Wavefront error correction optical imaging system and method

Abstract

The present application relates to wavefront detection and error correction technical field, especially to a kind of wavefront error correction optical imaging system and method.The system includes successively in the direction of light propagation: receiving optical unit, for collecting starlight and converging, then output spherical wavefront and transfer to collimating unit;Collimating unit, for converting spherical wavefront into plane wavefront;Wavefront measurement and imaging unit, including several micro-imaging channels, simultaneously complete wavefront detection and star point measurement;Detector is located on the best focal plane position of wavefront measurement and imaging unit, for obtaining the image of corresponding star point of the same object side target;Processor is used to process the star point image obtained by detector, realize wavefront error calculation, wavefront recovery, star point compensation and centroid calculation and star angular distance output.The advantage is that the integration of wavefront measurement, wavefront correction and starlight angular distance measurement is realized, without splitting, and the angular measurement accuracy is improved through multi-channel data fusion;More efficient, improve detection sensitivity.

Description

Technical Field

[0001] The present invention relates to the technical field of wavefront detection and error correction, and in particular to an optical imaging system and method for wavefront error correction. Background Art

[0002] As a core component of spacecraft, star sensors are widely used in navigation, positioning, attitude control, and other fields. Traditional star sensors still have significant room for improvement in measurement accuracy and anti-interference capabilities, especially in complex environments. In particular, at high speeds and under complex atmospheric conditions, aerodynamic turbulence and plasma luminescence can significantly affect the quality of starlight, resulting in a decrease in star sensor measurement accuracy. As a core component in aerospace, satellite navigation, and astronomical observation, star sensors primarily determine the platform's attitude information by analyzing star images. Traditional star sensors typically rely on the radiation characteristics of stars to obtain star point information and use image processing algorithms to calculate the star point's direction. However, as platforms continue to demand higher measurement accuracy, speed, and anti-interference capabilities, traditional star sensors face a series of challenges in complex environments.

[0003] In high-altitude or low-Earth orbit environments, aerodynamic turbulence and plasma luminescence are two major factors affecting the performance of star sensors. On the one hand, during high-speed flight or when subjected to dramatic atmospheric changes, aerodynamic turbulence can cause uneven air flow, resulting in wavefront distortion, affecting the quality of starlight and increasing errors in measured angles. The impact of aerodynamic turbulence is particularly pronounced on platforms flying at high speeds or experiencing significant atmospheric fluctuations, posing a serious threat to the star sensor's measurement accuracy. On the other hand, plasma luminescence interferes with the operation of star sensors. Under the influence of high-energy particle radiation, the plasma emits irregular background light, reducing the signal-to-noise ratio of starlight, blurring the star image, or even completely obscuring the target star. Existing star sensors have not yet effectively addressed this issue, limiting their application in complex environments.

[0004] Correcting image distortion caused by atmospheric turbulence has become a hot topic in the field of photoelectric detection. Numerous studies have focused on mitigating the effects of atmospheric turbulence, primarily using two approaches: adaptive optics and image processing. Adaptive optics employs a wavefront corrector that, in response to the output wavefront distortion signal, changes the mirror shape under an applied voltage, thereby altering the lightwave propagation path or modifying the refractive index of the output medium to correct the wavefront phase. While this approach can effectively compensate for wavefront distortion, it requires large, complex, and costly hardware and is commonly used in large ground-based astronomical telescope systems. While these systems offer significant advantages in improving image resolution, their high complexity, bulk, and high power consumption make them difficult to directly implement in small, lightweight, and low-power systems such as star sensors. Other studies have attempted to compensate for turbulence effects through post-processing image processing methods (such as lucky imaging, multi-frame fusion, and deep learning enhancement algorithms). However, these approaches are essentially ex post compensation mechanisms and still have limitations in improving real-time performance and accuracy.

[0005] In terms of wavefront measurement technology, some patent applications attempt to combine interferometry, adaptive optics, and star sensors. For example, US Patent Application No. US5684545A, published on November 4, 1997, and titled “Adaptive optics wave measurement and correction system,” discloses a real-time wavefront error measurement and compensation system for measuring and correcting wavefront distortion to improve image quality. This system uses a wavefront sensor in a large ground-based telescope to measure the wavefront and controls a deformable mirror to correct the wavefront. This solution separates the starlight measurement from the wavefront control process and is not suitable for lightweight space payloads. US Patent Application No. US7460245B2, published on December 2, 2008, and titled “Apparatus and method for measurement and compensation of atmospheric turbulence effects in wavefront interferometry,” discloses an apparatus and method for measuring and compensating for the effects of atmospheric turbulence on wavefront interferometry. It describes a method for measuring and compensating for the effects of air disturbances in an interferometer, but the apparatus is bulky. A U.S. patent application with publication number US20070077071A1, publication date April 5, 2007, and invention name “System for measuring atmospheric turbulence” discloses a system for measuring atmospheric turbulence, which adopts time-sharing or multi-path sampling to obtain wavefront changes, uses a wavefront sensor to measure starlight to estimate the wavefront error caused by turbulence, and models and estimates the starlight transmission disturbed by turbulence.

[0006] Although the above technologies have improved the adaptability to atmospheric disturbances to a certain extent, they generally have the following shortcomings: (1) the wavefront measurement is separated from the starlight measurement system, the structure is complex, and the signal coupling efficiency is low; (2) there is a lack of optical design optimized for star sensor accuracy, and the improvement of centroid extraction performance is limited. Therefore, most current star sensors are based on traditional optical designs and use independent star sensors and wavefront detection systems. Although these designs have met the basic starlight measurement needs to a certain extent, there are several significant problems in practical applications:

[0007] (1) Low anti-interference capability: Due to the influence of aerodynamic turbulence and plasma effects, traditional star sensors have difficulty in stable operation in complex environments. Some star sensors use additional hardware to compensate, but this method increases the complexity and weight of the system, making it difficult to adapt to the platform. Current star sensor systems fail to effectively cope with interference in complex environments, especially under the influence of high-energy particles and aerodynamic turbulence, and often suffer from inaccurate measurements.

