Adaptive optics control method without wavefront sensing based on moment estimation

Abstract

The present application relates to a wavefront sensing-free adaptive optical control method based on moment estimation, comprising the following steps: Step 1: construct a wavefront sensing-free adaptive optical system; Step 2: initialize the deformable mirror control voltage V, select the average radius MR as the performance index, and start iteration; Step 3: generate a random disturbance voltage δU, perform bidirectional disturbance on the deformable mirror control voltage V, and obtain the performance index change δJ; Step 4: calculate the corrected first-order moment estimate and the corrected second-order moment estimate according to the gradient descent term of the random parallel gradient descent algorithm, and update the control voltage; Step 5: determine whether the iteration meets the convergence condition. If so, the iteration ends, and the control voltage of the last iteration is the final correction voltage. If not, repeat steps 3 to 5. The method extracts the gradient descent term in SPGD and performs exponentially weighted moving average on the gradient descent term and the square of the gradient descent term, respectively, so as to achieve high-precision and fast wavefront correction.

Description

Technical Field

[0001] The invention relates to a wavefront-free correction method, and in particular to a wavefront-free sensing adaptive optical control method based on moment estimation. Background Art

[0002] As an active aberration correction technology in optics, wavefront sensorless adaptive optics (WFSless AO) can compensate for static and dynamic aberrations of optical systems in real time. The system has a simple structure, small size and low cost. WFSless AO control methods are mainly divided into blind search optimization algorithms and model-based control algorithms. Blind search optimization algorithms rely heavily on search space and optimization direction, have slow convergence speed and are prone to fall into local extreme values. See [Jiang Wenhan. Review of the development of adaptive optics [J]. Optoelectronic Engineering, 2018, 45(3)]. The model-based control algorithm establishes an approximate linear relationship from the second-order moment of far-field light intensity distribution to the square of the wavefront aberration gradient, but it requires multiple CCD sampling in each iteration, and the convergence speed improvement is extremely limited. See [Huang LH, Rao C H. Wavefront sensorless adaptive optics: a general model-based approach [J]. Optics Express, 2011, 19(1)]. Therefore, under the premise of ensuring the simplicity of the WFSless AO system structure, it is an urgent problem to improve the convergence speed of the WFSless AO control method and avoid the control method falling into local extreme values ​​after multiple iterations. Summary of the invention

[0003] The technical problem to be solved by the present invention is to overcome the problem that the WFSless AO control method has a slow convergence speed and the iteration is prone to fall into local extreme values ​​resulting in low convergence accuracy, and to achieve high-precision and fast wavefront restoration.

[0004] To achieve the above objectives, this application provides the following technical solutions:

[0005] The embodiment of the present application provides a wavefront sensing-free adaptive optics control method based on moment estimation, comprising the following steps:

[0006] Step 1: Build an adaptive optical system without wavefront sensing;

[0007] Step 2: Initialize the deformable mirror control voltage V, select the average radius MR as the performance indicator, and start iteration;

[0008] Step 3: Generate a random disturbance voltage δU, perform bidirectional disturbance on the deformable mirror control voltage V, and obtain the performance index change δJ;

[0009] Step 4: Calculate the corrected first-order moment estimate and the corrected second-order moment estimate according to the gradient descent term of the stochastic parallel gradient descent algorithm, and update the control voltage;

[0010] Step 5: Determine whether the iteration meets the convergence condition. If so, the iteration ends and the control voltage of the last iteration is the final correction voltage. If not, repeat steps 3 to 5.

[0011] The deformable mirror control voltage V in step 2 is an M-dimensional vector, where M is the number of deformable mirror units. The working principle of the deformable mirror is as follows:

[0012]

[0013]

[0014] Where Φ(x,y) is the incident wavefront, S i (x,y) is the influence function of the i-th deformable mirror unit, M is the number of deformable mirror units, v i is the control voltage of the i-th deformable mirror unit, e(x,y) is the wavefront fitting residual, (x i ,y i ) is the position of the i-th deformable mirror unit, d is the actuator spacing, p is the Gaussian function index, and q is the actuator cross-connection value.

[0015] The calculation formula of the mean radius MR in step 2 is as follows:

[0016]

[0017] Where I(x,y) is the far-field light intensity distribution, (x c ,y c ) are the centroid coordinates.

[0018] The random disturbance voltage δU in step 3 is an M-dimensional vector, where M is the number of deformable mirror units, and each component of δU is a set of independent and identically Bernoulli-distributed random variables.

