An astronomical image geometric distortion solving method and system

Abstract

The present application provides an astronomical image geometric distortion solving method and system, and relates to the technical field of astronomical observation and celestial measurement. The present application obtains dense star field images and auxiliary information of star tracking observation, obtains pixel coordinates through star image detection and centering, calculates celestial coordinates apparent position and converts it into standard coordinates after matching celestial measurement calibration star table information; fits forward high order, reverse high order and reverse first order polynomials for each image, converts and calculates to extract geometric distortion polynomials; divides pixel coordinate grid points and calculates distortion vectors, fits target geometric distortion polynomials after median processing. The present application does not need specific observation mode and iterative solving, has strong adaptability, quickly and accurately completes geometric distortion solving, and further effectively improves the universality and efficiency of geometric distortion solving, meets the application requirements of efficient and accurate control, rapid optical performance evaluation in astronomical telescope operation control field.

Description

Technical Field

[0001] This invention relates to the field of astronomical observation and astrometry technology, and in particular to a method and system for solving geometric distortion of astronomical images. Background Technology

[0002] In the field of telescope astronomical observation, due to factors such as assembly errors in the telescope's optical system and deviations in sensor manufacturing processes, astronomical images inevitably exhibit geometric distortions, manifested as pixel offsets, stretching, or compression relative to the actual position of the target celestial object. This geometric distortion not only directly affects the accuracy of pointing control during telescope operation but also impacts the accuracy of subsequent analyses such as celestial object positioning, distance measurement, and image fusion. Therefore, rapidly and accurately determining the geometric distortion parameters of astronomical images is a core requirement for the operational control of astronomical telescopes and the accurate measurement of astronomical image positions.

[0003] To address the problem of geometric distortion in astronomical images, a common approach in existing technologies is to observe multiple images of a specified sky region with different directions or orientations according to a preset pattern. There are certain requirements for the direction and number of images. Then, the correlation positional relationship between the stars in each image is solved, and finally, the geometric distortion of the astronomical image is iteratively solved.

[0004] However, this method based on observation mode matching and preset distortion model has obvious drawbacks. Its core drawbacks are: it requires specific pointing and orientation observations and a certain number of observation images; it also requires iterative solutions, which results in slow computation speed and makes it difficult to meet the needs of modern astronomical observations for multi-mode and efficient and precise control of the observation site. Summary of the Invention

[0005] This invention provides a method and system for solving geometric distortion in astronomical images. It can quickly and accurately solve geometric distortion without relying on telescopes for different pointing and orientation observation modes, thereby effectively improving the versatility and efficiency of geometric distortion solving and meeting the observation needs of modern astronomical observations for multi-mode observations and efficient and precise on-site control.

[0006] To achieve the above objectives, the embodiments of the present invention adopt the following technical solutions: In a first aspect, a method for solving geometric distortion in astronomical images is provided. The method includes: acquiring one or more dense star field images based on star-tracking observations, and auxiliary information corresponding to each dense star field image, the auxiliary information including initial pointing, exposure start time, exposure duration, observation position, and observation velocity vector; performing star image detection and centering on each dense star field image to obtain the pixel coordinates of each star image included in each dense star field image; acquiring astrometric calibration star catalog information within the field of view based on the initial pointing, matching the pixel coordinates with the astrometric calibration star catalog information to obtain star catalog information corresponding to each star image; and calculating the celestial coordinate viewing position based on the auxiliary information of each dense star field image and the star catalog information of each star image. The celestial coordinates of each star image are converted to standard coordinates via centripetal projection. For each dense star field image, fitting calculations are performed to obtain the forward higher-order polynomial, the backward higher-order polynomial, and the backward first-order polynomial from the pixel coordinates to the standard coordinates. The geometric twist polynomial is extracted by subtracting the corresponding terms of the backward higher-order polynomial and the backward first-order polynomial for each dense star field image. The pixel coordinates of each dense star field image are divided into grid points. Based on the forward higher-order polynomial and the geometric twist polynomial, the twist vector corresponding to the center of each grid point is calculated. The twist vectors of all dense star field images are processed by median value across the grid points. Based on the pixel coordinates of the grid points and the corresponding median twist vector, the target geometric twist polynomial is fitted.

[0007] The method provided by this invention systematically solves for geometric distortion in astronomical images through a complete process: acquiring dense star field images and auxiliary information, star image detection and centering, star catalog matching, calculation of apparent position of celestial coordinates and standard coordinate transformation, polynomial fitting, extraction of geometric distortion polynomials, grid division and distortion vector calculation, median processing and target polynomial fitting. This method does not rely on a specific observation mode; it can complete the solution with only one or more dense star field images and requires no iterative calculations. It effectively solves the problems of traditional methods, such as strong dependence on observation modes and low solution efficiency, providing reliable technical support for rapid calibration at the operational control site and high-precision telescope pointing. Furthermore, the method provided by this invention can quickly and accurately complete the geometric distortion solution, thereby effectively improving the versatility and efficiency of geometric distortion solution, meeting the observation needs of modern astronomical observations, which require multiple modes and efficient and precise control at the observation site.

[0008] In one possible implementation of the first aspect, the observation location is the location of an observation station or the telescope in space; star detection and centering are performed on each of the dense star field images to obtain the pixel coordinates of each star image included in each dense star field image, including: calculating the average background gray value and its standard deviation of each dense star field image; performing connected component detection on image regions exceeding N times the standard deviation, where N is a positive integer; and calculating the pixel coordinates of the centroid position of each detected star image using a modified moment centering algorithm.

[0009] The method provided by this invention clearly defines the observation location as the location of the observation station or the telescope in space, and refines the specific process of star image detection and centering: by calculating the average background gray value and standard deviation, performing connected component detection on regions exceeding N times the standard deviation and average background gray value, and using the modified moment centering algorithm, the pixel coordinates of the centroid position of the star image can be obtained quickly and accurately, ensuring the accuracy of the basic data for subsequent star catalog matching and coordinate transformation, and improving the reliability of the entire geometric distortion solution process.

[0010] In one possible implementation of the first aspect, the step of matching the pixel coordinates with the astrometric calibration star catalog information to obtain the star catalog information corresponding to each star image includes: constructing a star image position relationship matrix corresponding to the pixel coordinates based on a triangle matching algorithm; extracting the celestial coordinates of stars in the astrometric calibration star catalog information to construct a star catalog coordinate relationship matrix; matching the pixel coordinates with the stars in the star catalog according to the topological structure of the star image position relationship matrix and the star catalog coordinate relationship matrix; and, if the matching is successful, determining the right ascension, declination, proper motion of right ascension, proper motion of declination, parallax, and radial velocity of the celestial coordinates of each star image as the star catalog information corresponding to each star image.