[0008] (2) Weight and volume limitations: Especially for small satellites and space platforms, the strict weight and volume limitations make it difficult for existing designs to meet the requirements. Many high-performance star sensors require additional hardware and sensor components, resulting in system weight exceeding the platform's carrying capacity.

[0009] (3) Separation of wavefront detection and starlight measurement: Currently, the wavefront detection and starlight measurement of star sensors usually work independently. The wavefront detection system measures wavefront distortion through an independent sensor, while the star sensor independently locates the star point. Although this design can work under certain conditions, in complex environments, the separation of the two systems can easily lead to inconsistent information, affecting measurement accuracy.

[0010] Therefore, there is an urgent need to design a new optical system architecture to break through the bottlenecks of traditional star sensors in adaptability to complex environments, platform constraints and multi-parameter collaborative measurement, and simultaneously optimize the anti-interference ability, lightweight integration and measurement accuracy collaborative improvement mechanism to achieve high-precision, high-adaptability and high-integration starlight detection and star angular distance measurement under complex working conditions. Summary of the Invention

[0011] In order to solve the above problems, the present invention provides a wavefront error correction optical imaging system and method.

[0012] The first object of the present invention is to provide a wavefront error correction optical imaging system, which includes a receiving optical unit, a collimation unit, a wavefront measurement and imaging unit, a detector and a processor in sequence along the light propagation direction;

[0013] The receiving optical unit is used to collect and converge starlight, then output a spherical wavefront and transmit it to the collimation unit;

[0014] A collimating unit, used for converting the spherical wavefront output by the receiving optical unit into a plane wavefront;

[0015] The wavefront measurement and imaging unit includes N×N micro-imaging channels, each of which corresponds to a different detector area, and is used to simultaneously complete wavefront detection and star point measurement;

[0016] The detector is located at the optimal focal plane position of the wavefront measurement and imaging unit, and is used to obtain images of N×N star points corresponding to the same object space target;

[0017] The processor is used to process the star point image obtained by the detector to realize wavefront error calculation, wavefront recovery, star point compensation and centroid calculation and star angle distance output.

[0018] Preferably, the receiving optical unit includes an entrance pupil, a converging lens group and a field stop in sequence along the light propagation direction;

[0019] The entrance pupil is used to limit the effective aperture of the receiving optical unit; the converging lens group is used to converge the energy entering the system through the entrance pupil; the field stop is used to limit the imaging field of view of the converging lens group and suppress stray light outside the field of view.

[0020] Preferably, the collimating unit includes a collimating lens group and an exit pupil in sequence along the light propagation direction;

[0021] The front focal plane of the collimating lens group coincides with the rear focal plane of the receiving optical unit and the aperture angles match, and is used to convert the spherical wavefront output by the receiving optical unit into a plane wavefront; an aperture stop is set at the exit pupil to suppress stray light.

[0022] Preferably, the wavefront measurement and imaging unit uses an N×N microlens array to form N×N micro imaging channels; the microlens array performs wavefront segmentation and measurement operations on the exit pupil of the collimating unit, dividing the exit pupil of the collimating unit into N×N sub-pupils, and each sub-pupil is imaged separately on the sensitive surface of the detector;

[0023] The size of the detector sensitive surface is not less than the imaging range of the wavefront measurement and imaging unit.

[0024] Preferably, the working process of the processor includes:

[0025] Star point calculation: N×N star point image acquisition, centroid position calculation and energy distribution calculation;

[0026] Wavefront error calculation: Analyze the N×N star point energy distribution results, combine the micro-imaging channel parameters, calculate the wavefront error contained in the star point, and perform parameterized fitting of the wavefront error;

[0027] Wavefront recovery: Calculate the wavefront compensation parameters based on the wavefront error calculation results to compensate for the system's comprehensive residual wavefront error;

[0028] Star point compensation: Using the wavefront compensation parameters obtained from wavefront recovery, deconvolution operations are performed on the point spread functions corresponding to each star point in the N×N micro-imaging channel. This eliminates the influence of the system's comprehensive residual wavefront error on star point imaging, achieving error correction and quality improvement for N×N star points.

[0029] Centroid calculation: Use the weighted average method to recalculate the energy centroid position of the corrected N×N star point images and record the pixel coordinates of the centroid of each star point;

[0030] Centroid averaging: Based on the coordinate relationship between the detector and the wavefront measurement and imaging unit, the centroid positions of N×N star points are calibrated and normalized, and the average value of the centroid positions of N×N star points on the detector is calculated;

[0031] Star angle distance output: Based on the average value of the star point centroid position, combined with the focal length parameters of the receiving optical unit, collimation unit, detector and wavefront measurement and imaging unit, the angle between target star points in different object spaces and the system optical axis is calculated, and the star angle distance between different target stars is solved to achieve the measurement and output of the inter-satellite angle.

[0032] Preferably, the energy distribution calculation method is as follows:

[0033] With the energy centroid (xc, yc) as the center, gradually increase the radius r from small to large, and calculate the total energy EE(r) within the circle corresponding to each r until the minimum r that satisfies EE(r) ≥ 0.95 is found;

[0034] Choose a small radius increment dr; for each radius r, calculate the total energy EE(r) contained in a circle with radius r centered on the energy centroid; if EE(r) is less than 0.95, update r = r + dr;

[0035] Traverse all pixels (x,y) in the image;

[0036] Calculate the distance from the pixel to the centroid: ; Where d represents the distance between two points on the plane, (x, y) represents the pixel coordinates, and (xc, yc) represents the centroid coordinates;

[0037] If d≤r, add the pixel intensity value I(x, y) to the total energy C within the current radius;

[0038] Calculate the current encirclement energy: EE(r) = C;

[0039] Check: If EE(r)≥0.95, then EE95=r and the calculation ends; if EE(r)<0.95, return and continue to increase r;

[0040] The parameterized fitting method is as follows:

[0041] Calculate the Zernike polynomials of various orders corresponding to the full-aperture wavefront phase;

[0042] Fit the coefficients of each Zernike term;

[0043] Reconstruct the wavefront using the fitted coefficients;

[0044] Differentiate the reconstructed wavefront to obtain the wavefront slope;

[0045] The average slope within the subaperture is measured using a Shack-Hartmann wavefront detector;

[0046] The measurement results are converted into a matrix form to obtain a slope matrix;

[0047] Solve the coefficient matrix using the least squares minimum norm solution method;

[0048] The original wavefront parameters are solved using the solved coefficient matrix.