[0019] The random disturbance voltage δJ in step 3 is expressed as δJ in the kth iteration (k) The calculation method is as follows:

[0020] δJ (k) =J + -J - = J(V (k-1) +δU (k ))-J(V (k-1) -δU (k )) (4)

[0021] In the formula, J + is the performance index under positive disturbance, J- is the performance index for reverse disturbance, δU (k) is the random perturbation voltage of the kth iteration, V (k-1) is the control voltage of the deformable mirror at the last iteration, i.e., the k-1th iteration, V (0) is the initial deformable mirror control voltage.

[0022] The modified first-order moment estimation and the modified second-order moment estimation in step 4 respectively perform exponentially weighted moving average on the gradient descent term and the square of the gradient descent term of the gradient descent algorithm, and modify their coefficients. The calculation methods of the modified first-order moment estimation and the modified second-order moment estimation are as follows:

[0023] For a sequence {x1,x2,…,x n},make

[0024]

[0025] Wherein, weight p is a real number and p∈(0,1); {m1,m2,…,m n} is the sequence {x1,x2,…,x n}The new sequence obtained after exponential weighted moving average, the i-th item m of the new sequence i From the previous term m in the sequence i-1 and x i So, m i with {x1,x2,…,x i There is the following relationship

[0026]

[0027] In the formula, m i is a sequence {x1,x2,…,x n}Exponentially weighted moving average of the first i items; x j The corresponding weight is (1-p)p i-j , j = 1, 2…i, the closer j is to i, the greater the weight, and vice versa, the smaller the weight. n The sum of the weights of the first i items is

[0028]

[0029] According to formula (5), the gradient descent term δUδJ of the gradient descent algorithm is subjected to exponential weighted moving average to obtain the first-order moment estimate F. The first-order moment estimate F of the kth iteration is (k) The expression is

[0030] F (k) =β1F (k-1) +(1-β1)δU (k) δJ(k) (8)

[0031] In the formula, F (k) is the first-order moment estimate at the kth iteration, β1 is the first-order moment estimate weight coefficient, δU (k) δJ (k) is the gradient descent term of the kth iteration, which is an M-dimensional vector, where M is the number of deformable mirror units. From formula (7), we know that F (k) The sum of weights is not equal to 1, so weight correction is required:

[0032]

[0033] When the performance index iterates to the vicinity of the extreme value, if the step size is not constrained, the performance index may oscillate near the extreme value and fail to converge to the global extreme value. The second-order moment estimate S is introduced to constrain the step size. In the kth iteration, the second-order moment estimate S (k) The expression and weight correction are as follows:

[0034]

[0035] In the formula, β2 is the weight coefficient of the second-order moment estimation, To estimate the second-order moment after weight correction; [δU (k) δJ (k) ] 2 Indicates the relationship between δU (k) δJ (k) Each component in S is squared, which is also an M-dimensional vector. The second formula in equation (10) represents the (k) Constraints are imposed to ensure that the second-order moment estimate continues to increase as the number of iterations increases. In the kth iteration, the step size update formula is as follows:

[0036]

[0037] In the formula, ε is a small positive real number, usually 10 -8 ;

[0038] In summary, the update formula of the deformable mirror control voltage at the kth iteration is as follows:

[0039]

[0040] The convergence condition in step 5 is, under laboratory conditions, when the peak Strehl ratio P SR When it is greater than 0.8, the aberration is generally considered to be fully corrected, and the peak Strehl ratio P SR The formula is as follows:

[0041]

[0042] In the formula, I max,real Indicates the far-field peak light intensity when the actual wavefront is incident; I max,ideal Represents the far-field peak light intensity when an ideal wavefront is incident.

[0043] Compared with the prior art, the beneficial effect of the present invention is that under the premise of ensuring the simplicity of the WFSless AO system structure and the convergence accuracy, the convergence speed of the WFSless AO control method is greatly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments of the present application will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0045] Figure 1 It is the work flow chart of the present invention;

[0046] Figure 2 Schematic diagram of adaptive optical system without wavefront sensing;

[0047] Figure 3 This is a schematic diagram of the working principle of the first-order moment estimation;

[0048] Figure 4 Schematic diagram of the impact of first-order moment estimation on performance indicators;

[0049] Figure 5 Schematic diagram of the impact of first-order moment estimation and second-order moment estimation on performance indicators.

[0050] Figure 6 The curves showing the change of the average radius after thousands of iterations are (a) when D / r0=5 and (b) when D / r0=10.

[0051] Figure 7 The peak Strehl ratio P after thousands of iterations (a) when D / r0 = 5 and (b) when D / r0 = 10 SR The change curve. DETAILED DESCRIPTION

[0052] The technical solutions in the embodiments of the present application will be described below in conjunction with the drawings in the embodiments of the present application. It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in the subsequent drawings.

