Star sensor calibration method and system based on Zernike wave aberration model

Abstract

The invention discloses a star sensor calibration method based on a Zernike wave aberration model. The method comprises the following steps: collecting starlight calibration points based on a star sensor, a fixed star simulator and a two-axis turntable; establishing a Zernike wave aberration model, and calculating the image distortion of the starlight calibration point based on the Zernike wave aberration model; and iteratively calculating and calibrating model parameters of the Zernike wave aberration model based on a multi-order sequence optimization strategy. The invention also discloses a corresponding system and device. The device comprises a star sensor composed of an optical lens, an image detector and an imaging driver; wherein the optical lens is used for focusing starlight in a certain view field range and imaging the starlight on the surface of the image detector; the image detector is used for sensing starlight energy and collecting starlight images; the imaging driver is used for collecting starlight images; the fixed star simulator is used for simulating fixed star starlight; the two-axis turntable is used for changing the attitude of the star sensor; and the information processor is used for calculating the mass center position of the star point and the model parameters of the Zernike wave aberration model.

Description

Technical Field

[0001] The present invention relates to the technical fields of star sensors and camera calibration, and in particular to a star sensor calibration method and system based on a Zernike wave aberration model. Background Art

[0002] A star sensor is one of the most accurate instruments for obtaining spacecraft attitude. Its principle is to calculate the observation vector based on the centroid positions of the light spots of multiple stars in a captured star map. It then performs star map recognition and attitude calculation based on known star vectors in the star catalog to obtain the spacecraft attitude (Wei X, Zhang G, Fan Q, et al. Star sensor calibration based on integrated modelling with intrinsic and extrinsic parameters[J]. Measurement, 2014, 55: 117-125.). Reconstructing the observed stellar vector is a crucial step in determining the attitude of a star sensor (Beijing University of Aeronautics and Astronautics. A Laboratory Assessment Method and System for the Accuracy of Stellar Vector Observations of Star Sensors: 202310353527.1[P]. 2023-07-25.; Beijing Institute of Aerospace Metrology and Testing Technology, China Academy of Launch Vehicle Technology. A Calibration System and Method for Multi-Field-of-View Star Sensors Based on a Three-Axis Turntable: 201811366300.6[P]. 2019-03-12.). The star sensor parameters are a crucial basis for reconstructing the observed vector. Therefore, star sensor parameter calibration is a crucial factor in determining star sensor performance, and the star sensor parameter model is a crucial component in determining its calibration accuracy.

[0003] The purpose of star sensor parameter calibration is to determine the mapping relationship between the starlight vector and the position of the star sensor's spot mass center. The commonly used calibration method is the laboratory calibration method (Xiong Kun, Wang Chunxi, Wu Yue, et al. Multi-field star sensor calibration method based on a three-axis turntable [J]. Infrared and Laser Engineering, 2019, 48(04): 242-247.). This method uses a star simulator to simulate high-parallel starlight, and uses a high-precision turntable to accurately control the attitude angle change of the star sensor, thereby simulating the starlight vector of different incident angles and obtaining its star point image in the star sensor, and then constructing the corresponding relationship between the starlight vector and the star point image mass center position of the star sensor. Under ideal conditions, according to the pinhole imaging model, the starlight vector and the star point mass center position satisfy the linear transformation relationship, which is mathematically expressed as a composite transformation of the installation matrix, the rotation matrix and the projection matrix. Since the real lens system is affected by factors such as optical aberrations, manufacturing and processing errors, the imaging star point spot of the star sensor will have a position offset, which is usually called image distortion. This distortion can lead to a nonlinear relationship between the starlight vector and the star point centroid position, reducing the calibration accuracy of the star sensor and seriously affecting the attitude measurement accuracy of the star sensor. To compensate for the nonlinear effects of the actual optical system, Brown proposed a distortion model that includes the image plane principal point, focal length, radial distortion parameters, and eccentricity distortion parameters (Duane C B. Close-range camera calibration[J].Photogramm. Eng, 1971, 37(8): 855-866.), which describes the effects of radial distortion caused by lens manufacturing errors and tangential distortion caused by assembly errors. After correction by this model, the starlight vector and the corrected star point centroid position can approximately satisfy a linear transformation relationship. This model is widely used in fields such as computational vision and photogrammetry (Tian Sanhu, Zhao Jinsong, He Hongxing, et al. A distortion correction method for large-field-of-view infrared cameras [J]. Infrared Technology, 2024, 46(05): 584-591.; Lin Xudong, Zhang Xu. High-precision camera calibration method based on perspective distortion correction [J]. Progress in Laser and Optoelectronics, 2023, 60(16): 283-289.), and is referred to as the traditional distortion model in this invention.

[0004] However, existing traditional models suffer from unclear physical meaning, which limits calibration accuracy and hinders the improvement of attitude measurement accuracy of star sensors in high-precision scenarios. Traditional distortion models only use ray tracing to calculate decentration distortion, obtaining a basic form of decentration distortion. However, the higher-order terms of decentration distortion and the expanded form of radial distortion are derived from fitting actual physical experimental observations, without a theoretical explanation of the physical meaning of their expressions. This limits the model's versatility and calibration accuracy under different lens aberration conditions. Summary of the Invention

[0005] The present invention aims to provide a star sensor calibration method and system based on the Zernike wave aberration model. By characterizing the wavefront distortion distribution using Zernike polynomials, a physical model of wavefront aberration and image distortion is established. This method reveals the influence of optical aberrations such as coma and optical distortion on image distortion, improves the calibration accuracy of the star sensor, and thereby enhances the attitude measurement accuracy of the star sensor. The present invention considers principal point offset and focal length variation as part of image distortion, and the deviations caused by these two factors can be corrected using the first-order terms of the Zernike polynomials. Therefore, during the parameter optimization process, the present invention maintains the image plane principal point and focal length at nominal values ​​and only uses the Zernike polynomial coefficients as the parameters to be optimized for iterative calculation. During star vector reconstruction, the actual star point position is first corrected according to the Zernike wave aberration model, and then a geometric projection transformation is performed based on the nominal values ​​of the image plane principal point and focal length. The corrected star point position is converted into a star observation vector. The present invention achieves the separation of geometric projection parameters and distortion compensation parameters, effectively eliminating the coupling interference generated by the two during the optimization process.

