an even-order pupil coordinate.

Table 4 shows an explanation of each term in the formula (2).

Thus, decentering aberration sensitivity _{B jl (Ox, Oy, ρx} , ρy) when deployed with Zernike polynomials, each term of the polynomial, the term pupil coordinate is multiplied by the odd order function, the pupil coordinate is an even number It is divided into a term multiplied by a function of order.

Further, the decentration aberration sensitivity B _zjl (Ox, Oy) can also be developed by a polynomial expression. However, the expansion formula differs between a term multiplied by a function of odd-order pupil coordinates and a term multiplied by a function of even-order pupil coordinates.

The description will be made separately for the case where the subscript l in the decentering aberration sensitivity B _zjl (Ox, Oy) is l = 1 and l = 2.

When l = 1, the decentration aberration sensitivity B _zj1 (Ox, Oy) is the decentration aberration sensitivity of the term multiplied by the Z term of the Zernike term, and is decentered in proportion to the first power of the decentration amount on the j th surface. It represents the aberration sensitivity.

_Decentration aberration sensitivity B _zj1 (Ox, Oy) of a term whose pupil coordinates are multiplied by an odd-order function will be described. This decentering aberration sensitivity B _zj1 (Ox, Oy) is _multiplied by the second term, the third term, the seventh term, the eighth term, etc. (hereinafter referred to as “the second term of the Zernike term, etc.”) of the Zernike term. The decentration aberration sensitivity of the given term. This decentering aberration sensitivity B _zj1 (Ox, Oy) (z = 2, 3, 7, 8,...) Is expressed by the following equation (3).
B _zj1 (Ox, Oy) ＝ C _zj100 + C _zj120 Ox ² + C _zj111 OxOy + C _zj102 Oy ² + (3)

As shown in Equation (3), the decentration aberration sensitivity B _zj1 (Ox, Oy) of the term multiplied by the second term of the Zernike term, etc. Is an even function.

_Decentration aberration sensitivity B _zj1 (Ox, Oy) of a term whose pupil coordinates are multiplied by an even-order function will be described. This decentration aberration sensitivity B _zj1 (Ox, Oy) is the first term, the fourth term, the fifth term, the sixth term, the ninth term, etc. of the Zernike term (referred to as “the fourth term of the Zernike term, etc.”). Is the decentration aberration sensitivity of the term multiplied by. This decentering aberration sensitivity B _zj1 (Ox, Oy) (z = 1, 4, 5, 6, 9...) Is expressed by the following equation (4).
B _zj1 (Ox, Oy) = C _zj110 Ox + C _zj101 Oy + C _zj130 Ox ³ + C _zj121 Ox ² Oy
+ C _zj112 OxOy ² + C _zj103 Oy ³ + ... (4)

As shown in Equation (4), in the decentration aberration sensitivity proportional to the first power of the decentering amount, the decentration aberration sensitivity B _zj1 (Ox, Oy) of the term multiplied by the fourth term of the Zernike term is the object high coordinate. Is an odd function.

When l = 2, the decentration aberration sensitivity B _zj2 (Ox, Oy) is the decentration aberration sensitivity of the term multiplied by the Z term of the Zernike term, and is decentered in proportion to the square of the decentration amount on the j th surface. It represents the aberration sensitivity.

_Decentration aberration sensitivity B _zj1 (Ox, Oy) of a term whose pupil coordinates are multiplied by an odd-order function will be described. The decentration aberration sensitivity B _zj2 (Ox, Oy) is the decentration aberration sensitivity of a term multiplied by the second term of the Zernike term. The decentration aberration sensitivity B _zj2 (Ox, Oy) (z = 2, 3, 7, 8,...) Is expressed by the following equation (5).
B _zj2 (Ox, Oy) = C _zj210 Ox + C _zj201 Oy + C _zj230 Ox ³ + C _zj221 Ox ² Oy
+ C _zj212 OxOy ² + C _zj203 Oy ³ + ... (5)

As shown in Equation (5), in the decentration aberration sensitivity proportional to the square of the decentering amount, the decentration aberration sensitivity B _zj2 (Ox, Oy) of the term multiplied by the second term of the Zernike term is the object high coordinate. Is an odd function.

_Decentration aberration sensitivity B _zj1 (Ox, Oy) of a term whose pupil coordinates are multiplied by an even-order function will be described. The decentration aberration sensitivity B _zj2 (Ox, Oy) is the decentration aberration sensitivity of a term multiplied by the fourth term of the Zernike term. This decentering aberration sensitivity B _zj2 (Ox, Oy) (z = 1, 4, 5, 6, 9...) Is expressed by the following equation (6).
B _zj2 (Ox, Oy) ＝ C _zj200 + C _zj220 Ox ² + C _zj211 OxOy + C _zj202 Oy ² + (6)

As shown in equation (6), in the decentration aberration sensitivity proportional to the square of the decentering amount, the decentration aberration sensitivity B _zj2 (Ox, Oy) of the term multiplied by the fourth term of the Zernike term is the object high coordinate. Is an even function.

  In Expressions (3) to (6), C is a constant that does not depend on the object height coordinates, pupil coordinates, and eccentricity. The subscripts in C indicate the Z-th term of the Zernike term, the j-th surface, the value of l, the order at the object height coordinate Ox, and the order at the object height coordinate Oy in order from the left side.

As described above, the decentration aberration sensitivity B _zjl (Ox, Oy) is divided into an odd function for the object height coordinate and an even function for the object height coordinate, depending on conditions.

  As described above, aberration occurs due to the decentering of the lens surface in the test optical system. The generated aberration appears as wavefront aberration. Thus, the decentering of the lens surface and the aberration are closely related. The wavefront aberration is expressed by the amount of decentration and the decentration aberration sensitivity. Therefore, the amount of decentration can be obtained from the wavefront aberration and the decentration aberration sensitivity.

  The eccentricity measuring method of the present embodiment (hereinafter referred to as “the measuring method of the present embodiment”) will be described.

  The decentering amount measuring method of this embodiment is a method for measuring the amount of decentering by irradiating a test optical system arranged on a measurement axis with a light beam, and based on the light beam emitted from the test optical system. An acquisition step of acquiring data, a first extraction step of extracting a predetermined aberration component from the wavefront data, a second extraction step of extracting the first aberration component from the predetermined aberration component, and a first aberration component An analysis step of analyzing simultaneous linear equations for decentration aberration sensitivity and decentering amount, wherein the predetermined aberration component is an aberration component including an aberration component caused by decentration, and the first aberration component is predetermined Among the aberration components, the aberration component is proportional to the first power of the decentering amount, and the decentering aberration sensitivity is an aberration sensitivity proportional to the first power of the decentering amount.

  A flowchart of the measurement method of this embodiment is shown in FIG. The measurement method of this embodiment is a method of measuring the amount of eccentricity by irradiating a test optical system arranged on a measurement axis with a light beam. For this purpose, the measurement method of the present embodiment includes step S100, step S200, step S300, and step S400.

  Step S100 is an acquisition process. As described above, the test optical system is irradiated with the light beam. The light beam applied to the test optical system passes through the test optical system and exits from the test optical system. In step S100, wavefront data WFD is acquired based on the light beam emitted from the test 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. This predetermined aberration component is an aberration component including an aberration component caused by decentration.

  In a state where the lens surface is decentered in the test optical system (hereinafter referred to as “decentered state”), the wavefront of the light beam emitted from the test optical system includes wavefront aberration caused by the decentering. The wavefront data WFD is not data indicating the wavefront aberration itself, but includes information on the wavefront aberration.

  Wavefront aberration is the sum of various types of aberrations. In step S200, the amount of aberration in each aberration can be obtained by analyzing the wavefront data WFD. In this analysis, a polynomial is used. An example of the polynomial is a Zernike polynomial.

  When the wavefront aberration W is developed using the Zernike polynomial, the wavefront aberration W is expressed by the following equation (7). Here, the wavefront aberration is developed using up to the ninth term of the Zernike term.

W (Ox, Oy, ρx, ρy, Δ ₁ , Δ ₂ , ..., Δ _j )
= 1 ・ W ₁ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
+ ρx ・ W ₂ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
+ ρy · W ₃ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
+ {2 (ρx ² + ρy ² ) -1} · W ₄ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
+ (ρx ² -ρy ² ) ・ W ₅ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
+ 2ρxρy · W ₆ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
+ {3 (ρx ² + ρy ² ) ρx-2ρx} · W ₇ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
+ {3 (ρx ² + ρy ² ) ρy-2ρy} · W ₈ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
+ {6 (ρx ² + ρy ² ) ² -6 (ρx ² + ρy ² ) +1} · W ₉ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= f ₁ (ρx, ρy) ・ W ₁ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
+ f ₂ (ρx, ρy) ・ W ₂ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
+ f ₃ (ρx, ρy) ・ W ₃ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
+ f ₄ (ρx, ρy) ・ W ₄ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
+ f ₅ (ρx, ρy) ・ W ₅ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
+ f ₆ (ρx, ρy) ・ W ₆ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
+ f ₇ (ρx, ρy) ・ W ₇ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
+ f ₈ (ρx, ρy) ・ W ₈ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
+ f ₉ (ρx, ρy) ・ W ₉ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j ) (7)
here,
W _{1 to} W ₉ are aberration components,
f ₁ (ρx, ρy) to f ₉ (ρx, ρy) are functions representing Zernike terms,
It is.

Here, the wavefront aberration W _M obtained by analyzing the wavefront data WFD is known. Therefore, by changing W _{1 to} W ₉ in Equation (7), a combination of W _{1 to} W ₉ that minimizes the difference between the wavefront aberration W and the wavefront aberration W _M is obtained.

On the other hand, as described above, the wavefront aberration W can be expressed by Expression (1). Equation (1) is again shown below.
W (Ox, Oy, ρx, ρy, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₁₁ (Ox, Oy, ρx, ρy)
+ Δ ₁ ² B ₁₂ (Ox, Oy, ρx, ρy)
+ Δ ₂ B ₂₁ (Ox, Oy, ρx, ρy)
+ Δ ₂ ² B ₂₂ (Ox, Oy, ρx, ρy)
+ ...
+ Δ _j B _j1 (Ox, Oy, ρx, ρy)
+ Δ _j ² B _j2 (Ox, Oy, ρx, ρy) (1)

Further, the eccentric aberration sensitivity _{B jl (Ox, Oy, ρx} , ρy) can be expanded as shown in Equation (2 '). In Equation (2 ′), the Zernike term is represented by f _z (ρx, ρy). In addition, description is omitted for the fifth to eighth terms and the tenth term or more of the Zernike term.

_{B jl (Ox, Oy, ρx} , ρy)
= f ₁ (ρx, ρy) ・ B _1jl (Ox, Oy) + f ₂ (ρx, ρy) ・ B _2jl (Ox, Oy) + f ₃ (ρx, ρy) ・ B _3jl (Ox, Oy)
+ f ₄ (ρx, ρy) ・ B _4jl (Ox, Oy) + ・ ・ ・ + f ₉ (ρx, ρy) ・ B _9jl (Ox, Oy) (2 ')

When Expression (2 ′) is substituted into Expression (1), the following Expression (1-1) is obtained.
W (Ox, Oy, ρx, ρy, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ (f ₁ (ρx, ρy) ・ B ₁₁₁ (Ox, Oy) + f ₂ (ρx, ρy) ・ B ₂₁₁ (Ox, Oy) + f ₃ (ρx, ρy) ・ B ₃₁₁ (Ox, Oy )
+ f ₄ (ρx, ρy) ・ B ₄₁₁ (Ox, Oy) + ・ ・ ・ + f ₉ (ρx, ρy) ・ B ₉₁₁ (Ox, Oy)}
+ Δ ₁ ² (f ₁ (ρx, ρy) ・ B ₁₁₂ (Ox, Oy) + f ₂ (ρx, ρy) ・ B ₂₁₂ (Ox, Oy) + f ₃ (ρx, ρy) ・ B ₃₁₂ (Ox, Oy)
+ f ₄ (ρx, ρy) ・ B ₄₁₂ (Ox, Oy) + ・ ・ ・ + f ₉ (ρx, ρy) ・ B ₉₁₂ (Ox, Oy)}
+ Δ ₂ (f ₁ (ρx, ρy) ・ B ₁₂₁ (Ox, Oy) + f ₂ (ρx, ρy) ・ B ₂₂₁ (Ox, Oy) + f ₃ (ρx, ρy) ・ B ₃₂₁ (Ox, Oy )
+ f ₄ (ρx, ρy) ・ B ₄₂₁ (Ox, Oy) + ・ ・ ・ + f ₉ (ρx, ρy) ・ B ₉₂₁ (Ox, Oy)}
+ Δ ₂ ² (f ₁ (ρx, ρy) ・ B ₁₂₂ (Ox, Oy) + f ₂ (ρx, ρy) ・ B ₂₂₂ (Ox, Oy) + f ₃ (ρx, ρy) ・ B ₃₂₂ (Ox, Oy)
+ f ₄ (ρx, ρy) ・ B ₄₂₂ (Ox, Oy) + ・ ・ ・ + f ₉ (ρx, ρy) ・ B ₉₂₂ (Ox, Oy)}
+ ...
+ Δ _j (f ₁ (ρx, ρy) ・ B _1j1 (Ox, Oy) + f ₂ (ρx, ρy) ・ B _2j1 (Ox, Oy) + f ₃ (ρx, ρy) ・ B _3j1 (Ox, Oy )
+ f ₄ (ρx, ρy) ・ B _4j1 (Ox, Oy) + ・ ・ ・ + f ₉ (ρx, ρy) ・ B _9j1 (Ox, Oy)}
+ Δ _j ² (f ₁ (ρx, ρy) ・ B _1j2 (Ox, Oy) + f ₂ (ρx, ρy) ・ B _2j2 (Ox, Oy) + f ₃ (ρx, ρy) ・ B _3j2 (Ox, Oy)
+ f ₄ (ρx, ρy) ・ B _4j2 (Ox, Oy) + ・ ・ ・ + f ₉ (ρx, ρy) ・ B _9j2 (Ox, Oy)}
(1-1)

In Expression (1-1), the first of the subscript “f” and the subscript “B” both represents the Zernike term number. Therefore, when the Zernike terms are numbered together, equation (1-2) is obtained.
W (Ox, Oy, ρx, ρy, Δ ₁ , Δ ₂ , ..., Δ _j )
= f ₁ (ρx, ρy) ・ [{Δ ₁ B ₁₁₁ (Ox, Oy) + Δ ₂ B ₁₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _1j1 (Ox, Oy)}
+ {Δ ₁ ² B ₁₁₂ (Ox, Oy) + Δ ₂ ² B ₁₂₂ (Ox, Oy) + ・ ・ ・ + Δ _j ² B _1j2 (Ox, Oy)}]
+ f ₂ (ρx, ρy) ・ [{Δ ₁ B ₂₁₁ (Ox, Oy) + Δ ₂ B ₂₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _2j1 (Ox, Oy)}
+ {Δ ₁ ² B ₂₁₂ (Ox, Oy) + Δ ₂ ² B ₂₂₂ (Ox, Oy) + ・ ・ ・ + Δ _j ² B _2j2 (Ox, Oy)}]
+ f ₃ (ρx, ρy) ・ [{Δ ₁ B ₃₁₁ (Ox, Oy) + Δ ₂ B ₃₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _3j1 (Ox, Oy)}
+ {Δ ₁ ² B ₃₁₂ (Ox, Oy) + Δ ₂ ² B ₃₂₂ (Ox, Oy) + ・ ・ ・ + Δ _j ² B _3j2 (Ox, Oy)}]
+ f ₄ (ρx, ρy) ・ [{Δ ₁ B ₄₁₁ (Ox, Oy) + Δ ₂ B ₄₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _4j1 (Ox, Oy)}
+ {Δ ₁ ² B ₄₁₂ (Ox, Oy) + Δ ₂ ² B ₄₂₂ (Ox, Oy) + ・ ・ ・ + Δ _j ² B _4j2 (Ox, Oy)}]
+ ...
+ f ₉ (ρx, ρy) ・ [{Δ ₁ B ₉₁₁ (Ox, Oy) + Δ ₂ B ₉₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _9j1 (Ox, Oy)}
+ {Δ ₁ ² B ₉₁₂ (Ox, Oy) + Δ ₂ ² B ₉₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j ² B _9j2 (Ox, Oy)}]
(1-2)

From the equations (7) and (1-2), the following equations (8-1) to (8-9) are obtained.
W ₁ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= [{Δ ₁ B ₁₁₁ (Ox, Oy) + Δ ₂ B ₁₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _1j1 (Ox, Oy)}
+ {Δ ₁ ² B ₁₁₂ (Ox, Oy) + Δ ₂ ² B ₁₂₂ (Ox, Oy) +... + Δ _j ² B _1j2 (Ox, Oy)}] (8-1)
W ₂ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= [{Δ ₁ B ₂₁₁ (Ox, Oy) + Δ ₂ B ₂₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _2j1 (Ox, Oy)}
+ {Δ ₁ ² B ₂₁₂ (Ox, Oy) + Δ ₂ ² B ₂₂₂ (Ox, Oy) + ... + Δ _j ² B _2j2 (Ox, Oy)}] (8-2)
W ₃ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= [{Δ ₁ B ₃₁₁ (Ox, Oy) + Δ ₂ B ₃₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _3j1 (Ox, Oy)}
+ {Δ ₁ ² B ₃₁₂ (Ox, Oy) + Δ ₂ ² B ₃₂₂ (Ox, Oy) + ・ ・ ・ + Δ _j ² B _3j2 (Ox, Oy)}] (8-3)
W ₄ (Ox, OyΔ ₁ , Δ ₂ , ..., Δ _j )
= [{Δ ₁ B ₄₁₁ (Ox, Oy) + Δ ₂ B ₄₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _4j1 (Ox, Oy)}
+ {Δ ₁ ² B ₄₁₂ (Ox, Oy) + Δ ₂ ² B ₄₂₂ (Ox, Oy) + ・ ・ ・ + Δ _j ² B _4j2 (Ox, Oy)}] (8-4)
W ₅ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= [{Δ ₁ B ₅₁₁ (Ox, Oy) + Δ ₂ B ₅₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _5j1 (Ox, Oy)}
+ {Δ ₁ ² B ₅₁₂ (Ox, Oy) + Δ ₂ ² B ₅₂₂ (Ox, Oy) + ・ ・ ・ + Δ _j ² B _5j2 (Ox, Oy)}] (8-5)
W ₆ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= [{Δ ₁ B ₆₁₁ (Ox, Oy) + Δ ₂ B ₆₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _6j1 (Ox, Oy)}
+ {Δ ₁ ² B ₆₁₂ (Ox, Oy) + Δ ₂ ² B ₆₂₂ (Ox, Oy) +... + Δ _j ² B _6j2 (Ox, Oy)}] (8-6)
W ₇ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= [{Δ ₁ B ₇₁₁ (Ox, Oy) + Δ ₂ B ₇₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _7j1 (Ox, Oy)}
+ {Δ ₁ ² B ₇₁₂ (Ox, Oy) + Δ ₂ ² B ₇₂₂ (Ox, Oy) + ・ ・ ・ + Δ _j ² B _7j2 (Ox, Oy)}] (8-7)
W ₈ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= [{Δ ₁ B ₈₁₁ (Ox, Oy) + Δ ₂ B ₈₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _8j1 (Ox, Oy)}
+ {Δ ₁ ² B ₈₁₂ (Ox, Oy) + Δ ₂ ² B ₈₂₂ (Ox, Oy) +... + Δ _j ² B _8j2 (Ox, Oy)}] (8-8)
W ₉ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= [{Δ ₁ B ₉₁₁ (Ox, Oy) + Δ ₂ B ₉₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _9j1 (Ox, Oy)}
+ {Δ ₁ ² B ₉₁₂ (Ox, Oy) + Δ ₂ ² B ₉₂₂ (Ox, Oy) + ・ ・ ・ + Δ _j ² B _9j2 (Ox, Oy)}] (8-9)

Here, the right side of the equation (8-1) to (8-9) are both composed of the terms including a term and Δ ₁ ² ~Δ _j ² comprising Δ ₁ ~Δ _j. Thus, W _{1 to} W ₉ are all expressed using terms that are multiplied by the amount of eccentricity Δ. As described above, since the term multiplied by the decentering amount Δ is the “decentration aberration component”, W _{1 to} W ₉ are all decentering aberration components.

Further, as described above, the predetermined aberration component is an aberration component including an aberration component caused by decentration. W _{1 to} W ₉ are decentration aberration components, that is, aberration components generated by decentration. Therefore, W _{1 to} W ₉ are predetermined aberration components.

As described above, by analyzing the wavefront data WFD and obtaining the wavefront aberration, that is, by obtaining the combination of W _{1 to} W _9, a predetermined aberration component can be extracted from the wavefront data WFD.

  Step S300 is a second extraction step. In the second extraction step, the first aberration component is extracted from the predetermined aberration component. This first aberration component is an aberration component proportional to the first power of the amount of decentration.

  In the measurement method of the present embodiment, as will be described later, a simultaneous linear equation for the amount of eccentricity is created, and the amount of eccentricity is obtained by solving this simultaneous linear equation. The first aberration component is used in this simultaneous linear equation.

As described above, W _{1 to} W ₉ are predetermined aberration components. However, each of W _{1 to} W ₉ is composed of an aberration component proportional to the first power of the eccentricity and an aberration component proportional to the second power of the eccentricity. In this case, the amount of decentration and the amount of aberration do not have a linear relationship.

  Therefore, an aberration component proportional to the first power of the decentering amount, that is, a first aberration component is extracted from predetermined aberration components.

The first aberration component is obtained by removing the aberration component proportional to the square of the decentering amount from the equations (8-1) to (8-9). Therefore, if the first aberration component is W _{11 to} W ₉₁ , W _{11 to} W ₉₁ are expressed by the following equations (9-1) to (9-9).
W ₁₁ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₁₁₁ (Ox, Oy) + Δ ₂ B ₁₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _1j1 (Ox, Oy) (9-1)
W ₂₁ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₂₁₁ (Ox, Oy) + Δ ₂ B ₂₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _2j1 (Ox, Oy) (9-2)
W ₃₁ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₃₁₁ (Ox, Oy) + Δ ₂ B ₃₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _3j1 (Ox, Oy) (9-3)
W ₄₁ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₄₁₁ (Ox, Oy) + Δ ₂ B ₄₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _4j1 (Ox, Oy) (9-4)
W ₅₁ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₅₁₁ (Ox, Oy) + Δ ₂ B ₅₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _5j1 (Ox, Oy) (9-5)
W ₆₁ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₆₁₁ (Ox, Oy) + Δ ₂ B ₆₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _6j1 (Ox, Oy) (9-6)
W ₇₁ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₇₁₁ (Ox, Oy) + Δ ₂ B ₇₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _7j1 (Ox, Oy) (9-7)
W ₈₁ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₈₁₁ (Ox, Oy) + Δ ₂ B ₈₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _8j1 (Ox, Oy) (9-8)
W ₉₁ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₉₁₁ (Ox, Oy) + Δ ₂ B ₉₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _9j1 (Ox, Oy) (9-9)

Here, when description of Formula (9-1)-(9-9) is simplified, it represents with the following formula | equation (10-1)-(10-9).
W ₁₁ = Δ ₁ B ₁₁₁ + Δ ₂ B ₁₂₁ +... + Δ _j B _1j1 (10-1)
W ₂₁ = Δ ₁ B ₂₁₁ + Δ ₂ B ₂₂₁ +... + Δ _j B _2j1 (10-2)
W ₃₁ = Δ ₁ B ₃₁₁ + Δ ₂ B ₃₂₁ +... + Δ _j B _3j1 (10-3)
W ₄₁ = Δ ₁ B ₄₁₁ + Δ ₂ B ₄₂₁ +... + Δ _j B _4j1 (10-4)
W ₅₁ = Δ ₁ B ₅₁₁ + Δ ₂ B ₅₂₁ +... + Δ _j B _5j1 (10−5)
W ₆₁ = Δ ₁ B ₆₁₁ + Δ ₂ B ₆₂₁ +... + Δ _j B _6j1 (10−6)
W ₇₁ = Δ ₁ B ₇₁₁ + Δ ₂ B ₇₂₁ +... + Δ _j B _7j1 (10−7)
W ₈₁ = Δ ₁ B ₈₁₁ + Δ ₂ B ₈₂₁ +... + Δ _j B _8j1 (10−8)
W ₉₁ = Δ ₁ B ₉₁₁ + Δ ₂ B ₉₂₁ + ... + Δ _j B _9j1 (10-9)

  Step S400 is an analysis process. In the analysis step, simultaneous linear equations regarding the first aberration component, the decentration aberration sensitivity, and the decentering amount are analyzed.

  When the first aberration component is extracted, the relationship between the amount of decentration and the amount of aberration can be handled linearly. Further, if the relationship between the amount of decentration and the amount of aberration can be handled linearly, even if the amount of decentration of the optical system to be tested is large as a manufacturing error, the amount of decentration can be obtained with high accuracy by solving the simultaneous linear equations described later. it can.

As can be seen from the equations (10-1) to (10-9), when the first aberration component is extracted, simultaneous linear equations can be created. Here, the left side of the equations (10-1) to (10-9) is the aberration amount. On the other hand, units of Δ _{1 to} Δ _j are lengths or angles. Accordingly, in order to satisfy the expressions (10-1) to (10-9), for example, the unit of B ₁₁₁ is “aberration amount / length” or “aberration amount / angle”.

“Aberration amount / length” represents the amount of aberration generated when a single surface of the optical system to be tested is shifted by a unit decentering amount. “Aberration amount / angle” represents the amount of aberration that occurs when a single surface of the optical system under test is tilted by a unit eccentricity. Therefore, as described above, B _{111 to} B _9j1 represent the decentration aberration sensitivity.

The decentration aberration sensitivity can be calculated based on data when the test optical system is designed. Then, in the expressions (10-1) to (10-9), the first aberration component on the left side, that is, the aberration amount, and the decentration aberration sensitivity on the right side are known. Therefore, the eccentric amounts Δ _{1 to} Δ _j can be obtained by solving the simultaneous linear equations of the expressions (10-1) to (10-9).

  Note that the first aberration component is an amount proportional to the first power of the amount of decentration. Therefore, the decentration aberration sensitivity must also be an aberration sensitivity proportional to the first power of the decentration amount. Thus, the decentration aberration sensitivity proportional to the first power of the decentration amount is a change in decentration aberration per unit decentering amount of the aberration component proportional to the first power of the decentration amount.

  Here, the acquisition of the wavefront data is performed using a light beam emitted from the optical system to be detected. Therefore, the test optical system may be composed of one lens or a plurality of lenses. In addition, since the eccentricity that can be measured is shift and tilt, the lens surface may be spherical or aspherical. Moreover, since the eccentricity of the lens surface is not measured one by one, measurement can be performed in a short time.

  Thus, according to the eccentricity measuring method of the present embodiment, the eccentricity can be measured in a short time regardless of the shape of the lens surface and the number of lenses constituting the optical system.

  A preferred embodiment of the measurement method of the present embodiment will be described.

  In the measurement method of the present embodiment, in the acquisition process, light beams are irradiated from two irradiation positions, the two irradiation positions are symmetric with respect to the measurement axis, and the first extraction process is performed at one irradiation position. It is preferable to extract a predetermined aberration component from each of the wavefront data and the wavefront data at the other irradiation position.

  A flowchart of the measurement method of this embodiment is shown in FIG. In the measurement method of the present embodiment, Step S100 includes Step S110, Step S120, Step S130, and Step S140. Moreover, step S200 has step S210 and step S220.

  Step S100 is an acquisition process. The acquisition process includes step S110, step S120, step S130, and step S140.

  In the acquisition step in the measurement method of the present embodiment, the light beam is irradiated from two irradiation positions. Here, the two irradiation positions are different. FIGS. 6A and 6B are diagrams showing a state in which a test optical system is irradiated with a light beam. FIG. 6A shows irradiation from an irradiation position P, and FIG. 6B shows irradiation from an irradiation position P ′. .

  In step S110, a light source is arranged at the irradiation position P of the light projecting system 1. Here, the object height coordinate of the irradiation position P is (Ox, Oy, 0). A test light system 2 is irradiated with a light beam from a light source. A spherical wave 4 is emitted from the light source. The spherical wave 4 is incident on the test optical system 2. Since the test optical system 2 is decentered with respect to the Oz axis, a non-planar wave 7 is emitted from the test optical system 2. The Oz axis is a measurement axis.

