Simulation method of large-field-of-view telescope distorted star map based on actually measured star map

Abstract

The invention discloses a method for simulating a distorted star map of a large-field-of-view telescope based on an actually measured star map, and solves the problem of how to simulate the distorted star map shot by the large-field-of-view telescope. Belongs to the field of star map simulation. Comprising the steps of obtaining theoretical coordinates of fixed stars in a star catalogue according to a coordinate conversion equation; setting an angular distance threshold value, and matching actual coordinates of star image points in the actually measured star map with theoretical coordinates of fixed stars in the star catalogue through a cross matching method; subtracting the actual coordinate of the selected control point from the theoretical coordinate of the fixed star, and constructing a distortion model and a normalized distortion model according to a residual error result; eliminating outliers in the normalized distortion model through a Pauta criterion, and fitting parameters of the normalized distortion model through a least square method to obtain a fitting model; distortion is added to the theoretical coordinate position of each fixed star in the star catalogue through the fitting model, and simulation of the distorted star map shot by the large-field telescope is achieved. According to the method, the image shot by the large-view-field telescope is truly simulated through the fitting model.

Description

Technical Field

[0001] The invention belongs to the technical field of star map simulation, and relates to a simulation method of a distorted star map of a large-field telescope based on a measured star map. Background Art

[0002] Star map simulation is mainly used in the field of astronomical attitude determination based on star sensors and the field of measurement based on ground-based large-field telescopes. Large-field telescopes usually have a field of view of more than 3 degrees * 3 degrees and are mainly used for large-scale sky surveys. At present, the common star map simulation method can simulate star maps according to the optical axis position and the image plane rotation angle, and can generate different simulation results based on different image resolutions, pixel sizes, atmosphere, and optical system parameters.

[0003] The current star map simulation method does not consider the image distortion problem caused by ground-based large-field telescopes. Since the distortion of the actual image is not only related to the lens distortion of the large-field telescope itself, but also to natural environmental factors, the distortion of images taken at different positions, angles, and times is different. Using only conventional lens distortion models for simulation cannot meet the requirements. Summary of the invention

[0004] In order to solve the technical problem of how to simulate more realistic distorted star images taken by a wide-field telescope and narrow the gap between simulated data and measured data, the present invention provides a simulation method for a distorted star image of a wide-field telescope based on a measured star image. The method utilizes a fitting model obtained by fitting in the measured star image to simulate the dynamically distorted star image taken by the wide-field telescope, simulates the dynamic distortion of the wide-field telescope caused by natural factors, atmospheric conditions, etc., narrows the gap between simulated data and measured data, and more realistically simulates images taken by a wide-field telescope.

[0005] The purpose of the present invention is specifically achieved through the following technical solutions:

[0006] The present invention discloses a method for simulating a distorted star map of a large-field telescope based on a measured star map, the method comprising:

[0007] Step 1: According to the coordinate conversion equation, the theoretical coordinates of the stars in the star catalog in the image coordinate system are obtained; the angular distance threshold is set, and the actual coordinates of all the star image points in the measured star map obtained after preprocessing in the image coordinate system are matched with the theoretical coordinates of the stars in the star catalog by the cross matching method;

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

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

[0010] Step 4: Remove outliers in the normalized distortion model using the Laida criterion, and fit the parameters of the normalized distortion model using the least squares method to obtain a fitting model;

[0011] Step 5: Add distortion to the theoretical coordinate position of each star in the star catalog by fitting the model, obtain the center of mass point corresponding to the star, and realize the simulation of the distorted star map taken by a large field of view telescope.

[0012] In step 1, the method of obtaining the theoretical coordinates of the stars in the star catalog in the image coordinate system according to the coordinate conversion equation includes:

[0013] Screen the star catalog according to the set field of view, and select stars within the magnitude range from the star catalog according to the detection range of the large field telescope;

[0014] According to the coordinate conversion equation, the epoch observation position of the selected stars is converted into the image pixel coordinate system to obtain the theoretical coordinates of the stars in the star catalog in the image coordinate system; the coordinate conversion equation is:

[0015]

[0016] In the formula, (ζ i ,η i ) is the theoretical coordinate of the star in the star catalog in the image coordinate system, (α i ,θ i ) is the epoch observed position of the star in the star catalog, (α 0 ,θ 0 ) are the right ascension and declination of the center of the field of view of the wide field telescope.

[0017] In step 1, the preprocessing method of the measured star map includes:

[0018] The open source star image processing tool SExtractor is used to perform background suppression, non-uniformity correction, filtering denoising and image segmentation on the measured star map taken by a large field of view telescope, and then sub-pixel centroid positioning is performed; thus, the actual coordinates of all star image points in the measured star map in the image coordinate system are obtained.