[0006] A first aspect of the present invention is to provide a star sensor calibration method based on a Zernike wave aberration model, comprising:

[0007] S1, collects star cursor fixed points based on star sensor, star simulator and two-axis turntable;

[0008] S2, establishing a Zernike wave aberration model, and calculating the image distortion size of the star cursor fixed point based on the Zernike wave aberration model;

[0009] S3, iteratively calculate and calibrate the model parameters of the Zernike wave aberration model based on a multi-order sequence optimization strategy.

[0010] Preferably, the S1 includes:

[0011] S11, installing the star sensor on the two-axis turntable and aligning it with the star simulator;

[0012] S12, setting the star simulator according to a given parameter file to simulate the spectrum and magnitude of starlight;

[0013] S13, the two-axis turntable rotates the pitch angle and the yaw angle according to the given trajectory file;

[0014] S14, while the two-axis turntable rotates, the star sensor collects multiple starlight images within a given time; and calculates an average centroid position of the star point based on the multiple starlight images, wherein the average centroid position is used as the star cursor fixed point.

[0015] Preferably, the S2 includes:

[0016] S21, establishing a physical model of the Zernike wave aberration model based on properties of the wavefront, wherein the physical model is used to describe the relationship between the normal direction of the wave aberration and image distortion;

[0017] S22, deriving a Zernike wave aberration model expression of the image distortion using Zernike polynomials according to the physical model;

[0018] S23 , calculating the size of the image distortion corresponding to the average mass center position of the star points according to the expression and the average mass center position of the star points, and correcting the average mass center position of the star points.

[0019] Preferably, the physical model of establishing the Zernike wave aberration model in S21 includes:

[0020] The wavefront is defined as a curved surface formed by rays of equal optical path length, and the property of the wavefront is that the normal direction of the wavefront is consistent with the propagation direction of the wave. Under the assumption that the lens is a paraxial optical system, the normal direction of the wavefront at a certain point can be expressed as , where is the propagation direction of the ideal light wave, is the ideal wavefront; wave aberration is the actual wavefront With ideal wavefront Therefore, the normal direction of the wave aberration at a certain point is the deviation of the propagation direction of the actual wavefront and the ideal wavefront at that point. Under the assumption that the lens is a paraxial optical system, the directional deviation of the light wave at that point can be expressed as , where It is the directional deviation of the light wave at that point, that is, the normal direction of the wave aberration at a certain point. is the actual propagation direction of the light wave; therefore, the deviation of the direction of the light wave at this point The spot position shift on the image plane caused by ,in, is the distance from the exit pupil to the image plane, is the offset along the U and V directions; the offset of the average centroid position of the star point can be corrected according to the offset of the direction deviation of the light wave at this point.

[0021] Preferably, the Zernike wave aberration model expression of S22 includes:

[0022] The wave aberration of the Zernike wave aberration model expression is It is defined as the optical path difference between the actual wavefront and the ideal spherical wavefront, and is given by the pupil coordinates of the intersection of the ray and the exit pupil. and the image plane coordinates of the ideal perfect image point imaged onto the image plane Definition: Two Zernike polynomials are used to describe the Zernike wave aberration model expression, wherein the two Zernike polynomials are the image plane Zernike polynomial and the pupil plane Zernike polynomial. The wave aberration of the Zernike wave aberration model expression is shown in formula (1):

[0023] (1);

[0024] in, is the OAF coefficient, , is the image Zernike polynomial, is the pupil Zernike polynomial, and Zernike polynomials sorted for Zernike circle polynomials under ISO-14999 index;

[0025] According to the physical model of the Zernike wave aberration model in step S21, the direction change of the light wave after being affected by the aberration is It can be expressed as formula (2) and formula (3):

[0026] (2);

[0027] (3);

[0028] in, and is the directional deviation of the light wave on the X-axis and Y-axis, is the area of ​​the exit pupil, is the radius of the exit pupil; Under the fixed conditions, equations (2) and (3) can be rewritten as equations (4) and (5):

[0029] (4);

[0030] (5);

[0031] in, , , , ; After considering the influence of aberration, and The light wave with changing direction can be considered as projected from the exit pupil plane to the image plane, and the position offset of the center of mass of the imaging spot can be expressed as Equation (6) and Equation (7):

[0032] (6);

[0033] (7);

[0034] in, , ;

[0035] The star point position can be corrected according to the offset, as shown in formula (8):

[0036] (8);

[0037] in, is the corrected star point centroid position, is the actual star point centroid position, , ;

[0038] Equation (8) is the expression of the Zernike wave aberration model, which is used to compensate for the image distortion caused by the camera optical system.

[0039] Preferably, the S3 includes:

[0040] S31, setting the initial value of the model parameter of the Zernike wave aberration model to 0, and the star sensor external parameter to an ideal value; wherein the star sensor external parameter includes the three-axis rotation angle from the two-axis turntable coordinate system to the star sensor coordinate system and the right ascension and declination of the star vector of the star simulator ;

[0041] S32, according to the size of the image distortion, iteratively calculating the model parameters of the Zernike wave aberration model using a multi-order sequence optimization strategy.

