CN107941165A - Local sampling face shape restoration methods based on influence matrix Ritchey-Common test - Google Patents

Local sampling face shape restoration methods based on influence matrix Ritchey-Common test Download PDF

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CN107941165A
CN107941165A CN201711096670.8A CN201711096670A CN107941165A CN 107941165 A CN107941165 A CN 107941165A CN 201711096670 A CN201711096670 A CN 201711096670A CN 107941165 A CN107941165 A CN 107941165A
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mrow
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plane mirror
influence matrix
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李金鹏
林冬冬
胡明勇
郑锋华
朱庆生
毕勇
李季
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Nanjing Astronomical Instruments Co Ltd
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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
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02055—Reduction or prevention of errors; Testing; Calibration

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  • General Physics & Mathematics (AREA)
  • Testing Of Optical Devices Or Fibers (AREA)

Abstract

The invention discloses a kind of local sampling face shape restoration methods based on influence matrix Ritchey-Common test, the principle first with interferometer according to influence matrix Ritchey-Common test, obtains two width ellipse compression pattern under different auspicious strange angles.It is unit by pixel, to the corresponding points in two width ellipse patterns, two groups of influence matrix equations is established according to the tested actual incidence angle size of plane mirror respective point of its correspondence, auspicious strange angle is used without approximation.Two groups of influence matrix equations are combined, are solved to obtain the point Zernike coefficients with least square method, so as to recover this face graphic data.The procedure ergodic is entirely detected plane mirror, above-mentioned processing is performed to each point for being detected plane mirror, then each point face graphic data result is integrated, obtains the face shape after tested plane mirror recovers.

