CN101493375B - Splicing detection device based on small-caliber circular Hartmann-shack wavefront sensor - Google Patents

Abstract

Splicing detection device based on small-caliber circular Hartmann-shack wavefront sensor is characterized in that: comprises a Hartmann-shack wavefront sensor, an x-z two-dimensional electric control translation stage, a stepping motor controller, a computer, a mirror surface to be detected and a data acquisition card; the Hartmann-shack wavefront sensor is positioned behind the mirror surface to be detected to detect the mirror surface to be detected, a light spot lattice is formed on the Hartmann-shack wavefront sensor, and the light spot data is collected by the data acquisition card and transmitted to the computer for storage; and the computer sends an instruction to the stepping motor controller to control the two-dimensional electric control translation stage to move along the x axis and the z axis to scan and detect the mirror surface to be detected, the data acquisition card is used for sequentially acquiring light spot data at the wavelet surface of each frame, and then the centroid algorithm, the splicing method and the recovery algorithm are used for obtaining the wavelet surface to be detected. By adopting the device and the method, the formula is improved by analyzing and neglecting the defocusing error term theoretically; and the principle error of the translation error is eliminated, the splicing precision is improved, and the complexity of solving and calculating splicing parameters is reduced.

Description

Translated fromChinese

基于小口径圆形哈特曼-夏克波前传感器的拼接检测装置Splicing Detection Device Based on Small Aperture Circular Hartmann-Shack Wavefront Sensor

技术领域technical field

本发明涉及光学检测领域，特别是涉及一种大口径光学系统或元件的拼接检测系统。The invention relates to the field of optical detection, in particular to a large-diameter optical system or a splicing detection system for components.

背景技术Background technique

大口径光学元件正越来越多的应用于天文观测、空间光学、遥感观测、激光核聚变系统等领域，其加工和检测技术是当今国内外研究的难点和热点。在采用常规的测量方式时，随着口径的增大，在考虑成本的前提下提高测量精度是非常困难的。而采用小口径仪器去测量大口径光学元件能更好的解决提高测量精度与降低设备成本之间的矛盾，为光学元件的检测提供一种新方法。Large-aperture optical components are being increasingly used in astronomical observation, space optics, remote sensing observation, laser fusion systems and other fields, and their processing and detection technology is a difficult and hot research topic at home and abroad. When using the conventional measurement method, it is very difficult to improve the measurement accuracy under the premise of considering the cost as the caliber increases. The use of small-caliber instruments to measure large-diameter optical components can better solve the contradiction between improving measurement accuracy and reducing equipment costs, and provides a new method for the detection of optical components.

目前已出现了“子孔径拼接干涉仪”的检测方案。王孝坤，王丽辉，郑立功等在“子孔径拼接技术在大口径高陡度非球面检测中的应用”(强激光与粒子束，2007.7.Vol.19：1144-1148)中，张蓉竹，石琪凯，许乔等在“子孔径拼接干涉检测实验研究”(光学技术，2004.3(30))均实现了干涉仪拼接检测，但仅仅是三帧拼接，未扩展到更大的需多帧拼接的待测光学表面。At present, a detection scheme of "sub-aperture splicing interferometer" has appeared. Wang Xiaokun, Wang Lihui, Zheng Ligong, etc. in "Application of sub-aperture splicing technology in the detection of large-aperture and high-steep aspheric surfaces" (Strong Laser and Particle Beam, 2007.7.Vol.19: 1144-1148), Zhang Rongzhu, Shi Qikai , Xu Qiao et al. have achieved interferometer stitching detection in the "Experimental Research on Sub-aperture Stitching Interference Detection" (Optical Technology, 2004.3 (30)), but only three-frame stitching has not been extended to larger waiting frames that require multi-frame stitching. Measuring optical surfaces.

如图3所示，图中w1，w2分别表示在大口径待测面上进行的两次检测区域，它们之间有一定面积的重叠(图中阴影部分)，每一个区域对应的相位分布分别用φ(x，y)和φ′(x-x₀，y-y₀)表示，(x₀，y₀)为两个测量区域坐标系的相对移动量。理论上两次测量在重叠区域内的数据信息应该是相同的，然而在实际检测过程中，由于平移台的移动误差必然使得前后两次测量到的相位分布不在同一个面上，这就导致重叠区域两侧检测结果不一致。因此要对重叠区域的斜率测量数据进行最小二乘拟合得到两个子波面的拼接参数，把两个子波面斜率图统一到一个坐标系里。如果以w₁区域的相位分布φ(x，y)为基准，则对于现有的干涉仪检测有：As shown in Figure 3, w1 and w2 in the figure respectively represent the two detection areas carried out on the large-diameter surface to be measured, and there is a certain area of overlap between them (the shaded part in the figure), and the phase distribution corresponding to each area is respectively Expressed by φ(x, y) and φ′(xx₀ , yy₀ ), (x₀ , y₀ ) is the relative movement of the coordinate systems of the two measurement areas. Theoretically, the data information of the two measurements in the overlapping area should be the same. However, in the actual detection process, due to the movement error of the translation stage, the phase distributions of the two measurements are not on the same plane, which leads to overlap. The detection results on both sides of the area are inconsistent. Therefore, it is necessary to perform least square fitting on the slope measurement data in the overlapping area to obtain the splicing parameters of the two wavelets, and unify the slope maps of the two wavelets into one coordinate system. If the phase distribution φ(x, y) of the region w₁ is taken as the reference, for the existing interferometer detection:

φ(x，y)＝φ′(x-x₀，y-y₀)+ax+by+c(x²+y²)+d            (1)φ(x,y)=φ′(xx₀ ,yy₀ )+ax+by+c(x² +y² )+d (1)

其中a、b、c和d分别为两个子波面测量过程中的x轴和y轴的相对倾斜、离焦和平移误差。由最小二乘法有：where a, b, c, and d are the relative tilt, defocus, and translation errors of the x-axis and y-axis during the measurement of the two sub-wavefronts, respectively. According to the method of least squares:

δ＝∑{φ(x_i，y_i)-[φ′(x_i-x₀，y_i-y₀)+ax+by+c(x_i²+y_i²)+d]}²→min            (2)δ＝∑{φ(x_i , y_i )-[φ′(x_i -x₀ , y_i -y₀ )+ax+by+c(x_i² +y_i² )+d]}² → min (2)

令：可得：make: Available:

$\left(\begin{array}{c}\mathrm{<span><span>a</span>a</span>}\\ \mathrm{<span><span>b</span>b</span>}\\ \mathrm{<span><span>c</span>c</span>}\\ \mathrm{<span><span>d</span>d</span>}\end{array}\right)<span><span>=</span>=</span>{\left(\begin{array}{cccc}\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}{\mathrm{<span><span>x</span><figure-callout\; label="x"\; filenames="H2009100782563E00011.png"\; state="\{\{state\}\}">x</figure-callout></span>}}^{\mathrm{<span><span>2</span>2</span>}}& \mathrm{<span><span>\&Sigma;xy</span>\&Sigma;xy</span>}& \mathrm{<span><span>\&Sigma;x</span>\&Sigma;x</span>}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>& \mathrm{<span><span>\&Sigma;x</span>\&Sigma;x</span>}\\ \mathrm{<span><span>\&Sigma;xy</span>\&Sigma;xy</span>}& \mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}{\mathrm{<span><span>y</span>the<figure-callout\; label="y"\; filenames="H2009100782563E00011.png"\; state="\{\{state\}\}">y</figure-callout></span>}}^{\mathrm{<span><span>2</span>2</span>}}& \mathrm{<span><span>\&Sigma;y</span>\&Sigma;y</span>}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>& \mathrm{<span><span>\&Sigma;y</span>\&Sigma;y</span>}\\ \mathrm{<span><span>\&Sigma;x</span>\&Sigma;x</span>}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>& \mathrm{<span><span>\&Sigma;y</span>\&Sigma;y</span>}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>& \mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}{<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}& \mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>\\ \mathrm{<span><span>\&Sigma;x</span>\&Sigma;x</span>}& \mathrm{<span><span>\&Sigma;y</span>\&Sigma;y</span>}& \mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>& \mathrm{<span><span>n</span>no</span>}\end{array}\right)}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}\left(\begin{array}{c}\mathrm{<span><span>\&Sigma;x\&Delta;</span>\&Sigma;x\&Delta;</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>)</span>)</span>\\ \mathrm{<span><span>\&Sigma;y\&Delta;</span>\&Sigma;y\&Delta;</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>)</span>)</span>\\ \mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>)</span>)</span>\\ \mathrm{<span><span>\&Sigma;\&Delta;</span>\&Sigma;\&Delta;</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>)</span>)</span>\end{array}\right)<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>3</span>3</span>}<span><span>)</span>)</span>$

