A method for imaging instrument boresight calibration

Abstract

The application belongs to the technical field of space exploration imaging, and provides an imaging instrument view direction calibration method, comprising the following steps: obtaining a calibration image and identifying a target star point to find a predicted view line pointing center; obtaining a calibration view line pointing center of the imaging instrument in the calibration image and calculating a center pointing error; calculating lens parameters and star point fitting errors of the imaging instrument; generating an azimuth angle grid and an elevation angle grid of the lens view line pointing, and calculating a center pointing error and a star point fitting error of each grid point formed by the azimuth angle grid and the elevation angle grid to form a dispersion matrix and a fitting error matrix respectively; calculating a normalized goodness matrix and determining a lens optimized pointing. The method can realize accurate calibration of the imaging instrument lens pointing and lens parameters without knowing the lens view line center pointing, does not need to consider the lens field of view size, corrects the error caused by the imaging instrument pointing deviation, and improves the measurement accuracy.

Description

Technical Field

[0001] This application relates to the field of space exploration imaging technology, and in particular to an imager line-of-sight calibration method. Background Technology

[0002] In the fields of substorm and auroral dynamics research, auroral imagers are crucial observational instruments. Ground-based auroral images have been widely developed and used in related applications and scientific research, providing researchers with a wealth of valuable data. However, in actual observation processes, auroral images captured by auroral imagers are often affected by various factors, thus impacting the accuracy of their measurements.

[0003] First, due to the inherent characteristics of optical lenses, the captured images will exhibit varying degrees of distortion, which can affect the accuracy of measurements. Second, traditional all-sky imagers point their lenses towards a local zenith to reduce errors caused by image calibration. However, in practical applications, factors such as temperature changes and mechanical structure offsets can cause the lens center of the aurora imager to shift unpredictably relative to the local zenith. Furthermore, atmospheric turbulence and fluctuations can also affect the propagation path of light. These unpredictable shifts in camera center pointing and atmospheric disturbances all contribute to the inaccuracy of measurements.

[0004] To address the aforementioned issues, some all-sky imagers employ stellar coordinate correction techniques, using the azimuth and elevation angles of stars to fit lens parameters and correct lens distortion. However, these methods typically assume the lens is absolutely pointing towards the zenith and cannot correct for errors caused by camera pointing offsets. This is especially true for small-scale auroral imagers with narrow fields of view, where the lens pointing completely off-center from the local zenith. This makes existing calibration methods even more difficult to apply, posing significant challenges to data calibration. Summary of the Invention

[0005] In view of the shortcomings of the prior art described above, the purpose of this application is to provide an imager line-of-sight calibration method to solve the problems in the prior art, such as the difficulty in accurately calibrating the imager due to the unknown lens direction of the aurora imager.

[0006] To achieve the above and other related objectives, this application provides an imager line-of-sight calibration method, comprising the following steps:

[0007] Acquire calibration images;

[0008] Several target star points were identified from the calibration image;

[0009] Based on the target star points, several predicted lines of sight pointing to the center are found in the calibration image;

[0010] Based on the predicted line of sight center, the calibration line of sight center of the imager in the calibration image is obtained, and the center pointing error between the predicted line of sight center and the calibration line of sight center is calculated.

[0011] Based on the target star point and the center of the calibrated line of sight, the lens parameters and star point fitting error of the imager are calculated.

[0012] Generate the azimuth and elevation grids of the lens line of sight of the imager, and calculate the center pointing error and star point fitting error of each grid point formed by the azimuth and elevation grids to form the discreteness matrix and fitting error matrix respectively.

[0013] Based on the discreteness matrix and the fitting error matrix, the normalized goodness matrix is ​​calculated, and based on the normalized goodness matrix, the lens optimization direction of the imager is determined.

[0014] Optionally, identifying several target star points from the calibration image includes the following steps:

[0015] The standard deviation of the background noise of the calibration image was calculated;

[0016] Based on the background noise standard deviation, several target star points are identified from the calibration image;

[0017] Based on the imaging time and observation location of the calibration image, the coordinates of the target star point in the geodetic coordinate system are calculated.

[0018] Optionally, the imager line-of-sight calibration method further includes the following steps:

[0019] Obtain the initial elevation angle and initial azimuth angle of the imager's lens line of sight in the geodetic coordinate system;

[0020] The target star point is transformed to obtain its coordinates in the camera coordinate system.

[0021] Optionally, finding the predicted gaze center in the calibration image includes the following steps:

[0022] The target star points are arranged and combined to obtain several star point combinations. Each star point combination includes several star point groups, and each star point group includes two target star points.

[0023] The imager obtains the initial line of sight pointing to the center in the calibration image;

[0024] Calculate the azimuth difference between the two target stars in each star group relative to the initial line-of-sight center;

[0025] Based on the azimuth difference, a circle passing through the two corresponding target star points is formed in the calibration image;

[0026] Among the several circles formed, at least two intersect to produce two intersection points. The coordinates of the two intersection points are calculated, and the point among the two intersection points that is closer to the initial line of sight center is taken as the predicted line of sight center.

[0027] Optionally, arranging and combining the target stars includes the following steps:

[0028] Let N be the number of target stars, and select m target stars from the N target stars to form There are n star point combinations, where m is a positive integer greater than 2 and less than or equal to N;

[0029] Two target stars are selected from each of the star point combinations to form Grouped by star points.

[0030] Optionally, each star point combination includes four target star points; the step of obtaining the calibration line-of-sight center of the imager in the calibration image and calculating the center-of-sight error between the predicted line-of-sight center and the calibration line-of-sight center includes:

[0031] Let cj be the coordinate of the j-th predicted gaze direction center. The coordinates c of the center of the calibration line of sight are calculated.

[0032] according to The center pointing error E is calculated. c ;

[0033] Where j is less than or equal to Positive integers.

[0034] Optionally, the lens parameters include a fisheye lens function, and calculating the lens parameters of the imager includes the following steps:

[0035] Let G be the distance between the pixel in the calibration image and the center of the calibration line of sight, and let θ be the polar angle of the pixel in the calibration image relative to the center of the calibration line of sight in the camera coordinate system. Use G and θ as variables to construct a fisheye lens function containing several undetermined coefficients.

[0036] Obtain the distance G between the i-th target star point and the center of the calibrated line of sight. siAnd the polar angle θ of the i-th target star point in the camera coordinate system relative to the calibrated line-of-sight center. si , where i is a positive integer less than or equal to N, and N is the number of the target star points;

[0037] According to G si and θ si The undetermined coefficients in the fisheye lens function are calculated.