[0053] The terms "comprises," "comprising," or any other variation thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus that includes the element.

[0054] The present invention provides a wavefront sensing-free adaptive optical control method based on moment estimation, as shown in FIG1 . Figure 1 This is the workflow diagram of the adaptive optical control method without wavefront sensing based on moment estimation. The specific implementation process is as follows:

[0055] Step 1: Build the WFSless AO system. Figure 2 Schematic diagram of the WFSless AO system. Compared with conventional adaptive optical systems, the WFSless AO system only has a wavefront controller (i.e., control method) and a wavefront corrector (i.e., deformable mirror), but no wavefront detector. The WFSless AO control method indirectly obtains wavefront aberration information by extracting the far-field light intensity distribution through CCD, and the system structure is simple and easy to implement.

[0056] Step 2: Initialize the deformable mirror control voltage V, select the mean radius (MR) as the performance indicator, and start iteration.

[0057] Step 3: Generate a random disturbance voltage δU, perform bidirectional disturbance on the deformable mirror control voltage V, and obtain the performance index change δJ. δU is a set of independent and identically Bernoulli distributed random variables.

[0058] Step 4: Based on the gradient descent term of the gradient descent algorithm SPGD, the corrected first-order moment estimate and the corrected second-order moment estimate are calculated and the control voltage is updated. Figure 3 The working principle of the first-order moment estimation is given. Figure 3 The solid line in the middle is the gradient descent with the first-order moment estimation, and the dotted line is the gradient descent without the first-order moment estimation. It can be found that the first-order moment estimation reduces the oscillation of the performance index, thereby obtaining a larger gradient descent amount. Figure 4 shows the impact of the first-order moment estimation on the performance index. It can be found that the first-order moment estimation decreases faster at the beginning of the iteration, but when the iteration converges quickly, due to the large step size, both the first-order moment estimation and the non-first-order moment estimation converge to the local extreme value, so the second-order moment estimation is introduced to constrain the step size. Figure 5 The influence of first-order moment estimation and second-order moment estimation on performance indicators is given. It can be found that after introducing the second-order moment estimation, the iteration converges to the global extreme value.

[0059] Step 5: Determine whether the iteration meets the convergence condition. If so, the iteration ends, and the control voltage of the last iteration is the final correction voltage. If not, repeat steps 3 to 5. The convergence condition can be selected as the peak Strehl ratio greater than 0.8, or other convergence conditions can be selected, such as the bucket rate greater than 0.8.

[0060] The deformable mirror control voltage V in step 2 is an M-dimensional vector, where M is the number of deformable mirror units. The working principle of the deformable mirror is as follows:

[0061]

[0062]

[0063] Where Φ(x,y) is the incident wavefront, S i (x,y) is the influence function of the i-th deformable mirror unit, M is the number of deformable mirror units, v i is the control voltage of the i-th deformable mirror unit, e(x,y) is the wavefront fitting residual, (x i ,y i ) is the position of the i-th deformable mirror unit, d is the actuator spacing, p is the Gaussian function index, and q is the actuator cross-connection value.

[0064] The calculation formula of the mean radius MR in step 2 is as follows:

[0065]

[0066] Where I(x,y) is the far-field light intensity distribution, (x c ,y c ) are the centroid coordinates.

[0067] The random disturbance voltage δU in step 3 is an M-dimensional vector, where M is the number of deformable mirror units, and each component of δU is a set of independent and identically Bernoulli-distributed random variables.

[0068] The random disturbance voltage δJ in step 3 is expressed as δJ in the kth iteration (k) The calculation method is as follows:

[0069] δJ (k) =J + -J - = J(V (k-1) +δU (k) )-J(V (k-1) -δU (k) ) (4)

[0070] In the formula, J + is the performance index under positive disturbance, J - is the performance index for reverse disturbance, δU(k) is the random perturbation voltage of the kth iteration, V (k-1) is the control voltage of the deformable mirror at the last iteration, i.e., the k-1th iteration, V (0) is the initial deformable mirror control voltage.

