CN105824030A - Sparse optical synthetic aperture imaging method based on sub-aperture shutter modulation phase difference method - Google Patents

Abstract

Translated fromChinese

本发明涉及一种基于子孔径快门调制相位差法的稀疏光学合成孔径成像方法，可用于探测稀疏光学合成孔径成像系统中各个子孔径像差、多孔径间的共相误差和成像光束大气湍流畸变，并实时复原目标高分辨图像。本发明利用电子快门依次对稀疏光学合成孔径成像系统中的每个或者多个子孔径进行开关调制，并利用图像传感器记录相应的图像。通过使用基于子孔径快门调制相位差算法对记录的系列子图像进行处理，可以同时探测子孔径像差、多孔径间的共相误差和成像光束大气湍流畸变，并重建目标的高分辨图像。本发明采用快门空间调制以产生含有相位差异的子图像，集像差探测和图像复原于一体，具有像差探测精度高，结构紧凑，成本低廉，使用方便等优点。

The invention relates to a sparse optical synthetic aperture imaging method based on a sub-aperture shutter modulation phase difference method, which can be used to detect the aberration of each sub-aperture, the common phase error between multiple apertures and the atmospheric turbulence distortion of an imaging beam in a sparse optical synthetic aperture imaging system , and restore the target high-resolution image in real time. In the present invention, electronic shutters are used to sequentially switch and modulate each or multiple sub-apertures in the sparse optical synthetic aperture imaging system, and an image sensor is used to record corresponding images. By using the sub-aperture shutter modulation phase difference algorithm to process the recorded series of sub-images, the sub-aperture aberration, the common phase error between multi-apertures and the distortion of the atmospheric turbulence of the imaging beam can be detected simultaneously, and the high-resolution image of the target can be reconstructed. The invention uses shutter space modulation to generate sub-images with phase differences, integrates aberration detection and image restoration, and has the advantages of high aberration detection accuracy, compact structure, low cost, and convenient use.

Description

Translated fromChinese

一种基于子孔径快门调制相位差法的稀疏光学合成孔径成像方法A Sparse Optical Synthetic Aperture Imaging Method Based on Subaperture Shutter Modulation Phase Difference Method

技术领域technical field

本发明涉及一种稀疏光学合成孔径成像新方法，尤其是一种基于子孔径快门调制相位差法的稀疏光学合成孔径成像方法，可以探测稀疏光学合成孔径成像系统中子孔径像差、多孔径间的共相误差和成像光束大气湍流畸变，并实时复原目标的高分辨图像。The present invention relates to a new sparse optical synthetic aperture imaging method, in particular to a sparse optical synthetic aperture imaging method based on the sub-aperture shutter modulation phase difference method, which can detect sub-aperture aberrations and multi-aperture interspace in sparse optical synthetic aperture imaging systems. The common phase error and atmospheric turbulence distortion of the imaging beam, and restore the high-resolution image of the target in real time.

背景技术Background technique

随着科学技术的不断发展，航天遥感技术已经被广泛应用于对地高分辨成像、军事侦察、天文观测和深空探测等诸多领域。空间分辨率是评价航天遥感器观测能力的重要技术指标，分辨率越高，遥感器对目标细节的分辨能力越强，获取的信息越多。因此，高分辨率光学成像系统将是一个国家航天遥感科技实力的重要体现，也是各国争相发展的空间光学技术。对于目前普遍使用的单口径光学系统，为了提高空间分辨率势必要增大系统口径，但是系统口径的增大受到材料、工艺、制造成本、质量和有效载荷舱体积等诸多因素的限制，同时也必然会导致系统的体积和质量增加，给空基系统的发射带来困难。1970年。美国学者Meinel提出光学合成孔径的概念，旨在利用易制造的小孔径系统通过光学手段合成大孔径系统，从而满足高分辨率的成像要求。光学合成孔径成像一经提出，便引起了业内学者很大兴趣，在国际上快速发展起来，并一直是国际研究热点之一。除在航空遥感领域，该技术在激光传输、显微成像、三维成像等其他成像技术领域也有着广泛的应用前景。With the continuous development of science and technology, aerospace remote sensing technology has been widely used in many fields such as high-resolution imaging of the earth, military reconnaissance, astronomical observation and deep space exploration. Spatial resolution is an important technical index to evaluate the observation ability of aerospace remote sensors. The higher the resolution, the stronger the remote sensor's ability to distinguish target details and the more information it can obtain. Therefore, the high-resolution optical imaging system will be an important manifestation of the strength of a country's space remote sensing technology, and it is also a space optical technology that countries are competing to develop. For the single-aperture optical system commonly used at present, in order to improve the spatial resolution, it is necessary to increase the system caliber, but the increase of the system caliber is limited by many factors such as materials, processes, manufacturing costs, quality, and payload compartment volume. It will inevitably lead to an increase in the volume and mass of the system, which will bring difficulties to the launch of the space-based system. 1970. Meinel, an American scholar, proposed the concept of optical synthetic aperture, which aims to use the easy-to-manufacture small aperture system to synthesize a large aperture system by optical means, so as to meet the high-resolution imaging requirements. As soon as optical synthetic aperture imaging was proposed, it aroused great interest among scholars in the field, developed rapidly in the world, and has been one of the international research hotspots. In addition to the field of aerial remote sensing, this technology also has broad application prospects in other imaging technology fields such as laser transmission, microscopic imaging, and three-dimensional imaging.