[0049] Preferably, the system comprehensive residual wavefront error includes the wavefront error caused by external turbulence, the design residual wavefront error of the receiving optical unit and the collimation unit, and the integration error caused by processing and integration tolerances;

[0050] The average value of the centroid position The calculation formula is:

[0051] ;

[0052] Where: 、 Respectively represent the centroid positions of N×N star points x Direction and y The average value of the directional coordinates; 、 Represents the centroid of the i-th star point on the detector sensitive surface x Direction and y Pixel coordinates of the direction; Indicates the number of micro-imaging channels and the corresponding number of star point images.

[0053] A second object of the present invention is to provide a wavefront error correction optical imaging method, which uses a wavefront error correction optical imaging system for imaging, specifically comprising the following steps:

[0054] S1. Starlight Reception and Preliminary Optical Processing: Starlight is collected and concentrated by the receiving optical unit, and the spherical wavefront is output to the back-end collimator unit.

[0055] S2. Wavefront conversion and optical parameter matching: The spherical wavefront is converted into a planar wavefront through the collimation unit and output to the wavefront measurement and imaging unit;

[0056] S3. Wavefront Segmentation and Star Image Acquisition: Wavefront segmentation and star image acquisition are performed using the wavefront measurement and imaging unit and detector.

[0057] S4. Wavefront Error Calculation and Parameter Fitting: The processor performs wavefront error analysis on the N × N star point images collected by the detector and quantifies the wavefront error through energy distribution analysis.

[0058] S5. Wavefront recovery: The processor calculates the wavefront compensation parameters based on the wavefront error parameterization result obtained in step S4;

[0059] S6. Star image error compensation: Using the inverse convolution algorithm, the point spread function of the star point is inversely corrected based on the wavefront compensation parameters, and the corrected N×N star point images are output;

[0060] S7. Centroid Positioning Optimization and Star Angular Distance Output: The processor calculates and optimizes the centroid of the corrected star point image and ultimately outputs the star angular distance.

[0061] Preferably, step S4 specifically includes the following steps:

[0062] S401. Perform star point calculation: extract energy distribution data of star point image;

[0063] S402. Analyze the energy distribution characteristics and calculate the wavefront error of the star point based on the optical parameters of the micro-imaging channel;

[0064] S403. Perform parameter fitting on the wavefront error to obtain wavefront error parameters.

[0065] Preferably, step S7 specifically includes the following steps:

[0066] S701. Centroid calculation: Calculate the pixel coordinates of the energy centroid of the corrected N×N star points using the weighted average method;

[0067] S702. Centroid averaging: Calibrate and normalize the centroid coordinates based on the coordinate relationship between the detector, wavefront measurement, and imaging unit, and calculate the average value of N×N centroid positions; the average value of the centroid position The calculation formula is:

[0068] ;

[0069] Where: 、 Respectively represent the centroid positions of N×N star points x Direction and y The average value of the directional coordinates; 、 Represents the centroid of the i-th star point on the detector sensitive surface x Direction and y Pixel coordinates of the direction; Indicates the number of micro-imaging channels and the corresponding number of star point images;

[0070] S703. Star angular distance calculation: Combine the focal length parameters of the receiving optical unit, collimation unit, and wavefront measurement and imaging unit, calculate the angle between different target star points and the system optical axis based on the average value of the center of mass, solve the star angular distance between stars and output it.

[0071] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0072] (1) The wavefront correction and optical imaging system and method proposed in the present invention can realize the integration of wavefront measurement, wavefront correction and starlight angular distance measurement, and has the characteristics of simultaneous wavefront measurement, common aperture and common field of view. The wavefront error measured and corrected is the wavefront error contained in the current starlight imaging, which solves the problem that the wavefront measurement and correction of traditional systems and traditional methods cannot be simultaneous, common aperture or common field of view.

[0073] (2) No need to use spectroscopic form. Compared with the traditional method that needs to split part of the energy received by the system for wavefront error measurement, the system efficiency of this imaging method is higher, which is conducive to improving the detection sensitivity; and the system configuration is simpler;

[0074] (3) It can simultaneously correct the wavefront error caused by turbulence, the residual wave aberration of the optical system design, and the wavefront error caused by the system integration error. The wavefront error of the corrected imaging system is smaller, and the difficulty of designing and integrating the optical system is reduced;

[0075] (4) By averaging the centroid positions of N × N star point images corresponding to the same star point target in the object space, the random error of the centroid position can be greatly suppressed, and the centroid positioning accuracy is improved by N times;

[0076] (5) It has a real entrance pupil, a real exit pupil and an intermediate image plane, and can set an aperture stop and a field stop to suppress stray light outside the field of view, further improving the system's detection capability.

[0077] In summary, this invention proposes a novel star sensor design that integrates wavefront detection and starlight measurement. Utilizing microlens array technology and advanced compensation algorithms, it significantly improves the system's performance in complex environments, specifically addressing the effects of aerodynamic turbulence and plasma luminescence. Wavefront measurement and starlight detection share a common optical path and image plane, eliminating the need for spectroscopic analysis. This allows for both wavefront measurement and correction without compromising starlight detection sensitivity. While maintaining detection sensitivity, wavefront correction improves single-channel measurement accuracy. Furthermore, multi-channel data processing and fusion further eliminates random system errors, significantly enhancing starlight measurement accuracy. This results in higher efficiency and enhanced detection sensitivity. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1Schematic diagram of the composition of a wavefront error correction optical imaging system provided according to an embodiment of the present invention.

