JP2011122857A - Method and device for measuring aspherical object - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To achieve measurement of a face shift and a face tilt without being affected by the internal reflactive index distribution of an aspherical object and even if the aspherical object is not transmissive to a measurement light. <P>SOLUTION: A method for measuring an aspherical surface object includes a step of obtaining shape data of a first lens surface 91 and a second lens surface 92 of an aspherical lens 9 by reflected wave surface measurements using a first interferometer 1A and a second interferometer 1B, and a step of approximating each of the shape data with Zernike polynomial. Based on the values of coefficients Z<SB>1</SB>, Z<SB>2</SB>, Z<SB>6</SB>and Z<SB>7</SB>of Zernike polynomial, the shift and the tilt of the first lens surface 91 to a first measuring optical axis L1 and the shift and the tilt to a second lens surface 92 to a second measuring optical axis are determined. Based on the obtained respective shifts and tilts and relative position relation of the first interferometer 1A and the second interferometer 1B, the face shift and the face tilt are calculated. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention provides two front and back test surfaces (first test surface and second test surface) in an aspherical body such as an aspherical lens or a double-sided aspherical mirror used in various optical devices such as digital cameras and optical sensors. The present invention relates to an aspherical body measuring method and apparatus for measuring relative displacement amounts (surface displacement amount and surface tilt amount).

  When an aspherical lens is produced by molding, the surface of the molded aspherical lens is displaced due to the relative positional deviation between the molding dies (the rotation axes of the two lens surfaces that constitute the aspherical lens). Relative position shift) and surface tilt (relative tilt shift between the rotation axes of the two lens surfaces) may occur. Such surface misalignment and surface tilt are difficult to eliminate completely due to the mold mechanism, but are factors that increase the aberration (particularly rotationally asymmetric aberration such as coma aberration) of the molded aspheric lens. Therefore, it is desirable to correct the mold in the direction of decreasing, and it is important to grasp the amount of surface deviation and the amount of surface collapse that occurs.

  Conventionally, as a method for measuring the amount of surface deviation and the amount of surface tilt of such an aspheric lens, the shape of two lens surfaces is measured using a stylus-type shape measuring device, and based on the shape information. Although what calculates | requires the relative surface deviation | shift amount and surface inclination amount of two lens surfaces is known, there existed a problem that time for several hours or more was required for one measurement.

In recent years, a method described in Patent Document 1 below has been proposed as a method capable of greatly reducing the measurement time. This proposed method measures the transmitted wavefront of an aspheric lens using an interferometer, calculates the coma aberration of the transmitted wavefront based on the obtained transmitted wavefront data, and calculates the amount of surface deviation ( The amount of shift between the surfaces) and the amount of surface tilt (the amount of tilt between the surfaces) are obtained. Specifically, the transmitted wavefront data is approximated by a Zernike polynomial, and among the coefficients of the terms of the Zernike polynomial obtained at that time, the coefficient Z ₆ whose value changes in conjunction with the third-order coma aberration amount or Based on each value of Z ₇ and the coefficient Z ₁₃ or Z ₁₄ whose value changes in conjunction with the fifth-order coma aberration amount, the surface deviation amount and the surface tilt amount are obtained.

JP 2007-33343 A

  However, since the method described in Patent Document 1 is based on transmission wavefront measurement, there are the following problems.

  That is, the shape of the transmitted wavefront is greatly influenced not only by the surface deviation and surface tilt of the aspherical lens to be measured, but also by the internal refractive index distribution of the lens. In the method described in 1), there is a problem that it is difficult to measure only surface deviation or surface tilt with high accuracy while eliminating the influence of the refractive index distribution of the lens constituent material.

  Also, an aspherical body that does not transmit the measurement light of the interferometer, for example, an aspherical lens used for light of a special wavelength such as X-rays, or a double-sided aspherical surface having a reflecting surface formed of a rotating aspherical surface There is also a problem that it is difficult to measure the surface displacement amount and the surface collapse amount in an aspherical body such as a mirror.

  The present invention has been made in view of such circumstances, and is not affected by the internal refractive index distribution of the aspherical body to be measured, and the aspherical body does not transmit the measurement light of the interferometer. Therefore, an object of the present invention is to provide an aspherical body measuring method and apparatus capable of measuring the surface deviation amount and the surface tilt amount.

  In order to achieve the above object, an aspherical surface measuring method and apparatus according to the present invention have the following features.

That is, the aspherical body measuring method according to the present invention includes a first aspherical surface having a first aspherical surface that is a rotating aspherical surface and a second aspherical surface that is a rotating aspherical surface or a spherical surface. An aspherical body measuring method for measuring a relative surface displacement amount and a surface tilt amount between the first interferometer and the second test surface using a first interferometer and a second interferometer whose relative positional relationship is specified. There,
A first reflected wavefront of the first measurement light reflected from the first test surface by irradiating the first test light along the first measurement optical axis of the first interferometer; A first interference fringe acquisition step of obtaining image data of a first interference fringe formed by optical interference with the first reference wavefront of the first interferometer;
A second reflected wavefront of the second measurement light reflected from the second test surface by irradiating the second test light along the second measurement optical axis of the second interferometer; A second interference fringe acquisition step of obtaining image data of a second interference fringe formed by optical interference with the second reference wavefront of the second interferometer;
A first test surface shape data acquisition step of analyzing image data of the first interference fringes to obtain shape data of the first test surface;
A second test surface shape data acquisition step of analyzing image data of the second interference fringes to obtain shape data of the second test surface;
Approximating the shape data of the first test surface obtained in the first test surface shape data acquisition step with a Zernike polynomial, and among the coefficients of each term of the Zernike polynomial, A value of a first shift amount proportional coefficient whose value changes in proportion to a shift amount in a direction perpendicular to the first measurement optical axis, and a value proportional to a tilt amount of the first test surface with respect to the first measurement optical axis. A first Zernike coefficient value calculating step for obtaining a value of a first tilt amount proportional coefficient in which
Approximating the shape data of the second test surface obtained in the second test surface shape data acquisition step with a Zernike polynomial, and among the coefficients of each term of the Zernike polynomial, A value of a second shift amount proportional coefficient whose value changes in proportion to a shift amount in a direction perpendicular to the second measurement optical axis, and a value proportional to a tilt amount of the second test surface with respect to the second measurement optical axis. A second Zernike coefficient value calculating step for obtaining a value of a second tilt amount proportional coefficient in which
Based on the value of the first shift amount proportional coefficient and the value of the first tilt amount proportional coefficient obtained in the first Zernike coefficient value calculating step, the shift amount of the first test surface with respect to the first measurement optical axis And a first shift amount / tilt amount calculating step for obtaining a tilt amount;
Based on the value of the second shift amount proportional coefficient and the value of the second tilt amount proportional coefficient obtained in the second Zernike coefficient value calculating step, the shift amount of the second test surface with respect to the second measurement optical axis And a second shift amount / tilt amount calculating step for obtaining a tilt amount;
The shift amount and tilt amount of the first test surface obtained in the first shift amount / tilt amount calculation step and the second test surface obtained in the second shift amount / tilt amount calculation step. A surface misalignment amount / surface tilt amount calculating step for calculating the surface misalignment amount and the surface tilt amount based on a shift amount and a tilt amount and information on a relative positional relationship between the first interferometer and the second interferometer; Are included as measurement procedures.

In the aspherical surface measurement method of the present invention, the Zernike polynomial is a fourth-order or higher-order Zernike polynomial Z (ρ, θ) expressed in a polar coordinate format, where ρ is a distance from the pole, and θ is a deflection angle with respect to the starting line. Yes,
The first shift amount proportional coefficient and the second shift amount proportional coefficient are a coefficient Z _{1 of} a term expressed by the following formula (1), a coefficient Z _{2 of} a term expressed by the following formula (2), and the following formula ( 3) is a coefficient Z _{6 of the} term expressed by 3) and a coefficient Z ₇ of the term expressed by the following equation (4), and the first tilt amount proportional coefficient and the second tilt amount proportional coefficient are the coefficient Z ₁ And the coefficient Z ₂ .