[0011] The method provided by this invention is based on a triangle matching algorithm. By constructing a matrix of star image positions and a matrix of star catalog coordinates, it matches pixel coordinates with stars in the star catalog according to the topological structure. After a successful match, it obtains complete star catalog information such as the right ascension, declination, and proper motion of the star's celestial coordinates. This matching method has strong stability and outstanding anti-interference ability. It can achieve a precise one-to-one correspondence between star images and stars in the star catalog in dense star field scenes, providing accurate star catalog data support for subsequent calculation of the apparent position of celestial coordinates and ensuring the accuracy of the solution results.

[0012] In one possible implementation of the first aspect, the calculation of the celestial coordinate apparent position based on the auxiliary information of each of the dense star field images and the star catalog information of each star image includes: calculating the apparent position of each star image at the observation epoch based on the exposure start time, exposure duration, observation position and velocity vector in the auxiliary information, combined with the right ascension, declination, proper motion of right ascension, proper motion of declination, parallax and radial velocity of the celestial coordinates of the stars in the star catalog information, and determining the apparent position at the observation epoch as the celestial coordinate apparent position.

[0013] The method provided by this invention fully considers the error factors caused by the star's own motion and the observation environment, and can accurately calculate the actual observation position of the star, laying an accurate coordinate foundation for subsequent standard coordinate transformation and geometric distortion solution.

[0014] In one possible implementation of the first aspect, the formula for the cardiac projection is: ; Where (ξ,η) are the transformed standard coordinates, (α,δ) are the celestial coordinates of the stars, and (A,D) are the theoretical positions of the celestial coordinates to which the telescope's optical axis points.

[0015] The method provided by this invention clarifies the formula and parameter definitions of the centripetal projection, converts the celestial coordinates of stars into standard coordinates, and this projection method is suitable for the coordinate transformation requirements of astronomical observation. The transformation process is logically clear and computationally simple, and can quickly establish the correspondence between the celestial coordinates and the standard coordinates of the image, ensuring the rationality of subsequent polynomial fitting and providing a guarantee for the accurate extraction of geometric distortion polynomials.

[0016] In one possible implementation of the first aspect, the order of both the forward higher-order polynomial and the backward higher-order polynomial is M, where M is an integer greater than or equal to 2. The expression for the positive higher-order polynomial is: ; Where i and j are the orders of the x and y terms respectively, and a ij b ij Here are the polynomial coefficients, (x,y) are the pixel coordinates of the star image, and (ξ,η) are the standard coordinates. The expression for the inverse higher-order polynomial is: ; Where i and j are the orders of the ξ and η terms, respectively, and c ij d ij These are the polynomial coefficients; The expression for the inverse first-order polynomial is: ; Among them, e10 e 01 e 00 f 10 f 01 and f 00 These are the polynomial coefficients.

[0017] The method provided by this invention sets the order of the forward and reverse higher-order polynomials to be greater than 2 (e.g., 2-4), clarifying the specific expressions of the three types of polynomials and the meaning of each coefficient. This ensures the fitting accuracy of the polynomials to the coordinate transformation relationship, while avoiding the problem of excessive computational complexity caused by excessively high orders. At the same time, the reverse 1st-order polynomial can accurately separate translation, rotation, and scaling terms, creating favorable conditions for the subsequent extraction of geometric twist polynomials, thus balancing solution accuracy and computational efficiency.

[0018] In one possible implementation of the first aspect, the step of extracting the geometrically distorted polynomial by subtracting the corresponding terms of the inverse higher-order polynomial and the inverse first-order polynomial for each dense star field image includes: subtracting the coefficients of the first-order terms in the inverse higher-order polynomial from the corresponding coefficients of the first-order terms in the inverse first-order polynomial, and subtracting the coefficients of the constant terms in the inverse higher-order polynomial from the corresponding coefficients of the constant terms in the inverse first-order polynomial to obtain the corresponding coefficients of the first-order terms and the constant terms; retaining all terms and coefficients of order greater than or equal to 2 in the inverse higher-order polynomial, and constructing the geometrically distorted polynomial based on the corresponding coefficients of the first-order terms and the constant terms; The expression for the geometric twisted polynomial is: ; Where dx and dy are the geometric twist vectors of the pixel in the x and y directions, respectively, and g ij For all order coefficients in the x-direction, h ij The coefficients of all terms in the y-direction.

[0019] The method provided by this invention constructs a geometric distortion polynomial by subtracting the coefficients of the first-order terms and constant terms of the inverse higher-order polynomial from the coefficients of the first-order terms and constant terms of the inverse first-order polynomial, and combining the terms and coefficients of the inverse higher-order polynomial with an order greater than or equal to 2. This extraction method can accurately eliminate the effects of translation, rotation and scaling in coordinate transformation, and separate the geometric distortion-related components. The resulting geometric distortion polynomial directly reflects the distortion characteristics of the image, providing accurate model support for subsequent distortion vector calculation.

[0020] In one possible implementation of the first aspect, the step of dividing the pixel coordinates of each dense star field image into grid points, and calculating the torsion vector corresponding to the center of each grid point based on the forward higher-order polynomial and the geometric twist polynomial, includes: dividing the pixel coordinates of each dense star field image into uniformly distributed grid regions according to a preset number of rows and columns; calculating the pixel coordinates (x, y, x) of the center of each grid region. area ,y area ); Set the pixel coordinates (x, y) of the center of the grid point area ,y area Substituting the corresponding positive higher-order polynomial of the dense star field image into the equation, the corresponding standard coordinates (ξ) are calculated. area ,η area The standard coordinates (ξ) area ,η area Substitute the geometric twist polynomial corresponding to each of the dense star field images to calculate the twist component dx in the x direction and the twist component dy in the y direction for each grid point center, where (dx,dy) is the twist vector corresponding to the grid point center.

[0021] The method provided by this invention divides pixel coordinates into uniform grid regions according to a preset number of rows and columns. It converts the grid center pixel coordinates into standard coordinates through a forward high-order polynomial, and then substitutes them into a geometric twist polynomial to calculate the twist vector. This process discretizes continuous image twists into computable vector data through gridding, which not only ensures the comprehensiveness of the twist description but also reduces the computational complexity. It can efficiently obtain the twist features of each region and provide structured twist data for subsequent median processing.

[0022] In one possible implementation of the first aspect, the process of fitting a target geometric twist polynomial based on the pixel coordinates of grid points and the corresponding median of twist vectors includes: fitting a target geometric twist polynomial with the pixel coordinates of the center of each grid point as the independent variable and the median of the corresponding twist vector as the dependent variable; wherein the order of the target geometric twist polynomial is M', and M' is an integer greater than or equal to 1 and less than or equal to the order M of the inverse higher-order polynomial. The expression for the target geometric twist polynomial is: ; Where i and j are the orders of the x and y terms respectively, p ij q ij The coefficients of the target geometric twisted polynomial.