[0079] Figure 2 Schematic diagram of N×N micro-imaging channels of a wavefront measurement and imaging unit provided according to an embodiment of the present invention.

[0080] Figure 3 1 is an imaging optical path diagram of N×N micro imaging channels of a wavefront measurement and imaging unit provided according to an embodiment of the present invention.

[0081] Figure 4 These are images of N×N star points corresponding to the same object space target obtained by the detector provided by an embodiment of the present invention.

[0082] Reference numerals:

[0083] 1. Receiving optical unit;

[0084] 101. Entrance pupil; 102. Converging lens group; 103. Field stop;

[0085] 2. Collimation unit;

[0086] 201. Collimator lens assembly; 202. Exit pupil;

[0087] 3. Wavefront measurement and imaging unit;

[0088] 301. Microlens array;

[0089] 4. Detector;

[0090] 5. Processor. DETAILED DESCRIPTION

[0091] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In the following description, identical modules are denoted by identical reference numerals. In the case of identical reference numerals, their names and functions are also identical. Therefore, their detailed description will not be repeated.

[0092] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0093] In order to resolve the contradiction between the complex aerodynamic turbulence effect and the plasma luminescence effect on the wavefront detection capability, angular measurement accuracy and system weight constraint, the present invention provides a wavefront error correction optical imaging system, and innovatively proposes an integrated design of star sensor and wavefront detection; the system integrates the functions of the star sensor and the Hartmann wavefront detector into the same optical imaging system, thereby realizing common aperture detection. By designing the wavefront measurement and imaging components, the system can simultaneously complete wavefront detection and star point measurement in the same optical path. The schematic diagram of the system composition is shown in the figure below. Figure 1 As shown, along the light propagation direction, it includes a receiving optical unit 1, a collimating unit 2, a wavefront measurement and imaging unit 3, a detector 4 and a processor 5;

[0094] The receiving optical unit 1 is used to collect starlight and transmit it to the collimating unit 2 and wavefront measurement and imaging unit 3 at the rear end. It can adopt a transmission or reflection scheme and be configured as on-axis or off-axis.

[0095] Specifically, the receiving optical unit 1 includes an entrance pupil 101, a converging lens group 102 and a field stop 103; the entrance pupil 101 is located in front of the converging lens group 102, and is used to limit the effective aperture of the receiving optical unit. At the same time, an aperture stop can be set at the entrance pupil 101 to improve the system's stray light suppression capability; the converging lens group 102 is used to converge the energy entering the optical imaging system through the entrance pupil 101; the field stop 103 is located at the focal plane position of the converging lens group 102, and is used to limit the imaging field of view of the converging lens group 102, and also has the ability to suppress stray light outside the field of view; the wavefront output by the receiving optical unit is a spherical wave.

[0096] Collimation unit 2 is used to convert the spherical wavefront output by receiving optical unit 1 into a plane wavefront; the front focal plane of collimation unit 2 coincides with the back focal plane of receiving optical unit, and the aperture angles are matched; the exit pupil of collimation unit 2 is located at the rear end of collimation unit 2, and an aperture stop can be set to improve the system's stray light suppression capability;

[0097] Specifically, the collimating unit 2 includes a collimating lens group 201 and an exit pupil 202; the collimating lens group 201 is the core component of the collimating unit 2, and its function is to convert the spherical wavefront output by the receiving optical unit 1 into a plane wavefront; the collimating lens group 201 is located at the rear end of the receiving optical unit, the front focal plane coincides with the rear focal plane of the receiving optical unit, and the aperture angles are matched, ensuring accurate conversion of light; the design of the collimating lens group 201 can be a transmission or reflection scheme, and the optical configuration can be coaxial or off-axis, which can be flexibly selected according to actual needs and system requirements; the exit pupil 202 is located at the rear end of the collimating unit 2, and an aperture stop can be set at the exit pupil 202. By reasonably setting the aperture stop, the system's stray light suppression capability can be effectively improved, ensuring imaging quality and the accuracy of wavefront measurement.

[0098] The wavefront measurement and imaging unit 3 includes multiple micro-imaging channels, each of which corresponds to a different detector 4 area, and is used to simultaneously complete wavefront detection and star point measurement;

[0099] Specifically, the wavefront measurement and imaging unit 3 is located at the rear end of the collimating unit 2, and the exit pupil 202 of the collimating unit 2 matches the entrance pupil of the wavefront measurement and imaging unit 3; the wavefront measurement and imaging unit 3 uses an N×N microlens array 301 to form N×N micro imaging channels ( Figure 2 ), respectively, wavefront segmentation and measurement operations are performed on the exit pupil 202 of the collimating unit 2, and then the exit pupil 202 is divided into N×N sub-pupils. Each sub-pupil is imaged on the sensitive surface of the detector 4. For the same object space star point target, N×N star point images can be formed simultaneously; the imaging optical path diagram of the N×N micro imaging channels is shown in Figure 3 .

[0100] Detector 4, used to obtain N×N star point images of the same object space target;

[0101] Specifically, the detector 4 is located at the optimal focal plane position of the wavefront measurement and imaging unit 3. The detector 4 can obtain images of N×N star points corresponding to the same object space target. The relative coordinates of the position coordinates of the N×N star points on the detector 4 are consistent ( Figure 4 ); The size of the sensitive surface of the detector 4 is not less than the imaging range of the wavefront measurement and imaging unit 3.

