CN113300766B - Self-adaptive distortion wavefront corrector based on LQG and method thereof - Google Patents

Self-adaptive distortion wavefront corrector based on LQG and method thereof Download PDF

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CN113300766B
CN113300766B CN202110396002.7A CN202110396002A CN113300766B CN 113300766 B CN113300766 B CN 113300766B CN 202110396002 A CN202110396002 A CN 202110396002A CN 113300766 B CN113300766 B CN 113300766B
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deformable mirror
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柯熙政
刘婷婷
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Xian University of Technology
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Abstract

The invention discloses an adaptive distortion wavefront corrector based on LQG, which comprises a laser, wherein a deformable mirror is arranged along the propagation direction of light waves emitted by the laser, the deformable mirror reflects the light waves emitted by the laser, and beam splitting prisms are sequentially arranged along the direction of the reflected light waves and divide the reflected light waves into two beams of light waves by the beam splitting prisms, a focusing lens and a CCD camera are sequentially arranged in the propagation direction of one beam of light waves, an adaptive optical system is arranged in the propagation direction of the other beam of light waves and comprises a wavefront sensor arranged in the propagation direction of the light waves, the wavefront sensor is sequentially connected with a digital filter, a wavefront restorer, a wavefront controller, a D/A digital-to-analog converter and a high-voltage amplifier through electric signals, and the high-voltage amplifier is further connected with the deformable mirror through electric signals. The device has simple structure and can effectively realize the correction processing of the distorted wave signal containing the random white Gaussian noise. The invention also discloses an adaptive distortion wavefront correction method based on the LQG.

Description

Self-adaptive distortion wavefront corrector based on LQG and method thereof
Technical Field
The invention belongs to the technical field of wireless optical communication, relates to an adaptive distorted wavefront corrector based on LQG, and further relates to an adaptive distorted wavefront correction method based on LQG.
Background
In the wireless optical communication technology, optical signals are affected by atmospheric turbulence in the propagation process to cause optical wave distortion, which causes instability of channel transmission characteristics, so that communication quality and transmission distance are limited, and the performance of an optical system is seriously affected. The optimization of the adaptive optical system and the improvement of the information processing algorithm are effective means for improving the optical communication technology. Currently, adaptive optical technology has been applied in the fields of astronomical imaging, laser transmission, optical communication, industrial and medical imaging, and the like.
At present, a conventional adaptive optical system consists of a wavefront sensor, a wavefront controller and a wavefront corrector, and has the disadvantages of complex structure, high cost, large volume and difficulty in miniaturization, and the application field of the conventional adaptive optical system is difficult to expand and popularize. Therefore, the wavefront-free detection adaptive optical system is evolved on the basis of the conventional adaptive optical system, and compared with the conventional adaptive optical technology, the wavefront-free detection adaptive optical system does not need a wavefront detection link any more, so that the complexity of the system is greatly reduced, the cost is reduced, and the application range of the system is effectively enlarged. The wavefront-free detection adaptive optics system is a transfer from the research of a hardware device to a control algorithm.
Both the conventional adaptive optics system and the wavefront-free detection adaptive optics system have strong dependence on hardware equipment, and for example, the volume, sensitivity, service life, cost and the like of the hardware equipment are factors which restrict the development of the optical technology. To improve the wide application of optical systems, it is necessary to miniaturize the apparatus, simplify the system, and reduce the cost.
Disclosure of Invention
The invention aims to provide an LQG-based adaptive distorted wavefront corrector, which has a simple equipment structure and can effectively realize the correction processing of distorted wave signals containing random white Gaussian noise.
Another object of the present invention is to provide an LQG-based adaptive aberrated wavefront correction method.