[0038] Optionally, the step of calculating the lens parameters of the imager further includes:

[0039] Construct the expression for the fisheye lens function G(θ): g = k0 + k1θ + k2θ 2 +k3θ 3 ;

[0040] The fisheye lens function G(θ) is fitted using the least squares method to obtain the undetermined coefficients [k0,k1,k2,k3] of the fisheye lens function G(θ). T Θ) -1 Θ T G + ;

[0041] Where Θ=[ξ1,ξ2,…,ξ N ] T G + =[G s1 G s2 ,…,G sN ] T ,

[0042] Optionally, the lens parameters further include the inverse function of the fisheye lens, and the step of calculating the lens parameters of the imager further includes:

[0043] Construct the expression for the inverse function θ(G) of the fisheye lens: θ = k′0 + k′1G + k′2G 2 +k′3G 3 ;

[0044] The inverse function θ(G) of the fisheye lens is fitted using the least squares method to obtain the undetermined coefficients of the inverse function θ(G).

[0045] Where Λ=[g1,g2,…,g N ] T ,

[0046] Optionally, the lens parameters include the lens distortion coefficient, and calculating the lens parameters of the imager further includes the following steps:

[0047] Construct a distortion coefficient matrix η, wherein the distortion coefficient matrix η satisfies [p si ,q si ] T =η[1,x si ,y si ] T Where η = [η1, η2] T , eta1=[a0,a1,a2], eta2=[b0,b1,b2], (p si ,q si Let p be the coordinates of the i-th model star point corresponding to the i-th target star point in the standard camera coordinate system. si =G(θ) si sin(az) si ), q si =G(θ) si cos(az) si ), θ si and az si G(θ) represents the polar angle and azimuth angle of the i-th target star relative to the center of the calibrated line of sight, respectively. si ) represents the value of the fisheye lens function for the i-th target star point, where i is a positive integer less than or equal to N, and N is the number of the target star points;

[0048] According to η1=(Γ T Γ) -1 Γ T p + and η2=(Γ T Γ) -1 Γ T q + The distortion coefficient matrix η is calculated, where the least squares matrix Γ = [γ s1 ,γ s2 ,γ s3 ,…,γ sN ] T Vector γ si =[1,x si ,y si ],(x si ,y si P represents the coordinates of the i-th target star point in the image coordinate system. + =[p s1 ,p s2 ,…,p sN ], q + =[q s1 ,q s2 ,…,q sN ].

[0049] Optionally, calculating the star-point fitting error of the imager includes the following steps:

[0050] The coordinates (p) of the i-th model star point corresponding to the i-th target star point in the standard camera coordinate system are calculated. si ,q si )=η[1,x si ,y si ] T , where η is the distortion coefficient matrix, (x si ,y si Let be the coordinates of the i-th target star point in the image coordinate system;

[0051] according to and The coordinates of the i-th model star point in the camera coordinate system were calculated. Among them, G -1 The inverse function of the fisheye lens;

[0052] according to The radian difference E between the i-th model star point and the i-th target star point on a unit sphere is calculated. si ;

[0053] The star point fitting error was calculated. Where N is the number of target stars, and i is a positive integer less than or equal to N.

[0054] Optionally, calculating the normalized goodness matrix and determining the lens optimization orientation of the imager based on the normalized goodness matrix includes the following steps:

[0055] According to the two-dimensional Gaussian function E=E0+Aexp(-(a(x-x0)) 2 +2b(x-x0)(y-y0)+c(y-y0) 2 ))as well as and The center pointing error E of several grid points in the discreteness matrix is ​​respectively... c And the star-point fitting error E of several grid points in the fitting error matrix s A fitting process is performed to obtain the normalized pointing goodness of the grid points. Goodness of fit with star points in, and A c The center pointing error E of the grid point is respectively c The corresponding fitting coefficients E0 and A, and A s The star-point fitting error E with respect to the grid points are respectively s The corresponding fitting coefficients E0 and A;

[0056] according to The normalized goodness U of each grid point is calculated to form a normalized goodness matrix;

[0057] Based on the normalized goodness matrix, the direction of the grid point with the largest normalized goodness U value is used as the lens optimization direction.

[0058] Optionally, the imager line-of-sight calibration method further includes the following steps:

[0059] The lens optimization point calculated in the previous iteration is used as the center of the value range of the azimuth and elevation grids. The value range of the azimuth and elevation grids is compressed, and the azimuth and elevation grids are regenerated.

[0060] Based on the regenerated azimuth and elevation grids, the normalized goodness matrix for this iteration is calculated, and the lens optimization direction for this iteration is determined.

[0061] Repeat the above steps to proceed with the next iteration.

[0062] The optimized lens pointing obtained after n iterations is taken as the optimal lens pointing, where n is a positive integer.

[0063] As described above, compared with the prior art, the imager line-of-sight calibration method provided in this application has at least the following advantages:

[0064] In the imager gaze orientation calibration method of this application, based on several identified target star points, a geometric method is used to find several predicted gaze orientation centers of the imager in the calibration image, achieving accurate calibration of the gaze orientation centers in the calibration image. Based on the predicted gaze orientation centers, the calibration gaze orientation centers in the calibration image can be obtained, and the lens parameters and star point fitting errors of the imager are calculated according to the calibration gaze orientation centers, achieving accurate calibration of the lens parameters. Through the star point fitting error, the calibration accuracy of the lens gaze orientation centers in the image coordinate system can be judged more intuitively. The normalization goodness matrix contains the normalization goodness of each grid point. By comparing the normalization goodness of each grid point, the optimized lens orientation of the calibrated imager can be obtained, achieving accurate calibration of the lens gaze orientation of the imager.

[0065] In summary, this method can accurately calibrate the lens pointing and lens parameters of the imager even when the direction of the lens's line of sight center is unknown, without considering the size of the lens's field of view. This improves the reusability of the method, effectively corrects the errors caused by the imager's pointing offset, and improves the measurement accuracy of the imager. Attached Figure Description

[0066] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0067] Figure 1 The diagram shown is a flowchart illustrating an imager line-of-sight calibration method provided in an embodiment of this application.

[0068] Figure 2 The image shown is a structural schematic diagram of a calibration image provided in Embodiment 1 of this application.

[0069] Figure 3 The diagram shown is a schematic diagram of a structure for identifying target star points in a self-calibrated image, as provided in Embodiment 1 of this application.

[0070] Figure 4 and Figure 5 The elevation and azimuth angles are respectively displayed for each pixel of the image calibrated in the geodetic coordinate system provided in Embodiment 1 of this application.

[0071] Figure 6 and Figure 7 The elevation and azimuth angles corresponding to each pixel of the image in the camera coordinate system are shown respectively, as provided in Embodiment 1 of this application.

[0072] Figure 8 The image shown is a schematic diagram of the structure of three intersecting circles in a calibration image provided in Embodiment 1 of this application.

[0073] Figure 9 Displayed as Figure 8 A schematic diagram of the structure of the central region where the three circles intersect.