光学合成孔径成像系统最重要的问题是共相位问题。各子孔径产生的像场必须具有相同的相位，才能在爱里斑中心相互增强，同时使爱里斑变窄，提高图像分辨率，不然只能起到接收光能的作用。相位差法作为一种基于图像的间接波前探测技术，可用于探测光学合成孔径成像系统中的共相误差。早在1988年美国ERIM实验室就对相位差法用于检测拼接镜面望远镜像差性能进行了初步研究。1997年，Lee和Roggemann等人从理论角度分析了相位差法用于下一代空间望远镜NGST中像差检测的可行性和精度等问题。1998年，和Kendrick等人使用相位差法对KeckⅡ型望远系统中子孔径像差进行了检测。2009年，在Star-9系统中，LockheedMartin公司的RickKendrick等人采用相位差法实现了共相闭环。目前使用相位差法的光学合成孔径成像技术仍然存在多种局限：相位差法本质上是一种基于图像的反演技术，需要根据采集的图像信息来探测共相误差，作为先验信息而人为引入的像差势必会使图像丢失部分信息，从而影响共相探测的精度以及复原图像的质量；传统相位差法需要利用诸如光栅、分光镜等额外光学元件采集多个像面的图像，作为先验信息引入的离焦量也需要精密的控制平台，这些势必会增加系统的复杂度和成本，同时带来其他的系统像差和机械误差，影响共相探测的精度。The most important problem of optical synthetic aperture imaging system is the co-phase problem. The image fields generated by each sub-aperture must have the same phase, so as to enhance each other at the center of the Airy disk, narrow the Airy disk at the same time, and improve the image resolution, otherwise they can only receive light energy. As an image-based indirect wavefront detection technique, the phase difference method can be used to detect common phase errors in optical synthetic aperture imaging systems. As early as 1988, the ERIM laboratory in the United States conducted a preliminary study on the phase difference method used to detect the aberration performance of spliced mirror telescopes. In 1997, Lee and Roggemann et al. analyzed the feasibility and accuracy of the phase difference method for aberration detection in the next generation space telescope NGST from a theoretical point of view. 1998, and Kendrick et al. used the phase difference method to detect the sub-aperture aberration of the Keck II telescopic system. In 2009, in the Star-9 system, Rick Kendrick of Lockheed Martin and others realized the common phase closed loop by using the phase difference method. At present, the optical synthetic aperture imaging technology using the phase difference method still has many limitations: the phase difference method is essentially an image-based inversion technology, which needs to detect the common phase error based on the collected image information, which is artificially used as prior information. The introduced aberration will inevitably cause the image to lose part of the information, thereby affecting the accuracy of co-phase detection and the quality of the restored image; the traditional phase difference method needs to use additional optical elements such as gratings and beam splitters to collect images of multiple image planes as a first step. The defocus amount introduced by the experimental information also requires a precise control platform, which will inevitably increase the complexity and cost of the system, and at the same time bring other system aberrations and mechanical errors, which will affect the accuracy of common phase detection.

