CN104976962B - Method for measuring plane mirror absolute surface shape based on conjugate difference method - Google Patents
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Abstract
The invention discloses a method for measuring plane mirror absolute surface shape based on a conjugate difference method. The method comprises the following steps: a plane mirror to be measured and a standard plane mirror forming interference images on a CCD of an interferometer respectively, judging the sizes of light spots of the plane mirror to be measured and the standard plane mirror formed on the CCD of the interferometer and enabling the light spot of the standard plane mirror to be larger than the light spot of the plane mirror to be measured; determining translation amount delta of the plane mirror to be measured corresponding to one pixel in the CCD of the interferometer, delta＞0; defining the direction of optical axis of the interferometer as the z axis and carrying four-step test in the positive and negative directions of the x axis and y axis respectively and recording wavefront data phi (x+delta, y), phi (x-delta, y), phi (x, y+delta) and phi (x, y-delta) respectively; obtaining surface shape gradient of the plane mirror to be measured according to the measured wavefront data; and recovering the surface shape w of the plane mirror to be measured according to the surface shape gradient of the plane mirror to be measured by utilizing a wave surface recovering method. The method improves precision of differential approximation and prevents coupling between step-by-step tests, thereby improving stability of the test; and the method can also be used for measuring the absolute surface shape of a cylindrical mirror, a conical mirror and a spherical mirror.
Description
Technical field
The invention belongs to level crossing absolute sense technical field, particularly a kind of exhausted based on conjugation calculus of finite differences measurement plane mirror
The method of opposite shape.
Background technology
Mainly there are three planes mutually to examine method, liquid level basic taper method and calculus of finite differences i.e. puppet the research of level crossing absolute sense at present to cut
Cutting method.Three traditional planes mutually examine method and can not obtain the two-dimensional surface shape of the whole plane of tested surface, can only obtain the situation of a line,
Method after improvement can obtain the face shape situation of entire surface, but test process is all very complicated；Liquid level basic taper method adopts liquid
Body optical flat is used as index plane, but liquid level benchmark makes difficult, very high and not easily shifted to environmental condition requirement, in test result
Systematic error also cannot be eliminated；There is coupling each other with orthogonal two direction translation these three positions of position due to initial position in calculus of finite differences
Conjunction relation, needs to maintain the factor such as environment stable to guarantee that static error is constant in three tests, but external environment etc. because
Element is difficult to control to, and is difficult to maintain its stability constant so as to be difficult to ensure that static error, have impact on the accuracy of detection of calculus of finite differences.
The content of the invention
It is an object of the invention to provide a kind of certainty of measurement it is high, easy to operate based on conjugation calculus of finite differences measurement plane mirror
The method of absolute face shape.
The technical solution for realizing the object of the invention is：It is a kind of based on the conjugation absolute face shape of calculus of finite differences measurement plane mirror
Method, comprises the following steps：
1st step, level crossing to be measured forms interference image, criterion plane with standard flat mirror on the CCD of interferometer
Mirror with level crossing to be measured on the CCD of interferometer into hot spot size, make standard flat mirror hot spot be more than level crossing to be measured
Hot spot；
2nd step, determines level crossing translational movement δ to be measured, δ corresponding to 1 pixel in the CCD of interferometer>0；
3rd step, the optical axis direction for making interferometer is z-axis, and in x-axis, the positive negative direction of y-axis four pacing examinations are carried out, and is remembered respectively
(x+ δ, y), (x- δ, y), Φ (x, y+ δ), Φ (x, y- δ), size of data is all N × N to Φ, and N is positive integer for lower wave front data Φ；
4th step, according to the wave front data Φ for measuring, (x+ δ, y), (x- δ y), Φ (x, y+ δ), Φ (x, y- δ), are tried to achieve Φ
Face shape gradient dx (x, y) of level crossing to be measured, dy (x, y)；
5th step, using wave front recovering method, face shape gradient dx (x, y), dy (x, y) according to level crossing to be measured restores to treat
Survey face shape w of level crossing.
