A simulation method for large field-of-view telescope distortion star maps based on measured star maps

Abstract

This invention discloses a simulation method for distorted star maps taken by a large field-of-view telescope based on measured star maps, solving the problem of how to simulate distorted star maps taken by a large field-of-view telescope; belonging to the field of star map simulation; including: obtaining the theoretical coordinates of stars in the star catalog according to the coordinate transformation equation; setting an angular distance threshold, and matching the actual coordinates of star points in the measured star map with the theoretical coordinates of stars in the star catalog using the cross-matching method; subtracting the actual coordinates of selected control points from the theoretical coordinates of stars, and constructing a distortion model and a normalized distortion model from the residual results; removing outliers in the normalized distortion model using the Laida criterion, and fitting the parameters of the normalized distortion model using the least squares method to obtain a fitted model; adding distortion to the theoretical coordinate positions of each star in the star catalog using the fitted model, thereby simulating distorted star maps taken by a large field-of-view telescope. This invention realistically simulates images taken by a large field-of-view telescope through the fitted model.

Description

Technical Field

[0001] This invention belongs to the field of star map simulation technology and relates to a simulation method for large field-of-view telescope distortion star maps based on measured star maps. Background Technology

[0002] Star map simulation is mainly used in astronomical attitude determination based on star sensors and in measurement based on ground-based large field-of-view telescopes. Large field-of-view telescopes typically have a field of view of 3 degrees x 3 degrees or more and are mainly used for large-scale sky surveys. Currently, common star map simulation methods can simulate star maps based on the optical axis position and image plane rotation angle. At the same time, different simulation results can be generated by considering different image resolutions, pixel sizes, and the influence of atmospheric and optical system parameters.

[0003] Current star map simulation methods do not consider the image distortion caused by ground-based wide-field telescopes. The distortion of actual captured images is not only related to the lens distortion of the wide-field telescope itself, but also to natural environmental factors. Therefore, the distortion effects on images captured at different locations, angles, and times are different, and simply using conventional lens distortion models for simulation is insufficient. Summary of the Invention

[0004] To address the technical challenge of simulating more realistic distorted star charts captured by large field-of-view telescopes and narrowing the gap between simulated and measured data, this invention provides a simulation method for distorted star charts from large field-of-view telescopes based on measured star charts. This method utilizes a fitted model obtained from fitted data in the measured star charts to simulate dynamically distorted star charts captured by large field-of-view telescopes. It simulates the dynamic distortion caused by natural factors and atmospheric conditions, thereby narrowing the gap between simulated and measured data and providing a more realistic simulation of images captured by large field-of-view telescopes.

[0005] The objective of this invention is specifically achieved through the following technical solutions:

[0006] This invention discloses a simulation method for large field-of-view telescope distortion star maps based on measured star maps. The method includes:

[0007] Step 1: Based on the coordinate transformation equation, obtain the theoretical coordinates of the stars in the star catalog in the image coordinate system; set the angular distance threshold, and use the cross-matching method to match the actual coordinates of all star points in the preprocessed measured star image in the image coordinate system with the theoretical coordinates of the stars in the star catalog.

[0008] Step 2: Select control points for parameter fitting from among the successfully matched star points;

[0009] Step 3: Subtract the actual coordinates of the control points in the measured star map from the theoretical coordinates of the stars in the successfully matched star catalog, and use the resulting image coordinate residuals as the objective function to construct a distortion model; then normalize the distortion model to obtain a normalized distortion model.

[0010] Step 4: Remove outliers from the normalized distortion model using the Laida criterion, and fit the parameters of the normalized distortion model using the least squares method to obtain the fitted model.

[0011] Step 5: By fitting the model, distortion is added to the theoretical coordinate positions of each star in the catalog to obtain the corresponding centroid of the star, thus simulating the distorted star map taken by the large field-of-view telescope.

