A method for correcting offset errors of the slope response matrix of a deformable mirror

Abstract

The present invention discloses a method for correcting the offset error of the slope response matrix of a deformable mirror, belonging to the field of wavefront correction technology. By simultaneously driving multiple drivers to accurately measure the offset error of the deformable mirror relative to the original position of the system design, the measurement range and accuracy of the offset can be significantly expanded; breaking away from the conventional correction method of re-measuring the response matrix, the interpolation theory is introduced into the correction of the response matrix. The correction of the offset error of the deformable mirror response matrix can be achieved based only on the initial response matrix, thereby improving the closed-loop correction effect of the system. The present invention is not limited by the density and arrangement of the deformable mirror drivers. By measuring the offset error of the deformable mirror and correcting its response matrix, the stability of the system operation is guaranteed, the correction efficiency and accuracy of the system are improved, and it has the characteristics of simplicity and practicality.

Description

Technical Field

[0001] The present invention belongs to the field of wavefront correction technology, and specifically relates to a method for correcting the offset error of the slope response matrix of a deformable mirror, which is used to improve the accuracy and stability of the system wavefront correction. Background Art

[0002] In adaptive optics systems, a wavefront sensor monitors wavefront distortion caused by atmospheric turbulence and other factors in real time. A wavefront controller, through wavefront restoration and appropriate control algorithms, converts the wavefront distortion into a control signal. This signal is fed back to the deformable mirror in real time to adjust the deformable mirror to produce a conjugate surface shape, thereby correcting the distorted wavefront. The spatial detection capability of the wavefront sensor, the spatial fitting capability of the deformable mirror, and their spatial matching directly determine the correction performance of the entire system. In practical systems, the wavefront sensor and deformable mirror are optimally selected. Therefore, fully realizing the system's correction performance requires accurate measurement of the spatial matching relationship between the wavefront sensor subaperture position and the deformable mirror actuator position. In traditional PI control for adaptive optics, the controller input is strictly dependent on the deformable mirror's response matrix. This response matrix directly reflects the mapping between the wavefront sensor subaperture slope and the deformable mirror actuator voltage response. Therefore, it plays a crucial role in the correction performance of the adaptive optics system.

[0003] After the system remeasures the response matrix, the AO control platform enters a long-term running state. Affected by factors such as mechanical platform vibration and changes in environmental conditions, the wavefront sensor, deformable mirror and some optical elements in the intermediate optical path change, resulting in changes in the corresponding relationship between the wavefront sensor subaperture and the deformable mirror driver. That is, the position of the deformable mirror driver is offset relative to the position of the wavefront sensor subaperture. The response matrix cannot truly reflect the relationship between the driver and the subaperture slope, making it impossible for the deformable mirror to apply accurate correction. The deviation in wavefront correction affects the imaging quality. The error in the correction amount will cause feedback control deviation, making the system unable to converge to a stable state. The increase in the number of iterations and time reduces the correction efficiency.

[0004] In practical systems, closed-loop problems or pre-position offsets are typically detected using a single actuator. If offsets are present, the response matrix is ​​remeasured. However, this remeasurement method is time-consuming and labor-intensive, and requires a uniform near-field light source and no dynamic aberrations during measurement. Therefore, a simpler, more user-friendly method is urgently needed to correct offset errors in the slope response matrix of a deformable mirror. Summary of the Invention

[0005] In order to solve the above technical problems, the present invention provides a method for correcting the offset error of the slope response matrix of a deformable mirror, which solves the problem that the original response matrix cannot accurately aim at the slope response relationship between the deformable mirror driver and the wavefront sensor sub-aperture due to the displacement of the deformable mirror driver and wavefront sensor and the intermediate optical elements in the system optical path relative to the original design position of the system due to vibration of the mechanical platform, changes in environmental conditions, etc., and overcomes the shortcomings of the existing theoretical research on response matrix correction.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for correcting a deformable mirror slope response matrix offset error, comprising:

