Method for pointing correction of an astronomical telescope

Abstract

The application discloses an astronomical telescope pointing correction method, and the steps comprise the following steps: step 1, constructing a pointing correction model of the whole sky area; step 2, distinguishing inner points and outer points; and step 3, constructing a pointing correction model of a subarea. The dynamic local pointing correction model based on the spherical harmonic function firstly carries out relatively dense sampling measurement on the whole sky area, measures the pointing error of each sampling position, dynamically selects the sampling data near a target according to the actual position of the pointing target when the telescope works, and establishes a local spherical harmonic function correction model, so that the pointing correction precision can be extremely high for the local position. The method can be applied to the equatorial telescope, the horizontal telescope and other telescope frame forms.

Description

Technical Field

[0001] This invention belongs to the field of optical instruments, and specifically relates to a method for correcting the pointing of an astronomical telescope. Background Technology

[0002] An astronomical telescope is an extremely precise optical instrument. When a telescope points to a celestial target, due to various errors, there will be a small deviation between the pointed position and the actual position of the celestial object. This deviation is called pointing error or pointing accuracy. Pointing accuracy is a crucial technical indicator for optical instruments such as astronomical telescopes. Since the mechanical, optical, automatic control, and detector systems of an astronomical telescope inevitably contain some minute errors, pointing error is unavoidable; the only difference is the magnitude of the error. Pointing error can be decomposed into systematic error and random error. Systematic errors are recurring and regular, and therefore can be corrected using various digital methods by establishing a pointing correction digital model. This process is called pointing correction. Random errors are usually difficult to eliminate effectively. The pointing error that still exists after pointing correction is called residual error.

[0003] Common pointing correction models include spherical harmonic function models, fundamental parameter models, and gantry models. Spherical harmonic function models use spherical harmonic polynomials to fit pointing errors. Spherical harmonic polynomials are suitable for fitting errors with a spherical reference plane; the method is simple, and one advantage is that it can be applied to telescopes of any gantry structure and can fit various errors. The disadvantages are that it has many model parameters, none of which have actual physical meaning; the parameters are highly correlated; the model is unstable; and the calculated model parameters change significantly after remeasurement. For scenarios like telescopes where fitting needs to be performed over a hemispherical sky region, it cannot achieve very high accuracy. Fundamental parameter models use the most important parameters affecting telescope pointing accuracy, such as code disk zero-point error, deviation between the optical axis center and the CCD field of view center, dial eccentricity error, and zenith error, to establish a pointing model. The advantage is that each parameter has physical meaning, and the calculation is relatively simple; high accuracy can be achieved by measuring only a small amount of celestial data. The disadvantage is that it considers too few parameters, resulting in relatively low accuracy. The frame model is suitable for altazimuth telescopes. Through detailed analysis of the telescope frame structure, various factors affecting the telescope's pointing accuracy are considered, totaling 24 parameters. These parameters all have practical physical meaning and can achieve very high accuracy. For professional telescopes with relatively small random errors, the pointing accuracy across the entire sky can often reach 3-5 arcseconds. Therefore, the frame model has become the most commonly used pointing correction model for altazimuth telescopes.

[0004] Although the frame model considers many factors affecting pointing error, these factors exert the same effect on the entire sky area. With the increasing size of modern telescope apertures, the pointing error characteristics of telescopes vary slightly when the telescope tube is pointed at different azimuth and elevation angles under the influence of various factors such as gravity, wind, temperature, and air pressure. Therefore, it is difficult to use a unified parameter model to uniformly correct the pointing error of the entire sky area. This restricts the improvement of pointing accuracy and makes it difficult to meet the pointing accuracy requirements of daytime satellite tracking, laser lunar observation, and large radio telescopes. Summary of the Invention

[0005] This invention addresses the problem that pointing correction models based on spherical harmonics have many parameters and generate a large amount of noise due to spatiotemporal environmental interference, making it difficult to achieve high-precision all-sky pointing. It provides a pointing correction method for astronomical telescopes based on a dynamic local pointing correction model using spherical harmonics.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for correcting the pointing of an astronomical telescope includes the following steps:

[0008] Step 1: Construct a pointing correction model for the entire sky area;

[0009] N stars are selected evenly across the entire sky. The telescope is pointed at a selected star, and the position of the star in the CCD image observed by the telescope is adjusted to the center of the CCD target surface. The deviation between the current position of the telescope and the theoretical position is the pointing deviation at that star. The N selected stars are traversed, and a pointing correction model is constructed using spherical harmonic functions based on the record of the position deviation of the N stars for subsequent star pointing.