  In step S120, wavefront data WFD is acquired. The non-planar wave 7 emitted from the test optical system 2 enters the light receiving system 3. Therefore, wavefront data WFD is acquired by the light receiving system 3.

  In step S <b> 130, a light source is arranged at the irradiation position P ′ of the light projecting system 1. Here, the object height coordinate of the irradiation position P ′ is (−Ox, −Oy, 0). A test light system 2 is irradiated with a light beam from a light source. A non-planar wave 7 ′ is emitted from the test optical system 2.

  In step S140, wavefront data WFD 'is acquired. The non-planar wave 7 ′ emitted from the test optical system 2 enters the light receiving system 3. Therefore, the wavefront data WFD ′ is acquired by the light receiving system 3.

  Here, the irradiation position P and the irradiation position P ′ are symmetric with respect to the measurement axis. However, each lens surface of the test optical system is decentered with respect to the measurement axis. Therefore, the optical path passing through the optical system to be measured is asymmetrical between the beam irradiated from the irradiation position P and the beam irradiated from the irradiation position P ′. In this case, the non-planar wave 7 and the non-planar wave 7 ′ do not have a symmetrical wavefront shape. Therefore, the wavefront data WFD and the wavefront data WFD ′ are not symmetric data.

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

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

In step S300, the first aberration component is extracted. Step S400 is executed using the extracted first aberration component. By solving the simultaneous linear equations in step S400, the eccentric amounts Δ _{1 to} Δ _j can be obtained.

  Thus, according to the eccentricity measuring method of the present embodiment, the eccentricity can be measured in a short time regardless of the shape of the lens surface and the number of lenses constituting the optical system.

  In the measurement method of the present embodiment, the predetermined aberration component includes the second aberration component, and the second aberration component is an aberration component proportional to the square of the decentering amount of the predetermined aberration component. Yes, the object height coordinate is a coordinate representing the irradiation position, the predetermined function is a function representing the second aberration component and includes the object height coordinate as a variable, and the second extraction step includes: A first calculation step and a second calculation step. In the first calculation step, when the predetermined function is an odd function, the predetermined aberration component at one irradiation position and the predetermined calculation at the other irradiation position. In the second calculation step, when the predetermined function is an even function, the difference between the predetermined aberration component at one irradiation position and the predetermined aberration component at the other irradiation position is calculated. It is preferable to take.

  A flowchart of the measurement method of this embodiment is shown in FIG. In the measurement method of the present embodiment, Step S100 includes Step S110, Step S120, Step S130, and Step S140. Moreover, step S200 has step S210 and step S220. Step S300 includes step S310, step S320, and step S330. Detailed description of step S100 and step S200 is omitted.

  Also in the measurement method of the present embodiment, the test optical system is irradiated with a light beam from two irradiation positions symmetrical with respect to the measurement axis. As a result, the wavefront data WFD and the wavefront data WFD 'can be acquired (step S100).

  Then, a predetermined aberration component is extracted from each of the wavefront data WFD and the wavefront data WFD ′ (step S200).

  Here, if the object height coordinate of one irradiation position P is (Ox, Oy), the object height coordinate of the other irradiation position P ′ is (−Ox, −Oy). The light beam irradiation is performed in the OxOy plane (Oz = 0). Therefore, only Ox and Oy are used for the object height coordinates.

The wavefront aberration W is obtained by analyzing the wavefront data WFD. In this case, since the object height coordinate of the irradiation position P is (Ox, Oy), the predetermined aberration components W _{1 to} W ₉ extracted from the wavefront aberration W are the above-described equations (8-1) to (8-9). ).

Further, the wavefront aberration W is acquired by analyzing the wavefront data WFD ′. In this case, since the irradiation position P ′ object height coordinate is (−Ox, −Oy), the predetermined aberration components W _{1 to} W ₉ extracted from the wavefront aberration W are expressed by the following equations (8-1 ′) to ( 8-9 ′).

W ₁ (-Ox, -Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= [{Δ ₁ B ₁₁₁ (-Ox, -Oy) + Δ ₂ B ₁₂₁ (-Ox, -Oy) + ・ ・ ・ + Δ _j B _1j1 (-Ox, -Oy)}
+ {Δ ₁ ² B ₁₁₂ (−Ox, −Oy) + Δ ₂ ² B ₁₂₂ (−Ox, −Oy) +... + Δ _j ² B _1j2 (−Ox, −Oy)}] (8-1 ')
W ₂ (-Ox, -Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= [{Δ ₁ B ₂₁₁ (-Ox, -Oy) + Δ ₂ B ₂₂₁ (-Ox, -Oy) + ・ ・ ・ + Δ _j B _2j1 (-Ox, -Oy)}
+ {Δ ₁ ² B ₂₁₂ (−Ox, −Oy) + Δ ₂ ² B ₂₂₂ (−Ox, −Oy) +... + Δ _j ² B _2j2 (−Ox, −Oy)}] (8-2 ')
W ₃ (-Ox, -Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= [{Δ ₁ B ₃₁₁ (-Ox, -Oy) + Δ ₂ B ₃₂₁ (-Ox, -Oy) + ・ ・ ・ + Δ _j B _3j1 (-Ox, -Oy)}
+ {Δ ₁ ² B ₃₁₂ (-Ox, -Oy) + Δ ₂ ² B ₃₂₂ (-Ox, -Oy) + ... + Δ _j ² B _3j2 (-Ox, -Oy)}] (8-3 ')
W ₄ (-Ox, -Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= [{Δ ₁ B ₄₁₁ (-Ox, -Oy) + Δ ₂ B ₄₂₁ (-Ox, -Oy) + ・ ・ ・ + Δ _j B _4j1 (-Ox, -Oy)}
+ {Δ ₁ ² B ₄₁₂ (-Ox, -Oy) + Δ ₂ ² B ₄₂₂ (-Ox, -Oy) + ... + Δ _j ² B _4j2 (-Ox, -Oy)}] (8-4 ')
W ₅ (−Ox, −Oy, Δ ₁ , Δ ₂ ,..., Δ _j )
= [{Δ ₁ B ₅₁₁ (-Ox, -Oy) + Δ ₂ B ₅₂₁ (-Ox, -Oy) + ・ ・ ・ + Δ _j B _5j1 (-Ox, -Oy)}
+ {Δ ₁ ² B ₅₁₂ (−Ox, −Oy) + Δ ₂ ² B ₅₂₂ (−Ox, −Oy) +... + Δ _j ² B _5j2 (−Ox, −Oy)}] (8−5 ')
W ₆ (-Ox, -Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= [{Δ ₁ B ₆₁₁ (-Ox, -Oy) + Δ ₂ B ₆₂₁ (-Ox, -Oy) + ・ ・ ・ + Δ _j B _6j1 (-Ox, -Oy)}
+ {Δ ₁ ² B ₆₁₂ (−Ox, −Oy) + Δ ₂ ² B ₆₂₂ (−Ox, −Oy) +... + Δ _j ² B _6j2 (−Ox, −Oy)}] (8-6 ')
W ₇ (-Ox, -Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= [{Δ ₁ B ₇₁₁ (-Ox, -Oy) + Δ ₂ B ₇₂₁ (-Ox, -Oy) + ・ ・ ・ + Δ _j B _7j1 (-Ox, -Oy)}
+ {Δ ₁ ² B ₇₁₂ (−Ox, −Oy) + Δ ₂ ² B ₇₂₂ (−Ox, −Oy) +... + Δ _j ² B _7j2 (−Ox, −Oy)}] (8−7 ')
W ₈ (−Ox, −Oy, Δ ₁ , Δ ₂ ,..., Δ _j )
= [{Δ ₁ B ₈₁₁ (-Ox, -Oy) + Δ ₂ B ₈₂₁ (-Ox, -Oy) + ・ ・ ・ + Δ _j B _8j1 (-Ox, -Oy)}
+ {Δ ₁ ² B ₈₁₂ (−Ox, −Oy) + Δ ₂ ² B ₈₂₂ (−Ox, −Oy) +... + Δ _j ² B _8j2 (−Ox, −Oy)}] (8−8 ')
W ₉ (-Ox, -Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= [{Δ ₁ B ₉₁₁ (-Ox, -Oy) + Δ ₂ B ₉₂₁ (-Ox, -Oy) + ・ ・ ・ + Δ _j B _9j1 (-Ox, -Oy)}
+ {Δ ₁ ² B ₉₁₂ (-Ox, -Oy) + Δ ₂ ² B ₉₂₂ (-Ox, -Oy) + ... + Δ _j ² B _9j2 (-Ox, -Oy)}] (8-9 ')

  As described above, in the measurement method of the present embodiment, two predetermined aberration components are obtained. Therefore, the first aberration component is extracted using two predetermined aberration components. This extraction is performed in step S300. Step S300 is a second extraction step.

The second extraction step, that is, the step of extracting the first aberration component will be described. Here, description will be made using the following predetermined aberration components.
W ₂ (Ox, Oy, Δ ₁ , Δ ₂ ,..., Δ _j ) and W ₂ (−Ox, −Oy, Δ ₁ , Δ ₂ ,..., Δ _j ).
W ₄ (Ox, Oy, Δ ₁ , Δ ₂ ,..., Δ _j ) and W ₄ (−Ox, −Oy, Δ ₁ , Δ ₂ ,..., Δ _j ).

W ₂ (Ox, Oy, Δ ₁ , Δ ₂ ,..., Δ _j ) and W ₂ (−Ox, −Oy, Δ ₁ , Δ ₂ ,..., Δ _j ) are respectively expressed by equations (8− 2) and the formula (8-2 ′).

W ₂ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= [{Δ ₁ B ₂₁₁ (Ox, Oy) + Δ ₂ B ₂₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _2j1 (Ox, Oy)}
+ {Δ ₁ ² B ₂₁₂ (Ox, Oy) + Δ ₂ ² B ₂₂₂ (Ox, Oy) + ... + Δ _j ² B _2j2 (Ox, Oy)}] (8-2)
W ₂ (-Ox, -Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= [{Δ ₁ B ₂₁₁ (-Ox, -Oy) + Δ ₂ B ₂₂₁ (-Ox, -Oy) + ・ ・ ・ + Δ _j B _2j1 (-Ox, -Oy)}
+ {Δ ₁ ² B ₂₁₂ (−Ox, −Oy) + Δ ₂ ² B ₂₂₂ (−Ox, −Oy) +... + Δ _j ² B _2j2 (−Ox, −Oy)}] (8-2 ')

As described above, W ₂ includes an aberration component that is proportional to the first power of the decentering amount and an aberration component that is proportional to the second power of the decentering amount. Here, the aberration component proportional to the first power of the decentering amount is the first aberration component, and the aberration component proportional to the second power of the decentering amount is the second aberration component. Accordingly, the first aberration component is W ₂₁ and the second aberration component is W ₂₂ .

Table 5 shows the terms in the first aberration component W ₂₁ for the expressions (8-2) and (8-2 ′). For simplicity, W ₂₁ is represented only by the object height coordinates.

Table 6 shows the terms in the second aberration component W ₂₂ for the expressions (8-2) and (8-2 ′).

B _2j1 (Ox, Oy) and B _2j1 ( _-Ox , -Oy) in Table 5 are the decentration aberration sensitivities of the term multiplied by the second term of the Zernike term, and are the first power of the decentration amount on the j-th surface. The decentration aberration sensitivity proportional to is expressed.

In this case, as described above, the decentration aberration sensitivity B _zj1 (Ox, Oy) (z = 2, 3, 7, 8,...) _Of the term multiplied by the second term of the Zernike term is expressed by the equation (3). ). Equation (3) is again shown below.
B _zj1 (Ox, Oy) ＝ C _zj100 + C _zj120 Ox ² + C _zj111 OxOy + C _zj102 Oy ² + (3)

Therefore, B _2j1 (Ox, Oy) and B _2j1 ( _−Ox , −Oy) are expressed by equations (3 ′) and (3 ″) as follows from equation (3).
B _2j1 (Ox, Oy) = C _2j100 + C _2j120 Ox ² + C _2j111 OxOy + C _2j102 Oy ² + ... (3 ')
B _2j1 ( _-Ox , -Oy) = C _2j100 + C _2j120 Ox ² + C _2j111 OxOy + C _2j102 Oy ² + ... (3 ”)

As a result, B _2j1 ( _−Ox , −Oy) = B _2j1 (Ox, Oy). Thus, in the decentration aberration sensitivity proportional to the first power of the decentration amount, the decentration aberration sensitivity B _2j1 (Ox, Oy) of the term multiplied by the second term of the Zernike term is an even function with respect to the object height coordinate. It has become.

On the other hand, B _2j2 (Ox, Oy) and B _2j2 ( _-Ox , -Oy) in Table 6 are the decentration aberration sensitivity of the term multiplied by the second term of the Zernike term, and the amount of decentration on the j-th surface. It shows the decentration aberration sensitivity proportional to the square.

In this case, as described above, the decentration aberration sensitivity B _zj2 (Ox, Oy) (z = 2, 3, 7, 8,...) _Of the term multiplied by the second term of the Zernike term is expressed by the equation (5). ). Equation (5) is again shown below.
B _zj2 (Ox, Oy) = C _zj210 Ox + C _zj201 Oy + C _zj230 Ox ³ + C _zj221 Ox ² Oy
+ C _zj212 OxOy ² + C _zj203 Oy ³ + ... (5)

Therefore, B _2j2 (Ox, Oy) and B _2j2 ( _−Ox , −Oy) are expressed by the following equations (5 ′) and (5 ″) from the equation (5).
B _2j2 (Ox, Oy) = C _2j210 Ox + C _2j201 Oy + C _2j230 Ox ³ + C _2j221 Ox ² Oy
+ C _2j212 OxOy ² + C _2j203 Oy ³ + ... (5 ')
B _2j2 ( _-Ox , -Oy) =-C _2j210 Ox-C _2j201 Oy-C _2j230 Ox ³ -C _2j221 Ox ² Oy
-C _2j212 OxOy ² -C _2j203 Oy ³ _-...
=-{C _2j210 Ox + C _2j201 Oy + C _2j230 Ox ³ + C _2j221 Ox ² Oy
+ C _2j212 OxOy ² + C _2j203 Oy ³ + ...} (5 ”)

As a result, B _2j2 ( _−Ox , −Oy) = − B _2j2 (Ox, Oy). Thus, in the decentration aberration sensitivity proportional to the square of the decentration amount, the decentration aberration sensitivity B _2j2 (Ox, Oy) of the term multiplied by the second term of the Zernike term is an odd function with respect to the object high coordinate. It has become.

_{B 2j1 (-Ox, -Oy) =} B 2j1 (Ox, Oy) of the first aberration component W ₂₁ when the reflecting shown in Table 7. As can be seen from Table 7, when the two irradiation positions are symmetrical, that is, when the object height coordinates are (Ox, Oy) and (−Ox, −Oy), W ₂₁ (−Ox, −Oy) = W ₂₁ (Ox, Oy). As described above, the first aberration component W ₂₁ is an even function with respect to the object height coordinate.

_{Also, B 2j2 (-Ox, -Oy)} = - shows _B 2j2 (Ox, Oy) of the second aberration component W ₂₂ when the reflected in Table 8. As can be seen from Table 8, when the two irradiation positions are symmetrical, W ₂₂ (−Ox, −Oy) = − W ₂₂ (Ox, Oy). As described above, the second aberration component W ₂₂ is an odd function with respect to the object height coordinate.

On the other _{hand, W 4 (Ox, Oy,} Δ 1, Δ 2, ···, Δ j) and _{W 4 (-Ox, -Oy, Δ} 1, Δ 2, ···, Δ j) , respectively, wherein It is represented by (8-4) and Formula (8-4 ′).
W ₄ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= [{Δ ₁ B ₄₁₁ (Ox, Oy) + Δ ₂ B ₄₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _4j1 (Ox, Oy)}
+ {Δ ₁ ² B ₄₁₂ (Ox, Oy) + Δ ₂ ² B ₄₂₂ (Ox, Oy) + ・ ・ ・ + Δ _j ² B _4j2 (Ox, Oy)}] (8-4)
W ₄ (-Ox, -Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= [{Δ ₁ B ₄₁₁ (-Ox, -Oy) + Δ ₂ B ₄₂₁ (-Ox, -Oy) + ・ ・ ・ + Δ _j B _4j1 (-Ox, -Oy)}
+ {Δ ₁ ² B ₄₁₂ (-Ox, -Oy) + Δ ₂ ² B ₄₂₂ (-Ox, -Oy) + ... + Δ _j ² B _4j2 (-Ox, -Oy)}] (8-4 ')

As described above, W ₄ includes an aberration component that is proportional to the first power of the decentering amount and an aberration component that is proportional to the second power of the decentering amount. Here, the aberration component proportional to the first power of the decentering amount is the first aberration component, and the aberration component proportional to the second power of the decentering amount is the second aberration component. Therefore, the first aberration component is W ₄₁ , and the second aberration component is W ₄₂ .

Table 9 shows terms in the first aberration component W ₄₁ for the expressions (8-4) and (8-4 ′). For simplicity, W ₄₁ is represented only by the object height coordinates.

Further, Table 10 shows each term in the second aberration component W ₄₂ for Expression (8-4) and Expression (8-4 ′).

B _4j1 (Ox, Oy) and B _4j1 ( _-Ox , -Oy) in Table 10 are the decentration aberration sensitivity of the term multiplied by the fourth term of the Zernike term, and are the first power of the decentering amount on the j-th surface. The decentration aberration sensitivity proportional to is expressed.

In this case, as described above, the decentration aberration sensitivity B _zjl (Ox, Oy) (z = 1, 4, 5, 6, 9...) _Of the term multiplied by the fourth term of the Zernike term is It is represented by (4). Equation (4) is again shown below.
B _zj1 (Ox, Oy) = C _zj110 Ox + C _zj101 Oy + C _zj130 Ox ³ + C _zj121 Ox ² Oy
+ C _zj112 OxOy ² + C _zj103 Oy ³ + ... (4)

Therefore, B _4j1 (Ox, Oy) and B _4j1 ( _−Ox , −Oy) are expressed by equations (4 ′) and (4 ″) as follows from equation (4).
B _4j1 (Ox, Oy) = C _4j110 Ox + C _4j101 Oy + C _4j130 Ox ³ + C _4j121 Ox ² Oy
+ C _4j112 OxOy ² + C _4j103 Oy ³ + ... (4 ')
B _4j1 ( _-Ox , -Oy) =-C _4j110 Ox-C _4j101 Oy-C _4j130 Ox ³ -C _4j121 Ox ² Oy
-C _4j112 OxOy ² -C _4j103 Oy ³ _-...
=-{C _4j110 Ox + C _4j101 Oy + C _4j130 Ox ³ + C _4j121 Ox ² Oy
+ C _4j112 OxOy ² + C _4j103 Oy ³ + ...} (4 ”)

As a result, B _4j1 ( _−Ox , −Oy) = − B _4j1 (Ox, Oy). Thus, in the decentration aberration sensitivity proportional to the first power of the decentration amount, the decentration aberration sensitivity B _4j1 (Ox, Oy) of the term multiplied by the fourth term of the Zernike term is an odd function with respect to the object high coordinate. It has become.

On the other hand, B _4j2 (Ox, Oy) and B _4j2 ( _-Ox , -Oy) in Table 11 are the decentration aberration sensitivity of the term multiplied by the fourth term of the Zernike term, and the amount of decentration on the j-th surface. It shows the decentration aberration sensitivity proportional to the square.

In this case, as described above, the decentration aberration sensitivity B _zj2 (Ox, Oy) (z = 1, 4, 5, 6, 9...) _Of the term multiplied by the fourth term of the Zernike term is It is represented by (6). Equation (6) is again shown below.
B _zj2 (Ox, Oy) ＝ C _zj200 + C _zj220 Ox ² + C _zj211 OxOy + C _zj202 Oy ² + (6)

Therefore, B _4j2 (Ox, Oy) and B _4j2 ( _−Ox , −Oy) are expressed by the following equations (6 ′) and (6 ″) from the equation (6).
B _4j2 (Ox, Oy) = C _4j200 + C _4j220 Ox ² + C _4j211 OxOy + C _4j202 Oy ² + ... (6 ')
B _4j2 ( _-Ox , -Oy) = C _4j200 + C _4j220 Ox ² + C _4j211 OxOy + C _4j202 Oy ² + ... (6 ”)

As a result, B _4j2 ( _−Ox , −Oy) = B _4j2 (Ox, Oy). Thus, in the decentration aberration sensitivity proportional to the square of the decentering amount, the decentration aberration sensitivity B _4j2 (Ox, Oy) of the term multiplied by the fourth term of the Zernike term is an even function with respect to the object height coordinate. It has become.

_{B 4j1 (-Ox, -Oy) =} - B 4j1 (Ox, Oy) of the first aberration component W ₄₁ when the reflecting shown in Table 11. As can be seen from Table 11, when the two irradiation positions are symmetric, W ₄₁ (−Ox, −Oy) = − W ₄₁ (Ox, Oy). Thus, the first aberration component W ₄₁ is an odd function with respect to the object height coordinate.

Also shows _{B 4j2 (-Ox, -Oy) =} B 4j2 (Ox, Oy) of the second aberration component w ₄₂ when reflected in Table 12. As can be seen from Table 12, when the two irradiation positions are symmetric, W ₄₂ (−Ox, −Oy) = W ₄₂ (Ox, Oy). Thus, the second aberration component W ₄₂ is a even function with respect to the object height coordinates.

As described above, in the predetermined aberration component W ₂ , the function representing the first aberration component W ₂₁ is an even function and the function representing the first aberration component W ₂₂ is an odd function. On the other hand, in the predetermined aberration component W ₄ , the function representing the first aberration component W ₄₁ is an even function and the function representing the first aberration component W ₄₂ is an odd function.

  Here, if the predetermined function is a function representing the second aberration component and the object height coordinate is a variable, the predetermined function is divided into an even function and an odd function. .

  Therefore, step S310 is executed, and different operations are performed when the predetermined function is an odd function and when the predetermined function is an even function.

In the predetermined aberration component W ₂ , since the function representing the second aberration component 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 a first calculation step.

In the first calculation step, the sum of the predetermined aberration component at one irradiation position and the predetermined aberration component at the other irradiation position is taken. That is, 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 taken.

The result of taking the sum of both is shown in Equation (11).
W ₂ (Ox, Oy, Δ ₁ , Δ ₂ ,..., Δ _j ) + W ₂ (−Ox, −Oy, Δ ₁ , Δ ₂ ,..., Δ _j )
= 2 ・ {Δ ₁ B ₂₁₁ (Ox, Oy) + Δ ₂ B ₂₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _2j1 (Ox, Oy)} (11)

Here, the first aberration component W ₂₁ is expressed by Expression (9-2). Formula (9-2) is again shown below.
W ₂₁ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₂₁₁ (Ox, Oy) + Δ ₂ B ₂₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _2j1 (Ox, Oy) (9-2)

Therefore, Expression (11 ′) is obtained from Expression (11) and Expression (9-2).
W ₂ (Ox, Oy, Δ ₁ , Δ ₂ ,..., Δ _j ) + W ₂ (−Ox, −Oy, Δ ₁ , Δ ₂ ,..., Δ _j )
= 2 ・ {Δ ₁ B ₂₁₁ (Ox, Oy) + Δ ₂ B ₂₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _2j1 (Ox, Oy)}
= 2 · W ₂₁ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j ) (11 ')

As shown in Expression (11 ′), by taking the sum of the two, the first aberration component W ₂₁ remains and the second aberration component W ₂₂ disappears. Therefore, the first aberration component W ₂₁ can be extracted from the predetermined aberration component W ₂ .

On the other hand, in the predetermined aberration component W ₄ , since the function representing 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 a second calculation step.

In the second calculation step, the difference between the predetermined aberration component at one irradiation position and the predetermined aberration component at the other irradiation position is taken. _{That, W 4 (Ox, Oy,} Δ 1, Δ 2, ···, Δ j) and _{W 4 (-Ox, -Oy, Δ} 1, Δ 2, ···, Δ j) taking the difference between. The result of taking the difference between the two is shown in equation (12).
W ₄ (Ox, Oy, Δ ₁ , Δ ₂ ,..., Δ _j ) −W ₄ (−Ox, −Oy, Δ ₁ , Δ ₂ ,..., Δ _j )
= 2 ・ {Δ ₁ B ₄₁₁ (Ox, Oy) + Δ ₂ B ₄₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _4j1 (Ox, Oy)} (12)

Here, the first aberration component W ₄₁ is expressed by Expression (9-4). Formula (9-4) is again shown below.
W ₄₁ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₄₁₁ (Ox, Oy) + Δ ₂ B ₄₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _4j1 (Ox, Oy) (9-4)

Therefore, Expression (12 ′) is obtained from Expression (12) and Expression (9-4).
W ₄ (Ox, Oy, Δ ₁ , Δ ₂ ,..., Δ _j ) −W ₄ (−Ox, −Oy, Δ ₁ , Δ ₂ ,..., Δ _j )
= 2 ・ {Δ ₁ B ₄₁₁ (Ox, Oy) + Δ ₂ B ₄₂₁ (Ox, Oy) + ・ ・ ・ + Δ _j B _4j1 (Ox, Oy)}
= 2 · W ₄₁ (Ox, Oy, Δ ₁ , Δ ₂ , ..., Δ _j ) (12 ')

As shown in the equation (12 ′), by taking the difference between the two, the first aberration component W ₄₁ remains and the second aberration component W ₄₂ disappears. Therefore, the first aberration component W ₄₁ can be extracted from the predetermined aberration component W ₄ .

Table 13 shows a summary of a case where the first aberration component W _z1 and the second aberration component W _z2 are an even function with respect to the object height coordinate and an odd function with respect to the object height coordinate. In Table 13, here, the first aberration component is represented by W _z1 and the second aberration component is represented by W _z2 .

As can be seen from Table 13, for the following predetermined aberration component, the first aberration component can be extracted from the predetermined aberration component by executing the first calculation step.
W ₃ (Ox, Oy, Δ ₁ , Δ ₂ ,..., Δ _j ) and W ₃ (−Ox, −Oy, Δ ₁ , Δ ₂ ,..., Δ _j ).
W ₇ (Ox, Oy, Δ ₁ , Δ ₂ ,..., Δ _j ) and W ₇ (−Ox, −Oy, Δ ₁ , Δ ₂ ,..., Δ _j ).
W ₈ (Ox, Oy, Δ ₁ , Δ ₂ ,..., Δ _j ) and W ₈ (−Ox, −Oy, Δ ₁ , Δ ₂ ,..., Δ _j ).
As described above, the aberration component Wz multiplied by a function such as the second term of the Zernike term is multiplied as follows (z) = 2,3,7,8 ...).
_{Wz (Ox, Oy, Δ 1} , Δ 2, ···, Δ j) + Wz (-Ox, -Oy, Δ 1, Δ 2, ···, Δ j)
= 2Δ ₁ B _z11 (Ox, Oy) + ... + 2Δ _j B _zj1 (Ox, Oy)

For the following predetermined aberration component, the first aberration component can be extracted from the predetermined aberration component by executing the second calculation step.
W ₅ (Ox, Oy, Δ ₁ , Δ ₂ ,..., Δ _j ) and W ₅ (−Ox, −Oy, Δ ₁ , Δ ₂ ,..., Δ _j ).
W ₆ (Ox, Oy, Δ ₁ , Δ ₂ ,..., Δ _j ) and W ₆ (−Ox, −Oy, Δ ₁ , Δ ₂ ,..., Δ _j ).
W ₉ (Ox, Oy, Δ ₁ , Δ ₂ ,..., Δ _j ) and W ₉ (−Ox, −Oy, Δ ₁ , Δ ₂ ,..., Δ _j ).
As described above, the aberration component Wz multiplied by the function of the even-order pupil coordinates, that is, the aberration component Wz multiplied by the function such as the fourth term of the Zernike term in Wz is as follows (z = 1,4,5,6,9 ...).
_{Wz (Ox, Oy, Δ 1} , Δ 2, ···, Δ j) -Wz (-Ox, -Oy, Δ 1, Δ 2, ···, Δ j)
= 2Δ ₁ B _z11 (Ox, Oy) + ... + 2Δ _j B _zj1 (Ox, Oy)

  Thus, when the predetermined function, that is, the function representing the second aberration component is an odd function, the first calculation step is performed. In the first calculation step, the sum of the predetermined aberration component at one irradiation position and the predetermined aberration component at the other irradiation position is taken. As a result, the first aberration component can be extracted from the predetermined aberration component.