其中Δ(x，y)＝φ(x_i，y_i)-φ′(x_i-x₀，y_i-y₀)为两个相交子波面各个采样点处测量值之差，n为重叠区域采样点个数。每个子波面都需要计算四个拼接参数(a，b，c，d)。同时，干涉仪拼接检测方案还存在实验条件苛刻，对大气湍流、温度、振动、噪声敏感；每次移动后需要重新调整装置，检测速度慢等局限性。Where Δ(x, y) = φ(xi_, y_i )-φ′(xi_-x0 , y_i -y₀ ) is the difference between the measured values at each sampling point of the two intersecting wavelets, and n is the overlap The number of sampling points in the area. Four stitching parameters (a, b, c, d) need to be calculated for each sub-wavefront. At the same time, the interferometer splicing detection scheme also has limitations such as harsh experimental conditions, sensitivity to atmospheric turbulence, temperature, vibration, and noise; the need to readjust the device after each movement, and slow detection speed.

T.D.Raymond，D.R.Neal等在“High-speed，non-interferometric nanotopographiccharacterization of Si wafer surfaces，”(Proc.SPIE 4809，2002.208-216)中采用方形哈特曼-夏克波前传感器对硅片表面形貌进行了拼接检测，但未构建完整的适于任意拼接帧数的通用数学模型，且对于使用圆形口径哈特曼为主的国内外市场缺乏普适性。T.D.Raymond, D.R.Neal et al. used a square Hartmann-Shack wavefront sensor in "High-speed, non-interferometric nanotopographiccharacterization of Si wafer surfaces," (Proc.SPIE 4809, 2002.208-216) to measure the surface topography of silicon wafers. Splicing detection, but a complete general mathematical model suitable for any number of splicing frames has not been constructed, and it lacks universality for domestic and foreign markets that mainly use circular aperture Hartmann.

发明内容Contents of the invention

本发明要解决的技术问题是：克服现有技术的不足，设计出一种结构简单调试方便、检测速度快且精度高的拼接检测系统，并采用全局优化拼接方法求得各帧子波面斜率图相对于基准子波面斜率图的绝对拼接参数，大大降低了多帧扫描中误差累积和误差传递的影响，有利于拼接精度的提高。The technical problem to be solved by the present invention is: to overcome the deficiencies of the prior art, design a splicing detection system with simple structure, convenient debugging, fast detection speed and high precision, and use the global optimization splicing method to obtain the subwave surface slope diagram of each frame Compared with the absolute stitching parameters of the reference wavelet slope map, the influence of error accumulation and error transmission in multi-frame scanning is greatly reduced, which is beneficial to the improvement of stitching accuracy.

本发明要解决其技术问题所采用的技术方案是：基于小口径圆形哈特曼-夏克波前传感器的拼接检测装置，其特征在于：包含有哈特曼-夏克波前传感器、x-z二维电控平移台、步进电机控制器、计算机、待测镜面及数据采集卡；哈特曼-夏克波前传感器对待测镜面某个子区域进行检测，并且在哈特曼-夏克波前传感器形成光斑点阵，由数据采集卡采集上述光斑数据并传输到计算机中存储；计算机向步进电机控制器发出指令，控制二维电控平移台沿x轴与z轴移动对待测镜面进行扫描检测，利用数据采集卡依次采得各帧子波面处的光斑数据，然后利用质心算法、拼接方法及复原算法得到待测波面。The technical solution adopted by the present invention to solve the technical problems is: a splicing detection device based on a small-diameter circular Hartmann-Shack wavefront sensor, which is characterized in that it includes a Hartmann-Shack wavefront sensor, x-z two-dimensional electronic control Translation platform, stepper motor controller, computer, mirror to be tested and data acquisition card; Hartmann-Shack wavefront sensor detects a certain sub-area of the mirror to be tested, and forms a light spot array on the Hartmann-Shack wavefront sensor. The data acquisition card collects the above spot data and transmits them to the computer for storage; the computer sends instructions to the stepper motor controller to control the two-dimensional electronically controlled translation platform to move along the x-axis and z-axis to scan and detect the mirror surface to be tested, and use the data acquisition card to sequentially The light spot data at the sub-wavefronts of each frame is collected, and then the wavefront to be measured is obtained by using the centroid algorithm, splicing method and restoration algorithm.

所述的哈特曼-夏克波前传感器由点光源、准直透镜、反射镜、CCD及缩/扩束系统组成；点光源发出的光经过准直透镜形成平行光束，该平行光束经过反射镜转折后再经过扩束系统照射到待测镜面，待测镜面反射的光线经缩束系统，再经反射镜的透射在CCD上形成光斑点阵。The Hartmann-Shack wavefront sensor is composed of a point light source, a collimating lens, a mirror, a CCD and a beam shrinking/expanding system; the light emitted by the point light source passes through the collimating lens to form a parallel beam, and the parallel beam is turned by the mirror After that, it is irradiated to the mirror surface to be tested through the beam expander system, and the light reflected by the mirror surface to be tested passes through the beam shrinkage system, and then is transmitted through the mirror to form a spot matrix on the CCD.

所述的扩/缩束系统由微透镜阵列与过渡成像光组组成。The beam expansion/contraction system is composed of a microlens array and a transitional imaging light group.

所述的拼接方法采用的全局优化拼接方法处理重叠区域中的采样数据，得到各个子波面斜率图相对于基准子波面斜率图的拼接参数，恢复出全孔径波面斜率图。The splicing method adopts the global optimization splicing method to process the sampling data in the overlapping area, obtain the splicing parameters of each sub-wavefront slope map relative to the reference sub-wavefront slope map, and recover the full-aperture wavefront slope map.

