CN111221123B - Wavefront-sensor-free self-adaptive optical correction method based on model - Google Patents

Wavefront-sensor-free self-adaptive optical correction method based on model Download PDF

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CN111221123B
CN111221123B CN202010211955.7A CN202010211955A CN111221123B CN 111221123 B CN111221123 B CN 111221123B CN 202010211955 A CN202010211955 A CN 202010211955A CN 111221123 B CN111221123 B CN 111221123B
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董冰
任虹禧
张晓芳
胡新奇
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Beijing Institute of Technology BIT
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Abstract

The invention discloses a model-based wavefront-sensor-free adaptive optical correction method, belongs to the technical field of optics, and is used for solving the technical problems that the existing wavefront-sensor-free adaptive optical method depends on mode selection and has more iteration times. The method comprises the steps of adopting the reciprocal of the integral of the image power spectral density low-frequency space as the image quality evaluation function of an image, deducing the relation between the image quality evaluation function (the reciprocal of the integral of the image power spectral density low-frequency space) and a mode coefficient on the basis of a non-coherent imaging system model, collecting N +2 images to calculate the image quality evaluation function by introducing N +1 times of bias, calculating the mode coefficient according to the deduced relation, and generating conjugate wave front by a deformable mirror to achieve the purposes of correcting aberration and improving the image quality. The method is suitable for correcting any mode as a substrate, the iteration times are few, and the system bandwidth can be greatly improved.

