CN104913730A - Spherical surface shape rotation and translation absolute detection method - Google Patents

Spherical surface shape rotation and translation absolute detection method Download PDF

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Publication number
CN104913730A
CN104913730A CN201410089712.5A CN201410089712A CN104913730A CN 104913730 A CN104913730 A CN 104913730A CN 201410089712 A CN201410089712 A CN 201410089712A CN 104913730 A CN104913730 A CN 104913730A
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delta
measured
mirror
sphere
sigma
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高志山
史琪琪
杨忠明
李闽珏
王新星
田雪
王帅
成金龙
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Nanjing University of Science and Technology
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Nanjing University of Science and Technology
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Abstract

The invention discloses a spherical surface shape rotation and translation absolute detection method. According to the method of the invention, based on the measurement data of the rotation and translation of a detected spherical surface are utilized, an equation set of Zernike polynomial coefficients which are about the detected spherical surface and a reference surface is constructed through adopting a Zernike polynomial fitting-based rotation and translation algorithm, and the coefficients of a Zernike polynomial are solved through utilizing a least square method, and therefore, the absolute surface shapes of the detected spherical surface and the reference surface can be obtained; and adjustment errors in large-numerical value aperture spherical surface phase-shift detection are adopted as independent error terms, and the adjustment errors are applied to an absolute detection process, and the adjustment errors and interferometer system errors are removed together from test wave surface data, and therefore, computation accuracy can be improved, and the method has an important application value.

Description

A kind of spherical surface shape rotates translation absolute detection method
Technical field
The invention belongs to precision optics fields of measurement, particularly be a kind of sphere absolute detection method.
Background technology
Along with the development of Modern Optics Technology, spherical optics element machining precision is more and more higher, also more and more higher to the requirement of accuracy of detection, and rotating translation absolute sense technology can improve accuracy of detection effectively, obtains face shape information more accurately.
At present, the absolute detection method of sphere mainly contains two sphere methods and little method of spherical means, absolute sense mainly three plate methods and its extension of plane.Three plate methods need three pieces of flat boards, and wherein one flat plate needs turn-over, and in the detection under vertical condition, the factor of gravity effect cannot be eliminated.In two spherical methods of sphere absolute sense, the determination deviation of opal center can cause four leaf error and spherical aberrations; The reference surface time error detecting radius-of-curvature larger with bead averaging method is larger.Rotary flat shifting method can detect the reference surface of any radius-of-curvature, and what only need processing radius-of-curvature and it to match is just passable by side.Another similar method---translation shear absolute sense in the process of practical operation because translation mechanism can not completely ideal and cause producing larger method for quadratic term error, comprise astigmatism and out of focus.
Summary of the invention
A kind of spherical surface shape is the object of the present invention is to provide to rotate translation absolute detection method, using the alignment error existed during the phase shift of large-numerical aperture sphere detects as independent error item, and alignment error is put into absolute sense process remove in test corrugated data together with interferometer system error.。
The technical solution realizing the object of the invention is: a kind of spherical surface shape rotates translation absolute detection method, and prolong optical axis and put interferometer, reference mirror and mirror to be measured successively, step is as follows:
Definition alignment error W mis
W mis = ( c 2 - 1 Z 2 + c 2 - 2 Z 2 2 + c 2 - 3 Z 2 3 ) + ( c 3 - 1 Z 3 + c 3 - 2 Z 3 2 + c 3 - 3 Z 3 3 ) + ( c 4 Z 4 + c 8 Z 8 + c 15 Z 15 + c 24 Z 24 + c 35 Z 35 + c 48 Z 48 )
Wherein, c represents the coefficient of the Ze Nike item in alignment error item, Z ifor the Ze Nike item of correspondence,