  Further, when the predetermined function is an even function, the second calculation step is performed. In the second calculation step, the difference between the predetermined aberration component at one irradiation position and the predetermined aberration component at the other irradiation position is taken. As a result, the first aberration component can be extracted from the predetermined aberration component.

As described above, the first aberration component is extracted by executing step S300. Step S400 is executed using the extracted first aberration component. By solving the simultaneous linear equations in step S400, the eccentric amounts Δ _{1 to} Δ _j can be obtained.

  Thus, according to the eccentricity measuring method of the present embodiment, the eccentricity can be measured in a short time regardless of the shape of the lens surface and the number of lenses constituting the optical system.

  Further, in the measurement method of the present embodiment, the first aberration component can be extracted from the predetermined aberration component even when the design aberration component exists.

  In the above description, the wavefront aberration W is a deviation from the wavefront when the test optical system is not decentered. Here, the wavefront aberration W is described as a deviation from an ideal wavefront such as a plane wave or a spherical wave.

  The design aberration component will be described. The test optical system in the decentration measurement is an assembled lens, a group single unit, a lens single unit, or the like. The test optical system is manufactured based on design data. In designing an optical system, a plurality of lenses are combined so as to suppress the generation of aberration as much as possible. However, it is very difficult to reduce the generation amount of all aberrations to zero. In addition, some of the assembled lenses, for example, each group alone and each lens alone generate aberrations in design.

  Therefore, the test optical system has aberration at the design stage. Therefore, if this aberration is 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 expressed by the following equation (1-3).

W (Ox, Oy, ρx, ρy, Δ ₁ , Δ ₂ , ..., Δ _j )
= M (Ox, Oy, ρx, ρy)
+ Δ ₁ B ₁₁ (Ox, Oy, ρx, ρy)
+ Δ ₁ ² B ₁₂ (Ox, Oy, ρx, ρy)
+ Δ ₂ B ₂₁ (Ox, Oy, ρx, ρy)
+ Δ ₂ ² B ₂₂ (Ox, Oy, ρx, ρy)
+ ...
+ Δ _j B _j1 (Ox, Oy, ρx, ρy)
+ Δ _j ² B _j2 (Ox, Oy, ρx, ρy) (1-3)

  This 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 as a polynomial based on the aberration theory, similarly to the decentration aberration sensitivity. For example, when the Zernike polynomial is used, the design aberration component M (Ox, Oy, ρx, ρy) can be expanded by a polynomial as shown in the following equation (13).

M (Ox, Oy, ρx, ρy)
= 1 ・ M ₁ (Ox, Oy)
+ ρx ・ M ₂ (Ox, Oy)
+ ρy ・ M ₃ (Ox, Oy)
+ {2 (ρx ² + ρy ² ) -1} ・ M ₄ (Ox, Oy)
+ {ρx ² -ρy ² } ・ M ₅ (Ox, Oy)
+ 2ρxρy ・ M ₆ (Ox, Oy)
+ {3 (ρx ² + ρy ² ) ρx-2ρx} ・ M ₇ (Ox, Oy)
+ {3 (ρx ² + ρy ² ) ρy-2ρy} ・ M ₈ (Ox, Oy)
+ {6 (ρx ² + ρy ² ) ² -6 (ρx ² + ρy ² ) +1} ・ M ₉ (Ox, Oy)
+ ... (13)
here,
M ₁ (Ox, Oy) to M ₉ (Ox, Oy) are functions that depend on the object height coordinates,
It is.

Here, if a function that depends on the object height coordinate is expressed by M _z (Ox, Oy), M _z (Ox, Oy) is a function that depends on the object height coordinate and is multiplied by the Z term of the Zernike term. It is a function in the term. The Zernike term is a function that depends on the pupil coordinates. Therefore, M _z (Ox, Oy) is a function that depends on the object height coordinate, and can be said to be a function in a term multiplied by a function that depends on the pupil coordinate.

  In this way, when the design aberration component M (Ox, Oy, ρx, ρy) is expanded by a Zernike polynomial, each term of the polynomial is a term multiplied by a function whose pupil coordinate is an odd order, and the pupil coordinate is an even order. And the term multiplied by the function.

Furthermore, the function M _z (Ox, Oy) depending on the object height coordinate can also be expanded by a polynomial. However, the expansion formula differs between a term multiplied by a function of odd-order pupil coordinates and a term multiplied by a function of even-order pupil coordinates.

Terms the pupil coordinate is multiplied by the odd order of the function M _z (Ox, Oy) is the term for the second term such Zernike terms are multiplied by M _z (Ox, Oy). M _z (Ox, Oy) (z = 2, 3, 7, 8,...) In this case is expressed by the following equation (14).
M _z (Ox, Oy) ＝ C _zm10 Ox + C _zm01 Oy + C _zm30 Ox ³ + _zm21 Ox ² Oy + C _zm12 OxOy ² + C _zm03 Oy ³ + (14)

As shown in Expression (14), M _z (Ox, Oy) of a term multiplied by the second term of the Zernike term is an odd function with respect to the object high coordinate.

Terms the pupil coordinates are multiplied by the even order function M _z (Ox, Oy) is the term which is multiplied by the fourth term like Zernike term M _z (Ox, Oy). M _z (Ox, Oy) (z = 1, 4, 5, 6, 9...) In this case is expressed by the following equation (15).
M _z (Ox, Oy) = C _zm00 + C _zm20 Ox ² + C _zm11 OxOy + C _zm02 Oy ² + (15)

As shown in Expression (15), M _z (Ox, Oy) of a term multiplied by the fourth term of the Zernike term is an even function with respect to the object high coordinate.

The function representing the first aberration component, the function representing the second aberration component, and the function depending on the object height coordinate in the design aberration component (hereinafter referred to as “function representing the design aberration component”) become an even function; Table 14 shows the result of summarizing the case of an odd function.

  As described above, when the predetermined function, that is, the function representing the second aberration component is an odd function, when the first calculation step is performed, the second aberration component disappears. Here, as can be seen from Table 14, when the function representing the second aberration component is an odd function, the function representing the design aberration component is also an odd function. For this reason, when the first calculation step is performed, the design aberration component also disappears. As a result, the first aberration component can be extracted from the predetermined aberration component.

  When the predetermined function is an even function, the second aberration component disappears when the second calculation step is performed. Here, as can be seen from Table 14, when the function representing the second aberration component is an even function, the function representing the design aberration component is also an even function. For this reason, when the second calculation step is performed, the design aberration component also disappears. As a result, the first aberration component can be extracted from the predetermined aberration component.

Step S400 is executed using the extracted first aberration component. By solving the simultaneous linear equations in step S400, the eccentric amounts Δ _{1 to} Δ _j can be obtained.

  As described above, according to the decentering amount measuring method of the present embodiment, even when there is a design aberration in the test optical system, it is short regardless of the shape of the lens surface and the number of lenses constituting the optical system. The amount of eccentricity can be measured over time.

  In the measurement method of the present embodiment, the acquisition step includes a first rotation. In the first rotation, the optical system to be measured is rotated around the measurement axis, and the same irradiation position is used before the first rotation. It is preferable to acquire the wavefront data and the wavefront data after the first rotation.

  A flowchart of the measurement method of this embodiment is shown in FIG. In the measurement method of this embodiment, step S100 includes step S110, step S121, step S122, and step S150. Detailed descriptions of step S200, step S300, and step S400 are omitted.

  As described above, the wavefront data is data including information on wavefront aberration. Wavefront data is acquired by the light receiving system. For example, when the light receiving system is an interferometer, the wavefront data is phase data. When the light receiving system is a Shack-Hartmann sensor (hereinafter referred to as “SH sensor”), the wavefront data is data of the light spot image position. Details of the SH sensor will be described later.

  FIGS. 9A and 9B are diagrams for explaining system aberrations in the light projection system. FIG. 9A shows a state where no system aberration occurs, and FIG. 9B shows a state where system aberrations occur in the light projection system. . System aberration is an aberration of the measurement system itself. System aberration occurs in a light projecting system and a light receiving system.

  As shown in FIG. 9A, a light source is disposed at the irradiation position P of the light projecting system 10. When no system aberration occurs in the light projecting system 10, the spherical wave 40 is emitted from the light source. The spherical wave 40 enters the test optical system 20. Since the test optical system 20 is decentered with respect to the Oz axis, a non-planar wave 50 is emitted from the test optical system 20.

  For the wavefront of the irradiated light beam, aberration can be removed by using a spatial filter. However, sufficient removal may not be possible due to manufacturing errors. In this case, system aberration occurs in the light projecting system 10.

  When system aberration occurs in the light projecting system 10, the wavefront of the light beam applied to the test optical system 20 becomes a distorted wavefront 60, as shown in FIG. In this case, the non-planar wave 51 emitted from the test optical system 20 is different from the non-plane wave 50 when the spherical optical wave 40 is irradiated on the test optical system 20.

  10A and 10B are diagrams showing system aberrations in the light receiving system, in which FIG. 10A shows system aberrations in the sensor component constituent unit, and FIG. 10B shows system aberrations in the wavefront data acquisition unit.

  The light receiving system 30 includes, for example, a sensor component configuration unit 31 and a wavefront data acquisition unit 32. The non-planar wave 50 that has entered the light receiving system 30 reaches the wavefront data acquisition unit 32 after passing through the sensor component component 31.

  An optical system is arranged in the sensor component component 31 as necessary. For example, when it is necessary to make the diameter of the light beam incident on the light receiving system substantially coincide with the light receiving area in the wavefront data acquisition unit 32, the optical system is arranged in the sensor component constituting unit 31. In addition, an optical system is arranged in the sensor component constituent unit 31 when forming a plurality of light spot images.

  If there is a manufacturing error in this optical system, or if an error occurs in the mounting of this optical system, aberration occurs in the optical system. As a result, system aberration occurs in the sensor component component 31. In this case, system aberration is added to the non-planar wave 50. As a result, the non-planar wave 52 incident on the wavefront data acquisition unit 32 is different from the non-planar wave 50 as shown in FIG.

  Further, as described above, when the light receiving system 30 is an interferometer, interference fringes are formed in the wavefront data acquisition unit 32. When the light receiving system 30 is an SH sensor, a plurality of light spot images are formed in the wavefront data acquisition unit 32.

  Therefore, the wavefront data acquisition unit 32 divides the interference fringes into fine regions and acquires wavefront information. Alternatively, the wavefront data acquisition unit 32 detects the positions of a plurality of light spot images. Therefore, in the wavefront data acquisition unit 32, for example, minute light receiving elements 33 (hereinafter referred to as “light receiving elements”) are two-dimensionally arranged.

  When there is a manufacturing error in the wavefront data acquisition unit 32, for example, as shown in FIG. 10B, the light receiving elements 33 are not regularly arranged. Therefore, system aberration occurs in the wavefront data acquisition unit 32. Further, the size of the light receiving area of the light receiving element 33 may vary due to manufacturing errors. Also in this case, system aberration occurs in the wavefront data acquisition unit 32.

  Thus, when the light projection system 10 and the light receiving system 30 have system aberration, the system aberration is also included in the wavefront aberration. In this case, the wavefront data acquired by the light receiving system 30 is not data that accurately reflects the wavefront aberration caused by the eccentricity of the test optical system 20.

  When the system aberration component is Sys (Ox, Oy, ρx, ρy), the wavefront aberration W is expressed by the following equation (1-4). However, the wavefront aberration W here is described as a deviation from the wavefront when there is no decentering of the test optical system and no system aberration.

W (Ox, Oy, ρx, ρy, Δ ₁ , Δ ₂ , ..., Δ _j )
= Sys (Ox, Oy, ρx, ρy)
+ Δ ₁ B ₁₁ (Ox, Oy, ρx, ρy)
+ Δ ₁ ² B ₁₂ (Ox, Oy, ρx, ρy)
+ Δ ₂ B ₂₁ (Ox, Oy, ρx, ρy)
+ Δ ₂ ² B ₂₂ (Ox, Oy, ρx, ρy)
+ ...
+ Δ _j B _j1 (Ox, Oy, ρx, ρy)
+ Δ _j ² B _j2 (Ox, Oy, ρx, ρy) (1-4)

  Here, the system aberration component can be obtained in advance. FIG. 11 is a diagram showing a method for obtaining a system aberration component in advance. Here, it is assumed that system aberration occurs in the sensor component component 31.

In this method, an optical system 21 with very little aberration is used. In FIG. 11, the light beam emitted from the optical system 21 is in a state in which the angle, position, and light beam diameter incident on the light receiving system 30 coincide with the light beam emitted from the optical system 20 to be tested (FIG. 10A). Yes. That is, the irradiation position P _P , the irradiation angle, the position of the optical system 21, and the inclination of the optical system 21 with respect to the Oz axis are adjusted so as to achieve such a state.

In FIG. 11, the light source is arranged at the irradiation position P _P (0x _p , 0y _p , 0) of the light projecting system 10. Since no system aberration occurs in the light projecting system 10, the spherical wave 40 is emitted from the light source. The spherical wave 40 is incident on the optical system 21. The optical system 21 is an optical system with very little aberration. Therefore, the plane wave 53 is emitted from the optical system 21. The plane wave 53 is incident on the sensor component component 31.

  Here, system aberration in the sensor component component 31 is added to the plane wave 53. As a result, the non-planar wave 54 is emitted from the sensor component component 31. The non-planar wave 54 enters the wavefront data acquisition unit 32, and wavefront data is acquired.

The acquired wavefront data includes only system aberration information in the sensor component component 31. Therefore, the wavefront aberration W ′ obtained from this wavefront data is expressed by the following equation (16).
W ′ (Ox, Oy, ρx, ρy) = Sys (Ox, Oy, ρx, ρy) (16)

However, as described above, the light beam emitted from the optical system 21 is such that the angle, position, and light beam diameter incident on the light receiving system 30 coincide with the light beam emitted from the test optical system 20 (FIG. 10A). It has become. Therefore, the irradiation position P _P (0x _p , 0y _p , 0) of the light projecting system 10 in FIG. 11 corresponds to the irradiation position P (0x, 0y, 0) in FIG. Therefore, the object height coordinate of W ′ is represented by (0x, 0y).

Therefore, Sys (Ox, Oy, ρx, ρy) can be removed by performing the calculation of Expression (17).
W (Ox, Oy, ρx, ρy, Δ ₁ , Δ ₂ ,..., Δ _j ) −W ′ (Ox, Oy, ρx, ρy) (17)

  If there is only one irradiation position, this method can be easily performed. However, if the number of irradiation positions becomes very large, the number of data to be obtained in advance becomes enormous. Therefore, it is not easy to implement this method.

  Therefore, in the measurement method of the present embodiment, two wavefront data are acquired at the same irradiation position. For this purpose, step S100 is executed as shown in FIG.

  FIGS. 12A and 12B are diagrams showing the first rotation, in which FIG. 12A shows a state before the first rotation, and FIG. 12B shows a state after the first rotation. It is assumed that both the light projecting system and the light receiving system have system aberrations.

  In step S110, as shown in FIG. 12A, the test optical system 20 is irradiated with the light beam from the irradiation position P (Ox, Oy, 0). The wavefront 60 is incident on the test optical system 20. A non-planar wave 51 is emitted from the test optical system 20. The non-planar wave 51 includes the system aberration of the projection system 10 and the decentration aberration of the optical system 20 to be measured. The non-planar wave 51 enters the light receiving system 30. The light receiving system 30 also has system aberration. Therefore, the wavefront finally detected has the system aberration of the light projecting system 10, the decentration aberration of the optical system 20 to be measured, and the system aberration of the light receiving system 30.

  Subsequently, step S121 is executed. Thereby, wavefront data WFDθ1 is acquired. The wavefront data WFDθ1 includes information on the system aberration of the light projecting system 10, information on the decentration aberration of the test optical system 20, and information on 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 expressed by the following equation (1-5). Here, since the eccentricity of the optical system to be detected is a shift in the Y direction, the amount of eccentricity is represented by δ.

W (Ox, Oy, ρx, ρy, δ ₁ , δ ₂ , ..., δ _j )
= Sys (Ox, Oy, ρx, ρy)
+ δ ₁ B ₁₁ (Ox, Oy, ρx, ρy)
+ δ ₁ ² B ₁₂ (Ox, Oy, ρx, ρy)
+ δ ₂ B ₂₁ (Ox, Oy, ρx, ρy)
+ δ ₂ ² B ₂₂ (Ox, Oy, ρx, ρy)
+ ...
+ δ _j B _j1 (Ox, Oy, ρx, ρy)
+ δ _j ² B _j2 (Ox, Oy, ρx, ρy) (1-5)

  Next, step S150 is executed. In step S150, the first rotation is performed. In the first rotation, the test optical system 20 is rotated around the measurement axis. The rotation angle is, for example, 180 °. The position of the light projecting system 10 remains fixed. Therefore, the irradiation position P does not move. Further, the position of the light receiving system 30 remains fixed.

  After step S150 ends, step S110 is executed. In step S110, as shown in FIG. 12B, the optical system 20 is irradiated with a light beam from the irradiation position P (Ox, Oy, 0). The wavefront 60 is incident on the test optical system 20. A non-planar wave 55 is emitted from the test optical system 20. The non-plane wave 55 is different from the non-plane wave 51.

  The non-planar wave 55 includes the system aberration of the light projecting system 10 and the decentration aberration of the test optical system 20. The non-planar wave 55 enters the light receiving system 30. The light receiving system 30 also has system aberration. Therefore, the wavefront finally detected has the system aberration of the light projecting system 10, the decentration aberration of the optical system 20 to be measured, and the system aberration of the light receiving system 30.

  Subsequently, Step S122 is executed. Thereby, wavefront data WFDθ2 is acquired. The wavefront data WFDθ2 includes information on the system aberration of the light projecting system 10, information on the decentration aberration of the test optical system 20, and information on 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 expressed by the following equation (1-6).

W (Ox, Oy, ρx, ρy, -δ ₁ , -δ ₂ , ..., -δ _j )
= Sys (Ox, Oy, ρx, ρy)
+ (-δ ₁ ) B ₁₁ (Ox, Oy, ρx, ρy)
+ (-δ ₁ ) ² B ₁₂ (Ox, Oy, ρx, ρy)
+ (-δ ₂ ) B ₂₁ (Ox, Oy, ρx, ρy)
+ (-δ ₂ ) ² B ₂₂ (Ox, Oy, ρx, ρy)
+ ...
+ (-δ _j ) B _j1 (Ox, Oy, ρx, ρy)
+ (-δ _j ) ² B _j2 (Ox, Oy, ρx, ρy) (1-6)

  As described above, the system aberration component Sys (Ox, Oy, ρx, ρy) is an aberration component generated due to a manufacturing error of the light projecting system or the light receiving system. This system aberration component depends on the coordinates (Ox, Oy, ρx, ρy). If the decentered state does not change so much between the decentered state before rotating the optical system 20 and the decentered state after rotating, the system aberration component Sys (Ox, Oy, ρx, ρy) is substantially equal. It can be considered that it does not depend on the amount of eccentricity.

In the equations (1-5) and (1-6), the system aberration component is the same. Therefore, in step S200, the calculation of Expression (18) is performed. Since Sys (Ox, Oy, ρx, ρy) is removed by this calculation, a predetermined aberration component can be extracted.
W (Ox, Oy, ρx, ρy, δ ₁ , δ ₂ , ..., δ _j )
-W (Ox, Oy, ρx, ρy, -δ ₁ , -δ ₂ , ..., -δ _j ) (18)

  Here, as described above, in the measurement method of the present embodiment, two wavefront data are obtained. Therefore, the wavefront data acquired before the first rotation is referred to as reference data, and the wavefront data acquired after the first rotation is used as measurement data. In this case, the equation (18) analyzes the measurement data using the reference data as the wavefront standard. That is, the wavefront aberration expressed by the equation (18) is a deviation of the wavefront after the first rotation with respect to the wavefront before the first optical system rotates.

  For example, the change amount of the wavefront data from the reference data to the measurement data is obtained by analysis. In the case of the SH sensor, a vector to the light spot image position of the spot image for measurement is calculated based on the light spot image position of the reference spot image. There is a one-to-one correspondence between the light spot image for reference and the light spot image for measurement used in this vector calculation. Two light spot images corresponding one-to-one are light spot images formed through the same microlens array. In the case of an interferometer, the phase change amount of the phase data for measurement is calculated with reference to the phase data for reference.

  Here, the spot image is an image obtained by capturing a light spot image. The reference spot image is an image obtained by capturing a light spot image formed when the reference wavefront is incident on the SH sensor. The spot image for measurement is an image obtained by capturing a light spot image formed when the measurement wavefront is incident on the SH sensor. In the case of performing the first rotation, the reference spot image is an image obtained by capturing the light spot image in a state before the first rotation, and the measurement spot image is obtained after the first rotation. It is the image which imaged the light spot image in the state.

  In this way, final wavefront data is acquired from the reference data and the measurement data. Here, for example, when the rotation angle is 180 degrees, each lens of the test optical system is displaced by -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 represented by a spherical center. FIGS. 13A and 13B are diagrams showing how the ball center changes due to the first rotation. FIG. 13A shows the position of the ball core before the first rotation, and FIG. 13B shows the ball center after the first rotation. (C) shows the amount of movement of the ball center by the first rotation. In FIG. 13, the test optical system 22 is composed of four lens surfaces.

  As shown in FIG. 13A, in the state before the first rotation, the ball center 70, the ball center 71, the ball center 72, and the ball center 73 are located on one side of the first rotation axis. ing. When the first rotation is performed from this state, as shown in FIG. 13B, the ball center 70, the ball center 71, the ball center 72, and the ball center 73 move to the other side of the first rotation axis. . The other side is at a position opposite to the one side across the first rotation shaft.

  As shown in FIG. 13C, the eccentric amount of the sphere center with respect to the measurement axis is δ1 for the sphere center 70, δ2 for the sphere center 71, δ3 for the sphere center 72, and δ4 for the sphere center 73. Each of the spherical center 70, the spherical center 71, the spherical center 72, and the spherical center 73 is displaced by the rotation of the test optical system. This amount of displacement is -2 times the amount of eccentricity with respect to the measurement axis before rotation.

  In step S200, a predetermined aberration component is extracted from the final wavefront data. At this time, the predetermined aberration component is an amount of aberration corresponding to −2 times the amount of eccentricity with respect to the measurement axis. In this way, even when system aberration exists, it is possible to extract an amount of aberration that is -2 times the amount of eccentricity with respect to the measurement axis.

After step S200 is executed, step S300 is executed. By executing step S300, the first aberration component is extracted. Step S400 is executed using the extracted first aberration component. By solving the simultaneous linear equations in step S400, the eccentric amounts Δ _{1 to} Δ _j can be obtained.

The eccentric amounts Δ _{1 to} Δ _j at this time are −2 times the eccentric amount with respect to the measurement axis. When the amount of eccentricity obtained in step S400 is divided by -2, the amount of eccentricity with respect to the measurement axis can be obtained. Note that the amount of decentering at this time is the amount of decentering before the test optical system rotates.

  Thus, according to the eccentricity measuring method of the present embodiment, even when system aberration exists in the light projecting system and the light receiving system, regardless of the shape of the lens surface and the number of lenses constituting the optical system. The amount of eccentricity can be measured in a short time.

  When there are a plurality of lens surfaces, the amount of eccentricity between the lens surfaces may be evaluated. In this case, as shown in FIG. 13C, a new axis 80 is set so that the amount of eccentricity of the plurality of lens surfaces distributed in the space is minimized. Then, the eccentric amount of the lens surface may be evaluated using the new axis 80 as a reference.

  The new axis 80 is set by, for example, setting a temporary axis and taking the sum of squares for all lens surfaces with respect to the distance from the temporary axis to the sphere. Then, the temporary axis may be changed so that the temporary axis when the sum of squares becomes the minimum becomes a new axis. Alternatively, the sum of squares is calculated for all lens surfaces with respect to the amount obtained by dividing the distance from the temporary axis to the sphere center by the radius of curvature of the lens. Then, the temporary axis may be changed, and the temporary axis when the sum of squares is minimized may be a new axis.

  In the measurement method of the present embodiment, the design aberration component can be removed even when the design aberration component exists.

  The wavefront aberration W in the expressions (1-4), (1-5), and (1-6) has been described as a deviation from the wavefront when the test optical system is not decentered and there is no system aberration. When the wavefront aberration W is a deviation from an ideal wavefront such as a plane wave or a spherical wave, the same explanation can be made by adding the term of the design aberration component M (Ox, Oy, ρx, ρy) to W.

  The design aberration component M (Ox, Oy, ρx, ρy) is an aberration component that does not depend on the amount of decentering expressed only by the object height coordinate and the pupil coordinate. Therefore, it can be handled in the same manner as the system aberration component Sys (Ox, Oy, ρx, ρy).

  Therefore, Sys (Ox, Oy, ρx, ρy) in equation (1-5) and Sys (Ox, Oy, ρx, ρy) in equation (1-6) are respectively represented by M (Ox, Oy, ρx, ρy). Replace with In this case, the design aberration component M (Ox, Oy, ρx, ρy) is the same in the equations (1-5) and (1-6). Therefore, when the calculation of equation (18) is performed in step S200, M (Ox, Oy, ρx, ρy) is removed. As a result, a predetermined aberration component can be extracted.

  In general, the optical system to be tested has a rotationally symmetric manufacturing error such as a curvature radius error of each surface, a surface spacing error, and a refractive index error in addition to decentration. Therefore, the wavefront aberration W actually measured includes an aberration component caused by a manufacturing error. However, the wavefront aberration component caused by the rotationally symmetric manufacturing error is also an aberration component that does not depend on the amount of decentering expressed only by the object height coordinate and the pupil coordinate. Therefore, it can be handled in the same manner as the system aberration component Sys (Ox, Oy, ρx, ρy) and the design aberration component M (Ox, Oy, ρx, ρy). Therefore, even if there is a rotationally symmetric manufacturing error such as a curvature radius error, a surface distance error, and a refractive index error in each surface in the test optical system, a predetermined aberration component can be extracted.

  In 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 or a spherical wave. As shown in Expression (18), the test optical system may analyze the deviation of the wavefront after the first rotation with respect to the wavefront before the first rotation.

  Therefore, by analyzing the wavefront aberration from the deviation between the wavefront data WFDθ1 and the wavefront data WFDθ2, it is possible to remove the system aberration component and extract the predetermined aberration component.

  In the following description, similarly to the above, the deviation of the wavefront after the first rotation with respect to the wavefront before the first rotation of the optical system to be tested is analyzed. Therefore, in the following description, the method of taking the reference wavefront of the wavefront aberration W is omitted.

After step S200 is executed, step S300 is executed. By executing step S300, the first aberration component is extracted. Step S400 is executed using the extracted first aberration component. By solving the simultaneous linear equations in step S400, the eccentric amounts Δ _{1 to} Δ _j can be obtained.

  As described above, according to the decentering amount measuring method of the present embodiment, even when there is a design aberration in the test optical system, it is short regardless of the shape of the lens surface and the number of lenses constituting the optical system. The amount of eccentricity can be measured over time.

  Further, in the measurement method of the present embodiment, the aberration component of the light receiving optical system can be removed even when the light receiving optical system disposed between the test optical system and the light receiving system is decentered.

  The light receiving optical system will be described. As described above, the light beam emitted from the test optical system enters the light receiving system. Here, in order to make the diameter of the light beam incident on the light receiving system appropriate, a light receiving optical system may be arranged. FIG. 14 is a diagram illustrating a state in which the light receiving optical system is disposed between the test optical system and the light receiving system. Here, it is assumed that no system aberration or design aberration has occurred.

The light receiving optical system includes lens surfaces from the (j + 1) th lens surface to the mth lens surface. Here, when the lens surface of the light receiving optical system is decentered, aberration occurs. In FIG. 14 as well, the lens surface shift is represented using a spherical center. In FIG. 14, SC _{j + 1} , SC _{j + 2} ,..., SC _m represent the sphere centers of the lens surfaces. Further, δ _{j + 1} , δ _{j + 2} ,..., Δ _m represent the shift amount in the Y direction of each lens surface.