ρcosθ (1)
ρsinθ (2)
(3ρ ² −2) ρcos θ (3)
(3ρ ² −2) ρsinθ (4)

In addition, the aspherical body measuring apparatus according to the present invention is an aspherical body having a first test surface that is a rotating aspheric surface and a second test surface that is a rotating aspherical surface or a spherical surface. And an aspherical surface measuring apparatus for measuring a relative surface displacement amount and a surface tilt amount between the second test surface and the second test surface,
A first measurement light is applied to the first test surface along the first measurement optical axis, and the first reflected wavefront and the first reference wavefront reflected from the first test surface of the first measurement light are reflected. A first interferometer for obtaining image data of a first interference fringe formed by optical interference;
The second measurement light is irradiated onto the second test surface along the second measurement optical axis, and the second reflected wavefront reflected from the second test surface of the second measurement light and the second reference wavefront A second interferometer for obtaining image data of a second interference fringe formed by optical interference, the relative positional relationship with the first interferometer being specified;
First test surface shape data acquisition means for analyzing the image data of the first interference fringes to obtain shape data of the first test surface;
Second test surface shape data obtaining means for analyzing the image data of the second interference fringes and obtaining shape data of the second test surface;
Approximating the shape data of the first test surface obtained by the first test surface shape data acquisition means with a Zernike polynomial, and among the coefficients of each term of the Zernike polynomial, A value of a first shift amount proportional coefficient whose value changes in proportion to a shift amount in a direction perpendicular to the first measurement optical axis, and a value proportional to a tilt amount of the first test surface with respect to the first measurement optical axis. First Zernike coefficient value calculating means for obtaining a value of a first tilt amount proportional coefficient in which
Approximating the shape data of the second test surface obtained by the second test surface shape data acquisition means with a Zernike polynomial, and among the coefficients of each term of the Zernike polynomial, A value of a second shift amount proportional coefficient whose value changes in proportion to a shift amount in a direction perpendicular to the second measurement optical axis, and a value proportional to a tilt amount of the second test surface with respect to the second measurement optical axis. Second Zernike coefficient value calculating means for determining the value of the second tilt amount proportional coefficient in which
Based on the value of the first shift amount proportional coefficient and the value of the first tilt amount proportional coefficient obtained by the first Zernike coefficient value calculating means, the shift amount of the first test surface with respect to the first measurement optical axis And a first shift amount / tilt amount calculating means for obtaining a tilt amount;
Based on the second shift amount proportional coefficient value and the second tilt amount proportional coefficient value obtained by the second Zernike coefficient value calculating means, the shift amount of the second test surface with respect to the second measurement optical axis And a second shift amount / tilt amount calculating means for obtaining a tilt amount;
The shift amount and tilt amount of the first test surface obtained by the first shift amount / tilt amount calculating means, and the shift of the second test surface obtained by the second shift amount / tilt amount calculating means. A surface displacement amount / surface inclination amount calculating means for calculating the surface displacement amount and the surface inclination amount based on the amount and the tilt amount and information on the relative positional relationship between the first interferometer and the second interferometer; It is characterized by comprising.

  In the present invention, when the second lens surface is a spherical surface, the second lens surface generates a shift amount with respect to the second measurement optical axis but does not generate a tilt amount. Therefore, when calculating the tilt amount of the second test surface in the second shift amount / tilt amount calculating step and the second shift amount / tilt amount calculating means, the calculation is performed assuming that the tilt amount is zero. To do.

  The aspherical body measuring method and apparatus according to the present invention have the above-described features, and thus have the following effects.

  That is, the aspherical body measuring method and apparatus of the present invention are interference formed by reflected wavefronts from two test surfaces (a first test surface and a second test surface) included in the aspherical surface to be measured. Unlike the prior art based on transmitted wavefront measurement, the shape data of the two test surfaces is obtained based on the fringes, and the relative surface displacement and surface tilt amount of the two test surfaces are measured based on the shape data. It is possible to measure the amount of surface deviation and the amount of surface tilt without being affected by the internal refractive index distribution of the aspherical body and even when the aspherical body does not transmit the measurement light of the interferometer. Become.

It is a schematic block diagram of the aspherical surface measuring apparatus which concerns on one Embodiment. It is a schematic block diagram of the optical system of the aspherical surface measuring apparatus shown in FIG. It is a block diagram which shows the structure of the analysis control part shown in FIG. It is sectional drawing which shows the structure of the aspherical lens used as a measuring object. It is a figure which shows the relative positional relationship of a 1st measurement coordinate system and a 2nd measurement coordinate system. It is a figure which shows the simulation 1st interference fringe image. It is a figure which shows the simulation 2nd interference fringe image. Is a diagram showing the tilt sensitivity of the coefficient Z ₁ with respect to the simulated first lens surface. Is a diagram showing the tilt sensitivity of the coefficient Z ₁ with respect to the simulated second lens surface. It is a diagram showing a shift sensitivity of the coefficient Z ₁ with respect to the simulated first lens surface. It is a diagram showing a shift sensitivity of the coefficient Z ₁ with respect to the simulated second lens surface. It is a diagram showing a shift sensitivity of the coefficient Z ₆ for the simulated first lens surface. It is a diagram showing a shift sensitivity of the coefficient Z ₆ for the simulated first lens surface. It is a figure which shows the calculation error of the shift amount with respect to the simulation 1st lens surface. It is a figure which shows the calculation error of the shift amount with respect to the simulation 2nd lens surface. It is a figure which shows the calculation error of the tilt amount with respect to the simulation 1st lens surface. It is a figure which shows the calculation error of the tilt amount with respect to the simulation 1st lens surface.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the above-mentioned drawings. Each drawing used for describing the embodiment is a schematic explanatory diagram, and does not show a detailed shape or structure, but shows the size of each member, the distance between the members, and the like as appropriate.

  First, the configuration of the aspherical lens 9 as an aspherical body to be measured and the items to be measured will be described with reference to FIG.

Aspheric lens 9 as shown in FIG. 4, the design, the first lens surface 91 composed of a rotating aspheric around the first rotation axis A ₁ (first test surface in this embodiment), comprising a second lens surface 92 composed of a rotating aspheric surface around the second rotation axis a ₂ (second test surface in this embodiment), and a side surface 93 formed in a cylindrical surface shape .

Further, the first lens surface 91 is the intersection between the first rotation axis A _1, the center point P ₁ of the first lens surface 91, the design, normal curvature at center point P ₁ is the first lens surface 91 It is set as the umbilical point which becomes the same about the direction of all the tangents which touch. Similarly, the second lens surface 92 is the intersection between the second rotation axis A _2, the central point P ₂ of the second lens surface 92, design, middle normal curvature at center point P ₂ is a second lens surface 92 It is set as the umbilical point which becomes the same about the direction of all the tangents which touch.

The first rotation axis A ₁ and the second rotation axis A ₂ described above are configured so as to coincide (overlap) with each other by design. There may be troubles. For the sake of clarity in the figure, the first rotation axis A ₁ and has a larger representation for deviation from the second rotation axis A _2, but generally, a small amount of error in the wavelength order of light. In the present embodiment, the surface deviation amount and the surface tilt amount are defined as follows.

Surface deviation amount: A virtual plane perpendicular to the first rotation axis A ₁ or the second rotation axis A ₂ is set, and a first center point P ₁ (first point) that is the center point of the first lens surface 91 is set on the virtual plane. lens surface 91 and the intersection) between the first rotation axis a _1, the second center point P ₂ is the center point of the second lens surface 92 _(the intersection between the second lens surface 92 and the second rotation axis a ₂₎ when projected, a distance surface deviation amount between the projection point cross of the first central point P ₁ and the second center point P ₂ on the virtual plane. Note that an orthogonal coordinate system may be set on the virtual plane, and the surface deviation amount may be divided into components in each coordinate axis direction.

Tilt amount: If the first disjoint rotation axis A ₁ and the angle (both of the second rotation axis A ₂ is formed between the direction vector and the direction vector of the second rotation axis A ₂ of the first rotation axis A ₁ Angle) is defined as the amount of tilt. Note that an orthogonal coordinate system may be set on the virtual plane, and the surface tilt amount may be divided into components in each coordinate axis direction.

  Next, based on FIGS. 1-3, the structure of the aspherical object measuring apparatus which concerns on one Embodiment of this invention is demonstrated. The aspherical surface measuring apparatus shown in FIG. 1 measures and analyzes the surface deviation amount and the surface inclination amount of the aspherical lens 9 described above, and the first aspherical lens 9 disposed on the first lens surface 91 side. The interferometer 1A, the second interferometer 1B disposed on the second lens surface 92 side, the subject alignment unit 3 placed on the optical surface plate 2, and the first interferometer 1A for adjusting the position of the first interferometer 1A. 1 interferometer position adjustment unit 4A, second interferometer position adjustment unit 4B that adjusts the position of the second interferometer 1B, and control analysis unit that performs measurement analysis of the surface displacement amount and surface tilt amount of the aspherical lens 9 And 5.

