A method for calibrating primary and secondary mirrors of a telescope based on spot image moment features

Abstract

The application discloses a kind of based on spot image moment feature telescope primary and secondary mirror calibration method, belong to telescope computer-aided alignment field.The specific steps of the calibration method are as follows, first, randomly give the free degree misadjustment of telescope system secondary mirror, utilize unbiased finite impulse response moment to extract the spot image feature of multiple field of view within reasonable range under the misadjustment state of telescope;Then utilize fully connected neural network to construct the model between the free degree misadjustment of secondary mirror and the multiple field of view spot image feature matrix;In actual use, after the multiple field of view spot image collected by CCD camera is extracted into feature matrix using unbiased finite impulse response, it is input into the trained neural network model to solve the misadjustment of secondary mirror, to guide the alignment of telescope system.This method aims to wavefront sensor as the image quality evaluation benchmark of telescope without, and without multiple iterations, to improve the efficiency of system primary and secondary mirror alignment and the imaging quality of system.

Description

Technical Field

[0001] This invention belongs to the field of telescope assembly and adjustment, and addresses the problem of spatial misalignment between the secondary mirror and the primary mirror in an optical system. Specifically, it relates to a method for calibrating the primary and secondary mirrors of a telescope based on the characteristics of light spot image moments. Background Technology

[0002] Reflective optical systems are a common structural form in modern space-based and airborne large-aperture telescopes. To achieve wider field-of-view coverage, higher spatial and spectral resolution, and a wider spectral range, the performance requirements for optical systems are constantly increasing. Ensuring imaging quality across large fields of view and multiple spectral bands inevitably leads to greater complexity in optical systems, and the requirements for their positional accuracy are becoming increasingly stringent. Traditional alignment methods are no longer sufficient to meet these accuracy requirements. Especially for off-axis reflective systems, which have been widely used in recent years, achieving high-precision alignment has always been a highly challenging problem in the field of optical alignment. Unlike conventional refractive or coaxial reflective systems, the optical elements in off-axis reflective systems lack rotational symmetry, and the aberrations introduced by the misalignment degrees of freedom are mutually coupled, all of which bring significant difficulties to alignment. In fact, in the current development of optical instruments, the alignment level of the optical system is often the most critical factor restricting system performance. Therefore, finding a high-precision and real-time primary and secondary mirror alignment method is of great significance for improving the imaging quality of systems in engineering practice.

[0003] Early optical system assembly and adjustment relied primarily on technicians' experience and simple tools, resulting in significant randomness, low accuracy, and poor timeliness. Facing the demands of complex optical systems and high-precision, real-time requirements, coupled with advancements in computer technology, optical design, and manufacturing, computer-aided assembly and adjustment (CADA) technology was pioneered abroad and applied to practical optical system assembly and adjustment. CADA typically involves first establishing an optical system model using simulation software, then constructing a mathematical relationship between system wavefront aberrations (usually Zernike polynomial coefficients) and the misalignment of each optical element. During actual assembly and adjustment, the misalignment of each optical element is calculated using the Zernike polynomial coefficients detected by wavefront sensors and the mathematical model, guiding the actuators to make corresponding adjustments and significantly improving the accuracy and speed of optical system assembly and adjustment. CADA methods mainly fall into two categories: analytical methods based on vector aberration theory, which require detecting wavefront aberrations across the entire field of view to find aberration nodes and performing individual corrections for each type of aberration. Different complex analytical formulas need to be established for different optical systems, resulting in poor universality and difficulty in detecting aberration nodes during actual assembly and adjustment. Another type of numerical method, represented by the sensitivity matrix method, differential wavefront sampling method, and inverse optimization method, assumes a relationship between the misalignment and the Zernike polynomial coefficients characterizing the system aberrations. It constructs a model using numerical fitting and, during actual assembly and adjustment, substitutes the Zernike polynomial coefficients detected in real-time by the wavefront sensor into the model to solve for the system misalignment. This method is computationally intensive, inefficient, and lacks real-time performance. All of these assembly and adjustment methods require additional wavefront sensors for aberration detection, and the accuracy of the misalignment calculation depends heavily on the accuracy of the aberration detection, undoubtedly increasing the system complexity. In practical applications, the experimental requirements for using interferometers as wavefront sensors are extremely stringent. Finding a way to guide the assembly and adjustment of optical systems without employing wavefront sensors is a problem that needs to be solved by those skilled in the art. Summary of the Invention