[0102] Processor 5 is used to process the star point image obtained by detector 4 to realize wavefront error calculation, wavefront recovery, star point compensation and centroid calculation and star angular distance output. Processor 5 includes hardware circuit and embedded software. The working process of the processor includes:

[0103] Star point calculation: N×N star point images are collected. Based on the pixel response and coordinate position, the energy centroid of the star point is calculated. The energy distribution diameter of the star point image is calculated with the energy centroid as the center. The energy distribution calculation is completed using EE95 as the evaluation index. EE95 is an evaluation index of energy concentration (encircled energy), which specifically indicates the proportion of total energy contained in a specific area. The energy distribution calculation method is as follows:

[0104] (1) With the energy center of mass (xc, yc) as the center, gradually increase the radius r from small to large, and calculate the total energy EE(r) within the circle corresponding to each r until the minimum r is found that satisfies EE(r) ≥ 0.95;

[0105] (2) Choose a small radius increment dr (e.g., 0.1 pixel or less, depending on the accuracy requirements and computational effort); for each radius r, calculate the total energy EE(r) contained within a circle of radius r centered on the energy centroid; if EE(r) is less than 0.95, update r = r + dr;

[0106] (3) Traverse all pixels (x, y) in the image;

[0107] (4) Calculate the distance from the pixel to the centroid: ; Where d represents the distance between two points on the plane, (x, y) represents the pixel coordinates, and (xc, yc) represents the centroid coordinates;

[0108] (5) If d≤r, the intensity value I(x, y) of the pixel is added to the total energy C within the current radius;

[0109] (6) Calculate the current enveloping energy: EE(r) = C;

[0110] (7) Check: If EE(r) ≥ 0.95, then EE95 = r and the calculation ends; if EE(r) < 0.95, return to step (2) and continue to increase r.

[0111] Wavefront error calculation: Analyze the N×N star point energy distribution results, combine the micro-imaging channel parameters, calculate the wavefront error contained in the star point, and perform parameter fitting on the wavefront error. The parameter fitting method is as follows:

[0112] First, the Zernike polynomials of various orders corresponding to the full-aperture wavefront phase are calculated, and then the coefficients of each Zernike term are fitted to complete the wavefront reconstruction.

[0113] The Zernike polynomial of the wavefront on the circular domain is:

[0114] ;

[0115] Where, represents the coefficient of the kth Zernike polynomial; represents the kth Zernike polynomial; Z is the Zernike polynomial matrix; A is the coefficient matrix; M is the selected Zernike polynomial order.

[0116] It is known that the Shack-Hartmann wavefront detector measures the wavefront slope, so it is necessary to differentiate the above formula to obtain the following formula:

[0117]

[0118] Where, and is the measurement error.

[0119] Since the average slope within the subaperture is measured using a Shack-Hartmann wavefront detector, we have:

[0120] ;

[0121] Rewrite the above formula into matrix form, that is:

[0122] ;

[0123] Where G is a 2N-dimensional vector; D is a 2N×M matrix; and A is an M-dimensional vector.

[0124] Similar to the regional method, the above equation can also obtain the least squares minimum norm solution:

[0125] ;

[0126] After obtaining the coefficient matrix A, the original wavefront parameters can be solved.

[0127] Wavefront recovery: Based on the wavefront error calculation results, the wavefront compensation parameters are calculated to compensate for the system's comprehensive residual wavefront error. The system's comprehensive residual wavefront error is composed of the wavefront error caused by external turbulence, the design residual wavefront error of the receiving optical unit and the collimation unit, and the integration error caused by processing and integration tolerances.

[0128] Star point compensation: Using the wavefront compensation parameters obtained from wavefront recovery, deconvolution operations are performed on the point spread functions corresponding to each star point in the N×N micro-imaging channel to eliminate the influence of the system's comprehensive residual wavefront error on star point imaging, thus achieving error correction and quality improvement for N×N star points.

[0129] Centroid calculation: Use the weighted average method to recalculate the energy centroid position of the corrected N×N star point images and record the pixel coordinates of the centroid of each star point;

[0130] Centroid averaging: Based on the coordinate relationship between the detector, wavefront measurement and imaging unit, the centroid positions of N×N star points are calibrated and normalized, and the average value of the centroid positions of N×N star points on the detector is calculated, which reduces the random error of the centroid position of the star point by N times and improves the centroid positioning accuracy by N times; the average value of the centroid position The calculation formula is:

[0131] ;

[0132] Star angular distance output: Based on the average value of the star point centroid position obtained by centroid averaging, combined with the focal length parameters of the receiving optical unit, collimation unit, detector and wavefront measurement and imaging unit, the angle between the target star points in different object spaces and the system optical axis is calculated, and then the star angular distance between different target stars is solved, ultimately realizing the measurement and output of the inter-satellite angle.

[0133] Based on the above device, the present invention provides a wavefront error correction optical imaging method, which specifically includes the following steps:

[0134] S1. Starlight Reception and Preliminary Optical Processing: Starlight is collected and concentrated by the receiving optical unit, outputting a spherical wavefront to the back-end collimator. Specifically, the following steps are performed: the entrance pupil limits the effective aperture of the receiving optical unit, and an aperture stop is set there to suppress stray light; the converging lens group concentrates the starlight energy entering the entrance pupil to form a spherical wavefront; the field stop limits the imaging field of view, further suppressing stray light outside the field of view; and the receiving optical unit outputs the preliminarily processed spherical wavefront to the back-end collimator. This step achieves effective starlight reception, energy concentration, and stray light suppression, providing a stable input for subsequent wavefront conversion.

[0135] S2. Wavefront Conversion and Optical Parameter Matching: The spherical wavefront is converted into a plane wavefront via the collimator and then output to the wavefront measurement and imaging unit. Specifically, this involves: a collimator lens assembly receives the spherical wavefront and converts it into a plane wavefront; an aperture stop is placed at the exit pupil at the rear end of the collimator to suppress stray light during transmission and ensure the quality of the plane wavefront; and the collimator outputs the plane wavefront to the wavefront measurement and imaging unit. This step aims to provide standardized plane wavefront input for wavefront segmentation and star point imaging through wavefront conversion and parameter matching.