[0010] Step 2: Distinguish between interior and exterior points;

[0011] Let the threshold for stellar pointing error be TH, and the pointing error be e. In subsequent observations, a partitioned pointing correction model will be used. Stars with pointing errors less than TH will be classified as inliers, denoted as n. in Stars with a pointing error greater than TH are classified as outward points, denoted as n. out ;

[0012] Step 3: Construct a regional pointing correction model

[0013] Assuming the parent region satisfies the condition that the number of interior points is greater than N, and there is at least one exterior point within the region, the parent region will be divided into two sub-regions, and a partition pointing correction model based on spherical harmonic functions will be further constructed for the region with more exterior points.

[0014] As the sub-region becomes smaller, the pointing error model of the sub-region becomes more and more accurate, the number of outliers decreases, and the probability that the pointing error model is the best pointing error model in the region increases. Assuming that all errors are less than the threshold TH, the number of outliers is 0, the probability of building a good model is 1, and then the model is the best pointing error model.

[0015] Furthermore, in step 1, the number of stars selected is determined by the order of the spherical harmonic function.

[0016] Furthermore, in step 1, the accuracy and reliability of the pointing correction model for pointing across the entire sky depend on the quantity and quality of the observation data, as well as the order of the spherical harmonic function; the higher the order, the greater the amount of data required.

[0017] Furthermore, in step 2,

[0018] After observing more than N stars belonging to the inner point, the entire sky is divided into two regions. A new pointing correction model is reconstructed in the region with more stars belonging to the outer point, while the old pointing correction model is still used in the region with fewer outer points. In this dynamic process, as more and more stars are observed, the region division becomes more and more refined. The smaller the region, the higher the accuracy of the pointing correction model constructed and the fewer the number of outer points observed.

[0019] When there are only N stars in the divided region, adjust the threshold of star pointing error so that the smallest region appears earlier.

[0020] Furthermore, in step 3,

[0021] Assume the number of interior points in the parent region is n. in The number of outliers is n out Then the proportion t of the number of interior points is:

[0022]

[0023] A parent region can be divided into two sub-regions only if it has at least one outside point. Therefore, a sub-region with more outside points must have at least one outside point. The probability that the parent region has at least one outside point when calculating the pointing model is:

[0024] P f =1-t N

[0025] The smallest area is divided into all-day zones. If, in k iterations of region partitioning, at least one outlier appears in each iteration, then the probability of sampling N inlier points and constructing a good model is:

[0026] P = 1 - P f k .

[0027] Furthermore, in step 3,

[0028] For the all-sky pointing model, the probability of constructing a high-precision pointing correction model for region i is P. i The probability that the all-sky area pointing model, composed of all partitions, is high-precision is:

[0029]

[0030] In other words, the higher the precision of the sub-region, the fewer the number of outer points, and the higher the probability of high-precision pointing across the entire sky.

[0031] Furthermore, in step 3, the RANSAC algorithm based on region iteration is adopted. By reducing the dataset size, an accurate model based on a smaller dataset is reconstructed, reducing the number of outliers and achieving a high-precision regional pointing correction model.

[0032] Compared with the prior art, the beneficial effects of the present invention are:

[0033] This invention is based on a dynamic local pointing correction model using spherical harmonics. First, relatively dense sampling measurements are performed across the entire sky to determine the pointing error at each sampling location. During telescope operation, based on the actual position of the target, sampling data near the target is dynamically selected to establish a local spherical harmonic correction model. This model achieves extremely high pointing accuracy for specific local locations. This method is applicable to altazimuth telescopes as well as equatorial telescopes, horizontal telescopes, and other telescope rig configurations. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 This is a flowchart of the method of the present invention;

[0036] Figure 2 This is a schematic diagram of the region division proposed in this invention;

[0037] Figure 3 This is a schematic diagram of the k and k+1th order region division proposed in this invention;

[0038] Figure 4 This is a schematic diagram of the smallest region after regional iteration in the all-sky region proposed in this invention. Detailed Implementation

[0039] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0040] This invention addresses the problem that pointing correction models based on spherical harmonic functions have many parameters and generate a large amount of noise due to spatiotemporal environmental interference, making it difficult to achieve high-precision pointing across the entire sky. It proposes a dynamic local pointing correction model based on the regional iterative RANSAC algorithm and spherical harmonic functions, which dynamically improves the pointing accuracy of local sky regions and thus improves the pointing accuracy of the entire sky.