Step 1: utilize interferometer measurement to obtain one group of original graphic data W of the sphere of the mirror to be measured that numerical aperture is NA 1:
W 1 = W r + Σ i = 5 K a i Z i ( x , y ) + W Omis = W r + Σ i = 5 K a i Z i ( x , y ) + ( c O 2 - 1 Z 2 + c O 2 - 2 Z 2 2 + c O 2 - 3 Z 2 3 ) + ( c O 3 - 1 Z 3 + c O 3 - 2 Z 3 2 + c O 3 - 3 Z 3 3 ) + ( c O 4 Z 4 + c O 8 Z 8 + c O 15 Z 15 + c O 24 Z 24 + c O 35 Z 35 + c O 48 Z 48 )
Wherein W rrepresent the face shape error of reference surface, W omisrepresent original type alignment error, a ifor the zernike coefficient of every, Z ifor the Ze Nike item of correspondence, K is the item number of Ze Nike matching;
Step 2: the sphere prolonging x direction translation mirror to be measured, and record face graphic data W with interferometer 2:
W 2 = W r + Σ i = 5 K a i Z i ( x + Δx , y ) + W Xmis = W r + Σ i = 5 K a i Z i ( x + Δx , y ) + ( c X 2 - 1 Z 2 + c X 2 - 2 Z 2 2 + c X 2 - 3 Z 2 3 ) + ( c X 3 - 1 Z 3 + c X 3 - 2 Z 3 2 + c X 3 - 3 Z 3 3 ) + ( c X 4 Z 4 + c X 8 Z 8 + c X 15 Z 15 + c X 24 Z 24 + c X 35 Z 35 + c X 48 Z 48 )
Wherein, W xmisrepresent the alignment error after prolonging the sphere of x direction translation mirror to be measured, c xrepresent the coefficient of the Ze Nike item prolonged after the sphere of x direction translation mirror to be measured in alignment error item;
Step 3: prolong y direction, the i.e. sphere of vertical optical axis direction translation mirror to be measured, and with interferometer measurement face graphic data W 3:
W 3 = W r + Σ i = 5 K a i Z i ( x , y + Δy ) + W Ymis = W r + Σ i = 5 K a i Z i ( x , y + Δy ) + ( c Y 2 - 1 Z 2 + c Y 2 - 2 Z 2 2 + c Y 2 - 3 Z 2 3 ) + ( c Y 3 - 1 Z 3 + c Y 3 - 2 Z 3 2 + c Y 3 - 3 Z 3 3 ) + ( c Y 4 Z 4 + c Y 8 Z 8 + c Y 15 Z 15 + c Y 24 Z 24 + c Y 35 Z 35 + c Y 48 Z 48 )
Wherein, W ymisrepresent the alignment error after prolonging the sphere of y direction translation mirror to be measured, c yrepresent the coefficient of the Ze Nike item prolonged after the sphere of y direction translation mirror to be measured in alignment error item;
Step 4: take optical axis as rotation center, rotates the sphere of mirror to be measured, and records face graphic data W with interferometer 4:
W 4 = W r + Σ i = 5 K a i Z i ( r , θ + Δθ ) + W Rmis = W r + Σ i = 5 K a i Z i ( r , θ + Δθ ) + ( c R 2 - 1 Z 2 + c R 2 - 2 Z 2 2 + c R 2 - 3 Z 2 3 ) + ( c R 3 - 1 Z 3 + c R 3 - 2 Z 3 2 + c R 3 - 3 Z 3 3 ) + ( c R 4 Z 4 + c R 8 Z 8 + c R 15 Z 15 + c R 24 Z 24 + c R 35 Z 35 + c R 48 Z 48 )
Wherein, θ is the anglec of rotation, W rmisrepresent the alignment error after prolonging optical axis rotates the sphere of mirror to be measured, c rrepresent and prolong the coefficient that optical axis rotates the Ze Nike item after the sphere of mirror to be measured in alignment error item;
Step 5: in above-mentioned four steps, has often walked reference surface face graphic data W r, use W 2-W 1, W 3-W 1, W 4-W 1:
DxW = Σ i = 5 K a i Δ Z ix + ( c DX 2 - 1 Z 2 + c DX 2 - 2 Z 2 2 + c DX 2 - 3 Z 2 3 ) + ( c DX 3 - 1 Z 3 + c DX 3 - 2 Z 3 2 + c DX 3 - 3 Z 3 3 ) + ( c DX 4 Z 4 + c DX 8 Z 8 + c DX 15 Z 15 + c DX 24 Z 24 + c DX 35 Z 35 + c DX 48 Z 48 )
DyW = Σ i = 5 K a i Δ Z iy + ( c DY 2 - 1 Z 2 + c DY 2 - 2 Z 2 2 + c DY 2 - 3 Z 2 3 ) + ( c DY 3 - 1 Z 3 + c DY 3 - 2 Z 3 2 + c DY 3 - 3 Z 3 3 ) + ( c DY 4 Z 4 + c DY 8 Z 8 + c DY 15 Z 15 + c DY 24 Z 24 + c DY 35 Z 35 + c DY 48 Z 48 )
DrW = Σ i = 5 K a i Δ Z i + ( c DR 2 - 1 Z 2 + c DR 2 - 2 Z 2 2 + c DR 2 - 3 Z 2 3 ) + ( c DR 3 - 1 Z 3 + c DR 3 - 2 Z 3 2 + c DR 3 - 3 Z 3 3 ) + ( c DR 4 Z 4 + c DR 8 Z 8 + c DR 15 Z 15 + c DR 24 Z 24 + c DR 35 Z 35 + c DR 48 Z 48 )
Above-mentioned system of equations can be expressed as: GX=R
Wherein:
G = Δ Z 1 x ( 1,1 ) Δ Z 2 x ( 1,1 ) . . . Δ Z Kx ( 1,1 ) Z 2 ( 1,1 ) Z 2 2 ( 1,1 ) . . . Z 48 ( 1,1 ) 0 0 . . . 0 0 0 . . . 0 Δ Z 1 x ( 1,2 ) Δ Z 2 x ( 1,2 ) . . . Δ Z Kx ( 1,2 ) Z 2 ( 1,2 ) Z 2 2 ( 1,2 ) . . . Z 48 ( 1,2 ) 0 0 . . . 0 0 0 . . . 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Δ Z 1 x ( M , N ) Δ Z 2 x ( M , N ) . . . Δ Z Kx ( M , N ) Z 2 ( M , N ) Z 2 2 ( M , N ) . . . Z 48 ( M , N ) 0 0 . . . 0 0 0 . . . 0 Δ Z 1 y ( 1,1 ) Δ Z 2 y ( 1,1 ) . . . Δ Z Ky ( 1,1 ) 0 0 . . . 0 Z 2 ( 1,1 ) Z 2 2 ( 1,1 ) . . . Z 48 ( 1,1 ) 0 0 . . . 0 Δ Z 1 y ( 1,2 ) Δ Z 2 y ( 1,2 ) . . . Δ Z Ky ( 1,2 ) 0 0 . . . 0 Z 2 ( 1,2 ) Z 2 2 ( 1,2 ) . . . Z 48 ( 1,2 ) 0 0 . . . 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Δ Z 1 y ( M , N ) Δ Z 2 y ( M , N ) . . . Δ Z Ky ( M , N ) 0 0 . . . 0 Z 2 ( M , N ) Z 2 2 ( M , N ) . . . Z 48 ( M , N ) 0 0 . . . 0 Δ Z 1 r ( 1,1 ) Δ Z 2 r ( 1,1 ) . . . Δ Z Kr ( 1,1 ) 0 0 . . . 0 0 0 . . . 0 Z 2 ( 1,1 ) Z 2 2 ( 1,1 ) . . . Z 48 ( 1,2 ) Δ Z 1 r ( 1,2 ) Δ Z 2 r ( 1,2 ) . . . Δ Z Kr ( 1,2 ) 0 0 . . . 0 0 0 0 0 Z 2 ( 1,2 ) Z 2 2 . . . Z 48 ( 1,2 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Δ Z 1 r ( M , N ) Δ Z 2 r ( M , N ) . . . Δ Z Kr ( M . N ) 0 0 . . . 0 0 0 0 0 Z 2 ( M , N ) Z 2 2 ( M , N ) . . . Z 48 ( M , N )