Compared with prior art, its remarkable advantage is the present invention：（1）It is capable of achieving by interferometer, standard mirror, mirror to be measured
Absolute sense to flat mirror shape to be measured, it is simple structure, easy to operate；（2）Initial position can be omitted using conjugation difference
Test process, improves the precision that differential is approached；（3）Four step test process par wise irrelevances, i.e. two orthogonal direction test process phases
Mutually independently, it is independent of each other, further simplify experimental implementation, improves testing accuracy；（4）The method can also measure cylinder
Mirror, conic mirror, the absolute face shape of spherical mirror.
Description of the drawings
Fig. 1 is method hardware architecture diagram of the present invention based on the absolute face shape of conjugation calculus of finite differences measurement plane mirror.
Fig. 2 is four pacings examination process schematic of the present invention based on the absolute face shape of conjugation calculus of finite differences measurement plane mirror.
Specific embodiment
Below in conjunction with the accompanying drawings and specific embodiment is described in further detail to the present invention.
With reference to Fig. 1~2, method of the present invention based on the absolute face shape of conjugation calculus of finite differences measurement plane mirror, comprise the following steps：
1st step, level crossing to be measured forms interference image, criterion plane with standard flat mirror on the CCD of interferometer
Mirror with level crossing to be measured on the CCD of interferometer into hot spot size, make standard flat mirror hot spot be more than level crossing to be measured
Hot spot；
As shown in figure 1, the interferometer is Fizeau interferometers, the inclination between standard flat mirror and level crossing to be measured is less than
0.02 times of interferometer optical maser wavelength, because it is first order in wave aberration to incline item, it is just constant term to have asked after gradient, is used
Wave front recovering method cannot restore this, so to allow the very little as far as possible.If the hot spot of level crossing to be measured is more than standard
The hot spot of level crossing, then the square diaphragm of making one is placed on level crossing to be measured makes level crossing center to be measured with square diaphragm
Center superposition, makes the spot size of standard flat mirror more than the spot size of level crossing to be measured.
2nd step, determines level crossing translational movement δ to be measured, δ corresponding to 1 pixel in the CCD of interferometer>0；
Adoption rate method, level crossing to be measured translation is individual with the movement of pixel in the CCD of corresponding interferometer apart from length
Number makees ratio, is averaged by repeatedly measurement and obtains the translational movement δ of the level crossing to be measured corresponding to 1 pixel.
3rd step, the optical axis direction for making interferometer is z-axis, and in x-axis, the positive negative direction of y-axis four pacing examinations are carried out, and is remembered respectively
(x+ δ, y), (x- δ, y), Φ (x, y+ δ), Φ (x, y- δ), size of data is all N × N to Φ, and N is positive integer for lower wave front data Φ；
With reference to Fig. 2, four pacings examination detailed process is as follows：
Level crossing to be measured to x-axis negative direction move 1 pixel, write down wave front data Φ (x- δ, y)；Level crossing to be measured is to x
Axle positive direction move 2 pixels, write down wave front data Φ (x+ δ, y)；Level crossing to be measured to x-axis negative direction moves 1 pixel, returns
To initial position；Level crossing to be measured moves 1 pixel to y-axis positive direction again, writes down wave front data Φ (x, y+ δ)；It is last to be measured
Level crossing to y-axis negative direction moves 2 pixels, writes down wave front data Φ (x, y- δ).
4th step, according to the wave front data Φ for measuring, (x+ δ, y), (x- δ y), Φ (x, y+ δ), Φ (x, y- δ), are tried to achieve Φ
Face shape gradient dx (x, y) of level crossing to be measured, dy (x, y), formula is as follows：
5th step, using wave front recovering method, face shape gradient dx (x, y), dy (x, y) according to level crossing to be measured restores to treat
Survey face shape w of level crossing.Described wave front recovering method be fourier transform method, path integration method or least square method, each method
It is specific as follows：
（1）Fourier transform method
Frequency spectrum Dx (u, v), Dy (u, v) are respectively obtained as Fourier transformation by dx (x, y), dy (x, y), face shape frequency is thus sought
SpectrumOrFace is obtained as inverse Fourier transform to W
Shape w；
（2）Path integration method
Any point is used as starting point P on the recovery face of taking0(x0,y0), make the surface shape value be w (x0,y0)=0, then point P1(x0+△
x,y0) surface shape value bePoint P2(x0,y0+△
Y) surface shape value isBy that analogy, obtain
Entire surface shape w, wherein △ x=n1δ, △y=n2δ, n1、n2For integer；
（3）Least square method
Least square method is divided into two kinds of Zernike fitting of a polynomials and Hudgin wavefront sensings：
A, Zernike fitting of a polynomial
ByObtain Zernike coefficient Ck, its
Middle n is used Zernike multinomial item numbers, Zkx(x,y)、ZkY (x, y) is respectively Zernike multinomial Zk(x, y) is to certainly
The derivative of variable x, y, then the face shape of level crossing to be measured be
B, Hudgin wavefront sensing
A[q+(p-1)(N-1),q+(p-1)N]=-1
A [q+ (p-1) (N-1), 1+q+ (p-1) N]=1 (p=1 ..., N q=1 ..., N-1）
A[r+N(N-1),r]=-1
A [r+N (N-1), r+N]=- 1 (r=1 ..., N (N-1）)
Then w=(ATA)-1ATS, wherein S are the vectors of 2N × (N-1) the individual data comprising x-axis and y-axis direction face shape gradient,
A is 2N × (N-1) row N of Hudgin wavefront sensings2The matrix of row.