As shown in FIG. 2, the first interferometer 1A includes a first interference optical system 10A, a first interference fringe imaging system 20A, and a first alignment imaging system 25A. The first interference optical system 10A has a Fizeau type optical system arrangement, and includes a light source unit 11A that outputs a highly coherent light beam, and a beam diameter that expands the beam diameter of output light from the light source unit 11A. A magnifying lens 12A, a light beam branching optical element 13A that reflects the light beam from the beam diameter magnifying lens 12A toward the right in the figure, a collimator lens 14A that collimates the light beam from the light beam branching optical element 13A, and the collimator the first reference light and without and retroreflected in reference plane surface 15Aa part of plane waves from the lens 14A, and the plane reference plate 15A that transmits along its remaining in the first measurement optical axis L _1, the plane reference plate converting the light beam from 15A to the first measurement light composed of spherical waves, Bei and an objective lens 18A that irradiates the center of the first lens surface 91 (region including the first center point P ₁ above) Te becomes, and a reflected light from the first lens surface 91 so as to obtain the first reference light and combined to the first interference light.

Incidentally, the planar reference plate 15A is held by a fringe scan adapter 17A having a piezoelectric element 16A, is slightly moved to the first measuring optical axis L ₁ direction when fringe scan measurement or the like ing. Further, the objective lens 18A is configured to be retractable from the first on the measuring optical axis L _1.

  The first interference fringe imaging system 20A performs imaging when measuring the aspherical lens 9 (first lens surface 91). The first interference fringe imaging system 20A passes through the beam splitting optical elements 13A and 21A and proceeds to the left in the drawing. An imaging lens 22A for condensing one interference light and an imaging camera 23A having a two-dimensional image sensor 24A made of a CCD, a CMOS, or the like are provided. The imaging lens 22A causes the imaging lens 22A to be placed on the two-dimensional image sensor 24A. Image data of the formed interference fringes (first interference fringes) is acquired.

  The alignment imaging system 25A performs imaging when performing relative alignment adjustment or the like between the first interferometer 1A and the second interferometer 1B, and is reflected downward in the figure by the beam splitting optical element 21A. An imaging lens 26A for condensing the light beam and an imaging camera 27A having a two-dimensional image sensor 28A made of a CCD, a CMOS, or the like are provided.

The second interferometer 1B has the same configuration as the first interferometer 1A, and includes a second interference optical system 10B, a second interference fringe imaging system 20B, and a second alignment imaging system 25B. . The second interference optical system 10B has a Fizeau type optical system arrangement, and includes a light source unit 11B that outputs a highly coherent light beam, and a beam diameter that expands the beam diameter of output light from the light source unit 11B. A magnifying lens 12B, a beam splitting optical element 13B that reflects the beam from the beam diameter expanding lens 12B toward the left in the figure, a collimator lens 14B that collimates the beam from the beam splitting optical element 13B, and the collimator the second reference beam and without by retro-reflecting part of plane waves from the lens 14B at reference plane surface 15Ba, and the plane reference plate 15B that transmits along its remaining in the second measuring optical axis L _2, the plane reference plate converting the light beam from 15B to a second measuring beam composed of spherical waves, Bei and an objective lens 18B that irradiates the center of the second lens surface 92 (regions including the second center point P ₂ above) Te becomes, and a reflected light from the second lens surface 92 to obtain a second interference light multiplexes and the second reference light.

Incidentally, the planar reference plate 15B is held by a fringe scan adapter 17B having a piezoelectric element 16B, is slightly moved in the second measuring optical axis L ₂ direction when fringe scan measurement or the like ing. Further, the objective lens 18B is configured to be retractable from over the second measuring optical axis L _2.

  The second interference fringe imaging system 20B performs imaging at the time of measurement of the aspheric lens 9 (second lens surface 92). The second interference fringe imaging system 20B passes through the light beam splitting optical elements 13B and 21B and proceeds to the right in the drawing. An imaging lens 22B for condensing two interference light and an imaging camera 23B having a two-dimensional image sensor 24B made of CCD, CMOS, etc. are provided on the two-dimensional image sensor 24B by the imaging lens 22B. Image data of the formed interference fringes (second interference fringes) is obtained.

  The alignment imaging system 25B performs imaging when performing relative alignment adjustment or the like between the first interferometer 1A and the second interferometer 1B, and is reflected downward in the figure by the light beam splitting optical element 21B. An imaging lens 26B for condensing the luminous flux and an imaging camera 27B having a two-dimensional image sensor 28B made of CCD, CMOS or the like are provided.

On the other hand, as shown in FIG. 1, the subject alignment unit 3 includes a holding stage 31 that holds the aspheric lens 9, and an aspheric lens 9 (first lens surface 91, second lens) that is held by the holding stage 31. lens surface 92) of the lens tilt adjustment stage 32 that adjusts the inclination with respect to the first measuring optical axis L ₁ and the second measuring optical axis L _2, the first measuring optical axis L ₁ and the second measuring non with respect to the optical axis L ₂ A lens position adjustment stage 33 is provided for adjusting the position of the spherical lens 9 in the horizontal direction in the drawing and in the direction perpendicular to the paper surface.

  Further, as shown in FIG. 1, the first interferometer position adjustment unit 4A includes a first Z stage 41A that holds the first interferometer 1A so as to be movable in the vertical direction in the figure, and the first Z stage 41A. A first XY stage 42A that moves the first interferometer 1A in the left-right direction and the direction perpendicular to the paper surface in the drawing, and a tilt adjustment of the first interferometer 1A through the first XY stage 42A and the first Z stage 41A. 1 interferometer tilt adjustment stage 43A.

  Similarly, the second interferometer position adjusting unit 4B includes a second Z stage 41B that holds the second interferometer 1B so as to be movable in the vertical direction in the figure, and the second interferometer 1B via the second Z stage 41B. A second XY stage 42B that is moved in the left-right direction and the direction perpendicular to the paper surface in the figure, and a second interferometer tilt adjustment stage that performs tilt adjustment of the second interferometer 1B via the second XY stage 42B and the second Z stage 41B. 43B.

  Further, the control analysis unit 5 obtains shape data (first test surface shape data and second test surface shape data) of each central portion of the first lens surface 91 and the second lens surface 92, It is composed of a computer device that controls the driving of each stage of the subject alignment unit 3, the first interferometer position adjustment unit 4A, and the second interferometer position adjustment unit 4B. As shown in FIG. A first test surface shape data acquisition unit 51A, a second test surface shape data acquisition unit 51B, which are configured by a storage unit such as a CPU and a hard disk mounted in the computer device, and a program stored in the storage unit; First Zernike coefficient value calculating means 52A, second Zernike coefficient value calculating means 52B, first shift amount / tilt amount calculating means 53A, second shift amount / tilt amount calculating means 53B, and Consisting includes a shift amount, tilt amount calculation means 54.

  The first test surface shape data acquisition means 51A obtains first test surface shape data, which is shape data of the central portion of the first lens surface 91, based on the image data of the first interference fringes. This is obtained in the first measurement coordinate system set in 1A.

  The second test surface shape data acquisition unit 51B obtains second test surface shape data, which is shape data of the central portion of the second lens surface 92, based on the image data of the second interference fringes, as a second interferometer. This is obtained in the second measurement coordinate system set in 1B.

The first Zernike coefficient value calculation means 52A approximates the first test surface shape data with a Zernike polynomial, and among the coefficients of each term of the Zernike polynomial, the first measurement light of the first lens surface 91 is obtained. A value of a first shift amount proportional coefficient whose value changes in proportion to a shift amount in a direction perpendicular to the axis L ₁ and a tilt amount of the _first test surface 91 with respect to the first measurement optical axis L ₁ . The value of the first tilt amount proportional coefficient whose value changes is obtained.

The second Zernike coefficient value calculation means 52B approximates the second test surface shape data with a Zernike polynomial, and among the coefficients of each term of the Zernike polynomial, the second measurement light of the second lens surface 92 is obtained. The value of the second shift amount proportional coefficient whose value changes in proportion to the shift amount in the direction perpendicular to the axis L ₂ and the tilt amount of the second measured surface 92 with respect to the second measurement optical axis L ₂ . The value of the second tilt amount proportional coefficient whose value changes is obtained.

