Method for correcting offset error of slope response matrix of deformable mirror

Abstract

The invention discloses a method for correcting an offset error of a slope response matrix of a deformable mirror, and belongs to the technical field of wavefront correction. By simultaneously driving a plurality of drivers to accurately measure the offset error of the deformable mirror relative to the system design original position, the measurement range and precision of the offset can be obviously expanded; the conventional correction method of re-measuring the response matrix is broken, the interpolation theory is introduced into correction of the response matrix, correction of the deformation mirror response matrix about the offset error can be realized only according to the initial response matrix, and the closed-loop correction effect of the system is improved. The method is not limited by the density and arrangement of the deformable mirror drivers, the stability of system operation is ensured by measuring the offset error of the deformable mirror and correcting the response matrix of the deformable mirror, the correction efficiency and precision of the system are improved, and the method has the advantages of being simple and practical.

Description

Technical Field

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

[0002] In an adaptive optical system, a wavefront sensor monitors in real time the wavefront distortion caused by reasons such as atmospheric turbulence. The wavefront controller converts the wavefront distortion into a control signal through wavefront restoration and an appropriate control algorithm, and feeds it back to the deformable mirror in real time to adjust it to generate a surface shape conjugate to the wavefront distortion, so as to correct the distorted wavefront in real time. Among them, the spatial detection ability of the wavefront sensor, the spatial fitting ability of the deformable mirror, and their spatial matching relationship directly determine the correction performance of the entire system. In an actual system, the wavefront sensor and the deformable mirror are optimized and selected. Therefore, to fully exert the correction performance of the system, it is necessary to accurately measure the spatial matching relationship between the sub-aperture position of the wavefront sensor and the position of the deformable mirror actuator. In the traditional PI control of adaptive optics, the input of the controller strictly depends on the response matrix of the deformable mirror. The response matrix directly reflects the mapping relationship between the slope of the sub-aperture of the wavefront sensor and the voltage response of the deformable mirror actuator. Therefore, it plays an important role in the correction performance of the adaptive optical system.

[0003] After the system re-measures the response matrix, the AO control platform enters a long-term operation state. Affected by factors such as mechanical platform vibration and environmental condition changes, the wavefront sensor, the deformable mirror, and some optical elements in the intermediate optical path change, resulting in a change in the corresponding relationship between the sub-aperture of the wavefront sensor and the deformable mirror actuator, that is, the position of the deformable mirror actuator shifts relative to the sub-aperture position of the wavefront sensor. The response matrix cannot truly reflect the action relationship between the actuator and the sub-aperture slope, making it impossible for the deformable mirror to apply an accurate correction amount. The wavefront correction has a deviation, which affects the imaging quality. The correction amount error will cause a feedback control deviation, making the system unable to converge to a stable state, increasing the number of iterations and time, and reducing the correction efficiency.

[0004] In an actual system, generally, when a problem occurs in the closed loop or the position offset is detected in advance using a single actuator. If there is an offset, the response matrix is re-measured. However, the re-measurement method is time-consuming and laborious, and at the same time requires a uniform near-field light source and no dynamic aberration disturbance during measurement. Therefore, there is an urgent need for a method with simple operation, low requirements, and stronger applicability to realize the correction of the offset error of the slope response matrix of the deformable mirror. Summary of the Invention

[0005] 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 target the slope response relationship between the deformable mirror driver and the wavefront sensor sub-aperture due to the offset of the deformable mirror driver, the wavefront sensor, and the optical elements in the intermediate optical path relative to the original position of the system design caused by mechanical platform vibration, environmental condition changes, etc., and overcomes the deficiencies in 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 the offset error of the slope response matrix of a deformable mirror, comprising:

[0008] Step 1: Select a set of centrally symmetric drivers as the acting drivers according to the parameters of the deformable mirror and the Hartmann wavefront sensor;

[0009] Step 2: Apply voltage to the acting drivers, the wavefront sensor collects the corresponding wavefront slopes, and at the same time calculates the slope response matrix corresponding to different offsets of the drivers, and formulates the corresponding slope template of the system;

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

[0011] Step 4: Establish correction models for the offset error of the slope response matrix of the deformable mirror for non-edge sub-apertures and edge sub-apertures respectively based on the offset.