[0136] S3. Wavefront segmentation and star image acquisition: Wavefront segmentation and star image acquisition are completed through the wavefront measurement and imaging unit and the detector. Specifically, the wavefront measurement and imaging unit uses an N×N microlens array to form N×N micro-imaging channels. Its entrance pupil matches the exit pupil of the collimator unit, and wavefront segmentation is performed on the plane wavefront, dividing the collimator unit exit pupil into N×N sub-pupils. Each sub-pupil corresponds to a sensitive area of ​​the detector. After the same object space target star point is imaged by N×N micro-imaging channels, N×N star point images are formed on the detector. The detector collects N×N star point images as the raw data for subsequent wavefront error analysis.

[0137] S4. Wavefront Error Calculation and Parameter Fitting: The processor performs wavefront error analysis on the N×N star point images collected by the detector. It quantifies the wavefront error through energy distribution analysis and provides target parameters for subsequent compensation. This includes:

[0138] S401. Perform star point calculation: Extract energy distribution data of the star point image (based on the star point image in step S3). Specifically, collect N×N star point images; calculate the energy centroid of the star point based on the pixel response and coordinate position. Calculate the energy distribution diameter of the star point image with the energy centroid as the center, and use EE95 as the evaluation index to complete the energy distribution calculation. The energy distribution calculation method is as follows:

[0139] S4011. Calculate the total energy EE(r) within the circle for each circle with increasing radius r, starting from the energy centroid (xc, yc), until the minimum r is found that satisfies EE(r) ≥ 0.95.

[0140] S4012. Select a small radius increment dr (e.g., 0.1 pixel or smaller, depending on the accuracy requirements and computational complexity); for each radius r, calculate the total energy EE(r) contained within a circle of radius r centered at the energy centroid; if EE(r) is less than 0.95, update r = r + dr;

[0141] S4013. Traverse all pixels (x, y) in the image;

[0142] S4014. Calculate the distance from the pixel to the centroid: ; Where d represents the distance between two points on the plane, (x, y) represents the pixel coordinates, and (xc, yc) represents the centroid coordinates;

[0143] S4015. If d ≤ r, then add the intensity value I(x, y) of the pixel to the total energy C within the current radius;

[0144] S4016. Calculate the current enveloping energy: EE(r) = C;

[0145] S4017. Check: If EE(r) ≥ 0.95, then EE95 = r and the calculation ends; if EE(r) < 0.95, return to step S4012 and continue to increase r;

[0146] S402. Analyze the energy distribution characteristics based on the optical parameters of the micro-imaging channel (such as sub-pupil size, imaging focal length, etc.) and calculate the wavefront error contained in the star point;

[0147] S403. Perform parameter fitting on the wavefront error to obtain quantifiable wavefront error parameters. In a specific embodiment, Zernike polynomial fitting is used. The fitting method is as follows:

[0148] First, the Zernike polynomials of various orders corresponding to the full-aperture wavefront phase are calculated, and then the coefficients of each Zernike term are fitted to complete the wavefront reconstruction.

[0149] The Zernike polynomial of the wavefront on the circular domain is:

[0150] ;

[0151] Where, represents the coefficient of the kth Zernike polynomial; represents the kth Zernike polynomial; Z is the Zernike polynomial matrix; A is the coefficient matrix; M is the selected Zernike polynomial order.

[0152] It is known that the Shack-Hartmann wavefront detector measures the wavefront slope, so it is necessary to differentiate the above formula to obtain the following formula:

[0153]

[0154] Where, and is the measurement error. Since the average slope within the subaperture is measured using a Shack-Hartmann wavefront detector, we have:

[0155] ;

[0156] Rewrite the above formula into matrix form, that is:

[0157] ;

[0158] Where G is a 2N-dimensional vector; D is a 2N×M matrix; and A is an M-dimensional vector.

[0159] Similar to the regional method, the above equation can also obtain the least squares minimum norm solution:

[0160] ;

[0161] After obtaining the coefficient matrix A, the original wavefront parameters can be solved.

[0162] S5. Wavefront Recovery (Wavefront Compensation Parameter Calculation): The processor calculates wavefront compensation parameters based on the wavefront error parameters. This includes clarifying the composition of the system's comprehensive residual wavefront error, including the wavefront error caused by external turbulence, the design residual wavefront error of the receiving optical unit and collimator unit, and the integration error caused by machining and integration tolerances. Based on the wavefront error parameterization results obtained in step S4, the processor calculates the wavefront compensation parameters to offset this comprehensive residual error. This step generates compensation parameters that can be directly used for imaging correction, providing a basis for eliminating star image errors.

[0163] S6. Star image error compensation: The processor uses wavefront compensation parameters to correct the star image. Specifically, for the star images corresponding to the N×N micro-imaging channels, the point spread function (the imaging blur function affected by the wavefront error) of each star is extracted; an inverse convolution algorithm is used to inversely correct the point spread function of the star based on the wavefront compensation parameters to eliminate the blurring effect of the comprehensive residual wavefront error on the star imaging; and N×N error-compensated star images are output.

[0164] The purpose of this step is to eliminate the imaging distortion caused by wavefront error through image correction and restore the true energy distribution and shape of the star point.