Embodiment 1
Below by taking Fizeau interferometers as an example, according to the inventive method the absolute face shape of level crossing to be measured is measured.
First, measurement apparatus are as shown in figure 1, adjustment standard lens and frame knob：
（1）Open the application program of Fizeau interferometers；
（2）Standard flat mirror is installed：Angle is visited by 2 on camera lens frame to be put in the groove of interferometer bayonet socket support, dextrorotation
Transposable lenses, then tighten fixation；
（3）Adjustment standard flat mirror：" adjustment/test " button of remote control is pressed, display screen is switched to " adjustment "
, there is crosshair image in state in plane.Interferometer bayonet socket support knob is adjusted, until the bright spot on screen is in crosshair
It is middle；
（4）Tested level crossing is placed in five dimension adjustment frames, adjustment frame knob is adjusted, until the tested level crossing on screen
Bright spot also in the middle of crosshair.
2nd, criterion level crossing and level crossing to be measured into hot spot size, if the hot spot of level crossing to be measured is more than mark
The hot spot of directrix plane mirror, then making a square diaphragm and being placed on level crossing to be measured makes level crossing center to be measured and square light
Late center superposition, so as to reach the requirement of the spot size more than the spot size of level crossing to be measured of standard mirror.
3rd, it is z-axis direction to take optical axis direction, then x-axis and y-axis direction also determine.Simultaneously we will determine experiment
Used in interferometer 1 pixel corresponding to part to be measured translational movement, with rule of three by the length of a segment distance in experiment
Make ratio with its pixel size, averaged by repeatedly measurement and obtain the translational movement δ of the corresponding part to be measured of 1 pixel.
4th, standard mirror is first mixed up sufficiently small to reach inclination item with the position of mirror to be measured, less than 0.02 wavelength, experiment
The optical maser wavelength of Fizeau interferometers is 632.8nm, as shown in Fig. 2 moving 1 pixel to x-axis negative direction, writes down wave front data
Φ(x-δ,y)；To x-axis positive direction move 2 pixels, write down wave front data Φ (x+ δ, y)；1 picture is moved to x-axis negative direction
Element, returns to initial position；Again 1 pixel is moved to y-axis positive direction, write down wave front data Φ (x, y+ δ)；Most backward y-axis losing side
To mobile 2 pixels, wave front data Φ (x, y- δ) is write down.Wherein size of data is all N × N, i.e., arrange interferometer in an experiment
MetroPro softwares in Mask sizes be N × N, N is positive integer.
The test data measured in experiment is read in dat2txt.exe softwares, " Enter " key is pressed, its test is obtained
Txt file corresponding to data：fringe.txt、mask.txt、wave.txt.Wave files therein are exactly that we will be used for
Do the data of wave front recovering.