本发明提出一种基于子孔径快门调制相位差法的稀疏光学合成孔径成像方法，通过电子快门来进行空间调制以产生含有相位差异的系列图像，集像差探测和图像高清晰复原于一体，相对于目前使用传统相位差法的稀疏光学合成孔径成像方法，由于无需引入额外的分光器件和机械器件等，所以具有高的像差探测精度和图像复原清晰度。另外，该方法在系统结构、成本、使用方便性等方面，也有明显的优势。The present invention proposes a sparse optical synthetic aperture imaging method based on the sub-aperture shutter modulation phase difference method, which uses electronic shutters to perform spatial modulation to generate a series of images containing phase differences, which integrates aberration detection and image high-definition restoration. Compared with the current sparse optical synthetic aperture imaging method using the traditional phase difference method, it has high aberration detection accuracy and image restoration clarity because it does not need to introduce additional optical splitters and mechanical devices. In addition, this method also has obvious advantages in terms of system structure, cost, and ease of use.

发明内容Contents of the invention

为了克服现有技术存在的问题和实现的复杂程度，本发明提出了一种基于子孔径快门调制相位差法的稀疏光学合成孔径成像方法。In order to overcome the problems existing in the prior art and the complexity of implementation, the present invention proposes a sparse optical synthetic aperture imaging method based on a sub-aperture shutter modulation phase difference method.

本发明采用的技术方案是：一种基于子孔径快门调制相位差法的稀疏光学合成孔径成像方法，该方法包含以下步骤：The technical solution adopted in the present invention is: a sparse optical synthetic aperture imaging method based on the sub-aperture shutter modulation phase difference method, the method includes the following steps:

步骤(1)、利用电子快门依次对稀疏光学合成孔径成像系统的每个子孔径或者多个子孔径进行开关调制，并用图像传感器依次记录下稀疏合成孔径成像系统受到调制后所对应的图像；Step (1), using the electronic shutter to sequentially switch and modulate each sub-aperture or multiple sub-apertures of the sparse optical synthetic aperture imaging system, and sequentially record the modulated images corresponding to the sparse optical synthetic aperture imaging system with an image sensor;

步骤(2)、使用基于子孔径快门调制相位差算法对系列图像进行处理，探测子孔径的像差、多孔径之间的共相误差和成像光束大气湍流畸变，并重建目标高分辨的图像；具体处理算法如下：Step (2), using the sub-aperture shutter modulation phase difference algorithm to process the series of images, detecting the aberration of the sub-aperture, the common phase error between the multi-apertures and the distortion of the atmospheric turbulence of the imaging beam, and reconstructing the high-resolution image of the target; The specific processing algorithm is as follows:

步骤A、根据极大似然估计或最小二乘优化理论建立目标函数E：Step A, establish the objective function E according to the maximum likelihood estimation or the least squares optimization theory:

$\mathrm{<span><span>E</span>E.</span>}<span><span>=</span>=</span>\underset{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>x</span>x</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>y</span>the\; y</span>}}}{<span><span>\&Sigma;</span>\&Sigma;</span>}\underset{\mathrm{<span><span>k</span>k</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>K</span>K</span>}}{<span><span>\&Sigma;</span>\&Sigma;</span>}}<span><span>|</span>|</span>{\mathrm{<span><span>D</span>D.</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>x</span>x</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>y</span>the\; y</span>}}<span><span>)</span>)</span>{<span><span>|</span>|</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>-</span>-</span>\underset{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>x</span>x</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>y</span>the\; y</span>}}}{<span><span>\&Sigma;</span>\&Sigma;</span>}\frac{\underset{\mathrm{<span><span>k</span>k</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>K</span>K</span>}}{<span><span>\&Sigma;</span>\&Sigma;</span>}}<span><span>|</span>|</span>{\mathrm{<span><span>D</span>D.</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>x</span>x</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>y</span>the\; y</span>}}<span><span>)</span>)</span>{\mathrm{<span><span>H</span>h</span>}}_{\mathrm{<span><span>k</span>k</span>}}^{<span><span>*</span>*</span>}<span><span>(</span>(</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>x</span>x</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>y</span>the\; y</span>}}<span><span>)</span>)</span>{<span><span>|</span>|</span>}^{\mathrm{<span><span>2</span>2</span>}}}{\underset{\mathrm{<span><span>k</span>k</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>K</span>K</span>}}{<span><span>\&Sigma;</span>\&Sigma;</span>}}<span><span>|</span>|</span>{\mathrm{<span><span>H</span>h</span>}}_{\mathrm{<span><span>k</span>k</span>}}^{<span><span>*</span>*</span>}<span><span>(</span>(</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>x</span>x</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>y</span>the\; y</span>}}<span><span>)</span>)</span>{<span><span>|</span>|</span>}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>$