  When the lens surface of the receiving optical system is decentered, the wavefront aberration of the wavefront incident on the receiving system is the sum of the wavefront aberration generated by the decentering of the receiving optical system in addition to the wavefront aberration generated by the decentering of the test optical system. become. Therefore, the wavefront finally detected has the decentration aberration of the optical system to be detected and the decentration aberration of the light receiving optical system.

  Here, wavefront data WFDθ1 is acquired by executing Step S110 and Step S121. The wavefront data WFDθ1 includes information on the decentration aberration of the optical system to be measured and information on the decentration aberration of the light receiving optical system. The wavefront aberration W is obtained by analyzing the wavefront data WFDθ1. The wavefront aberration W is expressed by the following equation (1-7). Here, since the eccentricity is a shift in the Y direction, the amount of eccentricity is represented by δ.

W (Ox, Oy, ρx, ρy, δ ₁ , δ ₂ , ..., δ _j )
= δ ₁ B ₁₁ (Ox, Oy, ρx, ρy)
+ δ ₁ ² B ₁₂ (Ox, Oy, ρx, ρy)
+ δ ₂ B ₂₁ (Ox, Oy, ρx, ρy)
+ δ ₂ ² B ₂₂ (Ox, Oy, ρx, ρy)
+ ...
+ δ _j B _j1 (Ox, Oy, ρx, ρy)
+ δ _j ² B _j2 (Ox, Oy, ρx, ρy)
+ δ _{j + 1} B _{(j + 1) 1} (Ox, Oy, ρx, ρy)
+ δ _{j + 1} ² B _{(j + 1) 2} (Ox, Oy, ρx, ρy)
+ δ _{j + 2} B _{(j + 2) 1} (Ox, Oy, ρx, ρy)
+ δ _{j + 2} ² B _{(j + 2) 2} (Ox, Oy, ρx, ρy)
+ ...
+ δ _m B _m1 (Ox, Oy, ρx, ρy)
+ δ _m ² B _m2 (Ox, Oy, ρx, ρy) (1-7)

  Next, step S150 is executed. In step S150, the first rotation is performed. In the first rotation, the test optical system is rotated around the measurement axis. The rotation angle is, for example, 180 °. Note that the position of the light projecting system remains fixed. Therefore, the irradiation position P does not move. Further, the positions of the light receiving optical system and the light receiving system remain fixed.

  Subsequently, the wavefront data WFDθ2 is acquired by executing Step S110 and Step S122. The wavefront data WFDθ2 includes information on the decentration aberration of the optical system to be measured and information on the decentration aberration of the light receiving optical system. The wavefront aberration W is obtained by analyzing the wavefront data WFDθ2. The wavefront aberration W is expressed by the following equation (1-8).

W (Ox, Oy, ρx, ρy, -δ ₁ , -δ ₂ , ..., -δ _j )
= (-δ ₁ ) B ₁₁ (Ox, Oy, ρx, ρy)
+ (-δ ₁ ) ² B ₁₂ (Ox, Oy, ρx, ρy)
+ (-δ ₂ ) B ₂₁ (Ox, Oy, ρx, ρy)
+ (-δ ₂ ) ² B ₂₂ (Ox, Oy, ρx, ρy)
+ ...
+ (-δ _j ) B _j1 (Ox, Oy, ρx, ρy)
+ (-δ _j ) ² B _j2 (Ox, Oy, ρx, ρy)
+ δ _{j + 1} B _{(j + 1) 1} (Ox, Oy, ρx, ρy)
+ δ _{j + 1} ² B _{(j + 1) 2} (Ox, Oy, ρx, ρy)
+ δ _{j + 2} B _{(j + 2) 1} (Ox, Oy, ρx, ρy)
+ δ _{j + 2} ² B _{(j + 2) 2} (Ox, Oy, ρx, ρy)
+ ...
+ δ _m B _m1 (Ox, Oy, ρx, ρy)
+ δ _m ² B _m2 (Ox, Oy, ρx, ρy) (1-8)

Table 15 shows the result of comparing the decentration aberration component of the light receiving optical system with the equations (1-7) and (1-8). As can be seen from Table 15, the decentration aberration component of the light receiving optical system is the same in the equations (1-7) and (1-8).

  Therefore, in step S200, the calculation of Expression (18) is performed. Since the decentration aberration component of the light receiving optical system is removed by this calculation, a predetermined aberration component can be extracted.

After step S200 is executed, step S300 is executed. By executing step S300, the first aberration component is extracted. Step S400 is executed using the extracted first aberration component. By solving the simultaneous linear equations in step S400, the eccentric amounts Δ _{1 to} Δ _j can be obtained.

  As described above, according to the decentration amount measuring method of the present embodiment, even in the case where there is a decentered light receiving optical system, it takes a short time regardless of the shape of the lens surface and the number of lenses constituting the optical system. The amount of eccentricity can be measured.

  The case where the acquisition process includes the first rotation has been described above. Note that the execution of step S100 in FIG. 8 may be performed at a plurality of irradiation positions. For example, on the axis and on the axis, the wavefront of the light beam emitted from the test optical system is measured by the light receiving system, and the wavefront data is recorded. Thereafter, the first rotation is performed by a certain angle. Then, after the first rotation, the wavefront of the light beam emitted from the test optical system is measured by the light receiving system off-axis and on-axis, and the wavefront data is recorded. Here, the case where the irradiation position is on the measurement axis is referred to as on-axis, and the case where the irradiation position is not on the measurement axis is referred to as off-axis.

  In the measurement method of the present embodiment, the acquisition step includes a first rotation. In the first rotation, the test optical system is rotated around an axis parallel to the measurement axis, and the first irradiation position is the same at the same irradiation position. Wavefront data before one rotation and wavefront data after the first rotation can be acquired.

  In the measurement method of the present embodiment, the first rotation is performed around the first rotation axis. The first rotation axis is an axis different from the measurement axis, and is an axis that rotates the optical system to be measured about the optical axis.

FIG. 15 is a diagram illustrating a state where the first rotation axis is eccentric with respect to the measurement axis. In FIG. 15, the first rotation axis AX _R1 is shifted in the Y direction with respect to the measurement axis, that is, the Oz axis. Let E be the shift amount at this time.

  The measurement method of this embodiment also executes step S100 of the flowchart shown in FIG. First, step S110 is executed to irradiate the optical system to be examined from the irradiation position P (Ox, Oy, 0). Then, step S121 is executed to acquire the wavefront data WFDθ1. The wavefront aberration W is expressed by the following equation (1-9). Here, since the eccentricity of the optical system to be detected is a shift in the Y direction, the amount of eccentricity is represented by δ.

  In general, the magnitudes of E and δ can be suppressed to a very small amount. For terms that are proportional to the cube of the decentering amount or more, the amount of aberration in each term is considered to be very small and can be ignored. it can. Therefore, (1-9) does not include a term proportional to the cube of the eccentricity.

W (Ox, Oy, ρx, ρy, δ ₁ + E, δ ₂ + E, ..., δ _j + E)
= (δ ₁ + E) B ₁₁ (Ox, Oy, ρx, ρy)
+ (δ ₁ + E) ² B ₁₂ (Ox, Oy, ρx, ρy)
+ (δ ₂ + E) B ₂₁ (Ox, Oy, ρx, ρy)
+ (δ ₂ + E) ² B ₂₂ (Ox, Oy, ρx, ρy)
+ ...
+ (δ _j + E) B _j1 (Ox, Oy, ρx, ρy)
+ (δ _j + E) ² B _j2 (Ox, Oy, ρx, ρy) (1-9)

  Next, step S150 is executed. In step S150, the first rotation is performed. In the first rotation, the test optical system 20 is rotated around the measurement axis. The rotation angle is, for example, 180 °.

  After step S150 is completed, step S110 is executed to irradiate the optical system to be measured from the irradiation position P (Ox, Oy, 0). Then, step S122 is executed to obtain the wavefront data WFDθ2. The wavefront aberration W is expressed by the following equation (1-10).

W (Ox, Oy, ρx, ρy, -δ ₁ + E, -δ ₂ + E, ..., -δ _j + E)
= (-δ ₁ + E) B ₁₁ (Ox, Oy, ρx, ρy)
+ (-δ ₁ + E) ² B ₁₂ (Ox, Oy, ρx, ρy)
+ (-δ ₂ + E) B ₂₁ (Ox, Oy, ρx, ρy)
+ (-δ ₂ + E) ² B ₂₂ (Ox, Oy, ρx, ρy)
+ ...
+ (-δ _j + E) B _j1 (Ox, Oy, ρx, ρy)
+ (− δ _j + E) ² B _j2 (Ox, Oy, ρx, ρy) (1-10)

  Subsequently, Step S200 is executed. The wavefront data WFDθ1 acquired before the first rotation is reference data, and the wavefront data WFDθ2 acquired after the first rotation is measurement data. Therefore, the final wavefront aberration is obtained by analyzing the measurement data using the reference data as the wavefront standard.

In order to obtain the final wavefront aberration, specifically, the wavefront aberration represented by Expression (1-9) is used as reference data, and the wavefront aberration represented by Expression (1-10) is used as measurement data. The calculation of Expression (19) is performed.
W (Ox, Oy, ρx, ρy, -δ ₁ + E, -δ ₂ + E, ..., -δ _j + E)
-W (Ox, Oy, ρx, ρy, δ ₁ + E, δ ₂ + E, ..., δ _j + E) (19)

As a result, the final wavefront aberration is expressed by Expression (1-11).
W (Ox, Oy, ρx, ρy, -δ ₁ + E, -δ ₂ + E, ..., -δ _j + E)
-W (Ox, Oy, ρx, ρy, δ ₁ + E, δ ₂ + E, ..., δ _j + E)
= (-2δ ₁ ) B ₁₁ (Ox, Oy, ρx, ρy)
+ [(-δ ₁ + E) ^2- (δ ₁ + E) ² ] B ₁₂ (Ox, Oy, ρx, ρy)
+ (-2δ ₂ ) B ₂₁ (Ox, Oy, ρx, ρy)
+ [(-δ ₂ + E) ^2- (δ ₂ + E) ² ] B ₂₂ (Ox, Oy, ρx, ρy)
+ ...
+ (-2δ _j ) B _j1 (Ox, Oy, ρx, ρy)
+ [(-δ _j + E) ^2- (δ _j + E) ² ] B _j2 (Ox, Oy, ρx, ρy)
= (-2δ ₁ ) B ₁₁ (Ox, Oy, ρx, ρy)
+ (-4δ ₁ E) B ₁₂ (Ox, Oy, ρx, ρy)
+ (-2δ ₂ ) B ₂₁ (Ox, Oy, ρx, ρy)
+ (-4δ ₂ E) B ₂₂ (Ox, Oy, ρx, ρy)
+ ...
+ (-2δ _j ) B _j1 (Ox, Oy, ρx, ρy)
+ (-4δ _j E) B _j2 (Ox, Oy, ρx, ρy) (1-11)

  The wavefront aberration represented by Expression (1-11) is a deviation of the wavefront after the first rotation with respect to the wavefront before the first optical system rotates.

Here, δ ₁ and E both represent the amount of eccentricity. Therefore, it can be considered that (−4δ ₁ E) to (−4δ _j E) represent the square of the eccentricity. Table 16 shows the description of each term in the formula (1-11).

  As shown in Expression (1-11), the final wavefront aberration includes an aberration component proportional to the first power of the decentering amount and an aberration component proportional to the second power of the decentering amount, that is, the first aberration component and the second aberration. Aberration components. Thus, a predetermined aberration component is extracted by performing the calculation of Expression (19).

  The expressions (1-9) and (1-10) do not include the design aberration component, the system aberration component, and the decentration aberration component of the light receiving optical system. However, these aberration components may be included. However, these aberration components are removed by performing the calculation of equation (19). For these reasons, these aberration components are not described in the equations (1-9) and (1-10).

  Expression (1-11) includes the second aberration component. This is because the first rotation axis is shifted by the shift amount E with respect to the measurement axis. Therefore, the amount of eccentricity cannot be obtained using the equation regarding the first eccentric component as it is.

  Therefore, as shown in FIG. 7, the wavefront data before the first rotation and the wavefront data after the first rotation are acquired at the irradiation position P ′. Wavefront data before the first rotation is reference data, and wavefront data after the first rotation is measurement data. Therefore, the final wavefront aberration at the irradiation position P ′ is obtained by analyzing the measurement data using the reference data as the wavefront standard.

Since the irradiation position P ′ is symmetric with the irradiation position P, the object height coordinates are (−Ox, −Oy, 0). Therefore, the final wavefront aberration is expressed by Expression (1-12).
W (-Ox, -Oy, ρx, ρy, δ ₁ + E, δ ₂ + E, ..., δ _j + E)
-W (-Ox, -Oy, ρx, ρy, -δ ₁ + E, -δ ₂ + E, ..., -δ _j + E)
= (-2δ ₁ ) B ₁₁ (-Ox, -Oy, ρx, ρy)
+ (-4δ ₁ E) B ₁₂ (-Ox, -Oy, ρx, ρy)
+ (-2δ ₂ ) B ₂₁ (-Ox, -Oy, ρx, ρy)
+ (-4δ ₂ E) B ₂₂ (-Ox, -Oy, ρx, ρy)
+ ...
+ (-2δ _j ) B _j1 (-Ox, -Oy, ρx, ρy)
+ (-4δ _j E) B _j2 (-Ox, -Oy, ρx, ρy) (1-12)

  The wavefront aberration represented by Expression (1-12) is a deviation of the wavefront after the first rotation with respect to the wavefront before the first optical system rotates.

  As can be seen from the equations (1-11) and (1-12), the final wavefront aberration is proportional to the aberration component proportional to the first power of the decentering amount and the square of the decentering amount as the predetermined aberration component. It has an aberration component, that is, a first aberration component and a second aberration component.

  Subsequently, Step S300 is executed to extract the first aberration component. Here, the aberration component is represented by Wz. The aberration component Wz multiplied by the odd-order function of the pupil coordinates is an aberration component multiplied by the second term of the Zernike term. For this aberration component Wz (z = 2, 3, 7, 8,...), The sum of Expression (1-11) and Expression (1-12) is taken. The result is shown in equation (20).

Tz (Ox, Oy, δ _1, δ _2, ..., δ _j )
= [Wz (Ox, Oy, -δ ₁ + E, -δ ₂ + E, ..., -δ _j + E)
-Wz (Ox, Oy, δ ₁ + E, δ ₂ + E, ..., δ _j + E)]
+ [Wz (-Ox, -Oy, -δ ₁ + E, -δ ₂ + E, ..., -δ _j + E)
-Wz (-Ox, -Oy, δ ₁ + E, δ ₂ + E, ..., δ _j + E)]
= (-2δ ₁ ) [Bz ₁₁ (Ox, Oy) + Bz ₁₁ (-Ox, -Oy)]
+ (-4δ ₁ E) [Bz ₁₂ (Ox, Oy) + Bz ₁₂ (-Ox, -Oy)]
+ (-2δ ₂ ) [Bz ₂₁ (Ox, Oy) + Bz ₂₁ (-Ox, -Oy)]
+ (-4δ ₂ E) [Bz ₂₂ (Ox, Oy) + Bz ₂₂ (-Ox, -Oy)]
+ ...
+ (-2δ _j ) [Bz _j1 (Ox, Oy) + Bz _j1 (-Ox, -Oy)]
+ (-4δ _j E) [Bz _j2 (Ox, Oy) + Bz _j2 (-Ox, -Oy)] (20)

Here, Bz _j1 (−Ox, −Oy) = Bz _j1 (Ox, Oy) and Bz _j2 (−Ox, −Oy) = − Bz _j2 (Ox, Oy). Therefore, Expression (21) is obtained from Expression (20).
Tz (Ox, Oy, δ _1, δ _2, ..., δ _j )
= (-2δ ₁ ) [2Bz ₁₁ (Ox, Oy)]
+ (-2δ ₂ ) [2Bz ₂₁ (Ox, Oy)]
+ ...
+ (-2δ _j ) [2Bz _j1 (Ox, Oy)] (21)

As shown in Expression (20), by taking the sum of the two, the first aberration component remains and the second aberration component disappears. Therefore, the first aberration component Tz (Ox, Oy, δ _1, δ _2, ..., Δ _j ) can be extracted from the predetermined aberration component.

  On the other hand, the aberration component Wz multiplied by the function of even-order pupil coordinates is an aberration component multiplied by the fourth term of the Zernike term. For this aberration component Wz (z = 1, 4, 5, 6, 9...), The difference between the equations (1-11) and (1-12) is taken. The result is shown in Formula (22).

Tz (Ox, Oy, δ _1, δ _2, ..., δ _j )
= [Wz (Ox, Oy, -δ ₁ + E, -δ ₂ + E, ..., -δ _j + E)
-Wz (Ox, Oy, δ ₁ + E, δ ₂ + E, ..., δ _j + E)]
-[Wz (-Ox, -Oy, -δ ₁ + E, -δ ₂ + E, ..., -δ _j + E)
-Wz (-Ox, -Oy, δ ₁ + E, δ ₂ + E, ..., δ _j + E)]
= (-2δ ₁ ) [Bz ₁₁ (Ox, Oy) -Bz ₁₁ (-Ox, -Oy)]
+ (-4δ ₁ E) [Bz ₁₂ (Ox, Oy) -Bz ₁₂ (-Ox, -Oy)]
+ (-2δ ₂ ) [Bz ₂₁ (Ox, Oy) -Bz ₂₁ (-Ox, -Oy)]
+ (-4δ ₂ E) [Bz ₂₂ (Ox, Oy) -Bz ₂₂ (-Ox, -Oy)]
+ ...
+ (-2δ _j ) [Bz _j1 (Ox, Oy) -Bz _j1 (-Ox, -Oy)]
+ (-4δ _j E) [Bz _j2 (Ox, Oy) -Bz _j2 (-Ox, -Oy)] (22)

Here, Bz _j1 (−Ox, −Oy) = − Bz _j1 (Ox, Oy), Bz _j2 (−Ox, −Oy) = Bz _j2 (Ox, Oy). Therefore, Expression (23) is obtained from Expression (22).
Tz (Ox, Oy, δ _1, δ _2, ..., δ _j )
= (-2δ ₁ ) [2Bz ₁₁ (Ox, Oy)]
+ (-2δ ₂ ) [2Bz ₂₁ (Ox, Oy)]
+ ...
+ (-2δ _j ) [2Bz _j1 (Ox, Oy)] (23)

As shown in Expression (22), by taking the difference between the two, the first aberration component remains and the second aberration component disappears. Therefore, the first aberration component Tz (Ox, Oy, δ _1, δ _2, ..., Δ _j ) can be extracted from the predetermined aberration component.

Further, the formula (21) in equation (23), the coefficient is in the _{δ 1, δ 2, ···,} δ j. Here, as shown in FIG. 15, δ ₁ , δ ₂ ,..., Δ _j are eccentric amounts from the first rotation axis. Thus, it can be seen that the reference representing the amount of eccentricity is the first rotation axis. That is, the measurement axis is not a standard for representing the amount of eccentricity.

Subsequently, Step S400 is executed using the first aberration component Tz (Ox, Oy, δ _1, δ _2, ..., Δ _j ). In step S400, simultaneous linear equations are solved. As a result, a value that is −2 times the amount of eccentricity with respect to the first rotation axis is obtained as a solution.

As described above, the second aberration component disappears and the first aberration component is extracted, so that the displacement of each surface of the optical system to be measured and the aberration amount of the first aberration component can be handled linearly. Thus, even if the measurement axis Oz and the first rotation axis AX _R1 do not coincide with each other, the displacement amount of each surface accompanying the rotation around the first rotation axis AX _R1 of the optical system to be measured can be obtained. Therefore, the amount of eccentricity can be accurately obtained with reference to the first rotation axis.

  As described above, in the measurement method of the present embodiment, two wavefront data are acquired by rotating the optical system to be measured at an angle around the measurement axis or the first rotation axis. By analyzing the wavefront aberration using the wavefront data before the first rotation as the reference data and the wavefront data after the first rotation as the measurement data, the design aberration, the system aberration, and the decentration aberration of the light receiving optical system are reduced. Can be removed.

  Moreover, in the measurement method of this embodiment, it is preferable that the angle which rotates a test optical system is 10 degree | times or more. Furthermore, it is preferable that the angle at which the test optical system is rotated is 180 degrees.

  In the above description, the test optical system is rotated 180 degrees around the measurement axis or the first rotation axis. However, the rotation angle may be any number. A preferable rotation angle is 10 degrees or more, and a more preferable angle is 180 degrees.

  In addition, the first rotation axis may tilt with respect to the measurement axis. This point will be described.

  FIG. 16 is a diagram showing the relative relationship between the first rotation axis and the measurement axis, in which (a) shows a state in which the measurement axis and the first rotation axis coincide with each other, and (b) shows the measurement axis. The first rotating shaft is tilted.

  As described above, when the lens surface is a spherical surface, the amount of displacement of the spherical center due to the first rotation is −2 times the amount of eccentricity with respect to the measurement axis. On the other hand, when the lens surface of the test optical system 90 is an aspherical surface, the state of displacement by the first rotation is as shown in FIG. Here, as shown in FIG. 16A, the aspheric surface 91 is represented by an aspheric surface apex 92 and an aspheric surface axis 93.

When the rotation angle in the first rotation is 180 °, the displacement amount of the aspheric surface top and the displacement amount of the aspheric axis are −2 times the eccentricity with respect to the first rotation axis AX _R1 before the rotation. For example, the aspheric surface apex 92 is displaced to the position of the aspheric surface apex 92 ′ by the first rotation. In this case, the amount of displacement of the aspheric surface apex 92 is −2 × y1. Further, the displacement amount of the aspherical axis 93 is −2 × a1.

  As described above, the displacement amount of each surface accompanying rotation around the first rotation axis of the optical system to be measured can be obtained from the first aberration component. Based on this amount of displacement, the amount of eccentricity based on the first rotation axis of the optical system to be tested can be obtained. Therefore, the displacement amount of each surface accompanying the rotation of the test optical system around the first rotation axis needs to reflect the amount of eccentricity of the test optical system.

When performing the first rotation, it is desirable that the first rotation axis AX _R1 coincides with the measurement axis AX _M. However, a shift or tilt may occur on the first rotation axis AX _R1 with respect to the measurement axis AX _M. In this case, there is no practical problem if the shift amount and tilt amount are small. In particular, when the first rotation axis AX _R1 is shifted with respect to the measurement axis AX _M , the displacement amount associated with the first rotation is not affected. Therefore, in this case, the displacement amount of each surface accurately reflects the eccentric amount of each surface.

On the other hand, as shown in FIG. 16B, when the first rotation axis AX _R1 is tilted with respect to the measurement axis AX _M , the tilt affects the amount of displacement associated with the first rotation. For example, it is assumed that the first rotation axis AX _R1 is tilted at an angle θ with respect to the measurement axis AX _M. In this case, the displacement amount Y1 of the aspheric surface apex 92 is Y1 = −2 × y1 × cos θ.

Thus, compared to when the first rotational axis AX _R1 is not tilted, when the first rotary shaft AX _R1 is tilted theta, a change in the displacement amount becomes cosθ times. However, even if θ is about 1 °, the change from the displacement calculated in FIG. 16A is 0.02% or less. Therefore, in this case, the amount of displacement of the aspheric surface top 92 reflects the amount of eccentricity almost accurately.

Further, the displacement amount A1 of the aspherical shaft 93 is A1 = (− a1 + θ) − (a1−θ) = − 2 × a1. This is the same as the displacement calculated in FIG. Therefore, the displacement amount of the aspherical axis is not affected by the tilt of the first rotation axis AX _R1 . The same applies to the amount of displacement of the aspheric axis of each surface. Therefore, in this case, the amount of displacement of the aspherical axis of each surface accurately reflects the amount of eccentricity.

Therefore, even if there is a minute tilt of the first rotation axis AX _R1 with respect to the measurement axis AX _M , the decentration amount of the test optical system can be obtained without any problem.

Further, it is desirable that the first rotation axis AX _R1 is not shaken when the test optical system is rotated. Even if blurring occurs, there is no practical problem when the blurring amount generated on the first rotation axis AX _R1 is very small. FIG. 17 is a diagram illustrating a state in which the first rotation axis is blurred with respect to the measurement axis.

The blur generated on the first rotation axis AX _R1 can be represented by a shift and a tilt with respect to the measurement axis AX _M. For example, it is assumed that the first rotation axis AX _R1 is shifted by the distance T with respect to the measurement axis AX _M and tilted by the angle θ. In this case, the displacement amount Y1 of the aspheric surface top 92 is Y1 = −y1 + T−y1 × cos θ. However, as described above, even if θ is about 1 °, the change from the displacement calculated in FIG. 16A is 0.02% or less. Therefore, in this case, the amount of displacement of the aspheric surface top 92 reflects the amount of eccentricity almost accurately.

Further, the displacement amount A1 of the aspherical shaft 93 is A1 = (− a1 + θ) − (a1−θ) = − 2 × a1. This is the same as the displacement calculated in FIG. Therefore, the displacement amount of the aspherical axis is not affected by the tilt of the first rotation axis AX _R1 . The same applies to the amount of displacement of the aspheric axis of each surface. Therefore, in this case, the amount of displacement of the aspherical shaft 93 accurately reflects the amount of eccentricity.

Note that an extra displacement 95 occurs at the aspheric surface top other than the aspheric surface top 92. For example, the displacement 95 at the aspheric surface apex 94 is d4 sin θ. Therefore, the amount of displacement at the aspheric surface apex 94 is −y4 + T−y4 × cos θ + d4 sin θ. However d4 is the distance of the measuring axis AX _M direction of the aspheric surface apex 92 aspheric surface apex 94. That is, the displacement is added by sin θ times the distance in the measurement axis AX _M direction.

From this, it can be considered that a virtual rotation axis AX _I different from the first rotation axis AX _R1 has occurred. The virtual rotation axis AX _I is an axis shifted by a distance T / 2 with respect to the measurement axis AX _M and tilted by an angle θ / 2. It can be considered that the test optical system rotates around this virtual rotation axis AX _I. Therefore, the displacement amount of each surface associated with the rotation around the virtual rotation axis AX _I can be obtained from the first aberration component. Based on this amount of displacement, the amount of eccentricity based on the virtual rotation axis AX _I of the test optical system can be obtained. Therefore, even if the first rotation axis is tilted with respect to the measurement axis, there is no practical problem.

  Further, the first rotation can be performed even when the light beam is irradiated from a set of irradiation positions. An execution example of the first rotation will be described using execution example 1 and execution example 2.

  FIG. 18 is a flowchart of the execution example 1. In the execution example 1, first, the first rotation is performed at one irradiation position, and the wavefront data before the first rotation and the wavefront data after the first rotation are acquired. Thereafter, the irradiation position is changed, the first rotation is performed at the other irradiation position, and wavefront data before the first rotation and wavefront data after the first rotation are acquired.

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

  In step S100, step S110, step S121, step S150, step S110, and step S122 are executed. As a result, the wavefront data WFDθ1 before the first rotation and the wavefront data WFDθ2 after the first rotation are acquired at the irradiation position P.

  The state after the execution of step S122 is a state after the first rotation. Therefore, step S151 is executed to return the test optical system to the state before the first rotation.

  And step S130, step S141, step S150, step S130, and step S142 are performed. Thereby, at the irradiation position P ′, the wavefront data WFD′θ1 before the first rotation and the wavefront data WFD′θ2 after the first rotation are acquired.

  Thus, in the execution example 1, before the first rotation, the light source is driven in the OxOy direction, the light source is positioned at an arbitrary OxOy coordinate, and reference data is acquired. That is, reference data is acquired at an arbitrary object height coordinate (Ox, Oy). Thereafter, the first rotation is performed to rotate the test optical system.

  Then, measurement data is acquired after the first rotation. At this time, 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. Therefore, measurement data is acquired at the same object height coordinates (Ox, Oy) as before the first rotation.