The first shift amount / tilt amount calculating unit 53A is configured to perform the first measurement based on the first shift amount proportional coefficient value and the first tilt amount proportional coefficient value obtained by the first Zernike coefficient value calculating unit 52A. with respect to the optical axis L ₁ and requests the shift amount and the tilt amount of the first lens surface 91.

The second shift amount / tilt amount calculating unit 53A is configured to perform the second measurement based on the second shift amount proportional coefficient value and the second tilt amount proportional coefficient value obtained by the second Zernike coefficient value calculating unit 52B. with respect to the optical axis L ₂ and requests the shift amount and the tilt amount of the second lens surface 92.

  The surface deviation amount / surface tilt amount calculating means 54 includes the first shift amount proportional coefficient value and the first tilt amount proportional coefficient value obtained by the first shift amount / tilt amount calculating means 53A, and the second tilt amount proportional coefficient value. The value of the second shift amount proportional coefficient and the value of the second tilt amount proportional coefficient obtained by the shift amount / tilt amount calculating means 53B and the relative positional relationship between the first interferometer 1A and the second interferometer 1B (described above) Based on the information on the relative positional relationship between the first measurement coordinate system and the second measurement coordinate system), the surface displacement amount and the surface collapse amount are calculated.

  Hereinafter, an aspherical surface measuring method according to an embodiment of the present invention will be described. The aspherical body measuring method of this embodiment is performed using the above-mentioned aspherical body measuring apparatus.

(1) First, the relative alignment of the first interferometer 1A and the second interferometer 1B is adjusted. This alignment adjustment is for matching the first measuring optical axis of the first interferometer 1A L ₁ and the second measuring optical axis L ₂ of the second interferometer 1B to each other, the operator, the first interferometer Manual operation is performed using the position adjustment unit 4A and the second interferometer position adjustment unit 4B. The outline of the procedure is as follows.

<a> the objective lens 18B of the objective lens 18A and the second interferometer 1B in the first interferometer 1A is respectively retracted from the first on the measuring optical axis _{L 1} and on the second measuring optical axis _{L 2,} two parallel to each other A parallel plate jig (not shown) having an optical plane (optical flat) is disposed between the first interferometer 1A and the second interferometer 1B (the parallel plate jig can be held on the holding stage 31. ). In this arrangement stage, the two optical flat of the parallel flat plate performs a coarse adjustment so possible that it is perpendicular to the first measuring optical axis L ₁ and the second measuring optical axis L _2.

<B> A parallel light beam is irradiated from the first interferometer 1A to one optical plane (an optical plane on the first interferometer 1A side) of the parallel plate jig, and is formed by reflected light reflected from the one optical plane. And the spot image formed by the reflected light from the reference standard plane 15Aa are imaged by the imaging camera 27A of the alignment imaging system 25A, and the first interferometer tilt is set so that these two spot images overlap each other. The tilt of the first interferometer 1A is adjusted using the adjustment stage 43A. This inclination adjustment, the first measuring optical axis L ₁ of the first interferometer 1A is perpendicular to one optical flat of the parallel flat plate. Instead of such a method, an interference fringe formed by the reflected light reflected from one optical plane and the reflected light from the reference standard plane 15Aa is imaged by the imaging camera 23A, and the interference fringes are null fringes. The inclination of the first interferometer 1A may be adjusted so as to be in a state.

<C> Similarly, the reflected light reflected from the other optical plane is irradiated from the second interferometer 1B to the other optical plane of the parallel plate jig (the optical plane on the second interferometer 1B side). And the spot image formed by the reflected light from the reference standard plane 15Ba are picked up by the image pickup camera 27B of the alignment image pickup system 25B, and the second spot image is overlapped with each other. Using the interferometer tilt adjustment stage 43B, the tilt of the second interferometer 1B is adjusted. This inclination adjustment, the measurement optical axis L ₂ of the second interferometer 1B is perpendicular to the other optical flat of the parallel flat plate, whereby the first measuring optical axis L ₁ and on the second measuring optical axis L ₂ Are parallel to each other. Instead of such a method, an interference fringe formed by the reflected light reflected from the other optical plane and the reflected light from the reference standard plane 15Ba is imaged by the imaging camera 23B, and the interference fringes are null fringes. You may make it perform inclination adjustment of the 2nd interferometer 1B so that it may be in a state.

  <D> Instead of the parallel plate jig, a true sphere jig (not shown) that can be optically regarded as a true sphere is disposed between the first interferometer 1A and the second interferometer 1B.

<E> A plane wave is irradiated from the first interferometer 1A to the true spherical jig, and interference fringes (concentric) formed by the reflected light reflected from the true spherical jig and the reflected light from the reference standard plane 15Aa the a ring-shaped), as imaged by the imaging camera 23A of the first interference fringe imaging system 20A, the first measuring optical axis _{L 1} at the center of the interference fringes is located, the 1Z stage 41A and the first 1XY stage 42A Is used to adjust the position of the first interferometer 1A.

<F> Similarly, the interference fringes formed by the reflected light reflected from the true spherical jig by irradiating the true spherical jig with a plane wave from the second interferometer 1B and the reference light from the reference standard plane 15Ba the (a concentric ring shape), and imaged by the imaging camera 23B of the second interference fringe imaging system 20B, as the center of the interference fringes and the second measuring optical axis L ₂ positioned, the 2Z stage 41B and the The position of the second interferometer 1B is adjusted using the 2XY stage 42B. This positional adjustment, the first measuring optical axis L ₁ and on the second measuring optical axis L ₂ coincide with each other.

Incidentally, even if such an alignment, the mechanical accuracy of each stage causing the second measuring beam of the first measuring optical axis L ₁ and the second interferometer 1B in the first interferometer 1A it may not be possible to match the axis L ₂ perfectly. In such a case, first the measurement optical axis L ₁ relative positions and determine the shift amount of the slope of the second measurement optical axis L _2, stores those data.

(2) Next, the true sphere jig is removed, the first interferometer 1A of the objective lens 18A and the second interfering first measuring optical axis of the objective lens 18B of the meter 1B _{L 1} and on the second measuring optical axis _{L 2} The aspherical lens 9 is held on the holding stage 31, and the alignment of the aspherical lens 9 with respect to the first interferometer 1A and the second interferometer 1B is adjusted. This alignment adjustment is the first center point P ₁ and the second center point P ₂ of the above, the second measuring optical axis L of the first and near the second interferometer 1B in the measurement optical axis L ₁ of the first interferometer 1A ₂ , and the operator manually operates using the lens tilt adjustment stage 32 and the lens tilt adjustment stage 33.

  (3) Next, from the first interferometer 1A, the central portion of the first lens surface 91 is irradiated with the first measurement light, the return light of the first measurement light from the first lens surface 91 and the first reference light The first interference fringe image data formed by the optical interference is obtained by the imaging camera 23A (first interference fringe acquisition step).

  (4) Similarly, the second measurement light is irradiated from the second interferometer 1B to the center of the second lens surface 92, and the return light and the second reference light from the second lens surface 92 of the second measurement light. The image data of the second interference fringes formed by the optical interference with the imaging camera 23B is obtained (second interference fringe acquisition step).

  (5) Next, the image data of the first interference fringe is analyzed (a general fringe analysis method can be used), and the first test surface which is shape data of the central portion of the first lens surface 91 Shape data is obtained in the first measurement coordinate system set in the first interferometer 1A (first surface shape data acquisition step). This process is performed in the first test surface shape data acquisition means 51A shown in FIG.

  (6) Similarly, the image data of the second interference fringes is analyzed, and the second test surface shape data, which is the shape data of the center portion of the second lens surface 92, is set in the second interferometer 1B. Obtained in the second measurement coordinate system (second test surface shape data acquisition step). This process is performed in the second shape data acquisition means 51B shown in FIG.