The invention adopts the technical scheme that the self-adaptive distortion wavefront corrector based on the LQG comprises a laser, wherein a deformable mirror is arranged along the propagation direction of light waves emitted by the laser, the deformable mirror reflects the light waves emitted by the laser, and beam splitting prisms are sequentially arranged along the direction of the reflected light waves, the beam splitting prisms divide the reflected light waves into two light waves, one light wave is sequentially provided with a focusing lens and a CCD camera in the propagation direction, the other light wave is sequentially provided with a self-adaptive optical system in the propagation direction, the self-adaptive optical system comprises a wavefront sensor arranged in the propagation direction of the light waves, the wavefront sensor is sequentially connected with a digital filter, a wavefront restorer, a wavefront controller, a D/A digital-to-analog converter and a high-voltage amplifier through electric signals, and the high-voltage amplifier is further connected with the deformable mirror through electric signals.
Another technical solution adopted by the present invention is an adaptive aberrated wavefront correction method based on LQG, which adopts the above adaptive aberrated wavefront corrector based on LQG, and specifically includes: the laser emits light waves which are distorted due to the influence of atmospheric turbulence in the transmission process, residual aberration of the distorted waves to be corrected is reflected by a deformable mirror and then is split by a splitting prism, one light wave is continuously transmitted along a straight line and passes through a focusing lens and a CCD camera, the CCD camera images the incident light wave, the other light wave sequentially passes through a wavefront sensor to acquire light wave slope information, then a digital filter performs digital filtering pretreatment, wavefront restoration is performed by a wavefront restorer to provide distorted wavefront aberration data for the wavefront controller, the wavefront controller calculates driving voltage required by the deformable mirror by using an LQG method according to the distorted wavefront aberration data, then a D/A digital-to-analog converter converts the calculated digital driving voltage signal into an analog driving voltage signal, and then the high-voltage amplifier controls the deformable mirror to change the mirror surface structure to change the transmission optical path of the incident light beam, the correction of the distorted wave signals is realized, and the purpose of correcting the distorted incident beam waves is finally achieved.
The second aspect of the present invention is also characterized in that,
the LQG method is implemented according to the following steps:
step 1, establishing a self-adaptive optical system model according to a linear quadratic Gaussian control theory, and obtaining a state space equation of the self-adaptive optical system;
step 2, selecting minimized residual wave front as a linear quadratic performance index of the adaptive optical system according to the state space equation of the adaptive optical system obtained in the step 1;
step 3, according to the stepEstimating the state vector of the adaptive optical system by the state space equation of the adaptive optical system obtained in the step 2
Figure BDA0003018592710000031
And 4, completing the design of the self-adaptive optical system LQG controller according to the parameters obtained in the step 1-3, and calculating the final driving voltage u (k) of the deformable mirror.
The step 1 specifically comprises the following steps:
step 1.1, estimating each processing link of the adaptive optics system as a function form:
frequency domain function H of wavefront sensorW(s) is:
Figure BDA0003018592710000032
applying the frequency domain function H of a digital filterF(s) is:
Figure BDA0003018592710000033
frequency domain function H of wave front restorerL(s) is:
Figure BDA0003018592710000034
frequency domain function H of wave front controllerC(s) is:
Figure BDA0003018592710000035
frequency domain function H of D/A converterZ(s) is:
Figure BDA0003018592710000041
frequency domain function H of a high voltage amplifierH(s) is:
Figure BDA0003018592710000042
deformable mirror frequency domain function HD(s) is:
Figure BDA0003018592710000043
then the frequency domain open loop function estimated by each processing link of the adaptive optical control system is:
Figure BDA0003018592710000044