R = DxW ( 1,1 ) DxW ( 1,2 ) . . . DxW ( M , N ) DyW ( 1,1 ) DyW ( 1,2 ) . . . DyW ( M , N ) DrW ( 1,1 ) DrW ( 1,2 ) . . . DrW ( M , N )
X = a 5 a 6 . . . a K c DX 2 - 1 c DX 2 - 2 . . . c DX 48 c DY 2 - 1 c DY 2 - 2 . . . c DY 48 c DR 2 - 1 c DR 2 - 2 . . . c DR 48
Step 6: solve an equation and obtain X, obtains a then 5a k; Finally obtain tested surface shape
The present invention compared with prior art, its remarkable advantage: the 1. spherical surface shape that the present invention proposes rotates translation absolute detection method based on Zernike fitting of a polynomial, clear principle, and method is simply effective; 2. the spherical surface shape that the present invention proposes rotates translation absolute detection method using the alignment error existed in large-numerical aperture sphere phase shift detection as independent error item, and alignment error is put into absolute sense process remove in test corrugated data together with interferometer system error, effectively improve accuracy of detection, there is important using value.
Accompanying drawing explanation
Fig. 1 is detection architecture schematic diagram when tested sphere is concave mirror in the present invention.
Fig. 2 is that schematic diagram is detected in the original position of the sphere of mirror to be measured in the present invention.
Fig. 3 is the detection schematic diagram after the sphere of mirror to be measured in the present invention prolongs the displacement of x direction.
Fig. 4 is the detection schematic diagram after the sphere of mirror to be measured in the present invention prolongs the displacement of y direction.
Fig. 5 is the detection schematic diagram after the spherical rotary certain angle of mirror to be measured in the present invention.
Fig. 6 is the spherical surface type of the mirror to be measured resolving out after four face types detect.
Fig. 7 is method flow diagram of the present invention.
Embodiment
Below in conjunction with accompanying drawing, the present invention is described in further detail.
Composition graphs 1, a kind of spherical surface shape rotates translation absolute detection method, and prolong optical axis and put interferometer 1, reference mirror 2 and mirror to be measured 3 successively, wherein interferometer 1 comprises helium-neon laser, microcobjective, spatial filter, beam-splitter, collimator objective.
Be illustrated in figure 2 reference mirror and mirror to be measured to overlap in level and vertical direction, two spheres are in homocentric position.
The sphere of mirror 3 to be measured has carried out level, vertical displacement calculate its face graphic data on Fig. 2 position as shown in Figure 3,4.
The sphere of mirror 3 to be measured is after optical axis rotates to an angle as shown in Figure 5, and sphere and the reference surface of mirror 3 to be measured still keep homocentric position.
This method carries out four surface shape measurements to position behind position after position, vertical displacement after original position, horizontal shift and rotation, utilizes three face graphic data below to deduct original graphic data and calculates final face type data.The spherical surface shape that the present invention proposes rotates translation absolute detection method using the alignment error existed during the phase shift of large-numerical aperture sphere detects as independent error item, and alignment error is put into absolute sense process removes in test corrugated data together with interferometer system error.Effectively improve accuracy of detection, there is important using value.The detecting step of its method is as follows:
Composition graphs 7, a kind of spherical surface shape rotates translation absolute detection method, and prolong optical axis and put interferometer 1, reference mirror 2 and mirror to be measured 3 successively, step is as follows:
Definition alignment error W mis
W mis = ( c 2 - 1 Z 2 + c 2 - 2 Z 2 2 + c 2 - 3 Z 2 3 ) + ( c 3 - 1 Z 3 + c 3 - 2 Z 3 2 + c 3 - 3 Z 3 3 ) + ( c 4 Z 4 + c 8 Z 8 + c 15 Z 15 + c 24 Z 24 + c 35 Z 35 + c 48 Z 48 )
Wherein, c represents the coefficient of the Ze Nike item in alignment error item, Z ifor the Ze Nike item of correspondence, such as c 2-3represent the cube coefficient of Section 2 zernike polynomial.