Description

Local sampling face shape restoration methods based on influence matrix rayleigh-type waves
Technical field
The invention belongs to field of optical detection, and in particular to the technical field examined to heavy-calibre planar minute surface shape.
Background technology
Ritchey-Common method is a kind of method that large mirror face shape is examined using standard sphere, can realization osculum path interferometer Instrument measures the surface figure accuracy of large plane, effectively reduces testing cost, there is highly important meaning in field of optical detection Justice.A kind of Patent No. 200910195165.8, entitled device for testing and integrating large-caliber plane mirror by Ritchey-Common test, discloses one Kind examines the device of large plane.
Influence matrix method is the common face shape restoration methods of rayleigh-type waves.Existing tradition influence matrix Rui Qi-health In awns method, derivation has used approximate processing, in tan θ/2F#(θ is auspicious strange angle, F under conditions of≤1#It is the F of divergent beams Number), interferometer is sent the light beam incidence angle that difference is formed on tested plane mirror, is approximately auspicious strange angle θ to handle.It is actual During, since the light beam that interferometer is sent is by being incided in the form of diverging light on tested plane mirror after camera lens, so The incidence angle size of every bit and unequal on tested plane mirror；Due to examining scene and the limitation of tested plane aperture of mirror, differ Surely preferably meet tan θ/2F#≤ 1 approximate condition, can so recover to bring error to influence matrix normal plane shape.For existing The above-mentioned deficiency of technology, the present invention proposes rayleigh-type waves local sampling face shape restoration methods, because individually being built to every bit Vertical influence matrix, effectively reduces traditional influence matrix method difference error caused by incident angle difference.
The content of the invention
The technical problem to be solved in the present invention is solve in the prior art influence matrix rayleigh-type waves due to approximation at Manage the error produced；The invention discloses one kind to be based on influence matrix rayleigh-type waves method, and local sampling is individually built by point Respective influence matrix is found, recovering every bit face shape, comprehensive each point result obtains flat mirror shape again.
Illustrate the principle and device of existing traditional influence matrix rayleigh-type waves first, as shown in Figure 1, system by Interferometer, tested plane mirror, standard spherical mirror and chucking device composition, wherein the bore of standard spherical mirror is slightly larger than plane mirror. Interferometer focus is located at the center of curvature of the standard spherical mirror after being detected plane mirror reflection, and interferometer sends light beam through tested plane Mirror reflexes to director sphere up to standard, and plane to be measured is returned through standard spheric reflection, finally returns to interferometer focal point and joins with interferometer Examine corrugated and form interference.It is mapped to since light beam is oblique in plane to be measured, so the hot spot formed on pupil plane is oval. Wave-front phase can be launched into various aberrations and have good mathematical characteristic, Ritchey-Common test one by Zernike multinomials As described and fit Plane face shape error using Zernike multinomials.It is real according to caused by the face shape error of tested plane mirror The optical path difference of border wave surface and preferable wave surface, establishes tested influence function between plane surface shape error and system wave aberration, Obtain influence matrix equation：AS=W, A are influence matrix, and S is tested flat mirror shape error coefficient matrix, and W is system ripple picture Poor coefficient matrix.Change auspicious strange angle size, second group of influence matrix equation is obtained further according to rayleigh-type waves principle, by two Prescription journey combination is solved with least square method, obtains every Zernike coefficients of tested plane mirror face shape error, and then be fitted To tested flat mirror shape.
It is approximate in derivation that technical solution of the present invention emphasis corrects existing traditional influence matrix rayleigh-type waves Handle the error produced.(θ is auspicious under conditions of tan θ/2F#≤1 in traditional influence matrix rayleigh-type waves calculating process Strange angle, F# are the F numbers of divergent beams), interferometer is sent the light beam incidence angle that difference is formed on tested plane mirror, it is approximate Handled for auspicious strange angle θ.In real process, since the light beam that interferometer is sent is by being the incidence in the form of diverging light after camera lens Onto tested plane mirror, so the incidence angle size of every bit and unequal on tested plane mirror；Due to examining scene and being detected Plane aperture of mirror limits, and differs and surely preferably meets the approximate condition of tan θ/2F#≤1, can so give influence matrix normal plane shape extensive Error is brought again.
Local sampling face shape restoration methods proposed by the present invention, are examined with interferometer according to influence matrix Ritchey-Common first The principle tested, obtains two width ellipse compression pattern under different auspicious strange angles.It is unit by pixel, two width ellipse is compressed Corresponding points in pattern, the corresponding points in two width ellipse compression pattern correspond to the actual incidence angle of tested plane mirror respective point Size establishes two groups of influence matrix equations, and auspicious strange angle is used without approximation.Two groups of influence matrix equations are combined, use least square Method solves to obtain the point Zernike coefficients, so as to recover this face graphic data.The procedure ergodic is entirely detected plane mirror, it is right Each point of tested plane mirror, performs above-mentioned processing, then integrates each point face graphic data result, obtains tested plane mirror and recovers Face shape afterwards.
Specific algorithm is as follows：
Light beam is oblique to be mapped in plane to be measured, and the hot spot formed on pupil plane is oval, passes through seat in calculating process Pupil areal coordinate is converted to minute surface coordinate by mark conversion formula, and minute surface coordinate system and pupil coordinate system are obtained by geometrical relationship Relation is as follows：
θ is Rui Qijiao, F#It is the F numbers of divergent beams, xp、ypFor pupil areal coordinate, xs、ysFor minute surface coordinate；
