WO2018068199A1 - 非球面补偿器透射波前方程的测量装置和方法 - Google Patents

非球面补偿器透射波前方程的测量装置和方法 Download PDF

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WO2018068199A1
WO2018068199A1 PCT/CN2016/101770 CN2016101770W WO2018068199A1 WO 2018068199 A1 WO2018068199 A1 WO 2018068199A1 CN 2016101770 W CN2016101770 W CN 2016101770W WO 2018068199 A1 WO2018068199 A1 WO 2018068199A1
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compensator
aspherical
sub
wavefront
equation
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PCT/CN2016/101770
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French (fr)
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高松涛
苗二龙
武东城
隋永新
杨怀江
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中国科学院长春光学精密机械与物理研究所
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Priority to PCT/CN2016/101770 priority Critical patent/WO2018068199A1/zh
Publication of WO2018068199A1 publication Critical patent/WO2018068199A1/zh

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M11/00—Testing of optical apparatus; Testing structures by optical methods not otherwise provided for
    • G01M11/02—Testing optical properties
    • 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

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  • the invention relates to the field of optical detection technology, and in particular to a measuring device and method for transmitting a wavefront equation of an aspheric compensator.
  • the freedom of a single sphere for optimization is only the radius of curvature; the non-spherical surface has quadratic constants and high-order terms in addition to the radius of curvature of the vertex. Since aspheric surfaces have more design freedom than spherical surfaces, aspherical components are commonly used in many optical systems to reduce the complexity of the system and improve the imaging quality of the system.
  • the zero-compensation method is mostly used, that is, a compensating mirror or a computer-generated saturated hologram (CGH) is used as a compensator to convert the spherical wave emitted by the interferometer into an aspherical surface.
  • CGH computer-generated saturated hologram
  • the aspherical compensator is a key factor limiting the accuracy of the detection; if there is a problem with the compensator (such as a lens radius of curvature processing error or a lens spacing assembly error), it directly causes the processed aspheric surface to deviate from the design value. This has a serious impact on the optical system. For this reason, after the aspherical compensator is processed, it is very necessary to measure the transmitted wavefront to ensure that the processed aspheric compensator meets the design accuracy requirements.
  • a primary object of the present invention is to provide a measuring apparatus and method for an aspherical compensator transmission wavefront equation to achieve verification of an aspheric compensator.
  • the invention provides a measuring device for an aspherical compensator transmission wavefront equation, comprising: a phase shifting interferometer, a ranging interferometer and a reference spherical component; wherein an aspherical compensator as a measured object is placed in the shift Between the phase interferometer and the reference spherical component, and the aspherical compensator, the phase shifting interferometer and the reference spherical component are disposed coaxially, the reference spherical component is movable in the optical axis direction, and the phase shifting interferometer emits Light passes through the aspherical compensator and is reflected by the reference spherical component, and the reflected light passes through the aspherical compensator and is incident on the phase shifting interferometer, and the reference spherical component moves along the optical axis direction.
  • the reference spherical component comprises: a reference spherical surface, a clamping mechanism, a multi-dimensional adjustment platform, and a six-dimensional adjustment control unit, wherein the reference spherical surface is fixed to the multi-dimensional adjustment platform by the clamping mechanism, the six-dimensional adjustment
  • the control unit controls the movement of the multi-dimensional adjustment stage and drives the reference spherical surface to move.
  • the phase shifting interferometer comprises: a frequency stabilization laser, a collimating beam expanding system, a beam splitting prism, a converging mirror group, a phase shifting reference surface, an imaging mirror, a detector, and an image collecting unit; After passing through the collimating beam expanding system, the light enters the beam splitting prism, and the first beam of light split by the beam splitting prism is incident on the aspherical compensator through the converging mirror group, and the aspherical compensator transmits The wavefront is incident on the reference spherical surface, and the light reflected by the reference spherical surface sequentially passes through the aspherical compensator, the converging mirror group, and is reflected by the spectroscopic prism to the imaging mirror and the detector; the dichroic prism The separated second beam of light is incident on the phase shifting reference surface, and light reflected by the phase shifting reference surface is transmitted by the beam splitting prism to the imaging mirror and the detector.
  • the six-dimensional adjustment control unit controls the multi-dimensional adjustment stage to move along the optical axis direction, and the reference spherical surface is moved from the initial position along the optical axis direction, and the reference spherical surface and the aspherical compensator are in the detector.
  • the present invention also provides a measuring method of a measuring device using the above-described aspherical compensator transmission wavefront equation, the measuring method comprising: step A: moving the reference spherical surface, and measuring the transmitted wavefront of the aspheric compensator by using a phase shifting interferometer a ring-shaped top view formed with the reference spherical surface, the relative displacement corresponding to the annular surface map of the reference spherical surface is measured by a ranging interferometer; and step B: according to the annular surface shape measured by the phase shifting interferometer, Calculating a "zero-strip" radius of the circular contour map; step C: obtaining a derivative of the transmission wavefront height of the aspherical compensator based on the positional relationship between the reference spherical surface and the aspherical compensator transmission wavefront, thereby obtaining an aspheric surface
  • step D setting the derivative expression of the aspherical compensator wavefront equation, obtaining the second
  • the step B includes:
  • Sub-step B1 Calculate the radius of the "zero-strip" radius of the circular profile:
  • F i (x, y) represents the i-th circular surface map
  • r i represents the "zero-strip" radius of the i-th circular surface map
  • ⁇ represents the angular coordinate in polar coordinates
  • Sub-step B2 Using the numerical differentiation method for the calculation formula obtained in sub-step B1, the position distribution map of the “zero-streak” of the circular surface map is obtained, and then fitting is performed by the least squares method to obtain the “zero-streak” of the circular surface map. radius.
  • the step B comprises: sub-step B1: obtaining a calculation formula of the "zero-strip" radius of the annular top view:
  • F i (x, y) represents the i-th circular surface shape
  • r i represents the "zero-strip" radius of the i-th circular surface image
  • a 1 i and a 2 i represent the i-th circular surface shape, respectively.
  • Substep B2 Calculation Get the "zero stripe" radius of the ring shape:
  • the step C comprises: sub-step C1: obtaining a derivative of the transmission wavefront height of the aspherical compensator:
  • ⁇ i is the intersection of the transmitted wavefront of the ray and the aspherical compensator
  • z( ⁇ i ) represents the vector height of the transmitted wavefront of the aspherical compensator
  • z′( ⁇ i ) represents the derivative of the transmitted wavefront high of the aspherical compensator
  • r i is the i th annular face chart "zero stripes" radius
  • Z i is the high reference spherical vectors, s i aspheric surface to the i-th annular face chart corresponding to the relative displacement of the reference spherical surface
  • d i The propagation distance of the compensator transmitted wavefront, ⁇ i is the angle between the light and the optical axis;
  • Sub-step C2 The first derivative of the transmission wavefront equation of the aspherical compensator is obtained by the azimuth compensator transmitting the derivative of the wavefront vector height:
  • the step D comprises: sub-step D1: the derivative expression of the aspherical compensator transmission wavefront equation is:
  • ⁇ is the aspherical compensator transmission wavefront diameter coordinate
  • ⁇ max is the maximum value of the aspherical compensator transmission wavefront diameter coordinate
  • M is a constant
  • b n is a polynomial ⁇ P n ( The coefficient of x) ⁇ , and the polynomial ⁇ P n (x) ⁇ satisfies:
  • Sub-step D2 According to the derivative expression of the aspherical compensator transmission wavefront equation, the second expression of the aspherical compensator transmission wavefront equation is obtained:
  • T n (x) ⁇ P n (x)dx, n ⁇ 0.