[0165] S7. Centroid Positioning Optimization and Star Angular Distance Output: The processor calculates and optimizes the centroid of the compensated star point image and ultimately outputs the star angular distance, specifically including:

[0166] S701. Centroid calculation: Calculate the energy centroid pixel coordinates of the compensated (corrected) N×N star points using the weighted average method;

[0167] S702. Center of mass average: Based on the coordinate relationship between the detector, wavefront measurement and imaging unit, the center of mass coordinates are calibrated and normalized, and the average value of N×N center of mass positions is calculated (random error is reduced by N times, and positioning accuracy is improved by N times); the average value of the center of mass position The calculation formula is:

[0168] ;

[0169] Where: 、 Respectively represent the centroid positions of N×N star points x Direction and y The average value of the directional coordinates; 、 Represents the centroid of the i-th star point on the detector sensitive surface x Direction and y Pixel coordinates of the direction; Indicates the number of micro-imaging channels and the corresponding number of star point images; i The value range is from 1 to N×N, covering the centroid coordinates corresponding to all collected star point images;

[0170] S703. Star angular distance calculation: Combine the focal length parameters of the receiving optical unit, collimation unit, and wavefront measurement and imaging unit, calculate the angle between different target star points and the system optical axis based on the average value of the center of mass, solve the star angular distance between stars and output it.

[0171] The purpose of this step is to improve positioning accuracy through centroid optimization, complete star angular distance measurement in combination with optical parameters, and achieve the final imaging and measurement goals.

[0172] The core advantages of this method are: (1) targeted correction of the system's comprehensive residual wavefront error (covering external turbulence, design residuals, integration errors, etc.), significantly improving the quality of star point imaging; (2) based on the parallel imaging and averaging algorithm of N×N micro-imaging channels, the centroid positioning accuracy is improved by N times, providing a high-precision data basis for star angular distance measurement; (3) the combination of optical processing (stray light suppression, wavefront conversion) and digital correction (deconvolution, centroid optimization) takes into account both imaging stability and correction efficiency.

[0173] Brief description of the inventive concept of the present invention: (1) Integration of star sensor and Hartmann wavefront detection functions: A wavefront measurement and imaging component is introduced into the star sensor optical path. The wavefront measurement and imaging component has multiple micro-imaging channels, each channel corresponding to a different detector area; in this way, the detector is divided into N×N imaging areas that match the micro-imaging channels, so that the star sensor not only has the traditional star point imaging function, but also can perform the Hartmann wavefront detection function at the same time, realizing the efficient integration of wavefront detection and star point imaging. (2) Multi-target wavefront detection in a large field of view: The imaging field of view covered by each microlens is the same, so the system can extract sub-areas of the same target from N×N star sensor images; by processing the N Hartmann images of these sub-areas separately, multi-target wavefront detection in a large field of view is realized, thereby improving the coverage and efficiency of wavefront detection. (3) Accurate star point positioning and aberration compensation: The wavefront information obtained from the first wavefront detection is used to perform aberration compensation on the Hartmann image. In the compensated image, the star point positions are calculated based on the compensated star point images of each micro-imaging channel, and the star point positions from different micro-imaging channel images are averaged to achieve accurate positioning of the star point positions in a single frame image. (4) The workflow is summarized as follows: first, wavefront detection is performed, then the detected image is compensated using an algorithm; finally, the compensated star point image is processed to calculate and extract the angle measurement information.

[0174] It should be understood that the various forms of the processes shown above can be used to reorder, add, or delete steps. For example, the steps described in the present disclosure can be performed in parallel, sequentially, or in a different order, as long as the desired results of the technical solutions disclosed in the present disclosure can be achieved. This is not limited herein.

[0175] The above specific embodiments do not limit the scope of protection of the present invention. Those skilled in the art will appreciate that various modifications, combinations, sub-combinations, and substitutions may be made based on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection of the present invention.

Claims

1. A wavefront error correction optical imaging system, characterized by: Along the light propagation direction, it includes a receiving optical unit, a collimating unit, a wavefront measurement and imaging unit, a detector and a processor; The receiving optical unit is used to collect and converge starlight, then output a spherical wavefront and transmit it to the collimation unit; A collimating unit, used for converting the spherical wavefront output by the receiving optical unit into a plane wavefront; The wavefront measurement and imaging unit includes N×N micro-imaging channels, each of which corresponds to a different detector area, and is used to simultaneously complete wavefront detection and star point measurement; The detector is located at the optimal focal plane position of the wavefront measurement and imaging unit, and is used to obtain images of N×N star points corresponding to the same object space target; The processor is used to process the star point image obtained by the detector to realize wavefront error calculation, wavefront recovery, star point compensation and centroid calculation and star angle distance output.

2. The wavefront error correction optical imaging system according to claim 1, wherein: The receiving optical unit includes an entrance pupil, a converging lens group and a field stop in sequence along the light propagation direction; The entrance pupil is used to limit the effective aperture of the receiving optical unit; the converging lens group is used to converge the energy entering the system through the entrance pupil; The field stop is used to limit the imaging field of the converging lens group and suppress stray light outside the field of view.

3. The wavefront error correction optical imaging system according to claim 1, wherein: The collimating unit includes a collimating lens group and an exit pupil in sequence along the light propagation direction; The front focal plane of the collimating lens group coincides with the rear focal plane of the receiving optical unit and the aperture angles match, and is used to convert the spherical wavefront output by the receiving optical unit into a plane wavefront; an aperture stop is set at the exit pupil to suppress stray light.

4. The wavefront error correction optical imaging system according to claim 1, wherein: The wavefront measurement and imaging unit uses an N×N microlens array to form N×N micro-imaging channels; the microlens array performs wavefront segmentation and measurement operations on the exit pupil of the collimating unit, dividing the exit pupil of the collimating unit into N×N sub-pupils, and each sub-pupil is imaged on the sensitive surface of the detector; The size of the detector sensitive surface is not smaller than the imaging range of the wavefront measurement and imaging unit.