[0041] To achieve the above objectives, the present invention employs the following methods: Figure 1 The method shown, specifically the technical solution, is as follows:

[0042] 1. Construct a pointing correction model for the entire sky area.

[0043] N stars (determined by the order of the spherical harmonic function) are uniformly selected across the entire sky. The telescope is pointed at these selected stars, and the position of the star in the CCD image observed by the telescope is adjusted to the center of the CCD target surface. The deviation between the telescope's current position and the theoretical position is the pointing deviation at that star. Based on the recorded position deviations of the N stars, a basic, global pointing correction model is constructed using the spherical harmonic function for subsequent star pointing. The accuracy and reliability of this pointing correction model for pointing across the entire sky depend on the quantity and quality of the observational data, as well as the choice of the order of the spherical harmonic function; the higher the order, the larger the amount of data required.

[0044] 2. Distinguish between interior points and exterior points

[0045] Let the threshold for stellar pointing error be TH, and the pointing error be e. Then, in subsequent observations, a partitioned pointing correction model will be used. Stars with pointing errors less than TH will be classified as inliers, denoted as n. in Stars with a pointing error greater than TH are classified as outward points, denoted as n. out .

[0046] Assuming we use the above all-sky pointing correction model for star pointing, after observing more than N stars belonging to the inner points, the entire sky is divided into two regions. A new pointing correction model is reconstructed in the region with a larger number of outer-point stars (details in the next section). The region with fewer outer-point stars continues to use the old pointing correction model. The specific process is as follows; this is a dynamic process. As more stars are observed, the region division becomes increasingly detailed. Smaller regions result in higher accuracy of the pointing correction, thus reducing the number of observed outer-point stars.

[0047] Figure 1

[0048] The pointing model is most accurate when there are only N stars in the divided region. This is obviously impossible for a universe with an infinite number of stars. Therefore, we can adjust the threshold of star pointing error to allow the smallest region to appear earlier.

[0049] 3. Construct a regional pointing correction model

[0050] Assuming the parent region satisfies the condition that the number of interior points is greater than N, and there is at least one exterior point within the region, the parent region will be divided into two sub-regions, and a partition pointing correction model based on spherical harmonic functions will be further constructed for the region with a larger number of exterior points.

[0051] Assume the number of interior points in the parent region is n. in The number of outliers is n out Then the proportion t of the number of interior points is

[0052]

[0053] A parent region can be divided into two sub-regions only if it has at least one outside point. Therefore, a sub-region with more outside points must have at least one outside point. Thus, the probability that the parent region has at least one outside point when calculating the pointing model is...

[0054] P f =1-t N

[0055] The smallest area is divided into all-day zones. When, in k iterations of region partitioning, at least one outlier appears in each iteration, the probability of sampling N inlier points and constructing a good model is:

[0056] P = 1 - P f k

[0057] As the sub-region becomes smaller, the pointing error model for that sub-region becomes more accurate, the number of outliers decreases, and the probability that the pointing model is the best pointing error model for that region increases. Assuming all errors are less than the threshold TH, the number of outliers is 0, the probability of constructing a good model is 1, and therefore, this model is the best pointing error model.

[0058] Traditional RANSAC algorithms randomly sample a set of data from the entire dataset, making them uncertain algorithms that produce results with only one probability, which increases with the number of iterations. In contrast, region-based iterative RANSAC algorithms reconstruct a more accurate model based on a smaller dataset by reducing the number of outliers, thus achieving a high-precision, region-specific pointing correction model.

[0059] For the all-sky pointing model, the probability of constructing a high-precision pointing correction model for region i is P. i The probability that the all-sky area pointing model, composed of all partitions, is high-precision is:

[0060]

[0061] In other words, the higher the precision of the sub-region, the fewer the number of outer points, and the higher the probability of high-precision pointing across the entire sky.

[0062] The following specific examples will further illustrate this point.

[0063] First, N stars are uniformly selected across the entire sky. These selected stars are observed using a telescope. The positions of the stars in the telescope-observed CCD images are adjusted to the center of the CCD target surface, and the adjustment displacement is recorded as the pointing deviation. This set of deviation data is fitted using a spherical harmonic function to establish a basic, global pointing correction model.

[0064] The dynamic update process of the region pointing correction model will be described below:

[0065] Set an appropriate and suitable error threshold. In subsequent star observations, targets smaller than the error are recorded as inliers, and targets larger than the error are recorded as outliers. All inliers and outliers are recorded.