[0004] The purpose of this invention is to address the deviation between the spatial relative position and the ideal relative position of optical lenses by providing a telescope primary and secondary mirror calibration method based on the characteristics of light spot image moments. This method eliminates the need for wavefront sensors such as interferometers to detect wave aberrations and use them as the benchmark for evaluating the telescope's image quality. Instead, it directly uses the characteristics of the light spot image acquired by a CCD camera to solve for the misalignment of each component and align the components accordingly. This avoids the cumulative errors caused by aberration detection, effectively improving the efficiency of the system's primary and secondary mirror alignment and the system's imaging quality. It is also applicable to various complex multi-mirror systems, including coaxial and off-axis telescopes.

[0005] The system components of this invention mainly include: a primary and secondary mirror optical system, a secondary mirror displacement stage, a CCD camera, and a fully connected neural network. The neural network primarily consists of an input layer, multiple hidden layers (linear layers), and an output layer.

[0006] The principle of this invention is as follows: According to Fourier optics theory, the spatial pose deviation (misalignment of each degree of freedom) of the secondary mirror relative to the primary mirror in an optical system has a corresponding relationship with the spot image (point spread function) of multiple fields of view within a certain range. The misalignment of the secondary mirror is solved by using the multi-field spot image acquired by a CCD camera. On the other hand, the mathematical model between the features of the multi-field spot image and the misalignment of each degree of freedom of the secondary mirror within a certain range is complex, and neural networks have extremely strong nonlinear fitting capabilities. This invention extracts the feature matrix from the multi-field spot image acquired by the CCD camera using unbiased finite impulse response moments (UFIR moments) and then inputs it into a trained fully connected neural network model to solve for the misalignment of the secondary mirror, thereby guiding the assembly and adjustment of the telescope system.

[0007] The technical solution adopted in this invention is:

[0008] A method for calibrating primary and secondary mirrors of a telescope based on the moment features of a light spot image is provided to address the spatial misalignment of the secondary mirror relative to the primary mirror in a telescope system. The method includes the following steps:

[0009] Step 1: Set up the telescope system:

[0010] The system includes a primary mirror, a secondary mirror, a six-degree-of-freedom platform for controlling the secondary mirror, and a CCD camera.

[0011] Step Two: Construct a mathematical model between the misalignment of each degree of freedom of the secondary mirror and the features of the multi-field-of-view spot images. Unbiased finite impulse response moments are used to characterize the grayscale variation features of the spot images in each field of view under different misalignment states of the secondary mirror. The modeling method employed is a fully connected neural network algorithm. First, a neural network dataset is constructed, which includes a training set and a test set, comprising:

[0012] Step 2.1: Record the ideal spatial position of the secondary mirror when the telescope system is fully assembled and the spot images of multiple fields of view within a reasonable range under this state. Then, add known degrees of freedom misalignment to the secondary mirror and use a CCD camera to acquire spot images of multiple fields of view within a reasonable range under this state. Subsequently, use unbiased finite impulse response moments to extract the grayscale change features of the spot images of multiple fields of view. Take the degrees of freedom misalignment of the secondary mirror relative to the primary mirror and the corresponding feature matrix as a set of samples.

[0013] Step 2.2: Repeat step 2.1 N times to obtain a dataset, and divide it into a training set and a test set according to a certain ratio;

[0014] Step 3: Train the neural network model:

[0015] Step 3.1: Select a fully connected neural network model. This fully connected neural network includes an input layer, a hidden layer, and an output layer. The input is the feature matrix of the light spot image in multiple fields of view, and the output is the misalignment of each degree of freedom of the secondary mirror.

[0016] Step 3.2: Randomly select a portion of the dataset as the training set according to a certain proportion to train the fully connected neural network. When the network converges, the network model training is completed, and the remaining part of the dataset is used as the test set to verify the fitting ability of the fully connected neural network.