所述的全局化优化拼接方法为：The described global optimization splicing method is:

首先，对现有的干涉仪检测的公式(1)，First, the formula (1) detected by the existing interferometer,

φ(x，y)＝φ′(x-x₀，y-y₀)+ax+by+c(x²+y²)+d            (1)φ(x,y)=φ′(xx₀ ,yy₀ )+ax+by+c(x² +y² )+d (1)

其中：a、b、c和d分别为两个子波面测量过程中的x轴和y轴的相对倾斜、离焦和平移误差系数；但在实际工程中，考虑到短距离的光传输，当菲涅尔数Nf＞1000时，因衍射而产生的波前变化的误差将在1％以下，即波前畸变可以忽略不计，而实际测量中二维电动平移台的piston误差是毫米量级的，因此可以忽略离焦项，(1)可简化为：Among them: a, b, c and d are the relative tilt, defocus and translation error coefficients of the x-axis and y-axis in the measurement process of the two sub-wavefronts respectively; but in actual engineering, considering the short-distance optical transmission, when the When the Neel number Nf>1000, the error of the wavefront change due to diffraction will be less than 1%, that is, the wavefront distortion can be ignored, while the piston error of the two-dimensional electric translation stage in actual measurement is on the order of millimeters, Therefore, the out-of-focus term can be ignored, and (1) can be simplified as:

φ(x，y)＝φ′(x-x₀，y-y₀)+ax+by+d                        (4)φ(x,y)=φ′(xx₀ ,yy₀ )+ax+by+d (4)

分别对x、y求导得：Derivatives for x and y respectively:

$\left\{\begin{array}{c}\mathrm{<span><span>Gx</span>Gx</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>)</span>)</span><span><span>=</span>=</span>{\mathrm{<span><span>Gx</span>Gx</span>}}^{<span><span>\&prime;</span>\&prime;</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>-</span>-</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>+</span>+</span>\mathrm{<span><span>a</span>a</span>}\\ \mathrm{<span><span>Gy</span>Gy</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>)</span>)</span><span><span>=</span>=</span>{\mathrm{<span><span>Gy</span>Gy</span>}}^{<span><span>\&prime;</span>\&prime;</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>-</span>-</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}\end{array}\right.<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>5</span>5</span>}<span><span>)</span>)</span>$

哈特曼-夏克波前传感器检测消除了平移误差系数d的影响，仅仅考虑相对倾斜系数a、b，从而降低了拼接参数求解复杂度，以x方向斜率为例，即有：The Hartmann-Shack wavefront sensor detection eliminates the influence of the translation error coefficient d, and only considers the relative tilt coefficients a and b, thereby reducing the complexity of solving the stitching parameters. Taking the slope in the x direction as an example, there are:

δ_x＝∑{Gx(x_i，y_i)-[Gx′(x_i-x₀，y_i-y₀)+a]}²→min                (6)δ_x ＝∑{Gx(x_i , y_i )-[Gx′(x_i -x₀ , y_i -y₀ )+a]}² →min (6)

将公式(6)对a求导并令其值为零，可以求得拼接参数a；Y方向的斜率图类似；The splicing parameter a can be obtained by deriving formula (6) with respect to a and setting its value to zero; the slope diagram in the Y direction is similar;

当拼接区域大于两个时，假设共有M个子波面拼接，可以先选定其中任意的某个子波面作为基准，一般选择中心区域的子波面m作为参考标准；假设拼接参数分别为(a_i，b_i，c_1i，c_2i)(0≤i≤M-1，i≠m)，以x方向斜率为例，则各个子波面斜率图与基准子波面斜率图的关系为：When the splicing area is larger than two, assuming that there are M sub-wavefronts to be spliced, any one of them can be selected as a reference. Generally, the sub-wavefront m in the central area is selected as the reference standard; assuming that the splicing parameters are (a_i , b_i , c_1i , c_2i )(0≤i≤M-1, i≠m), taking the slope in the x direction as an example, the relationship between each wavelet slope map and the reference wavelet slope map is:

G_m(x，y)＝G_i(x-x₀，y-y₀)+a_i(0≤i≤M-1，i≠m)            (7)G_m (x, y) = G_i (xx₀ , yy₀ )+a_i (0≤i≤M-1, i≠m) (7)

利用最小二乘法：Using the method of least squares:

$\mathrm{<span><span>S</span>S</span>}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>\&NotEqual;</span>\&NotEqual;</span>\mathrm{<span><span>m</span>m</span>}}{\overset{\mathrm{<span><span>M</span>m</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}}{<span><span>\{</span>\{</span>\mathrm{<span><span>G</span>G</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>[</span>[</span>{\mathrm{<span><span>G</span>G</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>-</span>-</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>+</span>+</span>{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>]</span>]</span><span><span>\}</span>\}</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>\&RightArrow;</span>\&Right\; Arrow;</span>\mathrm{<span><span>min</span>min</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>8</span>8</span>}<span><span>)</span>)</span>$

令：$\frac{\&PartialD;S}{\&PartialD;a_i}=0$(0≤i≤M-1，i≠m)            (9)make:$\frac{\&PartialD;S}{\&PartialD;a_i}=0$ (0≤i≤M-1, i≠m) (9)

若令：$P_{\mathrm{ij}}=\underset{i\&cap;j}{\mathrm{\&Sigma;}}\mathrm{\&Delta;}(x,y)$Q_ij＝n_ij    R_i＝a_i        (10)If order:$P_{\mathrm{ij}}=\underset{i\&cap;j}{\mathrm{\&Sigma;}}\mathrm{\&Delta;}(x,\mathrm{the\; y})$ Q_ij =n_ij R_i =a_i (10)

其中Δ(x，y)＝G_i(x-x_i，y-y_i)-G_j(x-x_j，y-y_j)为第i，j帧子波面重叠区域内各个采样点处测量值之差，n_ij为采样点个数。则有：Where Δ(x, y)=G_i (xx_i , yy_i )-G_j (xx_j , yy_j ) is the difference between the measured values at each sampling point in the i-th and j-frame sub-wavefront overlapping areas, and n_ij is The number of sampling points. Then there are:

$<span><span>[</span>[</span>{<span><span>(</span>(</span>\underset{\mathrm{<span><span>k</span>k</span>}}{\overset{\mathrm{<span><span>M</span>m</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>ik</span>ik</span>}}<span><span>)</span>)</span>}_{\mathrm{<span><span>i</span>i</span>}}<span><span>]</span>]</span><span><span>=</span>=</span><span><span>[</span>[</span>{<span><span>(</span>(</span>{\mathrm{<span><span>Q</span>Q</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}\underset{\mathrm{<span><span>k</span>k</span>}}{\overset{\mathrm{<span><span>M</span>m</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>Q</span>Q</span>}}_{\mathrm{<span><span>ik</span>ik</span>}}<span><span>)</span>)</span>}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>]</span>]</span><span><span>[</span>[</span>{<span><span>(</span>(</span>{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>}_{\mathrm{<span><span>i</span>i</span>}}<span><span>]</span>]</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>11</span>11</span>}<span><span>)</span>)</span>$

其中${\mathrm{\&delta;}}_{\mathrm{ij}}=\left\{\begin{array}{cc}1& \mathrm{if\; i}=j\\ 0& \mathrm{if\; i}\&NotEqual;j\end{array}\right.$利用式(11)可得到各个子波面相对于基准子波面的拼接参数。in${\mathrm{\&delta;}}_{\mathrm{ij}}=\left\{\begin{array}{cc}1& \mathrm{if\; i}=j\\ 0& \mathrm{if\; i}\&NotEqual;j\end{array}\right.$ The splicing parameters of each wavelet relative to the reference wavelet can be obtained by using formula (11).

所述的待测镜面可以固定在二维电控平移台上，并随二维电控平移台同步移动；而保持哈特曼-夏克波前传感器固定来进行检测。The mirror surface to be measured can be fixed on the two-dimensional electronically controlled translation platform and move synchronously with the two-dimensional electronically controlled translation platform; and the Hartmann-Shack wavefront sensor is kept fixed for detection.

所述的哈特曼-夏克波前传感器口径的大小和形状可以改变。The size and shape of the Hartmann-Shack wavefront sensor aperture can vary.

本发明的工作原理：本发明以小口径圆形哈特曼-夏克波前传感器为核心元件，由于传感器测量的值是各个子波面的斜率值，克服了沿着垂直待测面方向的直线误差(piston error)的影响；同时采用的最小二乘拟合方法降低了每帧座标系之间的倾斜误差(tip/tilt error)的影响。Principle of work of the present invention: the present invention takes the small-diameter circular Hartmann-Shack wavefront sensor as the core element, because the value measured by the sensor is the slope value of each sub-wave surface, it overcomes the linear error along the vertical direction of the surface to be measured ( The influence of the piston error); the least square fitting method adopted at the same time reduces the influence of the tilt error (tip/tilt error) between the coordinate systems of each frame.