[0042] Preferably, the iterative calculation of the model parameters of the Zernike wave aberration model using a multi-order sequence optimization strategy in S32 includes:

[0043] According to the pinhole imaging model, the ideal projection position of the starlight vector on the image plane of the star sensor can be expressed as formula (9):

[0044] (9);

[0045] in, are the coordinates of the ideal image point, is the scaling factor, is the focal length of the lens, and is the physical size of the pixel of the star sensor image sensor on the U axis and V axis, is the principal point of the image plane, is the installation matrix between the star sensor and the turntable; the rotation matrix According to the rotation angle of the turntable, are the pitch and yaw angles of the turntable, respectively;

[0046] According to equations (8) and (9), the optimization objective of star sensor parameter calibration is established as equation (10):

[0047] (10);

[0048] in, Represents the vector composed of external parameters and internal parameters, represents the number of calibration points, and Respectively The ideal coordinates and corrected coordinates of the calibration points;

[0049] The multi-order sequential optimization strategy optimizes the star sensor parameters in multiple steps with odd orders of h as the ladder, wherein the first step optimizes the first-order and lower parameters, including 5 external parameters and first-order and lower model parameters, the second step optimizes the third-order and lower parameters, including 5 external parameters and second-order and third-order model parameters, and so on; after each step of optimization, the optimization result of that step is used as the initial value of the next step;

[0050] The Levenberg-Marquardt algorithm is used for each step of optimization, including:

[0051] make , , The iterative formula can be expressed as formula (11):

[0052] (11);

[0053] Where, is the damping factor, is the unit matrix, is the Jacobian matrix,

[0054] (12);

[0055] After the iteration is completed, a stable parameter value is obtained, and the stable parameter is the final calibration result of the model parameter.

[0056] A second aspect of the present invention is to provide a star sensor calibration system based on the Zernike wave aberration model, which is used to implement the method of the first aspect, comprising:

[0057] A star cursor fixed point acquisition module (101) is used to acquire star cursor fixed points based on a star sensor, a star simulator and a two-axis turntable;

[0058] A model building and calculation module (102) is used to build a Zernike wave aberration model and calculate the image distortion size of the star cursor fixed point based on the Zernike wave aberration model;

[0059] The model parameter calculation and calibration module (103) is used to iteratively calculate and calibrate the model parameters of the Zernike wave aberration model based on a multi-order sequence optimization strategy.

[0060] A third aspect of the present invention is to provide a star sensor calibration device based on the Zernike wave aberration model, comprising:

[0061] A star sensor for collecting starlight images; the star sensor includes an optical lens, an image detector, and an imaging driver; wherein the optical lens is used to focus starlight within a certain field of view so that it is imaged on the surface of the image detector; the image detector is used to sense starlight energy and collect starlight images within a given exposure time; and the imaging driver is used to collect the starlight images output by the image detector;

[0062] Stellar simulator, used to simulate starlight;

[0063] Two-axis turntable, used to change the attitude of the star sensor;

[0064] An information processor is used to calculate the centroid position of the star points, calculate the average centroid position of the star points and calculate the model parameters of the Zernike wave aberration model based on the starlight image.

[0065] Preferably, the information processor includes:

[0066] A processing unit, configured to execute a program of the method described in the first aspect;

[0067] A storage unit, configured to store a program for executing the method described in the first aspect, data, and variables required for storing the program during execution;

[0068] The communication unit is used to control the star sensor and the two-axis turntable to work and read the information collected by the star sensor, wherein the information includes starlight within a certain field of view and starlight images collected within a given exposure time.

[0069] A fourth aspect of the present invention provides an electronic device, comprising a processor and a memory, wherein the memory stores a plurality of instructions, and the processor is configured to read the instructions and execute the method described in the first aspect.

[0070] A fifth aspect of the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores a plurality of instructions, and the plurality of instructions can be read by a processor to execute the method described in the first aspect.

[0071] Beneficial effects of the method and system of the present invention:

[0072] This paper establishes a Zernike wave aberration model. First, a physical model is constructed based on the properties of wave aberration, which derives the directional changes in light propagation in an optical system and establishes its relationship with image distortion. Second, the model's image distortion correction expression is derived using Zernike polynomials, and the physical meaning of each term and its impact on image distortion are explained. This model can efficiently describe the distortion magnitude of star sensor lenses, effectively improving the accuracy of star sensor calibration and enabling high-precision measurement of star sensor attitude. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in related technologies, the following briefly introduces the drawings required for use in the specific embodiments or related technical descriptions. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0074] Figure 1 A flow chart of a star sensor calibration method based on the Zernike wave aberration model provided in an embodiment of the present invention;

[0075] Figure 2 Flowchart of step S1 of the star sensor calibration method based on the Zernike wave aberration model provided in an embodiment of the present invention;

[0076] Figure 3 Flowchart of step S2 of the star sensor calibration method based on the Zernike wave aberration model provided in an embodiment of the present invention;

[0077] Figure 4 Flowchart of step S3 of the star sensor calibration method based on the Zernike wave aberration model provided in an embodiment of the present invention;

[0078] Figure 5 A schematic diagram of the principle structure of a star sensor calibration system based on the Zernike wave aberration model provided by an embodiment of the present invention;

[0079] Figure 6 A structural diagram of an electronic device provided according to an embodiment of the present invention. DETAILED DESCRIPTION

[0080] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0081] In the description of the present invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings and are intended solely to facilitate and simplify the description of the present invention. They are not intended to indicate or imply that the devices or components referred to must have, be constructed, or operate in a specific orientation, and therefore should not be construed as limitations on the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0082] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be understood in a broad sense. For example, they may refer to fixed, detachable, or integral connections; mechanical or electrical connections; direct or indirect connections through an intermediate medium; and internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on the specific circumstances.