[0023] The method provided by this invention uses the grid center pixel coordinates as the independent variable and the median of the distortion vector as the dependent variable to fit a target geometric distortion polynomial. The order of the target polynomial is limited to 1 to M. This fitting method makes full use of the distortion data of multiple images, reduces the influence of random errors through median processing, and the order limitation takes into account both fitting accuracy and model simplicity. The final target geometric distortion polynomial can comprehensively and accurately describe the geometric distortion characteristics of astronomical images and can be directly used for subsequent image distortion correction and telescope optical system performance evaluation.

[0024] Secondly, the present invention provides an astronomical image geometric distortion solution system, the system comprising: an image acquisition module, used to acquire one or more dense star field images based on star tracking observations, and auxiliary information corresponding to each dense star field image, the auxiliary information including initial pointing, exposure start time, exposure duration, observation position, and observation velocity vector; a coordinate determination module, used to perform star image detection and centering on each dense star field image to obtain the pixel coordinates of each star image included in each dense star field image; a star catalog matching module, used to acquire astrometric calibration star catalog information within the field of view based on the initial pointing, and match the pixel coordinates with the astrometric calibration star catalog information to obtain star catalog information corresponding to each star image; and a coordinate transformation module, used to calculate celestial coordinates based on the auxiliary information of each dense star field image and the star catalog information of each star image. The system employs a three-part method: a viewing position module, which converts the celestial coordinates of each star image to standard coordinates via centripetal projection; a fitting calculation module, which performs fitting calculations on each dense star field image to obtain the forward higher-order polynomial, the backward higher-order polynomial, and the backward first-order polynomial from the pixel coordinates of each dense star field image to the standard coordinates; a distortion extraction module, which extracts the geometric distortion polynomial by subtracting the corresponding terms of the backward higher-order polynomial and the backward first-order polynomial of each dense star field image; a grid calculation module, which divides the pixel coordinates of each dense star field image into grid points and calculates the distortion vector corresponding to the center of each grid point based on the forward higher-order polynomial and the geometric distortion polynomial; and a result fitting module, which performs median processing on the distortion vectors of all dense star field images according to the grid points and fits the target geometric distortion polynomial based on the pixel coordinates of the grid points and the corresponding median distortion vector.

[0025] Thirdly, an electronic device is provided, the electronic device including a memory and one or more processors; the memory is coupled to the processors; wherein the memory stores computer program code, the computer program code including computer instructions, which, when executed by the processor, cause the electronic device to perform the method as described in any implementation of the first aspect.

[0026] Fourthly, a computer-readable storage medium is provided, including computer instructions that, when executed on an electronic device, cause the electronic device to perform a method as described in any implementation of the first aspect.

[0027] Fifthly, a computer program product is provided that, when run on a computer, causes the computer to perform the method in any implementation of the first aspect.

[0028] Understandably, the beneficial effects achieved by the system of the second aspect, the electronic device of the third aspect, the computer-readable storage medium of the fourth aspect, and the computer program product of the fifth aspect provided above can be referred to in light of the beneficial effects of the first aspect and any of its possible design embodiments, which will not be repeated here. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention; Figure 2 A flowchart of a method for solving the geometric distortion of astronomical images provided in an embodiment of the present invention; Figure 3 A median example of an 8×8 grid point geometric twist vector is provided as an embodiment of the present invention; Figure 4 A median example of a 16×16 grid point geometric twist vector provided for an embodiment of the present invention; Figure 5 A vector sample image of 16×16 grid points obtained by fitting a target geometric distortion polynomial using a third-order polynomial, provided as an embodiment of the present invention; Figure 6 This invention provides a vector sample image with 16×16 grid points obtained by fitting a target geometric distortion polynomial using a second-order polynomial. Figure 7 This is a schematic diagram of a geometric distortion solving system provided in an embodiment of the present invention. Detailed Implementation

[0030] The technical solutions of the embodiments of the present invention will be described below with reference to the accompanying drawings. In the description of the present invention, unless otherwise stated, " / " indicates that the objects before and after are in an "or" relationship. For example, A / B can represent A or B. The "or" in the present invention is merely a description of the relationship between the related objects, indicating that three relationships can exist. For example, A or B can represent: A alone, A and B simultaneously, and B alone. A and B can be singular or plural. Furthermore, in the description of the present invention, unless otherwise stated, "multiple" refers to two or more. "At least one of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items.

[0031] Furthermore, to facilitate a clear description of the technical solutions of the embodiments of the present invention, the terms "first" and "second" are used in the embodiments of the present invention to distinguish identical or similar items with essentially the same function and effect. Those skilled in the art will understand that the terms "first" and "second" do not limit the quantity or execution order, and that the terms "first" and "second" are not necessarily different.

[0032] In this embodiment of the invention, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design described as "exemplary" or "for example" in this embodiment of the invention should not be construed as superior or more advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner for ease of understanding.

[0033] In the field of telescope astronomical observation, due to factors such as assembly errors in the telescope's optical system and deviations in sensor manufacturing processes, astronomical images inevitably exhibit geometric distortions, manifested as pixel offsets, stretching, or compression relative to the actual position of the target celestial object. This geometric distortion not only directly affects the accuracy of pointing control during telescope operation but also impacts the accuracy of subsequent analyses such as celestial object positioning, distance measurement, and image fusion. Therefore, rapidly and accurately determining the geometric distortion parameters of astronomical images is a core requirement for the operational control of astronomical telescopes and the accurate measurement of astronomical image positions.

[0034] To address the problem of geometric distortion in astronomical images, a common approach in existing technologies is to observe multiple images of a specified sky region with different directions or orientations according to a preset pattern. There are certain requirements for the direction and number of images. Then, the correlation positional relationship between the stars in each image is solved, and finally, the geometric distortion of the astronomical image is iteratively solved.

[0035] However, this method based on observation mode matching and preset distortion model has obvious drawbacks. Its core drawbacks are: it requires specific pointing and orientation observations and a certain number of observation images; it also requires iterative solutions, which results in slow computation speed and makes it difficult to meet the needs of modern astronomical observations for multi-mode and efficient and precise control of the observation site.