本发明与现有技术相比的有益效果是：本发明采用基于H-S波前传感器的拼接检测装置，消除了平移误差(干涉仪拼接检测中主要的误差来源)此项原理误差，且通过理论分析忽略了离焦误差项，从而提高了拼接精度并降低了拼接参数求解计算复杂度。同时，采用圆形小口径的哈特曼-夏克波前传感器，成本低且系统结构简单；由于哈特曼-夏克不需要像干涉仪一样每次移动后重新调整，能在短时间内完成大口径光学元件的扫描，检测效率高；利用二维电控平移台控制，定位精度高且操作简易；所采用的全局优化拼接方法求得的是各帧子波面斜率图相对于基准子波面斜率图的绝对拼接参数，大大降低了多帧扫描中误差累积和误差传递的影响，有利于拼接精度的提高。Compared with the prior art, the present invention has the beneficial effects that: the present invention adopts the splicing detection device based on the H-S wavefront sensor, which eliminates the principle error of translation error (the main error source in the interferometer splicing detection), and through theoretical analysis The out-of-focus error term is ignored, which improves the stitching accuracy and reduces the computational complexity of solving the stitching parameters. At the same time, the circular small-caliber Hartmann-Shack wavefront sensor is used, which is low in cost and simple in system structure; since Hartmann-Shack does not need to be readjusted after each movement like an interferometer, it can complete large-scale detection in a short time The scanning of aperture optical components has high detection efficiency; the use of two-dimensional electronically controlled translation stage control has high positioning accuracy and easy operation; the global optimization stitching method adopted is obtained by comparing the wavelet slope graph of each frame with the reference wavelet slope graph The absolute splicing parameters greatly reduce the influence of error accumulation and error transmission in multi-frame scanning, which is conducive to the improvement of splicing accuracy.

附图说明Description of drawings

图1为本发明的结构示意图；Fig. 1 is a structural representation of the present invention;

图2为各个子波面在哈特曼动态的反应示意图；Figure 2 is a schematic diagram of the response of each sub-wave surface in the Hartmann dynamic;

图3为拼接检测相邻两帧示意图；Fig. 3 is a schematic diagram of splicing detection of two adjacent frames;

图4为本发明测量方法的流程图；Fig. 4 is the flowchart of measuring method of the present invention;

图中：1、点光源，2、准直透镜，3、反射镜，4、CCD，5、微透镜阵列，6、过渡成像光组，7、扩束系统，8、哈特曼-夏克波前传感器，9、X-Z双轴电控平移台待测镜面，10、步进电机控制器，11、计算机，12、待测镜面，13、数据采集卡。In the figure: 1. Point light source, 2. Collimator lens, 3. Mirror, 4. CCD, 5. Microlens array, 6. Transition imaging light group, 7. Beam expander system, 8. Hartmann-Shack wavefront Sensor, 9. X-Z biaxial electronically controlled translation stage mirror surface to be tested, 10. stepper motor controller, 11. computer, 12. mirror surface to be tested, 13. data acquisition card.

具体实施方式Detailed ways

下面结合附图及具体实施方式详细介绍本发明。The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

如图1所示，本发明的基于小口径圆形哈特曼-夏克波前传感器的拼接检测装置包含有哈特曼-夏克波前传感器8、x-z二维电控平移台9、步进电机控制器10、计算机11、待测镜面12及数据采集卡13；哈特曼-夏克波前传感器(8)对待测镜面(12)的某个区域进行检测并且在哈特曼-夏克波前传感器8形成光斑点阵，由数据采集卡13采集上述光斑数据并传输到计算机11中存储；计算机11向步进电机控制器10发出指令，控制二维电控平移台9沿x轴与z轴移动对待测镜面12进行扫描检测，利用数据采集卡13依次采得各帧子波面处的光斑数据，然后利用质心算法、拼接方法及复原算法得到待测波面。As shown in Figure 1, the splicing detection device based on the small-diameter circular Hartmann-Shack wavefront sensor of the present invention includes a Hartmann-Shack wavefront sensor 8, an x-z two-dimensional electronically controlledtranslation stage 9, and astepper motor controller 10, computer 11, mirror surface to be measured 12 anddata acquisition card 13; Hartmann-Shack wavefront sensor (8) detects a certain area of mirror surface to be measured (12) and forms light spot at Hartmann-Shack wavefront sensor 8 The above-mentioned light spot data is collected by thedata acquisition card 13 and stored in the computer 11; the computer 11 sends instructions to thestepper motor controller 10 to control the two-dimensional electronically controlledtranslation stage 9 to move along the x-axis and z-axis to themirror surface 12 to be tested Perform scanning detection, use thedata acquisition card 13 to sequentially collect the light spot data at the sub-wavefronts of each frame, and then use the centroid algorithm, splicing method and restoration algorithm to obtain the wavefront to be tested.

所述的哈特曼-夏克波前传感器8由点光源1、准直透镜2、反射镜3、CCD4及缩/扩束系统7组成；在每帧子波面处，点光源1发出的光经过准直透镜2形成平行光束，该平行光束经过反射镜3转折后再经过由过渡成像光组6与微透镜阵列5组成的扩束系统7照射到待测镜面12，待测镜面12反射的光线经缩束系统7，再经反射镜3的透射在CCD4上形成光斑点阵。Described Hartmann-Shack wavefront sensor 8 is made up of point light source 1,collimator lens 2,reflector 3, CCD4 and contraction/expansion beam system 7; Thestraight lens 2 forms a parallel light beam, which is turned by thereflector 3 and then irradiated to themirror surface 12 to be measured through thebeam expander system 7 composed of the transition imaging light group 6 and themicrolens array 5, and the light reflected by themirror surface 12 to be measured passes through Thebeam reduction system 7 forms a lattice of light spots on the CCD4 through the transmission of themirror 3 .

如图1所示，设置二维电控平移台9移动的距离和方向(x轴或者z轴)，利用计算机11向步进电机控制器10发出指令，控制二维电控平移台9移动到下一帧处；利用数据采集卡13将此帧处的光斑数据采集到计算机11内并存储；按上述方法完成整个待测面的扫描；采用质心算法计算出质心偏移量；采用全局优化拼接方法进行数据处理，再采用复原算法得到待测波面。As shown in Figure 1, set the distance and direction (x-axis or z-axis) that two-dimensional electronically controlledtranslation platform 9 moves, utilize computer 11 to send instruction tostepper motor controller 10, control two-dimensional electronically controlledtranslation platform 9 to move to At the next frame; use thedata acquisition card 13 to collect the light spot data at this frame into the computer 11 and store it; complete the scanning of the entire surface to be measured according to the above method; use the centroid algorithm to calculate the centroid offset; use global optimization splicing The method is to process the data, and then use the restoration algorithm to obtain the wave surface to be measured.

在整个检测过程开始之前，需要用标准平面反射镜进行标定，以标准平面反射镜在各个子孔径内所成光斑质心位置为中心原点。Before the whole detection process starts, a standard plane mirror needs to be used for calibration, and the position of the center of mass of the light spot formed by the standard plane mirror in each sub-aperture is taken as the center origin.

