CN103292738A

CN103292738A - Spherical surface shape error absolute detection method

Info

Publication number: CN103292738A
Application number: CN2013102595958A
Authority: CN
Inventors: 宋伟红; 侯溪; 李世芳; 赵文川; 吴高峰; 徐燕; 毛洁; 吴永前; 万勇建
Original assignee: Institute of Optics and Electronics of CAS
Current assignee: Institute of Optics and Electronics of CAS
Priority date: 2013-06-26
Filing date: 2013-06-26
Publication date: 2013-09-11
Anticipated expiration: 2033-06-26
Also published as: CN103292738B

Abstract

The invention discloses a spherical surface shape error absolute detection method, using the measurement data of multiple rotations and concentric translations of the measured spherical surface at the confocal position, and adopting a rotation translation algorithm based on Zernike polynomial fitting to construct a method about the measured spherical surface and The equation system of the Zernike polynomial coefficients on the reference surface is solved by using the least square method to obtain the Zernike polynomial coefficients, so as to obtain the absolute surface shape information of the measured spherical surface and the reference surface. This method can also be used in the detection of plane shape errors. Because the method adopts the idea of global optimization to solve the polynomial coefficients of the measured spherical surface and the reference surface at the same time, it can better suppress the systematic error and random noise, and has stronger anti-interference performance, which has important application value.

Description

A Method for Absolute Detection of Spherical Surface Error

技术领域technical field

本发明涉及一种面形误差的绝对检测方法，属于先进光学检测领域，特别是高精度的光学镜面绝对检测领域。The invention relates to an absolute detection method for surface shape errors, which belongs to the field of advanced optical detection, in particular to the field of high-precision absolute detection of optical mirror surfaces.

背景技术Background technique

随着现代光学技术的发展，光学元件的面形检测精度要求越来越高。高精度面形干涉检测一直是光学检测测试领域的热点和难点问题。球面作为光学系统中重要的元件，其检测精度受限于参考面的面形质量，而采用绝对检测技术可有效分离参考面和被测面的面形信息。With the development of modern optical technology, the requirements for surface shape detection accuracy of optical components are getting higher and higher. High-precision surface interference detection has always been a hot and difficult issue in the field of optical inspection and testing. As an important element in the optical system, the detection accuracy of the spherical surface is limited by the surface quality of the reference surface, and the absolute detection technology can effectively separate the surface information of the reference surface and the measured surface.

目前，常用的绝对检测方法有双球面法(K.E.Elssner，R.Burow，J.Grzanna，andR.Spolaczyk，“Absolute sphericity measurement，”Appl.Opt.28，4649-4661，1989；B.Truax，“Absolute interferometric testing ofspherical surfaces，”Proc.SPIE1400，61-68，1990)、奇偶函数法(SchreinerR，Schwider J，Lindlein N，and K.Mantel.“Absolute test of the referencesurface of a Fizeau interferometer through even/odd decompositions”，Appl.Opt，47，6134-6141，2008)和双通道自标定法(Jan Burke.“Rapid andreliable reference sphere calibration for Fizeau interferometry”，Opt Let，33，2536-2538，2008)。这些方法均包含有猫眼位置的测量，由于猫眼位置对调整误差不敏感，容易引入像散。另外一种常用的绝对检测方法是随机球标定法(R.E.Parks，C.J.Evans，L.Shao.“Calibration of interferometertransmission spheres”，Optical Fabrication and test Workshop OSATechnical Digest Series，12，80-83，1998)。该方法通过对一个标定球在大量随机位置进行相对检测，然后进行数据平均，标定球的误差随着检测次数的增加趋于零，平均结果将主要反映标准镜头参考面的面形误差信息。这种方法原理简单，但自动化检测装置的研制存在一定困难，检测过程比较耗时，其无法标定发散镜头。At present, the commonly used absolute detection method is the double spherical method (K.E.Elssner, R.Burow, J.Grzanna, and R.Spolaczyk, "Absolute sphericity measurement," Appl.Opt.28, 4649-4661, 1989; B.Truax, " Absolute interferometric testing of spherical surfaces," Proc.SPIE1400, 61-68, 1990), odd-even function method (SchreinerR, Schwider J, Lindlein N, and K.Mantel."Absolute test of the reference surface of a Fizeau interferometer through even/odd decompositions ", Appl.Opt, 47, 6134-6141, 2008) and two-channel self-calibration method (Jan Burke. "Rapid and reliable reference sphere calibration for Fizeau interferometry", Opt Let, 33, 2536-2538, 2008). These methods all include the measurement of the cat's eye position, since the cat's eye position is not sensitive to adjustment errors, it is easy to introduce astigmatism. Another commonly used absolute detection method is the random ball calibration method (R.E.Parks, C.J.Evans, L.Shao. "Calibration of interferometertransmission spheres", Optical Fabrication and test Workshop OSA Technical Digest Series, 12, 80-83, 1998). In this method, a calibration ball is relatively detected at a large number of random positions, and then the data is averaged. The error of the calibration ball tends to zero with the increase of the number of detections, and the average result will mainly reflect the surface error information of the standard lens reference surface. This method is simple in principle, but there are certain difficulties in the development of automatic detection equipment, the detection process is time-consuming, and it cannot calibrate the divergent lens.