[0083] Example 1

[0084] like Figure 1 As shown, this embodiment provides a star sensor calibration method based on the Zernike wave aberration model, including:

[0085] S1, collects star cursor fixed points based on star sensor, star simulator and two-axis turntable;

[0086] like Figure 2 As shown, as a preferred embodiment, the S1 includes:

[0087] S11, installing the star sensor on the two-axis turntable and aligning it with the star simulator;

[0088] S12, setting the star simulator according to a given parameter file to simulate the spectrum and magnitude of starlight;

[0089] S13, the two-axis turntable rotates the pitch angle and the yaw angle according to the given trajectory file;

[0090] S14, while the two-axis turntable rotates, the star sensor collects multiple starlight images within a given time; and calculates an average centroid position of the star point based on the multiple starlight images, wherein the average centroid position is used as the star cursor fixed point.

[0091] S2, establishing a Zernike wave aberration model, and calculating the image distortion size of the star cursor fixed point based on the Zernike wave aberration model;

[0092] like Figure 3 As shown, as a preferred embodiment, the S2 includes:

[0093] S21, establishing a physical model of the Zernike wave aberration model based on properties of the wavefront, wherein the physical model is used to describe the relationship between the normal direction of the wave aberration and image distortion;

[0094] S22, deriving a Zernike wave aberration model expression of the image distortion using Zernike polynomials according to the physical model;

[0095] S23 , calculating the size of the image distortion corresponding to the average mass center position of the star points according to the expression and the average mass center position of the star points, and correcting the average mass center position of the star points.

[0096] As a preferred embodiment, the physical model of establishing the Zernike wave aberration model in S21 includes:

[0097] The wavefront is defined as a curved surface formed by rays of equal optical path length, and the property of the wavefront is that the normal direction of the wavefront is consistent with the propagation direction of the wave. Under the assumption that the lens is a paraxial optical system, the normal direction of the wavefront at a certain point can be expressed as , where is the propagation direction of the ideal light wave, is the ideal wavefront; wave aberration is the actual wavefront With ideal wavefront Therefore, the normal direction of the wave aberration at a certain point is the deviation of the propagation direction of the actual wavefront and the ideal wavefront at that point. Under the assumption that the lens is a paraxial optical system, the directional deviation of the light wave at that point can be expressed as , where It is the directional deviation of the light wave at that point, that is, the normal direction of the wave aberration at a certain point. is the actual propagation direction of the light wave; therefore, the deviation of the direction of the light wave at this point The spot position shift on the image plane caused by ,in, is the distance from the exit pupil to the image plane, is the offset along the U and V directions; the offset of the average centroid position of the star point can be corrected according to the offset of the direction deviation of the light wave at this point.

[0098] As a preferred embodiment, the Zernike wave aberration model expression of S22 includes:

[0099] The wave aberration of the Zernike wave aberration model expression is It is defined as the optical path difference between the actual wavefront and the ideal spherical wavefront, and is given by the pupil coordinates of the intersection of the ray and the exit pupil. and the image plane coordinates of the ideal perfect image point imaged onto the image plane Definition: Two Zernike polynomials are used to describe the Zernike wave aberration model expression, wherein the two Zernike polynomials are the image plane Zernike polynomial and the pupil plane Zernike polynomial. The wave aberration of the Zernike wave aberration model expression is shown in formula (1):

[0100] (1);

[0101] in, is the OAF coefficient, , is the image Zernike polynomial, is the pupil Zernike polynomial, and Sorted Zernike polynomials for the ISO-14999 indexed Zernike circle polynomials.

[0102] Generally, under the usual space observation conditions of star sensors, starlight is simplified into a uniform parallel beam. Therefore, the light direction deviation caused by the aberration can be considered as the average value of the wave aberration in the normal direction of all points on the exit pupil surface O-xy, which is called the equivalent normal vector in this invention. Similar to the concept of center of mass in mass distribution, it is defined as a surface In the domain Points within All normal vectors of The average value of ,in Represents the domain area.

[0103] According to the physical model of the Zernike wave aberration model in step S21, the direction change of the light wave after being affected by the aberration is It can be expressed as formula (2) and formula (3):

[0104] (2);

[0105] (3);

[0106] in, and is the directional deviation of the light wave on the X-axis and Y-axis, is the area of ​​the exit pupil, is the radius of the exit pupil; Under the fixed conditions, equations (2) and (3) can be rewritten as equations (4) and (5):

[0107] (4);

[0108] (5);

[0109] in, , , , ; After considering the influence of aberration, and The light wave with changing direction can be considered as projected from the exit pupil plane to the image plane, and the position offset of the center of mass of the imaging spot can be expressed as Equation (6) and Equation (7):

[0110] (6);

[0111] (7);

[0112] in, , ;

[0113] The star point position can be corrected according to the offset, as shown in formula (8):

[0114] (8);

[0115] in, is the corrected star point centroid position, is the actual star point centroid position, , ;

[0116] Equation (8) is the expression of the Zernike wave aberration model, which is used to compensate for the image distortion caused by the camera optical system.

[0117] S3, iteratively calculate and calibrate the model parameters of the Zernike wave aberration model based on a multi-order sequence optimization strategy.

[0118] like Figure 4 As shown, as a preferred embodiment, the S3 includes:

[0119] S31, setting the initial value of the model parameter of the Zernike wave aberration model to 0, and the star sensor external parameter to an ideal value; wherein the star sensor external parameter includes the three-axis rotation angle from the two-axis turntable coordinate system to the star sensor coordinate system and the right ascension and declination of the star vector of the star simulator ;

[0120] S32, according to the size of the image distortion, iteratively calculating the model parameters of the Zernike wave aberration model using a multi-order sequence optimization strategy.