[0071] The modified first-order moment estimation and the modified second-order moment estimation in step 4 respectively perform exponentially weighted moving average on the gradient descent term and the square of the gradient descent term of the gradient descent algorithm, and modify their coefficients. The calculation methods of the modified first-order moment estimation and the modified second-order moment estimation are as follows:

[0072] For a sequence {x1,x2,…,x n},make

[0073]

[0074] Wherein, weight p is a real number and p∈(0,1); {m1,m2,…,m n} is the sequence {x1,x2,…,x n}The new sequence obtained after exponential weighted moving average, the i-th item m of the new sequence i From the previous term m in the sequence i-1 and x i So, m i with {x1,x2,…,x i There is the following relationship

[0075]

[0076] In the formula, m i is a sequence {x1,x2,…,x n}Exponentially weighted moving average of the first i items; x j The corresponding weight is (1-p)p i-j , j = 1, 2…i, the closer j is to i, the greater the weight, and vice versa, the smaller the weight. n The sum of the weights of the first i items is

[0077]

[0078] According to formula (5), the gradient descent term δUδJ of the gradient descent algorithm is subjected to exponential weighted moving average to obtain the first-order moment estimate F. The first-order moment estimate F of the kth iteration is (k) The expression is

[0079] F (k) =β1F (k-1) +(1-β1)δU (k) δJ (k) (8)

[0080] In the formula, F (k) is the first-order moment estimate at the kth iteration, β1 is the first-order moment estimate weight coefficient, δU (k) δJ (k) is the gradient descent term of the kth iteration, which is an M-dimensional vector, where M is the number of deformable mirror units. From formula (7), we know that F (k) The sum of weights is not equal to 1, so weight correction is required:

[0081]

[0082] When the performance index iterates to the vicinity of the extreme value, if the step size is not constrained, the performance index may oscillate near the extreme value and fail to converge to the global extreme value. The second-order moment estimate S is introduced to constrain the step size. In the kth iteration, the second-order moment estimate S (k) The expression and weight correction are as follows:

[0083]

[0084] In the formula, β2 is the weight coefficient of the second-order moment estimation, To estimate the second-order moment after weight correction; [δU (k) δJ (k) ] 2 Indicates the relationship between δU (k) δJ (k) Each component in S is squared, which is also an M-dimensional vector. The second formula in equation (10) represents the (k) Constraints are imposed to ensure that the second-order moment estimate continues to increase as the number of iterations increases. In the kth iteration, the step size update formula is as follows:

[0085]

[0086] In the formula, ε is a small positive real number, usually 10 -8 ;

[0087] In summary, the update formula of the deformable mirror control voltage at the kth iteration is as follows:

[0088]

[0089] The convergence condition in step 5 is, under laboratory conditions, when the peak Strehl ratio P SR When it is greater than 0.8, the aberration is generally considered to be fully corrected, and the peak Strehl ratio P SR The formula is as follows:

[0090]

[0091] In the formula, I max,realIndicates the far-field peak light intensity when the actual wavefront is incident; I max,ideal Represents the far-field peak light intensity when an ideal wavefront is incident.

[0092] Figure 6 The variation curve of the simulation performance index (i.e., the average radius) is given, and D / r0 represents the size of turbulence. The simulation results show that when D / r0=5, the average radius before correction is 15.575, and the average radius of the SPGD algorithm and the method proposed in the present invention is reduced to 4.791 and 4.095 respectively after thousands of iterations of correction, which is close to the average radius of 3.428 at the ideal wavefront incidence; when D / r0=10, the average radius before correction is 22.234, and the average radius of the two methods is reduced to 4.828 and 4.095 respectively after sufficient iteration. As the turbulence intensity increases, the correction effect of the SPGD algorithm is slightly reduced, but the correction effect of the method proposed in the present invention is almost unchanged and better than the correction effect of the SPGD algorithm, and the average radius is reduced by 0.694 and 0.733 respectively. When P SR When >0.8, the iteration is considered to have converged. Figure 7 It is known that when D / r0=5, the average number of iterations required for the two methods to converge are 757 and 233 respectively; when D / r0=10, the average number of iterations required for the two methods to converge are 850 and 257 respectively. Compared with SPGD, the convergence speed of the algorithm proposed in the present invention is increased by 3.25 times and 3.31 times respectively.