Step 1: utilize interferometer 1 to measure one group of original the graphic data W obtaining the sphere of the mirror to be measured 3 that numerical aperture is NA 1:
W 1 = W r + Σ i = 5 K a i Z i ( x , y ) + W Omis = W r + Σ i = 5 K a i Z i ( x , y ) + ( c O 2 - 1 Z 2 + c O 2 - 2 Z 2 2 + c O 2 - 3 Z 2 3 ) + ( c O 3 - 1 Z 3 + c O 3 - 2 Z 3 2 + c O 3 - 3 Z 3 3 ) + ( c O 4 Z 4 + c O 8 Z 8 + c O 15 Z 15 + c O 24 Z 24 + c O 35 Z 35 + c O 48 Z 48 )
Wherein W rrepresent the face shape error of reference surface, W omisrepresent original type alignment error, a ifor the zernike coefficient of every, Z ifor the Ze Nike item of correspondence, K is the item number of Ze Nike matching;
Step 2: the sphere prolonging x direction translation mirror 3 to be measured, and record face graphic data W with interferometer 1 2:
W 2 = W r + Σ i = 5 K a i Z i ( x + Δx , y ) + W Xmis = W r + Σ i = 5 K a i Z i ( x + Δx , y ) + ( c X 2 - 1 Z 2 + c X 2 - 2 Z 2 2 + c X 2 - 3 Z 2 3 ) + ( c X 3 - 1 Z 3 + c X 3 - 2 Z 3 2 + c X 3 - 3 Z 3 3 ) + ( c X 4 Z 4 + c X 8 Z 8 + c X 15 Z 15 + c X 24 Z 24 + c X 35 Z 35 + c X 48 Z 48 )
Wherein, W xmisrepresent the alignment error after prolonging the sphere of x direction translation mirror 3 to be measured, c xrepresent the coefficient of the Ze Nike item prolonged after the sphere of x direction translation mirror 3 to be measured in alignment error item;
Step 3: prolong y direction, the i.e. sphere of vertical optical axis direction translation mirror 3 to be measured, and with interferometer 1 measuring surface graphic data W 3:
W 3 = W r + Σ i = 5 K a i Z i ( x , y + Δy ) + W Ymis = W r + Σ i = 5 K a i Z i ( x , y + Δy ) + ( c Y 2 - 1 Z 2 + c Y 2 - 2 Z 2 2 + c Y 2 - 3 Z 2 3 ) + ( c Y 3 - 1 Z 3 + c Y 3 - 2 Z 3 2 + c Y 3 - 3 Z 3 3 ) + ( c Y 4 Z 4 + c Y 8 Z 8 + c Y 15 Z 15 + c Y 24 Z 24 + c Y 35 Z 35 + c Y 48 Z 48 )
Wherein, W ymisrepresent the alignment error after prolonging the sphere of y direction translation mirror 3 to be measured, c yrepresent the coefficient of the Ze Nike item prolonged after the sphere of y direction translation mirror 3 to be measured in alignment error item;
Step 4: take optical axis as rotation center, rotates the sphere of mirror 3 to be measured, and records face graphic data W with interferometer 1 4:
W 4 = W r + Σ i = 5 K a i Z i ( r , θ + Δθ ) + W Rmis = W r + Σ i = 5 K a i Z i ( r , θ + Δθ ) + ( c R 2 - 1 Z 2 + c R 2 - 2 Z 2 2 + c R 2 - 3 Z 2 3 ) + ( c R 3 - 1 Z 3 + c R 3 - 2 Z 3 2 + c R 3 - 3 Z 3 3 ) + ( c R 4 Z 4 + c R 8 Z 8 + c R 15 Z 15 + c R 24 Z 24 + c R 35 Z 35 + c R 48 Z 48 )
Wherein, θ is the anglec of rotation, W rmisrepresent the alignment error after prolonging optical axis rotates the sphere of mirror 3 to be measured, c rrepresent and prolong the coefficient that optical axis rotates the Ze Nike item after the sphere of mirror 3 to be measured in alignment error item;
Step 5: in above-mentioned four steps, has often walked reference surface face graphic data W r, use W 2-W 1, W 3-W 1, W 4-W 1:
DxW = Σ i = 5 K a i Δ Z ix + ( c DX 2 - 1 Z 2 + c DX 2 - 2 Z 2 2 + c DX 2 - 3 Z 2 3 ) + ( c DX 3 - 1 Z 3 + c DX 3 - 2 Z 3 2 + c DX 3 - 3 Z 3 3 ) + ( c DX 4 Z 4 + c DX 8 Z 8 + c DX 15 Z 15 + c DX 24 Z 24 + c DX 35 Z 35 + c DX 48 Z 48 )
DyW = Σ i = 5 K a i Δ Z iy + ( c DY 2 - 1 Z 2 + c DY 2 - 2 Z 2 2 + c DY 2 - 3 Z 2 3 ) + ( c DY 3 - 1 Z 3 + c DY 3 - 2 Z 3 2 + c DY 3 - 3 Z 3 3 ) + ( c DY 4 Z 4 + c DY 8 Z 8 + c DY 15 Z 15 + c DY 24 Z 24 + c DY 35 Z 35 + c DY 48 Z 48 )
DrW = Σ i = 5 K a i Δ Z i + ( c DR 2 - 1 Z 2 + c DR 2 - 2 Z 2 2 + c DR 2 - 3 Z 2 3 ) + ( c DR 3 - 1 Z 3 + c DR 3 - 2 Z 3 2 + c DR 3 - 3 Z 3 3 ) + ( c DR 4 Z 4 + c DR 8 Z 8 + c DR 15 Z 15 + c DR 24 Z 24 + c DR 35 Z 35 + c DR 48 Z 48 )
Above-mentioned system of equations can be expressed as: GX=R
Wherein:
G = Δ Z 1 x ( 1,1 ) Δ Z 2 x ( 1,1 ) . . . Δ Z Kx ( 1,1 ) Z 2 ( 1,1 ) Z 2 2 ( 1,1 ) . . . Z 48 ( 1,1 ) 0 0 . . . 0 0 0 . . . 0 Δ Z 1 x ( 1,2 ) Δ Z 2 x ( 1,2 ) . . . Δ Z Kx ( 1,2 ) Z 2 ( 1,2 ) Z 2 2 ( 1,2 ) . . . Z 48 ( 1,2 ) 0 0 . . . 0 0 0 . . . 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Δ Z 1 x ( M , N ) Δ Z 2 x ( M , N ) . . . Δ Z Kx ( M , N ) Z 2 ( M , N ) Z 2 2 ( M , N ) . . . Z 48 ( M , N ) 0 0 . . . 0 0 0 . . . 0 Δ Z 1 y ( 1,1 ) Δ Z 2 y ( 1,1 ) . . . Δ Z Ky ( 1,1 ) 0 0 . . . 0 Z 2 ( 1,1 ) Z 2 2 ( 1,1 ) . . . Z 48 ( 1,1 ) 0 0 . . . 0 Δ Z 1 y ( 1,2 ) Δ Z 2 y ( 1,2 ) . . . Δ Z Ky ( 1,2 ) 0 0 . . . 0 Z 2 ( 1,2 ) Z 2 2 ( 1,2 ) . . . Z 48 ( 1,2 ) 0 0 . . . 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Δ Z 1 y ( M , N ) Δ Z 2 y ( M , N ) . . . Δ Z Ky ( M , N ) 0 0 . . . 0 Z 2 ( M , N ) Z 2 2 ( M , N ) . . . Z 48 ( M , N ) 0 0 . . . 0 Δ Z 1 r ( 1,1 ) Δ Z 2 r ( 1,1 ) . . . Δ Z Kr ( 1,1 ) 0 0 . . . 0 0 0 . . . 0 Z 2 ( 1,1 ) Z 2 2 ( 1,1 ) . . . Z 48 ( 1,2 ) Δ Z 1 r ( 1,2 ) Δ Z 2 r ( 1,2 ) . . . Δ Z Kr ( 1,2 ) 0 0 . . . 0 0 0 0 0 Z 2 ( 1,2 ) Z 2 2 . . . Z 48 ( 1,2 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Δ Z 1 r ( M , N ) Δ Z 2 r ( M , N ) . . . Δ Z Kr ( M . N ) 0 0 . . . 0 0 0 0 0 Z 2 ( M , N ) Z 2 2 ( M , N ) . . . Z 48 ( M , N )
R = DxW ( 1,1 ) DxW ( 1,2 ) . . . DxW ( M , N ) DyW ( 1,1 ) DyW ( 1,2 ) . . . DyW ( M , N ) DrW ( 1,1 ) DrW ( 1,2 ) . . . DrW ( M , N )
X = a 5 a 6 . . . a K c DX 2 - 1 c DX 2 - 2 . . . c DX 48 c DY 2 - 1 c DY 2 - 2 . . . c DY 48 c DR 2 - 1 c DR 2 - 2 . . . c DR 48
Step 6: solve an equation and obtain X, obtains a then 5a k; Finally obtain tested surface shape
Embodiment
Utilize in embodiment method of the present invention to a radius-of-curvature be 36.7mm, numerical aperture is that the sphere of the mirror to be measured (3) of 0.7 detects, the step that the sphere of mirror to be measured (3) carries out rotating translation absolute sense is:
Step 1: utilize the sphere of Zygo GPI interferometer to mirror to be measured (3) to detect, wherein the optical wavelength of interferometer is 632.8nm, and peak valley (PV) value of surface testing precision is better than λ/10.One group of original graphic data of the sphere of the mirror to be measured (3) detected by interferometer:
W 1 = W r + Σ i = 5 K a i Z i ( x , y ) + W Omis = W r + Σ i = 5 K a i Z i ( x , y ) + ( c O 2 - 1 Z 2 + c O 2 - 2 Z 2 2 + c O 2 - 3 Z 2 3 ) + ( c O 3 - 1 Z 3 + c O 3 - 2 Z 3 2 + c O 3 - 3 Z 3 3 ) + ( c O 4 Z 4 + c O 8 Z 8 + c O 15 Z 15 + c O 24 Z 24 + c O 35 Z 35 + c O 48 Z 48 )
Wherein W rrepresent the face shape error of reference surface, W omisrepresent original type alignment error, a ifor the zernike coefficient of every, Z ifor the Ze Nike item of correspondence, K is the item number of Ze Nike matching.
W mis = ( c 2 - 1 Z 2 + c 2 - 2 Z 2 2 + c 2 - 3 Z 2 3 ) + ( c 3 - 1 Z 3 + c 3 - 2 Z 3 2 + c 3 - 3 Z 3 3 ) + ( c 4 Z 4 + c 8 Z 8 + c 15 Z 15 + c 24 Z 24 + c 35 Z 35 + c 48 Z 48 )
Wherein, c represents the coefficient of the Ze Nike item in alignment error item, such as c 2-3represent the cube coefficient of Section 2 zernike polynomial.
Step 2: the sphere prolonging x direction translation mirror to be measured (3), and measure one group of face graphic data with interferometer 1:
W 2 = W r + Σ i = 5 K a i Z i ( x + Δx , y ) + W Xmis = W r + Σ i = 5 K a i Z i ( x + Δx , y ) + ( c X 2 - 1 Z 2 + c X 2 - 2 Z 2 2 + c X 2 - 3 Z 2 3 ) + ( c X 3 - 1 Z 3 + c X 3 - 2 Z 3 2 + c X 3 - 3 Z 3 3 ) + ( c X 4 Z 4 + c X 8 Z 8 + c X 15 Z 15 + c X 24 Z 24 + c X 35 Z 35 + c X 48 Z 48 )
Wherein, W xmisrepresent the alignment error after prolonging the sphere of x direction translation mirror to be measured (3), c xrepresent the coefficient of the Ze Nike item prolonged after the sphere of x direction translation mirror to be measured (3) in alignment error item.