[0066] like Figure 2 As shown, when the number of internal points in the region is greater than N and the number of external points in the region is greater than 1, the region is divided into two equal parts. The sub-region with more external points will rebuild the pointing correction model, while the sub-region with fewer external points will still use the old pointing correction model, that is, the pointing correction model of the parent region.

[0067] When dividing the region for the kth time, as follows: Figure 3 As shown, the parent region is the lightest in color, satisfying the partitioning condition. It is divided into upper and lower parts by a horizontal dashed line. The darker regions have more outliers. During the (k+1)th partitioning, horizontal and vertical partitioning should be used alternately with the previous partitioning to ensure the region decreases proportionally. Regions with medium color depth are divided into left and right parts by a vertical dashed line. Similarly, the darker regions have more outliers. At this point, the overall region is divided into three parts, with regions of the same color using the same pointing correction model.

[0068] As the area of ​​the sub-region decreases, the stellar position dataset also shrinks, leading to higher accuracy in the pointing correction model and a reduction in the number of outliers. When the pointing accuracy is sufficiently high, all pointing parameters meet the error threshold, and no more outliers are generated. At this point, the sub-region will no longer be further subdivided. Figure 4As shown, after the sub-region is iteratively divided, all pointers meet the error threshold; at the same time, other regions are also updating the region iterative division synchronously.

[0069] In the process of dynamically updating the pointing correction model for a sub-region, the more stars observed, or the faster the observation speed, the faster the model updates; furthermore, the more concentrated the observed region, the faster the model updates in that region. Therefore, observers can manually control the speed and region of the model's dynamic updates.

[0070] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for correcting the pointing of an astronomical telescope, characterized in that, Includes the following steps: Step 1: Construct a pointing correction model for the entire sky area; Selected evenly across the entire day area Point the telescope at the selected star, then adjust the star's position in the CCD image observed by the telescope to the center of the CCD target surface. The deviation between the telescope's current position and the theoretical position is the pointing deviation at that star; according to The records of star position deviations are used to construct a pointing correction model using spherical harmonic functions for subsequent star pointing. Step 2: Distinguish between interior and exterior points; Let the threshold for star pointing error be... Pointing error In subsequent observations, the pointing correction model for the partitions was used. Pointing error less than The stars are classified as interior points, and the pointing error is greater than [missing information]. Stars are classified as outer points; Step 3: Construct a region-specific pointing correction model; Assume the parent region has a greater than 100 internal points. Under the condition that there is at least one external point in the region, the parent region will be divided into two sub-regions, and a partition pointing correction model based on spherical harmonic function will be further constructed for the region with a larger number of external points. As the sub-region becomes smaller, the pointing error model for that sub-region becomes more accurate, the number of outliers decreases, and the probability that the pointing error model is the best within that region increases; assuming all errors are less than a threshold. When the number of outliers is 0, the probability of constructing a good model is 1, then this model is the best pointing error model; Assume the number of interior points in the parent region is The number of external points is Then the proportion of interior points that is: ； A parent region can be divided into two sub-regions only if it has at least one outside point. Therefore, a sub-region with more outside points must have at least one outside point. The probability that the parent region has at least one outside point when calculating the pointing model is: ； The smallest area is divided into all-day zones. Time, that is If at least one outlier is found in each sub-region partitioning and calculation iteration, then the probability of sampling N inlier points and constructing a good model is: ； For the all-day pointing model, the region The probability of constructing a high-precision pointer correction model is The probability that the all-sky area pointing model, composed of all partitions, is high-precision is: 。 2. The method for correcting the pointing of an astronomical telescope according to claim 1, characterized in that, In step 1, the number of stars selected is determined by the order of the spherical harmonic function.

3. The method for correcting the pointing of an astronomical telescope according to claim 1, characterized in that, In step 2, When observation exceeds After identifying stars that are at the inner point, the entire sky is divided into two regions. A new pointing correction model is reconstructed in the region with a larger number of stars at the outer point, while the old pointing correction model is still used in the region with fewer outer points. When the divided area has only When there are several stars, adjust the threshold for star pointing error so that the minimum region appears earlier.

4. The method for correcting the pointing of an astronomical telescope according to claim 1, characterized in that, In step 3, the RANSAC algorithm based on region iteration is used to reconstruct an accurate model based on a smaller dataset by reducing the dataset size.

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