[0019] In step 1, the method of setting the angular distance threshold and matching the actual coordinates of all star image points in the measured star map obtained by preprocessing in the image coordinate system with the theoretical coordinates of the stars in the star catalog by cross matching method includes:

[0020] The angular distance threshold is set based on the distortion range and angular resolution of the large field of view telescope;

[0021] The actual coordinates of all star image points in the measured star map obtained after preprocessing in the image coordinate system are compared with the theoretical coordinates of the 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 image point is less than the set angular distance threshold, it is marked as a successful match.

[0022] Preferably, the setting range of the angular distance threshold is greater than 30 arc seconds and less than 100 arc seconds.

[0023] In step 2, among the successfully matched star image points, the method of selecting the control points for fitting includes:

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

[0025] In step 3, the method of subtracting the actual coordinates of the control point in the measured star map from the theoretical coordinates of the star in the successfully matched star catalog includes:

[0026]

[0027] Among them, Δx and Δy represent the image coordinate residuals; x d and d Indicates the actual coordinates of the control point in the measured star map; x u and u Indicates the theoretical coordinates of the star in the star catalog where the control point is successfully matched.

[0028] In step 3, the distortion model constructed is:

[0029]

[0030] Where Δx and Δy represent the image coordinate residuals; (a ij ,b ij ) are the parameters of the distortion model; m is the maximum order of the distortion model, m is 3 orders, and includes 20 parameters in total; x u and u Indicates the theoretical coordinates of the star in the star catalog where the control point is successfully matched.

[0031] In step 3, the normalized distortion model is:

[0032]

[0033] Among them, Δx and Δy represent the image coordinate residuals; Indicates the normalized theoretical coordinates of the stars in the star catalog for which the control points are successfully matched.

[0034] In step 4, the fitting model obtained is:

[0035]

[0036] The beneficial effects of the present invention are:

[0037] The present invention obtains the theoretical coordinates of stars in the star catalog in the image coordinate system according to the coordinate conversion equation; sets the angular distance threshold, and matches the actual coordinates of all star image points in the measured star catalog obtained after preprocessing in the image coordinate system with the theoretical coordinates of the stars in the star catalog through the cross matching method, thereby realizing the astronomical positioning of all star image points in the measured star catalog;

[0038] The present invention adds distortion to the theoretical coordinate position of each star in the star catalog by fitting the model, simulates the dynamic distortion caused by natural factors, atmospheric conditions, etc. of a large-field telescope, narrows the gap between the simulated data and the measured data, and simulates the image taken by the large-field telescope more realistically. The present invention solves the technical problem of how to simulate a more realistic distorted star map taken by a large-field telescope and narrow the gap between the simulated data and the measured data. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The present invention is further described in detail below based on the accompanying drawings and embodiments.

[0040] Figure 1 It is a schematic diagram of the selection of control points in the present invention. DETAILED DESCRIPTION

[0041] An embodiment of the present invention provides a method for simulating a distorted star map of a large-field telescope based on a measured star map, the method comprising:

[0042] Step 1: According to the coordinate conversion equation, the theoretical coordinates of the stars in the star catalog in the image coordinate system are obtained; the angular distance threshold is set, and the actual coordinates of all the star image points in the measured star map obtained after preprocessing in the image coordinate system are matched with the theoretical coordinates of the stars in the star catalog by the cross matching method;

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

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

[0045] Step 4: Remove outliers in the normalized distortion model using the Laida criterion, and fit the parameters of the normalized distortion model using the least squares method to obtain a fitting model;

[0046] Step 5: Add distortion to the theoretical coordinate position of each star in the star catalog by fitting the model, obtain the center of mass point corresponding to the star, and realize the simulation of the distorted star map taken by a large field of view telescope.

[0047] In step 1, the method of obtaining the theoretical coordinates of the stars in the star catalog in the image coordinate system according to the coordinate conversion equation includes:

[0048] Screen the star catalog according to the set field of view, and select stars within the magnitude range from the star catalog according to the detection range of the large field telescope;

[0049] According to the coordinate conversion equation, the epoch observation position of the selected stars is converted into the image pixel coordinate system to obtain the theoretical coordinates of the stars in the star catalog in the image coordinate system; the coordinate conversion equation is:

[0050]

[0051] In the formula, (ζ i ,η i ) is the theoretical coordinate of the star in the star catalog in the image coordinate system, (α i ,θ i ) is the epoch observed position of the star in the star catalog, (α 0 ,θ 0 ) are the right ascension and declination of the center of the field of view of the wide field telescope.

[0052] In step 1, the preprocessing method of the measured star map includes:

[0053] The open source star image processing tool SExtractor is used to perform background suppression, non-uniformity correction, filtering denoising and image segmentation on the measured star map taken by a large field of view telescope, and then sub-pixel centroid positioning is performed; thus, the actual coordinates of all star image points in the measured star map in the image coordinate system are obtained.