[0008] Step 1: Based on the parameters of the deformable mirror and Hartmann wavefront sensor, a set of centrosymmetric actuators are selected as the active actuators;

[0009] Step 2: Apply voltage to the actuator, and the wavefront sensor collects the corresponding wavefront slope. At the same time, the slope response matrix corresponding to different actuator offsets is calculated, and the slope template corresponding to the system is formulated;

[0010] Step 3: Calculate the similarity between the collected wavefront slope and the slope template, and based on the similarity, obtain the offset of all deformable mirror actuator positions relative to the original position in the current system;

[0011] Step 4: Based on the offset, a correction model of the deformable mirror slope response matrix offset error is established for the non-edge sub-aperture and the edge sub-aperture respectively.

[0012] The beneficial effects of the present invention are:

[0013] 1. The present invention measures the offset error based on the selection of the centrally symmetrical action driver, which effectively expands the offset error measurement range and improves the measurement accuracy and stability.

[0014] 2. The present invention proposes for the first time a response matrix offset error correction method based on interpolation. Compared with the re-measurement method, the present invention uses the initial response matrix to recalculate a new response matrix, which is fast, simple and easy to implement.

[0015] 3. The response matrix offset error correction method proposed in the present invention is applicable to deformable mirrors with different numbers, densities and arrangements of actuators and is universal. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a flow chart of a method for correcting a deformable mirror slope response matrix offset error according to the present invention;

[0017] Figure 2This is a comparison diagram of the positions of the deformable mirror actuator and the wavefront sensor before and after the offset;

[0018] Figure 3 is the phase interpolation relationship diagram;

[0019] Figure 4 This is a graph analyzing the accuracy of the offset calculation results;

[0020] Figure 5 This is a comparison chart before and after correction of the response matrix;

[0021] Figure 6 Comparison of the correction effects before and after response matrix correction when there is alignment offset error. DETAILED DESCRIPTION

[0022] The present invention will be further described below with reference to the accompanying drawings and examples.

[0023] The present invention provides a method for correcting offset errors in the slope response matrix of a deformable mirror. This method first applies voltage to a driver at a specific centrally symmetrical position. The offset of the driver relative to the original position is measured using slope response matrix data. Based on the offset, the original response matrix data is used to interpolate phase points and recalculate the slope response matrix of the driver corresponding to the current state. When measuring the offset, multiple drivers with centrally symmetrical positions are selected and a unit voltage is applied simultaneously, effectively expanding the offset measurement range and accuracy. When interpolating phase points in the original slope response matrix, the slope response matrix is ​​recalculated using interpolation theory at non-edge subapertures, and theoretical data is used to fill in edge subapertures, effectively ensuring the accuracy and completeness of the response matrix calculation.

[0024] In this embodiment, the deformable mirror actuators are arranged in a square pattern, and the number of actuators is , the number of valid drives is , the drive spacing is , the number of subapertures of the Hartmann sensor is , the subaperture size is , the number of near-field sampling points of a single aperture is , the CCD pixel size is The alignment offset of the deformable mirror relative to the wavefront sensor is 1.3 sub-aperture sizes to the right in the X direction and 2 sub-aperture sizes downward in the Y direction. The sub-aperture sizes are expressed as .

[0025] Figure 1 This is a flow chart of a method for repairing alignment errors of a deformable mirror response matrix based on interpolation according to the present invention, which specifically includes the following steps:

[0026] Step 1: Based on the parameters of the deformable mirror and Hartmann wavefront sensor, a set of centrosymmetric actuators are selected as the active actuators; Figure 2 A comparison of the positions of the deformable mirror actuators (five selected here) and the wavefront sensor before and after the offset is shown, with the selected active actuator positions bolded.