针对以上方法的不足，德国和日本的研究人员提出了基于旋转平移的球面绝对检测方法(Bernd

and Günther Seitz，″Interferometrictesting of optical surfaces at its current limit，″Optik.112，392-398，2001；Hajime Ichikawa and Takahiro Yamamoto.“Apparatus and method forwavefront absolute calibration and method of synthesizing wavefronts，”U.S.patent5,982,490，9November1999)，该方法通过处理等角度旋转被测面的检测数据来获得被测面旋转非对称的面形误差，而通过处理共心平移前后的数据来获得被测面旋转对称的面形误差。由于这种方法存在kNθ的理论误差，无法准确获得被测面的面形误差信息。随后美国的研究人员提出基于像素未知量计算的旋转平移算法(JohannesA.Soons and UlfGriesmann，“Absolute interferometric tests of spherical surfaces based onrotational and translational shears，”Proc.SPIE8493，84930G，2012)，这种方法对于900像素的通光口径，每个位置的检测数据均存在1.2×10⁶个未知量和6×10⁶个方程，计算量巨大且耗时。同时，公开技术的研究人员提出了采用Zernike多项式拟合的旋转平移法(Dongqi Su，Erlong Miao，Yongxin Sui and Huaijiang Yang，“Absolute surface figure testing byshift-rotation method using Zernike polynomials，”Opt.Lett.37，3198-3200，2012)，但该方法是基于局部优化的，解方程组时只能解算出被测面或参考面的Zernike多项式系数，故对检测数据中的环境噪声较为敏感，当环境噪声较大时计算结果容易产生较大偏差。In view of the shortcomings of the above methods, researchers in Germany and Japan proposed a spherical absolute detection method based on rotation and translation (Bernd

and Günther Seitz，″Interferometrictesting of optical surfaces at its current limit，″Optik.112，392-398，2001；Hajime Ichikawa and Takahiro Yamamoto.“Apparatus and method forwavefront absolute calibration and method of synthesizing wavefronts，”USpatent5,982,490，9November1999 ), this method obtains the rotationally asymmetric surface shape error of the measured surface by processing the detection data of the measured surface rotated at an equal angle, and obtains the rotationally symmetric surface shape error of the measured surface by processing the data before and after concentric translation. Due to the theoretical error of kNθ in this method, the surface shape error information of the measured surface cannot be obtained accurately. Subsequently, researchers in the United States proposed a rotation and translation algorithm based on pixel unknown calculation (JohannesA.Soons and UlfGriesmann, "Absolute interferometric tests of spherical surfaces based on rotational and translational shears," Proc. SPIE8493, 84930G, 2012), this method is for 900 The light aperture of the pixel, the detection data of each position has 1.2×10 ⁶ unknowns and 6×10 ⁶ equations, the calculation is huge and time-consuming. At the same time, researchers in the public technology proposed a rotation-translation method using Zernike polynomial fitting (Dongqi Su, Erlong Miao, Yongxin Sui and Huaijiang Yang, "Absolute surface figure testing by shift-rotation method using Zernike polynomials," Opt.Lett.37 , 3198-3200, 2012), but this method is based on local optimization. When solving the equations, only the Zernike polynomial coefficients of the measured surface or the reference surface can be solved, so it is more sensitive to the environmental noise in the detection data. When the environmental noise When the value is large, the calculation result is likely to have a large deviation.

发明内容Contents of the invention

为了解决高精度面形检测过程中，被测球面面形误差和参考面面形误差无法准确分离的问题，本发明提出了一种球面面形误差绝对检测方法。In order to solve the problem that the measured spherical surface shape error and the reference surface shape error cannot be accurately separated during the high-precision surface shape detection process, the invention proposes an absolute detection method for the spherical surface shape error.

为了实现上述的目的，本发明提供的一种球面面形误差绝对检测方法，所述球面面形误差绝对检测的步骤如下：In order to achieve the above-mentioned purpose, the present invention provides a spherical surface error absolute detection method, the steps of the spherical surface error absolute detection are as follows:

步骤S1：利用干涉仪，选取F数相匹配的标准镜对被测球面进行面形检测，获得初始位置处的面形检测数据T₁(x，y)并表示如下：Step S1: Using an interferometer, select a standard mirror with a matching F number to detect the surface shape of the measured spherical surface, and obtain the surface shape detection data T ₁ (x, y) at the initial position, which is expressed as follows:

T₁(x，y)＝W(x，y)+RS(x，y) (1)T ₁ (x, y) = W (x, y) + RS (x, y) (1)

公式1中：(x，y)为电荷耦合器件上的直角坐标系，x，y表示直角坐标系中的坐标点；W(x，y)和RS(x，y)分别表示被测球面和参考面的面形误差；In Formula 1: (x, y) is the Cartesian coordinate system on the CCD, x, y represent the coordinate points in the Cartesian coordinate system; W(x, y) and RS(x, y) represent the measured spherical surface and The surface shape error of the reference surface;

步骤S2：保持干涉仪系统参数不变，将被测球面绕干涉仪系统光轴转动一角度Δθ，获得转动一角度处的被测球面检测数据T₂(x，y)并表示如下：Step S2: Keeping the parameters of the interferometer system unchanged, rotate the measured sphere around the optical axis of the interferometer system by an angle Δθ, and obtain the detection data T ₂ (x, y) of the measured sphere at a rotation angle, which is expressed as follows:

T₂(ρ，θ)＝W(ρ，θ+Δθ)+RS(ρ，θ) (2)T ₂ (ρ,θ)=W(ρ,θ+Δθ)+RS(ρ,θ) (2)

公式2中：W(ρ，θ+Δθ)表示旋转一角度后的被测球面面形误差，RS(ρ，θ)表示参考面的面形误差，(ρ，θ)为(x，y)对应的极坐标系；θ表示角向坐标，Δθ为旋转角度，ρ表示径向坐标；In formula 2: W(ρ, θ+Δθ) represents the surface shape error of the measured spherical surface after rotating an angle, RS(ρ, θ) represents the surface shape error of the reference surface, and (ρ, θ) is (x, y) The corresponding polar coordinate system; θ represents the angular coordinate, Δθ represents the rotation angle, and ρ represents the radial coordinate;