其中，K为稀疏孔径成像系统子孔径的数目，D_k(f_x,f_y)是第k个子系统快门调制后采集的子图像的傅里叶变换，H_k(f_x,f_y)是第k个子系统快门调制后合成孔径成像系统的光学传递函数，是H_k(f_x,f_y)的共轭，其中k为0表示所有的快门都处于开启状态，f_x和f_y为频域坐标；Among them, K is the number of sub-apertures of the sparse aperture imaging system, D_k (f_x , f_y ) is the Fourier transform of the sub-image acquired after the shutter modulation of the k-th subsystem, H_k (f_x , f_y ) is The optical transfer function of the synthetic aperture imaging system after shutter modulation by the kth subsystem, is the conjugate of H_k (f_x ,f_y ), where k is 0 to indicate that all shutters are open, and f_x and f_y are frequency domain coordinates;

根据傅里叶光学理论，成像系统的光学传递函数为成像系统点扩散函数的傅里叶变换，成像系统的点扩散函数由成像系统的光瞳函数确定，稀疏孔径成像系统的光瞳函数可以表示为：According to the theory of Fourier optics, the optical transfer function of the imaging system is the Fourier transform of the point spread function of the imaging system. The point spread function of the imaging system is determined by the pupil function of the imaging system. The pupil function of the sparse aperture imaging system can be expressed as for:

${\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>q</span>q</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>K</span>K</span>}}{<span><span>\&Sigma;</span>\&Sigma;</span>}}{\mathrm{<span><span>p</span>p</span>}}_{\mathrm{<span><span>q</span>q</span>}}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>w</span>w</span>}}_{\mathrm{<span><span>q</span>q</span>}<span><span>,</span>,</span>\mathrm{<span><span>k</span>k</span>}}^{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>v</span>v</span>}}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span>\mathrm{<span><span>exp</span>exp</span>}<span><span>\&lsqb;</span>\&lsqb;</span>\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>w</span>w</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>)</span>)</span><span><span>\&rsqb;</span>\&rsqb;</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>2</span>2</span>}<span><span>)</span>)</span>$

其中，p_q(x,y)为每一个子孔径的光瞳函数，为子孔径快门调制所引入的相位差异函数，w(x,y)为稀疏光学合成孔径成像系统的像差分布，包括子孔径像差、子孔径之间的共相误差和成像光束的大气湍流畸变；Among them, p_q (x, y) is the pupil function of each sub-aperture, is the phase difference function introduced by the sub-aperture shutter modulation, w(x,y) is the aberration distribution of the sparse optical synthetic aperture imaging system, including sub-aperture aberration, common-phase error between sub-apertures and atmospheric turbulence of the imaging beam distortion;

${\mathrm{<span><span>w</span>w</span>}}_{\mathrm{<span><span>q</span>q</span>}<span><span>,</span>,</span>\mathrm{<span><span>k</span>k</span>}}^{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>v</span>v</span>}}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\left\{\begin{array}{cc}\mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>q</span>q</span>}<span><span>=</span>=</span>\mathrm{<span><span>k</span>k</span>}\\ \mathrm{<span><span>1</span>1</span>}& \mathrm{<span><span>q</span>q</span>}<span><span>\&NotEqual;</span>\&NotEqual;</span>\mathrm{<span><span>k</span>k</span>}\end{array}\right.<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>3</span>3</span>}<span><span>)</span>)</span>$

在执行过程中，采用基于Zernike函数组合表示的相位分布来近似表征稀疏光学合成孔径成像系统的像差w(x,y)的分布；During execution, a phase distribution based on a combination of Zernike functions is used To approximately characterize the distribution of the aberration w(x,y) of the sparse optical synthetic aperture imaging system;

其中，φ_q(x,y)为第q子孔径的相位分布，Z_n(x,y)表示第n阶Zernike函数，α_n表示第n阶Zernike函数的系数，目标函数E为Zernike函数系数矩阵{α_1,1,α_1,2,…,α_K,N}的函数；Among them, φ_q (x, y) is the phase distribution of the qth sub-aperture, Z_n (x, y) represents the nth order Zernike function, α_n represents the coefficient of the nth order Zernike function, and the objective function E is the Zernike function coefficient function of the matrix {α_1,1 ,α_1,2 ,…,α_K,N };

步骤B、采用随机并行梯度下降(SPGD)算法优化控制Zernike函数的模式系数，直至目标函数E达到最小，确定Zernike函数的模式系数分布，即可探测出子孔径像差、子孔径间的共相误差和成像光束大气湍流畸变；Step B, use the stochastic parallel gradient descent (SPGD) algorithm to optimize and control the mode coefficient of the Zernike function until the objective function E reaches the minimum, and determine the distribution of the mode coefficient of the Zernike function to detect the sub-aperture aberration and the common phase between the sub-apertures Errors and atmospheric turbulent distortions of imaging beams;