5. The wavefront error correction optical imaging system according to claim 1, characterized in that: The working process of the processor includes: Star point calculation: N×N star point image acquisition, centroid position calculation and energy distribution calculation; Wavefront error calculation: Analyze the N×N star point energy distribution results, combine the micro-imaging channel parameters, calculate the wavefront error contained in the star point, and perform parameterized fitting of the wavefront error; Wavefront recovery: Calculate the wavefront compensation parameters based on the wavefront error calculation results to compensate for the system's comprehensive residual wavefront error; Star point compensation: Using the wavefront compensation parameters obtained from wavefront recovery, deconvolution operations are performed on the point spread functions corresponding to each star point in the N×N micro-imaging channel. This eliminates the influence of the system's comprehensive residual wavefront error on star point imaging, achieving error correction and quality improvement for N×N star points. Centroid calculation: Use the weighted average method to recalculate the energy centroid position of the corrected N×N star point images and record the pixel coordinates of the centroid of each star point; Centroid averaging: Based on the coordinate relationship between the detector and the wavefront measurement and imaging unit, the centroid positions of N×N star points are calibrated and normalized, and the average value of the centroid positions of N×N star points on the detector is calculated; Star angle distance output: Based on the average value of the star point centroid position, combined with the focal length parameters of the receiving optical unit, collimation unit, detector and wavefront measurement and imaging unit, the angle between target star points in different object spaces and the system optical axis is calculated, and the star angle distance between different target stars is solved to achieve the measurement and output of the inter-satellite angle.

6. The wavefront error correction optical imaging system according to claim 5, characterized in that: The energy distribution calculation method is as follows: With the energy centroid (xc, yc) as the center, gradually increase the radius r from small to large, and calculate the total energy EE(r) within the circle corresponding to each r until the minimum r that satisfies EE(r) ≥ 0.95 is found; Choose a small radius increment dr; for each radius r, calculate the total energy EE(r) contained in a circle with radius r centered on the energy centroid; if EE(r) is less than 0.95, update r = r + dr; Traverse all pixels (x,y) in the image; Calculate the distance from the pixel to the centroid: ; Where d represents the distance between two points on the plane, (x, y) represents the pixel coordinates, and (xc, yc) represents the centroid coordinates; If d≤r, add the pixel intensity value I(x, y) to the total energy C within the current radius; Calculate the current enveloping energy: EE(r)=C; Check: If EE(r) ≥ 0.95, then EE95 = r and the calculation ends; if EE(r) < 0.95, return and continue to increase r; The parameterized fitting method is as follows: Calculate the Zernike polynomials of various orders corresponding to the full-aperture wavefront phase; Fit the coefficients of each Zernike term; Reconstruct the wavefront using the fitted coefficients; Differentiate the reconstructed wavefront to obtain the wavefront slope; The average slope within the subaperture is measured using a Shack-Hartmann wavefront detector; The measurement results are converted into a matrix form to obtain a slope matrix; Solve the coefficient matrix using the least squares minimum norm solution method; The original wavefront parameters are solved using the solved coefficient matrix.

7. The wavefront error correction optical imaging system according to claim 5, characterized in that: The comprehensive residual wavefront error of the system includes the wavefront error caused by external turbulence, the design residual wavefront error of the receiving optical unit and the collimation unit, and the integration error caused by processing and integration tolerances; The average value of the centroid position The calculation formula is: ； Where: 、 Respectively represent the centroid positions of N×N star points x Direction and y The average value of the directional coordinates; 、 Represents the centroid of the i-th star point on the detector sensitive surface x Direction and y Pixel coordinates of the direction; Indicates the number of micro-imaging channels and the corresponding number of star point images.

8. A wavefront error correction optical imaging method, using the wavefront error correction optical imaging system of claim 1 for imaging, characterized in that: The specific steps include: S1. Starlight Reception and Preliminary Optical Processing: Starlight is collected and concentrated by the receiving optical unit, and the spherical wavefront is output to the back-end collimator unit. S2. Wavefront conversion and optical parameter matching: The spherical wavefront is converted into a planar wavefront through the collimation unit and output to the wavefront measurement and imaging unit; S3. Wavefront Segmentation and Star Image Acquisition: Wavefront segmentation and star image acquisition are performed using the wavefront measurement and imaging unit and detector. S4. Wavefront Error Calculation and Parameter Fitting: The processor performs wavefront error analysis on the N × N star point images collected by the detector and quantifies the wavefront error through energy distribution analysis. S5. Wavefront recovery: The processor calculates the wavefront compensation parameters based on the wavefront error parameterization result obtained in step S4; S6. Star image error compensation: Using the inverse convolution algorithm, the point spread function of the star point is inversely corrected based on the wavefront compensation parameters, and the corrected N×N star point images are output; S7. Centroid Positioning Optimization and Star Angular Distance Output: The processor calculates and optimizes the centroid of the corrected star point image and ultimately outputs the star angular distance.

9. The optical imaging method for wavefront error correction according to claim 8, characterized in that: The step S4 specifically includes the following steps: S401. Perform star point calculation: extract energy distribution data of star point image; S402. Analyze the energy distribution characteristics and calculate the wavefront error of the star point based on the optical parameters of the micro-imaging channel; S403. Perform parameter fitting on the wavefront error to obtain wavefront error parameters.

10. The optical imaging method for wavefront error correction according to claim 8, characterized in that: The step S7 specifically includes the following steps: S701. Centroid calculation: Calculate the pixel coordinates of the energy centroid of the corrected N×N star points using the weighted average method; S702. Centroid averaging: Calibrate and normalize the centroid coordinates based on the coordinate relationship between the detector, wavefront measurement, and imaging unit, and calculate the average value of N×N centroid positions; the average value of the centroid position The calculation formula is: ； Where: 、 Respectively represent the centroid positions of N×N star points x Direction and y The average value of the directional coordinates; 、 Represents the centroid of the i-th star point on the detector sensitive surface x Direction and y Pixel coordinates of the direction; Indicates the number of micro-imaging channels and the corresponding number of star point images; S703. Star angular distance calculation: Combine the focal length parameters of the receiving optical unit, collimation unit, and wavefront measurement and imaging unit, calculate the angle between different target star points and the system optical axis based on the average value of the center of mass, solve the star angular distance between stars and output it.

Images