步骤S3：保持干涉仪系统参数不变，再将被测球面沿相对于初始位置的θ₁方向共心平移一定距离Δs，获得共心平移一距离处的被测球面检测数据T₃(x，y)并表示如下：Step S3: keep the parameters of the interferometer system unchanged, and then concentrically translate the measured spherical surface for a certain distance Δs along the direction of _θ1 relative to the initial position, and obtain the measured spherical surface detection data T ₃ (x, y) and expressed as follows:

T₃(x，y)＝W(x+sx，y+sy)+RS(x，y) (3)公式3中：sx＝Δs·cosθ₁，sy＝Δs·sinθ₁，s表示共心平移量；sx和sy分别表示被测球面沿X和Y方向的平移量，W(x+sx，y+sy)表示被测球面沿X和Y方向的平移量分别为sx和sy的面形误差；定义算子Γ(Δθ，Δs)如下表示：T ₃ (x, y)=W(x+sx, y+sy)+RS(x, y) (3) In formula 3: sx=Δs·cosθ ₁ , sy=Δs·sinθ ₁ , s means concentric Translation amount; sx and sy represent the translation amount of the measured spherical surface along the X and Y directions respectively, W(x+sx, y+sy) represents the surface shape of the measured spherical surface whose translation amounts along the X and Y directions are sx and sy respectively Error; define the operator Γ(Δθ, Δs) as follows:

$\{\begin{matrix} Δs Δs &NotEqual; &NotEqual; 00,, Γ Γ ((Δθ Δθ,, Δs Δs)) \cdot \cdot W W ((x x,, y the y)) = = W W ((x x + + sx sx,, y the y + + sy sy)),, sx sx = = Δs Δs \cdot &Center Dot; cos cos Δθ Δθ,, sy sy = = Δs Δs \cdot &Center Dot; sin sin Δθ Δθ \\ Δs Δs = = 00,, Γ Γ ((Δθ Δθ,, 00)) \cdot \cdot W W ((ρ ρ,, θ θ)) = = W W ((ρ ρ,, θ θ + + Δθ Δθ)),, \end{matrix} - - - - - - ((44))$

从而上述检测结果T₁(x，y)、T₂(x，y)、T₃(x，y)表示为如下的形式：Therefore, the above detection results T ₁ (x, y), T ₂ (x, y), and T ₃ (x, y) are expressed in the following form:

T_θ，s(x，y)＝Γ(θ，s)·W(x，y)+RS(x，y) (5)T _θ,s (x,y)=Γ(θ,s) W(x,y)+RS(x,y) (5)

Γ(θ，s)表示对被测球面进行的旋转和共心平移操作，T_θ，s(x，y)表示被测球面旋转平移后相应的面形检测数据；Γ(θ, s) represents the rotation and concentric translation operation on the measured spherical surface, and T _{θ, s} (x, y) represents the corresponding surface shape detection data after the measured spherical surface is rotated and translated;

步骤S4：利用矩阵运算工具，将上述方程式(5)改写为矩阵形式：Step S4: Using a matrix operation tool, rewrite the above equation (5) into a matrix form:

$(\begin{matrix} {A A}_{1111} & {A A}_{1212} \\ {A A}_{21 twenty one} & {A A}_{22 twenty two} \end{matrix}) \cdot &Center Dot; (\begin{matrix} {W W}_{a a} \\ {RS RS}_{c c} \end{matrix}) = = (\begin{matrix} {B B}_{11} \\ {B B}_{22} \end{matrix}) - - - - - - ((66))$

公式6中：In Formula 6:

${(({A A}_{1111}))}_{i i,, {i i}^{' '}} = = \underset{θ θ,, s the s}{Σ Σ} \underset{x x,, y the y}{Σ Σ} {Z Z}_{i i} ((x x,, y the y)) \cdot \cdot {Z Z}_{{i i}^{' '}} ((x x,, y the y)),,$

${(({A A}_{22 twenty two}))}_{i i,, {i i}^{' '}} = = \underset{θ θ,, s the s}{Σ Σ} \underset{x x,, y the y}{Σ Σ} [[Γ Γ ((θ θ,, s the s)) \cdot \cdot {Z Z}_{i i} ((x x,, y the y))]] \cdot &Center Dot; [[Γ Γ ((θ θ,, s the s)) \cdot \cdot {Z Z}_{{i i}^{' '}} ((x x,, y the y))]],,$

${(({A A}_{1212}))}_{i i,, {i i}^{' '}} = = \underset{θ θ,, s the s}{Σ Σ} \underset{x x,, y the y}{Σ Σ} {Z Z}_{i i} ((x x,, y the y)) \cdot &Center Dot; [[Γ Γ ((θ θ,, s the s)) \cdot &Center Dot; {Z Z}_{{i i}^{' '}} ((x x,, y the y))]],,$

${(({A A}_{21 twenty one}))}_{i i,, {i i}^{' '}} = = \underset{θ θ,, s the s}{Σ Σ} \underset{x x,, y the y}{Σ Σ} [[Γ Γ ((θ θ,, s the s)) \cdot &Center Dot; {Z Z}_{i i} ((x x,, y the y))]] \cdot \cdot {Z Z}_{{i i}^{' '}} ((x x,, y the y)),,$

${(({B B}_{11}))}_{i i} = = \underset{θ θ,, s the s}{Σ Σ} \underset{x x,, y the y}{Σ Σ} {Z Z}_{i i} ((x x,, y the y)) \cdot &Center Dot; {T T}_{θ θ,, s the s} ((x x,, y the y)),,$