where T is the sampling period of the wavefront sensor, τ1Time delay, τ, of sampling of the wavefront sensor2Is the delay time of the digital filter,. tau.3 is the delay time of the wavefront restorer,. tau.4Is the delay time of the wavefront controller, tau5Delay time of D/A digital-to-analog converter, tau6Is the delay time of the high-voltage amplifier, tau7Is the delay time of the deformable mirror, s is the complex frequency;
counting:
τ＝τ1+τ2+τ3+τ4+τ5+τ6+τ7 (9)
the formula (9) is substituted for the formula (8) to obtain
Figure BDA0003018592710000045
E in the formula (10)τsExpanding according to Taylor series to obtain:
Figure BDA0003018592710000046
since the delay time τ is small, therefore:
eτs≈1+τs (12)
the formula (12) is substituted for the formula (10) to obtain
Figure BDA0003018592710000047
Then the frequency domain closed loop function estimated by each processing link of the adaptive optical control system is:
Figure BDA0003018592710000051
step 1.2, solving a state space equation of the adaptive optical system, specifically:
output vector of adaptive optics:
y(k)＝M(φW(k+1)-φM(k+1))+w(k) (15)
where M is the influence matrix of the adaptive optics system on the processing of the incident wave signal, i.e. M is the matrix
Figure BDA0003018592710000052
φW(k +1) is the phase of the incident wavefront, phiM(k +1) is the wavefront phase generated by the deformable mirror, w (k) is the measurement noise, and k is the discrete time length;
u(k+1)＝(φW(k+1)-φM(k+1)) (17)
wherein, the wave front phase of the incident light wave is:
φW(k+1)＝FφW(k)+v(k) (18)
wherein F is a diagonal matrix and v (k) is process noise;
by substituting formula (17) for formula (15)
y(k)＝M(u(k+1))+w(k) (19)
The adaptive optics system state space model can be obtained according to the equations (18) and (19), and the state space equation expression of the adaptive optics system is as follows:
Figure BDA0003018592710000053
wherein (A, B, C, D) is an adaptive optics system state space matrix, x (k) is an adaptive optics system n-dimensional state vector, y (k) is an adaptive optics system l-dimensional output vector, u (k) is an adaptive optics system m-dimensional input vector, w (k) is measurement noise, wherein,
Figure BDA0003018592710000061
the linear quadratic performance index J of the adaptive optical system in the step 2 is as follows:
Figure BDA0003018592710000062
wherein phi isM(k +1) is the compensation wavefront, phi, generated by the control deformable mirrorW(k +1) is the incident wavefront collected by the wavefront sensor, Q, R is the weighting matrix, and N is the time length;
according to the principle of a linear quadratic state regulator, it is required to generate a control vector u (k) such that the value of equation (21) is always kept to a minimum for the state vector x (k).
The step 3 specifically comprises the following steps:
step 3.1, obtaining the optimal solution of equation (21) through iteration as:
u(k)＝Kx(k+1)/k (22)
the state feedback gain of the adaptive optics system is as follows:
K＝(R+DTQD)-1(BP+(CT+DTQD)) (23)
in equation (23), P is a solution of an algebraic ricati equation, and is obtained by solving the following equation:
P(A-B(R+DTQD)-1BTP+(CTQC-(CTQC-CTQD(R+DTQD)CTQD)))＝0 (24)；
and 3. step 3.2, estimated adaptive optics system state vector
Figure BDA0003018592710000063
Comprises the following steps:
Figure BDA0003018592710000064
the step 4 specifically comprises the following steps:
the state feedback process of the linear quadratic Gaussian controller of the adaptive optical system obtained by combining the formula (25) and the formula (22) is as follows:
Figure BDA0003018592710000071
then, the final control voltage u (k) of the deformable mirror is obtained by solving the equation (26).
The invention has the beneficial effects that:
compared with the existing self-adaptive optical distortion wave correction method, the method can more effectively realize correction processing on the distortion wave signal containing random white Gaussian noise, and has relatively simple equipment structure and wider application field.
The influence of noise interference factors on the correction effect is effectively considered in the application process of the LQG control method; compared with the current common PI control method, the factor is greatly reduced depending on human experience in the aspect of controlling parameter adjustment; the data calculation amount and the delay time are reduced, and the real-time performance of the system can be improved; compared with the LQG technology provided by the prior art, the invention can effectively improve the wavefront capability and effect of the adaptive optical system.