Here, the first measurement coordinate system and the second measurement coordinate system described above will be described. As shown in FIG. 5, the first measurement coordinate system is a right-handed three-dimensional orthogonal coordinate system having an X axis, a Y axis, and a Z axis orthogonal to each other, and the Z axis is the first measurement of the first interferometer 1A. It is set so as to coincide with the optical axis L _1. On the other hand, the second measurement coordinate system is a right-handed three-dimensional orthogonal coordinate system having a U axis, a V axis, and a W axis that are orthogonal to each other, and the W axis is the second measurement optical axis L _{2 of} the second interferometer 1B. Set to match. Further, the relative positional relation between the first measurement coordinate system and the second measurement coordinate system, when the first and the measurement optical axis L ₁ and the second measuring optical axis L ₂ is aligned adjusted to match perfectly The X axis, the U axis, the Y axis, and the V axis are set in parallel and in the same direction so that the Z axis and the W axis are positioned in the same direction on the same straight line. The first and the measurement optical axis L ₁ without the second measuring optical axis L ₂ and is consistent with one another, when relative displacement is generated between them, accordingly, the first measurement coordinate system And a relative positional shift between the second measurement coordinate system occurs. That is, when there is a relative deviation between the first measurement optical axis L ₁ and the second measurement optical axis L ₂ , these deviation amounts are compared with the first interferometer 1 A and the second interferometer in the procedure (1). It is obtained as relative position information with respect to the interferometer 1B, and based on this, the relative positional relationship between the first measurement coordinate system and the second measurement coordinate system is specified and stored.

(7) Then, approximating the first specimen surface geometric data with a Zernike polynomial, of the coefficients of the terms of the Zernike polynomial, the first lens surface 91, the first measuring optical axis L ₁ and the direction perpendicular of the first tilt amount proportionality coefficient value in proportion to the tilt amount changes the value in proportion to the shift amount with respect to the first measuring optical axis L ₁ of the first shift amount value of the proportional coefficients and the first lens surface 91 which changes A value is obtained (first Zernike coefficient value calculation step). This process is performed in the first Zernike coefficient value calculation means 52A shown in FIG.

(8) Similarly, the second specimen surface geometric data is approximated with a Zernike polynomial, of the coefficients of the terms of the Zernike polynomial, the second lens surface 92, a second measuring optical axis L ₂ perpendicular directions the second tilt amount proportionality coefficient value in proportion to the tilt amount with respect to the second measuring optical axis L ₂ value and the second lens surface 92 of the second shift amount proportionality coefficient changes the value in proportion to the shift amount changes of Is calculated (second Zernike coefficient value calculation step). This process is performed in the second Zernike coefficient value calculation means 52B shown in FIG.

In the present embodiment, as the Zernike polynomial, a 10th-order Zernike polynomial Z (ρ, θ) expressed in a polar coordinate format (ρ is a distance from the pole and θ is a declination with respect to the starting line) is used (the following formula ( A) shows nine terms up to the fourth order out of a total of 35 terms, where Z ₀ is a constant term).

Z (ρ, θ) = Z ₀ + Z ₁ ρcos θ + Z ₂ ρ sin θ + Z ₃ (2ρ ² −1)
+ Z ₄ ρ ² cos 2θ + Z ₅ ρ ² sin 2θ
+ Z ₆ (3ρ ² −2) ρcos θ + Z ₇ (3ρ ² −2) ρsinθ
+ Z ₈ (6ρ ⁴ −6ρ ² +1) (A)

Further, as the first shift amount proportional coefficient and the second shift amount proportional coefficient, the second term coefficient Z ₁ , the third term coefficient Z ₂ , the fifth term of the Zernike polynomial represented by the above formula (A). The coefficient Z ₆ of the second term and the coefficient Z ₇ of the sixth term are used, and the coefficient Z ₁ of the second term and the coefficient Z ₂ of the third term are used as the first tilt amount proportional coefficient and the second tilt amount proportional coefficient.

That is, in the first Zernike coefficient value calculation step, the first test surface shape data is approximated by the Zernike polynomial, and the values of the coefficients Z ₁ , Z ₂ , Z ₆ and Z ₇ at that time are shifted by the first shift. together determine the amount proportionality coefficient values to determine the respective values of the coefficients Z _1, Z ₂ even when the first tilt amount proportionality coefficients.

Similarly, in the second Zernike coefficient value calculation step, the second test surface shape data is approximated by the Zernike polynomial, and the values of the coefficients Z ₁ , Z ₂ , Z ₆ , Z ₇ at that time are set to the second value. While obtaining as a shift amount proportional coefficient value, each value of the coefficients Z ₁ and Z ₂ is also obtained as a second tilt amount proportional coefficient value.

(9) Next, based on the respective values of the coefficients Z ₁ , Z ₂ , Z ₆ , Z ₇ obtained in the first Zernike coefficient value calculation step, the first lens surface 91 with respect to the first measurement optical axis L ₁ Each value of the shift amount and the tilt amount is obtained in the first measurement coordinate system (first shift amount / tilt amount calculating step). This processing is performed using the following equations (5) to (8) in the first shift amount / tilt amount calculation means 53A shown in FIG.

s _X = Z _{6 (1-s, t)} / a _{6 (1-s)} (5)
s _Y = Z _{7 (1-s, t)} / a _{7 (1-s)} (6)
_{t X = (Z 1 (1} -s, t) -a 1 (1-s) · s X) / a 1 (1-t) ... (7)
_{t Y = (Z 2 (1} -s, t) -a 2 (1-s) · s X) / a 2 (1-t) ... (8)

Here, s _X and s _Y indicate shift amounts of the first lens surface 91 with respect to the first measurement optical axis L _{1 in} the X-axis direction (X direction) and the Y-axis direction (Y direction), and t _X And t _Y indicate the respective tilt amounts of the first lens surface 91 with respect to the first measurement optical axis L _{1 in} the X-axis direction and the Y-axis direction. Z _{1 (1-s, t)} , Z _{2 (1-s, t)} , Z _{6 (1-s, t)} and Z _{7 (1-s, t)} are the first Zernike coefficient value calculating step. The respective values of the coefficients Z ₁ , Z ₂ , Z ₆ and Z _{7 obtained in} the above are shown. Furthermore, a1 _(1-s) , a2 _(1-s) , a1 _(1-t) , a2 _(1-t) , a6 _(1-s) and a7 _(1-s) are Each proportionality constant calculated | required in the computer simulation mentioned later is shown.

(10) Similarly, based on the values of the coefficients Z ₁ , Z ₂ , Z ₆ , Z ₇ obtained in the second Zernike coefficient value calculation step, the second lens surface 92 with respect to the second measurement optical axis L ₂ The shift amount and the tilt amount are obtained in the second measurement coordinate system (second shift amount / tilt amount calculating step). This process is performed using the following equations (9) to (12) in the second shift amount / tilt amount calculation means 53B shown in FIG.

s _U = Z _{6 (2-s, t)} / a _{6 (2-s)} (9)
s _V = Z _{7 (2-s, t)} / a _{7 (2-s)} (10)
_{t U = (Z 1 (2} -s, t) -a 1 (2-s) · s X) / a 1 (2-t) ... (11)
_{t V = (Z 2 (1} -s, t) -a 2 (2-s) · s X) / a 2 (2-t) ... (12)

Here, s _U and s _V indicate respective shift amounts of the second lens surface 92 in the U-axis direction (U direction) and the V-axis direction (V direction) with respect to the second measurement optical axis L ₂ , and t _U and t _V shows the amount of tilt U axis and the V axis direction of the second lens surface 92 relative to the second measuring optical axis L _2. Z _{1 (2-s, t)} , Z _{2 (2-s, t)} , Z _{6 (2-s, t)} and Z _{7 (2-s, t)} are the second Zernike coefficient value calculation step. The respective values of the coefficients Z ₁ , Z ₂ , Z ₆ and Z _{7 obtained in} the above are shown. Furthermore, a1 _(2-s) , a2 _(2-s) , a1 _(2-t) , a2 _(2-t) , a6 _(2-s) , a7 _(2-s) are Each proportionality constant calculated | required in the computer simulation mentioned later is shown.

(11) Next, the shift amounts s _X , s _Y and the tilt amounts t _X , t _Y obtained in the first shift amount / tilt amount calculating step, and the second shift amount / tilt amount calculating step. The shift amounts s _U , s _V and tilt amounts t _U , t _V determined in step 1 and the relative positional relationship between the first interferometer 1A and the second interferometer 1B determined in the procedure (1) (first Based on the relative positional relationship between the first measurement coordinate system and the second measurement coordinate system), the above-described surface misalignment amount and surface tilt amount are calculated (surface misalignment amount / surface tilt amount calculating step). This processing is performed in the following procedure in the surface deviation amount / surface inclination amount calculation means 54 shown in FIG.

  <a> First, FIG. 5 shows a second measurement coordinate system in which a relative deviation from the first measurement coordinate system occurs due to the influence of the actual relative positional relationship between the first interferometer 1A and the second interferometer 1B. Appropriate state shown, that is, the W axis is located on the same straight line as the Z axis of the first measurement coordinate system, and the U axis and the V axis are parallel to the X axis and the Y axis of the first measurement coordinate system, respectively. To correct the state in the same direction.