  • Sub-step D3 making the first expression of the aspherical compensator transmission wavefront equation equal to the second expression, and obtaining an iterative expression of the aspherical compensator transmission wavefront equation:
  • the step E comprises: sub-step E1: making the propagation distance d i of the transmission surface of the aspherical compensator equal to the relative displacement s i of the reference spherical surface corresponding to the annular contour map; sub-step E2: forming the circular surface shape
  • the "zero-strip" radius r i of the graph gives the angle ⁇ i between the ray and the optical axis and the reference spherical height Z i , from the radius of the "zero-strip" r i , the angle ⁇ i between the ray and the optical axis,
  • the reference spherical vector height Z i the propagation distance d i , the intersection point of the ray and the aspherical compensator transmission wavefront ⁇ i ⁇ , and the aspherical compensator transmission wavefront vector height ⁇ z( ⁇ i ) ⁇
  • substep E3 setting an initial value of the best fit spherical curvature c,
  • d' i is the propagation distance of the re-calculated aspherical compensator transmission wavefront
  • z'( ⁇ i ) is the recalculated aspherical compensator transmission wavefront vector height
  • Sub-step E5 Calculation compensator aspherical wave front propagating from a transmission difference between the two iterations d 'i -d i, the propagation distance difference and the propagation distance threshold;
  • the propagation distance d' i recalculated in sub-step E4 is taken as the propagation distance d i of sub-step E2, and sub-step E2 to sub-step E5 are repeated;
  • the first iterative operation of the sub-step E3 comprises: sub-step E3a: assigning an initial value to the best-fit spherical curvature c; sub-step E3b: the best-fit spherical curvature c, the The relative displacement s i , the intersection point ⁇ i , and the aspherical compensator transmission wavefront vector height z( ⁇ i ) are substituted into the aspherical compensator transmission wavefront equation iterative expression, and the least squares method is used to fit the polynomial ⁇ P a coefficient ⁇ b n ⁇ of n (x) ⁇ ; a sub-step E3c: obtaining a second expression of the aspherical compensator transmission wavefront equation; a sub-step E3d: the intersection point ⁇ i , and the aspherical compensator The transmitted wavefront vector height z( ⁇ i ) is substituted into the second expression of the aspherical compensator transmission wavefront equation, and the
  • the initial value is subtracted to obtain the best fit spherical curvature difference; the sub-step E3e: the best fit spherical curvature difference is compared with the best fit spherical curvature threshold, if the best fit spherical curvature difference is greater than the most
  • the spherical curvature threshold is fitted, and the best fit spherical curvature is recalculated by sub-step E3d.
  • the ball curvature is best fitted, and sub-step E3b is repeated to sub-step E3e; otherwise, the second expression of the aspherical compensator wavefront equation obtained by sub-step E3c is output as an iterative operation result. .
  • the measuring device and the method for transmitting the wavefront equation of the aspheric compensator of the present invention have the following beneficial effects: the transmission wavefront of the aspherical compensator can be measured, thereby ensuring before performing aspherical processing.
  • the aspherical compensator is correct and avoids the aspherical compensator processing error, which has a serious impact on the final optical system.
  • the measuring method has high measurement accuracy, low measuring device cost and easy operation.
  • FIG. 1 is a schematic diagram of a measuring device for a transmission wavefront equation of an aspheric compensator according to an embodiment of the present invention
  • FIG. 2 is a flow chart of a method for measuring a transmission wavefront equation of an aspheric compensator according to an embodiment of the present invention
  • Figure 4 is a best fit circle calculated using the "zero stripe" position in Figure 3;
  • Figure 5 is a ring-shaped interferogram generated by simulation when the interference fringes are in communication with the center;
  • Figure 6 is a corresponding annular shape view of Figure 5;
  • Figure 7 is a ring-shaped interferogram generated by simulation
  • Figure 8 is a schematic diagram of transmission wavefront propagation of an aspheric compensator
  • Figure 9 is an optical structural view of the aspherical compensator
  • Figure 10 is a graph showing the deviation of the vector height from the design value of the transmitted wavefront of the aspherical compensator calculated by the method of the present invention.
  • S1-stabilized laser S2-collimation beam expanding system; S3-beam splitting prism; S4-concentrating mirror group; S5-phase shifting reference surface; S6-ranging interferometer; S7-reference spherical surface; S8-clamping mechanism; S9-multidimensional adjustment Taiwan; S10-imagescope; S11-detector; S12-image acquisition unit; S13-six-dimensional adjustment control unit.
  • FIG. 1 shows a measuring device for an aspherical compensator transmission wavefront equation according to an embodiment of the present invention, the measuring device comprising: a phase shifting interferometer, a ranging interferometer and a reference spherical component; wherein
  • the phase shifting interferometer comprises: a frequency stabilized laser S1, a collimated beam expanding system S2, a beam splitting prism S3, a converging mirror group S4, a phase shifting reference plane S5, an imaging mirror S10, a detector S11 and an image collecting unit S12;
  • the reference spherical surface assembly includes: a reference spherical surface S7, a clamping mechanism S8, a multi-dimensional adjustment stage S9, and a six-dimensional adjustment control unit S13.
  • the reference spherical surface S7 is fixed to the multi-dimensional adjustment stage S9 by the clamping mechanism S8, and the six-dimensional adjustment control unit S13 can control the multi-dimensional The adjustment table S9 moves.
  • the aspheric compensator S13 is placed between the phase shifting interferometer and the reference spherical component, and the aspherical compensator S13, the phase shifting interferometer and the reference spherical surface S7 are coaxially arranged.
  • the light emitted by the frequency stabilized laser S1 enters the dichroic prism S3 through the collimated beam expanding system S2, and the dichroic prism S3 divides the incident light into two beams, and the first beam propagates along the optical axis of the phase shifting interferometer, and the second beam of light Vertically propagating in the optical axis direction of the phase shifting interferometer, wherein the first beam is incident on the aspherical compensator S13 via the converging mirror group S4, and the transmitted wavefront of the aspherical compensator S13 is incident on the reference spherical surface S7 and reflected by the reference spherical surface S7
  • the light passes through the aspherical compensator S13, the converging mirror group S4, and is reflected by the dichroic prism S3 to the imaging mirror S10 and the detector S11; the second beam is incident on the phase shifting reference surface S5, and is reflected by the phase shifting reference surface S5.
  • Light is transmitted by the dichroic prism S3 to
  • the six-dimensional adjustment control unit S13 controls the multi-dimensional adjustment stage S9 to move along the optical axis direction of the phase shifting interferometer, thereby driving the reference spherical surface S7 to move from the initial position along the optical axis direction of the phase shifting interferometer, and the light and the reflected light reflected by the reference spherical surface S7.
  • the light reflected by the phase shifting reference surface S5 interferes, and the reference spherical surface S7 and the aspherical compensator S13 form a series of annular surface patterns on the detector S11, while the ranging interferometer S6 measures the reference spherical surface S7 relative to the initial position.
  • the moving distance, as a relative displacement corresponding to a series of annular contour maps, the image acquisition unit S12 utilizes the obtained circular shape
  • the aspherical compensator transmission wavefront equation is calculated from the histogram and relative displacement.
  • the measuring device for transmitting the wavefront equation of the aspheric compensator provided by the invention can realize the measurement of the transmitted wavefront of the aspherical compensator, thereby obtaining the parameters of the aspherical compensator before performing the aspherical processing, and the measuring device has low cost,
  • the structure is simple, and a series of annular surface images can be obtained by moving the reference spherical surface, thereby obtaining the transmission wavefront equation of the aspherical compensator, and the operation is convenient and flexible.