[0054] In step 1, the method of setting the angular distance threshold and matching the actual coordinates of all star image points in the measured star map obtained by preprocessing in the image coordinate system with the theoretical coordinates of the stars in the star catalog by cross matching method includes:

[0055] The angular distance threshold is set based on the distortion range and angular resolution of the large field of view telescope;

[0056] The actual coordinates of all star image points in the measured star map obtained after preprocessing in the image coordinate system are compared with the theoretical coordinates of the 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 image point is less than the set angular distance threshold, it is marked as a successful match.

[0057] Preferably, the setting range of the angular distance threshold is greater than 30 arc seconds and less than 100 arc seconds, so as to avoid the stars being unable to match due to distortion and facilitate the selection of subsequent control points.

[0058] In step 2, among the successfully matched star image points, the method of selecting the control points for fitting includes:

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

[0060] In step 3, the method of subtracting the actual coordinates of the control point in the measured star map from the theoretical coordinates of the star in the successfully matched star catalog includes:

[0061]

[0062] Among them, Δx and Δy represent the image coordinate residuals; x d and d Indicates the actual coordinates of the control point in the measured star map; x u and u Indicates the theoretical coordinates of the star in the star catalog where the control point is successfully matched.

[0063] In step 3, the distortion model constructed is:

[0064]

[0065] Where Δx and Δy represent the image coordinate residuals; (a ij ,b ij ) are the parameters of the distortion model; m is the maximum order of the distortion model, m is 3 orders, and includes 20 parameters in total; x u and u Indicates the theoretical coordinates of the star in the star catalog where the control point is successfully matched.

[0066] In step 3, the normalized distortion model is:

[0067]

[0068] Among them, Δx and Δy represent the image coordinate residuals; Indicates the normalized theoretical coordinates of the stars in the star catalog for which the control points are successfully matched.

[0069] In step 4, the fitting model obtained is:

[0070]

[0071] Verify the instance

[0072] ① Screening stars: Screen the star catalog according to the set field of view. The commonly used UCAC4 star catalog is selected.

[0073] The telescope's detection capability can screen out stars with magnitude less than 12.

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

[0075] Theoretical coordinates.

[0076] ③Build a fitting model based on the measured star map:

[0077] Preprocessing of measured star images: First, background suppression, non-uniformity correction, filtering and denoising, and image segmentation are performed on the measured star images taken by the telescope, and then sub-pixel centroid positioning is performed; thus, the actual coordinates of all star image points in the measured star image in the image coordinate system are obtained. This part is completed by SExtractor.

[0078] Star matching: The angular distance threshold is set to 50 arc seconds. The actual coordinates of all star image points in the measured star map obtained after preprocessing in the image coordinate system are matched with the theoretical coordinates of the stars in the star catalog through the cross matching method. When there is only one known star matching the measured star image point within 50 arc seconds, the match is considered successful.

[0079] Selection of control points: From the successfully matched star image points, select control points for fitting. The principle of selecting control points is accurate positioning and uniform distribution. Therefore, the entire field of view is divided into 12×12 areas of 144 equal sizes, and the star image point with the largest magnitude is found in the successfully matched star image points in each area as the control point. Figure 1 shown.

[0080] Residual distance calculation: The actual coordinates of the control point in the measured star map are subtracted from the theoretical coordinates of the stars in the successfully matched star catalog, and the result is used as the residual. In order to highlight the distortion effect, the distortion degree is increased by 10 times as follows.

[0081]

[0082] Taking the residual as the objective function, the distortion model constructed is as follows:

[0083] Where (a ij ,b ij ) is the distortion model parameter, and the third order (20 parameters) is used to effectively simulate the star image distortion of a large field of view telescope, which is expanded as follows:

[0084]

[0085] Since the degree of lens distortion is related to the size of the telescope's field of view and has nothing to do with the camera's resolution, the input pixel coordinates are normalized to the image resolution as follows:

[0086]

[0087] get

[0088]

[0089] Parameter fitting: First, the outliers are eliminated by the Laida criterion, and then the above 20 coefficients are fitted by the least squares method. The final fitting model is:

[0090]

[0091] According to the fitting model constructed by formula (5), by adding distortion to the theoretical coordinate position of each star, the star map taken by a large field of view telescope can be simulated.