[0074] Figure 10 The diagram shown is a flowchart illustrating an imager line-of-sight calibration method provided in Embodiment 2 of this application.

[0075] Figures 11 to 16 The figures displayed are the center pointing error, normalized pointing goodness, star point fitting error, and star point fitting goodness of each pixel in the first iteration process provided in Embodiment 2 of this application. And normalized goodness.

[0076] Figures 17 to 22 The figures displayed are the center pointing error, normalized pointing goodness, star point fitting error, and star point fitting goodness of each pixel in the second iteration process provided in Embodiment 2 of this application. And normalized goodness.

[0077] Figures 23 to 28 The values ​​displayed are the center pointing error, normalized pointing goodness, star point fitting error, and star point fitting goodness for each pixel in the third iteration process provided in Embodiment 2 of this application. And normalized goodness.

[0078] Figures 29 to 34 The figures displayed are the center pointing error, normalized pointing goodness, star point fitting error, and star point fitting goodness of each pixel in the fourth iteration process provided in Embodiment 2 of this application. And normalized goodness. Detailed Implementation

[0079] To make the technical objectives, technical solutions, and technical effects of this application clearer, the technical solutions in this application will be clearly and completely described below in conjunction with embodiments. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0080] Therefore, the following detailed description of embodiments of this application is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0081] In the description of this application, it should be noted that the terms "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with an implementation or example, which are included in at least one implementation or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same implementation or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more implementations or examples.

[0082] In existing technologies, when correcting lens distortion in imagers, it is only possible to assume that the lens is absolutely pointing towards the zenith, and it is impossible to correct errors caused by camera pointing. This is especially true for some small-scale aurora imagers with narrow fields of view, where the lens pointing will be completely deviated from the local zenith, further increasing the difficulty of correcting errors caused by camera pointing.

[0083] To address the aforementioned problems and improve the measurement accuracy of the imager by correcting errors caused by lens pointing deviation, this application provides an imager line-of-sight calibration method, referring to... Figure 1 This includes the following steps:

[0084] Acquire calibration images;

[0085] Several target star points were identified from the calibration image;

[0086] Based on the target star points, several predicted lines of sight pointing to the center are found in the calibration image;

[0087] Based on the predicted line of sight center, the calibration line of sight center of the imager in the calibration image is obtained, and the center pointing error between the predicted line of sight center and the calibration line of sight center is calculated.

[0088] Based on the target star point and the center of the calibrated line of sight, the lens parameters and star point fitting error of the imager are calculated.

[0089] Generate the azimuth and elevation grids of the lens line of sight of the imager, and calculate the center pointing error and star point fitting error of each grid point formed by the azimuth and elevation grids to form the discreteness matrix and fitting error matrix respectively.

[0090] Based on the discreteness matrix and the fitting error matrix, the normalized goodness matrix is ​​calculated, and based on the normalized goodness matrix, the lens optimization direction of the imager is determined.

[0091] The imager gaze orientation calibration method in this embodiment, based on several identified target star points, uses a geometric method to find several predicted line-of-sight centers of the imager in the calibration image, achieving accurate calibration of the lens line-of-sight center in the image coordinate system. Based on the predicted line-of-sight centers, the calibration line-of-sight center in the calibration image can be obtained, and the lens parameters and star point fitting errors of the imager can be calculated according to the calibration line-of-sight centers, achieving accurate calibration of the lens parameters. The star point fitting error can more intuitively reflect the accuracy of the calibration of the lens line-of-sight center in the image coordinate system. The normalization goodness matrix contains the normalization goodness of each grid point. By comparing the normalization goodness of each grid point, the calibration of the imager lens line-of-sight can be achieved.

[0092] Therefore, this method can accurately calibrate the lens pointing and lens parameters of the imager even when the direction of the lens's line of sight center is unknown, without considering the size of the lens's field of view. This improves the reusability of the method, effectively corrects the error caused by the imager's pointing offset, and improves the measurement accuracy of the imager.

[0093] To provide a more detailed explanation of the imager line-of-sight calibration method of this application, the technical solution of this application will be described below in conjunction with specific embodiments. It should be noted that, unless otherwise specified, the technical features and solutions in the following embodiments can be used in combination with each other.

[0094] Example 1

[0095] This embodiment provides a method for calibrating the line-of-sight of an imager, referring to... Figure 1 This includes the following steps:

[0096] S1. Obtain the calibration image;

[0097] S2. Several target star points are identified from the self-calibration image;

[0098] S3. Based on the target star points, find several predicted lines of sight pointing to the center in the calibration image;

[0099] S4. Based on the predicted line of sight center, obtain the calibration line of sight center of the imager in the calibration image, and calculate the center pointing error between the predicted line of sight center and the calibration line of sight center.

[0100] S5. Based on the target star points and the calibrated line of sight pointing center, calculate the lens parameters of the imager and the star point fitting error;

[0101] S6. Generate the azimuth and elevation grids of the imager's lens line of sight, and calculate the center pointing error and star point fitting error of each grid point formed by the azimuth and elevation grids to form the discreteness matrix and fitting error matrix respectively.

[0102] S7. Based on the discreteness matrix and the fitting error matrix, calculate the normalized goodness matrix, and determine the lens optimization direction of the imager based on the normalized goodness matrix.

[0103] In step S1, refer to Figure 2 The calibration image is the image data acquired by the imager, such as an aurora imager. The preferred time period for the imager to acquire the calibration image is during the night when the moon is below the horizon, the geomagnetic interaction is relatively calm, and the weather conditions are good. This time period avoids geomagnetic storms and substorms, and the aurora activity in the imager's field of view is weak, the weather is cloudless, and the atmospheric seeing is good. Under this time period, the imager can obtain a relatively clear calibration image.

[0104] In step S2, the target star points are the stars in the calibration image. The number of target star points is preferably multiple. Several target star points are obtained by performing image recognition on the calibration image.

[0105] In an optional embodiment, the step S2, which involves identifying several target stars from the calibration image, includes: calculating the standard deviation of background noise in the calibration image; identifying several target stars from the calibration image based on the standard deviation of background noise; and calculating the coordinates of the target stars in the geodetic coordinate system based on the imaging time and imaging position of each level of calibration image. The geodetic coordinate system is a spatial rectangular coordinate system. It can be established by using the geographic north direction of the imager's location as the x-axis, the geographic east direction as the y-axis, and the vertical downward direction as the z-axis. The coordinates of the target stars in the geodetic coordinate system can be represented by their elevation and azimuth angles, which can be obtained by consulting a star catalog.