Drawings
FIG. 1 is a schematic structural diagram of an adaptive aberration wave-front corrector based on LQG according to the present invention;
fig. 2 is a flow chart of an LQG method in the LQG-based adaptive aberrated wavefront correction method of the present invention.
In the figure, 1, a laser, 2, a deformable mirror, 3, a beam splitter prism, 4, a focusing lens, 5, a CCD camera, 6, a wavefront sensor, 7, a digital filter, 8, a wavefront restorer, 9, a wavefront controller, 10, a D/A digital-to-analog converter and 11, a high-voltage amplifier.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention relates to an adaptive distortion wavefront corrector based on LQG, the structure of which is shown in figure 1, and the adaptive distortion wavefront corrector comprises a laser 1, a deformable mirror 2 is arranged along the propagation direction of light waves emitted by the laser 1, the deformable mirror 2 reflects the light waves emitted by the laser 1, and a beam splitter prism 3 is sequentially arranged along the direction of the reflected light waves, the beam splitter prism 3 splits the reflected light waves into two light waves, the device comprises a focusing lens 4, a CCD camera 5 and a self-adaptive optical system, wherein the focusing lens 4 and the CCD camera 5 are sequentially arranged in the propagation direction of one light wave, the self-adaptive optical system is arranged in the propagation direction of the other light wave, the self-adaptive optical system comprises a wavefront sensor 6 arranged in the propagation direction of the light wave, the wavefront sensor 6 is sequentially connected with a digital filter 7, a wavefront restorer 8, a wavefront controller 9, a D/A (digital/analog) converter 10 and a high-voltage amplifier 11 through electric signals, and the high-voltage amplifier 11 is further connected with a deformable mirror 2 through electric signals.
LQG is: and (5) secondary Gaussian control.
Another technical solution adopted by the present invention is an adaptive aberrated wavefront correction method based on LQG, which adopts the above adaptive aberrated wavefront corrector based on LQG, and specifically includes: the laser 1 generates distortion due to the influence of atmospheric turbulence in the transmission process of light waves, residual aberration of distortion waves to be corrected after being reflected by a deformable mirror 2 is split by a splitting prism 3, one light wave continuously transmits along a straight line through a focusing lens 4 and a CCD camera 5, the CCD camera 5 images incident light waves, then the incident light waves enter a microprocessor for next operation, the other light wave sequentially passes through a wavefront sensor 6 to obtain light wave slope information, then a digital filter 7 performs digital filtering pretreatment, and then a wavefront restorer 8 performs wavefront restoration and provides distorted wavefront aberration data for a wavefront controller 9, the wavefront controller 9 calculates the driving voltage required by the deformable mirror 2 by an LQG method according to the distorted wavefront aberration data, then a D/A digital-to-analog converter 10 converts the calculated digital driving voltage signal into an analog driving voltage signal and then controls the deformable mirror 2 to change the mirror surface structure through a high-voltage amplifier 11, the transmission optical path of the incident beam is changed, the correction of the distorted wave signals is realized, and the purpose of correcting the distorted incident beam waves is finally achieved.
As shown in fig. 2, the LQG method is specifically implemented as follows:
step 1, establishing a self-adaptive optical system model according to a linear quadratic Gaussian control theory, and obtaining a state space equation of the self-adaptive optical system;
step 2, selecting minimized residual wave front as a linear quadratic performance index of the adaptive optical system according to the state space equation of the adaptive optical system obtained in the step 1;
step 3, estimating a state vector of the adaptive optics system according to the state space equation of the adaptive optics system obtained in the step 2
Figure BDA0003018592710000091
And 4, completing the design of the self-adaptive optical system LQG controller according to the parameters obtained in the step 1-3, and calculating the final driving voltage u (k) of the deformable mirror.