步骤C、根据探测到的波前像差分布，计算出稀疏光学合成孔径成像系统的光学传递函数H_k(f_x,f_y)，利用Wiener–Helstrom滤波器可以复原目标的高分辨图像，Step C, calculate the optical transfer function H_k (f_x , f_y ) of the sparse optical synthetic aperture imaging system according to the detected wavefront aberration distribution, and use the Wiener–Helstrom filter to restore the high-resolution image of the target,

$\mathrm{<span><span>R</span>R</span>}<span><span>(</span>(</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>x</span>x</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>y</span>the\; y</span>}}<span><span>,</span>,</span>\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\frac{\underset{\mathrm{<span><span>k</span>k</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>K</span>K</span>}}{<span><span>\&Sigma;</span>\&Sigma;</span>}}{\mathrm{<span><span>D</span>D.</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>x</span>x</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>y</span>the\; y</span>}}<span><span>)</span>)</span>{\mathrm{<span><span>H</span>h</span>}}_{\mathrm{<span><span>k</span>k</span>}}^{<span><span>*</span>*</span>}<span><span>(</span>(</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>x</span>x</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>y</span>the\; y</span>}}<span><span>)</span>)</span>}{\underset{\mathrm{<span><span>k</span>k</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>K</span>K</span>}}{<span><span>\&Sigma;</span>\&Sigma;</span>}}<span><span>|</span>|</span>{\mathrm{<span><span>H</span>h</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>x</span>x</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>y</span>the\; y</span>}}<span><span>)</span>)</span>{<span><span>|</span>|</span>}^{\mathrm{<span><span>2</span>2</span>}}}<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>$

R(f_x,f_y,α)为目标高清晰图像的傅里叶变换。R(f_x ,f_y ,α) is the Fourier transform of the target high-resolution image.

其中，该方法既可以探测像差，也可以复原目标的清晰图像；子图像之间的相位差异存在于电子快门的调制信息中，不引入额外像差，具有高的像差探测精度和图像复原清晰度。Among them, this method can not only detect aberrations, but also restore a clear image of the target; the phase difference between the sub-images exists in the modulation information of the electronic shutter, does not introduce additional aberrations, and has high aberration detection accuracy and image restoration clarity.

其中，该方法不仅仅可以适用于稀疏望远镜阵列系统的像差探测和图像高清晰复原，还可以适用于分片式子镜面拼接主镜系统的像差探测和图像高清晰复原。Among them, this method can not only be applied to aberration detection and high-definition image restoration of sparse telescope array systems, but also can be applied to aberration detection and high-definition image restoration of segmented sub-mirror splicing primary mirror systems.

其中，该方法所使用的优化算法为随机并行梯度下降(SPGD)算法、模拟退火算法、遗传算法、爬山法、高频振动法、神经网络算法中的一种。Wherein, the optimization algorithm used in the method is one of stochastic parallel gradient descent (SPGD) algorithm, simulated annealing algorithm, genetic algorithm, hill climbing method, high-frequency vibration method, and neural network algorithm.

其中，该方法所使用的算法控制器可以是计算机，也可以是集成电路芯片。Wherein, the algorithm controller used in the method may be a computer or an integrated circuit chip.

其中，该方法既适用于点光源的高清晰成像，也适用于扩展目标的高清晰成像。Among them, the method is suitable for both high-definition imaging of point light sources and high-definition imaging of extended targets.

其中，该方法既可以采用Zernike函数组合来表示相位分布，也可以采用Karhunen-Loeve函数组合和Lukosz-Zernike函数组合。Among them, the method can not only use Zernike function combination to represent the phase distribution, but also use Karhunen-Loeve function combination and Lukosz-Zernike function combination.

其中，该方法既可以依次对合成孔径成像系统各个子孔径成像光束进行调制，也可以分组方法依次同时对多个子孔径成像光束进行调制。Wherein, the method can not only sequentially modulate each sub-aperture imaging beam of the synthetic aperture imaging system, but also can sequentially and simultaneously modulate multiple sub-aperture imaging beams in a grouping method.