[0106] Specifically, star points in the calibration image whose gray-level peak value is higher than a certain multiple of the background noise standard deviation can be identified as target star points. For example, if the background noise standard deviation is denoted as σ, star points in the calibration image whose peak value is higher than 2σ, 3σ, 5σ, 6σ, or other suitable multiples can be identified as target star points. Preferably, identifying star points with a gray-level peak value higher than 5σ as target star points ensures effective removal of non-star noise star points in the calibration image, while also ensuring that a sufficient number of star points are obtained as target star points. Figure 3 The target star point with a grayscale peak height of 5σ is shown in the calibration image.

[0107] In an optional embodiment, the imager line-of-sight calibration method of this embodiment further includes the following steps: obtaining the initial elevation angle and initial azimuth angle of the imager's lens line of sight in the geodetic coordinate system, and determining the initial lens direction of the imager through the initial elevation angle and initial azimuth angle; performing coordinate transformation on the target star point to obtain the coordinates of the target star point in the camera coordinate system.

[0108] The initial elevation and azimuth angles of the imager's lens can be set according to actual needs. For example, the initial elevation and azimuth angles can be set to the zenith direction, meaning the imager's lens line of sight points to the zenith, which can reduce errors caused by image calibration. Based on the initial elevation and azimuth angles, the coordinate transformation matrix between the geodetic coordinate system and the camera coordinate system can be calculated. Using this transformation matrix, the coordinates of the target star in the geodetic coordinate system can be converted to their coordinates in the camera coordinate system. For example, the elevation and azimuth angles of the target star in the geodetic coordinate system can be converted to their elevation and azimuth angles in the camera coordinate system.

[0109] Reference Figures 4 to 7 , Figure 4 and Figure 5 The elevation and azimuth angles of each pixel in the geodetic coordinate system are shown. Figure 6 and Figure 7The elevation and azimuth angles of each pixel in the camera coordinate system are shown. The center of the lens line of sight of the imager in the image coordinate system is (238.83, 269.72).

[0110] In step S3, the predicted line-of-sight center is the predicted point of the lens line-of-sight center of the imager in the calibration image. It can be obtained by using a geometric method and several target star points obtained in step S2 to find several predicted line-of-sight centers of the lens line-of-sight center in the calibration image. The number of predicted line-of-sight centers can be one or more, preferably multiple.

[0111] In this embodiment, the steps of step S3 to find several predicted line-of-sight centers in the calibration image include the following steps: arranging and combining target star points to obtain several star point combinations, each star point combination including several star point groups, and each star point group including two target star points; obtaining the initial line-of-sight center of the imager in the calibration image; calculating the azimuth difference between the two target star points in each star point group and the initial line-of-sight center; forming a circle passing through the corresponding two target star points in the calibration image based on the azimuth difference; among the several circles formed, at least two intersect to produce two intersection points, calculating the coordinates of the two intersection points, and taking the point closer to the initial line-of-sight center among the two intersection points as the predicted line-of-sight center.

[0112] Several target stars, less than the total number, can be selected from a number of target stars to obtain several star point combinations. Then, each star point combination is divided to obtain several star point groups. Among them, four, six, or other suitable numbers of target stars can be selected from the number of target stars to form star point combinations. Two stars can be randomly selected from the number of target stars in each star point combination to form star point groups. Each star point combination can have one or more star point groups.

[0113] In an optional embodiment, arranging and combining the target stars includes the following steps: denoting the number of target stars as N, and selecting m target stars from the N target stars to form... There are n star point combinations, where m is a positive integer greater than 2 and less than or equal to N; two target star points are selected from each star point combination to form Grouped by star points.

[0114] Furthermore, each combination of star points may include, for example, four target star points. The permutation and combination of target star points includes the following steps: Let N be the number of target star points, and select four target star points from the N target star points to form... A combination of star points; select two target star points from each combination to form a... Grouped by star points.

[0115] The initial line-of-sight center can be set according to actual needs; for example, the center of the calibration image can be used as the initial line-of-sight center. In the camera coordinate system, the two target stars in each star point group have an azimuth difference relative to the initial line-of-sight center. This azimuth difference also applies in the image coordinate system. In the calibration image, a circle can be determined based on the azimuth difference and the corresponding two target stars. In the image coordinate system, this circle passes through the two target stars, and the circumference angle formed by the two target stars is the aforementioned azimuth difference. Therefore, each star point group in several star point combinations can determine a circle. Among the several circles formed, at least two circles intersect, producing two intersection points. The point closer to the initial line-of-sight center among the two intersection points is the predicted line-of-sight center.

[0116] Reference Figure 8 and Figure 9 , Figure 8 The calibration image shows three circles formed by three different star points. Two of these circles intersect, creating two intersection points, for a total of six intersection points. Figure 9 It shows Figure 8 An enlarged view of the central region where the three circles intersect. Among the six intersection points, after removing the three points that are relatively far from the initial line of sight center, the remaining three points are the predicted line of sight centers. By processing the three predicted line of sight centers, the calibrated line of sight center can be obtained, which is the point located within the area enclosed by the three predicted line of sight centers.

[0117] In an optional embodiment, the number of target stars is N, and each star combination includes four target stars, forming a total of N target stars. There are several star point combinations. From each star point combination, two target star points are selected to form star point groups. Each star point combination has a total of [number missing]. There are 1 star point groupings. Each star point combination comprises two star point groups, forming a total of 10 star point groups. There are several star point combinations with different star point grouping arrangements. In each star point combination, two star point groups can form two circles on the calibration image, and these two circles intersect at two points. Based on these two intersection points, a predicted line-of-sight direction center can be determined. That is, each star point combination with different star point grouping arrangements can form a predicted line-of-sight direction center, thus obtaining... The predicted line of sight is pointing towards the center.

[0118] In step S4, based on the predicted line-of-sight centers obtained in step S3, the coordinates of the calibrated line-of-sight center of the imager in the calibration image are calculated. Then, based on the predicted line-of-sight centers and the calibrated line-of-sight center, the center pointing error is calculated. Here, the calibrated line-of-sight center is the calibrated position of the imager's lens line-of-sight center in the calibration image, and the center pointing error is the dispersion between the predicted line-of-sight centers and the calibrated line-of-sight center. The smaller the center pointing error, the higher the accuracy of the calibrated line-of-sight center obtained from the target star points.

[0119] In an optional embodiment, the number of target stars is N, and the number of predicted lines of sight pointing to the center is N. The steps of executing step S4 include: setting the coordinates of the center of the j-th predicted gaze direction as cj, and according to... The coordinates c of the center of the calibration line of sight are calculated; according to The center pointing error E was calculated. c Where |cj-c| is the distance between the j-th predicted line-of-sight center and the calibrated line-of-sight center, and j is less than or equal to... Positive integers.

[0120] In step S5, the lens parameters include the imager's fisheye lens function and lens distortion coefficient. The fisheye lens function is used to reflect the distance between the target star point and the center of the calibrated line of sight in the camera coordinate system, and the lens distortion coefficient is the linear stretching distortion coefficient of the imager lens.