${(({B B}_{22}))}_{i i} = = \underset{θ θ,, s the s}{Σ Σ} \underset{x x,, y the y}{Σ Σ} [[Γ Γ ((θ θ,, s the s)) \cdot &Center Dot; {Z Z}_{i i} ((x x,, y the y))]] \cdot &Center Dot; {T T}_{θ θ,, s the s} ((x x,, y the y)),,$

Z_i(x，y)为第i项Zernike多项式；W_a＝[a₁，a₂，…，a_n]^T为被测球面的Zernike多项式系数，RS_c＝[c₁，c₂，…，c_n]^T为参考面的Zernike多项式系数，T为转置，i＝1，2，…n，n为Zernike多项式项数，采用最小二乘法，解此方程式，得到：Z _i (x, y) is the i-th Zernike polynomial; W _a = [a ₁ , a ₂ , ..., a _n ] ^T is the Zernike polynomial coefficient of the measured spherical surface, RS _c = [c ₁ , c ₂ , ... , c _n ] ^T is the Zernike polynomial coefficient of the reference surface, T is the transposition, i=1, 2, ... n, n is the number of Zernike polynomial items, adopt the least squares method to solve this equation, and obtain:

$(\begin{matrix} {W W}_{a a} \\ {RS RS}_{c c} \end{matrix}) = = {(\begin{matrix} {A A}_{1111} & {A A}_{1212} \\ {A A}_{21 twenty one} & {A A}_{22 twenty two} \end{matrix})}^{- - 11} \cdot &Center Dot; (\begin{matrix} {B B}_{11} \\ {B B}_{22} \end{matrix});;$

A₁₁，A₁₂，A₂₂，A₂₁B₁，B₂等参量，只是为了计算方便引入的过程参量，没有具体的物理意义；A ₁₁ , A ₁₂ , A ₂₂ , A ₂₁ B ₁ , B ₂ and other parameters are only process parameters introduced for the convenience of calculation, and have no specific physical meaning;

步骤S5：被测球面的面形误差

参考面的面形误差

a1_，a₂…，a_n为被测球面的各项Zernike多项式系数，c₁c₂…，c_n为参考面的各项Zernike多项式系数，其分别为相应的Zernike多项式系数，a_i＝a₁，a₂，…，a_n，c_i＝c₁，c₂，…，c_n。Step S5: Surface error of the measured spherical surface

Surface error of the reference surface

a1 _, a ₂ ..., a _n are the Zernike polynomial coefficients of the measured spherical surface, c ₁ c ₂ ..., c _n are the Zernike polynomial coefficients of the reference surface, which are the corresponding Zernike polynomial coefficients, a _i = a ₁ , a ₂ , ..., a _n , c _i =c ₁ , c ₂ , ..., c _n .

其中，所述的被测球面的旋转角度和共心平移量大小根据检测精度要求来选择。Wherein, the rotation angle and the concentric translation amount of the measured spherical surface are selected according to the detection accuracy requirements.

其中，所述的被测球面旋转测量和共心平移测量次数可选，至少包括1次旋转及1次共心平移。Wherein, the number of times of the measured spherical surface rotation measurement and concentric translation measurement is optional, including at least one rotation and one concentric translation.

其中，所述的被测球面和参考面面形误差是以Zernike多项式来表示的。Wherein, the surface shape errors of the measured spherical surface and the reference surface are represented by Zernike polynomials.

其中，构建矩阵方程式时，同时包括被测球面和参考面的Zernike多项式系数，解算矩阵方程时，同时解算出被测球面和参考面的Zernike多项式系数。Among them, when constructing the matrix equation, the Zernike polynomial coefficients of the measured spherical surface and the reference surface are included at the same time, and when the matrix equation is solved, the Zernike polynomial coefficients of the measured spherical surface and the reference surface are simultaneously solved.

其中，所述的绝对检测方法，应用于平面面形误差的检测。Wherein, the absolute detection method is applied to the detection of plane shape errors.

本发明与现有技术相比的优势在于：Compared with the prior art, the present invention has the following advantages:

1)本发明提出的球面面形误差绝对检测方法基于Zernike多项式拟合，原理清晰，方法简单有效。1) The absolute detection method of spherical surface error proposed by the present invention is based on Zernike polynomial fitting, the principle is clear, and the method is simple and effective.

2)本发明提出的球面面形误差绝对检测方法是采用了全局优化的思路，同时解算出被测球面和参考面的Zernike多项式系数的，更能抑制系统误差和环境噪声，抗干扰性更强。2) The absolute detection method of spherical surface error proposed by the present invention adopts the idea of global optimization, and solves and calculates the Zernike polynomial coefficients of the measured spherical surface and the reference surface at the same time, which can better suppress system errors and environmental noise, and has stronger anti-interference performance .

3)本发明提出的球面面形误差绝对检测方法，无需猫眼位置的测量，可标定发散镜头，更可以短光腔的形式检测长曲率半径的球面，通用性好。3) The absolute detection method of the spherical surface error proposed by the present invention does not need the measurement of the cat's eye position, can calibrate the divergent lens, and can detect the spherical surface with a long radius of curvature in the form of a short optical cavity, and has good versatility.

附图说明Description of drawings

图1为本发明中被测球面为凹面镜时的卧式检测装置示意图。Fig. 1 is a schematic diagram of a horizontal detection device when the spherical surface to be measured is a concave mirror in the present invention.

图2为本发明中立式条件下对被测球面进行旋转测量的检测装置示意图。Fig. 2 is a schematic diagram of the detection device for measuring the rotation of the measured spherical surface under the neutral condition of the present invention.