<B> Next, the shift amounts s _U and s _V and the tilt amounts t _U and t _V obtained in the second measurement coordinate system before correction are used as the shift amounts s in the second measurement coordinate system after correction. Corrections are made to _U ′, s _V ′ and tilt amounts t _U ′, t _V ′.

<C> The difference (s _X −s _U ′) between the shift amounts s _X and s _Y in the first measurement coordinate system and the shift amounts s _U ′ and s _V ′ in the corrected second measurement coordinate system. , S _Y −s _V ′) is calculated as the amount of surface displacement between the first lens surface 91 and the second lens surface 92 in the X-axis direction and the Y-axis direction.

<D> Similarly, each difference (t _X −t _U) between the tilt amounts t _X and t _Y in the first measurement coordinate system and the tilt amounts t _U ′ and t _V ′ in the corrected second measurement coordinate system. ', T _Y -t _V ') is calculated as the amount of surface tilt between the first lens surface 91 and the second lens surface 92 in the X-axis direction and the Y-axis direction.

  Here, the above-described computer simulation will be described with specific numerical values.

  In this computer simulation, first, based on the design data of the first lens surface 91 and the second lens surface 92, the simulated second lens surface corresponding to the first lens surface 91 and the simulated second lens corresponding to the second lens surface 92. Set the surface on the computer. In this embodiment, the aspheric coefficients of the simulated first lens surface and the simulated second lens surface are set to values shown in Table 1 below. As the aspherical surface, the one represented by the following equation (B) is used.

  Next, it corresponds to the first interference fringe image obtained when the optical interference measurement by the first interferometer 1A and the second interferometer 1B is performed on the simulated first lens surface and the simulated second lens surface. The simulated first interference fringe image (see FIG. 6) and the simulated second interference fringe image (see FIG. 7) corresponding to the second interference fringe image are created. Note that a mask for limiting the interference fringe region used for fringe analysis is appropriately set according to the fringe density of the created interference fringes.

Next, a simulated first interference fringe image and a simulated second interference fringe image are created each time a tilt amount that changes by 1 (mrad) is sequentially given to the simulated first lens surface and the simulated second lens surface. Then, the simulated first interference fringe image and the simulated second interference fringe image at each tilt amount are analyzed to obtain the shape data of the simulated first lens surface and the simulated second lens surface at each tilt amount, and these are used as the Zernike described above. Each value of the coefficients Z ₁ and Z ₂ when approximated by a polynomial is obtained.

Figure 8 is a simulated first lens surface to a given tilt amount t _{X (X} indicates a tilt amount of the X-axis direction of the first coordinate system for measurement) and the value Z ₁ of the coefficient Z _{1 (1 -T)} shows a relationship with (corrected so that the value when the tilt amount is 0 is 0). As shown in FIG. 8, the proportional relationship of the following formula (13) is established between Z _{1 (1-t)} and t _x, and the value of the proportional constant a _{1 (1-t)} is 0.059. I was asked.
_{Z 1 (1-t) =} a 1 (1-t) · t X ... (13)

Although not shown in the graph, the coefficient Z when the tilt amount t _Y (Y indicates the tilt amount in the Y-axis direction of the first measurement coordinate system) is given to the simulated first lens surface. ₂ value Z _{2 (1-t)} also between _(tilt amount value is corrected to be zero when the 0) and the tilt amount t _Y, likewise proportional of the formula (14) relationship is satisfied, the value of the proportionality constant a _{2 (1-t),} when the simulated first lens surface is the same 0.059 as the value of the proportionality constant a ₁ because it is rotationally symmetric surface _(1-t) I was asked.
_{Z 2 (1-t) =} a 2 (1-t) · t Y ... (14)

On the other hand, FIG. 9 shows the tilt amount t _U given to the simulated second lens surface (U indicates the tilt amount in the U-axis direction of the second measurement coordinate system) and the value Z ₁ of the coefficient Z _{1. (2-t)} shows a relationship with (corrected so that the value when the tilt amount is 0 is 0). As shown in FIG. 9, the proportional relationship of the following equation (15) is established between Z _{1 (2-t)} and t _U, and the value of the proportional constant a _{1 (2-t)} is 0.0721. I was asked.
Z _{1 (2-t)} = a _{1 (2-t)} · t _U (15)

Although not shown in the graph, the coefficient Z when the tilt amount t _V (V indicates the tilt amount in the V-axis direction of the second measurement coordinate system) is given to the simulated second lens surface. ₂ value Z _{2 (2-t)} also between the _(tilt amount is corrected so that the value of the time of 0 is 0) and the tilt amount t _V, likewise proportional of the formula (16) The relationship is established, and the value of the proportional constant a _{2 (2-t)} is 0.0721, which is the same as the value of the proportional constant a _{1 (2-t)} because the simulated second lens surface is a rotationally symmetric surface. I was asked.
_{Z 2 (1-t) =} a 2 (1-t) · t Y ... (16)

Next, the simulated first lens surface and the simulated second lens surface are sequentially given a shift amount that changes by 1 (μm) (the tilt amount is set to 0). A second interference fringe image is created. Then, the simulated first interference fringe image and the simulated second interference fringe image at each shift amount are analyzed to obtain the shape data of the simulated first lens surface and the simulated second lens surface at each shift amount. The values of the coefficients Z ₁ , Z ₂ , Z ₆ and Z ₇ when approximated by a polynomial are obtained.

Figure 10 is a simulated first shift amount given to the lens surface s _{X (X} indicates a shift amount of the X-axis direction of the first coordinate system for measurement) and the value Z ₁ of the coefficient Z _{1 (1 -S)} (the correction is made so that the value when the shift amount is 0 is 0). As shown in FIG. 10, the proportional relationship of the following equation (17) is established between Z _{1 (1-s)} and s _x, and the value of the proportional constant a _{1 (1-s)} is 0.1018. I was asked.
_{Z 1 (1-s) =} a 1 (1-s) · s X ... (17)

Although not shown in the graph, the coefficient Z when a shift amount s _Y (Y indicates the shift amount in the Y-axis direction of the first measurement coordinate system) is given to the simulated first lens surface. also between the _two values Z _{2 (1-s) (the} value when the shift amount is 0 is corrected to be zero) and the shift amount s _Y, likewise proportional of the formula (18) relationship is satisfied, the value of the proportionality constant a _{2 (1-s)} are determined to be the simulated first lens surface is 0.1018 the proportionality constant a _{1 (1-s)} and the same because it is rotationally symmetric surface It was.
Z _{2 (1-s)} = a _{2 (1-s)} · s _Y (18)

On the other hand, FIG. 11 shows the shift amount s _U given to the simulated second lens surface (U indicates the shift amount in the U-axis direction of the second measurement coordinate system) and the value Z ₁ of the coefficient Z _{1. (2-s)} shows the relationship with (corrected so that the value when the shift amount is 0 is 0). As shown in FIG. 11, the proportional relationship of the following equation (19) is established between Z _{1 (2-s)} and s _U, and the value of the proportional constant a _{1 (2-s)} is −0.0263. I was asked to be there.
Z _{1 (2-s)} = a _{1 (2-s)} · s _U (19)

Although not shown in the graph, the coefficient Z when a shift amount s _V (V indicates the shift amount in the V-axis direction of the second measurement coordinate system) is given to the simulated second lens surface. also between the _two values Z _{2 (2-s) (the} value when the shift amount is 0 is corrected to be zero) and the shift amount s _V, similarly proportional of the formula (20) The relationship is established, and the value of the proportional constant a _{2 (2-s)} is determined to be −0.0263 which is the same as the proportional constant a _{1 (2-s)} because the simulated second lens surface is a rotationally symmetric surface. It was.
Z _{2 (2-s)} = a _{2 (2-s)} · s _Y (20)

Similarly, FIG. 12 shows that the shift amount s _X given to the simulated first lens surface and the value Z _{6 (1-s) of} the coefficient Z ₆ (corrected so that the value when the shift amount is 0 is 0 _). It shows the relationship with As shown in FIG. 12, the proportional relationship of the following equation (21) is established between Z _{6 (1-s)} and s _X, and the value of the proportional constant a _{6 (1-s)} is 0.0002. I was asked.
Z _{6 (1-s)} = a _{6 (1-s)} · s _X (21)