[0121] In this embodiment, the lens parameters include a fisheye lens function. Calculating the imager's lens parameters in step S5 includes the following steps: Let G be the distance between a pixel in the calibration image and the center of the calibration line of sight; let θ be the polar angle of a pixel in the calibration image relative to the center of the calibration line of sight in the camera coordinate system; construct a fisheye lens function containing several undetermined coefficients using G and θ as variables; obtain the distance G between the i-th target star point and the center of the calibration line of sight. si And the polar angle θ of the i-th target star point in the camera coordinate system relative to the center of the calibrated line of sight. si Where i is a positive integer less than or equal to N, and N is the number of target stars; according to G si and θ si The undetermined coefficients in the fisheye lens function are calculated. Here, the polar angle is the angle between the target star point and the direction pointing to the zenith in the geodetic coordinate system, and the sum of the polar angle and the elevation angle is 90°.

[0122] Specifically, using either G or θ as the independent variable and the other as the dependent variable, a fisheye lens function containing several undetermined coefficients is constructed according to a specific functional form. For example, a fisheye lens function is constructed according to a polynomial function form, with G as the dependent variable and θ as the independent variable. The distance G to the obtained target star point is then... si and polar angle θ si Substitute these values ​​into the constructed fisheye lens function and solve for the undetermined coefficients to obtain the fisheye lens function.

[0123] In an optional embodiment, the lens parameters include a fisheye lens function, denoted as G(θ). The step of calculating the lens parameters of the imager further includes: constructing the expression for the fisheye lens function G(θ) as G=k0+k1θ+k2θ 2 +k3θ 3 The fisheye lens function G(θ) is fitted using the least squares method to obtain the undetermined coefficients [k0,k1,k2,k3] of the fisheye lens function G(θ). T Θ) -1 Θ T G + ; where the least squares matrix Θ=[ξ1,ξ2,…,ξ N ] T radial matrix G + =[G s1 G s2 ,…,G sN ] T ,vector A fisheye lens function is constructed using a third-order polynomial to calibrate the lens parameters of the imager, enabling precise measurement of distance G. si and polar angle θ si This establishes a relationship between the two functions, while saving computational resources, enabling fast and accurate correction of the fisheye lens function.

[0124] In an optional embodiment, the lens parameters include the inverse function of the fisheye lens, which is the inverse function of the fisheye lens function. The inverse function of the fisheye lens is denoted as θ(G), where θ(G) = G. -1 The steps for calculating the lens parameters of the imager also include: constructing the expression for the inverse function θ(G) of the fisheye lens: θ = k′0 + k′1G + k′2G 2 +k′3G 3 The inverse function θ(G) of the fisheye lens is fitted using the least squares method to obtain the undetermined coefficients of the inverse function θ(G). Where the least squares matrix Λ=[g1,g2,…,g N ] T radial matrix vector A third-order polynomial is used to construct the inverse function of the fisheye lens to calibrate the lens parameters of the imager, which can accurately reflect the polar angle θ. si and distance G si This method effectively addresses the relationship between the fisheye lens function and its inverse function, saving computational resources and enabling rapid and accurate correction. Furthermore, since solving higher-order polynomials is difficult, compared to calculating the inverse function of the fisheye lens function, using polynomial fitting to obtain the inverse function avoids the propagation of solution errors during the solution process. Moreover, the steps for fitting the fisheye lens function can be directly changed to substitute the data, enabling rapid and accurate fitting of the inverse function of the fisheye lens.

[0125] In this embodiment, the lens parameters also include lens distortion coefficients, and the distortion coefficient matrix η is used to describe the lens distortion coefficients of the imager. Optionally, the distortion coefficient matrix η is a 2×3 matrix, and calculating the lens parameters of the imager may further include the following steps: constructing the distortion coefficient matrix η, the distortion coefficient matrix η satisfying [p si ,q si ] T =η[1,x si ,y si ] T Where η = [η1, η2] T , eta1=[a0,a1,a2], eta2=[b0,b1,b2]; according to eta1=(Γ T Γ) -1 Γ T p + and η2=(Γ T Γ) -1 Γ T q + The distortion coefficient matrix η was calculated, thereby enabling the calibration of the lens distortion coefficient of the imager.

[0126] Among them, (p si ,q si Let p represent the coordinates of the i-th model star point corresponding to the i-th target star point in the standard camera coordinate system. The camera coordinate system is obtained by unfolding the lens viewpoint based on the initial line-of-sight center and the initial parameters set by the imager. The standard camera coordinate system is obtained by re-unfolding the lens viewpoint based on the obtained calibration line-of-sight center and the lens parameters of the imager. The standard camera coordinate system takes the calibration line-of-sight center as the lens line-of-sight center of the imager. si =G(θ) si sin(az) si ), q si =G(θ) si cos(az) si ), θ si and az siG(θ) represents the polar angle and azimuth angle of the i-th target star relative to the center of the calibrated line of sight, respectively. si ) represents the value of the fisheye lens function for the i-th target star point, where i is a positive integer less than or equal to N, and N is the number of target star points. The least squares matrix Γ = [γ s1 ,γ s2 ,γ s3 ,…,γ sN ] T Vector γ si =[1,x si ,y si ],(x si ,y si Let P be the coordinates of the i-th target star point in the image coordinate system. + =[p s1 ,p s2 ,…,p sN ], q + =[q s1 ,q s2 ,…,q sN ].

[0127] In step S5, the star point fitting error is the difference in radians between the real star point and the model star point on a unit sphere. The point corresponding to the coordinates of the star point obtained by looking up the star table is the real star point. The point corresponding to the coordinates of the star point in the standard camera coordinate system obtained based on the calculated calibration line-of-sight center and lens parameters is recorded as the model star point. There is a one-to-one correspondence between the real star point and the model star point. Based on the calibration line-of-sight center and the calculated lens parameters, the coordinates of the model star point in the standard camera coordinate system can be calculated, and thus the star point fitting error can be calculated.

[0128] In an optional embodiment, calculating the star point fitting error of the imager includes the following steps: calculating the coordinates (p) of the i-th model star point in the standard camera coordinate system. si ,q si )=η[1,x si ,y si ] T , where η is the distortion coefficient matrix, (x si ,y si Let be the coordinates of the i-th target star point in the image coordinate system. The coordinates of the target star point in the image coordinate system can be found, for example, by referring to... Figure 2 The horizontal axis coordinates at the bottom center and the vertical axis coordinates on the left; according to and The coordinates of the i-th model star point in the camera coordinate system were calculated. in, and G represents the polar angle and azimuth angle of the i-th model star point relative to the center of the calibration line of sight in the camera coordinate system. -1 The inverse function of the fisheye lens; according to The radian difference E between the i-th model star point and the i-th target star point on a unit sphere was calculated. si The star point fitting error was calculated. Where, θ si and az si Let be the polar angle and azimuth angle of the i-th target star point relative to the center of the calibrated line of sight in the camera coordinate system, respectively. Let N be the number of target stars, and i be a positive integer less than or equal to N. The star point fitting error describes the coordinate deviation between the target star point and the model star point. The smaller the star point fitting error, the more accurate the lens pointing of the imager and the higher the measurement accuracy.