Description

Wavefront-sensor-free self-adaptive optical correction method based on model
Technical Field
The invention relates to a wavefront-free sensor self-adaptive optical correction method, belonging to the technical field of optics.
Background
High-resolution imaging is a long-sought goal of human beings, and the traditional optical technology cannot solve the problem of influence of dynamic wavefront disturbance on image quality. Most optical systems are influenced by system aberration, atmospheric turbulence or adjustment error and the like, the wavefront aberration of the system is increased, and the imaging quality is obviously reduced. Error sources affecting the wavefront quality of an optical system can be divided into two categories, namely low frequency and high frequency according to time frequency. The method belongs to low-frequency error system design error, temperature, gravity deformation, mechanical deformation, machining and assembling error and the like. The high-frequency errors include external air heat influence, reflector deformation from gust, tracking error, atmosphere turbulence, thermal halo of laser transmitted through atmosphere, and the like. How to overcome the above influence of dynamic wavefront error is a subject of diligent research by optical workers.
The adaptive optics is a high-technology subject integrating light collection, mechanical collection, electrical collection, automatic control and chemistry, and the core content is to correct the wavefront distortion of a light beam in real time so as to improve the imaging quality of an optical system. The adaptive optical technology can effectively correct wavefront distortion, improve imaging quality and be successfully applied to relevant fields such as astronomical observation, free space optical communication and the like.
However, the conventional adaptive optics system needs to detect and reconstruct the measured light beam, which results in a complex system structure, is not favorable for the miniaturization application of the technology, and increases the system cost. In order to simplify the structure and reduce the system cost, the wavefront-less sensing adaptive optics concept is proposed and rapidly developed in recent years. It differs from conventional adaptive optics systems in that: the wavefront detection reconstruction is not required to be directly carried out, and the relationship between the evaluation function and the variable to be optimized is gradually converged to the correction limit.
Wavefront-less sensor adaptive optics is classified into two types, model-less methods and model-based methods, according to the correction method. The model-free method mainly comprises a random parallel gradient descent algorithm, a hill climbing method, a simulated annealing algorithm, a genetic algorithm and the like. The model-free optimization algorithm does not need to predict the specific mathematical relationship between the variable to be optimized and the optimization objective function, random wavefront change is introduced into the optical system by controlling the deformable mirror, corresponding image surface light intensity information is recorded, the evaluation function is calculated by the light intensity information, and the deformable mirror enables the evaluation function value to tend to be optimal through multiple iterations according to a certain search path. The main disadvantages of the modeless approach are: (1) multiple iterations are required to achieve the correction effect, and (2) local extrema are easily converged.
Compared with the model-free wavefront sensor-free adaptive optical method, the model-based wavefront sensor-free adaptive optical method has better real-time performance and does not need multiple iterations. The method comprises the steps of selecting a proper evaluation function, establishing a mathematical relation between the evaluation function and a mode coefficient, solving the mode coefficient, and finally controlling a deformable mirror to correct wavefront aberration. The existing model-based wavefront-free sensor adaptive optical method can be divided into a point target and an extended target according to different processing targets, and the invention mainly focuses on a correction method for the extended target. The existing model-based wavefront-sensor-free adaptive optical school correction method for extended target imaging needs to acquire 2N +1 images, which is also called as a 2N +1 algorithm. The method takes low-frequency space integral of image power spectral density as an evaluation function, uses a Lukosz mode or a deformable mirror eigenmode and other modes with derivative orthogonal characteristics as correction modes, applies positive and negative bias to each mode, so that 2N +1 images are required to be collected to estimate a mode coefficient when correcting an N-order mode, and finally, conjugate correction is carried out according to the estimated wavefront. The disadvantages of this method are: (1) only modes with derivative orthogonal properties can be selected as basis functions; (2) more images need to be acquired, so that the correction speed is low and the correction bandwidth is low.
Disclosure of Invention
The invention aims to solve the problems of the existing model-based wavefront-free sensor adaptive optics method for expanding target imaging, which comprises (1) mode selection dependence and (2) insufficient bandwidth when dynamic aberration is corrected, and creatively provides a new model-based wavefront-free sensor adaptive optics correction method.
The method has the innovation points that the reciprocal of the integral of the image power spectral density low-frequency space is used as an image quality evaluation function of the image, the relation between the image quality evaluation function and a mode coefficient is deduced on the basis of a non-coherent imaging system model, N +2 images are collected to calculate the image quality evaluation function by introducing N +1 times of bias, the mode coefficient is calculated according to the deduced relation, and a deformable mirror generates conjugate wavefront to achieve the purposes of correcting aberration and improving the image quality.
Advantageous effects
Compared with the existing model-based wavefront-free sensor adaptive optics method for expanding target imaging, the method provided by the invention has the following advantages:
(1) any pattern may be selected as the basis function. The method is a result obtained by derivation from any mode, and a derivative orthogonal mode is not required to be selected as a basis function.
(2) The real-time performance is good. The method can finish one round of correction by only applying the bias for N +1 times and acquiring N +2 images, and compared with the existing method, the method has the advantages that the efficiency is improved by nearly one time, and the correction bandwidth of the system is improved.
Drawings
FIG. 1 is a schematic flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of simulation and experimental optical paths in the method of the present invention;
FIG. 3 is a diagram of simulation results in the method of the present invention;
FIG. 4 is a graph showing the effect of the method of the present invention compared with other methods;
FIG. 5 is a graph showing the results of the experiment of the method of the present invention.
Detailed Description
The method of the present invention will be described in further detail with reference to the accompanying drawings and examples.
As shown in fig. 1, a model-based wavefront-sensor-free adaptive optics correction method includes the following steps:
step 1: an aberration representation mode is determined.
The wavefront error φ is represented using a linear superposition of arbitrary patterns:
φ＝KA (1)
A＝[a1 a2 … ai … aN]T (2)
wherein A is a mode coefficient vector, and the specific form is shown as formula 2; each column vector of K is Ki(i from 1 to N), KiIs the ith order of the mode (basis function), N is the total order of the mode, the value of N is determined by the fitting ability of the deformable mirror, aiAre coefficients of the mode of the ith order.
Step 2: and acquiring an image to obtain an initial evaluation function.
Acquiring an image I when the control voltages of all actuators of the deformable mirror are at an initial value0. Calculating the reciprocal of the integral of the low-frequency space of the power spectral density of the image as an image quality evaluation function g of the image0：
Figure BDA0002423128210000041
Wherein S is0(u, v) is the image I0Is a frequency domain coordinate, and R corresponds to an annular region m on the frequency domain1≤(u2+v2)1/2≤m2，m1And m2Is a preset value in the frequency domain that is less than the image cutoff frequency. Low frequency space finger m2Is small, and in general, m is1Taking a number, m, greater than 0 and less than or equal to the image cut-off frequency 1/1002Numbers greater than the image cutoff frequency 1/20 and less than the image cutoff frequency 1/10 are taken.
And step 3: and acquiring the N times of positive bias evaluation functions.
Respectively introducing positive bias phi with amplitude b to 1 to N orders of modes by using deformable mirrorsj+＝bKjAcquiring N images Ij+(j from 1 to N), obtaining an image quality evaluation function g of the imagej+：
Figure BDA0002423128210000042
Wherein S isj+(u, v) is the image Ij+Of the power spectral density of (c).
And 4, step 4: a negative bias evaluation function of 1 is obtained.
For any order s mode, s is any value from 1 to N, and negative bias phi with amplitude b is introduced by a deformable mirrors-＝-bKsAcquiring an image Is-Obtaining an image quality evaluation function g of the images-：
Figure BDA0002423128210000043
Wherein S iss-(u, v) is the image Is-Of the power spectral density of (c).
And 5: calculating a mode coefficient vector a as follows:
Figure BDA0002423128210000044
wherein:
G＝[g1+-g0 g2+-g0 … gN+-g0]T (7)
Figure BDA0002423128210000045
X＝[α11 α22 … αNN]T (9)
Y＝[α1s α2s … αNs] (10)
Figure BDA0002423128210000051
wherein the content of the first and second substances,
Figure BDA0002423128210000052
representing matrix inversion and T representing matrix transposition. In formulas 6, 8, 9 and 10,. alpha.ss、αNN、αNsIs calculated as alpha in formula 11ijThe calculation method is shown, wherein the value ranges of i and j are from 1 to N; ki、KjDenotes the mode of the corresponding order, # denotes the gradient operator, and P denotes the pupil integration area.
Step 6: conjugate correction was performed with a deformable mirror.
The mode coefficient vector a is obtained in step 5, the wavefront error to be corrected is given by formula 1, and the wavefront conjugate to the wavefront error is generated only by using a deformable mirror to correct the wavefront error.
Let F be the matrix of the impact function of the deformable mirror, where each column vector of F is the wavefront phase change when a unit voltage is applied to each actuator of the deformable mirror, and F can be measured in advance by an interferometer or other wavefront sensor, and is known during the calibration process. When the wavefront error is corrected by the deformable mirror, a vector formed by the voltage variation applied to each actuator is V. Therefore, there are:
FV＝-KA (12)
solving the equation set to obtain the voltage variation V of each actuator of the deformable mirror:
V＝-F+KA (13)
wherein, F+Representing the generalized inverse of matrix F.
And 7: and judging whether the corrected image quality meets the requirement or not. And if the requirements are not met, returning to the step 2. If the requirements are met, the correction procedure ends.
Simulation verification
The simulation and experimental effects of the invention are illustrated by the following simulation experiments:
1. and (5) simulating and testing the optical path.
Fig. 2 is a schematic diagram of simulation and experimental optical paths of the present invention.
2. And (5) simulation results.
Fig. 3 is a simulation result of the method, and it can be seen that the aberration is effectively corrected by the correction of the method, and the correction result is close to the ideal result. FIG. 4 is a graph comparing the method of the present invention (N +2 algorithm) with the prior 2N +1 algorithm. It can be seen that the method of the present invention has a significantly faster convergence rate and comparable convergence results than the existing methods. Fig. 5 is an experimental result of the method, and it can be seen that the experimental result is consistent with the simulation result, further proving the effectiveness of the method.