  Thereafter, the state before the first rotation is restored, the light source is driven in the OxOy direction, the light source is positioned at a coordinate different from the first OxOy coordinate, and reference data is acquired. That is, the reference data is acquired at object height coordinates (Ox ′, Oy ′) different from the first object height coordinates (Ox, Oy). Thereafter, the first rotation is performed to acquire measurement data.

  Thus, in the execution example 1, the acquisition of the reference data and the acquisition of the measurement data are alternately repeated. Then, after completing the acquisition of reference data and the acquisition of measurement data at all object height coordinates, wavefront analysis is performed.

  In the flowchart shown in FIG. 18, the rotation state after execution of step S122 is the state after the first rotation. Therefore, step S130 and step S142 may be executed without executing step S151 to acquire the wavefront data WFD'θ2. Thereafter, step S151 is executed to return the test optical system to the state before the first rotation. Then, step S130 and step S141 may be executed to acquire the wavefront data WFD'θ1.

  Thus, in the execution example 1, even when there are a plurality of irradiation positions, the wavefront data before the first rotation and the wavefront data after the first rotation can be acquired at each irradiation position. By analyzing the wavefront aberration using the wavefront data before the first rotation as the reference data and the wavefront data after the first rotation as the measurement data, the design aberration, the system aberration, and the decentration aberration of the light receiving optical system can be removed. .

  FIG. 19 is a diagram illustrating a flowchart of the execution example 2. In the execution example 2, first, wavefront data is acquired at one irradiation position and the other irradiation position. Thereafter, the first rotation is performed, and wavefront data is acquired again at one irradiation position and the other irradiation position.

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

  In step S100, first, step S110, step S121, step S130, and step S141 are executed. Thereby, the wavefront data WFDθ1 at the irradiation position P and the wavefront data WFD′θ1 at the irradiation position P ′ are acquired in the state before the first rotation.

  Next, step S150 is executed to rotate the test optical system. Subsequently, step S110, step S122, step S130, and step S142 are executed. Thereby, the wavefront data WFDθ2 at the irradiation position P and the wavefront data WFD′θ2 at the irradiation position P ′ are acquired in the state after the first rotation.

  Thus, in the execution example 2, before the first rotation, the light source is driven in the OxOy direction, the light source is positioned at a plurality of object height coordinates, and reference data is acquired. That is, all the acquisition of reference data is completed at a plurality of object height coordinates. Thereafter, the first rotation is performed to rotate the test optical system.

  After the first rotation, the light source is again driven in the OxOy direction to acquire measurement data. In acquiring the measurement data, the light source is positioned at the same OxOy coordinates as before the first rotation. That is, all acquisition of measurement data is completed at the same object height coordinates as before the first rotation. Then, after all the measurement data acquisition is completed, the wavefront analysis is performed.

  As described above, in the execution example 2, after all the acquisition of the reference data is acquired, the first rotation is executed.

  Then, by taking the sum or difference of the predetermined aberration components with respect to the symmetrical object height coordinates, the aberration component proportional to the first power of the decentering amount among the decentering aberrations accompanying the decentering of the optical system under test, that is, the first An aberration component can be extracted.

  In the flowchart shown in FIG. 19, the irradiation position after execution of step S150 is P ′. Therefore, step S142 may be executed to acquire the wavefront data WFD'θ2. Then, step S110 and step S122 may be executed to obtain the wavefront data WFDθ2.

  Thus, in the execution example 2, even when there are a plurality of irradiation positions, the wavefront data before the first rotation and the wavefront data after the first rotation can be acquired at each irradiation position. By analyzing the wavefront aberration using the wavefront data before the first rotation as the reference data and the wavefront data after the first rotation as the measurement data, the design aberration, the system aberration, and the decentration aberration of the light receiving optical system can be removed. .

  Moreover, in the measurement method of this embodiment, it is preferable to move one irradiation position and the other irradiation position, respectively, and to acquire wavefront data in the irradiation position after a movement.

  One lens has two lens surfaces. When the two lens surfaces are aspherical surfaces, the number of degrees of freedom in eccentricity is 8 when a shift and tilt occur on each lens surface. Further, in the case of two lenses, when the four lens surfaces are aspherical surfaces, the number of degrees of freedom in decentration is 16 when shift and tilt occur on each lens surface. Thus, as the number of decentered lens surfaces increases, the number of degrees of freedom in decentration increases.

An increase in the number of eccentric degrees of freedom means that the number of j increases in Δ ₁ to Δ _j in equations (9-1) to (9-9). Here, since Δ _{1 to} Δ _j are unknown numbers, if the number of linear equations is 9 at the maximum, Δ ₉ can be obtained, but Δ ₁₀ or more cannot be obtained.

Therefore, one irradiation position and the other irradiation position are moved, and wavefront data is acquired at the moved position. In this case, the following formulas (9-1 ′) to (9-9 ′) are obtained from the irradiation positions (Ox1, Oy1) and (−Ox1, −Oy1) before the movement.
w ₁₁ (Ox1, Oy1, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₁₁₁ (Ox1, Oy1) + Δ ₂ B ₁₂₁ (Ox1, Oy1) + ・ ・ ・ + Δ _j B _1j1 (Ox1, Oy1) (9-1 ′)
w ₂₁ (Ox1, Oy1, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₂₁₁ (Ox1, Oy1) + Δ ₂ B ₂₂₁ (Ox1, Oy1) + ・ ・ ・ + Δ _j B _2j1 (Ox1, Oy1) (9-2 ')
w ₃₁ (Ox1, Oy1, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₃₁₁ (Ox1, Oy1) + Δ ₂ B ₃₂₁ (Ox1, Oy1) + ・ ・ ・ + Δ _j B _3j1 (Ox1, Oy1) (9-3 ')
w ₄₁ (Ox1, Oy1, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₄₁₁ (Ox1, Oy1) + Δ ₂ B ₄₂₁ (Ox1, Oy1) + ・ ・ ・ + Δ _j B _4j1 (Ox1, Oy1) (9-4 ')
w ₅₁ (Ox1, Oy1, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₅₁₁ (Ox1, Oy1) + Δ ₂ B ₅₂₁ (Ox1, Oy1) + ・ ・ ・ + Δ _j B _5j1 (Ox1, Oy1) (9−5 ′)
w ₆₁ (Ox1, Oy1, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₆₁₁ (Ox1, Oy1) + Δ ₂ B ₆₂₁ (Ox1, Oy1) + ・ ・ ・ + Δ _j B _6j1 (Ox1, Oy1) (9−6 ′)
w ₇₁ (Ox1, Oy1, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₇₁₁ (Ox1, Oy1) + Δ ₂ B ₇₂₁ (Ox1, Oy1) + ・ ・ ・ + Δ _j B _7j1 (Ox1, Oy1) (9-7 ')
w ₈₁ (Ox1, Oy1, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₈₁₁ (Ox1, Oy1) + Δ ₂ B ₈₂₁ (Ox1, Oy1) + ・ ・ ・ + Δ _j B _8j1 (Ox1, Oy1) (9−8 ′)
w ₉₁ (Ox1, Oy1, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₉₁₁ (Ox1, Oy1) + Δ ₂ B ₉₂₁ (Ox1, Oy1) + ・ ・ ・ + Δ _j B _9j1 (Ox1, Oy1) (9−9 ′)

Furthermore, the following formulas (9-1 ″) to (9-9 ″) are obtained from the irradiation positions (Ox2, Oy2) and (−Ox2, −Oy2) after the movement.
w ₁₁ (Ox2, Oy2, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₁₁₁ (Ox2, Oy2) + Δ ₂ B ₁₂₁ (Ox2, Oy2) + ・ ・ ・ + Δ _j B _1j1 (Ox2, Oy2) (9-1 ”)
w ₂₁ (Ox2, Oy2, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₂₁₁ (Ox2, Oy2) + Δ ₂ B ₂₂₁ (Ox2, Oy2) + ・ ・ ・ + Δ _j B _2j1 (Ox2, Oy2) (9-2 ”)
w ₃₁ (Ox2, Oy2, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₃₁₁ (Ox2, Oy2) + Δ ₂ B ₃₂₁ (Ox2, Oy2) + ・ ・ ・ + Δ _j B _3j1 (Ox2, Oy2) (9-3 ”)
w ₄₁ (Ox2, Oy2, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₄₁₁ (Ox2, Oy2) + Δ ₂ B ₄₂₁ (Ox2, Oy2) + ・ ・ ・ + Δ _j B _4j1 (Ox2, Oy2) (9-4 ”)
w ₅₁ (Ox2, Oy2, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₅₁₁ (Ox2, Oy2) + Δ ₂ B ₅₂₁ (Ox2, Oy2) + ・ ・ ・ + Δ _j B _5j1 (Ox2, Oy2) (9-5 ”)
w ₆₁ (Ox2, Oy2, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₆₁₁ (Ox2, Oy2) + Δ ₂ B ₆₂₁ (Ox2, Oy2) + ・ ・ ・ + Δ _j B _6j1 (Ox2, Oy2) (9-6 ”)
w ₇₁ (Ox2, Oy2, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₇₁₁ (Ox2, Oy2) + Δ ₂ B ₇₂₁ (Ox2, Oy2) + ・ ・ ・ + Δ _j B _7j1 (Ox2, Oy2) (9-7 ”)
w ₈₁ (Ox2, Oy2, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₈₁₁ (Ox2, Oy2) + Δ ₂ B ₈₂₁ (Ox2, Oy2) + ・ ・ ・ + Δ _j B _8j1 (Ox2, Oy2) (9-8 ”)
w ₉₁ (Ox2, Oy2, Δ ₁ , Δ ₂ , ..., Δ _j )
= Δ ₁ B ₉₁₁ (Ox2, Oy2) + Δ ₂ B ₉₂₁ (Ox2, Oy2) + ・ ・ ・ + Δ _j B _9j1 (Ox2, Oy2) (9-9 ”)

  As a result, since the number of linear equations is 18 at the maximum, more degrees of freedom can be obtained.

  Thus, the number of linear equations can be increased by increasing the irradiation position. Therefore, according to the measurement method of this embodiment, the measurable degree of freedom of eccentricity can be increased.

  Further, in the measurement method of the present embodiment, one irradiation position is moved, all wavefront data is acquired at the irradiation position after movement, the other irradiation position is then moved, and the wavefront data is moved at the irradiation position after movement. It is preferable to acquire all.

  A flowchart of the measurement method of this embodiment is shown in FIG. In FIG. 20, step S200 and subsequent steps are omitted. FIG. 21 is a diagram showing the movement of the irradiation position, in which (a) shows the position before movement of one irradiation position, (b) shows the position after movement of one irradiation position, (C) shows the position before movement of the other irradiation position, and (d) shows the position after movement of the other irradiation position.

  In the measurement method of this embodiment, Step S100 includes Step S111, Step S123, Step S131, Step S143, Step S160, Step S161, Step S170, and Step S171.

  In step S100, the light beam is irradiated from the irradiation position Pn and the irradiation position P'n. Here, the irradiation position Pn is one irradiation position, and the irradiation position P′n is the other irradiation position. Further, the irradiation position Pn and the irradiation position P′n are symmetric with respect to the measurement axis.

  Before the execution of step S111, the number N of times of changing the irradiation position is set by the user. The number N is the scheduled number. The value of n is set to 0. n represents the number of movements of the irradiation position.

Subsequently, step S111 is executed. In step S111, the light beam is irradiated from the irradiation position Pn. Specifically, as shown in FIG. 21A, the light source is positioned at the irradiation position P0 (Ox0, Oy0, 0). Since target optical system 2 is eccentric relative to the measuring axis, the non-plane wave 9 ₀ is emitted from the optical system 2. Non plane wave 9 ₀ is detected by the light receiving system 3.

When step S111 ends, step S123 is executed. At step S123, the wavefront data WFDn is obtained based on the non-plane wave _{9 0.} Thereafter, step S160 is executed.

  In step S160, n and N are compared. When n and N are not equal, the number of movements of the irradiation position has not reached the scheduled number. Therefore, 1 is added to the current number of movements, and step S170 is executed. In step S170, the irradiation position is moved. The movement amount may be set in advance by the user.

After step S170 is executed, step S111 is executed again. At this time, since the irradiation position is moved, the light source is positioned at the irradiation position P1 (Ox1, Oy1,0) as shown in FIG. Non plane wave 9 ₁ from the optical system 2 is emitted. Non plane wave 9 ₁ is detected by the light receiving system 3.

Here, the irradiation position P1 (Ox1, Oy1,0) is different from the irradiation position P0 (Ox0, Oy, 0). Therefore, non-plane wave _{9 1} is different from the non-plane wave _{9 0.}

When step S111 ends, step S123 is executed. At step S123, the wavefront data WFDn is obtained based on the non-plane wave _{9 1.} The movement of the irradiation position and the acquisition of the wavefront data WFDn are performed until n and N are equal. All the acquired wavefront data WFDn is stored.

  If n and N are equal in step S160, the movement of the irradiation position is completed. In this way, the movement of one irradiation position and the acquisition of wavefront data at the irradiation position after the movement are completed. Then, the value of n is set to 0.

Subsequently, step S131 is executed. In step S131, the light beam is irradiated from the irradiation position P′n. Specifically, as shown in FIG. 21C, the light source is positioned at the irradiation position P′0 (−Ox0, −Oy0,0). The irradiation position P′0 (−Ox0, −Oy0,0) is a position symmetrical to the irradiation position P0 (Ox0, Oy0,0) with respect to the measurement axis. Non plane wave 9 _'0 from the optical system 2 is emitted. The non-planar wave 9 ′ ₀ is detected by the light receiving system 3.

Here, the irradiation position P′0 (−Ox0, −Oy0,0) is different from the irradiation position P0 (Ox0, Oy0,0) and the irradiation position P1 (Ox1, Oy1,0). Therefore, non-plane wave 9 _'0 is different from the non-plane wave _{9 0} and a non-plane wave _{9 1.}

When step S131 ends, step S143 is executed. In step S143, the wavefront data WFD'n is obtained based on the non-plane wave 9 _'0. Thereafter, step S161 is executed.

  In step S161, n and N are compared. When n and N are not equal, the number of movements of the irradiation position has not reached the scheduled number. Therefore, 1 is added to the current number of movements, and step S171 is executed. In step S171, the irradiation position is moved. The movement amount may be set in advance by the user.

After step S171 is executed, step S131 is executed again. At this time, since the irradiation position is moved, the light source is positioned at the irradiation position P′1 (−Ox1, −Oy1,0) as shown in FIG. The irradiation position P′1 (−Ox1, −Oy1,0) is a position symmetrical to the irradiation position P1 (Ox1, Oy1,0) with respect to the measurement axis. Non plane wave 9 _'1 from the optical system 2 is emitted. The non-planar wave 9 ′ ₁ is detected by the light receiving system 3.

Here, P′1 (−Ox1, −Oy1,0) is an irradiation position P′0 (−Ox0, −Oy0,0), P0 (Ox0, Oy0,0) and an irradiation position P1 (Ox1, Oy1,0). ) Is different. Therefore, non-plane wave 9 _'1, non-plane wave 9' _0, a non-plane wave _{9 0} and a non-plane wave _{9 1} differs.

When step S131 ends, step S143 is executed. In step S143, the wavefront data WFD'n is obtained based on the non-plane wave 9 _'1. The movement of the irradiation position and the acquisition of the wavefront data WFD′n are performed until n and N are equal. All the acquired wavefront data WFD′n is stored.

  If n and N are equal in step S161, the movement of the irradiation position is completed. In this way, the movement of the other irradiation position and the acquisition of the wavefront data at the irradiation position after the movement are completed.

  In FIG. 21, after the irradiation at the irradiation position P1 (Ox1, Oy1,0) is completed, the irradiation position P′0 (−Ox0, −Oy0, 0) is moved. However, it may be moved to the irradiation position P'1 (-Ox1, -Oy1,0) and then moved to the irradiation position P'0 (-Ox0, -Oy0,0).

  Thus, the number of linear equations can be increased by increasing the irradiation position. Therefore, according to the measurement method of this embodiment, the measurable degree of freedom of eccentricity can be increased.

  Further, in the measurement method of the present embodiment, the wavefront data is acquired at each of the one irradiation position and the other irradiation position, and then the one irradiation position and the other irradiation position are moved, and each of the irradiation positions after the movement is moved. It is preferable to acquire wavefront data at

  A flowchart of the measurement method of the present embodiment is shown in FIG. Note that step S200 and subsequent steps are omitted. FIG. 23 is a diagram showing the movement of the irradiation position, where (a) shows the position before movement of one irradiation position, (b) shows the position of the other irradiation position before movement, (C) shows the position after movement of one irradiation position, and (d) shows the position after movement of the other irradiation position.

  In the measurement method of this embodiment, Step S100 includes Step S111, Step S123, Step S131, Step S143, Step S162, and Step S172.

  First, step S111 is executed. In step S111, the light beam is irradiated from the irradiation position Pn. Specifically, as shown in FIG. 23A, the light source is located at the irradiation position P0 (Ox0, Oy0, 0).

When step S111 ends, step S123 is executed. At step S123, the wavefront data WFDn is obtained based on the non-plane wave _{9 0.}

  Subsequently, step S131 is executed. In step S131, the light beam is irradiated from the irradiation position P'n. Specifically, as shown in FIG. 23B, the light source is positioned at the irradiation position P′0 (−Ox0, −Oy0,0).

When step S131 ends, step S143 is executed. In step S143, the wavefront data WFD'n is obtained based on the non-plane wave 9 _'0. Thereafter, step S162 is executed.

  In step S162, n and N are compared. When n and N are not equal, the number of movements of the irradiation position has not reached the scheduled number. Therefore, 1 is added to the current number of movements, and step S172 is executed. In step S172, the irradiation position is moved. The movement amount may be set in advance by the user.

  After step S172 is executed, step S111 is executed again. At this time, since the irradiation position is moved, the light source is positioned at the irradiation position P1 (Ox1, Oy1,0) as shown in FIG.

When step S111 ends, step S123 is executed. At step S123, the wavefront data WFDn is obtained based on the non-plane wave _{9 1.}

  Subsequently, step S131 is executed. In step S131, the light beam is irradiated from the irradiation position P'n. At this time, since the irradiation position is moved, the light source is positioned at the irradiation position P′1 (−Ox1, −Oy1,0) as shown in FIG.

When step S131 ends, step S143 is executed. In step S143, the wavefront data WFD'n is obtained based on the non-plane wave 9 _'1. Thereafter, step S162 is executed.

  The movement of the irradiation position and the acquisition of the wavefront data WFDn and the wavefront data WFD′n are performed until n and N are equal. The acquired wavefront data WFDn and wavefront data WFD'n are all stored.

  If n and N are equal in step S162, the movement of the irradiation position is completed. In this way, the movement of one irradiation position and the other irradiation position and the acquisition of wavefront data at the irradiation position after the movement are completed.

  Thus, the number of linear equations can be increased by increasing the irradiation position. Therefore, according to the measurement method of this embodiment, the measurable degree of freedom of eccentricity can be increased.

  In FIGS. 21 and 23, the movement direction of the irradiation position is a direction approaching the Oz axis. However, the direction of movement of the irradiation position may be a direction away from the Oz axis. 21 and 23 show four irradiation positions, the irradiation positions are not limited to four. Further, the light beam may be irradiated from the origin (0,0,0).

  FIGS. 24A and 24B are diagrams showing how the irradiation position moves. FIG. 24A shows a case where the movement direction of the irradiation position is one direction, and FIG. 24B shows a case where the movement direction of the irradiation position is two directions. Yes.

  FIG. 24A shows the movement of the irradiation position in one direction. In FIG. 24A, the movement of the irradiation position is started from the negative maximum object height coordinate. Then, the irradiation position moves toward the positive maximum object height coordinate. That is, the irradiation position moves in the order of the irradiation position P′4 (−Ox4,0,0), the irradiation position P0 (0,0,0), and the irradiation position P4 (Ox4,0,0).

  FIG. 24B shows the movement of the irradiation position in two directions. In FIG.23 (b), the movement of the irradiation position is started from the axis. Then, the irradiation position moves toward the positive maximum object height. Next, the irradiation position is returned to the axis (on the Oz axis), and the irradiation position moves toward the negative maximum object height. That is, the irradiation position moves from the irradiation position P0 (0,0,0) toward the irradiation position P4 (Ox4,0,0), and then the irradiation position P ′ from the irradiation position P0 (0,0,0). The irradiation position moves toward 4 (-Ox4, 0, 0).

  In FIG. 24A, the irradiation position may be moved randomly between the irradiation position P4 (Ox4,0,0) and the irradiation position P4 '(-Ox4,0,0). Similarly, in FIG. 23B, from the irradiation position P0 (0,0,0) to the irradiation position P4 (Ox4,0,0), or from the irradiation position P0 (0,0,0) to the irradiation position P. The irradiation position may be moved randomly between '4 (-Ox4, 0, 0).

  Thus, the number of linear equations can be increased by increasing the irradiation position. Therefore, the measurable degree of eccentricity can be increased.

  25A and 25B are diagrams showing irradiation position patterns, where FIG. 25A shows a state in which the irradiation position is in two directions, FIG. 25B shows a state in which the irradiation position is concentric, and FIG. The state is shown.

  In FIG. 25A, the irradiation position in the light projecting system 1 is located only on the Ox axis and the Oy axis. In FIG. 25 (b) and FIG. 25 (c), the irradiation position in the light projecting system 1 is also located between the Ox axis and the Oy axis. In FIG.25 (b), the irradiation position is located concentrically or radially. In FIG.25 (c), the irradiation position is located in the grid | lattice form.

  Moreover, the standard of the pitch of the movement of the irradiation position in the light projection system 1 should just be about 1/50 of an effective aperture from about the effective aperture of a test optical system. In addition, when measuring the eccentricity with high accuracy, the movement pitch is made smaller and more wavefront data is acquired.

  Further, if the wavefront data is acquired using only the positive maximum object height and the negative maximum object height, the first aberration component can be extracted. Therefore, when the measurement is to be completed in a short time, the diameter of the irradiated light beam may be approximately the same as the diameter of the test optical system. However, in this case, the object height is made small so that the light beam is not scattered outside the effective aperture of the optical system to be tested.

  Thus, the number of linear equations can be increased by increasing the irradiation position. Therefore, the measurable degree of eccentricity can be increased.

  In the measurement method of the present embodiment, it is preferable that the wavefront data is acquired in the first irradiation state, and that the central ray of the light beam is parallel to the measurement axis in the first irradiation state.

  In the first irradiation state, the central ray of the light beam is parallel to the measurement axis. That is, as shown in FIG. 6, the central ray CR of the light beam emitted from the irradiation position P (Ox, Oy, 0) of the light projecting system 1 is parallel to the Oz axis, that is, the measurement axis. In this case, when the irradiation position P (Ox, Oy, 0) is changed in the OxOy plane, the light beam emitted from the test optical system 2 changes. Here, the incident angle of the light flux to the light receiving system 3 changes, but the incident position hardly changes. Therefore, the position adjustment between the light receiving system 3 and the light beam incident on the light receiving system 3 can be reduced.

  Further, in the measurement method of the present embodiment, it is preferable that the wavefront data is acquired in the second irradiation state, and in the second irradiation state, the central ray of the light beam intersects with the measurement axis at a predetermined angle.

  In the second irradiation state, the central ray of the light beam intersects the measurement axis at a predetermined angle. FIGS. 26A and 26B are diagrams showing a state in which a test optical system is irradiated with a light beam. FIG. 26A shows irradiation at an angle θ, and FIG. 26B shows irradiation at an angle θ ′. As shown in FIG. 26, the central ray CR of the light beam emitted from the irradiation position P (Ox, Oy, 0) of the light projecting system 1 intersects the Oz axis, that is, the measurement axis at an angle θ. Note that | θ | = | θ ′ |.

  Also in FIG. 26, the spherical wave 4 is emitted from the irradiation position P (Ox, Oy, 0). However, the test optical system 2 is irradiated with a light beam at a position and an angle different from those in FIG. Therefore, the non-plane waves 8 and 8 ′ emitted from the test optical system 2 are different from the non-plane waves 7 and 7 ′ in FIG. 6.

  In addition, when moving one irradiation position and the other irradiation position, respectively, and acquiring wavefront data at the irradiation position after movement, it is possible to acquire wavefront data by changing a predetermined angle at the irradiation position after movement. desirable.

In the measurement method of the present embodiment, the second extraction step is performed using a predetermined function system, and the predetermined function system is a function system indicating the first aberration component, and one irradiation position. It is preferable to apply the predetermined aberration component at and the predetermined aberration component at the other irradiation position to a predetermined function system.
In this way, an amount proportional to the first power of the amount of eccentricity Δ, that is, the first aberration component can be extracted.

  In the measurement method of the present embodiment, the acquisition step includes a second rotation. In the second rotation, the test optical system is rotated 180 degrees around an axis orthogonal to the measurement axis, and the second rotation is performed. It is preferable to acquire the wavefront data and the wavefront data after the second rotation.

  A flowchart of the measurement method of this embodiment is shown in FIG. In the measurement method of this embodiment, step S100 includes step S110, step S123, step S124, and step S180. Detailed descriptions of step S200, step S300, and step S400 are omitted.

  FIG. 28 is a diagram showing the second rotation, where (a) shows a state before the second rotation, and (b) shows a state after the second rotation.

  Here, for convenience, the test optical system 20 will be referred to as “front” and “back”. For example, when the test optical system 20 is irradiated with a light beam, the light beam can be irradiated from the lens 23 side or the light beam can be irradiated from the lens 25 side. When the case where the light beam is irradiated from the lens 23 side is “front”, the case where the light beam is irradiated from the lens 25 side is “back”.

  When the light beam is irradiated from the “front” to the test optical system 20 (hereinafter referred to as “front measurement”), and when the light beam is irradiated from the “back” to the test optical system 20 (hereinafter referred to as “rear measurement”). The decentration aberration sensitivity of each lens changes.

  When the optical system 20 to be tested is composed of six lens surfaces, the first surface, the second surface,. In the front side measurement, the first surface through which the light beam is transmitted is the first surface. In the rear side measurement, the light beam passes through the sixth surface, the fifth surface,... In this order, and the first surface is the last surface to be transmitted.

  Object points are relayed on each lens surface of the test optical system 20. Therefore, if a certain lens surface is decentered, the object point relayed to the rear side of the lens surface is shifted laterally from the ideal position. Then, it can be considered that this causes aberrations on the subsequent lens surfaces. In other words, the aberration caused by decentration is related to the order of the lens surfaces. This is the reason why the decentration aberration sensitivity changes depending on whether the test optical system 20 is measured on the front side or the rear side. In the measurement method of the present embodiment, the amount of information related to the first aberration component is increased by utilizing this fact.

  In step S110, as shown in FIG. 28A, the test optical system 20 is irradiated with a light beam from the irradiation position P (Ox, Oy, 0). At this time, the test optical system 20 is arranged so that the light projecting system 10 and the lens 23 face each other. Therefore, the light beam is irradiated onto the optical system 20 to be tested from the lens 23 side. A non-planar wave 51 is emitted from the test optical system 20. The non-planar wave 51 enters the light receiving system 30.

  Subsequently, step S123 is executed. Thereby, wavefront data WFDθ3 is acquired.

  Next, step S180 is executed. In step S180, the second rotation is performed. In the second rotation, the test optical system 20 is rotated around an axis orthogonal to the measurement axis. The rotation angle is 180 °. When the second rotation is performed, the test optical system 20 is arranged so that the light projecting system 10 and the lens 25 face each other. Therefore, the optical system 20 is irradiated with the light beam from the lens 25 side. The positions of the light projecting system 10 and the light receiving system 30 do not move.

  After step S180 is completed, step S110 is executed. In step S110, as shown in FIG. 28 (b), the optical system 20 is irradiated with a light beam from the irradiation position P (Ox, Oy, 0). The wavefront 60 is incident on the test optical system 20. A non-planar wave 55 is emitted from the test optical system 20. The non-plane wave 56 is different from the non-plane wave 51.

  Subsequently, step S124 is executed. Thereby, wavefront data WFDθ4 is acquired.

  Here, the wavefront data WFDθ3 and the wavefront data WFDθ4 are different. Therefore, finally, two first aberration components can be obtained.

  As described above, in the measurement method of the present embodiment, the light flux is irradiated while different wavefront data is acquired, and therefore the number of first aberration components can be increased. Therefore, the measurable degree of eccentricity can be increased.