[0012] In step one, the methods for obtaining the theoretical coordinates of stars in the star catalog in the image coordinate system based on the coordinate transformation equation include:

[0013] The star catalog is selected based on the set field of view, and stars within the magnitude range are selected from the star catalog based on the detection range of the wide field of view telescope.

[0014] Based on the coordinate transformation equation, the epoch observation positions of the selected stars are transformed into the image pixel coordinate system, yielding the theoretical coordinates of the stars in the star catalog within the image coordinate system; the coordinate transformation equation is as follows:

[0015]

[0016] In the formula, (ζ i ,η i ) represents the theoretical coordinates of stars in the star catalog within the image coordinate system, (α) i ,θ i (α0, θ0) represents the epochal observation position of a star in the catalog, and (α0, θ0) represents the right ascension and declination of the center of the field of view of the large field telescope.

[0017] In step one, the preprocessing methods for the measured star map include:

[0018] By using the open-source star image processing tool SExtractor, the measured star image captured by the large field-of-view telescope is subjected to background suppression, non-uniformity correction, filtering and noise reduction, and image segmentation, and then sub-pixel centroid localization is performed; thus, the actual coordinates of all star points in the measured star image in the image coordinate system are obtained.

[0019] In step one, setting an angular distance threshold and using cross-matching to match the actual coordinates of all star points in the preprocessed measured star image in the image coordinate system with the theoretical coordinates of stars in the star catalog includes the following methods:

[0020] Set the angular distance threshold by combining the distortion range and angular resolution of the large field-of-view telescope;

[0021] The actual coordinates of all star points in the preprocessed measured star image in the image coordinate system are compared with the theoretical coordinates of stars in the star catalog in the image coordinate system. When the angular distance difference between the theoretical coordinates of one and only one known star in the star catalog and the actual coordinates of the star point is less than the set angular distance threshold, it is marked as a successful match.

[0022] Preferably, the angular distance threshold is set within a range of 30 arcseconds to 100 arcseconds.

[0023] In step two, the methods for selecting control points for fitting from the successfully matched star points include:

[0024] The field of view is divided into a preset number of regions of equal size, and the star point with the largest magnitude among the successfully matched star points in each region is selected as the control point.

[0025] Step three involves subtracting the actual coordinates of the control points in the measured star map from the theoretical coordinates of the stars in the successfully matched star catalog. This includes:

[0026]

[0027] Where Δx and Δy represent the image coordinate residuals; x d and y d Indicates the actual coordinates of the control point in the measured star map; x u and y u This indicates the theoretical coordinates of stars in the catalog where control points were successfully matched.

[0028] In step three, the distortion model constructed is as follows:

[0029]

[0030] Where Δx and Δy represent the image coordinate residuals; (a ij ,b ij ) represents the parameters of the distortion model; m represents the maximum order of the distortion model, m is order 3, and it includes a total of 20 parameters; x u and y u This indicates the theoretical coordinates of stars in the catalog where control points were successfully matched.

[0031] In step three, the normalized distortion model is as follows:

[0032]

[0033] Where Δx and Δy represent the image coordinate residuals; This represents the normalized theoretical coordinates of stars in the catalog where control points have been successfully matched.

[0034] In step four, the resulting fitted model is:

[0035]

[0036] The beneficial effects of this invention are:

[0037] This invention obtains the theoretical coordinates of stars in the star catalog in the image coordinate system based on the coordinate transformation equation; sets an angular distance threshold, and uses a cross-matching method to match the actual coordinates of all star points in the preprocessed measured star image in the image coordinate system with the theoretical coordinates of stars in the star catalog, thereby realizing the astronomical positioning of all star points in the measured star image;

[0038] This invention adds distortion to the theoretical coordinates of stars in a star catalog by fitting a model, simulating the dynamic distortion caused by natural factors and atmospheric conditions in large field-of-view telescopes. This reduces the gap between simulated and measured data, providing a more realistic simulation of images captured by large field-of-view telescopes. It solves the technical problem of how to simulate more realistic distorted star charts captured by large field-of-view telescopes and narrow the gap between simulated and measured data. Attached Figure Description

[0039] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0040] Figure 1 This is a schematic diagram of the selection of control points in this invention. Detailed Implementation

[0041] This invention provides a simulation method for large field-of-view telescope distortion star maps based on measured star maps. The method includes:

[0042] Step 1: Based on the coordinate transformation equation, obtain the theoretical coordinates of the stars in the star catalog in the image coordinate system; set the angular distance threshold, and use the cross-matching method to match the actual coordinates of all star points in the preprocessed measured star image in the image coordinate system with the theoretical coordinates of the stars in the star catalog.