[0092] The beneficial effects of the present invention are:

[0093] The present invention obtains the theoretical coordinates of stars in the star catalog in the image coordinate system according to the coordinate conversion equation; sets the angular distance threshold, and matches the actual coordinates of all star image points in the measured star catalog obtained after preprocessing in the image coordinate system with the theoretical coordinates of the stars in the star catalog through the cross matching method, thereby realizing the astronomical positioning of all star image points in the measured star catalog;

[0094] The present invention adds distortion to the theoretical coordinate position of each star in the star catalog by fitting the model, simulates the dynamic distortion caused by natural factors, atmospheric conditions, etc. of a large-field telescope, narrows the gap between the simulated data and the measured data, and simulates the image taken by the large-field telescope more realistically. The present invention solves the technical problem of how to simulate a more realistic distorted star map taken by a large-field telescope and narrow the gap between the simulated data and the measured data.

[0095] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A simulation method for a distorted star map of a large-field telescope based on a measured star map, characterized in that: The method includes: Step 1: According to the coordinate conversion equation, the theoretical coordinates of the stars in the star catalog in the image coordinate system are obtained; the angular distance threshold is set, and the actual coordinates of all the star image points in the measured star map obtained after preprocessing in the image coordinate system are matched with the theoretical coordinates of the stars in the star catalog by the cross matching method; Step 2: Select control points for parameter fitting from among the successfully matched star image points; Step 3: Subtract the actual coordinates of the control point in the measured star map from the theoretical coordinates of the star in the successfully matched star catalog, and use the obtained image coordinate residual as the objective function to construct the distortion model; and normalize the distortion model to obtain a normalized distortion model; Step 4: Remove outliers in the normalized distortion model using the Laida criterion, and fit the parameters of the normalized distortion model using the least squares method to obtain a fitting model; Step 5: Add distortion to the theoretical coordinate position of each star in the star catalog by fitting the model, obtain the center of mass point corresponding to the star, and realize the simulation of the distorted star map taken by a large field of view telescope.

2. The method according to claim 1, characterized in that In step 1, the method of obtaining the theoretical coordinates of the stars in the star catalog in the image coordinate system according to the coordinate conversion equation includes: Screen the star catalog according to the set field of view, and select stars within the magnitude range from the star catalog according to the detection range of the large field telescope; According to the coordinate conversion equation, the epoch observation position of the selected stars is converted into the image pixel coordinate system to obtain the theoretical coordinates of the stars in the star catalog in the image coordinate system; the coordinate conversion equation is: In the formula, (ζ i ,η i ) is the theoretical coordinate of the star in the star catalog in the image coordinate system, (α i ,θ i ) is the epoch observed position of the star in the star catalog, and (α0,θ0) are the right ascension and declination of the center of the field of view of the large field telescope.

3. The method according to claim 1, characterized in that In step 1, the preprocessing method of the measured star map includes: The open source star image processing tool SExtractor is used to perform background suppression, non-uniformity correction, filtering denoising and image segmentation on the measured star map taken by a large field of view telescope, and then sub-pixel centroid positioning is performed; thus, the actual coordinates of all star image points in the measured star map in the image coordinate system are obtained.

4. The method according to any one of claims 1 to 3, characterized in that: In step 1, the method of setting the angular distance threshold and matching the actual coordinates of all star image points in the measured star map obtained by preprocessing in the image coordinate system with the theoretical coordinates of the stars in the star catalog by the cross matching method includes: The angular distance threshold is set based on the distortion range and angular resolution of the large field of view telescope; The actual coordinates of all star image points in the measured star map obtained after preprocessing in the image coordinate system are compared with the theoretical coordinates of the 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 image point is less than the set angular distance threshold, it is marked as a successful match.

5. The method according to claim 4, characterized in that The setting range of the angular distance threshold is greater than 30 arc seconds and less than 100 arc seconds.

6. The method according to claim 5, characterized in that In step 2, among the successfully matched star image points, the method of selecting the control points for fitting includes: The field of view is divided into a preset number of regions of equal size, and the star image point with the largest magnitude is found among the successfully matched star image points in each region as the control point.

7. The method according to claim 6, characterized in that In step 3, the method of subtracting the actual coordinates of the control point in the measured star map from the theoretical coordinates of the star in the successfully matched star catalog includes: Among them, Δx and Δy represent the image coordinate residuals; x d and d Indicates the actual coordinates of the control point in the measured star map; x u and u Indicates the theoretical coordinates of the star in the star catalog where the control point is successfully matched.

8. The method according to claim 7, characterized in that In step 3, the distortion model constructed is: Among them, Δx and Δy represent the image coordinate residuals; (a ij ,b ij ) are the parameters of the distortion model; m is the maximum order of the distortion model, m is 3 orders, and includes 20 parameters in total; x u and u Indicates the theoretical coordinates of the star in the star catalog where the control point is successfully matched.

9. The method according to claim 8, characterized in that In step 3, the normalized distortion model is: Among them, Δx and Δy represent the image coordinate residuals; Indicates the normalized theoretical coordinates of the stars in the star catalog for which the control points are successfully matched.

10. The method according to claim 9, characterized in that In step 4, the fitting model obtained is:

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