CN110966957A - Absolute inspection method for synchronous measurement of multiple spherical standard lenses - Google Patents

Absolute inspection method for synchronous measurement of multiple spherical standard lenses Download PDF

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CN110966957A
CN110966957A CN201911159836.5A CN201911159836A CN110966957A CN 110966957 A CN110966957 A CN 110966957A CN 201911159836 A CN201911159836 A CN 201911159836A CN 110966957 A CN110966957 A CN 110966957A
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spherical surface
axis
spherical
term
measurement
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陈磊
王云涛
孔璐
杨光
郑东晖
胡晨辉
王冲
吴志飞
陈佳
张正宇
崔鑫莹
马致遥
黄晨
马海颖
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Nanjing University of Science and Technology
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Nanjing University of Science and Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
    • G01B11/2441—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures using interferometry
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/16—Measuring arrangements characterised by the use of optical techniques for measuring the deformation in a solid, e.g. optical strain gauge
    • G01B11/161—Measuring arrangements characterised by the use of optical techniques for measuring the deformation in a solid, e.g. optical strain gauge by interferometric means

Abstract

The invention discloses an absolute inspection method for synchronous measurement of a plurality of spherical standard lenses. The method comprises the following steps: there are 3 spherical lenses, A, B, C respectively; taking the spherical surface B as a reference surface and the spherical surface A as a test surface, and carrying out primary interference measurement; taking the spherical surface B as a reference surface, taking the spherical surface A as a test surface after rotating around an axis anticlockwise by 90 degrees, and carrying out primary interference measurement; taking the spherical surface C as a reference surface, keeping the position of the spherical surface A during the first measurement as a test surface, and carrying out the first interference measurement; taking the spherical surface C as a reference surface and the spherical surface B as a test surface, and carrying out primary interference measurement; and (3) integrating the measurement results, and decomposing to obtain the parity function terms of the spherical surface A, B, C and obtain the respective absolute surface shape distribution of the spherical surface A, B, C by utilizing a parity function decomposition and Fourier series frequency selection method. The invention has the advantages of less measurement times, simplicity, practicability, accuracy and high efficiency, and the measurement result can ensure the information of the surface shape at all frequencies as far as possible.

Description

Absolute inspection method for synchronous measurement of multiple spherical standard lenses
Technical Field
The invention belongs to the technical field of light interference measurement, and particularly relates to an absolute detection method for synchronous measurement of a plurality of spherical standard lenses.
Background
In the interference detection, the detection precision of the surface shape error is mainly influenced by the quality of a reference surface. In order to obtain absolute surface shape error distribution information of a measured surface, the existing solution scheme is as follows: firstly, a reference surface with higher surface shape precision is provided, for example, a point diffraction interferometer is utilized to generate a reference surface close to an ideal spherical surface, and the method needs to additionally build the point diffraction interferometer, so that the realization difficulty is high; secondly, the error of the reference surface is calibrated, and the influence of the error of the reference surface is separated to improve the detection precision, namely an absolute detection technology.
The existing spherical absolute detection technology comprises a two-spherical method, a translational rotation method, a random sphere method, a three-spherical method and the like. When the two-sphere method is used for detection, the light path of the test light is inverted at the cat eye position and the common light path condition is lost, so that the interference detection result is insensitive to the adjustment error, and adjustment errors such as coma aberration and astigmatism can be introduced into the result, thereby affecting the accuracy of the absolute detection result. The translational rotation method needs to decompose the surface shape into a rotationally symmetric item and a rotationally asymmetric item, and the data processing is complex; moreover, the translation operation can introduce inclination, and an astigmatism term is generated on the surface shape and is difficult to eliminate. In order to realize high-precision measurement by the random sphere method, the precision of a small sphere is required to reach 2nm RMS, and the manufacturing cost is high; meanwhile, multi-measurement is required, and the time-space characteristics at different moments influence the repeatability of the measurement result; in addition, it is still impossible to quantitatively explain whether the non-correlated sampling region is satisfied between different tests, which affects the accuracy of result convergence. In 1971, the three-plane cross-checking method was introduced by Harris et al into the sphere testing field. In 1989, Elssner et al performed detailed theoretical studies and experimental tests on the absolute test of the three spherical surfaces. In 2008, Schreiner et al use odd-even term decomposition, and combine cat eye positions of two spherical surfaces to complete surface shape detection, and realize surface shape splicing, but the detection of cat eye position brings new aberration.