  • Another embodiment of the present invention further provides a measuring method.
  • the measuring method measures the transmission wavefront equation of the aspherical compensator by using the measuring device of the aspherical compensator transmitting wavefront equation.
  • Methods include:
  • Step A moving the reference spherical surface along the optical axis direction of the phase shifting interferometer, measuring the annular surface shape formed by the transmission wavefront and the reference spherical surface of the aspherical compensator by using a phase shifting interferometer, and measuring the reference spherical surface and the annular surface by using the ranging interferometer The relative displacement corresponding to the shape.
  • step A when step A is performed, as the reference spherical surface moves along the optical axis direction of the phase shifting interferometer, the aspherical compensator transmits a wavefront and a reference spherical surface to form a series of annular surface patterns, and at the same time, the ranging interferometer measures the reference spherical surface.
  • the moving distance at the initial position which is the relative displacement of the reference spherical surface, and records the relative displacement corresponding to the annular surface pattern, that is, the reference spherical surface corresponding to the i-th circular surface pattern in the series of annular surface images
  • the relative displacement s i The relative displacement s i .
  • Step B Calculate the “zero stripe” radius of the annular surface map according to the annular surface shape measured by the phase shifting interferometer.
  • step A a series of annular surface patterns are formed as the reference spherical surface moves.
  • the interference fringes of the partial annular surface pattern are in communication with the center of the annular surface pattern, and the partial annular surface shape
  • the interference fringes of the graph do not communicate with the center of the annular profile, but the "zero-streak" positions of both annular profiles are satisfied:
  • F(x, y) represents a torus profile and r represents the "zero-strip" radius of the torus.
  • step B calculate the "zero-strip" radius of the circular shape chart in the following two cases:
  • F i (x, y) represents the i-th circular profile in a series of circular profiles
  • r i represents the “zero-strip” radius of the i-th circular profile
  • the numerical differential method is used to set the appropriate threshold value to obtain the “zero-streak” position distribution map of the circular surface map, as shown in Fig. 3, and then the least square method is used for fitting to obtain the circular surface shape.
  • the "zero stripe" radius and center of the figure are shown in Figure 4.
  • F i (x, y) represents the i-th circular profile in a series of circular profiles
  • r i represents the "zero-strip" radius of the i-th circular profile
  • a 1 i and a 2 i The defocus and spherical aberration coefficients of the i-th circular histogram are respectively represented, which can be obtained by Zernike fitting the circular contour map.
  • Step C Based on the positional relationship between the reference spherical surface and the aspherical compensator transmission wavefront, the derivative of the transmitted wavefront vector height of the aspherical compensator is obtained, and then the first expression of the aspherical compensator transmission wavefront equation is obtained.
  • step C when the transmission surface of the aspherical compensator is perpendicular to the normal of any position in the radial direction of the reference sphere, a ring-shaped interferogram as shown in FIG. 7 appears, and the reference spherical surface and the aspherical compensator transmit the wavefront.
  • the positional relationship is shown in Figure 8.
  • P point is the point on the reference spherical surface corresponding to the "ull position" of the i-th circular surface map
  • point F is the light (the normal of the point P on the reference sphere) and the phase shifting interferometer light
  • the intersection of the axes, N points are the intersections of the rays (the normal of the point P on the spherical surface) and the transmitted wavefront of the aspherical compensator.
  • the coordinates of the points P and F can be expressed as (r i , Z i ) and O, s i ), where r i is the “zero-striped” radius of the i-th circular histogram, Z i is the reference spherical vector height, and s i is the relative displacement of the reference spherical surface corresponding to the i-th circular surface map
  • the distance PN between the point P and the point N is the propagation distance of the transmitted wavefront of the aspherical compensator, which is expressed as d i
  • the coordinates of the point N ( ⁇ i , z( ⁇ i )) are:
  • ⁇ i represents the angle between the line connecting point P and point F and the optical axis of the phase shifting interferometer, that is, the angle between the light and the optical axis
  • ⁇ i is the intersection of the light and the transmitted wavefront of the aspherical compensator, ie
  • the spherical compensator transmits the wavefront diameter coordinates
  • z( ⁇ i ) represents the vector height of the aspherical compensator's transmitted wavefront
  • z'( ⁇ i ) represents the derivative of the aspherical compensator's transmitted wavefront vector height.
  • Step D Set the derivative expression of the aspherical compensator transmission wavefront equation, and obtain the second expression of the aspherical compensator transmission wavefront equation, and then obtain the iterative expression of the aspherical compensator transmission wavefront equation.
  • step D in order to improve the measurement accuracy, the derivative expression of the aspherical compensator transmission wavefront equation is:
  • ⁇ is the aspherical compensator transmission wavefront diameter coordinate
  • ⁇ max is the maximum value of the aspherical compensator transmission wavefront diameter coordinate
  • M is manually set, which can be carried out according to actual needs an integer value
  • M preferably takes 6
  • b n represents the polynomial coefficients ⁇ P n (x) ⁇
  • polynomials ⁇ P n (x) ⁇ is satisfied:
  • T n (x) ⁇ P n (x)dx, n ⁇ 0.
  • Step E Using the relative displacement of the reference sphere corresponding to the annular profile (obtained from step A) and the "zero-strip" radius of the annular profile (obtained from step B), iterating the wavefront equation of the aspherical compensator The expression is iteratively operated to obtain the transmission wavefront equation of the aspherical compensator.
  • step E it includes:
  • Sub-step E1 Let the aspherical compensator of equation (5) transmit a wavefront with a propagation distance d i equal to the relative displacement s i of the reference sphere corresponding to the toroidal profile.
  • Sub-step E2 From the "zero-strip" radius r i of the circular histogram , the reference spherical equation can be used to obtain the angle ⁇ i between the light and the optical axis, and the reference spherical vector height Z i , r i , ⁇ i , Z i , d i into equation (5), to obtain the light transmittance and the intersection of the aspherical compensator wavefront and the aspheric wavefront compensator transmitting high vector ⁇ i ⁇ , ⁇ z ( ⁇ i) ⁇ .
  • Sub-step E3 setting the initial value of the best fit spherical curvature c, the relative displacement s i corresponding to the spherical surface of the reference spherical surface, the intersection ⁇ i of the ray and the aspherical compensator transmission wavefront, and the aspherical compensation
  • the transmitted wavefront vector height z( ⁇ i ) is substituted into the formula (12) to perform the first iterative operation, and the second expression of the aspherical compensator transmission wavefront equation is obtained.
  • the form of the second expression is shown in the formula (11).
  • Sub-step E4 Substituting the intersection of the ray with the aspherical compensator's transmitted wavefront ⁇ i into the second expression of the aspherical compensator wavefront equation obtained in sub-step E3, recalculating the transmitted wavefront height z' of the aspherical compensator ( ⁇ i ), and recalculate the propagation distance of the aspherical compensator's transmitted wavefront using equation (13):
  • d' i is the propagation distance of the recalculated aspherical compensator transmitting wavefront
  • z'( ⁇ i ) is the recalculated aspherical compensator transmitting wavefront vector height.
  • Sub-step E5 calculating a propagation distance difference d' i -d i of the transmitted wavefront of the aspherical compensator between the two iterations, comparing the propagation distance difference with the sensing distance threshold;
  • the transmission sub-step E4 recalculated compensator aspherical wave front propagation distance d 'i a d i a sub-step E2, repeats steps E2 to E5 sub-step;
  • the first iterative operation of the sub-step E3 specifically includes:
  • Sub-step E3a The initial value is assigned to the best fit spherical curvature c.