Although the graph is not shown, the value Z _{7 (1−s)} of the coefficient Z ₇ when the shift amount s _Y is given to the simulated first lens surface (the value when the shift amount is 0 is 0 ₎ Similarly, the proportional relationship of the following equation (22) is also established between the shift amount s _Y and the value of the proportional constant a _{7 (1-s)} is the simulated first value. Since the lens surface was a rotationally symmetric surface, it was determined to be 0.0002, which is the same as the proportional constant a6 _(1-s) .
Z _{7 (1-s)} = a _{7 (1-s)} · s _Y (22)

On the other hand, FIG. 13 shows that the shift amount s _U given to the simulated second lens surface and the value Z _{6 (2-s) of} the coefficient Z ₆ are corrected so that the value when the shift amount is 0 is zero. It shows the relationship. As shown in FIG. 13, the proportional relationship of the following equation (23) is established between Z _{6 (2-s)} and s _U, and the value of the proportional constant a _{6 (2-s)} is −0.0014. I was asked to be there.
Z _{6 (2-s)} = a _{6 (2-s)} · s _U (23)

Although the graph is not shown, the value Z _{7 (2-s)} of the coefficient Z ₇ when the shift amount s _V is given to the simulated second lens surface (the value when the shift amount is 0 is 0 ₎ Similarly, the proportional relationship of the following expression (24) is also established between the shift amount s _V and the shift amount s _V, and the value of the proportional constant a _{7 (2-s)} is the simulated second value. Since the lens surface is a rotationally symmetric surface, it was determined to be −0.0014, which is the same as the proportional constant a6 _(2-s) .
Z _{7 (2-s)} = a _{7 (2-s)} · s _V (24)

Further, the value Z _{1 (1-s, t)} of the coefficient Z ₁ when the tilt amount t _X and the shift amount s _X are simultaneously given to the simulated first lens surface, and the above-described Z _{1 (1-s)} , The relationship of the following equation (25) is established between Z _{1 (1−t)} and the coefficient Z ₂ when the tilt amount t _Y and the shift amount s _Y are simultaneously given to the simulated first lens surface. It was confirmed that the relationship of the following formula (26) was established between the value Z _{2 (1-s, t)} and the above-described Z _{2 (1-s)} , Z _{2 (1-t)} . .
Z1 _{(1-s, t)} = Z1 _(1-s) + Z1 _(1-t) (25)
Z2 _{(1-s, t)} = Z2 _(1-s) + Z2 _(1-t) (26)

Similarly, the value Z _{1 (2-s, t)} of the coefficient Z ₁ when the tilt amount t _U and the shift amount s _U are simultaneously given to the simulated second lens surface, and the above-described Z _{1 (2-s).} , Z _{1 (2-t)} , the following equation (27) holds, and the coefficient Z ₂ when the tilt amount t _V and the shift amount s _V are simultaneously given to the simulated second lens surface: It is confirmed that the relationship of the following formula (28) is established between the value Z _{2 (2-s, t)} of the above and Z _{2 (2-s)} , Z _{2 (2-t)} described above. It was.
Z1 _{(2-s, t)} = Z1 _(2-s) + Z1 _(2-t) (27)
Z2 _{(2-s, t)} = Z2 _(2-s) + Z2 _(2-t) (28)

Further, it was confirmed that the values of the coefficients Z ₆ and Z ₇ did not change with respect to the tilt of the simulated first lens surface and the simulated second lens surface, but changed only with respect to the shift. Furthermore, the above formulas (5) to (12) are derived from the respective formulas obtained by this computer simulation.

  Hereinafter, the results of computer simulation will be described for measurement errors (calculation errors) when the present invention is applied.

  FIG. 14 shows a result of measuring each shift amount by applying the present invention while giving predetermined shift amounts in the X direction and Y direction to the simulated first lens surface. The horizontal axis represents the shift amount as the input P, and the vertical axis represents the shift amount calculated by the measurement method of the present invention as the output Q. Since the results in the X direction and the Y direction are shown simultaneously, the results in the X direction are shown in the positive area of the graph, and the results in the Y direction are shown in the negative area of the graph. The mathematical expression described in the graph is an approximation of the relationship between the input P and the output Q by a linear expression. If there was no measurement error, Q = P, and only a minute error of about 0.8% was confirmed, and it was confirmed that the measurement according to the present invention was highly accurate.

  FIG. 15 shows a result of measuring each shift amount by applying the present invention while giving predetermined shift amounts in the U direction and V direction to the simulated second lens surface, respectively. The horizontal axis represents the shift amount as the input P, and the vertical axis represents the shift amount calculated by the measurement method of the present invention as the output Q. Since the results in the U direction and the V direction are shown simultaneously, the results in the U direction are shown in the positive area of the graph, and the results in the V direction are shown in the negative area of the graph. The mathematical expression described in the graph is an approximation of the relationship between the input P and the output Q by a linear expression. If there was no measurement error, Q = P, and only a minute error of 0.1% or less was confirmed, and it was confirmed that the measurement according to the present invention was highly accurate.

  FIG. 16 shows the results of measuring the respective tilt amounts by applying the present invention while giving predetermined tilt amounts in the X direction and the Y direction to the simulated first lens surface. The horizontal axis represents the tilt amount as the input K, and the vertical axis represents the tilt amount calculated by the measurement method of the present invention as the output J. Since the results in the X direction and the Y direction are shown simultaneously, the results in the X direction are shown in the positive area of the graph, and the results in the Y direction are shown in the negative area of the graph. The mathematical expression described in the graph is an approximation of the relationship between the input K and the output J by a linear expression. If there was no measurement error, J = K, and only a minute error of about 0.4% was confirmed, and it was confirmed that the measurement according to the present invention was highly accurate.

  FIG. 17 shows a result of measuring each tilt amount by applying the present invention while giving predetermined tilt amounts in the U direction and V direction to the simulated second lens surface, respectively. The horizontal axis represents the tilt amount as the input K, and the vertical axis represents the tilt amount calculated by the measurement method of the present invention as the output J. Since the results in the U direction and the V direction are shown simultaneously, the results in the U direction are shown in the positive area of the graph, and the results in the V direction are shown in the negative area of the graph. The mathematical expression described in the graph is an approximation of the relationship between the input K and the output J by a linear expression. If there was no measurement error, J = K, but only a minute error of 0.1% or less was confirmed, and it was confirmed that the measurement according to the present invention was highly accurate.

  Although one embodiment of the present invention has been described above, the present invention is not limited to the above-described embodiment, and various modifications can be made.

For example, in the above-described embodiment, both the first lens surface 91 and the second lens surface 92 are rotating aspheric surfaces, but the present invention can be applied even when the second lens surface 92 is a spherical surface. Is possible. When the second lens surface 92 is spherical, for the second lens surface 92, a shift amount with respect to the second measuring optical axis L ₂ is generated but the amount of tilt does not occur. Therefore, in the calculation of the tilt amount in the measurement procedure described above, the calculation may be performed assuming that the tilt amount is zero. Note that the relationship between the first lens surface 91 and the second lens surface 92 is relative, and the first lens surface 91 is the second test surface, and the second lens surface 92 is the first test surface. Good. In this case, even when the second lens surface 92 is a rotating aspherical surface and the first lens surface 91 is a spherical surface, the present invention can be similarly applied.

  In the above-described embodiment, as shown in FIG. 2, the first measurement light irradiated from the first interferometer 1A to the first lens surface 91 and the second lens surface 92 from the second interferometer 1B are irradiated. The second measurement light is a spherical wave, but the objective lenses 18A and 18B may be removed and a parallel light beam (plane wave) may be used as the first measurement light and the first measurement light.

  It is also possible to use a microscopic interferometer equipped with a Milo type or Michelson type objective optical system as the first interferometer and the second interferometer. This aspect is effective when the aspherical lens to be measured is small.

  Furthermore, in the above-described embodiment, the aspherical body as a measurement target is an aspherical lens. However, the present invention is configured by a first mirror surface configured by a rotating aspherical surface and a rotating aspherical surface or a spherical surface. An aspherical mirror having a second mirror surface can also be used as a measurement target. In this case, since the reflectance of each mirror surface is expected to be high, it is desirable to adjust the reflection / transmittance of the reference standard planes 15Aa and 15Ba accordingly. For example, when the reflectance of each mirror surface is 100%, the reference standard planes 15Aa and 15Ba may be set to about 50% reflectance (transmittance 50%).