Disclosure of Invention
The invention aims to provide an absolute detection method for synchronous measurement of a plurality of spherical standard lenses, which has high precision and is easy to realize.
The technical solution for realizing the purpose of the invention is as follows: an absolute inspection method for synchronous measurement of a plurality of spherical standard lenses comprises the following steps:
step 1, establishing a coordinate system by taking a test surface as a reference: the opposite direction of the emission of the optical axis of the Fizeau type laser interferometer is taken as a z axis, the vertical ground is taken as an upward y axis, and the x axis, the y axis and the z axis form a right-hand coordinate system of a thumb along the opposite direction of the optical axis; adopting a Fizeau type laser interferometer, taking a spherical surface B as a reference surface and taking a spherical surface A as a test surface, carrying out primary interference measurement to obtain a relative surface shape M1；
Step 2, taking the spherical surface B as a reference surface, taking the spherical surface A as a test surface after rotating around an axis anticlockwise by 90 degrees along the z-axis direction, and performing one-time interferometry to obtain a relative surface shape M2；
Step 3, the spherical surface B is changed into a spherical surface C, the spherical surface C is used as a reference surface, and the spherical surface A is clockwise along the z-axis directionRotating 90 degrees around the shaft, namely keeping the position during the first measurement as a test surface, and carrying out the first interferometry to obtain a relative surface shape M3；
Step 4, replacing the spherical surface A with a spherical surface B, taking the spherical surface C as a reference surface and the spherical surface B as a test surface, and performing one-time interferometry to obtain a relative surface shape M4；
And 5, integrating the measurement results of the steps 1-4, decomposing by using a parity function decomposition and Fourier series frequency selection method to obtain each term of the parity function of the spherical surface A, B, C, and finally determining the respective absolute surface shape distribution of the spherical surface A, B, C.
Further, in the step 1, a Fizeau type laser interferometer is adopted, the spherical surface B is used as a reference surface, the spherical surface A is used as a test surface, and interference measurement is carried out for one time to obtain a relative surface shape M1The formula is as follows:
M1＝Ws+[B(x,y)]T+[A(x,y)]180(1)
wherein A (x, y) represents the surface shape error of the spherical surface A, B (x, y) represents the surface shape error of the spherical surface B, and WsRepresents a systematic error [ ·]TRepresenting a mirror inversion of the face shape error B (x, y) along the y-axis [ ·]180Indicating that the face shape error a (x, y) is rotated 180 degrees along the z-axis.
Further, in the step 2, the spherical surface B is used as a reference surface, the spherical surface a rotates counterclockwise around the axis by 90 degrees along the z-axis direction and then is used as a test surface, and one-time interferometry is performed to obtain a relative surface shape M2The formula is as follows:
M2＝Ws+[B(x,y)]T+[A(x,y)90]180(2)
in the formula, A (x, y)90Representing the surface shape error of the spherical surface A after rotating 90 degrees around the z-axis anticlockwise, B (x, y) representing the surface shape error of the spherical surface B, WsRepresents a systematic error [ ·]TRepresenting a mirror inversion of the face shape error B (x, y) along the y-axis [ ·]180Representing the face shape error A (x, y) along the z-axis90And performing 180-degree rotation operation.
Further, the spherical surface C in the step 3 serves as a reference surface, and the spherical surface A is rotated around the axis clockwise along the z-axis directionKeeping the position at 90 degrees when measuring for the first time as a test surface, and carrying out interference measurement for one time to obtain a relative surface shape M3The formula is as follows:
M3＝Ws+[C(x,y)]T+[A(x,y)]180(3)
wherein A (x, y) represents the surface shape error of the spherical surface A, C (x, y) represents the surface shape error of the spherical surface C, and WsRepresents a systematic error [ ·]TRepresenting a mirror inversion of the face shape error C (x, y) along the y-axis [ ·]180Indicating that the face shape error a (x, y) is rotated 180 degrees along the z-axis.