[0027] Preferably, the selection of the active actuators is related to the number and density of the actuators in the deformable mirror and the parameters of the wavefront sensor, but the selection is required to be applicable to any actuator arrangement, and the number of active actuators is at least 4;

[0028] Step 2: Apply voltage to the actuators at the same time, and the wavefront sensor collects the corresponding wavefront slope. At the same time, the slope response matrix corresponding to different offsets of the actuators is calculated, and a system slope template is formulated. Apply the same unit voltage to the actuators at the same time, and the wavefront sensor collects the corresponding wavefront slope. , and calculate the slope influence matrix corresponding to different offsets , where the offset They represent the offset of the deformable mirror actuator relative to the original position in the X and Y directions, respectively, and are respectively set from -2.3 sub-aperture sizes to 2.3 sub-aperture sizes (i.e. -2.3 to 2.3 ) The interval within the range is 0.1 47 data, formulate the slope template corresponding to the system ;

[0029] Step 3: Calculate the similarity between the actual acquired wavefront slope and the system slope template using the minimum error method, correlation coefficient method, or other known algorithms, and calculate the offset of all actuator positions of the deformable mirror in the current system relative to the original position based on the maximum similarity coefficient;

[0030] Here, according to the minimum error method, the similarity coefficient between the actual acquired wavefront slope and the slope vector corresponding to different offsets in the slope template is expressed as:

[0031] ,

[0032] When the similarity coefficient At maximum, The corresponding offset is the offset of the deformable mirror actuator relative to the original position in the current system:

[0033] ,

[0034] In this embodiment, it is calculated that the deformable mirror actuator in the current system is offset to the right by 1.3 sub-aperture sizes relative to the original position in the X direction, and is offset downward by 2 sub-aperture sizes in the Y direction;

[0035] Step 4: Based on the offset, correction models for the offset error of the deformable mirror slope response matrix are established for the non-edge subapertures and the edge subapertures, respectively. After the offset of the deformable mirror actuator position relative to the original position is known, two layers of subapertures within the outer edge range of the target surface are selected as edge subapertures, and correction models for the offset error of the deformable mirror slope response matrix are established for the non-edge subapertures and the edge subapertures, respectively.

[0036] Step 4.1: For the response slope data corresponding to the non-edge sub-aperture, according to the offset, use the data corresponding to the slope response matrix when not offset , perform bilinear interpolation on the phase points, the bilinear interpolation relationship is as follows Figure 3 As shown in the figure, by deriving the functional relationship between each sub-aperture and its surrounding sub-apertures, the deformable mirror driver response matrix corresponding to the current state is recalculated. The relationship function between the non-edge sub-aperture response slope data and the offset is:

[0037] ,

[0038] in, Respectively represent the offset of the deformable mirror actuator relative to the original position in the X and Y directions, They represent the response slope data of the subaperture in the x and y directions in the rth row and cth column after the offset, They represent the response slope data of the subaperture in the x and y directions in the rth row and cth column when not offset. By changing the matrix, the data of different subaperture positions of the response matrix corresponding to the non-edge subaperture can be obtained;

[0039] The bilinear interpolation method may also be replaced by any of the methods such as nonlinear interpolation and function approximation interpolation.

[0040] Step 4.2: For the response slope data corresponding to the edge sub-aperture, use the theoretical data calculated by the deformable mirror shape response function to complete the completion of the slope response matrix of the edge sub-aperture. The calculation process is as follows:

[0041] ,

[0042] in, represents the surface shape influence function of the nth actuator of the deformable mirror, and It represents the partial derivatives of the nth driver surface influence function in the x and y directions, d represents the driver spacing, and ln represents the logarithm. Indicates the driver cross-link value, represents the voltage value applied to the nth actuator of the deformable mirror, represents the normalized area of ​​the mth subaperture, They represent the slope data of the response of the mth sub-aperture after the nth driver applies a unit voltage, and x and y represent the pixel position coordinates in the X and Y directions of the mth sub-aperture, respectively. Respectively represent the position coordinates of the nth driver in the X and Y directions.

[0043] Without loss of generality, methods for completing the response slope data corresponding to the edge sub-aperture include any one of the methods such as direct calculation of the response matrix, repeated boundary re-interpolation method, edge extension method, etc.