This method recovers the pattern that interferometer collects for unit by pixel, with arbitrary point (xp, yp) exemplified by push away The influence function of the dot system wave aberration and tested plane surface shape deviation is led, can when tested flat mirror shape error delta S is little To be shown as with Zemike polynomial tables：
Δs(xs, ys)=∑M, nSM, n(xs, ys)ZM, n(xs, ys) (2)
(xs, ys) it is point (xp, yp) corresponding minute surface coordinate, S in formulaM, n(xs, ys) represents that face shape error Zernike is multinomial The coefficient of formula, ZM, n(xs, ys) represent that tested plane mirror internal coordinate is (xs, ys) point the polynomial ground terms of each Zernike；
Arbitrary point (x on tested plane mirrorp, yp) the incidence angle I of interferometer incident light line is represented by：
In light path is examined, the surface form deviation of tested plane mirror can cause the light path of actual wave surface and preferable wave surface Difference, arbitrary point optical path difference OPD caused by tested plane mirror surface form deviation are represented by
OPD(xp, ypΔ s (the x of)=4s, ys)cosI(xp, yp)=∑M, nWM, nZM, n(xp, yp) (4)
WM, nThe Zernike coefficients of expression system wave aberration；
It can obtain the influence function of any dot system wave aberration and surface form deviation：
In formula, Zm, n (xp, yp) represent the Zernike multinomial ground terms of point (xp, yp) under pupil coordinate system；
Arbitrary point (x can be obtained according to Formula of Coordinate System Transformation (1) and influence function relation formula (5)p, yp) index impacts Matrix
By actually measuring ripple difference coefficientEstablish following matrix equation：
For the influence matrix, S (xs, ys) it is this face shape error coefficient matrix,For this Point actual measurement system wave aberration factor arrays；
Change auspicious strange angle according to Ritchey-Common test principle and resettle one group of influence matrix equation, asked with least square method Go out the point (xp, yp) face shape error every Zernike coefficient matrixes S (xs, ys), and then be fitted and obtain this face shape.
Compared with prior art, the present invention remarkable advantage is：Interferometer is sent light by traditional influence matrix Ritchey-Common method The beam incidence angle that difference is formed on tested plane mirror is approximately equal to auspicious strange angle θ to handle, compared to traditional influence matrix Rui Qi- Kang Mangfa, local sampling Ritchey-Common normal plane shape are recovered individually to establish influence matrix to every bit, effectively reduce traditional influence Matrix method difference error caused by interferometer incident light is to the tested actual incident angle difference of plane mirror.
Brief description of the drawings
Fig. 1 is the large plane rayleigh-type waves principle device of the present invention.
Fig. 2 is the minute surface coordinate and pupil coordinate graph of a relation of the present invention.
Embodiment
Below in conjunction with the accompanying drawings and specific embodiment is described in further details the present invention.
The present invention is based on existing influence matrix rayleigh-type waves, large plane Ritchey-Common as shown in Figure 1 Inspection principle device and basic light path, including interferometer, interferometer are equipped with interferometer camera lens, standard spherical mirror and tested plane Mirror, the face shape reset mode of the ellipse compression pattern for focusing on receiving interferometer of the invention are different.
In Ritchey-Common test, it is mapped to since light beam is oblique in plane to be measured, so the hot spot formed on pupil plane It is oval.Pupil areal coordinate is converted to by minute surface coordinate by Formula of Coordinate System Transformation in calculating process, according to Fig. 2, by several What relation obtains minute surface coordinate system and the relation of pupil coordinate system is as follows：
θ is Rui Qijiao, F#It is the F numbers of divergent beams, xp、ypFor pupil areal coordinate, xs、ysFor minute surface coordinate.
This method recovers the pattern that interferometer collects for unit by pixel, below with arbitrary point (xp, yp) be Example derives the influence function of the dot system wave aberration and tested plane surface shape deviation, other restoration methods of minute surface are consistent.Work as quilt When inspection flat mirror shape error delta S is little, it can be shown as with Zernike polynomial tables：
Δs(xs, ys)=∑M, n SM, n(xs, ys)ZM, n(xs, ys)
(xs, ys) it is point (xp, yp) corresponding minute surface coordinate, S in formulaM, n(xs, ys) represent that face shape error Zernike is multinomial The coefficient of formula, ZM, n(Xs, Ys) represent that tested plane mirror internal coordinate is (Xs, Ys) point the polynomial ground terms of each Zernike.
Arbitrary point is represented by the incidence angle I of interferometer incident light line on tested plane mirror：
In light path is examined, the surface form deviation of tested plane mirror can cause the light path of actual wave surface and preferable wave surface Difference.Optical path difference OPD caused by tested plane mirror surface form deviation is represented by
OPD(xp, ypThe Δ s cos I (x of)=4p, yp)=∑M, nWM, nZM, n(xp, yp)
WM, nThe Zemike coefficients of expression system wave aberration
It can obtain the influence function of any dot system wave aberration and tested plane mirror surface form deviation：
In formula, ZM, n(xp, yp) represent point (x under pupil coordinate systemp, yp) Zemike multinomial ground terms.For convenience of expression, IfThe Zernike coefficients W of system wave aberrationM, nA, b table can be used Show.Here face shape error and the system wave aberration that part is represented with first five rank Zernike multinomials (first five rank there are 21) are provided Relational expression example：
Various write as equation form by above-listed：
For the influence matrix, S (xs, ys) it is this face shape error coefficient matrix,For this Point actual measurement system wave aberration factor arrays；
Change auspicious strange angle according to Ritchey-Common test principle and resettle one group of influence matrix equation, asked with least square method Go out the point (xp, yp) face shape error every Zernike coefficient matrixes S (xs, ys), and then be fitted and obtain this face shape.
Because the value of a, b and the coordinate (x of minute surface each pointp, yp) related, so the influence matrix that plane mirror every bit is established All it is independent.The procedure ergodic is entirely detected plane mirror, remaining each point is established respective influence matrix and obtained in the same way After the shape of face, you can comprehensive each point face shape result obtains tested flat mirror shape.