图3为本发明中立式条件下对被测球面进行共心平移测量的检测装置示意图。Fig. 3 is a schematic diagram of the detection device for concentric translation measurement of the measured spherical surface under the neutral condition of the present invention.

图4为本发明中用发散镜头对长曲率半径被测球面进行检测的卧式检测装置示意图。Fig. 4 is a schematic diagram of a horizontal detection device using a diverging lens to detect a spherical surface with a long curvature radius in the present invention.

图5示出本发明球面面形误差绝对检测方法的流程图。Fig. 5 shows the flow chart of the absolute detection method of the spherical surface error of the present invention.

具体实施方式Detailed ways

下面结合附图以及具体实施方式来说明本发明。The present invention will be described below in conjunction with the accompanying drawings and specific embodiments.

如图1示出本发明中被测球面为凹面镜时的卧式检测装置，其中包括：标准镜1、参考面2、被测球面3、被测镜4、共心平移后的被测镜5，标准镜1的焦点与被测球面3的曲率中心重合，二者处于共心位置，将被测球面3绕系统光轴旋转后其与标准镜1的共心位置关系保持不变，将被测球面3沿某一方向作共心平移时，被测球面3与标准镜1的共心位置关系也保持不变。图中的XYZ是关于被测球面3位置的直角坐标系。As shown in Figure 1, the horizontal detection device when the measured spherical surface is a concave mirror in the present invention includes: a standard mirror 1, a reference surface 2, a measured spherical surface 3, a measured mirror 4, and a measured mirror after concentric translation 5. The focal point of the standard mirror 1 coincides with the center of curvature of the measured spherical surface 3, and the two are in a concentric position. After rotating the measured spherical surface 3 around the optical axis of the system, its concentric position relationship with the standard mirror 1 remains unchanged. When the measured spherical surface 3 is concentrically translated along a certain direction, the concentric positional relationship between the measured spherical surface 3 and the standard mirror 1 also remains unchanged. XYZ in the figure is a rectangular coordinate system about the position of the measured spherical surface 3.

如图2所示本发明中立式条件下对被测球面3进行旋转测量的检测装置，将被测球面3绕光轴旋转一角度Δθ后，被测球面3与标准镜1依然保持共心位置关系。图中的XYZ是关于参考面2和被测球面3位置的直角坐标系。As shown in Figure 2, the detection device for measuring the rotation of the tested spherical surface 3 under the neutral condition of the present invention, after the tested spherical surface 3 is rotated around the optical axis by an angle Δθ, the tested spherical surface 3 and the standard mirror 1 still remain concentric Positional relationship. XYZ in the figure is a rectangular coordinate system about the positions of the reference surface 2 and the measured spherical surface 3 .

如图3示出本发明中立式条件下对被测球面3进行共心平移测量的检测装置示意图，将被测球面3绕干涉仪系统光轴旋转一角度θ₁，并共心平移距离Δs后，其与标准镜1依然保持共心位置关系。Figure 3 shows a schematic diagram of the detection device for concentric translation measurement of the measured spherical surface 3 under the neutral condition of the present invention, the measured spherical surface 3 is rotated by an angle θ ₁ around the optical axis of the interferometer system, and the concentric translation distance Δs After that, it still maintains a concentric positional relationship with the standard mirror 1.

本发明方法利用被测球面3在共焦位置多次旋转和共心平移的测量数据，采用基于Zernike多项式拟合的旋转平移算法，构建关于被测球面3和参考面2的Zernike多项式系数的方程式，运用最小二乘法解得Zernike多项式系数，从而获得被测球面3和参考面2的绝对面形信息。由于该方法采用了全局优化的思路同时解算被测球面和参考面的多项式系数，因而更能抑制系统误差和随机噪声，抗干扰性更强，具有重要的应用价值。如图5示出利用本发明的装置实现对球面面形误差绝对检测，其方法的检测步骤如下：The method of the present invention utilizes the measurement data of multiple rotations and concentric translations of the measured spherical surface 3 at the confocal position, adopts a rotation-translation algorithm based on Zernike polynomial fitting, and constructs an equation about the Zernike polynomial coefficients of the measured spherical surface 3 and the reference surface 2 , using the least square method to solve the Zernike polynomial coefficients, so as to obtain the absolute surface shape information of the measured spherical surface 3 and the reference surface 2. Because the method adopts the idea of global optimization to solve the polynomial coefficients of the measured spherical surface and the reference surface at the same time, it can better suppress the systematic error and random noise, and has stronger anti-interference performance, which has important application value. As shown in Figure 5, the device of the present invention is utilized to realize the absolute detection of spherical surface error, and the detection steps of its method are as follows:

步骤S1：如图1所示，采用F数相匹配的标准镜1对被测球面3进行面形检测，获得初始位置处的面形检测数据T₁(x，y)(去除常数项、倾斜和离焦)，(x，y)为电荷耦合器件CCD上的直角坐标系，Step S1: As shown in Figure 1, use the standard mirror 1 with matching F number to detect the surface shape of the measured spherical surface 3, and obtain the surface shape detection data T ₁ (x, y) at the initial position (remove constant items, inclination and defocus), (x, y) is the Cartesian coordinate system on the charge-coupled device CCD,

T₁(x，y)＝W(x，y)+RS(x，y)，T ₁ (x, y) = W (x, y) + RS (x, y),

W(x，y)和RS(x，y)分别为被测球面3和参考面2的面形误差，x，y表示直角坐标系中的坐标点；W(x, y) and RS(x, y) are the surface error of the measured spherical surface 3 and the reference surface 2 respectively, and x, y represent the coordinate points in the Cartesian coordinate system;