[0017] Step 4: Solve for the misalignment of the secondary mirror and align the primary and secondary mirrors of the telescope, including:

[0018] Step 4.1: During the alignment of the primary and secondary mirrors in the actual telescope system, firstly, a CCD camera is used to acquire multi-field images of light spots within a reasonable range of the system. Then, unbiased finite impulse response moments are used to extract the grayscale change features of the light spot images. The feature matrix is ​​input into the trained neural network model, and then the misalignment of each degree of freedom of the secondary mirror is output. The opposite of this data is input into the six-degree-of-freedom platform of the actuator that controls the spatial position of the secondary mirror to guide the alignment of the primary and secondary mirrors.

[0019] Step 4.2: Extract the system spot image after correcting the secondary mirror position deviation again and compare it with the spot image under the ideal position of the secondary mirror. If the deviation of the compared spot images is within the allowable error range, the primary and secondary mirror alignment process is completed; otherwise, repeat step 4.1.

[0020] Furthermore, in step two, the spot image refers to the point spread function of the system, and multiple fields of view within a reasonable range refers to any multiple fields of view that are not on a straight line within the effective field of view, and the number of selected fields of view n is greater than or equal to 5.

[0021] Furthermore, in step 2.1, the known misalignment amount is added to the secondary mirror to add six degrees of freedom of misalignment error, which refers to the eccentricity error and tilt error on the X, Y and Z axes.

[0022] Furthermore, in step two, the grayscale variation characteristics of the light spot images in each field of view under different misalignment states of the secondary mirror are characterized using the unbiased finite impulse response moment, i.e., the UFIR moment, the specific calculation formula of which is:

[0023]

[0024] In the formula, n,m = 0, 1, 2, ..., N-1, the size of the light spot image is N×M, i,j are the two-dimensional coordinates of the light spot image in space, and their combination represents the position of each pixel. f(i,j) is the point spread function, representing the light spot image, where each pixel corresponds to a specific numerical value. Let represent the two-dimensional unbiased finite impulse response polynomials of the light spot image, respectively. Their recursive calculation formula is as follows:

[0025]

[0026] The coefficients are:

[0027]

[0028]

[0029] They are respectively:

[0030]

[0031]

[0032] In practical applications, the spot images of the p fields of view captured by the CCD camera are f1, f2, ... f p The k-th order gray-level variation features of each field-of-view spot image are extracted using unbiased finite impulse response moments, where U nm Let the subscripts n = 0, 1, ..., k; m = 0, 1, ..., k. The moment of the spot image for each field of view is a (k+1) × (k+1) feature matrix U, which is arranged row-wise into a 1 × [(k+1) × (k+1)] row vector. The expression for the moment of the spot image for p fields of view is:

[0033] U = [U1, U2, ..., U p (7)

[0034] The expression is a 1×[p×(k+1)×(k+1)] row vector, whose specific value is the input value of a sample in the dataset.

[0035] Furthermore, in step two, when the secondary mirror is in the nominal position, a set of degrees of freedom misalignment values ​​of the secondary mirror is given by human intervention, and the spot image feature matrix U of p fields of view in this state is calculated. The feature matrix U is used as the input of the neural network, and the degrees of freedom misalignment values ​​of the secondary mirror are used as the output, together forming a set of samples.

[0036] Compared with the prior art, the present invention has the following advantages:

[0037] (1) It eliminates the need for wavefront sensors, effectively reducing system complexity and avoiding the cumulative errors caused by wavefront sensor aberrations, thereby improving system accuracy. It is mainly applicable to real-time assembly and adjustment in the absence of wavefront sensors and has practical engineering value.

[0038] (2) Compared with other optimization algorithms that solve the secondary mirror misalignment by collecting spot images, this invention does not require multiple iterations. After the model parameters of the neural network are trained, the feature matrix neural network input to the multi-view spot image can quickly and accurately output the solved misalignment, effectively improving the system's assembly and adjustment efficiency. Moreover, the neural network has a strong nonlinear fitting ability, which solves the problem of small misalignment correction range and low accuracy of traditional methods, effectively improving the system's assembly and adjustment accuracy.