  • Sub-step E3b the best fit spherical curvature c, the relative displacement s i of the reference spherical surface corresponding to the annular surface map, the intersection ⁇ i of the ray and the aspherical compensator transmission wavefront, and the aspherical compensator transmitted wave
  • the front vector height z( ⁇ i ) is substituted into the formula (12), and the coefficient ⁇ b n ⁇ of the polynomial ⁇ P n (x) ⁇ is fitted by least squares method; the initial value of the best fit spherical curvature c can be manually set.
  • Sub-step E3c After obtaining the coefficient ⁇ b n ⁇ of the polynomial ⁇ P n (x) ⁇ , the second expression of the aspherical compensator transmission wavefront equation can be obtained, and the form of the second expression is shown in the formula (11).
  • Sub-step E3d the aspherical compensator transmission wavefront equation obtained by substituting the intersection of the ray with the aspherical compensator wavefront ⁇ i and the aspherical compensator wavefront vector z( ⁇ i ) into the sub-step E3c
  • the second expression recalculates the best fit spherical curvature, and subtracts the recalculated best fit spherical curvature from the initial value of the best fit spherical curvature to obtain the best fit spherical curvature difference.
  • Sub-step E3e comparing the best-fit spherical curvature difference with the best-fit spherical curvature threshold. If the best-fit spherical curvature difference is greater than the best-fit spherical curvature threshold, the sub-step E3d is recalculated. The best fit spherical curvature is used as the sub-step E3b to best fit the spherical curvature, and the sub-step E3b is repeated to the sub-step E3e; otherwise, the second expression of the aspherical compensator transmission wavefront equation obtained by sub-step E3c is obtained. The expression is output as an iterative result.
  • the above method is used to measure the equation of the transmission wavefront of a high-order even-order aspherical compensator.
  • the aspherical parameters compensated by the aspherical compensator are shown in Table 1.
  • the structure of the aspherical compensator itself is shown in Fig. 9. .
  • the measurement of the transmission wavefront equation of the aspheric compensator is completed by using steps A to E.
  • the vector height is calculated by finally obtaining the aspherical wavefront equation.
  • the deviation between the vector height and the design value is shown in Fig. 10.
  • the measurement method of the transmission wavefront equation of the aspherical compensator of the present invention can realize the measurement of the transmission wavefront of the aspherical compensator, thereby ensuring the correctness of the aspherical compensator before aspherical processing, and avoiding the aspherical surface.
  • the compensator processing error has a serious impact on the final optical system; the measuring method has the advantages of simple measuring method, low cost, convenient operation and high precision.

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Abstract

一种非球面补偿器（S13）透射波前方程的测量装置，包括移相干涉仪、测距干涉仪和参考球面组件，非球面补偿器（S13）置于移相干涉仪和参考球面组件之间，且三者同轴设置，参考球面组件沿光轴方向移动，参考球面组件与非球面补偿器（S13）形成环形面形图，测量参考球面组件的相对位移，利用环形面形图和相对位移计算非球面补偿器（S13）透射波前方程。还公开一种非球面补偿器（S13）透射波前方程的测量方法。可实现对非球面补偿器（S13）透射波前进行测量，从而在进行非球面加工之前确保非球面补偿器（S13）正确无误，避免非球面补偿器（S13）加工错误对最终光学***造成严重影响；测量方法的测量精度高，测量装置成本低，便于操作。

Description

非球面补偿器透射波前方程的测量装置和方法 技术领域
本发明涉及光学检测技术领域，尤其涉及一种非球面补偿器透射波前方程的测量装置和方法。