步骤S2：如图2示出本发明中对被测球面3进行旋转测量的检测示意，保持干涉仪系统参数不变，将被测球面3绕干涉仪系统光轴转动一定角度Δθ(大小可选)，获得此处的被测球面3检测数据T₂(x，y)(去除常数项、倾斜和离焦)，即T₂(ρ，θ)＝W(ρ，θ+Δθ)+RS(ρ，θ)，其中W(ρ，θ+Δθ)表示旋转一角度后的被测球面面形误差，RS(ρ，θ)表示参考面的面形误差，(ρ，θ)为对应的极坐标系；θ表示角向坐标，Δθ为旋转角度，ρ表示径向坐标；Step S2: As shown in Figure 2, the test schematic diagram of the rotation measurement of the measured spherical surface 3 is shown in the present invention, and the interferometer system parameters are kept constant, and the measured spherical surface 3 is rotated by a certain angle Δθ around the optical axis of the interferometer system (optional size ), to obtain the detected spherical surface 3 detection data T ₂ (x, y) (remove constant terms, tilt and defocus), that is, T ₂ (ρ, θ)=W(ρ, θ+Δθ)+RS( ρ, θ), where W(ρ, θ+Δθ) represents the surface shape error of the measured spherical surface after an angle of rotation, RS(ρ, θ) represents the surface shape error of the reference surface, and (ρ, θ) is the corresponding pole Coordinate system; θ represents the angular coordinate, Δθ represents the rotation angle, and ρ represents the radial coordinate;

步骤S3：如图3所示本发明中对被测球面进行共心平移测量的检测示意，保持干涉仪系统参数不变，再将被测球面3沿相对于初始位置的θ₁(初始位置大小可选)方向共心平移一距离Δs(大小可选)，获得共心平移一距离处的被测球面3检测数据T₃(x，y)(去除常数项、倾斜和离焦)，即T₃(x，y)＝W(x+sx，y+sy)+RS(x，y)，sx＝Δs·cosθ₁，sy＝Δs·sinθ₁，sx＝Δs·cosθ₁，sy＝Δs·sinθ₁，s表示共心平移量；sx和sy分别表示被测球面沿X和Y方向的平移量，W(x+sx，y+sy)表示被测球面沿X和Y方向的平移量分别为sx和sy的面形误差；定义算子Γ(θ₁，Δs)如下表示：Step S3: as shown in Figure 3, the present invention carries out the detection schematic diagram of concentric translation measurement to the measured spherical surface, keeps the interferometer system parameter constant, then moves the measured spherical surface 3 along the θ ₁ (initial position size) relative to the initial position Optional) The direction is concentrically translated by a distance Δs (the size is optional), and the detection data T ₃ (x, y) of the measured spherical surface 3 at the concentrically translated distance is obtained (removing constant items, tilt and defocus), that is, T ₃ (x, y)=W(x+sx, y+sy)+RS(x, y), sx=Δs·cosθ ₁ , sy=Δs·sinθ ₁ , sx=Δs·cosθ ₁ , sy=Δs· sinθ ₁ , s represents the concentric translation; sx and sy respectively represent the translation of the measured spherical surface along the X and Y directions, W(x+sx, y+sy) represents the translation of the measured spherical surface along the X and Y directions, respectively is the surface error of sx and sy; define the operator Γ(θ ₁ , Δs) as follows:

被测球面3旋转测量和共心平移测量次数可选，至少包括1次旋转及1次共心平移，从而上述检测结果均可表示为如下的一般形式：The measured number of 3-rotation measurements and concentric translation measurements of the tested spherical surface is optional, including at least one rotation and one concentric translation, so the above-mentioned test results can be expressed in the following general form:

T_θ，s(x，y)＝Γ(θ，s)·W(x，y)+RS(x，y)；T _θ,s (x,y)=Γ(θ,s) W(x,y)+RS(x,y);

步骤S4：利用矩阵运算工具，将上述方程式改写为矩阵形式：Step S4: Use the matrix operation tool to rewrite the above equation into a matrix form:

$(\begin{matrix} A_{11} & A_{12} \\ A_{21} & A_{22} \end{matrix}) \cdot (\begin{matrix} W_{a} \\ {RS}_{c} \end{matrix}) = (\begin{matrix} B_{1} \\ B_{2} \end{matrix}),$ 其中， $(\begin{matrix} A_{11} & A_{12} \\ A_{twenty one} & A_{twenty two} \end{matrix}) &Center Dot; (\begin{matrix} W_{a} \\ {RS}_{c} \end{matrix}) = (\begin{matrix} B_{1} \\ B_{2} \end{matrix}),$ in,

${(A_{11})}_{i, i^{'}} = \underset{θ, s}{Σ} \underset{x, y}{Σ} Z_{i} (x, y) \cdot Z_{i^{'}} (x, y),$ 为第i项Zernike多项式， ${(A_{11})}_{i, i^{'}} = \underset{θ, the s}{Σ} \underset{x, the y}{Σ} Z_{i} (x, the y) \cdot Z_{i^{'}} (x, the y),$ is the i-th Zernike polynomial,

${(({A A}_{22 twenty two}))}_{i i,, {i i}^{' '}} = = \underset{θ θ,, s the s}{Σ Σ} \underset{x x,, y the y}{Σ Σ} [[Γ Γ ((θ θ,, s the s)) \cdot &Center Dot; {Z Z}_{i i} ((x x,, y the y))]] \cdot &Center Dot; [[Γ Γ ((θ θ,, s the s)) \cdot &Center Dot; {Z Z}_{{i i}^{' '}} ((x x,, y the y))]],,$