本发明的基于小口径圆形哈特曼-夏克波前传感器的拼接检测装置，使用过程中需要注意以下几点：The splicing detection device based on the small-diameter circular Hartmann-Shack wavefront sensor of the present invention needs to pay attention to the following points during use:

(1)待测镜面12装配时需调整其表面与哈特曼-夏克面内置光源出射光线尽可能垂直，以保证各个子波面的光斑质心不会由于偏移量过大超出子孔径范围；(1) When assembling themirror surface 12 to be tested, it is necessary to adjust its surface to be as perpendicular as possible to the light emitted by the built-in light source on the Hartmann-Shack surface, so as to ensure that the spot centroid of each sub-wave surface will not exceed the sub-aperture range due to excessive offset;

(2)哈特曼-夏克波前传感器8的口径的大小可以改变；(2) The size of the aperture of the Hartmann-Shack wavefront sensor 8 can be changed;

(3)待测镜面12大小可以改变，只需相应地增加或减少扫描帧数；(3) The size of themirror surface 12 to be tested can be changed, only need to increase or decrease the number of scanning frames accordingly;

(4)二维电控平移台9每次移动的距离可根据待测镜面12与哈特曼-夏克波前传感器8的相对大小灵活设置，但必须保证移动距离是传感器子孔径大小的整数倍且相邻两帧之间存在重叠区域；(4) The distance of each movement of the two-dimensional electronically controlledtranslation stage 9 can be flexibly set according to the relative size of themirror surface 12 to be measured and the Hartmann-Shack wavefront sensor 8, but it must be ensured that the moving distance is an integer multiple of the sensor sub-aperture size and There is an overlapping area between two adjacent frames;

(5)也可以将待测镜面12固定在二维电控平移台上9而保持哈特曼-夏克波前传感器8固定来进行拼接检测；(5) It is also possible to fix themirror surface 12 to be tested on the two-dimensional electronically controlledtranslation platform 9 and keep the Hartmann-Shack wavefront sensor 8 fixed to carry out splicing detection;

如图2所示，哈特曼-夏克波前传感器8为微透镜阵列的哈特曼波前传感器，CCD 4位于微透镜阵列5的焦面上。哈特曼-夏克波前传感器8利用微透镜阵列对入射的信号波前进行子孔径分割，每个子孔径内光信号聚焦在其后的CCD上，利用CCD靶面能量的分布情况进行质心位置计算。As shown in Figure 2, Hartmann-Shack wavefront sensor 8 is the Hartmann wavefront sensor of microlens array, andCCD 4 is positioned at the focal plane ofmicrolens array 5. The Hartmann-Shack wavefront sensor 8 uses a microlens array to divide the incident signal wavefront into sub-apertures. The optical signal in each sub-aperture is focused on the subsequent CCD, and the centroid position is calculated using the energy distribution of the CCD target surface.

哈特曼-夏克波前传感器8主要是根据下面的公式(12)计算光斑的位置(x_i，y_i)，探测全孔径的波面误差信息：The Hartmann-Shack wavefront sensor 8 mainly calculates the spot position (_xi ,_yi ) according to the following formula (12), and detects the wavefront error information of the full aperture:

${\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>=</span>=</span>\frac{\underset{\mathrm{<span><span>m</span>m</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>M</span>m</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\underset{\mathrm{<span><span>n</span>no</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>nm</span>nm</span>}}{\mathrm{<span><span>I</span>I</span>}}_{\mathrm{<span><span>nm</span>nm</span>}}}{\underset{\mathrm{<span><span>m</span>m</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>M</span>m</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\underset{\mathrm{<span><span>n</span>no</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>I</span>I</span>}}_{\mathrm{<span><span>nm</span>nm</span>}}}$${\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>=</span>=</span>\frac{\underset{\mathrm{<span><span>m</span>m</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>M</span>m</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\underset{\mathrm{<span><span>n</span>no</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>nm</span>nm</span>}}{\mathrm{<span><span>I</span>I</span>}}_{\mathrm{<span><span>nm</span>nm</span>}}}{\underset{\mathrm{<span><span>m</span>m</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>M</span>m</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\underset{\mathrm{<span><span>n</span>no</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>I</span>I</span>}}_{\mathrm{<span><span>nm</span>nm</span>}}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>12</span>12</span>}<span><span>)</span>)</span>$

式中，m＝1～M，n＝1～N为子孔径映射到CCD光敏靶面上对应的像素区域，M，N为子孔径内在x和y方向上所含的CCD单元数，即子孔径的窗口宽度，I_nm是CCD光敏靶面上第(n，m)个像素接收到的信号，x_nm，y_nm分别为第(n，m)个像素的x坐标和y坐标。In the formula, m=1～M, n=1～N is that the sub-aperture is mapped to the corresponding pixel area on the CCD photosensitive target surface, and M and N are the number of CCD units contained in the x and y directions in the sub-aperture, that is, the sub-aperture The window width of the aperture, 1_nm is the signal received by the (n, m) pixel on the photosensitive target surface of the CCD, and x_nm , y_nm are respectively the x coordinate and the y coordinate of the (n, m) pixel.

再根据下面的公式(13)计算入射波前的波前斜率g_xi，g_yi：Then calculate the wavefront slopes g_xi and g_yi of the incident wavefront according to the following formula (13):

${\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>xi</span>xi</span>}}<span><span>=</span>=</span>\frac{\mathrm{<span><span>\&Delta;x</span>\&Delta;x</span>}}{\mathrm{<span><span>\&lambda;f</span>\&lambda;f</span>}}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>o</span>o</span>}}}{\mathrm{<span><span>\&lambda;f</span>\&lambda;f</span>}}$${\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>yi</span>yi</span>}}<span><span>=</span>=</span>\frac{\mathrm{<span><span>\&Delta;y</span>\&Delta;y</span>}}{\mathrm{<span><span>\&lambda;f</span>\&lambda;f</span>}}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>o</span>o</span>}}}{\mathrm{<span><span>\&lambda;f</span>\&lambda;\; f</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>13</span>13</span>}<span><span>)</span>)</span>$

式中，(x₀，y₀)为标准平面波标定哈特曼传感器获得的光斑中心基准位置；哈特曼传感器探测波前畸变时，如图2所示(图中实线所示为畸变波前实际聚焦的位置，虚线所示为标准平面波前的光线聚焦情况)，光斑中心偏移到(x_i，y_i)，完成哈特曼传感器对信号的检测。In the formula, (x₀ , y₀ ) is the reference position of the spot center obtained by standard plane wave calibration of the Hartmann sensor; when the Hartmann sensor detects wavefront distortion, as shown in Figure 2 (the solid line in the figure shows the distorted wave The dotted line shows the light focus of the standard plane wavefront), and the center of the spot is shifted to (_xi , yi₎ to complete the detection of the signal by the Hartmann sensor.

如图4所示，本发明基于小口径圆形哈特曼-夏克波前传感器的拼接检测装置，其测量步骤如下：As shown in Figure 4, the present invention is based on the splicing detection device of the small-diameter circular Hartmann-Shack wavefront sensor, and its measurement steps are as follows:

第一，开机，开启系统各光源及哈特曼-夏克波前传感器8，确认各硬件正常工作；First, turn on the system, turn on the light sources and the Hartmann-Shack wavefront sensor 8 of the system, and confirm that the hardware is working normally;

第二，启动电控平移台控制软件，移动哈特曼-夏克波前传感器8至第一帧子波面位置；Second, start the control software of the electronically controlled translation stage, and move the Hartmann-Shack wavefront sensor 8 to the sub-wavefront position of the first frame;

第二，用标准平面反射镜对哈特曼-夏克波前传感器8进行现场定标；Second, the Hartmann-Shack wavefront sensor 8 is calibrated on-site with a standard flat mirror;

第三，采集此帧子波面的光斑点阵图并存储；Third, collect and store the light spot bitmap of the sub-wavefront of this frame;

第四，根据哈特曼-夏克波前传感器8的与待测镜面12的相对大小设置二维电控平移台9移动的方向和距离，确保每次移动距离是哈特曼-夏克波前传感器8子孔径大小的整数倍且相邻两帧之间存在一定的重叠区域。然后控制哈特曼-夏克波前传感器8移动至下一帧位置；Fourth, according to the relative size of the Hartmann-Shack wavefront sensor 8 and themirror surface 12 to be measured, the direction and distance that the two-dimensional electronically controlledtranslation stage 9 moves are set to ensure that each moving distance is 8 sub-seconds of the Hartmann-Shack wavefront sensor 8. Integer multiples of the aperture size and there is a certain overlapping area between two adjacent frames. Then control the Hartmann-Shack wavefront sensor 8 to move to the next frame position;

第五，重复步骤三、步骤四直至扫描完成，要求扫描总区域能覆盖待测大口径光学元件。Fifth, repeat steps 3 and 4 until the scanning is completed, and the total scanning area is required to cover the large-aperture optical element to be tested.