[0121] As a preferred embodiment, the iterative calculation of the model parameters of the Zernike wave aberration model using a multi-order sequence optimization strategy in S32 includes:

[0122] According to the pinhole imaging model, the ideal projection position of the starlight vector on the image plane of the star sensor can be expressed as formula (9):

[0123] (9);

[0124] in, are the coordinates of the ideal image point, is the scaling factor, is the focal length of the lens, and is the physical size of the pixel of the star sensor image sensor on the U axis and V axis, is the principal point of the image plane, is the installation matrix between the star sensor and the turntable; the rotation matrix According to the rotation angle of the turntable, are the pitch and yaw angles of the turntable, respectively;

[0125] According to equations (8) and (9), the optimization objective of star sensor parameter calibration is established as equation (10):

[0126] (10);

[0127] in, Represents the vector composed of external parameters and internal parameters, represents the number of calibration points, and Respectively The ideal coordinates and corrected coordinates of the calibration points;

[0128] The multi-order sequential optimization strategy optimizes the star sensor parameters in multiple steps with odd orders of h as the ladder, wherein the first step optimizes the first-order and lower parameters, including 5 external parameters and first-order and lower model parameters, the second step optimizes the third-order and lower parameters, including 5 external parameters and second-order and third-order model parameters, and so on; after each step of optimization, the optimization result of that step is used as the initial value of the next step;

[0129] The Levenberg-Marquardt algorithm is used for each step of optimization, including:

[0130] make , , The iterative formula can be expressed as formula (11):

[0131] (11);

[0132] Where, is the damping factor, is the unit matrix, is the Jacobian matrix,

[0133] (12);

[0134] After the iteration is completed, a stable parameter value is obtained, and the stable parameter is the final calibration result of the model parameter.

[0135] Example 2

[0136] like Figure 5 As shown, this embodiment provides a star sensor calibration system based on the Zernike wave aberration model, which is used to implement the method of embodiment 1, including:

[0137] The star cursor fixed point acquisition module 101 is used to acquire the star cursor fixed point based on the star sensor, the star simulator and the two-axis turntable;

[0138] A model building and calculation module 102 is used to build a Zernike wave aberration model and calculate the image distortion size of the star cursor fixed point based on the Zernike wave aberration model;

[0139] The model parameter calculation and calibration module 103 is used to iteratively calculate and calibrate the model parameters of the Zernike wave aberration model based on a multi-order sequence optimization strategy.

[0140] Example 3

[0141] This embodiment provides a star sensor calibration device based on the Zernike wave aberration model, comprising:

[0142] A star sensor for collecting starlight images; the star sensor includes an optical lens, an image detector, and an imaging driver; wherein the optical lens is used to focus starlight within a certain field of view so that it is imaged on the surface of the image detector; the image detector is used to sense starlight energy and collect starlight images within a given exposure time; and the imaging driver is used to collect the starlight images output by the image detector;

[0143] Stellar simulator, used to simulate starlight;

[0144] Two-axis turntable, used to change the attitude of the star sensor;

[0145] An information processor is used to calculate the centroid position of the star points, calculate the average centroid position of the star points and calculate the model parameters of the Zernike wave aberration model based on the starlight image.

[0146] As a preferred embodiment, the information processor includes:

[0147] A processing unit, configured to execute a program of the method described in the first aspect;

[0148] A storage unit, configured to store a program for executing the method described in the first aspect, data, and variables required for storing the program during execution;

[0149] The communication unit is used to control the star sensor and the two-axis turntable to work and read the information collected by the star sensor, wherein the information includes starlight within a certain field of view and starlight images collected within a given exposure time.

[0150] The present invention also provides a memory storing a plurality of instructions, wherein the instructions are used to implement the method as in the first embodiment.

[0151] like Figure 6 As shown, the present invention also provides an electronic device, including a processor 301 and a memory 302 connected to the processor 301, the memory 302 stores multiple instructions, and the instructions can be loaded and executed by the processor to enable the processor to execute the method as in embodiment 1.

[0152] Application examples:

[0153] According to the Zernike wave aberration model established in the present invention, a specific embodiment of a 15-parameter Zernike wave aberration model is proposed. The specific forms of the 15 parameters are shown in Table 1.

[0154] Table 1

[0155]

[0156] The process of the star sensor calibration method based on the Zernike wave aberration model includes the following steps:

[0157] Step S100, using a star simulator and a two-axis turntable to collect star cursor fixed points;

[0158] Specifically, the method of collecting the star cursor fixed point using a star simulator and a two-axis turntable includes the following steps:

[0159] Step S110, installing the star sensor on a two-axis turntable and aligning it with the star simulator;

[0160] Step S120, setting the star simulator to emit simulated starlight in the red spectrum of magnitude 2;

[0161] Step S130: The two-axis turntable rotates in pitch and yaw according to the specified trajectory. The trajectory points are ;

[0162] Step S140: In step S130, while the two-axis turntable rotates, the star sensor is Internal Collection Take a star image and calculate the average centroid position of the star points .

[0163] Step S200, establishing a Zernike wave aberration model to calculate the image distortion size of the star cursor fixed point;

[0164] Specifically, the steps of establishing the Zernike wave aberration model and calculating the image distortion size of the star cursor fixed point include the following steps:

[0165] Step S210: Establishing a physical model of the Zernike wave aberration model based on the properties of the wavefront to describe the relationship between the normal direction of the wave aberration and the image distortion, specifically including:

[0166] The wavefront is defined as a surface formed by rays of equal optical path length, whose property is that its normal direction is consistent with the propagation direction of the wave. Under the assumption that the lens is a paraxial optical system, the normal direction of the wavefront at a certain point can be expressed as , where is the propagation direction of the ideal light wave, is the ideal wavefront. Wave aberration is the actual wavefront With ideal wavefront Therefore, the normal direction of the wave aberration at a certain point is the deviation of the propagation direction of the actual wavefront and the ideal wavefront at that point. Under the assumption that the lens is a paraxial optical system, the directional deviation of the light wave at that point can be expressed as , where is the normal direction of the wave aberration at a certain point, is the actual propagation direction of the light wave. Therefore, the deviation The spot position shift on the image plane caused by ,in, is the distance from the exit pupil to the image plane, It is the offset along the U and V directions. The star point centroid position offset can be corrected based on this offset.