Claims (2)

1. A wavefront-sensor-free adaptive optical correction method based on a model is characterized by comprising the following steps of:
step 1: determining an aberration representation mode;
the wavefront error φ is represented using a linear superposition of arbitrary patterns:
φ＝KA (1)
A＝[a1 a2 … ai … aN]T (2)
wherein A is a mode coefficient vector, and the specific form is shown as formula 2; each column vector of K is a pattern KiI takes values from 1 to N, KiIs the mode of the ith order, i.e., the basis function; n is the total order of the mode, the value of N is determined by the fitting capacity of the deformable mirror, aiIs a coefficient of the mode of the ith order;
step 2: acquiring an image to obtain an initial evaluation function;
acquiring an image I when the control voltages of all actuators of the deformable mirror are at an initial value0(ii) a Calculating the reciprocal of the integral of the low-frequency space of the power spectral density of the image as an image quality evaluation function g of the image0：
Figure FDA0002696227950000011
Wherein S is0(u, v) is the image I0Is a frequency domain coordinate, and R corresponds to an annular region m on the frequency domain1≤(u2+v2)1/2≤m2，m1And m2Is a preset value in the frequency domain smaller than the cut-off frequency of the image; wherein m is1Taking a number, m, greater than 0 and less than or equal to the image cut-off frequency 1/1002Taking numbers between greater than the image cutoff frequency 1/20 and less than the image cutoff frequency 1/10;
and step 3: acquiring a positive bias evaluation function for N times;
respectively introducing positive bias wavefront errors phi with the amplitude of b into the 1 to N-order modes by using deformable mirrorsj+＝bKjAcquiring N images Ij+J takes values from 1 to N to obtain an image quality evaluation function g of the imagej+：
Figure FDA0002696227950000012
Wherein S isj+(u, v) is the image Ij+The power spectral density of (d);
and 4, step 4: acquiring a negative bias evaluation function for 1 time;
for any s-th order mode, s is any value from 1 to N, and negative offset wavefront error phi with amplitude b is introduced by a deformable mirrors-＝-bKsAcquiring an image Is-Obtaining an image quality evaluation function g of the images-：
Figure FDA0002696227950000021
Wherein S iss-(u, v) is the image Is-The power spectral density of (d);
and 5: calculating a mode coefficient vector a as follows:
Figure FDA0002696227950000022
wherein:
G＝[g1+-g0 g2+-g0 … gN+-g0]T (7)
Figure FDA0002696227950000023
X＝[α11 α22 … αNN]T (9)
Y＝[α1s α2s … αNs] (10)
Figure FDA0002696227950000024
wherein the content of the first and second substances,
Figure FDA0002696227950000025
representing matrix inversion, and T representing matrix transposition; in formulas 6, 8, 9 and 10,. alpha.ss、αNN、αNsIs calculated as alpha in formula 11ijThe calculation method is shown, wherein the value ranges of i and j are from 1 to N; ki、KjMode representing the corresponding order, # represents the gradient operator, and P represents the pupil integration area;
step 6: performing conjugate correction by using a deformable mirror;
setting an influence function matrix of the deformable mirror as F, wherein each column vector of the F is the wave front phase change when unit voltage is applied to each actuator of the deformable mirror, and the F is known in the correction process; when wavefront errors are corrected by the deformable mirror, a vector formed by voltage variations applied to the actuators is V, and there are:
FV＝-KA (12)
solving the equation set to obtain the voltage variation V of each actuator of the deformable mirror:
V＝-F+KA (13)
wherein, F+A generalized inverse matrix representing matrix F;
and 7: judging whether the corrected image quality meets the requirements or not; if the requirement is not met, returning to the step 2; if the requirements are met, the correction procedure ends.
2. The model-based wavefront-sensor-free adaptive optics correction method of claim 1, wherein F is measured in advance.
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