[0044] Figure 2 A comparison of the positions of the deformable mirror actuator and the wavefront sensor before and after the offset is given. It can be seen that when there is a relative offset error, the position of the sub-aperture acted upon by the actuator changes significantly. Figure 4 Comparison of the alignment error measurement accuracy of the conventional method (left) and this method (right) using multiple actuators to measure alignment errors with single responses when the offset in both the X and Y directions is -2.3 to 2.3 sub-aperture sizes. It can be seen that the measurement accuracy of this method is 100%. Compared with the conventional method, the calculation accuracy and calculation range of this method have been improved. Figure 5 The numerical comparison of the response function before and after correction is given. The existence of the offset directly affects the overall numerical distribution of the response function. Figure 6 When the X direction is offset to the right by 1.3 sub-aperture sizes and the Y direction is offset downward by 2 sub-aperture sizes, the initial response matrix used to correct the far-field Sr of the control module is 0.0560, and the correction effect is very poor. The control voltage is erratic and the slope does not converge. After the correction, the response matrix is ​​used to correct the far-field Sr of the control module to 0.9365. The far-field Sr is increased by about 15.7 times, and the correction effect is significantly improved. The control voltage is stable at about -4 to 6V, and the slope converges between -0.5 and 0.5.

[0045] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above are only specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for correcting the offset error of a deformable mirror slope response matrix, characterized in that: include: Step 1: Based on the parameters of the deformable mirror and Hartmann wavefront sensor, a set of centrosymmetric actuators are selected as the active actuators; Step 2: Apply voltage to the actuator, and the wavefront sensor collects the corresponding wavefront slope. At the same time, the slope response matrix corresponding to different actuator offsets is calculated, and the slope template corresponding to the system is formulated; Step 3: Calculate the similarity between the collected wavefront slope and the slope template, and based on the similarity, obtain the offset of all deformable mirror actuator positions relative to the original position in the current system; Step 4: Based on the offset, a correction model for the offset error of the deformable mirror slope response matrix is ​​established for the non-edge sub-aperture and the edge sub-aperture, including: Step 4.1: For the slope response matrix corresponding to the non-edge sub-aperture, interpolate the phase points using the original slope response matrix data according to the offset. By deriving the functional relationship between each sub-aperture and its surrounding sub-apertures, recalculate the slope response matrix of the deformable mirror actuator corresponding to the current state; Step 4.2: For the slope response matrix corresponding to the edge sub-aperture, use the theoretical data calculated by the deformable mirror shape response function to complete the completion of the slope response matrix of the edge sub-aperture.

2. A method for correcting a deformable mirror slope response matrix offset error according to claim 1, characterized in that: In step 1, the number of active actuators is at least 4, and the selection thereof is related to the number and density of actuators in the deformable mirror and the parameters of the wavefront sensor.

3. The method for correcting the slope response matrix offset error of a deformable mirror according to claim 1, wherein: In step 2, the same unit voltage is applied to the active drivers simultaneously.

4. The method for correcting the offset error of the slope response matrix of a deformable mirror according to claim 1, wherein: In step 3, calculating the similarity between the collected wavefront slope and the slope template includes calculating the similarity coefficient between the collected wavefront slope and the slope template using any one of a minimum error method and a correlation coefficient method.

5. A method for correcting a deformable mirror slope response matrix offset error according to claim 4, characterized in that: When the similarity coefficient is the largest, the offset corresponding to the slope in the slope template is the offset of all deformable mirror actuators in the current system relative to the original position.

6. The method for correcting the offset error of the slope response matrix of a deformable mirror according to claim 1, characterized in that: In step 4.1, the interpolation method includes any one of linear interpolation, nonlinear interpolation, and function approximation interpolation methods.

7. The method for correcting the offset error of the slope response matrix of a deformable mirror according to claim 1, characterized in that: In step 4.2, the method for completing the response slope data corresponding to the edge sub-aperture includes any one of a direct calculation method of the response matrix, a repeated boundary re-interpolation method, and an edge extension method.

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