[0043] Step 2: Select control points for parameter fitting from among the successfully matched star points;

[0044] Step 3: Subtract the actual coordinates of the control points in the measured star map from the theoretical coordinates of the stars in the successfully matched star catalog, and use the resulting image coordinate residuals as the objective function to construct a distortion model; then normalize the distortion model to obtain a normalized distortion model.

[0045] Step 4: Remove outliers from the normalized distortion model using the Laida criterion, and fit the parameters of the normalized distortion model using the least squares method to obtain the fitted model.

[0046] Step 5: By fitting the model, distortion is added to the theoretical coordinate positions of each star in the catalog to obtain the corresponding centroid of the star, thus simulating the distorted star map taken by the large field-of-view telescope.

[0047] In step one, the methods for obtaining the theoretical coordinates of stars in the star catalog in the image coordinate system based on the coordinate transformation equation include:

[0048] The star catalog is selected based on the set field of view, and stars within the magnitude range are selected from the star catalog based on the detection range of the wide field of view telescope.

[0049] Based on the coordinate transformation equation, the epoch observation positions of the selected stars are transformed into the image pixel coordinate system, yielding the theoretical coordinates of the stars in the star catalog within the image coordinate system; the coordinate transformation equation is as follows:

[0050]

[0051] In the formula, (ζ i ,η i ) represents the theoretical coordinates of stars in the star catalog within the image coordinate system, (α) i ,θ i (α0, θ0) represents the epochal observation position of a star in the catalog, and (α0, θ0) represents the right ascension and declination of the center of the field of view of the large field telescope.

[0052] In step one, the preprocessing methods for the measured star map include:

[0053] By using the open-source star image processing tool SExtractor, the measured star image captured by the large field-of-view telescope is subjected to background suppression, non-uniformity correction, filtering and noise reduction, and image segmentation, and then sub-pixel centroid localization is performed; thus, the actual coordinates of all star points in the measured star image in the image coordinate system are obtained.

[0054] In step one, setting an angular distance threshold and using cross-matching to match the actual coordinates of all star points in the preprocessed measured star image in the image coordinate system with the theoretical coordinates of stars in the star catalog includes the following methods:

[0055] Set the angular distance threshold by combining the distortion range and angular resolution of the large field-of-view telescope;

[0056] The actual coordinates of all star points in the preprocessed measured star image in the image coordinate system are compared with the theoretical coordinates of stars in the star catalog in the image coordinate system. When the angular distance difference between the theoretical coordinates of one and only one known star in the star catalog and the actual coordinates of the star point is less than the set angular distance threshold, it is marked as a successful match.

[0057] Preferably, the angular distance threshold is set within a range of 30 arcseconds to 100 arcseconds. This avoids mismatches caused by star distortion and facilitates the selection of subsequent control points.

[0058] In step two, the methods for selecting control points for fitting from the successfully matched star points include:

[0059] The field of view is divided into a preset number of regions of equal size, and the star point with the largest magnitude among the successfully matched star points in each region is selected as the control point.

[0060] Step three involves subtracting the actual coordinates of the control points in the measured star map from the theoretical coordinates of the stars in the successfully matched star catalog. This includes:

[0061]

[0062] Where Δx and Δy represent the image coordinate residuals; x d and y d Indicates the actual coordinates of the control point in the measured star map; x u and y u This indicates the theoretical coordinates of stars in the catalog where control points were successfully matched.