Step 3: prolong y direction, the i.e. sphere of vertical optical axis direction translation mirror to be measured (3), and measure one group of face graphic data with interferometer 1:
W 3 = W r + Σ i = 5 K a i Z i ( x , y + Δy ) + W Ymis = W r + Σ i = 5 K a i Z i ( x , y + Δy ) + ( c Y 2 - 1 Z 2 + c Y 2 - 2 Z 2 2 + c Y 2 - 3 Z 2 3 ) + ( c Y 3 - 1 Z 3 + c Y 3 - 2 Z 3 2 + c Y 3 - 3 Z 3 3 ) + ( c Y 4 Z 4 + c Y 8 Z 8 + c Y 15 Z 15 + c Y 24 Z 24 + c Y 35 Z 35 + c Y 48 Z 48 )
Wherein, W ymisrepresent the alignment error after prolonging the sphere of y direction translation mirror to be measured (3), c yrepresent the coefficient of the Ze Nike item prolonged after the sphere of y direction translation mirror to be measured (3) in alignment error item.
Step 4: take optical axis as rotation center, rotates the sphere of mirror to be measured (3), and measures one group of face graphic data with interferometer 1:
W 4 = W r + Σ i = 5 K a i Z i ( r , θ + Δθ ) + W Rmis = W r + Σ i = 5 K a i Z i ( r , θ + Δθ ) + ( c R 2 - 1 Z 2 + c R 2 - 2 Z 2 2 + c R 2 - 3 Z 2 3 ) + ( c R 3 - 1 Z 3 + c R 3 - 2 Z 3 2 + c R 3 - 3 Z 3 3 ) + ( c R 4 Z 4 + c R 8 Z 8 + c R 15 Z 15 + c R 24 Z 24 + c R 35 Z 35 + c R 48 Z 48 )
Wherein, θ is the anglec of rotation, W rmisrepresent the alignment error after prolonging optical axis rotates the sphere of mirror to be measured (3), c rrepresent and prolong the coefficient that optical axis rotates the Ze Nike item after the sphere of mirror to be measured (3) in alignment error item.
Step 5: in 4 measuring processes, have reference surface face graphic data in each measurement, the equation that the equation obtained in step 2,3,4 deducts in step 1 obtains:
DxW = Σ i = 5 K a i Δ Z ix + ( c DX 2 - 1 Z 2 + c DX 2 - 2 Z 2 2 + c DX 2 - 3 Z 2 3 ) + ( c DX 3 - 1 Z 3 + c DX 3 - 2 Z 3 2 + c DX 3 - 3 Z 3 3 ) + ( c DX 4 Z 4 + c DX 8 Z 8 + c DX 15 Z 15 + c DX 24 Z 24 + c DX 35 Z 35 + c DX 48 Z 48 )
DyW = Σ i = 5 K a i Δ Z iy + ( c DY 2 - 1 Z 2 + c DY 2 - 2 Z 2 2 + c DY 2 - 3 Z 2 3 ) + ( c DY 3 - 1 Z 3 + c DY 3 - 2 Z 3 2 + c DY 3 - 3 Z 3 3 ) + ( c DY 4 Z 4 + c DY 8 Z 8 + c DY 15 Z 15 + c DY 24 Z 24 + c DY 35 Z 35 + c DY 48 Z 48 )
DrW = Σ i = 5 K a i Δ Z i + ( c DR 2 - 1 Z 2 + c DR 2 - 2 Z 2 2 + c DR 2 - 3 Z 2 3 ) + ( c DR 3 - 1 Z 3 + c DR 3 - 2 Z 3 2 + c DR 3 - 3 Z 3 3 ) + ( c DR 4 Z 4 + c DR 8 Z 8 + c DR 15 Z 15 + c DR 24 Z 24 + c DR 35 Z 35 + c DR 48 Z 48 )
Above-mentioned system of equations can be expressed as: GX=R
Wherein:
G = Δ Z 1 x ( 1,1 ) Δ Z 2 x ( 1,1 ) . . . Δ Z Kx ( 1,1 ) Z 2 ( 1,1 ) Z 2 2 ( 1,1 ) . . . Z 48 ( 1,1 ) 0 0 . . . 0 0 0 . . . 0 Δ Z 1 x ( 1,2 ) Δ Z 2 x ( 1,2 ) . . . Δ Z Kx ( 1,2 ) Z 2 ( 1,2 ) Z 2 2 ( 1,2 ) . . . Z 48 ( 1,2 ) 0 0 . . . 0 0 0 . . . 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Δ Z 1 x ( M , N ) Δ Z 2 x ( M , N ) . . . Δ Z Kx ( M , N ) Z 2 ( M , N ) Z 2 2 ( M , N ) . . . Z 48 ( M , N ) 0 0 . . . 0 0 0 . . . 0 Δ Z 1 y ( 1,1 ) Δ Z 2 y ( 1,1 ) . . . Δ Z Ky ( 1,1 ) 0 0 . . . 0 Z 2 ( 1,1 ) Z 2 2 ( 1,1 ) . . . Z 48 ( 1,1 ) 0 0 . . . 0 Δ Z 1 y ( 1,2 ) Δ Z 2 y ( 1,2 ) . . . Δ Z Ky ( 1,2 ) 0 0 . . . 0 Z 2 ( 1,2 ) Z 2 2 ( 1,2 ) . . . Z 48 ( 1,2 ) 0 0 . . . 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Δ Z 1 y ( M , N ) Δ Z 2 y ( M , N ) . . . Δ Z Ky ( M , N ) 0 0 . . . 0 Z 2 ( M , N ) Z 2 2 ( M , N ) . . . Z 48 ( M , N ) 0 0 . . . 0 Δ Z 1 r ( 1,1 ) Δ Z 2 r ( 1,1 ) . . . Δ Z Kr ( 1,1 ) 0 0 . . . 0 0 0 . . . 0 Z 2 ( 1,1 ) Z 2 2 ( 1,1 ) . . . Z 48 ( 1,2 ) Δ Z 1 r ( 1,2 ) Δ Z 2 r ( 1,2 ) . . . Δ Z Kr ( 1,2 ) 0 0 . . . 0 0 0 0 0 Z 2 ( 1,2 ) Z 2 2 . . . Z 48 ( 1,2 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Δ Z 1 r ( M , N ) Δ Z 2 r ( M , N ) . . . Δ Z Kr ( M . N ) 0 0 . . . 0 0 0 0 0 Z 2 ( M , N ) Z 2 2 ( M , N ) . . . Z 48 ( M , N )
R = DxW ( 1,1 ) DxW ( 1,2 ) . . . DxW ( M , N ) DyW ( 1,1 ) DyW ( 1,2 ) . . . DyW ( M , N ) DrW ( 1,1 ) DrW ( 1,2 ) . . . DrW ( M , N )
X = a 5 a 6 . . . a K c DX 2 - 1 c DX 2 - 2 . . . c DX 48 c DY 2 - 1 c DY 2 - 2 . . . c DY 48 c DR 2 - 1 c DR 2 - 2 . . . c DR 48
Step 6: solving an equation obtains X and then obtain a 5a k; Finally obtain tested surface shape result as shown in Figure 6.