第六，通过质心算法计算出子波面斜率矩阵，然后利用全局优化拼接方法拼接出全孔径波面斜率矩阵；Sixth, the wavefront slope matrix is calculated by the centroid algorithm, and then the full-aperture wavefront slope matrix is spliced using the global optimization splicing method;

所述的全局化优化拼接方法为：The described global optimization splicing method is:

首先，对于现有的干涉仪测量有：First, for existing interferometer measurements there are:

φ(x，y)＝φ′(x-x₀，y-y₀)+ax+by+c(x²+y²)+d                (1)φ(x,y)=φ′(xx₀ ,yy₀ )+ax+by+c(x² +y² )+d (1)

其中：a、b、c和d分别为两个子波面测量过程中的x轴和y轴的相对倾斜、离焦和平移误差系数；但在实际工程中，考虑到短距离的光传输，当菲涅尔数Nf＞1000时，因衍射而产生的波前变化的误差将在1％以下，即波前畸变可以忽略不计，而实际测量中二维电动平移台的piston误差是毫米量级的，因此可以忽略离焦项，(1)可简化为：Among them: a, b, c and d are the relative tilt, defocus and translation error coefficients of the x-axis and y-axis in the measurement process of the two sub-wavefronts respectively; but in actual engineering, considering the short-distance optical transmission, when the When the Neel number Nf>1000, the error of the wavefront change due to diffraction will be below 1%, that is, the wavefront distortion can be ignored, while the piston error of the two-dimensional electric translation stage in actual measurement is on the order of millimeters, Therefore, the out-of-focus term can be ignored, and (1) can be simplified as:

φ(x，y)＝φ′(x-x₀，y-y₀)+ax+by+d                    (4)φ(x,y)=φ′(xx₀ ,yy₀ )+ax+by+d (4)

分别对x、y求导得：Derivatives for x and y respectively:

$\left\{\begin{array}{c}\mathrm{<span><span>Gx</span>Gx</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>)</span>)</span><span><span>=</span>=</span>{\mathrm{<span><span>Gx</span>Gx</span>}}^{<span><span>\&prime;</span>\&prime;</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>-</span>-</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>+</span>+</span>\mathrm{<span><span>a</span>a</span>}\\ \mathrm{<span><span>Gy</span>Gy</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>)</span>)</span><span><span>=</span>=</span>{\mathrm{<span><span>Gy</span>Gy</span>}}^{<span><span>\&prime;</span>\&prime;</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>-</span>-</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}\end{array}\right.<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>5</span>5</span>}<span><span>)</span>)</span>$

哈特曼-夏克波前传感器检测消除了平移误差系数d的影响，仅仅考虑相对倾斜系数a、b，从而降低了拼接参数求解复杂度，以x方向斜率为例，即有：The Hartmann-Shack wavefront sensor detection eliminates the influence of the translation error coefficient d, and only considers the relative tilt coefficients a and b, thereby reducing the complexity of solving the stitching parameters. Taking the slope in the x direction as an example, there are:

δ_x＝∑{Gx(x_i，y_i)-[Gx′(x_i-x₀，y_i-y₀)+a]}²→min            (6)δ_x ＝∑{Gx(x_i , y_i )-[Gx′(x_i -x₀ , y_i -y₀ )+a]}² →min (6)

将公式(6)对a求导并令其值为零，可以求得拼接参数a；Y方向的斜率图类似；The splicing parameter a can be obtained by deriving formula (6) with respect to a and setting its value to zero; the slope diagram in the Y direction is similar;

当拼接区域大于两个时，假设共有M个子波面拼接，可以先选定其中任意的某个子波面作为基准，一般选择中心区域的子波面m作为参考标准；假设拼接参数分别为(a_i，b_i，c_1i，c_2i)(0≤i≤M-1，i≠m)，以x方向斜率为例，则各个子波面斜率图与基准子波面斜率图的关系为：When the splicing area is larger than two, assuming that there are M sub-wavefronts to be spliced, any one of them can be selected as a reference. Generally, the sub-wavefront m in the central area is selected as the reference standard; assuming that the splicing parameters are (a_i , b_i , c_1i , c_2i )(0≤i≤M-1, i≠m), taking the slope in the x direction as an example, the relationship between each wavelet slope map and the reference wavelet slope map is:

G_m(x，y)＝G_i(x-x₀，y-y₀)+a_i(0≤i≤M-1，i≠m)                (7)G_m (x, y) = G_i (xx₀ , yy₀ )+a_i (0≤i≤M-1, i≠m) (7)

利用最小二乘法：Using the method of least squares:

$\mathrm{<span><span>S</span>S</span>}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>\&NotEqual;</span>\&NotEqual;</span>\mathrm{<span><span>m</span>m</span>}}{\overset{\mathrm{<span><span>M</span>m</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}}{<span><span>\{</span>\{</span>\mathrm{<span><span>G</span>G</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>[</span>[</span>{\mathrm{<span><span>G</span>G</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>-</span>-</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>+</span>+</span>{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>]</span>]</span><span><span>\}</span>\}</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>\&RightArrow;</span>\&Right\; Arrow;</span>\mathrm{<span><span>min</span>min</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>8</span>8</span>}<span><span>)</span>)</span>$

令：$\frac{\&PartialD;S}{\&PartialD;a_i}=0$(0≤i≤M-1，i≠m)            (9)make:$\frac{\&PartialD;S}{\&PartialD;a_i}=0$ (0≤i≤M-1, i≠m) (9)

若令：$P_{\mathrm{ij}}=\underset{i\&cap;j}{\mathrm{\&Sigma;}}\mathrm{\&Delta;}(x,y)$Q_ij＝n_ij    R_i＝a_i                        (10)If order:$P_{\mathrm{ij}}=\underset{i\&cap;j}{\mathrm{\&Sigma;}}\mathrm{\&Delta;}(x,\mathrm{the\; y})$ Q_ij =n_ij R_i =a_i (10)

其中Δ(x，y)＝G_i(x-x_i，y-y_i)-G_j(x-x_j，y-y_j)为第i，j帧子波面重叠区域内各个采样点处测量值之差，n_ij为采样点个数。则有：Where Δ(x, y)=G_i (xx_i , yy_i )-G_j (xx_j , yy_j ) is the difference between the measured values at each sampling point in the i-th and j-frame sub-wavefront overlapping areas, and n_ij is The number of sampling points. Then there are:

$<span><span>[</span>[</span>{<span><span>(</span>(</span>\underset{\mathrm{<span><span>k</span>k</span>}}{\overset{\mathrm{<span><span>M</span>m</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>ik</span>ik</span>}}<span><span>)</span>)</span>}_{\mathrm{<span><span>i</span>i</span>}}<span><span>]</span>]</span><span><span>=</span>=</span><span><span>[</span>[</span>{<span><span>(</span>(</span>{\mathrm{<span><span>Q</span>Q</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}\underset{\mathrm{<span><span>k</span>k</span>}}{\overset{\mathrm{<span><span>M</span>m</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>Q</span>Q</span>}}_{\mathrm{<span><span>ik</span>ik</span>}}<span><span>)</span>)</span>}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>]</span>]</span><span><span>[</span>[</span>{<span><span>(</span>(</span>{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>}_{\mathrm{<span><span>i</span>i</span>}}<span><span>]</span>]</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>11</span>11</span>}<span><span>)</span>)</span>$

其中${\mathrm{\&delta;}}_{\mathrm{ij}}=\left\{\begin{array}{cc}1& \mathrm{if\; i}=j\\ 0& \mathrm{if\; i}\&NotEqual;j\end{array}\right.$利用式(11)可得到各个子波面相对于基准子波面的拼接参数。in${\mathrm{\&delta;}}_{\mathrm{ij}}=\left\{\begin{array}{cc}1& \mathrm{if\; i}=j\\ 0& \mathrm{if\; i}\&NotEqual;j\end{array}\right.$ The splicing parameters of each wavelet relative to the reference wavelet can be obtained by using formula (11).

第七，利用模式法复原出待测大口径波面。Seventh, the model method is used to restore the large-aperture wave surface to be measured.

由以上可知本发明的拼接检测装置采用了哈特曼-夏克波前传感器，消除了平移误差此项原理误差并且通过理论分析忽略了离焦误差项，克服了现有干涉仪拼接检测所存在的缺点，提高了拼接精度；并且本发明所采用的全局优化拼接方法求得的是各帧子波面斜率图相对于基准子波面斜率图的绝对拼接参数，大大降低了多帧扫描中误差累积和误差传递的影响，有利于拼接精度的提高。It can be seen from the above that the splicing detection device of the present invention adopts the Hartmann-Shack wavefront sensor, which eliminates the principle error of translation error and ignores the defocus error term through theoretical analysis, which overcomes the shortcomings of the existing interferometer splicing detection , improve the splicing accuracy; and the global optimization splicing method adopted in the present invention obtains the absolute splicing parameters of each frame wavelet slope map relative to the reference wavelet slope map, which greatly reduces error accumulation and error transmission in multi-frame scanning It is beneficial to improve the splicing accuracy.

以上所述仅为本发明的优选实施例而已，并不用于限制本发明，而且在实施例中未作详细描述的内容，均为本领域所熟知的现有技术，The above is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and the content not described in detail in the embodiments is the prior art well known in the art.

Claims (5)