背景技术
在光学设计中，单个球面可以供优化的自由度只有曲率半径；而非球面除了顶点曲率半径之外，还有二次曲面常数和高阶项系数。由于非球面比球面拥有更多设计的自由度，所以在很多光学***中，都普遍采用非球面元件来减小***的复杂度，并提高***的成像质量。
当前，对于高精度非球面的检测，大都采用零位补偿法，即采用补偿镜或者计算全息图(Computer-Generated Hologram，CGH)作为补偿器，将干涉仪发出的球面波转化为与非球面相匹配的非球面波，从而实现零位检测。在检测过程中，非球面补偿器是限制检测精度的关键性因素；如果补偿器存在问题(如透镜的曲率半径加工出错或者透镜间隔装配错误)，则直接导致加工出的非球面偏离设计值，从而给光学***造成严重的影响。为此，当非球面补偿器加工完成之后，非常有必要对其透射波前进行测量，从而保证加工出的非球面补偿器满足设计精度的要求。
因此，研发一种非球面补偿器透射波前方程的测量装置和方法，成为人们亟待解决的问题。
发明内容
本发明的主要目的在于提供一种非球面补偿器透射波前方程的测量装置和方法，以实现对非球面补偿器的校验。
本发明提供了一种非球面补偿器透射波前方程的测量装置，包括：移相干涉仪、测距干涉仪和参考球面组件；其中，作为被测对象的非球面补偿器置于所述移相干涉仪和参考球面组件之间，且所述非球面补偿器、移相干涉仪和参考球面组件同轴设置，所述参考球面组件可沿光轴方向移动，所述移相干涉仪发出的光经过所述非球面补偿器，并由所述参考球面组件反射，反射光经过所述非球面补偿器后入射至所述移相干涉仪，所述参考球面组件沿光轴方向移动，在所述移相干涉仪内形成参考球面组件与非球 面补偿器之间的环形面形图，所述测距干涉仪测量参考所述球面组件的相对位移，所述移相干涉仪利用所述环形面形图和相对位移计算非球面补偿器透射波前方程。
优选地，所述参考球面组件包括：参考球面、夹持机构、多维调整台以及六维调整控制单元，所述参考球面由所述夹持机构固定于所述多维调整台，所述六维调整控制单元控制所述多维调整台的移动，并带动所述参考球面移动。
优选地，所述移相干涉仪包括：稳频激光器、准直扩束***、分光棱镜、汇聚镜组、移相参考面、成像镜、探测器和图像采集单元；所述稳频激光器发出的光经所述准直扩束***后进入所述分光棱镜，所述分光棱镜分出的第一束光经所述汇聚镜组入射至所述非球面补偿器，所述非球面补偿器的透射波前入射至所述参考球面，经所述参考球面反射的光依次经过所述非球面补偿器、所述汇聚镜组，并由所述分光棱镜反射至所述成像镜和探测器；分光棱镜分出的第二束光入射至所述移相参考面，经所述移相参考面反射的光由所述分光棱镜透射至所述成像镜和探测器。
优选地，所述六维调整控制单元控制所述多维调整台沿光轴方向移动，带动所述参考球面由初始位置沿光轴方向移动，所述参考球面与非球面补偿器在所述探测器上形成一系列环形面形图，所述测距干涉仪测量参考球面相对于初始位置的移动距离，作为与一系列环形面形图相对应的相对位移，所述图像采集单元利用环形面形图和相对位移计算出非球面补偿器透射波前方程。
本发明还提供了一种利用上述非球面补偿器透射波前方程的测量装置的测量方法，所述测量方法包括：步骤A：移动参考球面，利用移相干涉仪测量非球面补偿器透射波前与参考球面形成的环形面形图，利用测距干涉仪测量所述参考球面的与所述环形面形图对应的相对位移；步骤B：依据所述移相干涉仪测量的环形面形图，计算所述环形面形图的“零条纹”半径；步骤C：基于所述参考球面与非球面补偿器透射波前的位置关系，得到非球面补偿器透射波前矢高的导数，进而得到非球面补偿器透射波前方程的第一表达式；步骤D：设定非球面补偿器透射波前方程的导数表达式，得到非球面补偿器透射波前方程第二表达式，进而得到非球面补偿器 透射波前方程的迭代表达式；以及步骤E：利用所述参考球面的与环形面形图对应的相对位移和所述环形面形图的“零条纹”半径，对非球面补偿器透射波前方程迭代表达式进行迭代运算，得到非球面补偿器透射波前方程。
优选地，对于干涉条纹与中心不连通的环形面形图，所述步骤B包括：
子步骤B1：得到环形面形图的“零条纹”半径的计算公式：
Figure PCTCN2016101770-appb-000001
其中，Fi(x，y)表示第i个环形面形图，ri表示第i个环形面形图的“零条纹”半径，θ表示极坐标下的角度坐标；
子步骤B2：对子步骤B1得到的计算公式采用数值微分法，得到环形面形图的“零条纹”位置分布图，再采用最小二乘法进行拟合，得到环形面形图的“零条纹”半径。
优选地，对于干涉条纹与中心连通的环形面形图，所述步骤B包括：子步骤B1：得到环形面形图的“零条纹”半径的计算公式：
Figure PCTCN2016101770-appb-000002
其中，Fi(x，y)表示第i个环形面形图，ri表示第i个环形面形图的“零条纹”半径，a1 i和a2 i分别表示第i个环形面形图的离焦和球差系数；
子步骤B2：计算
Figure PCTCN2016101770-appb-000003
得到环形面形图的“零条纹”半径：
Figure PCTCN2016101770-appb-000004
优选地，所述步骤C包括：子步骤C1：得到非球面补偿器透射波前矢高的导数：
Figure PCTCN2016101770-appb-000005
其中，ρi为光线与非球面补偿器透射波前的交点，z(ρi)表示非球面补偿器透射波前的矢高，z′(ρi)表示非球面补偿器透射波前矢高的导数，且
Figure PCTCN2016101770-appb-000006
其中，ri为第i个环形面形图的“零条纹”半径，Zi为参考球面矢高，si为参考球面的与第i个环形面形图对应的相对位移，di为非球面补偿器透射波前的传播距离，θi为光线与光轴的夹角；
子步骤C2：由非球面补偿器透射波前矢高的导数，得到非球面补偿器透射波前方程第一表达式：
Figure PCTCN2016101770-appb-000007
优选地，所述步骤D包括：子步骤D1：非球面补偿器透射波前方程的导数表达式为：
Figure PCTCN2016101770-appb-000008
其中，c为最佳拟合球曲率，ρ为非球面补偿器透射波前径坐标，ρmax为非球面补偿器透射波前径坐标最大值，M为常数，bn表示多项式{Pn(x)}的系数，且多项式{Pn(x)}满足：
Figure PCTCN2016101770-appb-000009
子步骤D2：根据非球面补偿器透射波前方程的导数表达式，得到非球面补偿器透射波前方程第二表达式：
Figure PCTCN2016101770-appb-000010
其中，Tn(x)＝∫Pn(x)dx，n≥0。
子步骤D3：令非球面补偿器透射波前方程第一表达式与第二表达式相等，得到非球面补偿器透射波前方程迭代表达式：
Figure PCTCN2016101770-appb-000011
优选地，所述步骤E包括：子步骤E1：令非球面补偿器透射波前的传播距离di等于参考球面的与环形面形图对应的相对位移si；子步骤E2：由环形面形图的“零条纹”半径ri得到光线与光轴的夹角θi以及参考球面矢高Zi，由所述“零条纹”半径ri、所述光线与光轴的夹角θi、所述参考球面矢高Zi、所述传播距离di得到光线与非球面补偿器透射波前的交点{ρi}、以及非球面补偿器透射波前矢高{z(ρi)}；子步骤E3：设置最佳拟合球曲率c的初始值，将所述相对位移si、所述交点ρi、以及所述非球面补偿器透射波前矢高z(ρi)代入非球面补偿器透射波前方程迭代表达式进行第一迭代运算，得到非球面补偿器透射波前方程第二表达式；子步骤E4：将所述交点ρi代入子步骤E3得到的非球面补偿器透射波前方程第二表达式，重新计算非球面补偿器透射波前矢高z′(ρi)，并利用下式重新计算非球面补偿器透射波前的传播距离：
Figure PCTCN2016101770-appb-000012
其中，d′i为重新计算的非球面补偿器透射波前的传播距离，z′(ρi)为重新计算的非球面补偿器透射波前矢高；
子步骤E5：计算两次迭代之间非球面补偿器透射波前的传播距离差值d′i-di，将传播距离差值与传播距离阈值比较；
若传播距离差值大于传播距离阈值，将子步骤E4重新计算的传播距离d′i作为子步骤E2的传播距离di，重复子步骤E2至子步骤E5；