Claims (2)

  1. A kind of 1. local sampling face shape restoration methods based on influence matrix rayleigh-type waves, it is characterised in that：Step 1： According to the principle of influence matrix rayleigh-type waves, two width ellipse compression pattern is obtained under different auspicious strange angles with interferometer；
    Step 2：It is unit by pixel, to the corresponding points in two width ellipse compression pattern, is corresponded to according to above-mentioned corresponding points The tested actual incidence angle size of plane mirror respective point establishes two groups of influence matrix equations, and auspicious strange angle is used without approximation；
    Step 3：Two groups of influence matrix equations are combined, are solved to obtain the point Zernike coefficients with least square method, so that extensive Multiple this face graphic data；
    Step 4：The procedure ergodic is entirely detected plane mirror, above-mentioned processing is performed to each point for being detected plane mirror, then will Each point face graphic data result synthesis, obtains the face shape after tested plane mirror recovers.
  2. 2. rayleigh-type waves local sampling face shape restoration methods according to claim 1, it is characterised in that：Light beam is oblique Incide in plane to be measured, the hot spot formed on pupil plane is oval, by Formula of Coordinate System Transformation by light in calculating process Pupil areal coordinate is converted to minute surface coordinate, and the relation that minute surface coordinate system and pupil coordinate system are obtained by geometrical relationship is as follows：
    θ is Rui Qijiao, F#It is the F numbers of divergent beams, xp、ypFor pupil areal coordinate, xs、ysFor minute surface coordinate；
    This method recovers the pattern that interferometer collects for unit by pixel, with arbitrary point (xp, yp) exemplified by derive should The influence function of dot system wave aberration and tested plane surface shape deviation, when tested flat mirror shape error delta S is little, Ke Yiyong Zernike polynomial tables are shown as：
    Δs(xs, ys)=∑M, nSM, n(xs, ys)ZM, n(xs, ys) (2)
    (xs, ys) it is point (xp, yp) corresponding minute surface coordinate, S in formulaM, n(xs, ys) represent the polynomial systems of face shape error Zemike Number, ZM, n(xs, ys) represent that tested plane mirror internal coordinate is (xs, ys) point the polynomial ground terms of each Zernike；
    Arbitrary point (x on tested plane mirrorp, yp) the incidence angle I of interferometer incident light line is represented by：
    <mrow> <mi>cos</mi> <mi>I</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>p</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mo>&amp;lsqb;</mo> <mi>&amp;theta;</mi> <mo>&amp;PlusMinus;</mo> <msup> <mi>tan</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mfrac> <mrow> <mn>2</mn> <msup> <mi>F</mi> <mo>#</mo> </msup> </mrow> <msub> <mi>x</mi> <mi>p</mi> </msub> </mfrac> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    In light path is examined, the surface form deviation of tested plane mirror can cause the optical path difference of actual wave surface and preferable wave surface, quilt Arbitrary point optical path difference OPD caused by inspection plane mirror surface form deviation is represented by
    OPD(xp, ypΔ s (the x of)=4s, ys)cos I(xp, yp)=∑M, nWM, nZM, n(xp, yp) (4)
    WM, nThe Zernike coefficients of expression system wave aberration；
    It can obtain the influence function of any dot system wave aberration and surface form deviation：
    <mrow> <msub> <mi>&amp;Sigma;</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <msub> <mi>S</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>s</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>Z</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>s</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>4</mn> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mo>&amp;lsqb;</mo> <mi>&amp;theta;</mi> <mo>&amp;PlusMinus;</mo> <msup> <mi>tan</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mfrac> <mrow> <mn>2</mn> <msup> <mi>F</mi> <mo>#</mo> </msup> </mrow> <msub> <mi>x</mi> <mi>p</mi> </msub> </mfrac> <mo>&amp;rsqb;</mo> </mrow> </mfrac> <msub> <mi>&amp;Sigma;</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <msub> <mi>W</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <msub> <mi>Z</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>p</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    In formula, Zm, n (xp, yp) represent the Zernike multinomial ground terms of point (xp, yp) under pupil coordinate system；
    Arbitrary point (x can be obtained according to Formula of Coordinate System Transformation (1) and influence function relation formula (5)p, yp) index impacts matrix
    By actually measuring ripple difference coefficientEstablish following matrix equation：
    <mrow> <msub> <mi>A</mi> <mrow> <msub> <mi>x</mi> <mi>s</mi> </msub> <mo>&amp;RightArrow;</mo> <msub> <mi>x</mi> <mi>p</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>s</mi> </msub> <mo>&amp;RightArrow;</mo> <msub> <mi>y</mi> <mi>p</mi> </msub> </mrow> </msub> <mi>S</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>s</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mover> <mi>W</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>p</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
    For the influence matrix, S (xs, ys) it is this face shape error coefficient matrix,It is real for the point Border measuring system wave aberration factor arrays；
    Change auspicious strange angle according to Ritchey-Common test principle and resettle one group of influence matrix equation, this is obtained with least square method Point (xp, yp) face shape error every Zernike coefficient matrixes S (xs, ys), and then be fitted and obtain this face shape.
CN201711096670.8A 2017-11-08 2017-11-08 Local sampling face shape restoration methods based on influence matrix Ritchey-Common test Pending CN107941165A (en)

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Publication number Priority date Publication date Assignee Title
CN109780992A (en) * 2018-12-28 2019-05-21 西安交通大学 Interferometer measuration system error calibrating method based on the processing of optical flat stripe pattern
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CN110779461A (en) * 2019-10-16 2020-02-11 中国航空工业集团公司洛阳电光设备研究所 Testing device and method for plane reflector surface type in refraction and reflection convergence light path
CN110779461B (en) * 2019-10-16 2021-09-21 中国航空工业集团公司洛阳电光设备研究所 Testing device and method for plane reflector surface type in refraction and reflection convergence light path

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