[0039] (3) Selecting multiple light spot images that are not on a straight line within the effective field of view can effectively avoid the situation where the offset of the secondary mirror and the point spread function cannot correspond one-to-one due to the coupling of the degrees of freedom of the secondary mirror.

[0040] (4) By extracting the moment features of multi-view spot images as neural network input, a logarithmic dataset is constructed, which greatly reduces training time cost and hardware requirements compared with directly training spot images and misalignment. Attached Figure Description

[0041] Figure 1 This is a flowchart of a telescope primary and secondary mirror calibration method based on the moment characteristics of light spot images.

[0042] Figure 2 This is a schematic diagram of the spot image under the condition of misalignment in the secondary mirror. Detailed Implementation

[0043] The specific implementation steps of the present invention will be further described below with reference to the accompanying drawings.

[0044] like Figure 1 As shown in the flowchart, the telescope primary and secondary mirror calibration method based on spot image moment features is mainly divided into two parts. Figure 1 The left part shows the preliminary work for aligning the primary and secondary mirrors of the telescope system, namely the training process of the neural network model weight parameters. The right part shows the actual alignment process of the primary and secondary mirrors of the system, which includes the following steps:

[0045] Step 1: Set up the telescope system:

[0046] The system includes a primary mirror, a secondary mirror, a six-degree-of-freedom platform for controlling the secondary mirror, and a CCD camera.

[0047] Step Two: Construct a mathematical model between the misalignment of each degree of freedom of the secondary mirror and the features of the multi-field-of-view spot images. Unbiased finite impulse response moments are used to characterize the grayscale variation features of the spot images in each field of view under different misalignment states of the secondary mirror. The modeling method employed is a fully connected neural network algorithm. First, a neural network dataset is constructed, which includes a training set and a test set, comprising:

[0048] Record the ideal spatial position of the secondary mirror when the telescope system is fully assembled and adjusted, as well as the multi-field light spot images within a reasonable range under this condition.

[0049] like Figure 2 As shown, the spot images acquired from several fields of view within the effective field of view when the secondary mirror has misalignment in each degree of freedom are represented by the point spread function.

[0050] Then, known degrees of freedom misalignment amounts are added to the secondary mirror, and CCD cameras are used to acquire multi-field spot images within a reasonable range under this state. Subsequently, unbiased finite impulse response moments are used to extract the grayscale change features of the multi-field spot images. The degrees of freedom misalignment amounts of the secondary mirror relative to the primary mirror and the corresponding feature matrices are used as a set of samples.

[0051] Repeat the above steps N times to obtain a dataset, and divide it into a training set and a test set according to a certain ratio;

[0052] Step 3: Train the neural network model:

[0053] A fully connected neural network model is selected, which includes an input layer, a hidden layer, and an output layer. The input is the feature matrix of the spot image in the multi-view field, and the output is the misalignment of each degree of freedom of the secondary mirror.

[0054] A certain proportion of the dataset is randomly selected as the training set to train the fully connected neural network. When the network converges, the entire network model training is completed. The remaining part of the dataset is used as the test set to verify the fitting ability of the fully connected neural network.

[0055] Step 4: Solve for the misalignment of the secondary mirror and align the primary and secondary mirrors of the telescope, including:

[0056] like Figure 1In the actual alignment process of the primary and secondary mirrors of the telescope system, a CCD camera is first used to acquire multi-field images of the light spot within a reasonable range of the system. Then, unbiased finite impulse response moments are used to extract the grayscale change features of the light spot images. This feature matrix is ​​input into a trained neural network model, and then the misalignment of each degree of freedom of the secondary mirror is output. The negative of this data is input into the six-degree-of-freedom platform of the actuator that controls the spatial position of the secondary mirror to guide the alignment of the primary and secondary mirrors. The system light spot image moment features after correcting the positional deviation of the secondary mirror are extracted and compared with the light spot image moment features under the ideal position of the secondary mirror. If the light spot image deviation is within the allowable error range, the alignment process of the primary and secondary mirrors is completed; otherwise, the above steps are repeated to form a closed-loop control.