Process according to the face graphic data of above-mentioned steps to the sphere of mirror to be measured (3), calculating its PV value for 35.3975nm, RMS value is 3.6809nm, has higher precision.

Claims (1)

1. spherical surface shape rotates a translation absolute detection method, prolongs optical axis and puts interferometer (1), reference mirror successively
(2) and mirror to be measured (3), it is characterized in that, step is as follows:
Definition alignment error W mis
W mis = ( c 2 - 1 Z 2 + c 2 - 2 Z 2 2 + c 2 - 3 Z 2 3 ) + ( c 3 - 1 Z 3 + c 3 - 2 Z 3 2 + c 3 - 3 Z 3 3 ) + ( c 4 Z 4 + c 8 Z 8 + c 15 Z 15 + c 24 Z 24 + c 35 Z 35 + c 48 Z 48 )
Wherein, c represents the coefficient of the Ze Nike item in alignment error item, Z ifor the Ze Nike item of correspondence;
Step 1: utilize interferometer (1) to measure and obtain one group of original graphic data W that numerical aperture is the sphere of the mirror to be measured (3) of NA 1:
W 1 = W r + Σ i = 5 K a i Z i ( x , y ) + W Omis = W r + Σ i = 5 K a i Z i ( x , y ) + ( c O 2 - 1 Z 2 + c O 2 - 2 Z 2 2 + c O 2 - 3 Z 2 3 ) + ( c O 3 - 1 Z 3 + c O 3 - 2 Z 3 2 + c O 3 - 3 Z 3 3 ) + ( c O 4 Z 4 + c O 8 Z 8 + c O 15 Z 15 + c O 24 Z 24 + c O 35 Z 35 + c O 48 Z 48 )
Wherein W rrepresent the face shape error of reference surface, W omisrepresent original type alignment error, a ifor the zernike coefficient of every, Z ifor the Ze Nike item of correspondence, K is the item number of Ze Nike matching;
Step 2: the sphere prolonging x direction translation mirror to be measured (3), and record face graphic data W with interferometer (1) 2:
W 2 = W r + Σ i = 5 K a i Z i ( x + Δx , y ) + W Xmis = W r + Σ i = 5 K a i Z i ( x + Δx , y ) + ( c X 2 - 1 Z 2 + c X 2 - 2 Z 2 2 + c X 2 - 3 Z 2 3 ) + ( c X 3 - 1 Z 3 + c X 3 - 2 Z 3 2 + c X 3 - 3 Z 3 3 ) + ( c X 4 Z 4 + c X 8 Z 8 + c X 15 Z 15 + c X 24 Z 24 + c X 35 Z 35 + c X 48 Z 48 )
Wherein, W xmisrepresent the alignment error after prolonging the sphere of x direction translation mirror to be measured (3), c xrepresent the coefficient of the Ze Nike item prolonged after the sphere of x direction translation mirror to be measured (3) in alignment error item;
Step 3: prolong y direction, the i.e. sphere of vertical optical axis direction translation mirror to be measured (3), and with interferometer (1) measuring surface graphic data W 3:
W 3 = W r + Σ i = 5 K a i Z i ( x , y + Δy ) + W Ymis = W r + Σ i = 5 K a i Z i ( x , y + Δy ) + ( c Y 2 - 1 Z 2 + c Y 2 - 2 Z 2 2 + c Y 2 - 3 Z 2 3 ) + ( c Y 3 - 1 Z 3 + c Y 3 - 2 Z 3 2 + c Y 3 - 3 Z 3 3 ) + ( c Y 4 Z 4 + c Y 8 Z 8 + c Y 15 Z 15 + c Y 24 Z 24 + c Y 35 Z 35 + c Y 48 Z 48 )
Wherein, W ymisrepresent the alignment error after prolonging the sphere of y direction translation mirror to be measured (3), c yrepresent the coefficient of the Ze Nike item prolonged after the sphere of y direction translation mirror to be measured (3) in alignment error item;
Step 4: take optical axis as rotation center, rotates the sphere of mirror to be measured (3), and records face graphic data W with interferometer (1) 4:
W 4 = W r + Σ i = 5 K a i Z i ( r , θ + Δθ ) + W Rmis = W r + Σ i = 5 K a i Z i ( r , θ + Δθ ) + ( c R 2 - 1 Z 2 + c R 2 - 2 Z 2 2 + c R 2 - 3 Z 2 3 ) + ( c R 3 - 1 Z 3 + c R 3 - 2 Z 3 2 + c R 3 - 3 Z 3 3 ) + ( c R 4 Z 4 + c R 8 Z 8 + c R 15 Z 15 + c R 24 Z 24 + c R 35 Z 35 + c R 48 Z 48 )