[0036] In view of this, embodiments of the present invention provide a method and system for solving geometric distortion of astronomical images. The method includes: acquiring one or more dense star field images based on star tracking observations, and auxiliary information corresponding to each dense star field image, the auxiliary information including initial pointing, exposure start time, exposure duration, observation position, and observation velocity vector; performing star image detection and centering on each dense star field image to obtain the pixel coordinates of each star image included in each dense star field image; acquiring astrometric calibration star catalog information within the field of view according to the initial pointing, matching the pixel coordinates with the astrometric calibration star catalog information to obtain the star catalog information corresponding to each star image; and calculating the celestial sphere based on the auxiliary information of each dense star field image and the star catalog information of each star image. The celestial coordinates of each star image are converted to standard coordinates via centripetal projection. For each dense star field image, fitting calculations are performed to obtain the forward higher-order polynomial, the backward higher-order polynomial, and the backward first-order polynomial from the pixel coordinates to the standard coordinates. The geometric twist polynomial is extracted by subtracting the corresponding terms of the backward higher-order polynomial and the backward first-order polynomial for each dense star field image. The pixel coordinates of each dense star field image are divided into grid points. Based on the forward higher-order polynomial and the geometric twist polynomial, the twist vector corresponding to the center of each grid point is calculated. The twist vectors of all dense star field images are processed by median value across the grid points. Based on the pixel coordinates of the grid points and the corresponding median twist vector, the target geometric twist polynomial is fitted.

[0037] The method provided by this invention systematically solves for geometric distortion in astronomical images through a complete process: acquiring dense star field images and auxiliary information, star image detection and centering, star catalog matching, calculating the apparent position of celestial coordinates and transforming to standard coordinates, polynomial fitting, geometric distortion polynomial extraction, grid division and distortion vector calculation, median processing, and target polynomial fitting. This method does not rely on specific observation modes and can complete the solution with only one or more dense star field images, without iterative calculations. It effectively solves the problems of traditional methods, such as strong dependence on observation modes and low solution efficiency, providing reliable technical support for rapid calibration on-site and high-precision pointing control of telescopes. Furthermore, the method provided by this invention can quickly and accurately complete the geometric distortion solution, thereby effectively improving the versatility and efficiency of geometric distortion solutions and meeting the observation requirements of multi-mode, high-efficiency, and precise control in modern astronomical observations.

[0038] In some embodiments, the astronomical image geometric distortion solution method provided by the present invention can be executed by an astronomical image geometric distortion solution system 100 (hereinafter referred to as geometric distortion solution system 100).

[0039] As an example, the geometry distortion solving system 100 can be any electronic device 200 with data processing capabilities, such as a general-purpose computer, personal computer, laptop computer, switch, or tablet computer. The specific implementation of the geometry distortion solving system 100 is not limited here.

[0040] Figure 1 A schematic diagram of the hardware structure of an electronic device provided in an embodiment of the present invention is shown. The electronic device 200 includes a processor 210, a memory 220, and a communication interface 230.

[0041] Processor 210 may include one or more processing cores. Processor 210 connects to various parts within electronic device 200 using various interfaces and lines, and performs various functions and processes data of electronic device 200 by running or executing instructions, programs, code sets, or instruction sets stored in memory 220, and by calling data stored in memory 220. Optionally, processor 210 may be implemented using at least one of the following hardware forms: Central Processing Unit (CPU), Graphics Processing Unit (GPU), Digital Signal Processing (DSP), Field-Programmable Gate Array (FPGA), and Programmable Logic Array (PLA).

[0042] The memory 220 may include random access memory (RAM) or read-only memory (ROM). Optionally, the memory 220 may include a non-transitory computer-readable storage medium. The memory 220 may be used to store instructions, programs, code, code sets, or instruction sets. The memory 220 may include a program storage area. This program storage area may store instructions for implementing an operating system, instructions for implementing at least one function, instructions for implementing the various method embodiments described above, etc.

[0043] Communication interface 230 is used to communicate with other devices, equipment or communication networks, such as data storage devices, image processing devices or Ethernet, wireless access network (RAN), wireless local area network (WLAN), etc.

[0044] In terms of physical implementation, the aforementioned devices (such as processor 210, memory 220, and communication interface 230) can each be devices within the same device (such as a laptop computer). Alternatively, at least two of these devices can be located within the same device, i.e., as different devices within the same device, similar to the deployment of devices or components in a distributed system.

[0045] It is understood that the structure illustrated in this embodiment does not constitute a specific limitation on the electronic device 200. In other embodiments of the present invention, the electronic device 200 may include more or fewer components than illustrated, or combine some components, or split some components, or have different component arrangements. The illustrated components may be implemented in hardware, software, or a combination of software and hardware.

[0046] The following description, in conjunction with the accompanying drawings, illustrates a method for solving geometric distortion in astronomical images provided by an embodiment of the present invention.

[0047] Figure 2 This is a flowchart illustrating a method for solving geometric distortion in astronomical images, provided as an embodiment of the present invention. Optionally, this method can be... Figure 1 The illustrated electronic device 200 performs this method, which includes the following steps: S1. Acquire one or more dense star field images based on star tracking observations, as well as auxiliary information corresponding to each dense star field image.

[0048] Specifically, the auxiliary information includes initial pointing, exposure start time, exposure duration, observation position, and observation velocity vector; wherein, the observation position is the location of the observation station or the telescope in space.

[0049] It should be noted that when there are multiple dense star field images, random errors can be effectively reduced, thereby improving the accuracy of geometric distortion solution.

[0050] S2. Perform star image detection and centering on each of the dense star field images to obtain the pixel coordinates of each star image included in each of the dense star field images.

[0051] In one possible implementation, the above S2 specifically includes: Calculate the average background gray value and its standard deviation for each of the dense star field images; perform connected component detection on image regions that exceed N times the standard deviation, where N is a positive integer; and use the modified moment centering algorithm to calculate the pixel coordinates of the centroid position of each detected star image.

[0052] In one example, N equals 5.

[0053] The method provided by this invention clearly defines the observation location as the location of the observation station or the telescope in space, and refines the specific process of star image detection and centering: by calculating the average background gray value and standard deviation, performing connected component detection on regions exceeding N times the standard deviation and average background gray value, and using the modified moment centering algorithm, the pixel coordinates of the centroid position of the star image can be obtained quickly and accurately, ensuring the accuracy of the basic data for subsequent star catalog matching and coordinate transformation, and improving the reliability of the entire geometric distortion solution process.

[0054] S3 obtains the astronomical calibration star catalog information within the field of view based on the initial pointing, and matches the pixel coordinates with the astronomical calibration star catalog information to obtain the star catalog information corresponding to each star image.

[0055] In some embodiments, matching the pixel coordinates with the astrometric calibration star catalog information to obtain the star catalog information corresponding to each star image includes: constructing a star image position relationship matrix corresponding to the pixel coordinates based on a triangle matching algorithm; extracting the celestial coordinates of stars in the astrometric calibration star catalog information to construct a star catalog coordinate relationship matrix; matching the pixel coordinates with the stars in the star catalog according to the topological structure of the star image position relationship matrix and the star catalog coordinate relationship matrix; and, if the matching is successful, determining the right ascension, declination, proper motion of right ascension, proper motion of declination, parallax, and radial velocity of the celestial coordinates of each star image as the star catalog information corresponding to each star image.