Further, the spherical surface C in the step 4 is used as a reference surface, the spherical surface B is used as a test surface, and one-time interference measurement is carried out to obtain a relative surface shape M4The formula is as follows:
M4＝Ws+[C(x,y)]T+[B(x,y)]180(4)
wherein B (x, y) represents the surface shape error of the spherical surface B, C (x, y) represents the surface shape error of the spherical surface C, and WsRepresents a systematic error [ ·]TRepresenting a mirror inversion of the face shape error C (x, y) along the y-axis [ ·]180Indicating that the face shape error B (x, y) is rotated 180 degrees along the z-axis.
Further, in step 5, the measurement results of steps 1 to 4 are integrated, and the parity function terms of the spherical surface A, B, C are obtained by decomposition by using a parity function decomposition and Fourier series frequency selection method, so as to finally determine the respective absolute surface shape distribution of the spherical surface A, B, C, specifically as follows:
Figure BDA0002285763680000031
Figure BDA0002285763680000032
Figure BDA0002285763680000041
Figure BDA0002285763680000042
Figure BDA0002285763680000043
in the formula, Aoe、Aeo、Aee、AooRepresents four terms of parity term, even-odd term, even-even term and odd-odd term obtained by decomposing the parity function of the spherical surface A, and Boe、Beo、Bee、BooRepresents four terms of parity term, even-odd term, even-even term and odd-odd term obtained by decomposing the spherical surface B by a parity function, Coe、Ceo、Cee、CooRepresents four terms of parity term, even-odd term, even-even term and odd-odd term obtained by decomposing the parity function of the spherical surface C, Aoo,2oddγFundamental frequency term representing the singular term of sphere A, Boo,2oddγFundamental frequency term, C, representing the singular term of sphere Boo,2oddγFundamental frequency term representing the singular term of sphere C [ ·]TRepresenting a mirror inversion of the face shape error C (x, y) along the y-axis [ ·]θRepresenting the theta degree rotation operation of the face shape error B (x, y) along the z-axis; m is1、m3、m4、m1'、m2'、m4' are different combined measurements during the calculation;
finally determining the respective absolute surface shape distribution of the spherical surface A, B, C
Figure BDA0002285763680000044
The formula is as follows:
Figure BDA0002285763680000045
compared with the prior art, the invention has the following remarkable advantages: (1) the measurement result is not influenced by the system error of the interferometer and the surface shape precision of the reference surface, and the measurement precision is high; (2) the detection of the cat eye position of the two spherical methods and the detection of the transverse translation position of the translation rotation method can be avoided in the measuring process, and the measuring cost is lower than that of the random sphere method; (3) the information of 3 spherical surfaces at all frequencies can be ensured as far as possible by utilizing the odd-even function decomposition and Fourier series frequency selection method, the measurement process is simple and convenient, and the structure is simple.
The present invention is described in further detail below with reference to the attached drawing figures.
Drawings
FIG. 1 is a schematic diagram of a designated coordinate system according to the present invention.
Fig. 2 is a schematic diagram of interferometry for a reference surface sphere B and a test surface sphere a.
FIG. 3 is a schematic diagram of interferometric measurements of a reference surface sphere B and a test surface sphere A rotated 90 degrees counterclockwise about the z-axis.
Fig. 4 is a schematic diagram of interferometric measurement of the reference surface sphere C and the test surface sphere a while maintaining the first measurement position.
Fig. 5 is a schematic diagram of interferometric measurement of a reference surface sphere C and a test surface sphere B.