[0167] Step S220, based on the physical model obtained in step S210, deriving an expression for image distortion using Zernike polynomials, specifically includes:

[0168] Wave aberration It is defined as the optical path difference between the actual wavefront and the ideal spherical wavefront, which is determined by the pupil coordinates of the intersection of the ray and the exit pupil surface. and the image plane coordinates of the ideal perfect image point imaged onto the image plane Definition, can be described by two Zernike polynomials,

[0169] (1);

[0170] in, is the OAF coefficient, , is the image Zernike polynomial, is the pupil Zernike polynomial, and Sorted Zernike polynomials for the ISO-14999 indexed Zernike circle polynomials.

[0171] Generally, under the usual space observation conditions of star sensors, starlight is simplified into a uniform parallel beam. Therefore, the light direction deviation caused by the aberration can be considered as the average value of the wave aberration in the normal direction of all points on the exit pupil surface O-xy, which is called the equivalent normal vector in this invention. Similar to the concept of center of mass in mass distribution, it is defined as a surface In the domain Points within All normal vectors of The average value of ,in Represents the domain area.

[0172] According to the Zernike wave aberration model physical model of step S210, the direction change of the light wave after being affected by the aberration It can be expressed as

[0173] (2);

[0174] (3);

[0175] in, and is the directional deviation of the light wave on the X-axis and Y-axis, is the area of ​​the exit pupil, is the radius of the exit pupil. Under the fixed conditions, the above formula can be rewritten as

[0176] (4);

[0177] (5);

[0178] in, , , , After considering the influence of aberration, and The light wave with changing direction can be considered as projected from the exit pupil plane to the image plane, and the position offset of the center of mass of the imaging spot can be expressed as

[0179] (6);

[0180] (7);

[0181] in, , The star point position can be corrected according to the offset, as shown in formula (8):

[0182] (8);

[0183] in, is the corrected star point centroid position, is the actual star point centroid position, , The above formula is the expression of the Zernike wave aberration model, which can be used to compensate for the image distortion caused by the camera optical system.

[0184] Step S230: The star point centroid position obtained in step S220 is obtained according to the expression obtained in step S140. , calculate the image distortion size corresponding to the star point centroid position And correct the centroid position to get the corrected centroid position .

[0185] Step S300, proposing a multi-order sequence optimization strategy to iteratively calculate the parameters of the Zernike wave aberration model;

[0186] Specifically, the proposed multi-order sequence optimization strategy and the iterative calculation of the parameters of the Zernike wave aberration model include:

[0187] Step S310: Set the initial value of the Zernike wave aberration model parameter to 0, the star sensor external parameter to an ideal value, and the star sensor external parameter includes the three-axis rotation angle from the turntable coordinate system to the star sensor coordinate system. and the right ascension and declination of the star vector of the star simulator ;

[0188] Step S320, based on the image distortion size obtained in step S140 and step S230, iteratively calculating the Zernike wave aberration model parameters using a multi-order sequence optimization strategy, specifically comprising:

[0189] According to the pinhole imaging model, the ideal projection position of the starlight vector on the star sensor image plane can be expressed as

[0190] (9);

[0191] in, are the coordinates of the ideal image point, is the scaling factor, is the focal length of the lens, and is the physical size of the pixel of the star sensor image sensor on the U axis and V axis, is the principal point of the image plane, is the installation matrix between the star sensor and the turntable. Rotation matrix is obtained based on the rotation angle of the turntable, where are the pitch and yaw angles of the turntable respectively.

[0192] According to equations (8) and (9), the optimization objective of star sensor parameter calibration is established as

[0193] (10);

[0194] in, Represents the vector composed of external parameters and internal parameters, represents the number of calibration points, and Respectively The ideal coordinates and corrected coordinates of the calibration points.

[0195] The multi-order sequence optimization strategy optimizes the star sensor parameters in order with odd orders of h. The first step is to optimize the first-order and lower parameters, including 5 external parameters and 5 first-order and lower model parameters, namely , the second step optimizes the third-order and lower parameters including the 10 parameters in the first step and 9 second-order and third-order model parameters, namely , the third step is to optimize the parameters of the fifth order and below, including the 19 parameters in the second step and 1 fifth-order model parameter, that is, After each step of optimization, the optimization result of that step is used as the initial value of the next step.

[0196] The Levenberg-Marquardt algorithm is used for each step optimization. , , The iterative formula can be expressed as

[0197] (11);

[0198] Where, is the damping factor, is the unit matrix, is the Jacobian matrix,

[0199] (12);

[0200] After the iteration, a stable parameter value is obtained, and the parameter at this time is the calibration result of the final model parameter.

[0201] The specific implementation process of the calibration method of the present invention is described in detail below through specific examples:

[0202] Step S100, using a star simulator and a two-axis turntable to collect star cursor fixed points;

[0203] Step S110, installing the star sensor on a two-axis turntable and aligning it with the star simulator;

[0204] Step S120, setting the star simulator to emit simulated starlight in the red spectrum of magnitude 2;

[0205] Step S130: The two-axis turntable rotates in pitch and yaw according to the specified trajectory. The trajectory points are ;

[0206] Step S140: In step S130, while the two-axis turntable rotates, the star sensor is Internal Collection Take a star image and calculate the average centroid position of the star points .