否则，将子步骤E3得到的非球面补偿器透射波前方程第二表达式，作为非球面补偿器透射波前方程。
优选地，所述子步骤E3的第一迭代运算包括：子分步骤E3a：将初始值赋予最佳拟合球曲率c；子分步骤E3b：将所述最佳拟合球曲率c、所述相对位移si、所述交点ρi、以及所述非球面补偿器透射波前矢高z(ρi)代入非球面补偿器透射波前方程迭代表达式，采用最小二乘法拟合出多项式{Pn(x)}的系数{bn}；子分步骤E3c：得到非球面补偿器透射波前方程第二表达式；子分步骤E3d：将所述交点ρi、以及所述非球面补偿器透射波前矢高z(ρi)代入非球面补偿器透射波前方程第二表达式，重新计算最佳拟合 球曲率，将重新计算的最佳拟合球曲率与最佳拟合球曲率的初始值相减，获得最佳拟合球曲率差值；子分步骤E3e：将最佳拟合球曲率差值与最佳拟合球曲率阈值比较，若最佳拟合球曲率差值大于最佳拟合球曲率阈值，将子分步骤E3d重新计算的最佳拟合球曲率作为子分步骤E3b最佳拟合球曲率，重复执行子分步骤E3b至子分步骤E3e；否则，将子分步骤E3c得到的非球面补偿器透射波前方程第二表达式作为迭代运算结果输出。
从上述技术方案可以看出，本发明的非球面补偿器透射波前方程的测量装置和方法具有以下有益效果：可实现对非球面补偿器透射波前进行测量，从而在进行非球面加工之前确保非球面补偿器正确无误，避免非球面补偿器加工错误对最终光学***造成严重影响；该测量方法的测量精度高，测量装置成本低，便于操作。
附图说明
附图是用来提供对本发明的进一步理解，并且构成说明书的一部分，与下面的具体实施方式一起用于解释本发明，但并不构成对本发明的限制。在附图中：
图1为本发明实施例的非球面补偿器透射波前方程的测量装置示意图；
图2为本发明实施例的非球面补偿器透射波前方程的测量方法流程图；
图3为当干涉条纹与中心不连通时，满足设定阈值的“零条纹”位置分布图；
图4为利用图3中“零条纹”位置计算出的最佳拟合圆；
图5为当干涉条纹与中心连通时，仿真生成的环形干涉图；
图6为图5对应的环形面形图；
图7为仿真生成的环形干涉图；
图8为非球面补偿器透射波前传播示意图；
图9为非球面补偿器光学结构图；
图10为采用本发明方法计算出的非球面补偿器透射波前的矢高与设计值的偏差。
符号说明
S1-稳频激光器；S2-准直扩束***；S3-分光棱镜；S4-汇聚镜组；S5-移相参考面；S6-测距干涉仪；S7-参考球面；S8-夹持机构；S9-多维调整 台；S10-成像镜；S11-探测器；S12-图像采集单元；S13-六维调整控制单元。
具体实施方式
为使本发明的目的、技术方案和优点更加清楚明白，以下结合具体实施例，并参照附图，对本发明进一步详细说明。
参见图1，图1示出了本发明实施例的非球面补偿器透射波前方程的测量装置，该测量装置包括：移相干涉仪、测距干涉仪和参考球面组件；其中，
移相干涉仪包括：稳频激光器S1、准直扩束***S2、分光棱镜S3、汇聚镜组S4、移相参考面S5、成像镜S10、探测器S11和图像采集单元S12；
参考球面组件包括：参考球面S7、夹持机构S8、多维调整台S9以及六维调整控制单元S13，参考球面S7由夹持机构S8固定于多维调整台S9，六维调整控制单元S13可以控制多维调整台S9移动。
非球面补偿器S13置于移相干涉仪和参考球面组件之间，且非球面补偿器S13、移相干涉仪和参考球面S7同轴设置。
稳频激光器S1发出的光经准直扩束***S2后进入分光棱镜S3，分光棱镜S3将入射光分为两束，第一束光沿移相干涉仪光轴方向传播，第二束光沿垂直于移相干涉仪光轴方向传播，其中，第一束光经汇聚镜组S4入射至非球面补偿器S13，非球面补偿器S13的透射波前入射至参考球面S7，经参考球面S7反射的光依次经过非球面补偿器S13、汇聚镜组S4，并由分光棱镜S3反射至成像镜S10和探测器S11；第二束光入射至移相参考面S5，经移相参考面S5反射的光由分光棱镜S3透射至成像镜S10和探测器S11。
其中，六维调整控制单元S13控制多维调整台S9沿移相干涉仪光轴方向移动，从而带动参考球面S7由初始位置沿移相干涉仪光轴方向移动，经参考球面S7反射的光与经移相参考面S5反射的光发生干涉，参考球面S7与非球面补偿器S13在探测器S11上形成一系列环形面形图，与此同时，测距干涉仪S6测量参考球面S7相对于初始位置的移动距离，作为与一系列环形面形图相对应的相对位移，图像采集单元S12利用得到的环形 面形图和相对位移计算出非球面补偿器透射波前方程。
本发明提供的非球面补偿器透射波前方程的测量装置，可实现对非球面补偿器透射波前的测量，从而在进行非球面加工之前得到非球面补偿器的参数，该测量装置成本低、结构简单，通过移动参考球面即可得到一系列环形面形图，从而得到非球面补偿器透射波前方程，操作方便灵活。
本发明的另一实施例还提供了一种测量方法，参见图2，该测量方法利用上述非球面补偿器透射波前方程的测量装置，对非球面补偿器透射波前方程进行测量，该测量方法包括：
步骤A：沿移相干涉仪光轴方向移动参考球面，利用移相干涉仪测量非球面补偿器透射波前与参考球面形成的环形面形图，利用测距干涉仪测量参考球面的与环形面形图对应的相对位移。
执行步骤A时，随着参考球面沿移相干涉仪光轴方向移动，非球面补偿器透射波前与参考球面会形成一系列环形面形图，与此同时，测距干涉仪测量参考球面相对于初始位置的移动距离，该移动距离作为参考球面的相对位移，并记录环形面形图相对应的相对位移，即对于一系列环形面形图中的第i个环形面形图对应一参考球面的相对位移si。
步骤B：依据所述移相干涉仪测量的环形面形图，计算环形面形图的“零条纹”半径。
由步骤A可知，随着参考球面的移动会形成一系列环形面形图，对于这些环形面形图来说，部分环形面形图的干涉条纹与环形面形图中心相连通，部分环形面形图的干涉条纹不与环形面形图中心连通，但这两种环形面形图的“零条纹”位置均满足：
Figure PCTCN2016101770-appb-000013
其中，F(x，y)表示环形面形图，r表示环形面形图的“零条纹”半径。
对于步骤B来说，分以下两种情况计算环形面形图的“零条纹”半径：
情况一：当环形面形图的干涉条纹与环形面形图中心不连通时，为了便于计算，将公式(1)改写为：
Figure PCTCN2016101770-appb-000014
其中，Fi(x，y)表示一系列环形面形图中的第i个环形面形图，ri表示第i个环形面形图的“零条纹”半径，θ表示极坐标下的角度坐标，i＝1，2，...N。
对公式(2)采用数值微分法，设置合适的阈值，得到环形面形图的“零条纹”位置分布图，如图3所示，然后采用最小二乘法进行拟合，即可得到环形面形图的“零条纹”半径与中心，如图4所示。
情况二：当环形面形图的干涉条纹与环形面形图中心连通时，如图5、图6所示，环形面形图主要由离焦和球差项组成，即：
Figure PCTCN2016101770-appb-000015
其中，Fi(x，y)表示一系列环形面形图中的第i个环形面形图，ri表示第i个环形面形图的“零条纹”半径，a1 i和a2 i分别表示第i个环形面形图的离焦和球差系数，其可以通过对环形面形图进行Zernike拟合获得。
然后将公式(3)带入公式(1)，可得到环形面形图的“零条纹”半径：
Figure PCTCN2016101770-appb-000016
步骤C：基于参考球面与非球面补偿器透射波前的位置关系，得到非球面补偿器透射波前矢高的导数，进而得到非球面补偿器透射波前方程的第一表达式。
在步骤C中，当非球面补偿器透射波前与参考球面径向任一位置的法线垂直时，会出现如图7所示的环形干涉图，参考球面与非球面补偿器透射波前的位置关系如图8所示。其中，P点为第i个环形面形图“零条纹”位置(Null Position)对应的参考球面上的点，F点为光线(参考球面上过P点的法线)与移相干涉仪光轴的交点，N点为光线(参考球面上过P点的法线)与非球面补偿器透射波前的交点，P点与F点的坐标可以分别表 示为(ri，Zi)和(O，si)，其中，ri为第i个环形面形图的“零条纹”半径，Zi为参考球面矢高，si为参考球面的与第i个环形面形图对应的相对位移，P点与N点的距离PN为非球面补偿器透射波前的传播距离，其表示为di，则N点坐标(ρi，z(ρi))为：