Detailed Description
The invention discloses an absolute detection method for synchronous measurement of a plurality of spherical standard lenses, which comprises the following steps:
step 1, establishing a coordinate system by taking a test surface as a reference: the opposite direction of the emission of the optical axis of the Fizeau type laser interferometer is taken as a z axis, the vertical ground is taken as an upward y axis, and the x axis, the y axis and the z axis form a right-hand coordinate system of a thumb along the opposite direction of the optical axis; adopting a Fizeau type laser interferometer, taking a spherical surface B as a reference surface and taking a spherical surface A as a test surface, carrying out primary interference measurement to obtain a relative surface shape M1；
Step 2, taking the spherical surface B as a reference surface, taking the spherical surface A as a test surface after rotating around an axis anticlockwise by 90 degrees along the z-axis direction, and performing one-time interferometry to obtain a relative surface shape M2；
And 3, replacing the spherical surface B with a spherical surface C, taking the spherical surface C as a reference surface, rotating the spherical surface A by 90 degrees around a clockwise shaft along the z-axis direction, namely keeping the position during the first measurement as a test surface, and performing one-time interference measurement to obtain a relative surface shape M3；
Step 4, replacing the spherical surface A with a spherical surface B, taking the spherical surface C as a reference surface and the spherical surface B as a test surface, and performing one-time interferometry to obtain a relative surface shape M4；
And 5, integrating the measurement results of the steps 1-4, decomposing by using a parity function decomposition and Fourier series frequency selection method to obtain each term of the parity function of the spherical surface A, B, C, and finally determining the respective absolute surface shape distribution of the spherical surface A, B, C.
Further, in the step 1, a Fizeau type laser interferometer is adopted, the spherical surface B is used as a reference surface, the spherical surface A is used as a test surface, and interference measurement is carried out for one time to obtain a relative surface shape M1The formula is as follows:
M1＝Ws+[B(x,y)]T+[A(x,y)]180(1)
wherein A (x, y) represents the surface shape error of the spherical surface A, B (x, y) represents the surface shape error of the spherical surface B, and WsRepresents a systematic error [ ·]TRepresenting a mirror inversion of the face shape error B (x, y) along the y-axis [ ·]180Indicating that the face shape error a (x, y) is rotated 180 degrees along the z-axis.
Further, in the step 2, the spherical surface B is used as a reference surface, the spherical surface a rotates counterclockwise around the axis by 90 degrees along the z-axis direction and then is used as a test surface, and one-time interferometry is performed to obtain a relative surface shape M2The formula is as follows:
M2＝Ws+[B(x,y)]T+[A(x,y)90]180(2)
in the formula, A (x, y)90Representing the surface shape error of the spherical surface A after rotating 90 degrees around the z-axis anticlockwise, B (x, y) representing the surface shape error of the spherical surface B, WsRepresents a systematic error [ ·]TRepresenting a mirror inversion of the face shape error B (x, y) along the y-axis [ ·]180Representing the face shape error A (x, y) along the z-axis90And performing 180-degree rotation operation.
Further, the spherical surface C in the step 3 is used as a reference surface, the spherical surface a is rotated by 90 degrees clockwise around the axis along the z-axis direction, namely, the position of the spherical surface a during the first measurement is kept as a test surface, and the interference measurement is performed for one time to obtain the opposite surface shape M3The formula is as follows:
M3＝Ws+[C(x,y)]T+[A(x,y)]180(3)
wherein A (x, y) represents the surface shape error of the spherical surface A, C (x, y) represents the surface shape error of the spherical surface C, and WsRepresents a systematic error [ ·]TRepresenting a mirror inversion of the face shape error C (x, y) along the y-axis [ ·]180Indicating that the face shape error a (x, y) is rotated 180 degrees along the z-axis.
Further, the spherical surface C in the step 4 is used as a reference surface, the spherical surface B is used as a test surface, and one-time interference measurement is carried out to obtain a relative surface shape M4The formula is as follows:
M4＝Ws+[C(x,y)]T+[B(x,y)]180(4)
wherein B (x, y) represents the surface shape error of the spherical surface B, C (x, y) represents the surface shape error of the spherical surface C, and WsRepresents a systematic error [ ·]TRepresenting a mirror inversion of the face shape error C (x, y) along the y-axis [ ·]180Indicating that the face shape error B (x, y) is rotated 180 degrees along the z-axis.