${(({A A}_{21 twenty one}))}_{i i,, {i i}^{' '}} = = \underset{θ θ,, s the s}{Σ Σ} \underset{x x,, y the y}{Σ Σ} [[Γ Γ ((θ θ,, s the s)) \cdot &Center Dot; {Z Z}_{i i} ((x x,, y the y))]] \cdot &Center Dot; {Z Z}_{{i i}^{' '}} ((x x,, y the y)),,$

${(({B B}_{11}))}_{i i} = = \underset{θ θ,, s the s}{Σ Σ} \underset{x x,, y the y}{Σ Σ} {Z Z}_{i i} ((x x,, y the y)) \cdot \cdot {T T}_{θ θ,, s the s} ((x x,, y the y)),,$

${(({B B}_{22}))}_{i i} = = \underset{θ θ,, s the s}{Σ Σ} \underset{x x,, y the y}{Σ Σ} [[Γ Γ ((θ θ,, s the s)) \cdot \cdot {Z Z}_{i i} ((x x,, y the y))]] \cdot &Center Dot; {T T}_{θ θ,, s the s} ((x x,, y the y)),,$

步骤S5：被测球面3的面形误差

参考面2的面形误差a₁，a₂…，a_n为被测球面的各项Zernike多项式系数，c₁c₂…，c_n为参考面的各项Zernike多项式系数，其分别为相应的Zernike多项式系数，a_i＝a₁，a₂…，a_n，c_i＝c₁，c₂…，c_n。Step S5: Surface error of the measured spherical surface 3

Surface shape error of reference surface 2 a ₁ , a ₂ ..., a _n are the Zernike polynomial coefficients of the measured spherical surface, c ₁ c ₂ ..., c _n are the Zernike polynomial coefficients of the reference surface, which are the corresponding Zernike polynomial coefficients respectively, a _i = a ₁ , a ₂ ..., a _n , c _i = c ₁ , c ₂ ..., c _n .

本发明的绝对检测方法可应用于以发散镜头6检测标定长曲率半径的被测球面7进行检测的示意，如图4所示。The absolute detection method of the present invention can be applied to a schematic diagram of detection by a diverging lens 6 to detect a calibrated long curvature radius spherical surface 7 , as shown in FIG. 4 .

同样本发明的绝对检测方法也可应用于平面面形误差的检测中。Likewise, the absolute detection method of the present invention can also be applied to the detection of plane shape errors.

以上所述，仅为本发明中的具体实施方式，但本发明的保护范围并不局限于此，任何熟悉该技术的人在本发明所揭露的技术范围内的局部修改或替换，都应涵盖在本发明的包含范围之内。The above is only a specific implementation mode in the present invention, but the protection scope of the present invention is not limited thereto, any partial modification or replacement within the technical scope disclosed in the present invention by anyone familiar with the technology shall cover within the scope of the present invention.

Claims

1. an absolute detection method of spherical surface error, is characterized in that comprising the following steps:

Step S1: Using an interferometer, select a standard mirror with a matching F number to detect the surface shape of the measured spherical surface, and obtain the surface shape detection data T ₁ (x, y) at the initial position, which is expressed as follows:

T ₁ (x, y) = W (x, y) + RS (x, y) (1)

In Formula 1: (x, y) is the Cartesian coordinate system on the CCD, x, y represent the coordinate points in the Cartesian coordinate system; W(x, y) and RS(x, y) represent the measured spherical surface and The surface shape error of the reference surface;

Step S2: Keeping the parameters of the interferometer system unchanged, rotate the measured sphere around the optical axis of the interferometer system by an angle Δθ, and obtain the detection data T ₂ (x, y) of the measured sphere at a rotation angle, which is expressed as follows:

T ₂ (ρ,θ)=W(ρ,θ+Δθ)+RS(ρ,θ) (2)

In formula 2: W(ρ, θ+Δθ) represents the surface shape error of the measured spherical surface after rotating an angle, RS(ρ, θ) represents the surface shape error of the reference surface, and (ρ, θ) is (x, y) The corresponding polar coordinate system; θ represents the angular coordinate, Δθ represents the rotation angle, and ρ represents the radial coordinate;

Step S3: keep the parameters of the interferometer system unchanged, and then concentrically translate the measured spherical surface for a certain distance Δs along the _θ1 direction relative to the initial position, and obtain the measured spherical surface detection data T ₃ (x, y) and expressed as follows:

T ₃ (x,y)=W(x+sx,y+sy)+RS(x,y) (3)

In formula 3: sx=Δs·cosθ ₁ , sy=Δs·sinθ ₁ , s represents the concentric translation amount; sx and sy represent the translation amount of the measured spherical surface along the X and Y directions respectively, W(x+sx, y+ sy) means that the translation of the measured spherical surface along the X and Y directions is the surface shape error of sx and sy respectively; the definition operator Γ(Δθ, Δs) is expressed as follows:

\{\begin{matrix} Δs Δs &NotEqual; &NotEqual; 00,, Γ Γ ((Δθ Δθ,, Δs Δs)) \cdot \cdot W W ((x x,, y the y)) = = W W ((x x + + sx sx,, y the y + + sy sy)),, sx sx = = Δs Δs \cdot \cdot cos cos Δθ Δθ,, sy sy = = Δs Δs \cdot \cdot sin sin Δθ Δθ \\ Δs Δs = = 00,, Γ Γ ((Δθ Δθ,, 00)) \cdot &Center Dot; W W ((ρ ρ,, θ θ)) = = W W ((ρ ρ,, θ θ + + Δθ Δθ)),, \end{matrix} - - - - - - ((44))

Therefore, the above detection results T ₁ (x, y), T ₂ (x, y), and T ₃ (x, y) are expressed in the following form:

T _θ,s (x,y)=Γ(θ,s) W(x,y)+RS(x,y) (5)

Γ(θ, s) represents the rotation and concentric translation operation on the measured spherical surface, and T _{θ, s} (x, y) represents the corresponding surface shape detection data after the measured spherical surface is rotated and translated;

Step S4: Using a matrix operation tool, rewrite the above equation (5) into a matrix form:

(\begin{matrix} {A A}_{1111} & {A A}_{1212} \\ {A A}_{21 twenty one} & {A A}_{22 twenty two} \end{matrix}) \cdot &Center Dot; (\begin{matrix} {W W}_{a a} \\ {RS RS}_{c c} \end{matrix}) = = (\begin{matrix} {B B}_{11} \\ {B B}_{22} \end{matrix}) - - - - - - ((66))

In Formula 6:

{(({A A}_{1111}))}_{i i,, {i i}^{' '}} = = \underset{θ θ,, s the s}{Σ Σ} \underset{x x,, y the y}{Σ Σ} {Z Z}_{i i} ((x x,, y the y)) \cdot &Center Dot; {Z Z}_{{i i}^{' '}} ((x x,, y the y)),,

{(({A A}_{22 twenty two}))}_{i i,, {i i}^{' '}} = = \underset{θ θ,, s the s}{Σ Σ} \underset{x x,, y the y}{Σ Σ} [[Γ Γ ((θ θ,, s the s)) \cdot &Center Dot; {Z Z}_{i i} ((x x,, y the y))]] \cdot &Center Dot; [[Γ Γ ((θ θ,, s the s)) \cdot &Center Dot; {Z Z}_{{i i}^{' '}} ((x x,, y the y))]],,

{(({A A}_{1212}))}_{i i,, {i i}^{' '}} = = \underset{θ θ,, s the s}{Σ Σ} \underset{x x,, y the y}{Σ Σ} {Z Z}_{i i} ((x x,, y the y)) \cdot &Center Dot; [[Γ Γ ((θ θ,, s the s)) \cdot &Center Dot; {Z Z}_{{i i}^{' '}} ((x x,, y the y))]],,

{(({A A}_{21 twenty one}))}_{i i,, {i i}^{' '}} = = \underset{θ θ,, s the s}{Σ Σ} \underset{x x,, y the y}{Σ Σ} [[Γ Γ ((θ θ,, s the s)) \cdot \cdot {Z Z}_{i i} ((x x,, y the y))]] \cdot \cdot {Z Z}_{{i i}^{' '}} ((x x,, y the y)),,

{(({B B}_{11}))}_{i i} = = \underset{θ θ,, s the s}{Σ Σ} \underset{x x,, y the y}{Σ Σ} {Z Z}_{i i} ((x x,, y the y)) \cdot \cdot {T T}_{θ θ,, s the s} ((x x,, y the y)),,

{(({B B}_{22}))}_{i i} = = \underset{θ θ,, s the s}{Σ Σ} \underset{x x,, y the y}{Σ Σ} [[Γ Γ ((θ θ,, s the s)) \cdot \cdot {Z Z}_{i i} ((x x,, y the y))]] \cdot \cdot {T T}_{θ θ,, s the s} ((x x,, y the y)),,

Z _i (x, y) is the i-th Zernike polynomial; W _a = [ _a 1, a ₂ , ..., a _n ] ^T is the Zernike polynomial coefficient of the measured spherical surface, RS _c = [c ₁ , c ₂ , ... , c _n ] ^T is the Zernike polynomial coefficient of the reference surface, T is the transposition, i=1, 2, ... n, n is the number of Zernike polynomial items, adopt the least squares method to solve this equation, and obtain:

(\begin{matrix} {W W}_{a a} \\ {RS RS}_{c c} \end{matrix}) = = {(\begin{matrix} {A A}_{1111} & {A A}_{1212} \\ {A A}_{21 twenty one} & {A A}_{22 twenty two} \end{matrix})}^{- - 11} \cdot \cdot (\begin{matrix} {B B}_{11} \\ {B B}_{22} \end{matrix});;

A ₁₁ , A ₁₂ , A ₂₂ , A ₂₁ B ₁ , B ₂ and other parameters are only process parameters introduced for the convenience of calculation, and have no specific physical meaning;

Step S5: Surface error of the measured spherical surface

Surface error of the reference surface

a ₁ , a ₂ ,..., a _n are the Zernike polynomial coefficients of the measured spherical surface, c ₁ c ₂ ..., c _n are the Zernike polynomial coefficients of the reference surface, which are the corresponding Zernike polynomial coefficients, a _i =a ₁ , a ₂ , . . . , a _n , c _i =c ₁ , c ₂ , . . . , c _n .

2. The absolute detection method of spherical surface error according to claim 1, characterized in that the rotation angle and concentric translation of the measured spherical surface are selected according to the detection accuracy requirements.

3. The absolute detection method of spherical surface error according to claim 1, characterized in that the number of times of rotation measurement and concentric translation measurement of the measured spherical surface is optional, including at least one rotation and one concentric translation.

4. The absolute detection method of spherical surface error according to claim 1, characterized in that, the surface error of the measured spherical surface and the reference surface is represented by a Zernike polynomial.

5. the spherical surface shape error absolute detection method according to claim 1, is characterized in that, when constructing matrix equation, simultaneously comprises the Zernike polynomial coefficient of measured spherical surface and reference surface, when solving matrix equation, solves and calculates measured simultaneously Zernike polynomial coefficients for sphere and reference surface.

6. The absolute detection method according to any one of claims 1-5, which is applied to the detection of plane shape errors.