[0057] After the neural network model parameters are trained, the neural network can quickly and accurately output the secondary mirror misalignment after inputting the feature matrix of the multi-field spot image acquired by the CCD camera. This effectively improves the system's assembly and adjustment efficiency and accuracy. It can be used for static assembly and adjustment before the telescope system is put into use, as well as for real-time dynamic correction of misalignment errors during the operation of the telescope system.

[0058] Furthermore, in step two, the spot image refers to the point spread function of the system, and multiple fields of view within a reasonable range refers to any multiple fields of view that are not on a straight line within the effective field of view. The number of fields of view n selected is greater than or equal to 5. Compared with the single spot imaging of the traditional system, this can effectively avoid the situation where the offset of the secondary mirror and the point spread function cannot correspond one-to-one due to the coupling of the degrees of freedom of the secondary mirror.

[0059] Furthermore, in step two, the use of unbiased finite impulse response moments to extract the grayscale variation features of the light spot images in each field of view under different misalignment states of the secondary mirror is because this discrete orthogonal moment, compared with the traditional continuous orthogonal moment, can avoid the error caused by approximate numerical integration during the calculation process. Moreover, the cumulative error increases as the order of the extracted moment increases. In addition, the polynomial calculation of this moment has no factorial coefficients, which can greatly improve the computational efficiency of the algorithm.

[0060] Furthermore, in step three, the model selected is a fully connected neural network. This algorithm is suitable for solving regression problems where the input is numerical and the output is also numerical, and the training time cost of this neural network model is relatively low.

[0061] Furthermore, in step four, in a practical telescope system, when faced with a new primary and secondary mirror misalignment system, a small sample is used for rapid training based on the weight parameters of the previously trained neural network model. This method can meet system requirements with relatively small datasets and time costs, and is easy to implement in engineering.

[0062] The above descriptions are merely implementation examples and preferred solutions of the present invention. However, the application scenarios and algorithms of the present invention are not limited to these. This method is not only applicable to optical systems with misalignment between primary and secondary mirrors, but also applicable to solving the lens misalignment of various complex systems. It should be noted that those skilled in the art can make several improvements, enhancements and optimizations based on the principles of the present invention, and these improvements, enhancements and optimizations should also be within the protection scope of the present invention.

Claims

1. A method for calibrating primary and secondary mirrors of a telescope based on the moment features of a light spot image, characterized in that, The method includes the following specific steps: Step 1: Set up the telescope system: The system includes a primary mirror, a secondary mirror, a six-DOF platform for controlling the secondary mirror, and a CCD camera; Step 2: Construct a mathematical model between the misalignment of each degree of freedom of the secondary mirror and the characteristics of the multi-field spot image. Use unbiased finite impulse response moments to characterize the gray-scale change characteristics of the spot images in each field of view under different misalignment states of the secondary mirror. The modeling approach uses a fully connected neural network algorithm. The first step is to construct a neural network dataset, which includes a training set and a test set, comprising: Step 2.1: Record the ideal spatial position of the secondary mirror when the telescope system is fully assembled and the spot images of multiple fields of view within a reasonable range under this state. Then, add known degrees of freedom misalignment to the secondary mirror and use a CCD camera to acquire spot images of multiple fields of view within a reasonable range under this state. Subsequently, use unbiased finite impulse response moments to extract the grayscale change features of the spot images of multiple fields of view. Take the degrees of freedom misalignment of the secondary mirror relative to the primary mirror and the corresponding feature matrix as a set of samples. Step 2.2: Repeat step 2.1 N times to obtain a dataset, and divide it into a training set and a test set according to a certain ratio; Step 3: Train the neural network model: Step 3.1: Select a fully connected neural network model. This fully connected neural network includes an input layer, a hidden layer, and an output layer. The input is the feature matrix of the light spot image in multiple fields of view, and the output is the misalignment of each degree of freedom of the secondary mirror. Step 3.2: Randomly select a portion of the dataset as the training set according to a certain proportion to train the fully connected neural network. When the network converges, the network model training is completed, and the remaining part of the dataset is used as the test set to verify the fitting ability of the fully connected neural network. Step 4: Solve for the misalignment of the secondary mirror and align the primary and secondary mirrors of the telescope, including: Step 4.1: During the alignment of the primary and secondary mirrors in the actual telescope system, firstly, a CCD camera is used to acquire multi-field images of light spots within a reasonable range of the system. Then, unbiased finite impulse response moments are used to extract the grayscale change features of the light spot images. The feature matrix is ​​input into the trained neural network model, and then the misalignment of each degree of freedom of the secondary mirror is output. The opposite of this data is input into the six-degree-of-freedom platform of the actuator that controls the spatial position of the secondary mirror to guide the alignment of the primary and secondary mirrors. Step 4.2: Extract the system spot image after correcting the secondary mirror position deviation again and compare it with the spot image under the ideal position of the secondary mirror. If the deviation of the compared spot images is within the allowable error range, the primary and secondary mirror alignment process is completed; otherwise, repeat step 4.