[0129] In step S6, the azimuth and elevation angles of the imager lens's line of sight are divided to obtain azimuth and elevation grids respectively. The range of azimuth and elevation angles and the number of grids can be set according to actual needs. The intersection of the azimuth and elevation grids yields several grid points. The elevation and azimuth angles corresponding to each grid point are used as the imager's lens line of sight, and steps S1 to S5 are executed to obtain the center pointing error and star point fitting error of each grid point. The center pointing errors of several grid points are combined to form a dispersion matrix, and the star point fitting errors of several grid points are combined to form a fitting error matrix.

[0130] In step S7, the normalized goodness matrix is ​​formed by combining the normalized goodness of each grid point. The normalized goodness matrix can be calculated using the fitting error matrix and the discreteness matrix.

[0131] In an optional embodiment, calculating the normalized goodness matrix in step S7 includes the following steps: using the two-dimensional Gaussian function E = E0 + Aexp(-(a(x-x0)) 2 +2b(x-x0)(y-y0)+c(y-y0) 2 ))as well as and The center pointing error E of several grid points in the discreteness matrix is ​​respectively... c And the star-point fitting error E of several grid points in the fitting error matrix. s Two-dimensional Gaussian fitting is performed to obtain the normalized pointing goodness of the grid points. Goodness of fit with star points according to The normalized goodness U of each grid point is calculated to form a normalized goodness matrix.

[0132] Where E0, A, a, b, c, x0, and y0 are the fitting coefficients of the two-dimensional Gaussian function. and A c The center pointing error E of the grid points are respectively c The corresponding parameters E0 and A, and A s The star-point fitting error E with respect to the grid points are respectively s The corresponding parameters are E0 and A. Calculation and analysis revealed that the distributions of center pointing error and star point fitting error at different grid points approximate a Gaussian distribution. Using a two-dimensional Gaussian fitting method, a normalized Gaussian fit goodness of fit was calculated, which improved the fitting accuracy for center pointing error and star point fitting error. Furthermore, the normalized goodness of fit matrix more accurately reflects both the calibration optimization effect on lens line-of-sight pointing and the improvement in measurement accuracy.

[0133] In this embodiment, the step of determining the optimal lens orientation of the imager in step S7 includes: taking the direction of the grid point with the largest normalized goodness U value as the optimal lens orientation according to the normalized goodness matrix, so as to calibrate the lens line of sight of the imager.

[0134] As described above, the imager sight orientation calibration method of this embodiment, based on the identified target star points and the azimuth difference between two target star points, uses a geometric method to find the center of the calibration line of sight, thereby calibrating the lens center direction in the image coordinate system. Based on the obtained center of the calibration line of sight, a third-order function is used to correct the fisheye function, and a first-order function is used to correct the lens distortion coefficient, thereby achieving rapid and accurate calibration of lens parameters. The calculated normalization goodness can simultaneously reflect the calibration effect on the lens center direction in the image coordinate system and the improvement effect on measurement accuracy. Furthermore, based on the formed elevation and azimuth grids, the normalization goodness matrix can be used to determine the grid point direction with the optimal direction, thus achieving the calibration of the imager lens center direction.

[0135] Therefore, the imager orientation calibration method of this embodiment can accurately calibrate the pointing center and lens parameters of the imager when the pointing center of the imager lens is unknown, without having to consider the size of the lens field of view. This improves the reusability of the method, effectively corrects the error caused by the pointing offset of the imager, and improves the measurement accuracy of the imager.

[0136] Example 2

[0137] This embodiment provides another imager line-of-sight calibration method, which also includes steps S1 to S7 of Embodiment 1. The similarities with Embodiment 1 will not be repeated, the difference being that... Figure 10The imager orientation calibration method in this embodiment further includes step S8: compressing the value range of the azimuth angle grid and the elevation angle grid, regenerating the normalized goodness matrix, and performing several iterations to obtain the optimal lens orientation.

[0138] In this embodiment, step S8 may include the following steps: using the optimized lens pointing obtained from the previous iteration as the center of the value range of the azimuth and elevation grids, compressing the value range of the azimuth and elevation grids, and regenerating the azimuth and elevation grids; calculating the normalized goodness matrix of the current iteration based on the regenerated azimuth and elevation grids, and determining the optimized lens pointing of the current iteration; repeating the above steps for the next iteration; and using the optimized lens pointing obtained after n iterations as the optimal lens pointing, where n is a positive integer. The number of iterations n is the number of times steps S1 to S8 are executed. By performing n data iterations, the optimal lens pointing of the imager can be accurately obtained, achieving a more accurate calibration of the imager lens's line-of-sight center pointing, and further improving the measurement accuracy of the imager.

[0139] In an optional embodiment, when n is 1, it means that after one execution of steps S1 to S7, the center of the azimuth grid range and the center of the elevation grid range can be set according to actual needs. For example, the center of the azimuth grid range can be set to 70° or other suitable values, and the center of the azimuth grid range can be set to 0° or other suitable values. Further, Figure 11 and Figure 16 The table shows the center pointing error, normalized pointing goodness, star point fitting error, and star point fitting goodness for each pixel during the first iteration. And normalized goodness, Figures 11 to 16 In the initial lens pointing elevation angle grid search range is 50° to 90°, and the azimuth angle grid search range is -180° to 180°. The coordinates of the initial line of sight center in the image coordinate system are (235, 269). The results show that the azimuth angle of the optimized lens pointing is -72° and the elevation angle is 70°. This optimized lens pointing can be used as the optimal lens pointing to calibrate the pointing of the imager's lens line of sight center.

[0140] In an optional embodiment, when n is 2, it means that after completing two steps S1 to S8, the optimized lens pointing obtained in the previous iteration is used as the center of the elevation angle grid range and azimuth angle grid range in the current iteration, and the elevation angle grid range and azimuth angle grid range of the previous iteration are compressed, for example, to 0.1 times the original or other suitable multiples. In the second iteration, the calibration line pointing center calculated in the previous iteration can also be used as the initial line pointing center in the current iteration. Further, Figures 17 to 22 The following figures are shown for each pixel during the second iteration: center pointing error, normalized pointing goodness of reference, star point fitting error, and star point fitting goodness of reference. And normalized goodness, Figures 17 to 22 In the initial lens pointing elevation angle grid search range, the search range is 68° to 72°, and the azimuth angle grid search range is -90° to -54°. The coordinates of the initial line-of-sight center in the image coordinate system are (234.93, 275.09). The results show that the optimized lens pointing azimuth angle is -72.72° and the elevation angle is 70.24°. This optimized lens pointing can be taken as the optimal lens pointing to calibrate the pointing of the imager's lens line-of-sight center.