[0056] The method provided by this invention is based on a triangle matching algorithm. By constructing a matrix of star image positions and a matrix of star catalog coordinates, it matches pixel coordinates with stars in the star catalog according to the topological structure. After a successful match, it obtains complete star catalog information such as the right ascension, declination, and proper motion of the star's celestial coordinates. This matching method has strong stability and outstanding anti-interference ability. It can achieve a precise one-to-one correspondence between star images and stars in the star catalog in dense star field scenes, providing accurate star catalog data support for subsequent calculation of the apparent position of celestial coordinates and ensuring the accuracy of the solution results.

[0057] S4. Calculate the apparent celestial coordinates based on the auxiliary information of each of the dense star field images and the star catalog information of each star image, and convert the apparent celestial coordinates of each star image into standard coordinates through centripetal projection.

[0058] In one possible implementation, calculating the apparent celestial coordinates based on auxiliary information of each of the dense star field images and star catalog information of each star image includes: Based on the exposure start time, exposure duration, observation position, and velocity vector in the auxiliary information, and combined with the right ascension, declination, proper motion of right ascension, proper motion of declination, parallax, and radial velocity of the stars in the star catalog information, the apparent position of each star image at the observation epoch is calculated, and the apparent position at the observation epoch is determined as the apparent position of the celestial coordinates.

[0059] The method provided by this invention fully considers the error factors caused by the star's own motion and the observation environment, and can accurately calculate the actual observation position of the star, laying an accurate coordinate foundation for subsequent standard coordinate transformation and geometric distortion solution.

[0060] In another possible implementation, the formula for the cardiac projection is: ; Where (ξ,η) are the transformed standard coordinates, (α,δ) are the celestial coordinates of the stars, and (A,D) are the theoretical positions of the celestial coordinates to which the telescope's optical axis points.

[0061] The method provided by this invention clarifies the formula and parameter definitions of the centripetal projection, converts the celestial coordinates of stars into standard coordinates, and this projection method is suitable for the coordinate transformation requirements of astronomical observation. The transformation process is logically clear and computationally simple, and can quickly establish the correspondence between the celestial coordinates and the standard coordinates of the image, ensuring the rationality of subsequent polynomial fitting and providing a guarantee for the accurate extraction of geometric distortion polynomials.

[0062] S5. Perform fitting calculations on each of the dense star field images to obtain the forward higher-order polynomial, the backward higher-order polynomial, and the backward first-order polynomial of the pixel coordinates to the standard coordinates corresponding to each dense star field image.

[0063] In some embodiments, the order of both the forward higher-order polynomial and the backward higher-order polynomial is M, where M is an integer greater than or equal to 2. Furthermore, the expression for the forward higher-order polynomial is: ; Where i and j are the orders of the x and y terms respectively, and a ij b ij ξ represents the polynomial coefficients, (x,y) represents the pixel coordinates of the star image, and (ξ,η) represents the standard coordinates.

[0064] It should be noted that, in one example, if it is a 3rd order polynomial (M=3), the parameter to be determined is a ij and b ijEach contains 10 parameters. If it is a 4th-order polynomial (M=4), the parameter to be determined is a. ij and b ij Each polynomial contains 15 parameters. The purpose of solving this polynomial is to easily and accurately transform the pixel coordinates of each image to standard coordinates.

[0065] The expression for the inverse higher-order polynomial is: ; Where i and j are the orders of the ξ and η terms, respectively, and c ij d ij These are the polynomial coefficients; It should be understood that, similarly, if it is a 3rd order polynomial (M=3), the parameter to be found, a... ij and b ij Each contains 10 parameters. If it is a 4th-order polynomial (M=4), the parameter to be determined is a. ij and b ij Each solution contains 15 parameters. The polynomial to be solved mainly includes geometric distortion, translation, rotation, and scaling effects in an image.

[0066] The expression for the inverse first-order polynomial is: ; Where e 10 e 01 e 00 f 10 f 01 and f 00 These are the polynomial coefficients.

[0067] Specifically, the polynomial is of order 1 and has 6 parameters to be determined, namely e 10 e 01 e 00 f 10 f 01 and f 00 Among them, e 00 f 00 The two parameters are the translation terms for coordinate axis transformation, e 10 e 01 f 10 f 01 It incorporates the rotation and scaling effects of the coordinate axes. The purpose of solving this polynomial is to facilitate the extraction of observation-related translation, rotation, and scaling effects from the parameters of the inverse higher-order polynomial.

[0068] The method provided by this invention sets the order of the forward and reverse higher-order polynomials to be greater than 2 (e.g., 2-4), clarifying the specific expressions of the three types of polynomials and the meaning of each coefficient. This ensures the fitting accuracy of the polynomials to the coordinate transformation relationship, while avoiding the problem of excessive computational complexity caused by excessively high orders. At the same time, the reverse 1st-order polynomial can accurately separate translation, rotation, and scaling terms, creating favorable conditions for the subsequent extraction of geometric twist polynomials, thus balancing solution accuracy and computational efficiency.

[0069] S6. By subtracting the corresponding terms of the inverse higher-order polynomial of each dense star field image from the corresponding terms of the inverse first-order polynomial, the geometric twist polynomial is extracted.

[0070] In one possible implementation, S6 above includes: subtracting the coefficients of the first-order terms in the inverse higher-order polynomial from the corresponding coefficients of the first-order terms in the inverse first-order polynomial, and subtracting the coefficients of the constant terms in the inverse higher-order polynomial from the corresponding coefficients of the constant terms in the inverse first-order polynomial, to obtain the corresponding coefficients of the first-order terms and the constant terms; retaining all terms and coefficients of order greater than or equal to 2 in the inverse higher-order polynomial, and constructing a geometrically distorted polynomial based on the corresponding coefficients of the first-order terms and the constant terms; Specifically, by subtracting the corresponding coefficients of the first-order terms of the inverse higher-order polynomial parameters obtained from the above steps from the first-order terms of the inverse first-order model polynomial parameters obtained from the above steps, we obtain four first-order term coefficients and two constant term coefficients.

[0071] Specifically, g 10 =c 10 -e 10 g 01 =c 01 -e 01 g 00 =c 00 -e 00 h 10 =d 10 -f 10 h 01 =d 01 -f 01 h 00 =d 00 -f 00 .

[0072] Next, a new geometrically twisted polynomial is obtained by combining the coefficients. The order of the new polynomial is the same as that of the inverse higher-order polynomial. The higher-order terms (order greater than or equal to 2) of the geometrically twisted polynomial are obtained by using the coefficients of the inverse higher-order polynomial, while the lower-order terms are obtained by using the coefficient g. 10 g 01 g 00 h 10 h 01 h00 .