Figure PCTCN2016101770-appb-000017
Figure PCTCN2016101770-appb-000018
其中，θi表示P点和F点的连线与移相干涉仪光轴的夹角，即光线与光轴的夹角，ρi为光线与非球面补偿器透射波前的交点，即非球面补偿器透射波前径坐标，z(ρi)表示非球面补偿器透射波前的矢高，z′(ρi)表示非球面补偿器透射波前矢高的导数。
为了便于计算，将公式(6)改写为：
Figure PCTCN2016101770-appb-000019
由公式(7)得到非球面补偿器透射波前方程第一表达式：
Figure PCTCN2016101770-appb-000020
步骤D：设定非球面补偿器透射波前方程的导数表达式，得到非球面补偿器透射波前方程第二表达式，进而得到非球面补偿器透射波前方程的迭代表达式。
在步骤D中，为了提高测量精度，非球面补偿器透射波前方程的导数表达式为：
Figure PCTCN2016101770-appb-000021
其中，c为最佳拟合球曲率，ρ为非球面补偿器透射波前径坐标，ρmax 为非球面补偿器透射波前径坐标最大值，M由人工设定，其可以根据实际需要进行整数取值，优选M取6，bn表示多项式{Pn(x)}的系数，且多项式{Pn(x)}满足：
Figure PCTCN2016101770-appb-000022
其中，当m＝n时，δmn＝1；当m≠n时，δmn＝0。
根据公式(9)，得到非球面补偿器透射波前方程第二表达式：
Figure PCTCN2016101770-appb-000023
其中，Tn(x)＝∫Pn(x)dx，n≥0。
令非球面补偿器透射波前方程第一表达式与第二表达式相等，得到非球面补偿器透射波前方程迭代表达式：
Figure PCTCN2016101770-appb-000024
步骤E：利用参考球面的与环形面形图对应的相对位移(由步骤A得到)和环形面形图的“零条纹”半径(由步骤B得到)，对非球面补偿器透射波前方程迭代表达式进行迭代运算，得到非球面补偿器透射波前方程。
在步骤E中，包括：
子步骤E1：令公式(5)的非球面补偿器透射波前的传播距离di等于参考球面的与环形面形图对应的相对位移si。
子步骤E2：由环形面形图的“零条纹”半径ri，利用参考球面方程可以得到光线与光轴的夹角θi，以及参考球面矢高Zi，将ri、θi、Zi、di代入公式(5)，得到光线与非球面补偿器透射波前的交点、以及非球面补偿器透射波前矢高{ρi}、{z(ρi)}。
子步骤E3：设置最佳拟合球曲率c的初始值，将参考球面的与环形面形图对应的相对位移si、光线与非球面补偿器透射波前的交点ρi、以及非球面补偿器透射波前矢高z(ρi)代入公式(12)进行第一迭代运算，得到非球面补偿器透射波前方程第二表达式，该第二表达式的形式参见公式(11)。
子步骤E4：将光线与非球面补偿器透射波前的交点ρi代入子步骤E3得到的非球面补偿器透射波前方程第二表达式，重新计算非球面补偿器透射波前矢高z′(ρi)，并利用公式(13)重新计算非球面补偿器透射波前的传播距离：
Figure PCTCN2016101770-appb-000025
其中，d′i为重新计算的非球面补偿器透射波前的传播距离，z′(ρi)为重新计算的非球面补偿器透射波前矢高。
子步骤E5：计算两次迭代之间非球面补偿器透射波前的传播距离差值d′i-di，将传播距离差值与传感距离阈值比较；
若传播距离差值大于传播距离阈值，将子步骤E4重新计算的非球面补偿器透射波前的传播距离d′i作为子步骤E2的di，重复子步骤E2至子步骤E5；
否则，将子步骤E3得到的非球面补偿器透射波前方程第二表达式，作为非球面补偿器透射波前方程。
其中，子步骤E3的第一迭代运算具体包括：
子分步骤E3a：将初始值赋予最佳拟合球曲率c。
子分步骤E3b：将最佳拟合球曲率c、参考球面的与环形面形图对应的相对位移si、光线与非球面补偿器透射波前的交点ρi、以及非球面补偿器透射波前矢高z(ρi)代入公式(12)，采用最小二乘法拟合出多项式{Pn(x)}的系数{bn}；最佳拟合球曲率c的初始值可由人工设定。
子分步骤E3c：得到多项式{Pn(x)}的系数{bn}后，可以得到非球面补偿器透射波前方程第二表达式，该第二表达式的形式参见公式(11)。
子分步骤E3d：将光线与非球面补偿器透射波前的交点ρi、以及非球 面补偿器透射波前矢高z(ρi)代入子分步骤E3c得到的非球面补偿器透射波前方程第二表达式，重新计算最佳拟合球曲率，将重新计算的最佳拟合球曲率与最佳拟合球曲率的初始值相减，获得最佳拟合球曲率差值。
子分步骤E3e：将最佳拟合球曲率差值与最佳拟合球曲率阈值比较，若最佳拟合球曲率差值大于最佳拟合球曲率阈值，将子分步骤E3d重新计算的最佳拟合球曲率作为子分步骤E3b最佳拟合球曲率，重复执行子分步骤E3b至子分步骤E3e；否则，将子分步骤E3c得到的非球面补偿器透射波前方程第二表达式作为迭代运算结果输出。
通过上述方法针对一高次偶次非球面补偿器透射波前的方程进行测量，此非球面补偿器所补偿的非球面参数如表1所示，非球面补偿器本身的结构如图9所示。
表1
Figure PCTCN2016101770-appb-000026
利用步骤A至步骤E完成了对非球面补偿器透射波前方程的测量，利用最终获得非球面透射波前方程计算出矢高，此矢高与设计值的偏差如图10所示。
由此可见，本发明的非球面补偿器透射波前方程的测量方法，可实现对非球面补偿器透射波前进行测量，从而在进行非球面加工之前确保非球面补偿器正确无误，避免非球面补偿器加工错误对最终光学***造严重的影响；该测量方法具有测量方法简单，成本低，便于操作、精度高等优点。
至此，已经结合附图对本实施例进行了详细描述。依据以上描述，本领域技术人员应当对本发明的非球面补偿器透射波前方程的测量装置和方法有了清楚的认识。
需要说明的是，在附图或说明书正文中，未绘示或描述的实现方式，均为所属技术领域中普通技术人员所知的形式，并未进行详细说明。此外，上述对各元件的定义并不仅限于实施例中提到的各种具体结构和形状，本领域普通技术人员可对其进行简单地更改或替换。
以上所述的具体实施例，对本发明的目的、技术方案和有益效果进行 了进一步详细说明，所应理解的是，以上所述仅为本发明的具体实施例而已，并不用于限制本发明，凡在本发明的精神和原则之内，所做的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。

Claims (11)

  1. 一种非球面补偿器透射波前方程的测量装置，其特征在于，包括：移相干涉仪、测距干涉仪和参考球面组件；其中，
    作为被测对象的非球面补偿器置于所述移相干涉仪和参考球面组件之间，且所述非球面补偿器、移相干涉仪和参考球面组件同轴设置，所述参考球面组件可沿光轴方向移动；
    所述移相干涉仪发出的光经过所述非球面补偿器，并由所述参考球面组件反射，反射光经过所述非球面补偿器后入射至所述移相干涉仪，所述参考球面组件沿光轴方向移动，在所述移相干涉仪内形成参考球面组件与非球面补偿器之间的环形面形图，所述测距干涉仪测量参考所述球面组件的相对位移，所述移相干涉仪利用所述环形面形图和相对位移计算非球面补偿器透射波前方程。
  2. 如权利要求1所述的测量装置，其特征在于，所述参考球面组件包括：参考球面、夹持机构、多维调整台以及六维调整控制单元，所述参考球面由所述夹持机构固定于所述多维调整台，所述六维调整控制单元控制所述多维调整台的移动，并带动所述参考球面移动。
  3. [根据细则26改正16.11.2016]
    如权利要求２所述的测量装置，其特征在于，所述移相干涉仪包括：稳频激光器、准直扩束***、分光棱镜、汇聚镜组、移相参考面、成像镜、探测器和图像采集单元；
    所述稳频激光器发出的光经所述准直扩束***后进入所述分光棱镜，所述分光棱镜分出的第一束光经所述汇聚镜组入射至所述非球面补偿器，所述非球面补偿器的透射波前入射至所述参考球面，经所述参考球面反射的光依次经过所述非球面补偿器、所述汇聚镜组，并由所述分光棱镜反射至所述成像镜和探测器；分光棱镜分出的第二束光入射至所述移相参考面，经所述移相参考面反射的光由所述分光棱镜透射至所述成像镜和探测器。