本发明与现有技术相比，具有如下优点：Compared with the prior art, the present invention has the following advantages:

(1)、基于传统相位差法的稀疏光学合成孔径成像方法，需要额外采用辅助光学器件，通过引入离焦量和分光的方法，产生离焦图像，基于焦面图像和离焦图像来获取系统的像差，对辅助光学器件的性能提出了很到的要求。本发明通过采用电子快门进行空间调制，得到包含相位差异的系列图像，没有引入调制误差，具有更高的像差测量精度。(1) The sparse optical synthetic aperture imaging method based on the traditional phase difference method requires additional auxiliary optical devices to generate a defocused image by introducing the defocus amount and light splitting method, and obtain the system based on the focal plane image and the defocused image The aberration of the optical device puts forward great requirements on the performance of the auxiliary optical device. The invention obtains a series of images including phase differences by using the electronic shutter for spatial modulation, without introducing modulation errors, and has higher aberration measurement accuracy.

(2)、本发明仅在稀疏光学合成孔径成像系统的每个子孔径里增加了一个电子快门，降低了系统对其他辅助光学元件的需求，结构简单紧凑，成本低廉，稳定性高。(2) The present invention only adds an electronic shutter in each sub-aperture of the sparse optical synthetic aperture imaging system, which reduces the system's demand for other auxiliary optical elements, and has a simple and compact structure, low cost and high stability.

附图说明Description of drawings

图1为基于子孔径快门调制的2孔径望远镜阵列合成成像系统结构示意图；Figure 1 is a schematic structural diagram of a composite imaging system with 2 aperture telescope arrays based on sub-aperture shutter modulation;

图2为4孔径望远镜阵列合成成像系统平面图；Fig. 2 is a plan view of a composite imaging system of a 4-aperture telescope array;

图3为本发明方法像差探测结果，左图为加载的像差分布，右图为探测的像差分布；Fig. 3 is the aberration detection result of the method of the present invention, the left figure is the loaded aberration distribution, and the right figure is the detected aberration distribution;

图4为本发明方法合成孔径成像目标图像高清晰复原结果，左图为单一孔径成像模糊图像，右图为恢复的四孔径合成孔径成像清晰图像。Fig. 4 is the high-definition restoration result of the synthetic aperture imaging target image by the method of the present invention, the left picture is a single aperture imaging blurred image, and the right picture is the restored four-aperture synthetic aperture imaging clear image.

具体实施方式detailed description

下面结合附图以及具体实施方式进一步说明本发明。The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

以2孔径望远镜阵列系统为例，基于子孔径快门调制的稀疏光学合成孔径成像系统结构如图1所示，由两台望远镜组成。图中1为望远镜，2为电子快门，3为反射镜，4为合束器，5为成像透镜，6为成像探测系统，7为控制处理计算机。控制处理计算机，一方面，控制电子快门实现成像光束的依次通断，实现对合成成像系统的空间调制，另一方面，控制成像探测系统，采集相对应的调制图像，并对调制图像进行实时处理，获取子孔径像差、子孔径间共相误差、成像光束大气湍流畸变和目标的高清晰图像。Taking the 2-aperture telescope array system as an example, the structure of the sparse optical synthetic aperture imaging system based on sub-aperture shutter modulation is shown in Figure 1, which consists of two telescopes. In the figure, 1 is a telescope, 2 is an electronic shutter, 3 is a mirror, 4 is a beam combiner, 5 is an imaging lens, 6 is an imaging detection system, and 7 is a control processing computer. The control processing computer, on the one hand, controls the electronic shutter to realize the sequential on-off of the imaging beam, and realizes the spatial modulation of the composite imaging system; on the other hand, controls the imaging detection system, collects the corresponding modulated image, and performs real-time processing on the modulated image , to obtain high-definition images of sub-aperture aberrations, co-phase errors between sub-apertures, atmospheric turbulent distortion of imaging beams, and targets.

下面以4孔径成像系统为例对本发明做进一步的描述。图2所示为一个4孔径成像系统结构示意简图，分别由子系统1，2，3和4组成。其具体的工作过程为：The present invention will be further described below by taking a 4-aperture imaging system as an example. FIG. 2 is a schematic structural diagram of a 4-aperture imaging system, which is composed of subsystems 1, 2, 3 and 4, respectively. Its specific working process is:

(1)关闭子系统1的电子快门，采集相应图像；打开子系统1的电子快门，关闭子系统2的电子快门，采集相应图像；打开子系统2的电子快门，关闭子系统3的电子快门，采集相应图像；打开子系统3的电子快门，关闭子系统4的电子快门，采集相应图像；打开子系统4的电子快门，保持4个电子快门都为开启状态，采集相应图像。(1) Close the electronic shutter of subsystem 1, and collect corresponding images; open the electronic shutter of subsystem 1, close the electronic shutter of subsystem 2, and collect corresponding images; open the electronic shutter of subsystem 2, and close the electronic shutter of subsystem 3 , collect the corresponding image; open the electronic shutter of subsystem 3, close the electronic shutter of subsystem 4, and collect the corresponding image; open the electronic shutter of subsystem 4, keep all 4 electronic shutters in the open state, and collect the corresponding image.