[0207] Step S200, establishing a Zernike wave aberration model to calculate the image distortion size of the star cursor fixed point;

[0208] Step S210, establishing a physical model of the Zernike wave aberration model based on the properties of the wavefront, and describing the relationship between the normal direction of the wave aberration and the image distortion;

[0209] Step S220, deriving an expression for image distortion using Zernike polynomials based on the physical model obtained in step S210;

[0210] Step S230: The star point centroid position obtained in step S220 is obtained according to the expression obtained in step S140. , calculate the image distortion size corresponding to the star point centroid position And correct the centroid position to get the corrected centroid position .

[0211] Step S300, proposing a multi-order sequence optimization strategy to iteratively calculate the parameters of the Zernike wave aberration model;

[0212] Step S310: Set the initial value of the Zernike wave aberration model parameter to 0, the star sensor external parameter to an ideal value, and the star sensor external parameter includes the three-axis rotation angle from the turntable coordinate system to the star sensor coordinate system. and the right ascension and declination of the star vector of the star simulator ;

[0213] Step S320 , based on the image distortion magnitudes obtained in step S140 and step S230 , iteratively calculating the Zernike wave aberration model parameters using a multi-order sequence optimization strategy.

[0214] According to another aspect of an embodiment of the present invention, a star sensor calibration system based on the Zernike wave aberration model is provided, comprising: a star sensor for collecting starlight images; a star simulator for simulating starlight; a two-axis turntable for changing the attitude of the star sensor; and an information processor for calculating the average center of mass position of star points and the parameters of the Zernike wave aberration model.

[0215] Optionally, the star sensor includes: an optical lens for focusing starlight within a certain field of view so that it is imaged on the surface of an image detector; an image detector for sensing starlight energy and capturing starlight images within a given exposure time; and an imaging driver for capturing images output by the image detector and calculating the centroid position of the star point.

[0216] Optionally, the information processor includes: a processing unit for executing a program of the method described in any one of claims 1 to 4; a storage unit for storing a program, data, and variables required to be stored during the execution of the method described in any one of claims 1 to 4; and a communication unit for controlling the star sensor and the two-axis turntable described in claim 5 to operate and read information collected by the star sensor.

[0217] Through the above-described embodiments, a Zernike wave aberration model is established, which can effectively describe the distortion of the star sensor lens, effectively improve the accuracy of star sensor calibration, and achieve high-precision measurement of the star sensor attitude. The serial numbers of the above-described embodiments of the present invention are for descriptive purposes only and do not represent the advantages or disadvantages of the embodiments.

[0218] In summary, the present invention uses a star simulator and a two-axis turntable to collect star cursor fixed points; establishes a Zernike wave aberration model to calculate the image distortion of the star cursor fixed points; and proposes a multi-order sequence optimization strategy to iteratively calculate the parameters of the Zernike wave aberration model. The present invention establishes a Zernike wave aberration model. First, based on the properties of wave aberration, its physical model is constructed to obtain the directional change of light propagating in the optical system and establish its connection with image distortion. Secondly, the image distortion correction expression of the model is derived using Zernike polynomials, and the physical meaning of each term and its influence on image distortion are explained. This model can efficiently describe the distortion size of the star sensor lens, effectively improve the accuracy of star sensor calibration, and realize high-precision measurement of the star sensor attitude.

[0219] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A star sensor calibration method based on the Zernike wave aberration model, characterized in that: include: S1, collects star cursor fixed points based on star sensor, star simulator and two-axis turntable; S2, establishing a Zernike wave aberration model, and calculating the image distortion size of the star cursor fixed point based on the Zernike wave aberration model; S3, iteratively calculate and calibrate the model parameters of the Zernike wave aberration model based on a multi-order sequence optimization strategy.

2. The star sensor calibration method based on the Zernike wave aberration model according to claim 1, characterized in that: Said S1 comprises: S11, installing the star sensor on the two-axis turntable and aligning it with the star simulator; S12, setting the star simulator according to a given parameter file to simulate the spectrum and magnitude of starlight; S13, the two-axis turntable rotates the pitch angle and the yaw angle according to the given trajectory file; S14, while the two-axis turntable rotates, the star sensor collects multiple starlight images within a given time; and calculates an average centroid position of the star point based on the multiple starlight images, wherein the average centroid position is used as the star cursor fixed point.

3. The star sensor calibration method based on the Zernike wave aberration model according to claim 2, characterized in that: The S2 includes: S21, establishing a physical model of the Zernike wave aberration model based on properties of the wavefront, wherein the physical model is used to describe the relationship between the normal direction of the wave aberration and image distortion; S22, deriving a Zernike wave aberration model expression of the image distortion using Zernike polynomials according to the physical model; S23 , calculating the size of the image distortion corresponding to the average mass center position of the star points according to the expression and the average mass center position of the star points, and correcting the average mass center position of the star points.

4. The star sensor calibration method based on the Zernike wave aberration model according to claim 3, characterized in that: The physical model of establishing the Zernike wave aberration model in S21 includes: The wavefront is defined as a curved surface formed by rays of equal optical path length, and the property of the wavefront is that the normal direction of the wavefront is consistent with the propagation direction of the wave. Under the assumption that the lens is a paraxial optical system, the normal direction of the wavefront at a certain point can be expressed as , where is the propagation direction of the ideal light wave, is the ideal wavefront; wave aberration is the actual wavefront With ideal wavefront Therefore, the normal direction of the wave aberration at a certain point is the deviation of the propagation direction of the actual wavefront and the ideal wavefront at that point. Under the assumption that the lens is a paraxial optical system, the directional deviation of the light wave at that point can be expressed as , where It is the directional deviation of the light wave at that point, that is, the normal direction of the wave aberration at a certain point. is the actual propagation direction of the light wave; therefore, the deviation of the direction of the light wave at this point The spot position shift on the image plane caused by ,in, is the distance from the exit pupil to the image plane, is the offset along the U and V directions; the offset of the average centroid position of the star point can be corrected according to the offset of the direction deviation of the light wave at this point.