5th, according to measured phase place：Φ(x,y)=φTreat level transit(x,y)-ΨWith reference to flat mirror(x, y), so as to through x-axis and y
After axial translation, similar four phase equation is obtained：
Φ(x-δ,y)=φTreat level transit(x-δ,y)-ΨWith reference to flat mirror(x,y)
Φ(x+δ,y)=φTreat level transit(x+δ,y)-ΨWith reference to flat mirror(x,y)
Φ(x,y+δ)=φTreat level transit(x,y+δ)-ΨWith reference to flat mirror(x,y)
Φ(x,y-δ)=φTreat level transit(x,y-δ)-ΨWith reference to flat mirror(x,y)
Two equatioies of conjugation are subtracted each other, is obtained：
Φ(x+δ,y)-Φ(x-δ,y)=φTreat level transit(x+δ,y)-φTreat level transit(x-δ,y)
Φ(x,y+δ)-Φ(x,y-δ)=φTreat level transit(x,y+δ)-φTreat level transit(x,y-δ)
So as to seek the face shape gradient of level crossing to be measured：
6th, using wave front recovering method, face shape gradient dx (x, y), dy (x, y) according to level crossing to be measured is restored to be measured flat
Face shape w of face mirror.Described wave front recovering method is fourier transform method, path integration method or least square method, and each method is concrete
It is as follows：
（1）Fourier transform method
Frequency spectrum Dx (u, v), Dy (u, v) are respectively obtained as Fourier transformation by dx (x, y), dy (x, y), face shape frequency is thus sought
SpectrumOrFace shape w is obtained as inverse Fourier transform to W；
（2）Path integration method
Any point is used as starting point P on the recovery face of taking0(x0,y0), make the surface shape value be w (x0,y0)=0, then point P1(x0+△
x,y0) surface shape value bePoint P2(x0,y0+△
Y) surface shape value isBy that analogy, obtain
Entire surface shape w, wherein △ x=n1δ, △ y=n2δ, n1、n2For integer；
（3）Least square method
Least square method is divided into two kinds of Zernike fitting of a polynomials and Hudgin wavefront sensings：
A, Zernike fitting of a polynomial
ByObtain Zernike coefficient Ck, its
Middle n is used Zernike multinomial item numbers, Zkx(x,y)、ZkY (x, y) is respectively Zernike multinomial Zk(x, y) is to certainly
The derivative of variable x, y, then the face shape of level crossing to be measured be
B, Hudgin wavefront sensing
A[q+(p-1)(N-1),q+(p-1)N]=-1
A [q+ (p-1) (N-1), 1+q+ (p-1) N]=1 (p=1 ..., N q=1 ..., N-1）
A[r+N(N-1),r]=-1
A [r+N (N-1), r+N]=- 1 (r=1 ..., N (N-1）)
Then w=(ATA)-1ATS, wherein S are the vectors of 2N × (N-1) the individual data comprising x-axis and y-axis direction face shape gradient,
A is 2N × (N-1) row N of Hudgin wavefront sensings2The matrix of row.
In sum, the present invention is the method based on the absolute face shape of conjugation calculus of finite differences measurement plane mirror, and conjugation difference is not only
The precision that differential is approached can be improved, but also be avoided that the coupling between test step by step, so as to reduce environmental factor impact,
The stability of test is improved, the method can also be applied to measurement cylindrical mirror, conic mirror, the situation of spherical mirror surface shape.
Claims (1)
1. a kind of method based on the conjugation absolute face shape of calculus of finite differences measurement plane mirror, it is characterised in that comprise the following steps：
1st step, level crossing to be measured and standard flat mirror form interference image on the CCD of interferometer, criterion level crossing with
Level crossing to be measured on the CCD of interferometer into hot spot size, make the hot spot of standard flat mirror more than the light of level crossing to be measured
Spot；
2nd step, determines level crossing translational movement δ to be measured, δ ＞ 0 corresponding to 1 pixel in the CCD of interferometer；
3rd step, the optical axis direction for making interferometer is z-axis, and in x-axis, the positive negative direction of y-axis four pacing examinations are carried out, and ripple is write down respectively
(x+ δ, y), (x- δ, y), Φ (x, y+ δ), Φ (x, y- δ), size of data is all N × N to Φ, and N is positive integer for front data Φ；
4th step, according to the wave front data Φ for measuring, (x+ δ, y), (x- δ y), Φ (x, y+ δ), Φ (x, y- δ), are tried to achieve to be measured Φ
Face shape gradient dx (x, y) of level crossing, dy (x, y)；
5th step, using wave front recovering method, face shape gradient dx (x, y), dy (x, y) according to level crossing to be measured is restored to be measured flat