[0073] The expression for the geometric twisted polynomial is: ; Where dx and dy are the geometric twist vectors of the pixel in the x and y directions, respectively, and g ij For all order coefficients in the x-direction, h ij The coefficients of all terms in the y-direction.

[0074] In this way, by constructing a geometrically warped polynomial, the translation, rotation, and scaling effects in the inverse higher-order polynomial can be subtracted, resulting in a transformation from standard coordinates (ξ, η) to pixel coordinates (x, η). c y c The geometric twisted vector polynomial of ).

[0075] The method provided by this invention constructs a geometric distortion polynomial by subtracting the coefficients of the first-order terms and constant terms of the inverse higher-order polynomial from the coefficients of the first-order terms and constant terms of the inverse first-order polynomial, and combining the terms and coefficients of the inverse higher-order polynomial with an order greater than or equal to 2. This extraction method can accurately eliminate the effects of translation, rotation and scaling in coordinate transformation, and separate the geometric distortion-related components. The resulting geometric distortion polynomial directly reflects the distortion characteristics of the image, providing accurate model support for subsequent distortion vector calculation.

[0076] S7. Divide the pixel coordinates of each dense star field image into grid points, and calculate the torsion vector corresponding to the center of each grid point based on the positive higher-order polynomial and the geometric twist polynomial.

[0077] In one possible implementation, the above S7 includes: The pixel coordinates of each of the dense star field images are divided into uniformly distributed grid regions according to a preset number of rows and columns; the pixel coordinates (x, y, y) of the center of each grid region are calculated. area ,y area ); Set the pixel coordinates (x, y) of the center of the grid point area ,y area Substituting the corresponding positive higher-order polynomial of the dense star field image into the equation, the corresponding standard coordinates (ξ) are calculated. area ,η area The standard coordinates (ξ) area ,η area Substitute the geometric twist polynomial corresponding to each of the dense star field images to calculate the twist component dx in the x direction and the twist component dy in the y direction for each grid point center, where (dx,dy) is the twist vector corresponding to the grid point center.

[0078] In one example, the pixel coordinates of the dense star field image are divided into image regions of 8×8 grid points or 16×16 grid points. Then, the pixel coordinates (x, y, z) of the center of each grid region are calculated. area , y area ); where the pixel coordinates (x, y) of the center of each grid region. area , y area ) represents the average pixel coordinates of the region boundary.

[0079] Solve for the pixel coordinates (x) of the center of each grid region. area , y area The corresponding twist vector (dx, dy) is first transformed to standard coordinates (ξ) by a positive higher-order polynomial transformation. area η area Then, the corresponding twist vector (dx, dy) is obtained by calculating the geometric twist polynomial extracted above.

[0080] It should be noted that for each image being solved, the pixel coordinates (x, y) of the center of each grid region are... area , y area The corresponding distortion vectors (dx, dy) can be calculated for each of the observed images. If multiple observation images exist, the distortion vector (dx, dy) for each corresponding region can be calculated. area ,y area The median (dx) of the twist vector area dy area If there is only one observed image, the corresponding region (x) area , y area The median (dx) of the twist vector area dy area The distortion vector (dx, dy) of the image is represented by this vector. For example, Figure 3 A median example of an 8×8 grid point geometric twist vector is provided as an embodiment of the present invention; Figure 4 This is a median example of a 16×16 grid point geometric twist vector provided for an embodiment of the present invention.

[0081] The method provided by this invention divides pixel coordinates into uniform grid regions according to a preset number of rows and columns. It converts the grid center pixel coordinates into standard coordinates through a forward high-order polynomial, and then substitutes them into a geometric twist polynomial to calculate the twist vector. This process discretizes continuous image twists into computable vector data through gridding, which not only ensures the comprehensiveness of the twist description but also reduces the computational complexity. It can efficiently obtain the twist features of each region and provide structured twist data for subsequent median processing.

[0082] S8. Perform median processing on the twist vectors of all dense star field images according to the grid points, and fit the target geometric twist polynomial based on the pixel coordinates of the grid points and the corresponding median of the twist vectors.

[0083] In some embodiments, the step of fitting the target geometric twist polynomial based on the pixel coordinates of the grid points and the corresponding median of the twist vector includes: fitting the target geometric twist polynomial with the pixel coordinates of the center of each grid point as the independent variable and the median of the corresponding twist vector as the dependent variable. Based on the above example, fit the order of the polynomial expression for the geometric distortion as needed, and fit the final geometric distortion expression. We intend to use pixel coordinates (x... area y area ) and the corresponding twist vector is (dx area dy area The fitted polynomial expression is as follows: ; Where i and j are the orders of the x and y terms respectively, and p ij q ij The coefficients of the target geometric twisted polynomial.

[0084] It should be understood that the order of the target geometric twist polynomial is M', where M' is an integer greater than or equal to 1 and less than or equal to the order M of the inverse higher-order polynomial; For example, Figure 5 A vector sample image of 16×16 grid points obtained by fitting a target geometric distortion polynomial using a third-order polynomial, provided as an embodiment of the present invention; Figure 6 This invention provides a vector sample image with 16×16 grid points obtained by fitting a target geometric distortion polynomial using a second-order polynomial.

[0085] The method provided by this invention uses the grid center pixel coordinates as the independent variable and the median of the distortion vector as the dependent variable to fit a target geometric distortion polynomial. The order of the target polynomial is limited to 1 to M. This fitting method makes full use of the distortion data of multiple images, reduces the influence of random errors through median processing, and the order limitation takes into account both fitting accuracy and model simplicity. The final target geometric distortion polynomial can comprehensively and accurately describe the geometric distortion characteristics of astronomical images and can be directly used for subsequent image distortion correction and telescope optical system performance evaluation.

[0086] As described in S1-S8 above, the method provided by this invention systematically solves for geometric distortion in astronomical images through a complete process including acquiring dense star field images and auxiliary information, star image detection and centering, star catalog matching, calculation of apparent position of celestial coordinates and standard coordinate transformation, polynomial fitting, extraction of geometric distortion polynomials, grid division and distortion vector calculation, median processing and target polynomial fitting. This method does not rely on a specific observation mode; it can complete the solution with only one or more dense star field images and requires no iterative calculation. It effectively solves the problems of traditional methods being highly dependent on observation modes and having low solution efficiency, providing reliable technical support for rapid calibration at the operation and control site and high-precision pointing of telescopes. Furthermore, the method provided by this invention can quickly and accurately complete the geometric distortion solution, thereby effectively improving the versatility and efficiency of geometric distortion solution and meeting the observation needs of modern astronomical observations for multi-mode, high-efficiency, and precise control.