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

[0013] 1. The present invention measures the offset error based on the selection of centrally symmetric acting drivers, effectively expanding the measurement range of the offset error and improving the measurement accuracy and stability.

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

[0015] 3. The method for correcting the offset error of the response matrix proposed by the present invention is applicable to deformable mirrors with different numbers, densities and arrangements of drivers, and has universality. Description of the Drawings

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

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

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

[0019] Figure 4 It is an analysis diagram of the accuracy of the offset calculation result;

[0020] Figure 5 It is a comparison diagram before and after the response matrix is corrected;

[0021] Figure 6 It is a comparison diagram of the correction effects before and after the response matrix is corrected when there is an alignment offset error. Specific implementation mode

[0022] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0023] The present invention provides a method for correcting the offset error of the slope response matrix of a deformable mirror. This method first applies a voltage to the drivers at specific centrosymmetric positions, measures the offset of the deformable mirror driver relative to the original position at this time through the slope response matrix data, and according to the offset, uses the original response matrix data to interpolate the phase points and recalculate the slope response matrix of the deformable mirror driver corresponding to the current state. When measuring the offset, multiple drivers with a centrosymmetric position relationship are selected to apply a unit voltage simultaneously, which can effectively expand the measurement range and accuracy of the offset. When interpolating the phase points of the original slope response matrix, the non-edge sub-apertures use the interpolation theory to recalculate the slope response matrix, and the edge sub-apertures are filled with theoretical data, effectively ensuring the accuracy and integrity of the response matrix calculation.

[0024] In this embodiment, the deformable mirror drivers are arranged in a square pattern, and the number of drivers is , the number of effective drivers is , the driver spacing is , the number of sub-apertures of the Hartmann sensor is , the sub-aperture size is , the number of near-field sampling points per single sub-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 down in the Y direction, and the sub-aperture size is represented as .

[0025] Figure 1 It is a flowchart of a method for repairing the alignment error of the deformable mirror response matrix based on interpolation according to the present invention, specifically including the following steps:

[0026] Step 1: Select a group of centrosymmetric drivers as the acting drivers according to the parameters of the deformable mirror and the Hartmann wavefront sensor;Figure 2 A comparison diagram of the positions of deformable mirror drivers (5 are selected here) before and after the offset of the wavefront sensor is shown, where the positions of the selected active drivers are in bold;

[0027] Preferably, the selection of the active drivers is related to the number, density of the drivers in the deformable mirror, and the parameters of the wavefront sensor. However, the selection requirements are applicable to any driver arrangement, and the minimum number of active drivers is 4;

[0028] Step 2: Apply voltages to the active drivers simultaneously. The wavefront sensor collects the corresponding wavefront slopes, and at the same time, calculate the slope response matrix corresponding to different offsets of the active drivers, and formulate a system slope template; apply the same unit voltage to the active drivers simultaneously, and the wavefront sensor collects the corresponding wavefront slopes and calculate the slope influence matrix corresponding to different offsets , where the offset respectively represent the offsets of the deformable mirror drivers in the X and Y directions relative to the original positions. Here, the values are taken from -2.3 sub-aperture sizes to 2.3 sub-aperture sizes (i.e., -2.3 to 2.3 ), and 47 data with a spacing of 0.1 in the range are taken to formulate the corresponding slope template of the system ;

[0029] Step 3: Use the minimum error method or the correlation coefficient method or other known algorithms to calculate the similarity between the actually collected wavefront slopes and the system slope template, and calculate the offsets of all the drivers of the deformable mirror in the current system relative to the original positions according to the maximum similarity coefficient;

[0030] Here, according to the minimum error method, the similarity coefficient between the actually collected wavefront slopes and the slope vectors corresponding to different offsets in the slope template is expressed as:

[0031] ,

[0032] When the similarity coefficient is the largest, the corresponding offset is the offset of the deformable mirror drivers in the current system relative to the original positions:

[0033] ,

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

[0035] Step 4: Based on the offset, establish correction models for the slope response matrix offset errors of non-edge sub-apertures and edge sub-apertures respectively; after knowing the offset of the deformable mirror driver position relative to the original position, select two layers of sub-apertures within the outer edge range of the target surface as edge sub-apertures, and establish correction models for the slope response matrix offset errors of non-edge sub-apertures and edge sub-apertures respectively;