  In addition, when performing 2nd rotation, it needs to be careful about the handling of a measurement result. FIGS. 29A and 29B are diagrams for explaining the change of the coordinate axes due to the second rotation, in which FIG. 29A shows a state before the second rotation, and FIG. 29B shows the state after the second rotation. Indicates the state. Here, the test optical system is rotated by 180 ° around the Oy axis.

In the state before performing the second rotation, the front side measurement is performed. In the front side measurement, as shown in FIG. 29A, the lens L1 is arranged on the origin (0, 0, 0) side, and the lens L2 is arranged after the lens L1. Therefore, the lens surfaces are the lens surface L1 ₁ , the lens surface L1 ₂ , the lens surface L2 ₁ , and the lens surface L2 _{2 in} order from the origin (0, 0, 0) side. Here, the coordinate axis _XL2 and the Ox axis are in the same direction.

  In this state, the light beam is irradiated from the irradiation position P (Ox, Oy, 0) to the optical system to be measured. The light beam is irradiated in the order of the lens L1 and the lens L2.

On the other hand, in the state after the second rotation, the rear side measurement is performed. In the rear side measurement, as shown in FIG. 29B, the lens L2 is disposed on the origin (0, 0, 0) side, and the lens L1 is disposed subsequent to the lens L2. Therefore, the lens surfaces are the lens surface L2 ₂ , the lens surface L2 ₁ , the lens surface L2 ₂ , and the lens surface L2 _{1 in} order from the origin (0, 0, 0) side. Here, coordinate axes X _L2 has become Ox axis and opposite direction.

In the front measurement and the rear measurement, the direction of the coordinate axis Y _L2 is not changed, but the direction of the coordinate axis X _L2 is reversed. Here, in the front measurement, it is assumed that the sphere center of the lens L2 is positioned on the plus side. In this case, the rear side measurement, when the reference coordinate axes X _L2, spherical center lens L5 are located on the positive side. However, with the Ox axis as a reference, the center of the lens L2 is positioned on the minus side in the rear measurement.

When the test optical system is rotated around the Ox axis, the direction of the coordinate axis X _L2 does not change, but the direction of the coordinate axis Y _L2 differs by 180 °. Therefore, when the Oy axis is used as a reference, for example, if the sign of the ball center position in the front measurement is positive, the sign of the ball center position in the rear measurement is negative.

  For this reason, it is necessary to invert the sign of the numerical value in the processing after step S200 for the measurement result obtained by the rear side measurement.

  Further, in the measurement method of the present embodiment, the amount of eccentricity when acquiring the wavefront data before the second rotation and the amount of eccentricity when acquiring the wavefront data after the second rotation have the same absolute value. Preferably there is.

  As described above, in the first rotation, the test optical system is rotated around the measurement axis. By doing in this way, the displacement amount which arises with this rotation can be calculated | required about each lens. In the measurement by the second rotation, the same measurement system as that by the first rotation is used. In the second rotation, the test optical system is arranged so that the front and back of the test optical system are reversed. Then, the first aberration component is extracted by performing the same processing as the measurement in the first rotation.

  However, the absolute value of the distance between the lens and the rotation axis needs to be the same between the front side measurement and the rear side measurement. For example, it is assumed that the test optical system has six lens surfaces. Here, all of the six lens surfaces are spherical. Then, it is assumed that the eccentric amounts of the first surface, the second surface,..., The sixth surface during the front side measurement are (X1, Y1), (X2, Y2), (X6, Y6). The decentering amount of each lens surface is expressed by XY coordinates based on the first rotation axis.

  At the time of rear side measurement, the optical system to be tested at the time of front side measurement is rotated around the Y axis. As a result, the direction of the test optical system is reversed. Then, the rear side measurement is performed. At this time, the decentering amount of each lens surface in the rear side measurement becomes (−X1, Y1), (−X2, Y2)... (−X6, Y6). Thus, the test optical system is arranged.

  When placing the measurement for performing the back side measurement, it is necessary to place the test optical system so that the absolute value of the predetermined distance is the same between the back side measurement and the front side measurement. The predetermined distance is a distance between the spherical center of each lens surface of the optical system to be measured and the first rotation axis at the time of front side measurement.

  Note that the first rotation may also be performed in the measurement method of the present embodiment. A plurality of wavefront data is acquired before and after the first rotation in the front side measurement. Subsequently, the second rotation is performed so that the rear side measurement is possible. By the second rotation, the front and back of the test optical system are reversed.

  When the lens surface is a spherical surface, if the lens surface is decentered, the spherical center moves by the first rotation. FIG. 30 is a diagram illustrating the movement of the ball center by the first rotation, in which (a) shows the movement of the ball center during the front side measurement, and (b) shows the movement of the ball center during the rear side measurement. Show. In FIG. 30, the lens surface in the vicinity of the spherical center is indicated by a circle. Thus, each of the two circles only displays a part of the same lens surface.

  The movement of the ball center at the time of the front side measurement will be described with reference to FIG. Prior to the first rotation, the ball center 96 is located in the first quadrant of the OxOy coordinate system. Then, after the first rotation, the ball center 96 is located in the third quadrant. The movement amount of the ball center 96 is δf, the x component is δX, and the y component is δY.

  The movement of the ball center at the time of rear side measurement will be described with reference to FIG. Before the first rotation, the ball center 96 is located in the second quadrant of the OxOy coordinate system. Then, after the first rotation, the ball center 96 is located in the fourth quadrant. The movement amount of the ball center 96 is δr, the x component is δX, and the y component is δY.

  As described above, in the measurement that performs the second rotation, the test optical system is arranged so that the absolute value of the predetermined distance is the same between the rear side measurement and the front side measurement. Therefore, | δf | = | δr |.

  In the vector indicating the movement of the ball center 96, the direction of the Y component vector is the same between the front side measurement and the rear side measurement. On the other hand, the direction of the X component vector is reversed between the front side measurement and the back side measurement.

  For this reason, it is necessary to invert the sign of the numerical value in the processing after step S200 for the measurement result obtained by the rear side measurement.

  FIG. 31 is a diagram showing the movement of the ball center due to the first rotation and the second rotation, where (a) shows the position of the ball center before the first rotation at the time of front measurement, and (b) At the time of the front side measurement, the position of the ball center after the first rotation is shown, (c) at the time of the back side measurement, showing the position of the ball center before the first rotation, and (d) at the time of the back side measurement. The position of the ball center after the first rotation is shown.

  The origin of the OxOy coordinate is the position of the first rotation axis. That is, FIG. 31 shows the position of the ball center with respect to the first rotation axis. In addition, when the test lens includes an aspheric surface, the movement of the surface due to the first rotation and the second rotation of the aspheric surface is as follows. It can be indicated by the position of the surface top and the position of the aspherical axis. However, in FIG. 31, when the position of the aspherical axis is displayed, the Ox axis indicates the tilt amount in the B direction, and the Oy axis indicates the tilt amount in the A direction.

  At the time of the front side measurement, in the state before the first rotation, as shown in FIG. 31A, the ball center 96 is located in the first quadrant of the OxOy coordinate system. When the first rotation is performed in this state, the state after the first rotation is obtained at the time of the front side measurement. In this state, as shown in FIG. 31B, the ball center 96 is located in the third quadrant of the OxOy coordinate system.

  Returning to the state before the first rotation from this state, the second rotation is performed. Thereby, it will be in the state before the 1st rotation at the time of backside measurement. In this state, as shown in FIG. 31 (c), the ball center 96 is located in the second quadrant of the OxOy coordinate system. When the first rotation is performed in this state, a state after the first rotation is obtained at the time of rear side measurement. In this state, as shown in FIG. 31 (d), the spherical center 96 is located in the fourth quadrant of the OxOy coordinate system.

  The absolute value of the amount of displacement of the ball core 96 due to the first rotation is the same in FIG. 31 (b) and FIG. 31 (d). Moreover, it can also be seen from FIGS. 31B and 31D that the X direction of the movement vector of the ball center is opposite between the front side measurement and the back side measurement.

  Therefore, if the sign is inverted for the decentering aberration sensitivity of the X-direction shift in the rear side measurement, the solution of the simultaneous linear equations for the decentering amount is the same for the front side measurement and the rear side measurement. Accordingly, simultaneous linear equations for the eccentricity can be solved by simultaneously using the eccentric aberration sensitivity proportional to the first power of the eccentricity of the front side measurement and the decentration aberration sensitivity proportional to the first power of the eccentricity of the rear side measurement. . In other words, the amount of decentration with many degrees of freedom can be obtained with high accuracy by using more cues for decentration aberration sensitivity. The obtained eccentricity is the position of the ball center in the state of FIG.

  If the test optical system includes an aspherical surface, the signs of the decentering aberration sensitivity of the aspherical surface are solved by reversing the signs of the decentering aberration sensitivity of the X-direction shift and the A-direction tilt. That's fine. Similarly, the obtained tilt amount in the A direction is the aspherical axis tilt amount based on the first rotation axis before the first rotation at the time of the front side measurement.

  Note that the second rotation is performed after the measurement in the front measurement is completed, but at this time, the rear measurement may be performed without returning to the state before the first rotation. This measurement is the same as the state in which the ball center 96 is located in the fourth quadrant as shown in FIG.

  In the measurement method of the present embodiment, the first extraction step is preferably performed using a Zernike polynomial, and the predetermined aberration component is preferably a coefficient of the Zernike polynomial.

  The wavefront data includes wavefront aberration information. Therefore, by applying the wavefront data to the Zernike polynomial, the aberration component in the wavefront aberration can be decomposed into spherical aberration, coma aberration, astigmatism, and the like, and the amount of aberration can be quantified for each aberration component.

  When wavefront data is acquired by performing the first rotation, the coefficient of each term of the Zernike polynomial does not represent the wavefront aberration itself of the wavefront emitted from the test optical system. System aberration components and design aberration components of the test optical system are excluded from the aberration components represented by the coefficients of the terms. The elimination of the system aberration component and the design aberration component is as described above.

  Further, as described above, when the Zernike polynomial is used, the results shown in the equations (3) to (6) are obtained.

In the decentration aberration sensitivity in the aberration component proportional to the first power of the decentration amount, as described above, the decentration aberration sensitivity B _zj1 (Ox, Oy) (z = 2,3) of the term multiplied by the second term of the Zernike term, etc. , 7,8... Is expressed by the following equation (3).
B _zj1 (Ox, Oy) ＝ C _zj100 + C _zj120 Ox ² + C _zj111 OxOy + C _zj102 Oy ² + (3)

Also, the decentration aberration sensitivity B _zjl (Ox, Oy) (z = 1,4,5,6,9...) _Of the term multiplied by the fourth term of the Zernike term is expressed by the following equation (4). expressed.
B _zj1 (Ox, Oy) = C _zj110 Ox + C _zj101 Oy + C _zj130 Ox ³ + C _zj121 Ox ² Oy
+ C _zj112 OxOy ² + C _zj103 Oy ³ + ... (4)

In the decentration aberration sensitivity in the aberration component proportional to the square of the decentration amount, as described above, the decentration aberration sensitivity B _zj2 (Ox, Oy) (z = 2,3) of the term multiplied by the second term of the Zernike term, etc. , 7,8... Is expressed by the following equation (5).
B _zj2 (Ox, Oy) = C _zj210 Ox + C _zj201 Oy + C _zj230 Ox ³ + C _zj221 Ox ² Oy
+ C _zj212 OxOy ² + C _zj203 Oy ³ + ... (5)

Also, the decentration aberration sensitivity B _zj2 (Ox, Oy) (z = 1,4,5,6,9...) _Of the term multiplied by the fourth term of the Zernike term is expressed by the following equation (6). expressed.
B _zj2 (Ox, Oy) ＝ C _zj200 + C _zj220 Ox ² + C _zj211 OxOy + C _zj202 Oy ² + (6)

  The wavefront aberration due to the decentering of the test optical system can be decomposed into each aberration component by a Zernike polynomial. The distribution of the resolved aberration component at each object height coordinate is theoretically known (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]).

Therefore, based on this theory, the distribution of the function with the object height coordinate as a variable (hereinafter referred to as “object height function”) is arranged for the decentration aberration sensitivity B _zjl (Ox, Oy). Hereafter, the organized results are shown briefly. In each table below, an aberration component (l = 1) proportional to the first power of the decentering amount, an aberration component (l = 2) proportional to the second power of the decentering amount, and an aberration component (1) proportional to the third power of the decentering amount. = 3). However, the Zernike term Z1 term, which is the piston component of the wavefront aberration, is omitted because it may be difficult to measure accurately by actual wavefront measurement.

First, Table 17 shows a _{summary of} the decentering aberration sensitivities B _2jl (Ox, Oy) and B _3jl (Ox, Oy).

In the decentration aberration sensitivities B _2jl (Ox, Oy) and B _3jl (Ox, Oy) in the aberration component proportional to the first power of the decentration amount, the object height function appears at the 0th power and the second power of the object height coordinate. Therefore, the aberration component proportional to the first power of the decentration amount is an even function with respect to the object height coordinate. For the aberration component proportional to the square of the decentration amount, the object height function appears at the first and third powers of the object height coordinate. Therefore, the aberration component proportional to the square of the decentration amount is an odd function with respect to the object height coordinate. For the aberration component proportional to the cube of the decentering amount, the object height function appears in the square of the object height coordinate. Therefore, the aberration component proportional to the cube of the decentering amount is an even function with respect to the object height coordinate.

FIG. 32 is a diagram showing an object height function appearing in decentering aberration sensitivities B _2jl (Ox, Oy) and B _3jl (Ox, Oy), where (a) shows a case where the optical system to be _tested is not decentered. (B) and (c) show a case where the optical system to be tested is decentered. In the figure, a function indicated by l = 1 indicates an object height function that appears in an aberration component that is proportional to the first power of the eccentricity, and a function indicated by l = 2 indicates an object that appears in an aberration component that is proportional to the second power of the eccentricity. A function indicated by a high function, i = 3, indicates an object height function that appears in an aberration component proportional to the cube of the decentering amount.

Here, B _2jl (Ox, Oy) represents the x component of the wavefront tilt (coma aberration), and B _3jl (Ox, Oy) represents the y component of the wavefront tilt (coma aberration). As shown in FIGS. 32B and 32C, in the wavefront tilt (x component), the aberration component proportional to the first power of the decentration amount is expressed by an even function with respect to the object height coordinate. The aberration component proportional to the square of the amount of eccentricity is expressed by an odd function with respect to the object height coordinate. The aberration component proportional to the third power of the eccentricity is expressed by an even function with respect to the object height coordinate.

  Therefore, for the wavefront tilt (x component), the first aberration component can be extracted by taking the sum of the predetermined aberration component at one irradiation position and the predetermined aberration component at the other irradiation position. For example, if the object height coordinate is represented by (Ox, Oy), (Ox, Oy) and (0, 4) and (0, -4), (1, 2) and (-1, -2), etc. In a symmetrical object height coordinate such as -Ox, -Oy), a predetermined aberration component at one irradiation position and a predetermined aberration component at the other irradiation position may be extracted, and the sum of the two may be calculated. Note that the amount of decentration handled in this embodiment is very small, and the aberration component proportional to the cube of the amount of decentration is very small and can be ignored.

  The same applies to the wavefront tilt (y component).

Next, Table 18 shows a _{summary of} the decentration aberration sensitivity B _4jl (Ox, Oy).

In the decentration aberration sensitivity B _4jl (Ox, Oy) in the aberration component proportional to the first power of the decentration amount, the object height function appears at the first and third powers of the object height coordinate. Therefore, the aberration component proportional to the first power of the decentration amount is an odd function with respect to the object height coordinate. For the aberration component proportional to the square of the amount of decentration, the object height function appears in the square of the object height coordinate. Therefore, the aberration component proportional to the square of the decentration amount is an even function with respect to the object height coordinate. For the aberration component proportional to the cube of the decentering amount, the object height function appears at the cube of the object height coordinate. Therefore, the aberration component proportional to the cube of the decentering amount is an odd function with respect to the object height coordinate.

FIG. 33 is a diagram showing an object height function appearing in the decentration aberration sensitivity B _4jl (Ox, Oy), where (a) shows a case where the optical system to be _tested is not decentered, and (b) and (c) This shows a case where the test optical system is decentered. In the figure, a function indicated by l = 1 indicates an object height function that appears in an aberration component that is proportional to the first power of the eccentricity, and a function indicated by l = 2 indicates an object that appears in an aberration component that is proportional to the second power of the eccentricity. A function indicated by a high function, i = 3, indicates an object height function that appears in an aberration component proportional to the cube of the decentering amount.

Here, B _4jl (Ox, Oy) represents spherical aberration (focus). As shown in FIGS. 33B and 33C, in the spherical aberration (focus), an aberration component proportional to the first power of the decentering amount is expressed by an odd function with respect to the object high coordinate. The aberration component proportional to the square of the amount of decentration is expressed by an even function with respect to the object high coordinate. The aberration component proportional to the third power of the eccentricity is expressed by an odd function with respect to the object height coordinate.

  Therefore, for spherical aberration (focus), the first aberration component can be extracted by taking the difference between the predetermined aberration component at one irradiation position and the predetermined aberration component at the other irradiation position. For example, if the object height coordinate is represented by (Ox, Oy), (Ox, Oy) and (0, 4) and (0, -4), (1, 2) and (-1, -2), etc. In a symmetrical object height coordinate such as -Ox, -Oy), a predetermined aberration component at one irradiation position and a predetermined aberration component at the other irradiation position may be extracted, and the difference between them may be taken. Note that the amount of decentration handled in this embodiment is very small, and the aberration component proportional to the cube of the amount of decentration is very small and can be ignored.

First, Table 19 shows a _{summary of} the decentering aberration sensitivities B _5jl (Ox, Oy) and B _6jl (Ox, Oy).

In the decentration aberration sensitivities B _5jl (Ox, Oy) and B _6jl (Ox, Oy) in the aberration component proportional to the first power of the decentration amount, the object height function appears at the first power and the third power of the object height coordinate. Therefore, the aberration component proportional to the first power of the decentration amount is an odd function with respect to the object height coordinate. For the aberration component proportional to the square of the amount of decentration, the object height function appears at the 0th and 2nd powers of the object height coordinate. Therefore, the aberration component proportional to the square of the decentration amount is an even function with respect to the object height coordinate. For the aberration component proportional to the third power of the eccentricity, the object height function appears at the first and third power of the object height coordinate. Therefore, the aberration component proportional to the cube of the decentering amount is an even function with respect to the object height coordinate.

FIG. 34 is a diagram showing an object height function appearing in the decentration aberration sensitivities B _5jl (Ox, Oy) and B _6jl (Ox, Oy), where (a) shows a case where the test optical system is not decentered, (B) and (c) show a case where the optical system to be tested is decentered. In the figure, a function indicated by l = 1 indicates an object height function that appears in an aberration component that is proportional to the first power of the eccentricity, and a function indicated by l = 2 indicates an object that appears in an aberration component that is proportional to the second power of the eccentricity. A function indicated by a high function, i = 3, indicates an object height function that appears in an aberration component proportional to the cube of the decentering amount.

Here, both B _5jl (Ox, Oy) and B _6jl (Ox, Oy) represent astigmatism. As shown in FIGS. 34B and 34C, in astigmatism, an aberration component proportional to the first power of the decentering amount is expressed by an odd function with respect to the object height coordinate. The aberration component proportional to the square of the amount of decentration is expressed by an even function with respect to the object high coordinate. The aberration component proportional to the third power of the eccentricity is expressed by an odd function with respect to the object height coordinate.

  Therefore, astigmatism, the first aberration component can be extracted by taking the difference between the predetermined aberration component at one irradiation position and the predetermined aberration component at the other irradiation position. For example, if the object height coordinate is represented by (Ox, Oy), (Ox, Oy) and (0, 4) and (0, -4), (1, 2) and (-1, -2), etc. In a symmetrical object height coordinate such as -Ox, -Oy), a predetermined aberration component at one irradiation position and a predetermined aberration component at the other irradiation position may be extracted, and the difference between them may be taken. Note that the amount of decentration handled in this embodiment is very small, and the aberration component proportional to the cube of the amount of decentration is very small and can be ignored.

First, Table 20 shows a _{summary of} the decentering aberration sensitivities B _2jl (Ox, Oy) and B _3jl (Ox, Oy).

In the decentration aberration sensitivities B _7jl (Ox, Oy) and B _8jl (Ox, Oy) in the aberration component proportional to the first power of the decentration amount, the object height function appears at the 0th power and the second power of the object height coordinate. Therefore, the aberration component proportional to the first power of the decentration amount is an even function with respect to the object height coordinate. For the aberration component proportional to the square of the decentration amount, the object height function appears at the first and third powers of the object height coordinate. Therefore, the aberration component proportional to the square of the decentration amount is an odd function with respect to the object height coordinate. For the aberration component proportional to the cube of the decentering amount, the object height function appears in the square of the object height coordinate. Therefore, the aberration component proportional to the cube of the decentering amount is an even function with respect to the object height coordinate.

FIG. 35 is a diagram showing an object height function appearing in decentering aberration sensitivities B _7jl (Ox, Oy) and B _8jl (Ox, Oy), and (a) shows a case where the optical system to be _tested is not decentered, (B) and (c) show a case where the optical system to be tested is decentered. In the figure, a function indicated by l = 1 indicates an object height function that appears in an aberration component that is proportional to the first power of the eccentricity, and a function indicated by l = 2 indicates an object that appears in an aberration component that is proportional to the second power of the eccentricity. A function indicated by a high function, i = 3, indicates an object height function that appears in an aberration component proportional to the cube of the decentering amount.

Here, B _7jl (Ox, Oy) and B _8jl (Ox, Oy) both represent coma aberration. As shown in FIGS. 35B and 35C, in the coma aberration, the aberration component proportional to the first power of the decentering amount is expressed by an even function with respect to the object height coordinate. The aberration component proportional to the square of the amount of eccentricity is expressed by an odd function with respect to the object height coordinate. The aberration component proportional to the third power of the eccentricity is expressed by an even function with respect to the object height coordinate.

  Therefore, with respect to coma aberration, the first aberration component can be extracted by taking the sum of the predetermined aberration component at one irradiation position and the predetermined aberration component at the other irradiation position. For example, if the object height coordinate is represented by (Ox, Oy), (Ox, Oy) and (0, 4) and (0, -4), (1, 2) and (-1, -2), etc. In a symmetrical object height coordinate such as -Ox, -Oy), a predetermined aberration component at one irradiation position and a predetermined aberration component at the other irradiation position may be extracted, and the sum of the two may be calculated. Note that the amount of decentration handled in this embodiment is very small, and the aberration component proportional to the cube of the amount of decentration is very small and can be ignored.

  By fitting a predetermined aberration component extracted from the wavefront data at the irradiation position P and a predetermined aberration component extracted from the wavefront data at the irradiation position P ′ into a predetermined function system for each object height, The amount of decentration aberration 2 may be extracted. Functional terms 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, a method for calculating the decentration aberration sensitivity will be described. As described above, the test optical system may have a design aberration. The eccentricity measuring device may have system aberration. In some cases, the light receiving optical system is decentered. In addition, when the first rotation is performed, the first rotation axis may be shifted with respect to the measurement axis.

When such an aberration component exists, the wavefront aberration W is expressed by the following equation (1-13).
W (Ox, Oy, ρx, ρy, δ 1 + E, δ 2 + E, ···, δ j + E, δ j + 1, δ j + 2, ···, δ m)
= M (Ox, Oy, ρx, ρy)
+ Sys (Ox, Oy, ρx, ρy)
+ (δ ₁ + E) B ₁₁ (Ox, Oy, ρx, ρy)
+ (δ ₁ + E) ² B ₁₂ (Ox, Oy, ρx, ρy)
+ (δ ₂ + E) B ₂₁ (Ox, Oy, ρx, ρy)
+ (δ ₂ + E) ² B ₂₂ (Ox, Oy, ρx, ρy)
+ ...
+ (δ _j + E) B _j1 (Ox, Oy, ρx, ρy)
+ (δ _j + E) ² B _j2 (Ox, Oy, ρx, ρy)
+ δ _{j + 1} B _{(j + 1) 1} (Ox, Oy, ρx, ρy)
+ δ _{j + 1} ² B _{(j + 1) 2} (Ox, Oy, ρx, ρy)
+ δ _{j + 2} B _{(j + 2) 1} (Ox, Oy, ρx, ρy)
+ δ _{j + 2} ² B _{(j + 2) 2} (Ox, Oy, ρx, ρy)
+ ...
+ δ _m B _l1 (Ox, Oy, ρx, ρy)
+ δ _m ² B _l2 (Ox, Oy, ρx, ρy) (1-13)

  On the other hand, the decentration aberration sensitivity is obtained using optical simulation software, for example. In the optical simulation software, the amount of wavefront aberration that occurs when the degree of freedom of decentering is decentered by a unit amount is calculated for each lens of the test optical system. This amount of wavefront aberration is the decentration aberration sensitivity.

  In the optical simulation, an optical system for actually measuring the wavefront is set using the design values of the lens of the test optical system, the light projecting system, and the light receiving system. A situation is set in which there is no system aberration or shift of the first rotation axis with respect to the measurement axis. A situation is set in which there is no decentration of the test optical system, light projecting system, and light receiving system.

In this case, δ ₁ = 0, δ ₂ = 0,..., Δ _m = 0, E = 0, and Sys (Ox, Oy, ρx, ρy) = 0. Therefore, the wavefront aberration W when the decentration aberration sensitivity is obtained is expressed by Expression (1-14). Here, M (Ox, Oy, ρx, ρy) is a design aberration of the test optical system, the light projecting system, and the light receiving system.

W (Ox, Oy, ρx, ρy, δ ₁ = 0, δ ₂ = 0, ..., δ _m = 0)
= M (Ox, Oy, ρx, ρy) (1-14)

Therefore, procedure 1 is first executed. In procedure 1, a ray tracing simulation is executed in a state where the amount of eccentricity Δ _i = δ _i = 0 of the test optical system, and wavefront data is obtained by calculation.

  Next, procedure 2 is executed. In procedure 2, a unit decentering amount (for example, Δo = 0.01 mm) is given only to the first surface of the optical system to be tested in the formula (1-14). In this case, the wavefront aberration W is expressed by Expression (1-15).

W (Ox, Oy, ρx, ρy, δ ₁ = Δo = 0.01 mm, δ ₂ = 0, ..., δ _m = 0)
= M (Ox, Oy, ρx, ρy)
+ ΔoB ₁₁ (Ox, Oy, ρx, ρy)
+ Δo ² B ₁₂ (Ox, Oy, ρx, ρy) (1-15)

In step 2, a ray tracing simulation is executed in a state where the amount of eccentricity Δo = δ ₁ = 0 of the test optical system, and wavefront data is obtained by calculation.

  When an SH sensor is used as the wavefront detection device, a ray tracing simulation is executed to obtain light spot image position data. The data of the light spot image position corresponds to the wavefront aberration of the formula (1-14) and the wavefront aberration of the formula (1-15) differentiated by pupil coordinates.

  Step 3 is executed. In the procedure 3, the wavefront data obtained in the procedure 2 is analyzed with reference to the wavefront data obtained in the procedure 1, and the wavefront aberration is obtained. In this case, the wavefront aberration is expressed by Expression (1-16). The wavefront aberration expressed by the equation (1-16) is a deviation of the wavefront when a single surface is decentered with respect to the wavefront when the test optical system is not decentered. Therefore, actually, it is not necessary to directly calculate the wavefront aberration W of the equation (1-15).

W (Ox, Oy, ρx, ρy, δ ₁ = Δo = 0.01, δ ₂ = 0, ..., δ _m = 0)
-W (Ox, Oy, ρx, ρy, δ ₁ = 0, δ ₂ = 0, ..., δ _m = 0)
= ΔoB ₁₁ (Ox, Oy, ρx, ρy)
+ Δo ² B ₁₂ (Ox, Oy, ρx, ρy) (1-16)

  Step 4 is executed. In the procedure 4, the procedure 2 and the procedure 3 are executed for the object height coordinates (-Ox, -Oy) symmetrical to the object height coordinates (Ox, Oy). In this case, the wavefront aberration W is expressed by Expression (1-17).