[0087] The foregoing mainly describes the solutions of the embodiments of the present invention from a methodological perspective. It is understood that, in order to achieve the above-mentioned functions, the geometric distortion solving system 100 includes at least one of the hardware structures and software modules corresponding to the execution of each function. Those skilled in the art should readily recognize that, in conjunction with the units and algorithm steps of the various examples described in the embodiments disclosed herein, the embodiments of the present invention can be implemented in hardware or a combination of hardware and computer software. Whether a function is executed in hardware or by computer software driving hardware depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the embodiments of the present invention.

[0088] In this embodiment of the invention, the geometric distortion solving system 100 can be divided into functional units according to the above method example. For example, the geometric distortion solving system 100 can be divided into functional units corresponding to various functions, or two or more functions can be integrated into one processing unit. The integrated unit can be implemented in hardware or as a software functional unit. It should be noted that the unit division in this embodiment of the invention is illustrative and only represents one logical functional division; other division methods may be used in actual implementation.

[0089] For example, Figure 7This diagram illustrates the hardware structure of a geometric distortion solving system according to an embodiment of the present invention. The geometric distortion solving system 100 includes: an image acquisition module 110, used to acquire one or more dense star field images based on star tracking observations, and auxiliary information corresponding to each dense star field image, the auxiliary information including initial pointing, exposure start time, exposure duration, observation position, and observation velocity vector; a coordinate determination module 120, used to perform star image detection and centering on each dense star field image to obtain the pixel coordinates of each star image included in each dense star field image; a star catalog matching module 130, used to acquire astrometric calibration star catalog information within the field of view based on the initial pointing, and match the pixel coordinates with the astrometric calibration star catalog information to obtain star catalog information corresponding to each star image; and a coordinate transformation module 140, used to calculate the apparent celestial coordinate position based on the auxiliary information of each dense star field image and the star catalog information of each star image, and transform the coordinates using a centering method. The projection transforms the celestial coordinates of each star image into standard coordinates; the fitting calculation module 150 is used to perform fitting calculations on each of the dense star field images to obtain the forward higher-order polynomial, the backward higher-order polynomial, and the backward first-order polynomial of the pixel coordinates to standard coordinates for each dense star field image; the distortion extraction module 160 is used to extract the geometric distortion polynomial by subtracting the corresponding terms of the backward higher-order polynomial and the backward first-order polynomial of each dense star field image; the grid calculation module 170 is used to divide the pixel coordinates of each dense star field image into grid points, and calculate the distortion vector corresponding to the center of each grid point based on the forward higher-order polynomial and the geometric distortion polynomial; the result fitting module 180 is used to perform median processing on the distortion vectors of all dense star field images according to the grid points, and fit the target geometric distortion polynomial based on the pixel coordinates of the grid points and the corresponding median of the distortion vectors.

[0090] It should be understood that specific descriptions of the above-mentioned optional methods can be found in the foregoing method embodiments, and will not be repeated here. Furthermore, explanations of any of the geometric distortion solution systems 100 provided above, as well as descriptions of their beneficial effects, can be found in the corresponding method embodiments described above, and will not be repeated here.

[0091] This invention also provides a computer-readable storage medium storing at least one computer instruction, which is loaded and executed by a processor to implement the methods of the various embodiments described above. Explanations of the relevant content and descriptions of the beneficial effects of any of the computer-readable storage media provided above can be found in the corresponding embodiments described above, and will not be repeated here.

[0092] This invention also provides a chip. This chip integrates a control circuit for implementing the functions of the aforementioned geometric distortion solving system 100 and one or more ports. Optionally, the functions supported by this chip are as described above and will not be repeated here.

[0093] Those skilled in the art will understand that the program for implementing all or part of the steps of the above embodiments, which can be executed by a program instructing related hardware, can be stored in a computer-readable storage medium. The storage medium mentioned above can be a read-only memory, a random access memory, etc. The processing unit or processor mentioned above can be a central processing unit, a general-purpose processor, an application-specific integrated circuit (ASIC), a microprocessor (DSP), a field-programmable gate array (FPGA), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof.

[0094] This invention also provides a computer program product containing instructions that, when executed on a computer, cause the computer to perform any of the methods described in the above embodiments. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the flow or function according to the embodiments of this invention is generated. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, computer instructions may be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium may be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available medium may be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., SSD), etc.

[0095] It should be noted that the devices for storing computer instructions or computer programs provided in the embodiments of the present invention, such as, but not limited to, the aforementioned memory, computer-readable storage medium, and communication chip, are all non-transitory. Those skilled in the art should recognize that the functions described in the embodiments of the present invention in one or more of the above examples can be implemented using hardware, software, firmware, or any combination thereof. When implemented using software, these functions can be stored in a computer-readable storage medium or transmitted as one or more instructions or code on a computer-readable storage medium. Computer-readable storage media include computer storage media and communication media, wherein communication media include any medium that facilitates the transmission of computer programs from one place to another. Storage media can be any available medium accessible to general-purpose or special-purpose computers.

[0096] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for solving the geometric distortion of astronomical images, characterized in that, The method includes: Acquire one or more dense star field images based on star tracking observations, and auxiliary information corresponding to each dense star field image, including initial pointing, exposure start time, exposure duration, observation position and observation velocity vector; Each of the dense star field images is subjected to star image detection and centering to obtain the pixel coordinates of each star image included in each dense star field image; Based on the initial direction, obtain the astrometry calibration star catalog information within the field of view, match the pixel coordinates with the astrometry calibration star catalog information, and obtain the star catalog information corresponding to each star image; The celestial coordinates of each star image are calculated based on the auxiliary information of each dense star field image and the star catalog information of each star image, and the celestial coordinates of each star image are converted into standard coordinates through centripetal projection. For each of the dense star field images, a fitting calculation is performed to obtain the forward higher-order polynomial, the backward higher-order polynomial, and the backward first-order polynomial of the pixel coordinates to the standard coordinates corresponding to each dense star field image. The geometric twisted polynomial is extracted by subtracting the corresponding terms of the inverse higher-order polynomial of each dense star field image from the corresponding terms of the inverse first-order polynomial. The pixel coordinates of each dense star field image are divided into grid points. Based on the positive higher-order polynomial and the geometric twist polynomial, the twist vector corresponding to the center of each grid point is calculated. The twist vectors of all dense star field images are processed by median value of grid points. Based on the pixel coordinates of the grid points and the corresponding median value of the twist vectors, the target geometric twist polynomial is fitted.

2. The method for solving the geometric distortion of astronomical images according to claim 1, characterized in that, The observation location refers to the location of the observation station or the telescope in space; star image detection and centering are performed on each of the dense star field images to obtain the pixel coordinates of each star image included in each dense star field image, including: Calculate the average background gray value and its standard deviation for each of the dense star field images; Connectivity detection is performed on image regions that exceed N times the standard deviation, where N is a positive integer; For each detected star image, the modified moment centering algorithm is used to calculate the pixel coordinates of the star image's centroid position.