Further, in step 5, the measurement results of steps 1 to 4 are integrated, and the parity function terms of the spherical surface A, B, C are obtained by decomposition by using a parity function decomposition and Fourier series frequency selection method, so as to finally determine the respective absolute surface shape distribution of the spherical surface A, B, C, specifically as follows:
Figure BDA0002285763680000071
Figure BDA0002285763680000072
Figure BDA0002285763680000073
Figure BDA0002285763680000074
Figure BDA0002285763680000075
in the formula, Aoe、Aeo、Aee、AooRepresents the parity of sphere A obtained by the decomposition of parity functionFour terms of term, even and odd term, even and even term and odd term, Boe、Beo、Bee、BooRepresents four terms of parity term, even-odd term, even-even term and odd-odd term obtained by decomposing the spherical surface B by a parity function, Coe、Ceo、Cee、CooRepresents four terms of parity term, even-odd term, even-even term and odd-odd term obtained by decomposing the parity function of the spherical surface C, Aoo,2oddγFundamental frequency term representing the singular term of sphere A, Boo,2oddγFundamental frequency term, C, representing the singular term of sphere Boo,2oddγFundamental frequency term representing the singular term of sphere C [ ·]TRepresenting a mirror inversion of the face shape error C (x, y) along the y-axis [ ·]θRepresenting the theta degree rotation operation of the face shape error B (x, y) along the z-axis; m is1、m3、m4、m1'、m2'、m4' are different combined measurements during the calculation;
finally determining the respective absolute surface shape distribution of the spherical surface A, B, C
Figure BDA0002285763680000081
The formula is as follows:
Figure BDA0002285763680000082
the invention is described in further detail below with reference to the figures and the embodiments.
Examples
With reference to fig. 1, all the measurement processes in the present invention are performed in the designated coordinate system shown in fig. 1. And establishing a coordinate system by taking the test surface as a reference, taking the opposite direction of the optical axis emission of the Fizeau type laser interferometer as a z-axis and taking the vertical ground as an upward y-axis, wherein the x-axis, the y-axis and the z-axis can form a right-hand coordinate system of the thumb along the opposite direction of the optical axis.
With reference to fig. 2 to 5, the absolute inspection method for synchronous measurement of a plurality of spherical standard lenses of the present invention comprises the following steps:
step 1, as shown in fig. 2, using a fizeau type laser interferometer to make a pair of a sphere B as a reference surface and a sphere a as a test surface,performing one-time interference measurement to obtain a measurement result M1The formula is as follows:
M1＝Ws+[B(x,y)]T+[A(x,y)]180(1)
wherein A (x, y) represents the surface shape error of the spherical surface A, B (x, y) represents the surface shape error of the spherical surface B, and WsRepresents a systematic error [ ·]TRepresenting a mirror inversion of the face shape error B (x, y) along the y-axis [ ·]180Indicating that the face shape error a (x, y) is rotated 180 degrees along the z-axis.
Step 2, as shown in fig. 3, rotating the spherical surface a by 90 degrees counterclockwise around the z-axis, performing one-time interferometric measurement on the spherical surface B serving as the reference surface and the spherical surface a serving as the test surface after rotating by 90 degrees counterclockwise around the z-axis, and obtaining a measurement result M2The formula is as follows:
M2＝Ws+[B(x,y)]T+[A(x,y)90]180(2)
in the formula, A (x, y)90Representing the surface shape error of the spherical surface A after rotating 90 degrees around the z-axis anticlockwise, B (x, y) representing the surface shape error of the spherical surface B, WsRepresents a systematic error [ ·]TRepresenting a mirror inversion of the face shape error B (x, y) along the y-axis [ ·]180Representing the face shape error A (x, y) along the z-axis90And performing 180-degree rotation operation.
Step 3, as shown in fig. 4, the spherical surface B is removed, the spherical surface C is replaced, the spherical surface a is rotated by 90 degrees along the z-axis direction, and the spherical surface C as the reference surface and the spherical surface a as the test surface when the first measurement position is maintained are subjected to one-time interference measurement to obtain a result M3The formula is as follows:
M3＝Ws+[C(x,y)]T+[A(x,y)]180(3)
wherein A (x, y) represents the surface shape error of the spherical surface A, C (x, y) represents the surface shape error of the spherical surface C, and WsRepresents a systematic error [ ·]TRepresenting a mirror inversion of the face shape error C (x, y) along the y-axis [ ·]180Indicating that the face shape error a (x, y) is rotated 180 degrees along the z-axis.