[0036] Step 4.1: For the response slope data corresponding to non-edge sub-apertures, according to the offset, use the data corresponding to the slope response matrix when there is no offset , perform bilinear interpolation on the phase points. The bilinear interpolation relationship is as Figure 3 shown. By deriving the functional relationship between each sub-aperture and its surrounding sub-apertures, recalculate the deformable mirror driver response matrix corresponding to the current state. The function relationship between the non-edge sub-aperture response slope data and the offset is:

[0037] ,

[0038] where respectively represent the offsets of the deformable mirror driver in the X and Y directions relative to the original position, respectively represent the response slope data of the r-th row and c-th column sub-aperture in the X and Y directions after offset, respectively represent the response slope data of the r-th row and c-th column sub-aperture in the X and Y directions when there is no offset. Through matrix transformation, the data of different sub-aperture positions corresponding to the response matrix of non-edge sub-apertures can be obtained;

[0039] Among them, the bilinear interpolation method can also be replaced by any one of non-linear interpolation, function approximation interpolation and other methods.

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

[0041] ,

[0042] where represents the surface shape influence function of the n-th driver of the deformable mirror, and represent the partial derivatives of the n-th driver surface shape influence function in the x and y directions. d represents the driver spacing, ln represents taking the logarithm, represents the driver cross-coupling value, represents the voltage value applied to the n-th driver of the deformable mirror, represents the normalized area of the m-th sub-aperture, respectively represent the slope data of the response of the m-th sub-aperture after the n-th driver applies a unit voltage, where x and y respectively represent the pixel position coordinates in the X and Y directions in the m-th sub-aperture. respectively represent the position coordinates of the n-th driver in the X and Y directions.

[0043] Without loss of generality, the method for filling the response slope data corresponding to the edge sub-apertures includes any one of the direct calculation method of the response matrix, the repeated boundary re-interpolation method, the edge expansion method, etc.

[0044] Figure 2 The figure showing the comparison of the positions of the deformable mirror driver before and after the offset with the wavefront sensor is given. It can be seen that when there is a relative offset error, the position of the sub-aperture affected by the driver changes significantly. Figure 4 It is the comparison chart of the alignment error measurement accuracy of the traditional method (left figure) and the present method (right figure) when the offset amounts in the X and Y directions are both from -2.3 to 2.3 sub-aperture sizes, and multiple drivers are used to measure the alignment error separately and once. It can be seen that the measurement accuracy of the present method is 100% in all cases. Compared with the traditional method, the calculation accuracy and calculation range of this method have been improved. Figure 5 The numerical comparison before and after the correction of the response function is given. The existence of the offset directly affects the overall numerical distribution of the response function. Figure 6 When the offset in the X direction is 1.3 sub-aperture sizes to the right and the offset in the Y direction is 2 sub-aperture sizes downward, for the initial response matrix used for the correction of the control module, the far field Sr is 0.0560, and the correction effect is very poor, the control voltage is erratic, and the slope does not converge. After the corrected response matrix is used for the correction of the control module, the far field Sr is 0.9365, and the far field Sr has increased by about 15.7 times. The correction effect has been 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 elaborate on the purpose, technical solution and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not used to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for correcting the slope response matrix offset error of a deformable mirror, characterized in that: include: Step 1: According to the deformable mirror and Hartmann wavefront sensor parameters, a set of centrosymmetric actuators are selected as the action 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 offsets of the actuator 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 obtain the offset of all deformable mirror actuator positions relative to the original position in the current system based on the similarity; 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.

2. A method for correcting the slope response matrix offset error of a deformable mirror 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 the actuators in the deformable mirror and the parameters of the wavefront sensor.

3. A method for correcting the slope response matrix offset error of a deformable mirror according to claim 1, characterized in that: In the step 2, the same unit voltage is applied to the action drivers simultaneously.

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

5. A method for correcting the slope response matrix offset error of a deformable mirror 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. A method for correcting the slope response matrix offset error of a deformable mirror according to claim 1, characterized in that: The step 4 comprises: 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, and recalculate the slope response matrix of the deformable mirror driver corresponding to the current state by deriving the functional relationship between each sub-aperture and its surrounding sub-apertures; 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.

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

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

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