3. The method for solving the geometric distortion of astronomical images according to claim 1, characterized in that, The step of matching the pixel coordinates with the astrometric calibration star catalog information to obtain the star catalog information corresponding to each star image includes: Based on the triangle matching algorithm, construct the star image position relationship matrix corresponding to the pixel coordinates; Extract the celestial coordinates of stars from the astrometry calibration catalog information and construct a catalog coordinate relationship matrix; The pixel coordinates are matched with the stars in the star catalog based on the topological structure of the star image position relationship matrix and the star catalog coordinate relationship matrix. If a match is successful, the right ascension, declination, proper motion of right ascension, proper motion of declination, parallax, and radial velocity of the star corresponding to each star image are determined as the star catalog information for each star image.

4. The method for solving the geometric distortion of astronomical images according to claim 1, characterized in that, The calculation of the apparent celestial coordinates based on auxiliary information of each of the dense star field images and star catalog information of each star image includes: Based on the exposure start time, exposure duration, observation position, and velocity vector in the auxiliary information, and combined with the right ascension, declination, proper motion of right ascension, proper motion of declination, parallax, and radial velocity of the stars in the star catalog information, the apparent position of each star image at the observation epoch is calculated, and the apparent position at the observation epoch is determined as the apparent position of the celestial coordinates.

5. The method for solving the geometric distortion of astronomical images according to claim 4, characterized in that, The formula for the cardiac projection is: ； Where (ξ,η) are the transformed standard coordinates, (α,δ) are the celestial coordinates of the stars, and (A,D) are the theoretical positions of the celestial coordinates to which the telescope's optical axis points.

6. The method for solving the geometric distortion of astronomical images according to claim 1, characterized in that, The order of both the forward and reverse higher-order polynomials is M, where M is an integer greater than or equal to 2. The expression for the positive higher-order polynomial is: ； Where i and j are the orders of the x and y terms respectively, and a ij b ij Here are the polynomial coefficients, (x,y) are the pixel coordinates of the star image, and (ξ,η) are the standard coordinates. The expression for the inverse higher-order polynomial is: ； Where i and j are the orders of the ξ and η terms, respectively, and c ij d ij These are the polynomial coefficients; The expression for the inverse first-order polynomial is: ； Among them, e 10 e 01 e 00 f 10 f 01 and f 00 These are the polynomial coefficients.

7. The method for solving the geometric distortion of astronomical images according to claim 1, characterized in that, The geometric distortion polynomial is extracted by subtracting the corresponding terms of the inverse higher-order polynomial and the inverse first-order polynomial of each dense star field image, including: Subtract the coefficients of the first-order terms in the inverse higher-order polynomial from the corresponding coefficients of the first-order terms in the inverse first-order polynomial, and subtract the coefficients of the constant terms in the inverse higher-order polynomial from the corresponding coefficients of the constant terms in the inverse first-order polynomial to obtain the corresponding coefficients of the first-order terms and constant terms. Retain all terms and coefficients of degree 2 or higher in the inverse higher-order polynomial, and construct the geometrically twisted polynomial based on the corresponding first-order term coefficients and constant term coefficients. The expression for the geometric twisted polynomial is: ； Where dx and dy are the geometric twist vectors of the pixel in the x and y directions, respectively, and g ij For all order coefficients in the x-direction, h ij The coefficients of all terms in the y-direction.

8. The method for solving the geometric distortion of astronomical images according to claim 1, characterized in that, The process of dividing the pixel coordinates of each dense star field image into grid points, and calculating the torsion vector corresponding to the center of each grid point based on the forward higher-order polynomial and the geometric twist polynomial, includes: The pixel coordinates of each of the dense star field images are divided into uniformly distributed grid regions according to a preset number of rows and columns; Calculate the pixel coordinates (x, y) of the center of each grid region. area ,y area ); Set the pixel coordinates (x, y) of the center of the grid point area ,y area Substituting the corresponding positive higher-order polynomial of the dense star field image into the equation, the corresponding standard coordinates (ξ) are calculated. area ,η area ); The standard coordinates (ξ) area ,η area Substitute the geometric twist polynomial corresponding to each of the dense star field images to calculate the twist component dx in the x direction and the twist component dy in the y direction for each grid point center, where (dx,dy) is the twist vector corresponding to the grid point center.

9. The method for solving the geometric distortion of astronomical images according to claim 1, characterized in that, The target geometric distortion polynomial is obtained by fitting the pixel coordinates based on the grid points and the corresponding median of the distortion vector, including: Using the pixel coordinates of the center of each grid point as the independent variable and the median of the corresponding twist vector as the dependent variable, a target geometric twist polynomial is obtained by fitting; wherein, the order of the target geometric twist polynomial is M', and M' is an integer greater than or equal to 1 and less than or equal to the order M of the inverse higher-order polynomial; The expression for the target geometric twist polynomial is: ； Where i and j are the orders of the x and y terms respectively, p ij q ij The coefficients of the target geometric twisted polynomial.

10. A system for solving geometric distortion in astronomical images, characterized in that, The system includes: The image acquisition module is used to acquire one or more dense star field images based on star tracking observations, as well as auxiliary information corresponding to each dense star field image. The auxiliary information includes initial pointing, exposure start time, exposure duration, observation position, and observation velocity vector. The coordinate determination module is used to perform star image detection and centering on each of the dense star field images to obtain the pixel coordinates of each star image included in each dense star field image; The star catalog matching module is used to obtain astrometry calibration star catalog information within the field of view based on the initial pointing, and match the pixel coordinates with the astrometry calibration star catalog information to obtain the star catalog information corresponding to each star image; The coordinate transformation module is used to calculate the apparent celestial coordinates of each star image based on the auxiliary information of each dense star field image and the star catalog information of each star image, and to convert the apparent celestial coordinates of each star image into standard coordinates through centripetal projection. The fitting calculation module is used to perform fitting calculations on each of the dense star field images to obtain the forward higher-order polynomial, the backward higher-order polynomial, and the backward first-order polynomial of the pixel coordinates to the standard coordinates corresponding to each dense star field image. The distortion extraction module is used to extract the geometric distortion polynomial by subtracting the corresponding terms of the inverse higher-order polynomial and the inverse first-order polynomial of each dense star field image. The grid calculation module is used to divide the pixel coordinates of each dense star field image into grid points, and calculate the torsion vector corresponding to the center of each grid point based on the forward higher-order polynomial and the geometric twist polynomial. The result fitting module is used to perform median processing on the twist vectors of all dense star field images according to the grid points, and to fit the target geometric twist polynomial based on the pixel coordinates of the grid points and the corresponding median of the twist vectors.

Images