[0093] The above description is only an embodiment of the present application and is not intended to limit the protection scope of the present application. For those skilled in the art, the present application may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A wavefront-sensing-free adaptive optical control method based on moment estimation, characterized in that: The following steps are involved: Step 1: Build an adaptive optical system without wavefront sensing; Step 2: Initialize the deformable mirror control voltage V, select the average radius MR as the performance indicator, and start iteration; Step 3: Generate a random disturbance voltage δU, perform bidirectional disturbance on the deformable mirror control voltage V, and obtain the performance index change δJ; Step 4: Calculate the corrected first-order moment estimate and the corrected second-order moment estimate according to the gradient descent term of the stochastic parallel gradient descent algorithm, and update the control voltage; Step 5: Determine whether the iteration meets the convergence condition. If so, the iteration ends, and the control voltage of the last iteration is the final correction voltage. If not, repeat steps 3 to 5. The deformable mirror control voltage V in step 2 is an M-dimensional vector, where M is the number of deformable mirror units. The working principle of the deformable mirror is as follows: Where Φ(x,y) is the incident wavefront, S i (x,y) is the influence function of the i-th deformable mirror unit, M is the number of deformable mirror units, v i is the control voltage of the i-th deformable mirror unit, e(x,y) is the wavefront fitting residual, (x i ,y i ) is the position of the i-th deformable mirror unit, d is the actuator spacing, p is the Gaussian function index, and q is the actuator cross-connection value; The calculation formula of the mean radius MR in step 2 is as follows: Where I(x,y) is the far-field light intensity distribution, (x c ,y c ) are the coordinates of the centroid; The random disturbance voltage δU in step 3 is an M-dimensional vector, where M is the number of deformable mirror units, and each component of δU is a set of independent and identically Bernoulli-distributed random variables; The random disturbance voltage δJ in step 3 is expressed as δJ in the kth iteration (k) The calculation method is as follows: δJ (k) =J + -J - =J(V (k-1) +δU (k) )-J(V (k-1) -δU (k) ) (4) In the formula, J + is the performance index under positive disturbance, J - is the performance index for reverse disturbance, δU (k) is the random perturbation voltage of the kth iteration, V (k-1) is the control voltage of the deformable mirror at the last iteration, i.e., the k-1th iteration, V (0) is the initial deformable mirror control voltage; The modified first-order moment estimation and the modified second-order moment estimation in step 4 respectively perform exponentially weighted moving average on the gradient descent term and the square of the gradient descent term of the gradient descent algorithm, and modify their coefficients. The calculation methods of the modified first-order moment estimation and the modified second-order moment estimation are as follows: For a sequence {x1,x2,…,x n },make Wherein, weight p is a real number and p∈(0,1); {m1,m2,…,m n } is the sequence {x1,x2,…,x n }The new sequence obtained after exponentially weighted moving average, the i-th item m of the new sequence i From the previous term m in the sequence i-1 and x i So, m i with {x1,x2,…,x i There is the following relationship In the formula, m i is a sequence {x1,x2,…,x n }Exponentially weighted moving average of the first i items; x j The corresponding weight is (1-p)p i-j , j = 1, 2…i, the closer j is to i, the greater the weight, and vice versa, the smaller the weight. n The sum of the weights of the first i items is According to formula (5), the gradient descent term δU δJ of the gradient descent algorithm is subjected to exponential weighted moving average to obtain the first-order moment estimate F. The first-order moment estimate F of the kth iteration is (k) The expression is F (k) =β1F (k-1) +(1-β1)δU (k) δJ (k) (8) In the formula, F (k) is the first-order moment estimate at the kth iteration, β1 is the first-order moment estimate weight coefficient, δU (k) δJ (k) is the gradient descent term of the kth iteration, which is an M-dimensional vector, where M is the number of deformable mirror units. From formula (7), we know that F (k) The sum of weights is not equal to 1, so weight correction is required: When the performance index iterates to the vicinity of the extreme value, if the step size is not constrained, the performance index may oscillate near the extreme value and fail to converge to the global extreme value. The second-order moment estimate S is introduced to constrain the step size. In the kth iteration, the second-order moment estimate S (k) The expression and weight correction are as follows: In the formula, β2 is the weight coefficient of the second-order moment estimation, To estimate the second-order moment after weight correction; [δU (k) δJ (k) ] 2 Indicates the relationship between δU (k) δJ (k) Each component in S is squared, which is also an M-dimensional vector. The second formula in equation (10) represents the (k) Constraints are imposed to ensure that the second-order moment estimate continues to increase as the number of iterations increases. In the kth iteration, the step size update formula is as follows: In the formula, ε is a small positive real number, usually 10 -8 ; In summary, the update formula of the deformable mirror control voltage at the kth iteration is as follows:

2. The method for controlling adaptive optics without wavefront sensing based on moment estimation according to claim 1, characterized in that: The convergence condition in step 5 is, under laboratory conditions, when the peak Strehl ratio P SR When it is greater than 0.8, the aberration is generally considered to be fully corrected, and the peak Strehl ratio P SR The formula is as follows: In the formula, I max,real Indicates the far-field peak light intensity when the actual wavefront is incident; I max,ideal Represents the far-field peak light intensity when an ideal wavefront is incident.

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