5. The star sensor calibration method based on the Zernike wave aberration model according to claim 4, characterized in that: The Zernike wave aberration model expression of S22 includes: The wave aberration of the Zernike wave aberration model expression is It is defined as the optical path difference between the actual wavefront and the ideal spherical wavefront, and is given by the pupil coordinates of the intersection of the ray and the exit pupil. and the image plane coordinates of the ideal perfect image point imaged onto the image plane Definition: Two Zernike polynomials are used to describe the Zernike wave aberration model expression, wherein the two Zernike polynomials are the image plane Zernike polynomial and the pupil plane Zernike polynomial. The wave aberration of the Zernike wave aberration model expression is shown in formula (1): （1）； in, is the OAF coefficient, , is the image Zernike polynomial, is the pupil Zernike polynomial, and Zernike polynomials sorted for Zernike circle polynomials under ISO-14999 index; According to the physical model of the Zernike wave aberration model in step S21, the direction change of the light wave after being affected by the aberration is It can be expressed as formula (2) and formula (3): （2）； （3）； in, and is the directional deviation of the light wave on the X-axis and Y-axis, is the area of ​​the exit pupil, is the radius of the exit pupil; Under the fixed conditions, equations (2) and (3) can be rewritten as equations (4) and (5): （4）； （5）； in, , , , ; After considering the influence of aberration, and The light wave with changing direction can be considered as projected from the exit pupil plane to the image plane, and the position offset of the center of mass of the imaging spot can be expressed as Equation (6) and Equation (7): （6）； （7）； in, , ; The star point position can be corrected according to the offset, as shown in formula (8): （8）； in, is the corrected star point centroid position, is the actual star point centroid position, , ; Equation (8) is the expression of the Zernike wave aberration model, which is used to compensate for the image distortion caused by the camera optical system.

6. The star sensor calibration method based on the Zernike wave aberration model according to claim 5, characterized in that: The S3 includes: S31, setting the initial value of the model parameter of the Zernike wave aberration model to 0, and the star sensor external parameter to an ideal value; wherein the star sensor external parameter includes the three-axis rotation angle from the two-axis turntable coordinate system to the star sensor coordinate system and the right ascension and declination of the star vector of the star simulator ; S32, according to the size of the image distortion, iteratively calculating the model parameters of the Zernike wave aberration model using a multi-order sequence optimization strategy.

7. The star sensor calibration method based on the Zernike wave aberration model according to claim 6, characterized in that: The model parameters of the Zernike wave aberration model iteratively calculated using a multi-order sequence optimization strategy in S32 include: According to the pinhole imaging model, the ideal projection position of the starlight vector on the image plane of the star sensor can be expressed as formula (9): （9）； in, are the coordinates of the ideal image point, is the scaling factor, is the focal length of the lens, and is the physical size of the pixel of the star sensor image sensor on the U axis and V axis, is the principal point of the image plane, is the installation matrix between the star sensor and the turntable; the rotation matrix According to the rotation angle of the turntable, are the pitch and yaw angles of the turntable, respectively; According to equations (8) and (9), the optimization objective of star sensor parameter calibration is established as equation (10): （10）； in, Represents the vector composed of external parameters and internal parameters, represents the number of calibration points, and Respectively The ideal coordinates and corrected coordinates of the calibration points; The multi-order sequential optimization strategy optimizes the star sensor parameters in multiple steps with odd orders of h as the ladder, wherein the first step optimizes the first-order and lower parameters, including 5 external parameters and first-order and lower model parameters, the second step optimizes the third-order and lower parameters, including 5 external parameters and second-order and third-order model parameters, and so on; after each step of optimization, the optimization result of that step is used as the initial value of the next step; The Levenberg-Marquardt algorithm is used for each step of optimization, including: make , , The iterative formula can be expressed as formula (11): （11）； Where, is the damping factor, is the unit matrix, is the Jacobian matrix, （12）； After the iteration is completed, a stable parameter value is obtained, and the stable parameter is the final calibration result of the model parameter.

8. A star sensor calibration system based on the Zernike wave aberration model, used to implement the method according to any one of claims 1 to 7, characterized in that: include: A star cursor fixed point acquisition module (101) is used to acquire star cursor fixed points based on a star sensor, a star simulator and a two-axis turntable; A model building and calculation module (102) is used to build a Zernike wave aberration model and calculate the image distortion size of the star cursor fixed point based on the Zernike wave aberration model; The model parameter calculation and calibration module (103) is used to iteratively calculate and calibrate the model parameters of the Zernike wave aberration model based on a multi-order sequence optimization strategy.

9. A star sensor calibration device based on the Zernike wave aberration model, used to form the system of claim 8, characterized in that: include: A star sensor for collecting starlight images; the star sensor includes an optical lens, an image detector, and an imaging driver; wherein the optical lens is used to focus starlight within a certain field of view so that it is imaged on the surface of the image detector; the image detector is used to sense starlight energy and collect starlight images within a given exposure time; and the imaging driver is used to collect the starlight images output by the image detector; Stellar simulator, used to simulate starlight; Two-axis turntable, used to change the attitude of the star sensor; An information processor is used to calculate the centroid position of the star points, calculate the average centroid position of the star points and calculate the model parameters of the Zernike wave aberration model based on the starlight image.

10. The device according to claim 9, characterized in that The information processor includes: A processing unit, configured to execute a program of the method described in the first aspect; A storage unit, configured to store a program for executing the method described in the first aspect, data, and variables required for storing the program during execution; The communication unit is used to control the star sensor and the two-axis turntable to work and read the information collected by the star sensor, wherein the information includes starlight within a certain field of view and starlight images collected within a given exposure time.

Images