Translated fromChinese

1.基于小口径圆形哈特曼-夏克波前传感器的拼接检测装置，其特征在于：包含有哈特曼-夏克波前传感器(8)、x-z二维电控平移台(9)、步进电机控制器(10)、计算机(11)、待测镜面(12)及数据采集卡(13)；哈特曼-夏克波前传感器(8)对待测镜面(12)的某个区域进行检测，并且在哈特曼-夏克波前传感器(8)形成光斑点阵，由数据采集卡(13)采集上述光斑数据并传输到计算机(11)中存储；计算机(11)向步进电机控制器(10)发出指令，控制二维电控平移台(9)沿x轴与z轴移动对待测镜面(12)进行扫描检测，利用数据采集卡(13)依次采得各帧子波面处的光斑数据，然后利用质心算法、拼接方法及复原算法得到待测波面；所述的哈特曼-夏克波前传感器(8)由点光源(1)、准直透镜(2)、反射镜(3)、CCD(4)及缩/扩束系统(7)组成；1. A splicing detection device based on a small-diameter circular Hartmann-Shack wavefront sensor, characterized in that it includes a Hartmann-Shack wavefront sensor (8), an x-z two-dimensional electronically controlled translation stage (9), and a stepping motor Controller (10), computer (11), mirror surface to be measured (12) and data acquisition card (13); Hartmann-Shack wavefront sensor (8) detects a certain area of mirror surface to be measured (12), and in The Hartmann-Shack wavefront sensor (8) forms a light spot lattice, and the above-mentioned light spot data is collected by the data acquisition card (13) and is transmitted to the computer (11) for storage; the computer (11) sends the stepper motor controller (10) command, control the two-dimensional electronically controlled translation stage (9) to move along the x-axis and the z-axis to scan and detect the mirror surface to be measured (12), and use the data acquisition card (13) to sequentially acquire the spot data at each frame sub-wave surface, and then use Centroid algorithm, splicing method and restoration algorithm obtain the wavefront to be measured; the Hartmann-Shack wavefront sensor (8) consists of a point light source (1), a collimating lens (2), a mirror (3), and a CCD (4) and beam shrinkage/expansion system (7);所述的拼接方法采用全局优化拼接方法处理重叠区域中的采样数据，得到各个子波面斜率图相对于基准子波面斜率图的拼接参数，恢复出全孔径波面斜率图；The splicing method adopts the global optimization splicing method to process the sampling data in the overlapping area, obtains the splicing parameters of each sub-wavefront slope map relative to the reference sub-wavefront slope map, and restores the full-aperture wavefront slope map;所述全局化优化拼接方法为：首先，对于现有的干涉仪测量有：The global optimization mosaic method is as follows: first, for the existing interferometer measurement:φ(x，y)＝φ′(x-x₀，y-y₀)+ax+by+c(x²+y²)+d        (1)φ(x,y)=φ′(xx₀ ,yy₀ )+ax+by+c(x² +y² )+d (1)其中：a、b、c和d分别为两个子波面测量过程中的x轴和y轴的相对倾斜、离焦和平移误差系数；(x₀，y₀)为标准平面波标定哈特曼传感器获得的光斑中心基准位置；但在实际工程中，考虑到短距离的光传输，当菲涅尔数Nf＞1000时，因衍射而产生的波前变化的误差将在1％以下，即波前畸变忽略不计，而实际测量中二维电控平移台的平移误差是毫米量级的，因此忽略离焦项，(1)简化为：Among them: a, b, c and d are the relative tilt, defocus and translation error coefficients of the x-axis and y-axis in the measurement process of the two sub-wavefronts respectively; (x₀ , y₀ ) is obtained by standard plane wave calibration Hartmann sensor However, in actual engineering, considering the short-distance light transmission, when the Fresnel number Nf>1000, the error of the wavefront change due to diffraction will be less than 1%, that is, the wavefront distortion Negligible, but the translation error of the two-dimensional electronically controlled translation stage in actual measurement is on the order of millimeters, so the defocus item is ignored, and (1) is simplified as:φ(x，y)＝φ′(x-x₀，y-y₀)+ax+by+d                    (4)φ(x,y)=φ′(xx₀ ,yy₀ )+ax+by+d (4)分别对x、y求导得：Derivatives for x and y respectively:$\left\{\begin{array}{c}\mathrm{<span><span>Gx</span>Gx</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>)</span>)</span><span><span>=</span>=</span>{\mathrm{<span><span>Gx</span>Gx</span>}}^{<span><span>\&prime;</span>\&prime;</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>-</span>-</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>+</span>+</span>\mathrm{<span><span>a</span>a</span>}\\ \mathrm{<span><span>Gy</span>Gy</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>)</span>)</span><span><span>=</span>=</span>{\mathrm{<span><span>Gy</span>Gy</span>}}^{<span><span>\&prime;</span>\&prime;</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>-</span>-</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}\end{array}\right.<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>5</span>5</span>}<span><span>)</span>)</span>$哈特曼-夏克波前传感器检测消除了平移误差系数d的影响，仅仅考虑相对倾斜系数a、b，从而降低了拼接参数求解复杂度；其中x方向斜率为：The Hartmann-Shack wavefront sensor detection eliminates the influence of the translation error coefficient d, and only considers the relative tilt coefficients a and b, thereby reducing the complexity of solving the stitching parameters; where the slope in the x direction is:δ_x＝∑{Gx(x_i，y_i)-[Gx′(x_i-x₀，y_i-y₀)+a]}²→min                (6)δ_x ＝∑{Gx(x_i , y_i )-[Gx′(x_i -x₀ , y_i -y₀ )+a]}² →min (6)将公式(6)对a求导并令其值为零，求得拼接参数a；Y方向的斜率图类似；Deriving formula (6) with respect to a and making its value zero to obtain the splicing parameter a; the slope diagram in the Y direction is similar;当拼接区域大于两个时，假设共有M个子波面拼接，先选定其中任意的某个子波面作为基准，选择中心区域的子波面m作为参考标准；假设拼接参数分别为(a_i，b_i，c_i，d_i)(0≤i≤M-1，i≠m)，那么在x方向的斜率，各个子波面斜率图与基准子波面斜率图的关系为：When the splicing area is larger than two, assuming that there are M sub-wavefronts to be spliced, first select any sub-wavefront as a reference, and select the sub-wavefront m in the central area as a reference standard; assuming that the splicing parameters are (a_i , b_i , c_i , d_i )(0≤i≤M-1, i≠m), then the slope in the x direction, the relationship between each wavelet slope map and the reference wavelet slope map is:G_m(x，y)＝G_i(x-x₀，y-y₀)+a_i(0≤i≤M-1，i≠m)                (7)G_m (x, y) = G_i (xx₀ , yy₀ )+a_i (0≤i≤M-1, i≠m) (7)利用最小二乘法：Using the method of least squares:$\mathrm{<span><span>S</span>S</span>}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>\&NotEqual;</span>\&NotEqual;</span>\mathrm{<span><span>m</span>m</span>}}{\overset{\mathrm{<span><span>M</span>m</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}}{<span><span>\{</span>\{</span>\mathrm{<span><span>G</span>G</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>[</span>[</span>{\mathrm{<span><span>G</span>G</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>-</span>-</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>+</span>+</span>{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>]</span>]</span><span><span>\}</span>\}</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>\&RightArrow;</span>\&Right\; Arrow;</span>\mathrm{<span><span>min</span>min</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>8</span>8</span>}<span><span>)</span>)</span>$令：$\frac{\&PartialD;S}{\&PartialD;a_i}=0$(0≤i≤M-1，i≠m)        (9)make:$\frac{\&PartialD;S}{\&PartialD;a_i}=0$ (0≤i≤M-1, i≠m) (9)若令：$P_{\mathrm{ij}}=\underset{i\&cap;j}{\mathrm{\&Sigma;}}\mathrm{\&Delta;}(x,y)$Q_ij＝n_ij    R_i＝a_i                (10)If order:$P_{\mathrm{ij}}=\underset{i\&cap;j}{\mathrm{\&Sigma;}}\mathrm{\&Delta;}(x,\mathrm{the\; y})$ Q_ij =n_ij R_i =a_i (10)其中Δ(x，y)＝G_i(x-x_i，y-y_i)-G_j(x-x_j，y-y_j)为第i，j帧子波面重叠区域内各个采样点处测量值之差，n_ij为采样点个数；则有：Where Δ(x, y)=G_i (xx_i , yy_i )-G_j (xx_j , yy_j ) is the difference between the measured values at each sampling point in the i-th and j-frame sub-wavefront overlapping areas, and n_ij is The number of sampling points; then:$<span><span>[</span>[</span>{<span><span>(</span>(</span>\underset{\mathrm{<span><span>k</span>k</span>}}{\overset{\mathrm{<span><span>M</span>m</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>ik</span>ik</span>}}<span><span>)</span>)</span>}_{\mathrm{<span><span>i</span>i</span>}}<span><span>]</span>]</span><span><span>=</span>=</span><span><span>[</span>[</span>{<span><span>(</span>(</span>{\mathrm{<span><span>Q</span>Q</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}\underset{\mathrm{<span><span>k</span>k</span>}}{\overset{\mathrm{<span><span>M</span>m</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>Q</span>Q</span>}}_{\mathrm{<span><span>ik</span>ik</span>}}<span><span>)</span>)</span>}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>]</span>]</span><span><span>[</span>[</span>{<span><span>(</span>(</span>{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>}_{\mathrm{<span><span>i</span>i</span>}}<span><span>]</span>]</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>11</span>11</span>}<span><span>)</span>)</span>$其中${\mathrm{\&delta;}}_{\mathrm{ij}}=\left\{\begin{array}{cc}1& \mathrm{if\; i}=j\\ 0& \mathrm{if\; i}\&NotEqual;j\end{array}\right.$利用式(11)得到各个子波面相对于基准子波面的拼接参数。in${\mathrm{\&delta;}}_{\mathrm{ij}}=\left\{\begin{array}{cc}1& \mathrm{if\; i}=j\\ 0& \mathrm{if\; i}\&NotEqual;j\end{array}\right.$ Using formula (11) to get the splicing parameters of each wavelet relative to the reference wavelet.2.根据权利要求1所述的基于小口径圆形哈特曼-夏克波前传感器的拼接检测装置，其特征在于：点光源(1)发出的光经过准直透镜(2)形成平行光束，该平行光束经过反射镜(3)转折后再经过缩/扩束系统(7)照射到待测镜面(12)，待测镜面(12)反射的光线经缩/扩束系统(7)，再经反射镜(3)的透射在CCD(4)上形成光斑点阵。2. the splicing detection device based on the small-diameter circular Hartmann-Shack wavefront sensor according to claim 1, characterized in that: the light sent by the point light source (1) forms a parallel beam through a collimator lens (2), the The parallel light beam is turned by the reflector (3) and then irradiates the mirror surface to be tested (12) through the beam shrinking/expanding system (7), and the light reflected by the mirror surface (12) to be tested is passed through The transmission of the mirror (3) forms a light spot lattice on the CCD (4).3.根据权利要求2所述的基于小口径圆形哈特曼-夏克波前传感器的拼接检测装置，其特征在于：所述的缩/扩束系统(7)由微透镜阵列(5)与过渡成像光组(6)组成。3. the splicing detection device based on the small-diameter circular Hartmann-Shack wavefront sensor according to claim 2, characterized in that: the described beam shrinkage/expansion system (7) consists of a microlens array (5) and a transition The imaging light group (6) is composed.4.根据权利要求1所述的基于小口径圆形哈特曼-夏克波前传感器的拼接检测装置，其特征在于：将待测元件所述的待测镜面(12)固定在二维电控平移台(9)上，并随二维电控平移台(9)同步移动；而保持哈特曼-夏克波前传感器(8)固定来进行检测。4. The splicing detection device based on the small-diameter circular Hartmann-Shack wavefront sensor according to claim 1, characterized in that: the mirror to be measured (12) described in the element to be measured is fixed in a two-dimensional electronically controlled translation on the stage (9), and move synchronously with the two-dimensional electronically controlled translation stage (9); and keep the Hartmann-Shack wavefront sensor (8) fixed for detection.5.根据权利要求1所述的基于小口径圆形哈特曼-夏克波前传感器的拼接检测装置，其特征在于：哈特曼-夏克波前传感器(8)口径的大小和形状能够改变。5. The splicing detection device based on a small-diameter circular Hartmann-Shack wavefront sensor according to claim 1, characterized in that: the size and shape of the Hartmann-Shack wavefront sensor (8) aperture can be changed.

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