(2)使用基于子孔径快门调制的相位差算法对所采集的5幅子图像进行处理，探测子孔径的像差和多孔径之间的光束共相误差，并重建高分辨的图像。四孔径合成孔径成像像差探测和目标图像高清晰复原结果分别如图3和图4所示。图3中，左图为加载的像差分布，主要包括多孔径间的共相误差和其它像差，右图为探测出来的像差分布；加载像差分布和探测像差分布基本一致，均方根误差小于0.05λ(λ为成像光束波长)。由图可知，本发明方法可以有效地探测合成孔径成像系统的像差分布和实现目标图像的高清晰复原。(2) Use the phase difference algorithm based on sub-aperture shutter modulation to process the collected 5 sub-images, detect the aberration of the sub-aperture and the common phase error of the beam between multiple apertures, and reconstruct a high-resolution image. The results of four-aperture synthetic aperture imaging aberration detection and target image high-definition restoration are shown in Figure 3 and Figure 4, respectively. In Fig. 3, the left picture shows the loaded aberration distribution, which mainly includes the common-phase error and other aberrations between multi-apertures, and the right picture shows the detected aberration distribution; the loading aberration distribution and the detection aberration distribution are basically the same, both The square root error is less than 0.05λ (λ is the wavelength of the imaging beam). It can be seen from the figure that the method of the present invention can effectively detect the aberration distribution of the synthetic aperture imaging system and realize high-definition restoration of the target image.

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。只要是通过电子快门对稀疏光学合成孔径成像系统进行空间调制，并利用相位差算法进行共相误差探测并且复原高分辨图像，均属于本发明的保护范围。The above descriptions are only specific implementation methods in the present invention, but the protection scope of the present invention is not limited thereto. As long as the spatial modulation of the sparse optical synthetic aperture imaging system is performed through the electronic shutter, and the phase difference algorithm is used to detect the common phase error and restore the high-resolution image, all belong to the protection scope of the present invention.

Claims (8)

1. a sparse optical synthesis aperture formation method based on sub-aperture shutter phase modulation difference method, it is characterised in that the method includes the steps of:

Step (1), utilize electronic shutter that each sub-aperture of sparse optical synthesis aperture imaging system or multiple sub-aperture carry out switch modulation successively, and record successively with imageing sensor sparse synthesis aperture imaging system modulated after corresponding image；

Image series is processed by step (2), use based on sub-aperture shutter phase modulation difference algorithm, detects the common phase error between the aberration of sub-aperture, multiple aperture and the distortion of imaging beam atmospheric turbulance, and rebuilds the high-resolution image of target；Concrete Processing Algorithm is as follows:

Step A, set up object function E according to Maximum-likelihood estimation or Least-squares minimization theory:

$E=\underset{f_x,f_y}{\mathrm{\&Sigma;}}\underset{k=0}{\overset{K}{\mathrm{\&Sigma;}}}|D_k(f_x,f_y){|}^2-\underset{f_x,f_y}{\mathrm{\&Sigma;}}\frac{\underset{k=0}{\overset{K}{\mathrm{\&Sigma;}}}|D_k(f_x,f_y)H_k^{*}(f_x,f_y){|}^2}{\underset{k=0}{\overset{K}{\mathrm{\&Sigma;}}}|H_k^{*}(f_x,f_y){|}^2}---\left(1\right)$

Wherein, K is the number of sparse aperture imaging system sub-aperture, D_k(f_x,f_y) it is the Fourier transformation of the subimage of collection, H after kth subsystem shutter is modulated_k(f_x,f_y) it is the optical transfer function of synthesis aperture imaging system after kth subsystem shutter is modulated,It is H_k(f_x,f_y) conjugation, wherein k is that the 0 all of shutter of expression is all in opening, f_xAnd f_yFor frequency domain coordinates；