[0063] In step three, the distortion model constructed is as follows:

[0064]

[0065] Where Δx and Δy represent the image coordinate residuals; (a ij ,b ij ) represents the parameters of the distortion model; m represents the maximum order of the distortion model, m is order 3, and it includes a total of 20 parameters; x u and y u This indicates the theoretical coordinates of stars in the catalog where control points were successfully matched.

[0066] In step three, the normalized distortion model is as follows:

[0067]

[0068] Where Δx and Δy represent the image coordinate residuals; This represents the normalized theoretical coordinates of stars in the catalog where control points have been successfully matched.

[0069] In step four, the resulting fitted model is:

[0070]

[0071] Verification Instance

[0072] ① Star Selection: The star catalog is selected based on the set field of view. The commonly used UCAC4 star catalog is chosen.

[0073] The telescope's detection capabilities allow it to filter out stars with a magnitude of less than 12.

[0074] ② Coordinate Transformation: Based on the coordinate transformation equation, the selected stars are transformed into the image coordinate system to obtain the coordinates of each star.

[0075] Theoretical coordinates.

[0076] ③ Construct a fitting model based on measured star charts:

[0077] Preprocessing of the measured star image: First, the measured star image captured by the telescope is subjected to background suppression, non-uniformity correction, filtering and noise reduction, and image segmentation. Then, sub-pixel centroid localization is performed. This gives the actual coordinates of all star points in the measured star image in the image coordinate system. This part is done by SExtractor.

[0078] Star matching: The angular distance threshold is set to 50 arcseconds. The actual coordinates of all star points in the preprocessed measured star image in the image coordinate system are matched with the theoretical coordinates of stars in the star catalog using the cross-matching method. When there is one and only one known star that matches the measured star point within 50 arcseconds, the match is considered successful.

[0079] Selection of control points: Among the successfully matched star points, control points are selected for fitting. The principle for selecting control points is accurate positioning and uniform distribution. Therefore, the entire field of view is divided into 12×12 regions, totaling 144 equal-sized regions. Within each region, the star point with the largest magnitude among the successfully matched star points is selected as the control point. For example... Figure 1 As shown.

[0080] Residual distance calculation: The difference between the actual coordinates of the control points in the measured star map and the theoretical coordinates of the stars in the successfully matched star catalog is used as the residual. To highlight the distortion effect, the distortion level is increased by a factor of 10 as follows.

[0081]

[0082] The distortion model constructed using the residuals as the objective function is as follows:

[0083] Where (a) ij ,b ij The parameters are denoted as follows: The third-order (20 parameters) model effectively simulates star chart distortion from a large field-of-view telescope.

[0084]

[0085] Since the degree of lens distortion is related to the telescope's field of view and not to the camera's resolution, the input pixel coordinates are normalized with respect to the image resolution as follows:

[0086]

[0087] get

[0088]

[0089] Parameter fitting: First, outliers were removed using the Laida criterion. Then, the 20 coefficients were fitted using the least squares method. The final fitted model is as follows:

[0090]

[0091] The fitting model constructed based on equation (5) adds distortion to the theoretical coordinate positions of each star, which can simulate the star map taken by a large field-of-view telescope.

[0092] The beneficial effects of this invention are:

[0093] This invention obtains the theoretical coordinates of stars in the star catalog in the image coordinate system based on the coordinate transformation equation; sets an angular distance threshold, and uses a cross-matching method to match the actual coordinates of all star points in the preprocessed measured star image in the image coordinate system with the theoretical coordinates of stars in the star catalog, thereby realizing the astronomical positioning of all star points in the measured star image;

[0094] This invention adds distortion to the theoretical coordinates of stars in a star catalog by fitting a model, simulating the dynamic distortion caused by natural factors and atmospheric conditions in large field-of-view telescopes. This reduces the gap between simulated and measured data, providing a more realistic simulation of images captured by large field-of-view telescopes. It solves the technical problem of how to simulate more realistic distorted star charts captured by large field-of-view telescopes and narrow the gap between simulated and measured data.