Step 4, as shown in FIG. 5, the spherical surface A is removed and replaced with a spherical surfaceB, performing one-time interference measurement on the spherical surface C as a reference surface and the spherical surface B as a test surface to obtain a result M4The formula is as follows:
M4＝Ws+[C(x,y)]T+[B(x,y)]180(4)
and 5, integrating the measurement results of the steps 1-4, and decomposing by using an odd-even function decomposition and Fourier series frequency selection method to obtain the odd-even function terms of the spherical surface A, B, C:
Figure BDA0002285763680000091
Figure BDA0002285763680000092
Figure BDA0002285763680000101
Figure BDA0002285763680000102
Figure BDA0002285763680000103
and 6, integrating the measurement results of the steps 1 to 4, and combining formulas (1) to (9) by using an odd-even function decomposition and Fourier series frequency selection method to obtain respective absolute surface shape distribution of the spherical surface A, B, C:
Figure BDA0002285763680000104
in conclusion, the measurement result of the invention is not affected by the system error of the interferometer and the surface shape precision of the reference surface, the detection of the cat eye position of the two-sphere method and the transverse translation position of the translation rotation method can be avoided in the measurement process, the measurement cost is lower than that of the random sphere method, the information of 3 spheres at all frequencies can be ensured as far as possible by utilizing the odd-even function decomposition and Fourier series frequency selection method, the measurement precision is high, the measurement frequency is few, and the realization is easy.

Claims (6)

1. An absolute inspection method for synchronous measurement of a plurality of spherical standard lenses is characterized by comprising the following steps:
step 1, establishing a coordinate system by taking a test surface as a reference: the opposite direction of the emission of the optical axis of the Fizeau type laser interferometer is taken as a z axis, the vertical ground is taken as an upward y axis, and the x axis, the y axis and the z axis form a right-hand coordinate system of a thumb along the opposite direction of the optical axis; adopting a Fizeau type laser interferometer, taking a spherical surface B as a reference surface and taking a spherical surface A as a test surface, carrying out primary interference measurement to obtain a relative surface shape M1；
Step 2, taking the spherical surface B as a reference surface, taking the spherical surface A as a test surface after rotating around an axis anticlockwise by 90 degrees along the z-axis direction, and performing one-time interferometry to obtain a relative surface shape M2；
And 3, replacing the spherical surface B with a spherical surface C, taking the spherical surface C as a reference surface, rotating the spherical surface A by 90 degrees around a clockwise shaft along the z-axis direction, namely keeping the position during the first measurement as a test surface, and performing one-time interference measurement to obtain a relative surface shape M3；
Step 4, replacing the spherical surface A with a spherical surface B, taking the spherical surface C as a reference surface and the spherical surface B as a test surface, and performing one-time interferometry to obtain a relative surface shape M4；
And 5, integrating the measurement results of the steps 1-4, decomposing by using a parity function decomposition and Fourier series frequency selection method to obtain each term of the parity function of the spherical surface A, B, C, and finally determining the respective absolute surface shape distribution of the spherical surface A, B, C.
2. The absolute inspection method for synchronous measurement of multiple spherical standard lenses according to claim 1, wherein step 1 comprises performing an interferometric measurement using a Fizeau laser interferometer, a sphere B as a reference plane, and a sphere A as a test plane to obtain a relative surface shape M1The formula is as follows:
M1＝Ws+[B(x,y)]T+[A(x,y)]180(1)
wherein A (x, y) represents a spherical surface AB (x, y) represents the surface shape error of the spherical surface B, WsRepresents a systematic error [ ·]TRepresenting a mirror inversion of the face shape error B (x, y) along the y-axis [ ·]180Indicating that the face shape error a (x, y) is rotated 180 degrees along the z-axis.