Face shape w of face mirror；
Interferometer described in above-mentioned 1st step is Fizeau interferometers, and the inclination between standard flat mirror and level crossing to be measured is less than interference
0.02 times of instrument optical maser wavelength；
Criterion level crossing described in above-mentioned 1st step with level crossing to be measured on interferometer CCD into hot spot size, make mark
The hot spot of directrix plane mirror is more than the hot spot of level crossing to be measured, specially：If the hot spot of level crossing to be measured is more than standard flat mirror
Hot spot, then the square diaphragm of making one is placed on level crossing to be measured makes level crossing center to be measured with square diaphragm center weight
Close, make the spot size of standard flat mirror more than the spot size of level crossing to be measured；
The level crossing translational movement δ to be measured corresponding to 1 pixel in the CCD of interferometer is determined described in above-mentioned 2nd step, specially：
Adoption rate method, ratio is made by what level crossing to be measured was translated apart from length with the moving number of pixel in the CCD of corresponding interferometer,
Averaged by repeatedly measurement and obtain the translational movement δ of the level crossing to be measured corresponding to 1 pixel；
Carry out four pacing examinations in x-axis, the positive negative direction of y-axis described in above-mentioned 3rd step, write down respectively wave front data Φ (x+ δ, y),
Φ (x- δ, y), Φ (x, y+ δ), Φ (x, y- δ), specially：Level crossing to be measured to x-axis negative direction moves 1 pixel, writes down ripple
Front data Φ (x- δ, y)；Level crossing to be measured to x-axis positive direction move 2 pixels, write down wave front data Φ (x+ δ, y)；It is to be measured flat
Face mirror to x-axis negative direction moves 1 pixel, returns to initial position；Level crossing to be measured moves 1 pixel, note to y-axis positive direction again
Lower wave front data Φ (x, y+ δ)；Last level crossing to be measured moves 2 pixels to y-axis negative direction, writes down wave front data Φ (x, y-
δ)；
Described in above-mentioned 4th step according to measure wave front data Φ (x+ δ, y), Φ (x- δ, y), Φ (x, y+ δ), Φ (x, y- δ),
Face shape gradient dx (x, y), the dy (x, y) of level crossing to be measured are tried to achieve, formula is as follows：
Wave front recovering method described in above-mentioned 5th step is fourier transform method, path integration method or least square method, and each method has
Body is as follows：
(1) fourier transform method
Frequency spectrum Dx (u, v), Dy (u, v) are respectively obtained as Fourier transformation by dx (x, y), dy (x, y), face shape frequency spectrum is thus soughtOrFace shape w is obtained as inverse Fourier transform to W；
(2) path integration method
Any point is used as starting point P on the recovery face of taking0(x0,y0), make the surface shape value be w (x0,y0)=0, then point P1(x0+Δx,
y0) surface shape value bePoint P2(x0,y0+Δy)
Surface shape value beBy that analogy, obtain whole
Face shape w, wherein Δ x=n1δ, Δ y=n2δ, n1、n2For integer；
(3) least square method
Least square method is divided into two kinds of Zernike fitting of a polynomials and Hudgin wavefront sensings：
A, Zernike fitting of a polynomial
ByObtain Zernike coefficient Ck, wherein n
For the Zernike multinomial item numbers for being used, Zkx(x,y)、ZkY (x, y) is respectively Zernike multinomial Zk(x, y) is to from change
The derivative of x, y is measured, then the face shape of level crossing to be measured is
B, Hudgin wavefront sensing
A [q+ (p-1) (N-1), q+ (p-1) N]=- 1
A [q+ (p-1) (N-1), 1+q+ (p-1) N]=1 (p=1 ..., N q=1 ..., N-1)
A [r+N (N-1), r]=- 1
A [r+N (N-1), r+N]=- 1 (r=1 ..., N (N-1))
Then w=(ATA)-1ATS, wherein S are the vectors of 2N × (N-1) the individual data comprising x-axis and y-axis direction face shape gradient, and A is
The 2N of Hudgin wavefront sensings × (N-1) row N2The matrix of row.
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| CN109458944A (en) * | 2018-12-17 | 2019-03-12 | 南京理工大学 | The absolute verifying attachment of plane and its detection method based on synchronous conjugation differential interferometry |
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