1.

2. The telescope primary and secondary mirror calibration method based on light spot image moment features according to claim 1, characterized in that, In step two, the spot image refers to the point spread function of the system, and multiple fields of view within a reasonable range refers to any multiple fields of view that are not on a straight line within the effective field of view. The number of fields of view n selected is greater than or equal to 5.

3. The telescope primary and secondary mirror calibration method based on light spot image moment features according to claim 1, characterized in that, In step 2.1, the known misalignment amount is added to the secondary mirror to add six degrees of freedom misalignment error, which refers to the eccentricity error and tilt error on the X, Y and Z axes.

4. The telescope primary and secondary mirror calibration method based on light spot image moment features according to claim 1, characterized in that, In step two, the gray-level variation characteristics of the spot images in each field of view under different misalignment states of the secondary mirror are characterized using the unbiased finite impulse response moment, i.e., the UFIR moment, which is calculated using the following formula: In the formula, n,m = 0, 1, 2, ..., N-1, the size of the light spot image is N×M, i,j are the two-dimensional coordinates of the light spot image in space, and their combination represents the position of each pixel. f(i,j) is the point spread function, representing the light spot image, where each pixel corresponds to a specific numerical value. Let represent the two-dimensional unbiased finite impulse response polynomials of the light spot image, respectively. Their recursive calculation formula is as follows: The coefficients are: They are respectively: In practical applications, the spot images of the p fields of view captured by the CCD camera are f1, f2, ... f p The k-th order gray-level variation features of each field-of-view spot image are extracted using unbiased finite impulse response moments, where U nm Let the subscripts n = 0, 1, ..., k; m = 0, 1, ..., k. The moment of the spot image for each field of view is a (k+1) × (k+1) feature matrix U, which is arranged row-wise into a 1 × [(k+1) × (k+1)] row vector. The expression for the moment of the spot image for p fields of view is: U=[U1,U2,...,U p ] (7) The expression is a 1×[p×(k+1)×(k+1)] row vector, whose specific value is the input value of a sample in the dataset.

5. The telescope primary and secondary mirror calibration method based on light spot image moment features according to claim 1, characterized in that, In step two, unbiased finite impulse response moments are used to extract the grayscale variation features of the light spot images in each field of view under different misalignment states of the secondary mirror.

6. The method for calibrating primary and secondary mirrors of a telescope based on the moment features of a light spot image according to claim 1, characterized in that, In step three, the model selected is a fully connected neural network.

7. The telescope primary and secondary mirror calibration method based on light spot image moment features according to claim 1, characterized in that, In step four, the actuator uses a six-degree-of-freedom displacement platform to control the six-degree-of-freedom spatial position of the secondary mirror relative to the primary mirror.

8. The telescope primary and secondary mirror calibration method based on light spot image moment features according to claim 1, characterized in that, In step four, during the actual calibration of the telescope's primary and secondary mirrors, a new dataset is constructed, and the previous network model weight parameters are used for retraining. Alternatively, a small sample is created based on the weight parameters of a previously trained neural network model and the idea of ​​transfer learning is used for rapid training.

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