[0095] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A simulation method for large field-of-view telescope distortion star maps based on measured star maps, characterized in that, The method includes: Step 1: Based on the coordinate transformation equation, obtain the theoretical coordinates of the stars in the star catalog in the image coordinate system; set the angular distance threshold, and use the cross-matching method to match the actual coordinates of all star points in the preprocessed measured star image in the image coordinate system with the theoretical coordinates of the stars in the star catalog. Step 2: Select control points for parameter fitting from among the successfully matched star points; Step 3: Subtract the actual coordinates of the control points in the measured star map from the theoretical coordinates of the stars in the successfully matched star catalog, and use the resulting image coordinate residuals as the objective function to construct a distortion model; then normalize the distortion model to obtain a normalized distortion model. Step 4: Remove outliers from the normalized distortion model using the Laida criterion, and fit the parameters of the normalized distortion model using the least squares method to obtain the fitted model. Step 5: By fitting the model, distortion is added to the theoretical coordinate positions of each star in the catalog to obtain the corresponding centroid of the star, thus realizing the simulation of the distorted star map taken by the large field-of-view telescope. In step one, setting an angular distance threshold and using cross-matching to match the actual coordinates of all star points in the preprocessed measured star image in the image coordinate system with the theoretical coordinates of stars in the star catalog includes the following methods: Set the angular distance threshold by combining the distortion range and angular resolution of the large field-of-view telescope; The actual coordinates of all star points in the preprocessed measured star image in the image coordinate system are compared with the theoretical coordinates of stars in the star table in the image coordinate system. When the angular distance difference between the theoretical coordinates of one and only one known star in the star table and the actual coordinates of the star point is less than the set angular distance threshold, it is marked as a successful match. In step one, the methods for obtaining the theoretical coordinates of stars in the star catalog in the image coordinate system based on the coordinate transformation equation include: The star catalog is selected based on the set field of view, and stars within the magnitude range are selected from the star catalog based on the detection range of the wide field of view telescope. Based on the coordinate transformation equation, the epoch observation positions of the selected stars are transformed into the image pixel coordinate system, yielding the theoretical coordinates of the stars in the star catalog within the image coordinate system; the coordinate transformation equation is as follows: In the formula, (ζ i η i ) represents the theoretical coordinates of stars in the star catalog within the image coordinate system, (α) i θ i ) represents the epochal observation position of the star in the star catalog, and (α0, θ0) represents the right ascension and declination of the center of the field of view of the large field telescope. In step one, the preprocessing methods for the measured star map include: By using the open-source star image processing tool SExtractor to perform background suppression, non-uniformity correction, filtering and noise reduction, and image segmentation on the measured star image captured by the large field-of-view telescope, and then performing sub-pixel centroid localization, the actual coordinates of all star points in the measured star image in the image coordinate system can be obtained. The angular distance threshold can be set within a range of 30 arcseconds to 100 arcseconds. In step two, the methods for selecting control points for fitting from the successfully matched star points include: The field of view is divided into a preset number of regions of equal size, and the star point with the largest magnitude is found among the successfully matched star points in each region as the control point; Step three involves subtracting the actual coordinates of the control points in the measured star map from the theoretical coordinates of the stars in the successfully matched star catalog. This includes: Where Δx and Δy represent the image coordinate residuals; x d and y d Indicates the actual coordinates of the control point in the measured star map; x u and y u The theoretical coordinates of stars in the star catalog where control points have been successfully matched; In step three, the distortion model constructed is as follows: Where Δx and Δy represent the image coordinate residuals; (a ij b ij ) represents the parameters of the distortion model; m represents the maximum order of the distortion model, m is order 3, and it includes a total of 20 parameters; x u and y u The theoretical coordinates of stars in the star catalog where control points have been successfully matched; In step three, the normalized distortion model is as follows: Where Δx and Δy represent the image coordinate residuals; Normalized theoretical coordinates of stars in the catalog where control points were successfully matched; In step four, the resulting fitted model is:

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