[0141] In an optional embodiment, when n is 3, it means that after completing three steps S1 to S8, the optimized lens pointing obtained in the previous iteration is used as the center of the elevation angle grid range and azimuth angle grid range in the current iteration, and the elevation angle grid range and azimuth angle grid range of the previous iteration are compressed. In the third iteration, the calibration line pointing center calculated in the previous iteration can also be used as the initial line pointing center for this iteration. Further, Figures 23 to 28 The following figures are shown for each pixel during the third iteration: center pointing error, normalized pointing goodness of reference, star point fitting error, and star point fitting goodness of reference. And normalized goodness, Figures 23 to 28 In the initial lens pointing elevation angle grid search range, the search range is 70.04°~70.44°, and the search range is -74.52°~-70.92°. The coordinates of the initial line-of-sight center in the image coordinate system are (237.21, 273.31). The results show that the optimized lens pointing azimuth angle is -73.584° and the elevation angle is 70.393°. This optimized lens pointing can be taken as the optimal lens pointing to calibrate the pointing of the imager's lens line-of-sight center.

[0142] In an optional embodiment, when n is 4, it means that after completing three steps S1 to S8, the optimized lens pointing obtained in the previous iteration is used as the center of the elevation angle grid range and azimuth angle grid range in the current iteration, and the elevation angle grid range and azimuth angle grid range of the previous iteration are compressed. In the fourth iteration, the calibration line pointing center calculated in the previous iteration can also be used as the initial line pointing center for this iteration. Further, Figures 29 to 34 The following figures are shown for each pixel during the third iteration: center pointing error, normalized pointing goodness of reference, star point fitting error, and star point fitting goodness of reference. And normalized goodness, Figures 29 to 34 In the initial lens pointing elevation angle grid search range, the search range is 70.372°~70.412°, and the search range is -73.764°~-73.404°. The coordinates of the initial line-of-sight center in the image coordinate system are (238.68, 270.43). The results show that the optimized lens pointing azimuth angle is -73.764° and the elevation angle is 70.4032°. This optimized lens pointing can be taken as the optimal lens pointing to calibrate the pointing of the imager's lens line-of-sight center.

[0143] In practical applications, after calibrating the optimal lens orientation using the imager orientation calibration method of this embodiment, it can be used to calculate geographic coordinates. Specifically, it corresponds to the i-th target star point (x) in the image coordinate system. i ,y i ), calculate the coordinates (p) of the i-th target star point in the standard camera coordinate system. i ,q i ), And the star point obtained through the i-th target star point in the standard camera coordinate system is denoted as the model star point, based on the coordinate transformation relationship between the camera coordinate system and the standard camera coordinate system (az). i =arctan(p i ,q i )as well as Obtain the coordinates of the i-th model star point in the camera coordinate system. Then, based on the optimal lens orientation, rotate the coordinates of the i-th model star point to the geodetic coordinate system to obtain its elevation and azimuth angles. It is assumed that the aurora resides on a fixed spherical shell above the Earth's surface. For the 570nm wavelength range, the aurora's emission height is 150km, and for the 630nm wavelength range, it is 300km. Let the emission height be denoted as H, and the radius of the aurora imager's location from the Earth's center be R = Re + H. sta H sta Let Re be the altitude of the observation location, and Re = 6371.2 km be the Earth's radius. For the i-th target star point (x... i,y i The direction in the corresponding geodetic coordinate system The puncture point on the spherical shell is denoted as Pi. The origin of the geodetic coordinate system is at the Earth's center. Translating the geodetic coordinate system to the Earth's center, in this coordinate system with its origin at the Earth's center, the polar angle of the puncture point on the spherical shell is... Azimuth angle is The radial distance is Re+H. Multiply the coordinates of the puncture point by the local coordinate rotation matrix R. rot .

[0144] The imager orientation calibration method of this embodiment also includes steps S1 to S7 in embodiment one. Therefore, the imager orientation calibration method of this embodiment also has the beneficial effects of embodiment one. Furthermore, in this embodiment, by performing n iterations, the optimal pointing of the imager lens can be accurately obtained, achieving more accurate calibration of the pointing of the imager lens's line of sight center, and further improving the measurement accuracy of the imager.

[0145] The above embodiments are merely illustrative of the principles and effects of this application and are not intended to limit this application. Any person skilled in the art can modify, alter, or combine the above embodiments without departing from the spirit and scope of this application. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in this application should still be covered by the claims of this application.

Claims

1. A method for imaging instrument boresight calibration, the method comprising: The method comprises the following steps: acquiring a calibration image; identifying a plurality of target stars from the calibration image; finding a plurality of predicted line-of-sight centering points in the calibration image according to the target stars; acquiring a calibration line-of-sight centering point of the imager in the calibration image according to the predicted line-of-sight centering points, and calculating a centering error between the predicted line-of-sight centering points and the calibration line-of-sight centering point; calculating a lens parameter and a star fitting error of the imager based on the target stars and the calibration line-of-sight centering point; generating an azimuth grid and an elevation grid of a line-of-sight direction of the lens of the imager, and calculating a centering error and a star fitting error of each grid point formed by the azimuth grid and the elevation grid to form a dispersion matrix and a fitting error matrix, respectively; calculating a normalized goodness matrix according to the dispersion matrix and the fitting error matrix, and determining an optimized pointing direction of the lens of the imager according to the normalized goodness matrix.

2. The method of imaging instrument boresight calibration of claim 1, wherein, The step of identifying a plurality of target stars from the calibration image comprises the following steps: calculating a background noise standard deviation of the calibration image; identifying a plurality of target stars from the calibration image according to the background noise standard deviation; calculating coordinates of the target stars in a geodetic coordinate system according to an imaging time and an observation position of the calibration image.

3. The imaging instrument boresight method of claim 2, wherein, The method further comprises the following steps: acquiring an initial elevation and an initial azimuth of the line-of-sight direction of the lens of the imager in the geodetic coordinate system; performing coordinate conversion on the target stars to obtain coordinates of the target stars in a camera coordinate system.

4. The method of imaging instrument boresight calibration of claim 1, wherein, The step of finding a plurality of predicted line-of-sight centering points in the calibration image comprises the following steps: performing permutation and combination on the target stars to obtain a plurality of star combinations, each star combination comprising a plurality of star groups, and each star group comprising two target stars; acquiring an initial line-of-sight centering point of the imager in the calibration image; calculating an azimuth difference between the two target stars in each star group relative to the initial line-of-sight centering point; forming a circle passing through the corresponding two target stars in the calibration image according to the azimuth difference; of the plurality of circles formed, at least two circles intersect to form two intersection points, and the coordinates of the two intersection points are calculated, and the point closer to the initial line-of-sight centering point among the two intersection points is taken as the predicted line-of-sight centering point.