W (-Ox, -Oy, ρx, ρy, δ ₁ = Δo = 0.01, δ ₂ = 0, ..., δ _m = 0)
-W (-Ox, -Oy, ρx, ρy, δ ₁ = 0, δ ₂ = 0, ..., δ _m = 0)
= ΔoB ₁₁ (-Ox, -Oy, ρx, ρy)
+ Δo ₁ ² B ₁₂ (-Ox, -Oy, ρx, ρy) (1-17)

  Step 5 is executed. In Procedure 5, Expressions (1-16) and (1-17) are expanded with Zernike polynomials, respectively. Here, each term of the Zernike term is divided into a term in which the pupil coordinates are multiplied by an odd-order function and a term in which the pupil coordinates are multiplied by an even-order function.

  The aberration component including a term whose pupil coordinates are multiplied by an odd-order function is an aberration component including a term multiplied by the second term of the Zernike term. In this case, the aberration components (z = 2, 3, 7, 8,...) Are summed. As a result, Expression (24) is obtained.

Sz ₁ (Ox, Oy)
= [Wz (Ox, Oy, δ ₁ = Δo = 0.01, δ ₂ = 0,..., Δ _m = 0) −W (Ox, Oy, ρx, ρy, δ ₁ = 0, δ ₂ = 0, ..., δ _m = 0)]
+ [Wz (−Ox, −Oy, δ ₁ = Δo = 0.01, δ ₂ = 0,..., Δ _m = 0) −W (−Ox, −Oy, ρx, ρy, δ ₁ = 0, δ ₂ = 0, ..., δ _m = 0)]
= Δo [2Bz ₁₁ (Ox, Oy)] (24)

  The aberration component including a term in which the pupil coordinates are multiplied by an even-order function is an aberration component including a term multiplied by the fourth term of the Zernike term. In this case, a difference is taken for each aberration component (z = 1, 4, 5, 6, 9...). As a result, Expression (25) is obtained.

Sz ₁ (Ox, Oy)
= [Wz (Ox, Oy, δ ₁ = Δo = 0.01, δ ₂ = 0,..., Δ _m = 0) −W (Ox, Oy, ρx, ρy, δ ₁ = 0, δ ₂ = 0, ..., δ _m = 0)]
-[Wz (-Ox, -Oy, δ ₁ = Δo = 0.01, δ ₂ = 0, ..., δ _m = 0) -W (-Ox, -Oy, ρx, ρy, δ ₁ = 0, δ ₂ = 0, ..., δ _m = 0)]
= Δo [2Bz ₁₁ (Ox, Oy)] (25)

When formula (25) is transformed, formula (25 ′) is obtained.
Bz ₁₁ (Ox, Oy) = Sz ₁ (Ox, Oy) / (2Δo) (25 ′)

Here, Δo is known. The following four wavefront aberration amounts can also be obtained from the ray tracing simulation. Therefore, Sz ₁ (Ox, Oy) is also known.
W (Ox, Oy, δ ₁ = Δo = 0.01, δ ₂ = 0, ..., δ _m = 0)
W (Ox, Oy, ρx, ρy, δ ₁ = 0, δ ₂ = 0, ..., δ _m = 0)
W (−Ox, −Oy, δ ₁ = Δo = 0.01, δ ₂ = 0,..., Δ _m = 0)
W (-Ox, -Oy, ρx, ρy, δ ₁ = 0, δ ₂ = 0, ..., δ _m = 0)

Therefore, Bz ₁₁ (Ox, Oy) can be obtained from the equation (25 ′). Bz ₁₁ (Ox, Oy) shown in Expression (25 ′) is the decentration aberration sensitivity on the first surface of the optical system to be tested. This decentration aberration sensitivity is the decentration aberration sensitivity proportional to the first power of the decentration amount, and is the decentration aberration sensitivity per unit decentration amount in the Z-term of the Zernike term and the object height coordinate (Ox, Oy).

Step 6 is executed. In step 6, all the eccentric degrees of freedom (δ ₁・ ・ δ _i・ ・ δ _j ) and all object height coordinates (Ox1, Oy1) ... (Oxq, Oyq) (q point) for wavefront measurement Then, the procedure 1 to the procedure 5 are carried out to obtain the decentration aberration sensitivity Bz _i1 (Ox, Oy).

  For aspheric surfaces, tilt decentration aberration sensitivity calculation is performed. At this time, the rotation center of the tilt may be selected from the top of the aspheric surface, or another place on the aspheric axis. However, when a location other than the top of the aspheric surface is selected as the center of tilt, it is necessary to define the eccentricity of the shift as the eccentricity of that location.

When the execution of the procedure 6 is completed, a decentration aberration sensitivity matrix is obtained as follows.

The simultaneous linear equations using this decentration aberration sensitivity matrix are as follows.

  The left side of the simultaneous linear equations shown in Equation 2 is composed of Tz calculated from data obtained by actual wavefront measurement. That is, it is a matrix of measurement data. The matrix multiplied by the matrix of the decentration aberration sensitivity on the right side is a matrix of the amount of displacement accompanying rotation when the test optical system is rotated by a certain angle by the first rotation axis. This is the displacement matrix.

  Here, the degree of freedom of eccentricity is j. For example, when there are two spherical surfaces and two aspheric surfaces, the degrees of freedom on one spherical surface are X and Y, the degrees of freedom on the other spherical surface are X and Y, and the degree of freedom on one aspheric surface is X, Since the degrees of freedom in Y, A, and B and the other aspheric surface are X, Y, A, and B, the degree of freedom j is 12. The Zernike term uses 2 to n. The object height is q points of (Ox1, Oy1)... (Oxq, Oyq).

  In this simultaneous linear equation, the amount of eccentricity is analyzed by substituting Tz measured for each object height coordinate as it is. However, Tz is a process of removing the second aberration component, and has a value twice the original first aberration component amount with respect to the decentration aberration sensitivity. Cracking.

  Note that the decentration aberration sensitivity varies depending on the object height coordinates. Therefore, the decentration aberration sensitivity is obtained at each object high coordinate.

Here, as described above, the decentration aberration sensitivity of the term in which the pupil coordinates are multiplied by the odd-order function is the decentration aberration sensitivity multiplied by the second term of the Zernike term. In this case, the decentration aberration sensitivity B _zj1 (Ox, Oy) (z = 2, 3, 7, 8,...) Is expressed by Expression (3).
B _zj1 (Ox, Oy) ＝ C _zj100 + C _zj120 Ox ² + C _zj111 OxOy + C _zj102 Oy ² + (3)

This equation (3) can be described as the following equation (26).
Bz _j1 (Ox, Oy)
= Dzj ₁₀・ g ₀ (Ox, Oy) + Dzj ₁₂・ g ₂ (Ox, Oy) + Dzj ₁₄・ g ₄ (Ox, Oy) + ・ ・ ・ （26）
here,
g ₀ (Ox, Oy) is a function whose maximum order of the object height coordinate is 0th order,
g ₂ (Ox, Oy) is a function whose maximum order of the object height coordinate is quadratic,
g ₄ (Ox, Oy) is a function whose maximum order of the object height coordinate is the fourth order,
It is.

Further, the decentration aberration sensitivity of the term in which the pupil coordinates are multiplied by the even-order function is the decentration aberration sensitivity multiplied by the fourth term of the Zernike term. In this case, the decentration aberration sensitivity B _zj1 (Ox, Oy) (z = 1, 4, 5, 6, 9...) Is expressed by the following equation (4).
B _zj1 (Ox, Oy) = C _zj110 Ox + C _zj101 Oy + C _zj130 Ox ³ + C _zj121 Ox ² Oy
+ C _zj112 OxOy ² + C _zj103 Oy ³ + ... (4)

This equation (4) can be described as the following equation (27).
Bz _j1 (Ox, Oy)
= Dzj ₁₁・ g ₁ (Ox, Oy) + Dzj ₁₃・ g ₃ (Ox, Oy) + Dzj ₁₅・ g ₅ (Ox, Oy) + ・ ・ ・ （27）
here,
g ₁ (Ox, Oy) is a function whose maximum order of the object height coordinate is the first order,
g ₃ (Ox, Oy) is the function whose maximum order of the object height coordinate is the third order,
g ₅ (Ox, Oy) is the function whose maximum order of the object height coordinate is the fifth order,
It is.

  In Expressions (26) to (27), D is a constant that does not depend on the object height coordinates, pupil coordinates, and eccentricity. The subscripts in D indicate the Z-th term of the Zernike term, the j-th surface, the value of l, and the order in the object high coordinate in order from the left side.

As the function g _k (Ox, Oy) (K = 1, 2, 3,...), An orthogonal function system may be used or Field terms may be used.

Similarly, the expression (21) can be similarly developed. The aberration component including a term whose pupil coordinates are multiplied by an odd-order function is an aberration component multiplied by the second term of the Zernike term. The aberration component Tz (Ox, Oy, δ _1, δ _2, ..., Δ _j ) / 2 in this case can be described as the following equation (28).
Tz (Ox, Oy, δ _1, δ _2, ..., δ _j ) / 2
= Ez ₁₀・ g ₀ (Ox, Oy) + Ez ₁₂・ g ₂ (Ox, Oy) + Ez ₁₄ + ・ g ₄ (Ox, Oy) (28)
here,
g ₀ (Ox, Oy) is a function whose maximum power is 0th order of Ox, Oy,
g ₂ (Ox, Oy) is a function of maximum degree Ox, Oy power,
g ₄ (Ox, Oy) is the function of maximum order 4th order power of Ox, Oy,
It is.

An aberration component including a term in which pupil coordinates are multiplied by an even-order function is an aberration component multiplied by the fourth term of the Zernike term. The aberration component Tz (Ox, Oy, δ _1, δ _2, ..., Δ _j ) / 2 in this case can be described as the following equation (29).
Tz (Ox, Oy, δ _1, δ _2, ..., δ _j ) / 2
= Ez ₁₁・ g ₁ (Ox, Oy) + Ez ₁₃・ g ₃ (Ox, Oy) + Ez ₁₅・ g ₅ (Ox, Oy) + ・ ・ ・ (29)
here,
g ₁ (Ox, Oy) is a function of maximum degree Ox, Oy power,
g ₃ (Ox, Oy) is the function of the maximum degree of the power of Ox, Oy,
g ₅ (Ox, Oy) is a function whose maximum power is Ox, Oy,
It is.

  E in the equations (28) to (29) is a constant that does not depend on the object height coordinates, pupil coordinates, and eccentricity. The subscripts in E indicate the Z-term of the Zernike term, the value of l, and the degree in the object height coordinate in order from the left side.

Fitting is performed on Tz obtained from wavefront data measured for each object height coordinate and Bz _j1 obtained by calculation, and aberrations are applied to coefficients E and D.

  Note that D may be obtained by fitting from the data of the expressions (1-16) and (1-17) including the second aberration component. By fitting, the second aberration component can be eliminated and applied to D.

  Note that E may be obtained by fitting from the data of the expressions (1-11) and (1-12) including the second aberration component. By fitting, the second aberration component can be eliminated and applied to E.

As a result, the simultaneous linear equations can be expressed as follows.

  In this simultaneous linear equation, E is obtained by fitting from Tz calculated from wavefront data measured for each object height coordinate, and is substituted into the equation to analyze the eccentricity.

  In this simultaneous linear equation, if an orthogonal function system is adopted as the object height function, a certain kind of filtering is performed on Tz calculated from the wavefront data obtained by actual wavefront measurement, and the influence of the Tz error is affected. Can be reduced. However, it is necessary to increase the number of object height coordinates in wavefront measurement, and an analysis process for applying Tz to E is required.

  Although two types of simultaneous linear equations have been described above, either of the simultaneous linear equations may be used.

  Since the data excluding the aberration component proportional to the square of the amount of decentration is used, if the aberration component proportional to the third power of the amount of decentration can be ignored, the matrix of measurement data, the matrix of decentration aberration sensitivity, and the decentration The product of the matrix of quantities can be considered equal. Therefore, an equation is established in which the measurement data matrix is equal to the product of the decentration aberration sensitivity matrix and the decentration amount matrix. Then, the amount of eccentricity of each degree of eccentricity can be obtained using a fitting algorithm such as a least square method.

  Since the measurement data matrix and the aberration component proportional to the first power of the matrix eccentricity of the decentration aberration sensitivity are configured, even when the eccentricity is large as a manufacturing error, the eccentricity can be obtained with high accuracy.

For example, when the test optical system is rotated 180 degrees by the first rotation axis, the displacement amount of each lens surface is −2 times the eccentric amount of each lens surface based on the rotation axis. At this time, each element (δ ₁ , δ ₂ ,..., Δ _j ) of the displacement amount matrix obtained by analyzing the simultaneous linear equations shown in Equation ₂ is the − of the eccentric amount of each lens surface based on the rotation axis. Doubled. Therefore, by dividing each element (δ ₁ , δ ₂ ,..., Δ _j ) of the obtained displacement amount matrix by −2, the amount of eccentricity of each lens based on the rotation axis before rotation of the test optical system Can be requested.

  In addition, when the rotation angle in the first rotation is different from 180 degrees, it may be 90 degrees, for example. In this case, the amount of eccentricity for each degree of eccentricity of each lens surface based on the rotation axis can be obtained in consideration of the amount of displacement of each lens surface that occurs with rotation.

  Since the measurement data matrix and the decentration aberration sensitivity matrix are composed of aberration components proportional to the first power of the decentration amount, even if the first rotation axis is deviated from the measurement axis, the decentration is highly accurate. The amount can be determined.

  In addition, the degree of measurement error such as repeatability may be known for each Zernike coefficient. In such a case, if an equation is weighted based on the measurement error and the simultaneous linear equation is solved, the error of the eccentricity obtained by the analysis is also reduced.

When the second rotation is performed, simultaneous linear equations can be established as follows. However, the first aberration component data of the front measurement is Tz, the decentration aberration sensitivity is B, the first aberration component data of the rear measurement is T′z, and the decentration aberration sensitivity is B ′. As the number 4, displacement at the front side measuring _{(δ 1, δ 2, ···} , δ j) displacement at the rear side measurement _{(δ 1, δ 2, ···} , δ j) so are the same Therefore, it is necessary to consider the sign of sensitivity in consideration of the second rotation of the optical system to be tested. For example, when the second rotation of the test optical system is performed about the Y axis, the decentration aberration sensitivity of the rear side measurement is the front side measurement of the decentration aberration sensitivity of the eccentricity shift of the X direction and the tilt in the A direction. In contrast, the sign is inverted.

  The degree of freedom of eccentricity that can be measured by the measurement method of the present embodiment will be described. In the measurement method of this embodiment, the amount of decentering for each lens is measured for each lens using information on the wavefront aberration at the wavefront transmitted through the test optical system. For this reason, as the degree of freedom of eccentricity increases, it becomes difficult to distinguish the amount of eccentricity for each degree of freedom of eccentricity. Therefore, the standard of the degree of eccentricity that can be measured is presented.

  Table 21 circles a term that is proportional to the first power of the amount of eccentricity when the wavefront aberration is expanded in terms of pupil coordinates, object height, and amount of eccentricity. The term indicated by these circles is the first aberration component. For example, the first aberration component multiplied by the function of the Z2 term includes a component proportional to the 0th power of the object height, a component proportional to the square, and so on. The first aberration component multiplied by the function of the Z4 term includes a component proportional to the first power of the object height, a component proportional to the third power, and so on. In Table 21, a hyphen (-) indicates that the first aberration component does not exist.

Further, the degree of eccentricity in the table indicates a first aberration component generated by the degree of eccentricity. Even if the data of the first aberration component is used at many object heights in the simultaneous linear equations shown in Equation 2, the number of decentered degrees of freedom that can be measured is summarized in the number of circles in Table 21. Conceivable. That is, the number of circles can be considered as the amount of information regarding substantial eccentricity.

  In order to make it easy to understand the degree of freedom of decentration that can be measured in this embodiment, the first aberration component of the optical system under test is the third or lower order of the pupil coordinates (the second to eighth terms of the Zernike term), the object height coordinate It is considered that the first and lower order components are generated.

  In this case, the first aberration component can be represented by a black circle in Table 21. The number of black circles is 8. Since the amount of information is considered to be aggregated into 8, the number of required eccentric degrees of freedom is also 8.

  For example, in the case of a spherical surface, the number of degrees of freedom of eccentricity is 2. Therefore, when the optical system to be tested is configured with four lens surfaces, the number of degrees of freedom of decentering of each lens surface is eight. Therefore, in this case, the amount of eccentricity on each lens surface can be measured. For example, in the case of an aspherical surface, the number of degrees of freedom of eccentricity is 4. Therefore, when the aspherical surface is composed of two lens surfaces, the number of eccentric degrees of freedom of each lens surface is eight. Therefore, also in this case, the amount of eccentricity on each lens surface can be measured.

  However, since the order of the pupil coordinate and the height of the object height coordinate that can be measured increases depending on the nature of the aberration of the optical system to be measured and the wavefront measurement conditions, the eight are the order of the object height coordinate and the pupil coordinate. It is a standard when limiting to low order.

  In addition, when the front side measurement and the rear side measurement are performed using the second rotation, black circle information can be similarly obtained in each measurement. However, since the decentration aberration sensitivity differs between the front side measurement and the rear side measurement as described above, the number of black circles, that is, the number of first aberration components increases to 16. Therefore, the eccentricity measurement of 16 eccentricity degrees of freedom can be performed.

  By obtaining the condition number of the decentration aberration sensitivity matrix shown in Equations 2, 3, and 4, it is obtained when an error is included in Tz calculated from data obtained by actual wavefront measurement. The degree of error propagation to the amount of eccentricity can be evaluated. The condition number can be calculated by the ratio of the maximum singular value and the minimum singular value of the matrix. The value of the condition number decreases as the error propagation degree decreases. The minimum value of the condition number is 1. When measuring the wavefront of the test optical system, there are an infinite number of beam injection methods to the test optical system, but if you select an injection method that reduces the condition number, the accuracy of the required eccentricity can be improved. can do.

  According to the measurement method of the present embodiment, by using an SH sensor as a wavefront sensor, wavefront measurement for each of a plurality of object heights can be easily performed in a short time. Therefore, the amount of eccentricity can be easily measured in a short time. In addition, it is possible to accurately extract the amount of decentration of the test optical system by eliminating the aberration component caused by various manufacturing errors in the measurement system and the design aberration component of the test optical system. It can be performed.

  Note that the test optical system targeted by the measurement method of the present embodiment is a rotationally symmetric optical system.

  Wavefront data in the SH sensor and a wavefront aberration analysis method using the wavefront data will be described. The SH sensor includes a microlens array and an imager (CCD or CMOS). When the focal length of the micro lens is f, the micro lens array and the imager are fixed apart by f.

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

  A measurement apparatus including an SH sensor usually has a manufacturing error, which is a system aberration. Hereinafter, a normal method for removing the system aberration will be described.

  A wavefront Wo having no aberration is incident on the SH sensor, and the light spot image position (Sox (ρx, ρy), Soy (ρx, ρy)) formed at that time is measured. Here, this light spot image position is called wavefront data. (ρx, ρy) are the coordinates (pupil coordinates) of the position of the microlens.

The light spot image position (Sox, Soy) includes the influence of the system aberration sys (ρx, ρy). In this case, (Sox, Soy) is expressed by the following equations (30) and (31).
Sox (ρx, ρy)
= ∂ (Wo (ρx, ρy) + sys (ρx, ρy)) / ∂ρx · f
= ∂Wo (ρx, ρy) / ∂ρx + бsys (ρx, ρy) / ∂ρx · f (30)
Soy (ρx, ρy)
= ∂ (Wo (ρx, ρy) + sys (ρx, ρy)) / ∂ρy · f
= ∂Wo (ρx, ρy) / ∂ρy + бsys (ρx, ρy) / ∂ρy · f (31)

Next, a wavefront W having an aberration is incident, and a light spot image position (Sx, Sy) formed at that time is measured. In this case, (Sx, Sy) is expressed by the following equations (32) and (33).
Sx (ρx, ρy)
= б (W (ρx, ρy) + sys (ρx, ρy)) / ∂ρx · f
= ∂W (ρx, ρy) / ∂ρx + ∂sys (ρx, ρy) / ∂ρx · f (32)
Sy (ρx, ρy)
= б (W (ρx, ρy) + sys (ρx, ρy)) / ∂ρy · f
= ∂W (ρx, ρy) / ∂ρy + ∂sys (ρx, ρy) / ∂ρy · f (33)

Taking the difference between Equation (30) and Equation (32) yields Equation (34).
Sx (ρx, ρy) -Sox (ρx, ρy)
= ∂ (W (ρx, ρy) −Wo (ρx, ρy)) / ∂ρx · f (34)

Further, when the difference between Expression (31) and Expression (33) is taken, Expression (35) is obtained.
Sy (ρx, ρy) -Soy (ρx, ρy)
= ∂ (W (ρx, ρy) −Wo (ρx, ρy)) / ∂ρy · f (35)

  Expressions (34) and (35) are data indicating the differential amount of the wavefront. There are two methods for determining the wavefront from this data.

  The first method is a method of obtaining the Zernike coefficient by fitting the equations (34) and (35) with a function obtained by differentiating the Zernike polynomial with ρx and a function differentiated with ρy (wavefront analysis 1).

  The second method is a method of obtaining the wavefront by integrating the equations (34) and (35) with ρx and ρy (wavefront analysis 2).

  In a normal method, one of these two methods is used. However, when this method is used, it is necessary to input wavefront Wo having no aberration to the SH sensor to obtain wavefront calibration data. In this case, a wavefront Wo having no aberration is made incident on the SH sensor at a plurality of object height coordinates, and wavefront data is acquired. However, this is expensive.

  On the other hand, in the measurement method of the present embodiment, the wavefront Wo having no aberration is not incident on the SH sensor. Instead, the test optical system is rotated around 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 the light spot image position (S1x (ρx, ρy), S1y (ρx, ρy)) created at that time is measured. Subsequently, the first rotation is performed, the wavefront W2 is incident on the SH sensor, and the light spot image positions (S2x (ρx, ρy), S2y (ρx, ρy)) created at that time are measured.

Then, when the difference between the two is taken, Expression (36) and Expression (37) are obtained.
S2x (ρx, ρy) -S1x (ρx, ρy)
= ∂ (W2 (ρx, ρy) −W1 (ρx, ρy)) / ∂ρx · f (36)
S2y (ρx, ρy) -S1y (ρx, ρy)
= ∂ (W2 (ρx, ρy) −W1 (ρx, ρy)) / ∂ρy · f (37)

  In order to obtain the wavefront from this data, the wavefront is analyzed by one of the following two methods.

  The first method is a method of obtaining the Zernike coefficient by fitting Equation (36) and Equation (37) with a function obtained by differentiating Zernike polynomials by ρx and a function differentiated by ρy (wavefront analysis 1).

  The second is a method of obtaining the wavefront by integrating the equations (36) and (37) with ρx and ρy (wavefront analysis 2).

  When an SH sensor is used in the light receiving system, for example, the wavefront data used in the above description of (IV) is the data of the light spot image position. The wavefront aberration is analyzed from the wavefront data by performing the processing shown in Expression (36) and the processing shown in Expression (37) on the light spot image position data obtained in two types of states, and then analyzing the wavefront analysis 1 Alternatively, it means that wavefront analysis 2 is performed to determine wavefront aberration.

  Further, the eccentricity measuring device of the present embodiment includes a light projecting system disposed at one end of the measurement axis, a light receiving system disposed at the other end of the measurement axis, a holding member that holds the optical system to be measured, and a wavefront And a processing device connected to the measuring device, the holding member is disposed between the light projecting system and the light receiving system, and the light projecting system is provided at a position for irradiating the test optical system with a light beam. In the apparatus, an acquisition step, a first extraction step, a second extraction step, and an analysis step are executed. In the acquisition step, wavefront data is acquired based on the light beam emitted from the optical system to be tested, and the first step In the 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 component. In the analysis step, the first aberration component and the eccentric aberration sensitivity are extracted. And simultaneous linear equations for the amount of decentration are analyzed, and the predetermined aberration component is decentered. The first aberration component is an aberration component proportional to the first power of the decentering amount of the predetermined aberration components, and the decentration aberration sensitivity is the first power of the decentering amount. Aberration sensitivity proportional to

  FIG. 36 shows an eccentricity measuring apparatus according to this embodiment. The eccentricity measuring device 100 includes a light projecting system 102, a light receiving system 103, and a holding member 104. Further, the eccentricity measuring device 100 has a main body 101. The main body 101 is provided with a light projecting system 102, a light receiving system 103, and a holding member 104.

The light projecting system 102 is disposed on one side of the measurement axis AX _M , and the light receiving system 103 is disposed on the other side. The holding member 104 is disposed between the light projecting system 102 and the light receiving system 103. Thus, the light projecting system 102 and the light receiving system 103 are provided so as to face each other with the holding member 104 interposed therebetween.

  The light projecting system 102 generates a light beam that irradiates the test optical system 105. For this purpose, the light projecting system 102 has a light source. Examples of the light source include a laser, an LED, a halogen lamp, and a xenon lamp.

  The light projecting system 102 may include an optical system. A spherical wave can be generated by condensing the light emitted from the light source by the optical system.

  In the eccentricity measuring apparatus 100, the light projecting system 102 is fixed on the drive stage 107 via the holding member 106. The drive stage 107 is fixed on the drive stage 108. The drive stage 108 is fixed to the main body 101.

Each of the drive stage 107 and the drive stage 108 is a stage that moves in one direction. The moving direction of the driving stage 107 and the moving direction of the driving stage 108 are orthogonal. Therefore, the light projecting system 102 can be moved by the drive stage 107 and the drive stage 108 within a plane orthogonal to the measurement axis AX _M (hereinafter referred to as “OxOy plane”). The measurement axis AX _M coincides with the Oz axis.

A test optical system 105 is placed on the holding member 104. Here, the test optical system 105 is in an eccentric state. Therefore, to match the approximate center of the optical system to be measured 105 in the measurement axis AX _M, thus placing the tested optical system 105. Therefore, it is preferable that the position of the test optical system 105 is adjustable in the OxOy plane.

  For example, the holding member 109 is disposed between the holding member 104 and the test optical system 105. The holding member 109 is composed of two drive stages. At this time, the two drive stages are combined in the same manner as the drive stage 107 and the drive stage 108. In this way, the position of the test optical system 105 can be adjusted in the OxOy plane.

  Thus, the holding member 109 has an adjustment function in the OxOy plane. The holding member 109 can have other functions. Other functions will be described later.

Note that after mounting the holding member 109 of the tested optical system 105 irradiates from the measuring axis AX _M light flux optical system to be measured 105. Then, a predetermined aberration component is extracted from the wavefront data obtained by the light receiving system 103. The position of the test optical system 105 may be adjusted so that the predetermined aberration component is minimized.

  For example, when a Zernike polynomial is used, an aberration amount relating to tilt, an aberration amount relating to coma aberration, and an aberration amount relating to focus are extracted. Therefore, the position of the test optical system 105 may be adjusted so that the amount of aberration related to tilt and the amount of aberration related to coma are minimized, and the amount of aberration related to focus is about the aberration at the time of design.

  Further, there are optical systems with various specifications as the test optical system 105. Therefore, the front focal position and the rear focal position of the test optical system 105 differ depending on the test optical system 105. In the decentration amount measuring apparatus 100, the light projecting system 102 is arranged at the front focal position of the optical system 105 to be tested, and the light receiving system 103 is arranged at the rear focal position of the optical system 105 to be examined.

To be able to measure the eccentric amount for various target optical system 105, the light projecting system 102, among the holding member 104 and the light receiving system 103, at least two, needs to move along the measuring axis AX _M is there. In the eccentricity measuring apparatus 100, the holding member 104 is held by the moving mechanism 110. By driving the drive mechanism 110, the holding member 104, i.e., it can be moved along the target optical system 105 to the measuring axis AX _M.

However, only the movement of the holding member 104 can make only one of the light projecting system 102 and the light receiving system 103 coincide with the focal position. Therefore, either the light projecting system 10 and the light receiving system 103, so as to move along the measuring axis AX _M. Alternatively, the light projecting system 102 and the light receiving system 103 may be movable instead of having the moving mechanism 110.