  In the present invention, measurement is performed using two interferometers. However, if the technical idea of the present invention is used, another measuring device (for example, a contact type or a non-contact type) is used instead of the interferometer. It is also easy to recall a measuring method and apparatus using a shape measuring apparatus using a probe and a moire fringe shape measuring apparatus).

DESCRIPTION OF SYMBOLS 1A 1st interferometer 1B 2nd interferometer 2 Optical surface plate 3 Subject alignment part 4A 1st interferometer position adjustment part 4B 2nd interferometer position adjustment part 5 Control analysis part 9 Aspherical lens (aspherical body)
10A 1st interference optical system 10B 2nd interference optical system 11A, 11B Light source part 12A, 12B Beam diameter expansion lens 13A, 21A, 13B, 21B Beam splitting optical element 14A, 14B Collimator lens 15A, 15B Plane reference plates 15Aa, 15Ba Reference plane 16A, 16B Piezo element 17A, 17B Fringe scan adapter 18A, 18B Objective lens 20A First interference fringe imaging system 20B Second interference fringe imaging system 22A, 26A, 22B, 26B Imaging lens 23A, 27A, 23B, 27B Camera 24A, 24B, 28A, 28B Two-dimensional image sensor 25A, 25B Alignment imaging system 31 Holding stage 32 Lens tilt adjustment stage 33 Lens position adjustment stage 41A First Z stage 41B Second Z stage 42A First XY Stage 42B Second XY stage 43A First interferometer tilt adjustment stage 43B Second interferometer tilt adjustment stage 51A First shape data acquisition means 51B Second shape data acquisition means 53 Surface deviation / surface tilt analysis means 91 First lens surface 92 First 2 lens surfaces 93 side surfaces L ₁ first measurement optical axis L ₂ second measurement optical axis P ₁ first center point P ₂ second center point A ₁ first rotation axis A ₂ second rotation axis

Claims (3)

In an aspherical body having a first test surface that is a rotating aspheric surface and a second test surface that is a rotating aspherical surface or a spherical surface, a relative surface between the first test surface and the second test surface An aspherical body measurement method for measuring a deviation amount and a surface tilt amount using a first interferometer and a second interferometer whose relative positional relationship is specified,
A first reflected wavefront of the first measurement light reflected from the first test surface by irradiating the first test light along the first measurement optical axis of the first interferometer; A first interference fringe acquisition step of obtaining image data of a first interference fringe formed by optical interference with the first reference wavefront of the first interferometer;
A second reflected wavefront of the second measurement light reflected from the second test surface by irradiating the second test light along the second measurement optical axis of the second interferometer; A second interference fringe acquisition step of obtaining image data of a second interference fringe formed by optical interference with the second reference wavefront of the second interferometer;
A first test surface shape data acquisition step of analyzing image data of the first interference fringes to obtain shape data of the first test surface;
A second test surface shape data acquisition step of analyzing image data of the second interference fringes to obtain shape data of the second test surface;
Approximating the shape data of the first test surface obtained in the first test surface shape data acquisition step with a Zernike polynomial, and among the coefficients of each term of the Zernike polynomial, A value of a first shift amount proportional coefficient whose value changes in proportion to a shift amount in a direction perpendicular to the first measurement optical axis, and a value proportional to a tilt amount of the first test surface with respect to the first measurement optical axis. A first Zernike coefficient value calculating step for obtaining a value of a first tilt amount proportional coefficient in which
Approximating the shape data of the second test surface obtained in the second test surface shape data acquisition step with a Zernike polynomial, and among the coefficients of each term of the Zernike polynomial, A value of a second shift amount proportional coefficient whose value changes in proportion to a shift amount in a direction perpendicular to the second measurement optical axis, and a value proportional to a tilt amount of the second test surface with respect to the second measurement optical axis. A second Zernike coefficient value calculating step for obtaining a value of a second tilt amount proportional coefficient in which
Based on the value of the first shift amount proportional coefficient and the value of the first tilt amount proportional coefficient obtained in the first Zernike coefficient value calculating step, the shift amount of the first test surface with respect to the first measurement optical axis And a first shift amount / tilt amount calculating step for obtaining a tilt amount;
Based on the value of the second shift amount proportional coefficient and the value of the second tilt amount proportional coefficient obtained in the second Zernike coefficient value calculating step, the shift amount of the second test surface with respect to the second measurement optical axis And a second shift amount / tilt amount calculating step for obtaining a tilt amount;
The shift amount and tilt amount of the first test surface obtained in the first shift amount / tilt amount calculation step and the second test surface obtained in the second shift amount / tilt amount calculation step. A surface misalignment amount / surface tilt amount calculating step for calculating the surface misalignment amount and the surface tilt amount based on a shift amount and a tilt amount and information on a relative positional relationship between the first interferometer and the second interferometer; A method for measuring an aspherical body, comprising: The Zernike polynomial is a fourth or higher order Zernike polynomial Z (ρ, θ) expressed in a polar coordinate format (ρ is a distance from the pole, θ is a declination with respect to the starting line),
The first shift amount proportional coefficient and the second shift amount proportional coefficient are a coefficient Z _{1 of} a term expressed by the following formula (1), a coefficient Z _{2 of} a term expressed by the following formula (2), and the following formula ( 3) is a coefficient Z _{6 of the} term expressed by 3) and a coefficient Z ₇ of the term expressed by the following equation (4), and the first tilt amount proportional coefficient and the second tilt amount proportional coefficient are the coefficient Z ₁ The aspherical body measurement method according to claim 1, wherein the coefficient is Z ₂ .
ρcosθ (1)
ρsinθ (2)
(3ρ ² −2) ρcos θ (3)
(3ρ ² −2) ρsinθ (4) In an aspherical body having a first test surface that is a rotating aspheric surface and a second test surface that is a rotating aspherical surface or a spherical surface, a relative surface between the first test surface and the second test surface An aspherical surface measuring device for measuring a deviation amount and a surface tilt amount,
A first measurement light is applied to the first test surface along the first measurement optical axis, and the first reflected wavefront and the first reference wavefront reflected from the first test surface of the first measurement light are reflected. A first interferometer for obtaining image data of a first interference fringe formed by optical interference;
The second measurement light is irradiated onto the second test surface along the second measurement optical axis, and the second reflected wavefront reflected from the second test surface of the second measurement light and the second reference wavefront A second interferometer for obtaining image data of a second interference fringe formed by optical interference, the relative positional relationship with the first interferometer being specified;
First test surface shape data acquisition means for analyzing the image data of the first interference fringes to obtain shape data of the first test surface;
Second test surface shape data obtaining means for analyzing the image data of the second interference fringes and obtaining shape data of the second test surface;
Approximating the shape data of the first test surface obtained by the first test surface shape data acquisition means with a Zernike polynomial, and among the coefficients of each term of the Zernike polynomial, A value of a first shift amount proportional coefficient whose value changes in proportion to a shift amount in a direction perpendicular to the first measurement optical axis, and a value proportional to a tilt amount of the first test surface with respect to the first measurement optical axis. First Zernike coefficient value calculating means for obtaining a value of a first tilt amount proportional coefficient in which
Approximating the shape data of the second test surface obtained by the second test surface shape data acquisition means with a Zernike polynomial, and among the coefficients of each term of the Zernike polynomial, A value of a second shift amount proportional coefficient whose value changes in proportion to a shift amount in a direction perpendicular to the second measurement optical axis, and a value proportional to a tilt amount of the second test surface with respect to the second measurement optical axis. Second Zernike coefficient value calculating means for determining the value of the second tilt amount proportional coefficient in which
Based on the value of the first shift amount proportional coefficient and the value of the first tilt amount proportional coefficient obtained by the first Zernike coefficient value calculating means, the shift amount of the first test surface with respect to the first measurement optical axis And a first shift amount / tilt amount calculating means for obtaining a tilt amount;
Based on the second shift amount proportional coefficient value and the second tilt amount proportional coefficient value obtained by the second Zernike coefficient value calculating means, the shift amount of the second test surface with respect to the second measurement optical axis And a second shift amount / tilt amount calculating means for obtaining a tilt amount;
The shift amount and tilt amount of the first test surface obtained by the first shift amount / tilt amount calculating means, and the shift of the second test surface obtained by the second shift amount / tilt amount calculating means. A surface displacement amount / surface inclination amount calculating means for calculating the surface displacement amount and the surface inclination amount based on the amount and the tilt amount and information on the relative positional relationship between the first interferometer and the second interferometer; An aspherical body measuring apparatus comprising:

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