3. The absolute inspection method of synchronous measurement of multiple spherical standard lenses according to claim 1, wherein in step 2, the spherical surface B is used as a reference surface, the spherical surface A rotates 90 degrees along the z-axis counterclockwise around the axis and is used as a test surface, and one interferometric measurement is performed to obtain the relative surface shape M2The formula is as follows:
M2＝Ws+[B(x,y)]T+[A(x,y)90]180(2)
in the formula, A (x, y)90Representing the surface shape error of the spherical surface A after rotating 90 degrees around the z-axis anticlockwise, B (x, y) representing the surface shape error of the spherical surface B, WsRepresents a systematic error [ ·]TRepresenting a mirror inversion of the face shape error B (x, y) along the y-axis [ ·]180Representing the face shape error A (x, y) along the z-axis90And performing 180-degree rotation operation.
4. The absolute inspection method for synchronous measurement of multiple spherical standard lenses according to claim 1, wherein the spherical surface C of step 3 is used as a reference surface, the spherical surface A is rotated by 90 degrees clockwise around the axis along the z-axis direction, that is, the position of the spherical surface A during the first measurement is kept as a test surface, and the interference measurement is performed once to obtain the relative surface shape M3The formula is as follows:
M3＝Ws+[C(x,y)]T+[A(x,y)]180(3)
wherein A (x, y) represents the surface shape error of the spherical surface A, C (x, y) represents the surface shape error of the spherical surface C, and WsRepresents a systematic error [ ·]TRepresenting a mirror inversion of the face shape error C (x, y) along the y-axis [ ·]180Indicating that the face shape error a (x, y) is rotated 180 degrees along the z-axis.
5. The plurality of spherical standards of claim 1The absolute inspection method for lens synchronous measurement is characterized in that the spherical surface C in the step 4 is used as a reference surface, the spherical surface B is used as a test surface, and one-time interference measurement is carried out to obtain a relative surface shape M4The formula is as follows:
M4＝Ws+[C(x,y)]T+[B(x,y)]180(4)
wherein B (x, y) represents the surface shape error of the spherical surface B, C (x, y) represents the surface shape error of the spherical surface C, and WsRepresents a systematic error [ ·]TRepresenting a mirror inversion of the face shape error C (x, y) along the y-axis [ ·]180Indicating that the face shape error B (x, y) is rotated 180 degrees along the z-axis.
6. The absolute inspection method for synchronous measurement of multiple spherical standard lenses according to claim 1, wherein in step 5, the measurement results of steps 1 to 4 are integrated, and the parity function terms of the spherical surface A, B, C are obtained by decomposition by using a parity function decomposition and Fourier series frequency selection method, so as to finally determine the respective absolute surface shape distribution of the spherical surface A, B, C, specifically as follows:
Figure FDA0002285763670000021
Figure FDA0002285763670000031
Figure FDA0002285763670000032
Figure FDA0002285763670000033
Figure FDA0002285763670000034
in the formula, Aoe、Aeo、Aee、AooRepresenting sphere A JingqiFour terms of parity term, even and odd term, even and even term and odd term obtained by even function decomposition, Boe、Beo、Bee、BooRepresents four terms of parity term, even-odd term, even-even term and odd-odd term obtained by decomposing the spherical surface B by a parity function, Coe、Ceo、Cee、CooRepresents four terms of parity term, even-odd term, even-even term and odd-odd term obtained by decomposing the parity function of the spherical surface C, Aoo,2oddγFundamental frequency term representing the singular term of sphere A, Boo,2oddγFundamental frequency term, C, representing the singular term of sphere Boo,2oddγFundamental frequency term representing the singular term of sphere C [ ·]TRepresenting a mirror inversion of the face shape error C (x, y) along the y-axis [ ·]θRepresenting the theta degree rotation operation of the face shape error B (x, y) along the z-axis; m is1、m3、m4、m1'、m2'、m4' are different combined measurements during the calculation;
finally determining the respective absolute surface shape distribution of the spherical surface A, B, C
Figure FDA0002285763670000035
The formula is as follows:
Figure FDA0002285763670000041
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