Wherein, θ is the anglec of rotation, W rmisrepresent the alignment error after prolonging optical axis rotates the sphere of mirror to be measured (3), c rrepresent and prolong the coefficient that optical axis rotates the Ze Nike item after the sphere of mirror to be measured (3) in alignment error item;
Step 5: in above-mentioned four steps, has often walked reference surface face graphic data W r, use W 2-W 1, W 3-W 1, W 4-W 1:
DxW = Σ i = 5 K a i Δ Z ix + ( c DX 2 - 1 Z 2 + c DX 2 - 2 Z 2 2 + c DX 2 - 3 Z 2 3 ) + ( c DX 3 - 1 Z 3 + c DX 3 - 2 Z 3 2 + c DX 3 - 3 Z 3 3 ) + ( c DX 4 Z 4 + c DX 8 Z 8 + c DX 15 Z 15 + c DX 24 Z 24 + c DX 35 Z 35 + c DX 48 Z 48 )
DyW = Σ i = 5 K a i Δ Z iy + ( c DY 2 - 1 Z 2 + c DY 2 - 2 Z 2 2 + c DY 2 - 3 Z 2 3 ) + ( c DY 3 - 1 Z 3 + c DY 3 - 2 Z 3 2 + c DY 3 - 3 Z 3 3 ) + ( c DY 4 Z 4 + c DY 8 Z 8 + c DY 15 Z 15 + c DY 24 Z 24 + c DY 35 Z 35 + c DY 48 Z 48 )
DrW = Σ i = 5 K a i Δ Z i + ( c DR 2 - 1 Z 2 + c DR 2 - 2 Z 2 2 + c DR 2 - 3 Z 2 3 ) + ( c DR 3 - 1 Z 3 + c DR 3 - 2 Z 3 2 + c DR 3 - 3 Z 3 3 ) + ( c DR 4 Z 4 + c DR 8 Z 8 + c DR 15 Z 15 + c DR 24 Z 24 + c DR 35 Z 35 + c DR 48 Z 48 )
Above-mentioned system of equations can be expressed as: GX=R
Wherein:
G = Δ Z 1 x ( 1,1 ) Δ Z 2 x ( 1,1 ) . . . Δ Z Kx ( 1,1 ) Z 2 ( 1,1 ) Z 2 2 ( 1,1 ) . . . Z 48 ( 1,1 ) 0 0 . . . 0 0 0 . . . 0 Δ Z 1 x ( 1,2 ) Δ Z 2 x ( 1,2 ) . . . Δ Z Kx ( 1,2 ) Z 2 ( 1,2 ) Z 2 2 ( 1,2 ) . . . Z 48 ( 1,2 ) 0 0 . . . 0 0 0 . . . 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Δ Z 1 x ( M , N ) Δ Z 2 x ( M , N ) . . . Δ Z Kx ( M , N ) Z 2 ( M , N ) Z 2 2 ( M , N ) . . . Z 48 ( M , N ) 0 0 . . . 0 0 0 . . . 0 Δ Z 1 y ( 1,1 ) Δ Z 2 y ( 1,1 ) . . . Δ Z Ky ( 1,1 ) 0 0 . . . 0 Z 2 ( 1,1 ) Z 2 2 ( 1,1 ) . . . Z 48 ( 1,1 ) 0 0 . . . 0 Δ Z 1 y ( 1,2 ) Δ Z 2 y ( 1,2 ) . . . Δ Z Ky ( 1,2 ) 0 0 . . . 0 Z 2 ( 1,2 ) Z 2 2 ( 1,2 ) . . . Z 48 ( 1,2 ) 0 0 . . . 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Δ Z 1 y ( M , N ) Δ Z 2 y ( M , N ) . . . Δ Z Ky ( M , N ) 0 0 . . . 0 Z 2 ( M , N ) Z 2 2 ( M , N ) . . . Z 48 ( M , N ) 0 0 . . . 0 Δ Z 1 r ( 1,1 ) Δ Z 2 r ( 1,1 ) . . . Δ Z Kr ( 1,1 ) 0 0 . . . 0 0 0 . . . 0 Z 2 ( 1,1 ) Z 2 2 ( 1,1 ) . . . Z 48 ( 1,2 ) Δ Z 1 r ( 1,2 ) Δ Z 2 r ( 1,2 ) . . . Δ Z Kr ( 1,2 ) 0 0 . . . 0 0 0 0 0 Z 2 ( 1,2 ) Z 2 2 . . . Z 48 ( 1,2 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Δ Z 1 r ( M , N ) Δ Z 2 r ( M , N ) . . . Δ Z Kr ( M . N ) 0 0 . . . 0 0 0 0 0 Z 2 ( M , N ) Z 2 2 ( M , N ) . . . Z 48 ( M , N )
R = DxW ( 1,1 ) DxW ( 1,2 ) . . . DxW ( M , N ) DyW ( 1,1 ) DyW ( 1,2 ) . . . DyW ( M , N ) DrW ( 1,1 ) DrW ( 1,2 ) . . . DrW ( M , N )
X = a 5 a 6 . . . a K c DX 2 - 1 c DX 2 - 2 . . . c DX 48 c DY 2 - 1 c DY 2 - 2 . . . c DY 48 c DR 2 - 1 c DR 2 - 2 . . . c DR 48
Step 6: solve an equation and obtain X, obtains a then 5a k; Finally obtain tested surface shape
CN201410089712.5A 2014-03-12 2014-03-12 Spherical surface shape rotation and translation absolute detection method Pending CN104913730A (en)

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CN113804122A (en) * 2021-09-06 2021-12-17 中国科学院光电技术研究所 Method for detecting plane mirror shape containing defocusing aberration by using translation and rotation absolute detection method
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