  Further, a holding member 111 may be provided between the light projecting system 102 and the holding member 104. The holding member 111 is provided at a position for holding the optical system 105 to be tested. When the entire length of the test optical system 105 is long, the test optical system 105 can be stably held by the holding member 111. The holding member 111 can have other functions. Other functions will be described later.

  The light receiving system 103 has a wavefront measuring device. The wavefront measuring apparatus is disposed on the rear focal plane of the optical system 105 to be tested. The wavefront measuring device is, for example, an SH sensor. 37A and 37B are diagrams showing the structure and function of the SH sensor. FIG. 37A shows a state when a plane wave is incident on the SH sensor, and FIG. 37B shows a state when a non-plane wave is incident on the SH sensor. ing.

  The SH sensor 120 includes a microlens array 121 and an image sensor 122. The image sensor 122 is, for example, a CCD or a CMOS. Here, it is assumed that the microlenses are arranged at equal intervals, and each microlens has no aberration.

  In the SH sensor 120, the light beam incident on the SH sensor 120 is collected by the microlens array 121. At this time, the same number of light spot images as the number of microlenses through which the luminous flux has passed are formed at the condensing position. An image sensor 122 is disposed at the condensing position. Each of the light spot images is received by the image sensor 122. Here, in the image sensor 122, minute light receiving elements are two-dimensionally arranged. Therefore, the position of each light spot image can be known.

  When a plane wave enters the SH sensor 120, as shown in FIG. 37A, each of the light spot images is formed at equal intervals. On the other hand, when a non-plane wave is incident on the SH sensor 120, as shown in FIG. 37B, the light spot images are not formed at regular intervals. Thus, the position of each light spot image depends on the shape of the wavefront incident on the SH sensor 120, that is, the amount of wavefront aberration generated.

  When a wavefront to be measured is incident on the SH sensor 120, the wavefront is divided by the microlens array 121. As a result, the wavefront is projected as a plurality of light spot images on the imaging surface of the imaging element 122. Wavefront aberration can be measured from the amount of deviation of the plurality of light spot image positions from the reference position.

  The reference position is the position of the light spot image when a plane wave to be referenced is incident on the SH sensor in advance and the plane wave is projected (see: Data Processing of Shack-Hartmann Specular Surface Measurement System) of the National Astronomical Observatory of Japan (Vol.2, No.2) (Vol.2, No.2), pp.431-446). This is the position of each light spot image in FIG.

  As described above, when measuring the amount of eccentricity with high accuracy, it is preferable to obtain a larger amount of information by reducing the movement pitch of the irradiation position. If the moving pitch is made smaller, the number of measurement points increases. Since the SH sensor only captures a light spot image with an image sensor, acquisition of wavefront data can be completed in a short time. Therefore, for example, the wavefront data can be acquired in a very short time compared to the interferometer fringe scan method. Thus, if an SH sensor is used, measurement can be performed in a sufficiently practical time.

  As described above, the light receiving system 103, that is, the wavefront measuring apparatus may have system aberration. 38A and 38B are diagrams showing system aberrations in the SH sensor 120. FIG. 38A shows a case where the substrate is distorted, FIG. 38B shows a case where the substrate is tilted, and FIG. 38C shows an error in the lens pitch. (D) shows a case where the focal lengths of the lenses are different.

  In the SH sensor 120, the microlens array 121 includes a substrate 121a and a microlens 121b. In FIG. 38A, the focal length of each microlens 121b is the same, but the substrate 121a is curved. In this case, the arrangement of the microlenses 121b is irregular. Therefore, even if a plane wave is incident, the intervals between the light spot images are irregular.

  Furthermore, the direction of the optical axis of the microlens 121b is directed outward as the position of the microlens 121b is closer to the periphery. For this reason, the interval between the light spot images becomes wider toward the periphery.

  In FIG. 38B, the substrate 121a is not distorted, and the microlenses 121b are also regularly arranged. The focal length of each microlens 121b is also the same. However, the entire microlens array 121 is inclined with respect to the image sensor 122. In this case, when a plane wave is incident, light spot images are formed at equal intervals. However, the entire light spot image moves to a position shifted from the original position.

  In FIG. 38C, the substrate 121a is not distorted, and the focal length of each microlens 121b is the same. However, the arrangement of the microlenses 121b is irregular. Therefore, even if a plane wave is incident, the intervals between the light spot images are irregular.

  In FIG. 38D, the substrate 121a is not distorted. However, there are variations in the focal length of the microlens 121b. In this case, since there are microlenses having different external shapes, the arrangement of the microlenses 121b becomes irregular. Therefore, even if a plane wave is incident, the intervals between the light spot images are irregular.

  Thus, when a manufacturing error occurs in the microlens 121b, the wavefront measuring apparatus 103 has system aberration. In this case, the position of each light spot image formed on the image sensor 122 is different from the position of the light spot image formed on the wavefront to be measured.

  In this case, there is a method in which a plane wave is incident on the SH sensor 120 in advance to obtain the position of each light spot image, and the obtained position is set as a reference position. The plane wave when the reference position is obtained and the wavefront to be measured pass through almost the same measurement system. Therefore, if the reference position is obtained in advance, even if system aberration exists, it is possible to cancel the system aberration and accurately measure the wavefront to be measured.

  However, it is expensive to produce a highly accurate plane wave. In addition, when measuring the wavefront when the light beam is irradiated from the off-axis, it is necessary to match the angle of the light beam incident on the SH sensor with high accuracy between the wavefront to be measured and the wavefront when obtaining the reference position. Arise.

  Even if the two wavefronts can be matched with high accuracy, rotational errors such as the design aberration of the test optical system, the radius of curvature error of each surface of the test optical system, and the surface spacing error can occur. It is difficult to distinguish aberrations accompanying aberrations and aberrations caused by manufacturing errors of the projection system such as the projection system from aberrations caused by decentration.

  Therefore, even when the SH sensor is used, such a problem can be solved by performing the first rotation and acquiring the wavefront data.

  In the eccentricity measuring apparatus 100, the light projecting system 102 is arranged at the front focal position of the optical system 105 to be tested. When the light source of the light projecting system 102 is a point light source, a spherical wave is emitted from the light emitting portion of the light source. In this case, the light projecting system 102 is arranged so that the front focal plane of the optical system 105 to be tested and the light emitting unit coincide.

  The light source of the light projecting system 102 is not limited to a point light source. The light source of the light projecting system 102 only needs to have a light emitting unit that can be regarded as a point light source. Further, the light emitting unit itself may not emit light. For example, by illuminating the pinhole, a spherical wave is emitted from the pinhole. In this case, the pinhole can be regarded as the light emitting part.

  The light beam emitted from the light source of the light projecting system 102 passes through the off-axis region of the test optical system 105. The light beam emitted from the test optical system 105 is projected onto the rear focal plane of the test optical system 105.

  As described above, the light source of the light projecting system 102 can be moved in the OxOy plane by the drive stage 107 and the drive stage 108. Therefore, by moving the irradiation position within the OxOy plane, the position of the light beam passing through the optical system 105 to be measured can be changed.

  Here, the light receiving system 103, for example, the wavefront measuring device is disposed at the rear focal position of the optical system 105 to be detected. Therefore, even if the position of the light beam passing through the test optical system 105 changes, the incident angle of the light beam incident on the light receiving system (wavefront measuring device) 103 only changes.

  Thus, in the eccentricity measuring device 100, the light source (object point) of the light projecting system 102 is moved in the OxOy plane, so that the test optical system 105 and the light receiving system (wavefront measuring device) 103 are not moved. Wavefront data off-axis and on-axis can be acquired.

  The purpose of obtaining off-axis wavefront data is to obtain many types of aberration components due to decentration. That is, only the information of the aberration component proportional to the zero power of the object height can be obtained from the on-axis wavefront data. In contrast, off-axis wavefront data provides information on aberration components proportional to the first power of the object height.

  Further, the eccentricity measuring device 100 includes a processing device 112. A light projecting system 102, a light receiving system 103, a drive stage 107 and a drive stage 108 are connected to the processing apparatus 112 via a cable 113. The light projecting system 102 is connected to the processing apparatus 112 via the holding member 106, but it is not necessary to pass the holding member 106. Further, the connection with the holding member 109 may be determined according to the function of the holding member 109.

  In the processing apparatus 112, an acquisition process, a first extraction process, a second extraction process, and an analysis process are executed. In the acquisition step, wavefront data is acquired based on the light beam emitted from the test optical system. In the first extraction step, a predetermined aberration component is extracted from the wavefront data. In the second extraction step, a predetermined aberration component is acquired. The first aberration component is extracted from the above, and in the analysis step, simultaneous linear equations regarding the first aberration component, the decentration aberration sensitivity, and the decentering amount are analyzed.

  The predetermined aberration component is an aberration component including an aberration component caused by decentration, and the first aberration component is an aberration component proportional to the first power of the decentering amount of the predetermined aberration component. Sensitivity is aberration sensitivity proportional to the first power of the amount of eccentricity.

  Each step, aberration component, predetermined aberration component, first aberration component, and decentration aberration sensitivity have already been described using the flowchart of FIG. Therefore, the description here is omitted.

  Thus, the eccentricity measuring device 100 can implement the eccentricity measuring method of the present embodiment. Therefore, according to the eccentricity measuring device of the present embodiment, the eccentricity can be measured in a short time regardless of the shape of the lens surface and the number of lenses constituting the optical system.

  A modification of the light projecting system is shown in FIG. FIG. 39 shows a modification of the light projecting system. FIG. 39A shows a first modification, and FIG. 39B shows a second modification.

  A first modification is shown in FIG. The light projecting system 130 includes a light source 131, an optical fiber 132, and an emitting unit 133. One side of the optical fiber 132 is connected to the light source 131, and the other side is connected to the emitting unit 133.

  The light emitted from the light source 131 enters the optical fiber 132, travels through the optical fiber 132, and reaches the emitting unit 133. In the light projecting system 130, even if the light source 131 is large, the emission part 133 is small. Since the emission part 133 should just be attached to the eccentricity measuring device 100, the enlargement of the eccentricity measuring device 100 can be prevented. In addition, the emission part 133 may have an optical system as needed.

  In the light projecting system 130, the light source 131 and the emitting unit 133 are connected by an optical fiber 132. In this case, the relative position of the light source 131 and the emission part 133 can be freely changed. Therefore, it is not necessary to attach the light source 131 to the eccentricity measuring device 100. As a result, even if the light source 131 is large, it is possible to prevent the eccentricity measuring device 100 from becoming large.

  A second modification is shown in FIG. In the second modification, the light projecting system 140 includes a substrate 141 and a light source 142. The light sources 142 are arranged in a grid pattern. By irradiating the light beam from any one light source 142, the irradiation position can be changed. Therefore, in the second modification, the drive stage 107 and the drive stage 108 in the eccentricity measuring device 100 are not necessary.

  The eccentricity measuring device 100 may perform the first rotation. When the first rotation is performed, the holding member 109 may be a rotation stage. 40A and 40B are diagrams showing the positional relationship between the holding member and the measurement axis. FIG. 40A shows the case where the first rotation axis coincides with the measurement axis, and FIG. 40B shows the measurement by the first rotation axis. The case where it does not correspond to the axis is shown.

When the holding member 109 is a rotation stage, the holding member 109 can perform the first rotation. Here, as shown in FIG. 40A, the rotation axis AX _R1 of the holding member 109, that is, the first rotation axis, preferably coincides with the measurement axis AX _M. In this case, the system aberration component and the design aberration component can be removed by using Expression (18).

However, in practice, it is difficult to make the rotation axis AX _R1 of the holding member 109 coincide with the measurement axis AX _M. Therefore, as shown in FIG. 40B, the rotation axis AX _R1 of the holding member 109 does not coincide with the measurement axis AX _M. In this case, the system aberration component and the design aberration component can be removed by using Expression (20).

As described above, the holding member 109, and adjustment functions in OxOY plane, instead of the adjustment function in the direction along the measuring axis AX _M, may have the rotation function. Alternatively, these three functions may be provided.

  A modification of the holding member 109 will be described. FIGS. 41A and 41B are diagrams showing a modified example of the holding member. FIG. 41A shows a first modified example, and FIG. 41B shows a second modified example.

In the eccentricity measuring device 100 shown in FIG. 36, the eccentricity measuring device 100 is configured so that the measurement axis AX _M coincides with the vertical direction in the drawing. However, the eccentricity measuring device 100 may be configured such that the eccentricity measuring device 100 is rotated by 90 ° so that the measurement axis AX _M coincides with the horizontal direction in the drawing. In the configuration in which the measurement axis AX _M coincides with the horizontal direction in the drawing, the holding member 109 can be structured as follows.

  In the first modified example, the holding member 109 is constituted by a V block 150 as shown in FIG. Here, the test optical system 105 is held by a cylindrical jig 151. And the jig | tool 151 is hold | maintained at the V-shaped recessed part. The two inclined surfaces of the recess and the outer peripheral surface of the jig 151 are in contact with each other. The first rotation can be performed by rotating the lens barrel while maintaining the contact state.

  In the second modified example, as shown in FIG. 41 (b), the holding member 109 is composed of a rotary motor 152. The test optical system 105 is held by a jig 151. The jig 151 is connected to the rotary motor 152. By rotating the rotary motor 152, the first rotation can be performed.

  Further, although the holding member 111 has a function of holding the optical system 105 to be auxiliary, the holding member 111 may have a function of performing the second rotation. FIGS. 42A and 42B are diagrams illustrating a state in which the second rotation is performed. FIG. 42A illustrates a state before the holding member is moved, and FIG. 42B illustrates a state after the holding member is moved.

  When the holding member 111 has a rotation function, the holding member 111 can perform the second rotation. The holding member 111 includes an annular part 111a and a rotation mechanism 111b. The test optical system 105 is held by the annular portion 111 a of the holding member 111.

The annular portion 111a is rotatable around the rotation axis AX _R2 by the rotation mechanism 111b. Since the rotation axis AX _R2 is orthogonal to the measurement axis AX _M , the rotation axis AX _R2 is a second rotation axis. Therefore, the test optical system 105 can be rotated around the second rotation axis AX _R2 by rotating the annular portion 111a.

At this time, as shown in FIG. 42A, a part of the test optical system 105 is positioned inside the holding member 109. Therefore, the second rotation cannot be performed as it is. Therefore, as shown in FIG. 42B, the holding member 104 is slightly moved toward the light receiving system 103 side. Thereby, a gap is formed between the test optical system 105 and the holding member 109. As a result, the test optical system 105 can be rotated around the second rotation axis AX _R2 .

  Note that the second rotation can also be performed in the first modification of the holding member. In this case, the user lifts the test optical system 105 and reverses the front and back of the test optical system 105. Then, the test optical system 105 is disposed on the V block 150. Also in this case, the outer peripheral surface of the jig 151 is brought into contact with two inclined surfaces of the recess. Therefore, the absolute value of the eccentricity with respect to the rotation axis does not change before and after the second rotation.

  The second rotation can also be performed in the second modification of the holding member. In this case, the user pulls out the test optical system 105 from the jig 151 so that the front and back of the test optical system 105 are reversed. Then, the test optical system 105 is inserted into the jig 151. At this time, the jig 151 remains connected to the rotary motor 152. Therefore, the absolute value of the eccentricity with respect to the rotation axis does not change before and after the second rotation.

  Thus, in both the first modification and the second modification, the absolute value of the eccentricity with respect to the rotation axis does not change before and after the second rotation. The absolute value of the amount of eccentricity with respect to the rotation axis is | δr | in FIG.

  A case where the test optical system has negative refractive power will be described. FIG. 43 is a diagram illustrating a light projecting system when the optical system to be tested has negative refractive power.

  As shown in FIG. 43, the light projecting system 160 includes a light source 161 and an optical system 162. The optical system 162 includes a lens 163 and a lens 164. The light beam emitted from the light projecting system 160 is converted into a parallel light beam by the lens 163. The parallel light beam is converted into a convergent light beam by the lens 164. Therefore, the test optical system 170 is arranged so that the rear focal position coincides with the converging position of the converged light beam.

  By doing so, even when the test optical system has negative refractive power, the amount of decentration can be measured in a short time regardless of the shape of the lens surface and the number of lenses constituting the optical system.

  A modification of the light receiving system 103 will be described. FIG. 44 is a diagram showing a modification of the light receiving system.

  The light receiving system 180 includes an optical system 181 and a wavefront measuring device 184. The optical system 181 is a variable magnification optical system, and includes a lens 182 and a lens 183. The light beam 185 emitted from the test optical system 190 is collected by the lens 182. Then, it is converted into a light beam 186 by the lens 183. Here, by making the focal length of the lens 182 and the focal length of the lens 183 different, the diameter of the light beam 185 and the diameter of the light beam 186 can be made different.

  When the wavefront measuring device 184 is an SH sensor, it is preferable that a parallel light beam is incident on many microlens arrays. If the diameter of the parallel light beam 185 is small, the parallel light beam cannot be incident on many microlens arrays.

  Therefore, the beam diameter is enlarged by the variable magnification optical system 181. Thereby, the light beam 186 having a large light beam diameter can be made incident on the microlens array. In this case, the number of microlens arrays that occupy the irradiation range of the light beam 186 is significantly larger than when the light beam diameter is small. That is, the number of light spot images formed by the microlens array is remarkably increased. Therefore, the spatial resolution in the SH sensor can be increased.

  As a result, wavefront data can be acquired with high spatial resolution. This means that the amount of spatial information in wavefront data can be increased. By acquiring wavefront data with high spatial resolution, it is possible to fit Zernike coefficients with high accuracy. Thereby, since the predetermined aberration component and the first aberration component can be extracted with high accuracy, the decentering amount can be obtained with high accuracy.

  A first modification of the eccentricity measuring device will be described. FIG. 45 is a diagram illustrating a first modification of the eccentricity measuring device. A wavefront measuring device 103 will be described as a light receiving system.

  In the eccentricity measuring apparatus 100, the test optical system 105 is irradiated with a spherical wave. However, the light beam applied to the test optical system 105 may be a plane wave. As shown in FIG. 45, in the eccentricity measuring apparatus 200, the plane wave 210 is irradiated to the optical system 220 to be measured. The object height coordinate in this case can be expressed using the angle of the plane wave with respect to the measurement axis.

  The plane wave 210 is collected at the rear focal position of the test optical system 220. For this reason, even if the wavefront measuring device 103 is arranged at the rear focal position, it is difficult to perform wavefront measurement due to insufficient spatial resolution.

  Therefore, the decentering amount measuring apparatus 200 includes a lens 230 between the optical system 220 to be measured and the wavefront measuring apparatus 103. The lens 230 is arranged so that the front focal position of the lens 230 coincides with the condensing position. Thereby, the condensed light is converted into a substantially parallel light beam by the lens 230. As a result, the light beam can be incident on the entire light receiving surface of the wavefront measuring apparatus 103.

  In the eccentricity measuring apparatus 200, when the irradiation position is changed, the incident angle of the plane wave 210 with respect to the optical system 220 to be measured is changed. In this case, the direction of the wavefront emitted from the test optical system 220 changes. Therefore, it is not necessary to provide the drive stages 107 and 108 in the eccentricity measuring apparatus 100.

  A second modification of the eccentricity measuring device will be described. FIG. 46 is a diagram illustrating a second modification of the eccentricity measuring device.

  As described above, in the eccentricity measuring apparatus 100, the irradiation position matches the front focal position of the optical system 105 to be measured. However, the irradiation position does not have to coincide with the front focal position of the test optical system 105. As shown in FIG. 46, in the eccentricity measuring device 240, the irradiation position of the spherical wave 250 is a position farther from the test optical system 220 than the front focal position of the test optical system 220.

  The spherical wave 250 is collected by the test optical system 220. Therefore, the lens 230 is arranged between the optical system 220 to be measured and the wavefront measuring device 103 as in the case of the eccentricity measuring device 200.

  Since the functions and operations of the lens 230 and the wavefront measuring apparatus 103 have been described in the eccentricity measuring apparatus 200, description thereof is omitted here.

  A third modification will be described. FIG. 47 is a diagram illustrating a third modification of the eccentricity measuring device.

As described above, the eccentricity measuring apparatus 100 acquires the wavefront data by moving the irradiation position. However, the wavefront data may be acquired with the irradiation position fixed. As shown in FIG. 47, in the eccentricity measuring device 260, the incident position and the incident angle of the plane wave 210 are fixed. Then, the test optical system 220 is rotated around the axis 270. The object height coordinates in case can be expressed using the rotation angle of the optical system to be measured 220 with respect to the measuring axis AX _M.

  The plane wave 210 is collected by the test optical system 220. Therefore, the lens 230 is arranged between the optical system 220 to be measured and the wavefront measuring device 103 as in the case of the eccentricity measuring device 200.

  In the eccentricity measuring device 260, the condensing position moves in the vertical direction in the drawing as the optical system 220 to be tested rotates. Therefore, the light beam incident on the wavefront measuring apparatus 103 also moves in the vertical direction. If the light receiving surface of the wavefront measuring apparatus 103 is sufficiently wide, the wavefront measuring apparatus 103 does not need to be moved. In addition, by setting the rotation position of the optical system 220 to be tested as the rear principal point of the optical system 220 to be measured, the vertical movement amount of the light beam incident on the wavefront measuring device 103 is reduced, and the light reception of the wavefront measuring device 103 is reduced. The surface is minimal.

  As described above, the present invention is suitable for an eccentricity amount measuring method and an eccentricity amount measuring apparatus capable of measuring an eccentricity amount in a short time regardless of the shape of the lens surface and the number of lenses constituting the optical system.

DESCRIPTION OF SYMBOLS 1, 10 Light projection system 2, 20, 22 Test optical system 3, 30 Light reception system 4 Spherical wave 7, 7 ', 8, 8', 9 ₀ , 9 ' ₀ , 9 ₁ , 9' ₁ Non-planar wave 21 Optical System 23, 24, 25 Lens 31 Sensor component component 32 Wavefront data acquisition unit 33 Light receiving element 40 Spherical wave 50, 51, 52, 54, 55, 56 Non-planar wave 53 Plane wave 60 Distorted wavefront 70, 71, 72, 73 Sphere Center 80 New axis 90 Optical system to be tested 91 Aspheric surface 92, 92 ', 94 Top of aspheric surface 93 Aspheric surface 95 Displacement 96 Ball center 100 Eccentricity measuring device 101 Main body 102 Light projecting system 103 Light receiving system, Wavefront measurement Device 104 Holding member 105 Optical system to be tested 106 Holding member 107 Driving stage 108 Driving stage 109 Holding member 110 Moving mechanism 111 Holding member 111a Annular portion 111b Rotating mechanism 11 Processing device 113 Cable 120 SH sensor 121 Microlens array 121a Substrate 121b Microlens 122 Image sensor 130 Projection system 131 Light source 132 Optical fiber 133 Emitting unit 140 Projection system 141 Substrate 142 Light source 150 V block 151 Jig 152 Rotating motor 160 Projection System 161 Light source 162 Optical system 163, 164 Lens 170 Optical system to be tested 180 Light receiving system 181 Optical system 182, 183 Lens 184 Wavefront measuring device 185, 186 Light beam 190 Optical system to be tested 200 Eccentricity measuring device 210 Plane wave 220 Test optical system 230 Lens 240, 260 Eccentricity Measurement Device 250 Spherical Wave 270 Axis AX _M Measurement Axis AX _R1 First Rotation Axis AX _R2 Second Rotation Axis CR Central Ray E Shift Amount LS1, LS2, LS3 Lens surface LS ₁ , LS ₂ , LS _j lens surface L ₁ , L ₂ lens L _{1 1} , L 1 ₂ , L _{2 1} , L _{2 2} lens surface IM 1, IM 2, IM 3 image OB object X, Y, A, B Degree of freedom SC ₁ , SC ₂ ,..., SC _j , SC _{j + 1} , SC _{j + 2} ,..., SC _m ball center δ ₁ , δ ₂ , ..., δ _j , δ _{j + 1} , δ _{j + 2} , ..., δ _m Y-direction shift amount

Claims (10)

A method of irradiating a test optical system arranged on a measurement axis with a light beam from a plurality of object height coordinates outside the measurement axis and measuring an eccentricity amount,
An acquisition step of acquiring wavefront data for each of the plurality of object height coordinates based on the light flux emitted from the test optical system;
A first extraction step of extracting a predetermined aberration component from the wavefront data;
A second extraction step of extracting a first aberration component from the predetermined aberration component using the relationship between the predetermined aberration components of the plurality of object high coordinates ;
An analysis step of analyzing simultaneous linear equations for the first aberration component, decentration aberration sensitivity, and decentration amount, and
The predetermined aberration component is an aberration component including an aberration component caused by decentration,
The first aberration component is an aberration component proportional to the first power of the decentration amount of the predetermined aberration component,
The decentration aberration measuring method, wherein the decentration aberration sensitivity is an aberration sensitivity proportional to the first power of the decentering amount. The obtaining step includes a first rotation;
In the first rotation, the test optical system is rotated around the measurement axis,
With the same object height coordinate, obtain wavefront data before the first rotation and wavefront data after the first rotation,
2. The predetermined aberration component is extracted in the first extraction step by using a difference between the wavefront data after the first rotation and the wavefront data before the first rotation. The eccentricity measuring method described in 1. The eccentricity measuring method according to claim 2, wherein in the first rotation, the optical system to be measured is rotated around an axis substantially parallel to the measurement axis. The eccentricity measuring method according to claim 2 or 3, wherein an angle at which the test optical system is rotated is 10 degrees or more. The eccentricity measuring method according to any one of claims 2 to 4, wherein an angle at which the optical system to be tested is rotated is 180 degrees. The obtaining step includes a second rotation;
In the second rotation, the test optical system is rotated by 180 degrees around an axis orthogonal to the measurement axis,
6. The eccentricity measuring method according to claim 1, wherein the wavefront data before the second rotation and the wavefront data after the second rotation are acquired. The absolute value of the amount of eccentricity when acquiring the wavefront data before the second rotation and the amount of eccentricity when acquiring the wavefront data after the second rotation are the same. 6. The eccentricity measuring method according to 6. The plurality of object height coordinates have a plurality of sets of two object height coordinates arranged symmetrically with respect to the measurement axis,
The first extraction step extracts the predetermined aberration component from each of the wavefront data at one object height coordinate and the wavefront data at the other object height coordinate of the set of the two object height coordinates,
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 decentration among the predetermined aberration components,
The predetermined function is a function representing the second aberration component, and is a function including the object height coordinate as a variable,
The second extraction step includes a first calculation step and a second calculation step,
In the first calculation step, when the predetermined function is an odd function, a sum of the predetermined aberration component at the one object height coordinate and the predetermined aberration component at the other object height coordinate is calculated. ,
In the second calculation step, when the predetermined function is an even function, a difference between the predetermined aberration component at the one object height coordinate and the predetermined aberration component at the other object height coordinate is obtained. The eccentricity measuring method according to any one of claims 1 to 7, wherein the amount of eccentricity is measured. The second extraction step is performed using a predetermined function system,
The predetermined function system is a function system indicating the first aberration component,
The predetermined aberration component at one irradiation position and the predetermined aberration component at the other irradiation position are applied to the predetermined function system, according to any one of claims 1 to 7. Eccentricity measurement method. A light projecting system arranged at one end of the measurement axis;
A light receiving system disposed at the other end of the measurement axis;
A holding member for holding the test optical system;
A processing device connected to the wavefront measuring device,
The holding member is disposed between the light projecting system and the light receiving system,
The light projecting system is provided at a position for irradiating the test optical system with a light beam,
The test optical system arranged on the measurement axis is irradiated with a light beam from a plurality of object height coordinates outside the measurement axis,
In the processing apparatus, an acquisition process, a first extraction process, a second extraction process, and an analysis process are executed,
In the acquisition step, wavefront data for each of the plurality of object height coordinates is acquired based on the luminous flux emitted from the test 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 component using the relationship of the predetermined aberration component of the plurality of object height coordinates,
In the analysis step, simultaneous linear equations about the first aberration component, decentration aberration sensitivity, and decentration amount are analyzed,
The predetermined aberration component is an aberration component including an aberration component caused by decentration,
The first aberration component is an aberration component proportional to the first power of the decentration amount of the predetermined aberration component,
The decentering aberration sensitivity is an aberration sensitivity proportional to the first power of the decentering amount.

Images