  4. [根据细则26改正16.11.2016]　
    如权利要求３所述的测量装置，其特征在于，所述六维调整控制单元控制所述多维调整台沿光轴方向移动，带动所述参考球面由初始位置沿光轴方向移动，所述参考球面与非球面补偿器在所述探测器上形成一系列环形面形图，所述测距干涉仪测量参考球面相对于初始位置的移动距离，作为与一系列环形面形图相对应的相对位移，所述图像采集单元利用环形面形图和相对位移计算出非球面补偿器透射波前方程。
  5. 一种利用权利要求1所述的非球面补偿器透射波前方程的测量装置的测量方法，其特征在于，所述测量方法包括：
    步骤A：移动参考球面，利用移相干涉仪测量非球面补偿器透射波前与参考球面形成的环形面形图，利用测距干涉仪测量所述参考球面的与所述环形面形图对应的相对位移；
    步骤B：依据所述移相干涉仪测量的环形面形图，计算所述环形面形图的“零条纹”半径；
    步骤C：基于所述参考球面与非球面补偿器透射波前的位置关系，得到非球面补偿器透射波前矢高的导数，进而得到非球面补偿器透射波前方程的第一表达式；
    步骤D：设定非球面补偿器透射波前方程的导数表达式，得到非球面补偿器透射波前方程第二表达式，进而得到非球面补偿器透射波前方程的迭代表达式；以及
    步骤E：利用所述参考球面的与环形面形图对应的相对位移和所述环形面形图的“零条纹”半径，对非球面补偿器透射波前方程迭代表达式进行迭代运算，得到非球面补偿器透射波前方程。
  6. [根据细则26改正16.11.2016]　
    如权利要求5所述的测量方法，其特征在于，对于干涉条纹与中心不连通的环形面形图，所述步骤B包括：
    子步骤B1：得到环形面形图的“零条纹”半径的计算公式：
    Figure PCTCN2016101770-appb-100001
    其中，Fi(x，y)表示第i个环形面形图，ri表示第i个环形面形图的“零条纹”半径，θ表示极坐标下的角度坐标；
    子步骤B2：对子步骤B1得到的计算公式采用数值微分法，得到环形面形图的“零条纹”位置分布图，再采用最小二乘法进行拟合，得到环形面形图的“零条纹”半径。
  7. [根据细则26改正16.11.2016]　
    如权利要求5所述的测量方法，其特征在于，对于干涉条纹与中心连通的环形面形图，所述步骤B包括：
    子步骤B1：得到环形面形图的“零条纹”半径的计算公式：
    Fi(x，y)＝a1 i(2ri 2-1)+a2 i(6ri 4-6ri+1)
    其中，Fi(x，y)表示第i个环形面形图，ri表示第i个环形面形图的“零条纹”半径，a1 i和a2 i分别表示第i个环形面形图的离焦和球差系数；
    子步骤B2：计算
    Figure PCTCN2016101770-appb-100002
    得到环形面形图的“零条纹”半径：
    Figure PCTCN2016101770-appb-100003
  8. [根据细则26改正16.11.2016]　
    如权利要求5所述的测量方法，其特征在于，所述步骤C包括：
    子步骤C1：得到非球面补偿器透射波前矢高的导数：
    Figure PCTCN2016101770-appb-100004
    其中，ρi为光线与非球面补偿器透射波前的交点，z(ρi)表示非球面补偿器透射波前的矢高，z′(ρi)表示非球面补偿器透射波前矢高的导数，且
    Figure PCTCN2016101770-appb-100005

    其中，ri为第i个环形面形图的“零条纹”半径，Zi为参考球面矢高，si为参考球面的与第i个环形面形图对应的相对位移，di为非球面补偿器透射波前的传播距离，θi为光线与光轴的夹角；
    子步骤C2：由非球面补偿器透射波前矢高的导数，得到非球面补偿器透射波前方程第一表达式：
    Figure PCTCN2016101770-appb-100006
  9. [根据细则26改正16.11.2016]　
    如权利要求5所述的测量方法，其特征在于，所述步骤D包括：
    子步骤D1：非球面补偿器透射波前方程的导数表达式为：
    Figure PCTCN2016101770-appb-100007
    其中，c为最佳拟合球曲率，ρ为非球面补偿器透射波前径坐标，ρmax为非球面补偿器透射波前径坐标最大值，M为常数，bn表示多项式{Pn(x)}的系数，且多项式{Pn(x)}满足：
    Figure PCTCN2016101770-appb-100008
    子步骤D2：根据非球面补偿器透射波前方程的导数表达式，得到非球面补偿器透射波前方程第二表达式：
    Figure PCTCN2016101770-appb-100009
    其中，Tn(x)＝∫Pn(x)dx，n≥0。
    子步骤D3：令非球面补偿器透射波前方程第一表达式与第二表达式相等，得到非球面补偿器透射波前方程迭代表达式：
    Figure PCTCN2016101770-appb-100010
  10. [根据细则26改正16.11.2016]　
    如权利要求5所述的测量方法，其特征在于，所述步骤E包括：
    子步骤E1：令非球面补偿器透射波前的传播距离di等于参考球面的与环形面形图对应的相对位移si；
    子步骤E2：由环形面形图的“零条纹”半径ri得到光线与光轴的夹角θi以及参考球面矢高Zi，由所述“零条纹”半径ri、所述光线与光轴的夹角θi、所述参考球面矢高Zi、所述传播距离di得到光线与非球面补偿器透射波前的交点{ρi}、以及非球面补偿器透射波前矢高{z(ρi)}；
    子步骤E3：设置最佳拟合球曲率c的初始值，将所述相对位移si、所述交点ρi、以及所述非球面补偿器透射波前矢高z(ρi)代入非球面补偿器透射波前方程迭代表达式进行第一迭代运算，得到非球面补偿器透射波前方程第二表达式；
    子步骤E4：将所述交点ρi代入子步骤E3得到的非球面补偿器透射波前方程第二表达式，重新计算非球面补偿器透射波前矢高z′(ρi)，并利用下式重新计算非球面补偿器透射波前的传播距离：
    Figure PCTCN2016101770-appb-100011
    其中，di′为重新计算的非球面补偿器透射波前的传播距离，z′(ρi)为重新计算的非球面补偿器透射波前矢高；
    子步骤E5：计算两次迭代之间非球面补偿器透射波前的传播距离差值di′-di，将传播距离差值与传播距离阈值比较；
    若传播距离差值大于传播距离阈值，将子步骤E4重新计算的传播距离di′作为子步骤E2的传播距离di，重复子步骤E2至子步骤E5；
    否则，将子步骤E3得到的非球面补偿器透射波前方程第二表达式，作为非球面补偿器透射波前方程。
  11. [根据细则26改正16.11.2016]
    如权利要求10所述的测量方法，其特征在于，所述子步骤E3的第一迭代运算包括：
    子分步骤E3a：将初始值赋予最佳拟合球曲率c；
    子分步骤E3b：将所述最佳拟合球曲率c、所述相对位移si、所述交点ρi、以及所述非球面补偿器透射波前矢高z(ρi)代入非球面补偿器透射波前方程迭代表达式，采用最小二乘法拟合出多项式{Pn(x)}的系数{bn}；
    子分步骤E3c：得到非球面补偿器透射波前方程第二表达式；
    子分步骤E3d：将所述交点ρi、以及所述非球面补偿器透射波前矢高z(ρi)代入非球面补偿器透射波前方程第二表达式，重新计算最佳拟合球曲率，将重新计算的最佳拟合球曲率与最佳拟合球曲率的初始值相减，获得最佳拟合球曲率差值；
    子分步骤E3e：将最佳拟合球曲率差值与最佳拟合球曲率阈值比较，
    若最佳拟合球曲率差值大于最佳拟合球曲率阈值，将子分步骤E3d重新计算的最佳拟合球曲率作为子分步骤E3b最佳拟合球曲率，重复执行子分步骤E3b至子分步骤E3e；
    否则，将子分步骤E3c得到的非球面补偿器透射波前方程第二表达式作为迭代运算结果输出。
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