5. The imaging instrument boresight method of claim 4, wherein, The step of performing permutation and combination on the target stars comprises the following steps: The number of the target star points is denoted as N, and m target star points are selected from the N target star points to form a star point combination, wherein m is a positive integer greater than 2 and less than or equal to N. selecting two of the target stars from each of the star groupings to form a star grouping.

6. The imaging instrument boresight method of claim 5, wherein, each star combination comprises four target stars; and the step of acquiring a calibration line-of-sight centering point of the imager in the calibration image and calculating a centering error between the predicted line-of-sight centering points and the calibration line-of-sight centering point comprises: The coordinate of the jth predicted line-of-sight pointing center is denoted as cj, and according to The coordinate c of the calibrated line-of-sight pointing center is calculated. According to The center pointing error E is calculated c ; where j is a positive integer less than or equal to the number of bits in the input data.

7. The method of imaging instrument boresight calibration of claim 1, wherein, the lens parameter comprises a fisheye lens function, and the step of calculating the lens parameter of the imager comprises the following steps: A distance between the pixel point in the calibration image and the center of the pointing direction of the calibration visual line is denoted as G, and a polar angle of the pixel point in the calibration image relative to the center of the pointing direction of the calibration visual line in the camera coordinate system is denoted as θ, and a fisheye lens function containing several undetermined coefficients is constructed with G and θ as variables; obtaining a distance G between the i-th target star point and the pointing center of the calibration line of sight si and an polar angle θ of the i-th target star point relative to the pointing center of the calibration line of sight in the camera coordinate system si wherein i is a positive integer less than or equal to N, and N is the number of the target star points. According to G si and θ si , the undetermined coefficients in the fisheye lens function are calculated.

8. The imaging instrument boresight method of claim 7, wherein, The step of calculating the lens parameters of the imager further includes: An expression G = k0+ k1θ + k2θ 2 +k3θ 3 is constructed for the fish-eye lens function G(θ). The fish-eye lens function G(θ) is fitted by using the least square method to obtain undetermined coefficients [k0, k1, k2, k3] of the fish-eye lens function G(θ) T Θ) -1 Θ T G + ; where Θ = [ξ1, ξ2,..., ξN]T, and N ] T , G + = [G s1 , G s2 ,..., G sN ] T , 9. The imaging instrument boresight method of claim 7, wherein, The lens parameters further include a fisheye lens inverse function, and the step of calculating the lens parameters of the imager further includes: An expression of a fish-eye lens inverse function θ(G) is constructed as θ = k'0 + k'1G + k'2G 2 +k'3G 3 ; fitting the fish-eye lens inverse function θ(G) by using the least square method to obtain undetermined coefficients of the fish-eye lens inverse function θ(G) where Λ = [g1, g2,..., g N ] T , 10. The imaging instrument boresight method of claim 1, wherein, The lens parameters include a lens distortion coefficient, and the step of calculating the lens parameters of the imager further includes: A distortion coefficient matrix η is constructed, which satisfies [p si ,q si ] T =η[1,x si ,y si ] T , wherein η=[η1,η2] T , η1=[a0,a1,a2], η2=[b0,b1,b2], (p si ,q si ) is the coordinate of the i-th model star point corresponding to the i-th target star point in the standard camera coordinate system, p si =G(θ si )sin(az si ), q si =G(θ si )cos(az si ), θ si and az si are the polar angle and azimuth angle of the i-th target star point relative to the center of the pointing line of sight, respectively, G(θ si ) is the value of the fisheye lens function of the i-th target star point, i is a positive integer less than or equal to N, and N is the number of the target star points. According to η1= (Γ T Γ) -1 Γ T p + and η2= (Γ T Γ) -1 Γ T q + , the distortion coefficient matrix η is calculated, wherein a least square matrix Γ = [γ s1 , γ s2 , γ s3 , …, γ sN ] T , a vector γ si = [1, x si , y si ], (x si , y si ) are coordinates of the i-th target star point in an image coordinate system, P + = [p s1 , p s2 , …, p sN ], and q + = [q s1 , q s2 , …, q sN ].

11. The imaging instrument boresight method of claim 1, wherein, The step of calculating the star point fitting error of the imager includes: The coordinates of the i-th model star point in the standard camera coordinate system corresponding to the i-th target star point are calculated as follows: si q si )=η[1,x si ,y si ] T wherein η is a distortion coefficient matrix, and (x si ,y si ) are the coordinates of the i-th target star point in the image coordinate system. According to and The coordinates of the i-th model star point in the camera coordinate system are calculated Where G -1 is the inverse function of the fisheye lens. According to The radian difference E between the i-th model star point and the i-th target star point on the unit sphere is calculated si ; The star point fitting error is calculated where N is the number of the target star points, and i is a positive integer less than or equal to N.

12. The imaging instrument boresight method of claim 1, wherein, The step of calculating the normalized goodness matrix and determining the lens optimization pointing direction of the imager according to the normalized goodness matrix includes: According to a two-dimensional Gaussian function E = E0 + Aexp(-(a(x-x0) 2 + 2b(x-x0)(y-y0) + c(y-y0) 2 ), and and the center pointing error E c of several grid points in the dispersion matrix and the star fitting error E s of several grid points in the fitting error matrix are fitted respectively to obtain the normalized pointing goodness of the grid points and the star fitting goodness wherein E0, A, a, b, c, x0, y0 are fitting coefficients of the two-dimensional Gaussian function, and A c are the fitting coefficients E0 and A corresponding to the center pointing error E c of the grid points, and A s are the fitting coefficients E0 and A corresponding to the star fitting error E s of the grid points. According to The normalized merit U of each lattice point is calculated to form a normalized merit matrix; According to the normalized goodness matrix, a grid direction with the maximum value of the normalized goodness U is taken as the lens optimization pointing direction.

13. The imaging instrument boresight method of claim 1, wherein, The steps further include: Taking the lens optimization pointing direction calculated in the previous iteration process as the center of the value range of the azimuth angle grid and the elevation angle grid, compressing the value range of the azimuth angle grid and the elevation angle grid, and regenerating the azimuth angle grid and the elevation angle grid; According to the regenerated azimuth angle grid and the elevation angle grid, calculating the normalized goodness matrix of the current iteration process and determining the lens optimization pointing direction of the current iteration process; Repeating the above steps to perform the next iteration process; Taking the lens optimization pointing direction obtained after n iterations as the optimal lens pointing direction, wherein n is a positive integer.

Images