According to Fourier optics theory, the optical transfer function of imaging system is the Fourier transformation of imaging system point spread function, and the point spread function of imaging system is determined by the pupil function of imaging system, and the pupil function of sparse aperture imaging system can be expressed as:

$P_k(x,y)=\underset{q=0}{\overset{K}{\&Sigma;}}{p}_q(x,y)\&times;w_{q,k}^{div}(x,y)\&times;\exp \&lsqb;iw(x,y)\&rsqb;---\left(2\right)$

Wherein, p_q(x, y) is the pupil function of each sub-aperture,For the sub-aperture shutter introduced phase difference function of modulation, (x, y) is the aberration profile of sparse optical synthesis aperture imaging system to w, and the atmospheric turbulance including the common phase error between sub-aperture aberration, sub-aperture and imaging beam distorts；

$w_{q,k}^{div}(x,y)=\left\{\begin{array}{cc}0& q=k\\ 1& q\&NotEqual;k\end{array}\right.---\left(3\right)$

In the process of implementation, the PHASE DISTRIBUTION represented based on Zernike combination of function is usedApproximate aberration w (x, distribution y) characterizing sparse optical synthesis aperture imaging system；

Wherein, φ_q(x y) is the PHASE DISTRIBUTION of q sub-aperture, Z_n(x y) represents n-th order Zernike function, α_nRepresenting the coefficient of n-th order Zernike function, object function E is Zernike function coefficients matrix { α_1,1,α_1,2,…,α_K,NFunction；

Step B, employing stochastic parallel gradient descent (SPGD) algorithm optimization control the mode coefficient of Zernike function, until object function E minimizes, determine the mode coefficient distribution of Zernike function, the common phase error between sub-aperture aberration, sub-aperture and the distortion of imaging beam atmospheric turbulance can be detected；

The wave front aberration distribution that step C, basis detect, calculates the optical transfer function H of sparse optical synthesis aperture imaging system_k(f_x,f_y), utilize Wiener Helstrom wave filter can with the full resolution pricture of rejuvenation target,

$R(f_x,f_y,\mathrm{\&alpha;})=\frac{\underset{k=0}{\overset{K}{\&Sigma;}}{D}_k(f_x,f_y)H_k^{*}(f_x,f_y)}{\underset{k=0}{\overset{K}{\&Sigma;}}|H_k(f_x,f_y){|}^2}---\left(5\right)$

R(f_x,f_y, α) and it is the Fourier transformation of target HD image.

Sparse optical synthesis aperture formation method based on sub-aperture shutter phase modulation difference method the most according to claim 1, it is characterised in that the method both can detect aberration, it is also possible to the picture rich in detail of rejuvenation target；Phase difference between subimage is present in the modulation intelligence of electronic shutter, does not introduce additional aberration, has high aberration detection accuracy and image restoration definition.

Sparse optical synthesis aperture formation method based on sub-aperture shutter phase modulation difference method the most according to claim 1, it is characterized in that, the method not only goes for aberration detection and the recovery of image high-resolution of sparse telescope array system, it is also possible to the aberration detection and the image high-resolution that are applicable to burst formula minute surface splicing master lens system are restored.

Sparse optical synthesis aperture formation method based on sub-aperture shutter phase modulation difference method the most according to claim 1, it is characterized in that, the optimized algorithm that the method is used is the one in stochastic parallel gradient descent (SPGD) algorithm, simulated annealing, genetic algorithm, climbing method, high-frequency vibration method, neural network algorithm.

Sparse optical synthesis aperture formation method based on sub-aperture shutter phase modulation difference method the most according to claim 1, it is characterised in that the algorithmic controller that the method is used can be computer, it is also possible to be IC chip.

Sparse optical synthesis aperture formation method based on sub-aperture shutter phase modulation difference method the most according to claim 1, it is characterised in that the method is not only suitable for the high-resolution imaging of point source, is also applied for the high-resolution imaging of Extended target.

Sparse optical synthesis aperture formation method based on sub-aperture shutter phase modulation difference method the most according to claim 1, it is characterized in that, the method both can use Zernike group of functions incompatible expression PHASE DISTRIBUTION, it would however also be possible to employ Karhunen-Loeve combination of function and Lukosz-Zernike combination of function.

Sparse optical synthesis aperture formation method based on sub-aperture shutter phase modulation difference method the most according to claim 1, it is characterized in that, each sub-aperture image light beam of synthesis aperture imaging system both can be modulated by the method successively, it is also possible to multiple sub-aperture image light beams are modulated by group technology the most simultaneously.