The step 1 specifically comprises the following steps:
step 1.1, estimating each processing link of the adaptive optics system as a function form:
frequency domain function H of wavefront sensor 6W(s) is:
Figure BDA0003018592710000092
the frequency domain function H of the digital filter 7F(s) is:
Figure BDA0003018592710000093
frequency domain function H of wavefront restorer 8L(s) is:
Figure BDA0003018592710000094
frequency domain function H of the wavefront controller 9C(s) is:
Figure BDA0003018592710000095
frequency domain function H of D/A digital-to-analog converter 10Z(s) is:
Figure BDA0003018592710000096
frequency domain function H of high voltage amplifier 11H(s) is:
Figure BDA0003018592710000098
deformable mirror 2 frequency domain function HD(s) is:
Figure BDA0003018592710000097
then the frequency domain open loop function estimated by each processing link of the adaptive optical control system is:
Figure BDA0003018592710000101
where T is the sampling period of the wavefront sensor 6, τ1Time delay, τ, of sampling of the wavefront sensor 62Is the delay time, tau, of the digital filter 73Is the delay time, tau, of the wave front restorer 84Is the delay time of the wavefront controller 9, tau5Is the delay time of the D/A digital-to-analog converter 10, tau6Is the delay time, tau, of the high voltage amplifier 117Is the delay time of the deformable mirror 2, s is the complex frequency;
counting:
τ＝τ1+τ2+τ3+τ4+τ5+τ6+τ7 (9)
the formula (9) is substituted for the formula (8) to obtain
Figure BDA0003018592710000102
E in the formula (10)τsExpanding according to Taylor series to obtain:
Figure BDA0003018592710000103
since the delay time τ is small, therefore:
eτs≈1+τs (12)
the formula (12) is substituted for the formula (10) to obtain
Figure BDA0003018592710000104
Then the frequency domain closed loop function estimated by each processing link of the adaptive optical control system is:
Figure BDA0003018592710000105
step 1.2, solving a state space equation of the adaptive optical system, specifically:
output vector of adaptive optics:
y(k)＝M(φW(k+1)-φM(k+1))+w(k) (15)
where M is the influence matrix of the adaptive optics system on the processing of the incident wave signal, i.e. M is the matrix
Figure BDA0003018592710000111
φW(k +1) is the phase of the incident wavefront, phiM(k +1) is the wavefront phase, w, produced by the anamorphic mirror(k) To measure noise, k is the discrete time length;
u(k+1)＝(φW(k+1)-φM(k+1)) (17)
wherein, the wave front phase of the incident light wave is:
φW(k+1)＝FφW(k)+v(k) (18)
wherein F is a diagonal matrix and v (k) is process noise;
by substituting formula (17) for formula (15)
y(k)＝M(u(k+1))+w(k) (19)
The adaptive optics system state space model can be obtained according to the equations (18) and (19), and the state space equation expression of the adaptive optics system is as follows:
Figure BDA0003018592710000112
wherein (A, B, C, D) is an adaptive optics system state space matrix, x (k) is an adaptive optics system n-dimensional state vector, y (k) is an adaptive optics system l-dimensional output vector, u (k) is an adaptive optics system m-dimensional input vector, w (k) is measurement noise, wherein,
Figure BDA0003018592710000113
the linear quadratic performance index J of the adaptive optical system in the step 2 is as follows:
Figure BDA0003018592710000121
wherein phi isM(k +1) is the compensation wavefront, phi, generated by the control deformable mirrorW(k +1) is the incident wavefront collected by the wavefront sensor, Q, R is the weighting matrix, and N is the time length;
according to the principle of a linear quadratic state regulator, it is required to generate a control vector u (k) such that the value of equation (21) is always kept to a minimum for the state vector x (k).
The step 3 specifically comprises the following steps:
step 3.1, obtaining the optimal solution of equation (21) through iteration as:
u(k)＝Kx(k+1)/k (22)
the state feedback gain of the adaptive optics system is as follows:
K＝(R+DTQD)-1(BP+(CT+DTQD)) (23)
in equation (23), P is a solution of an algebraic ricati equation, and is obtained by solving the following equation:
P(A-B(R+DTQD)-1BTP+(CTQC-(CTQC-CTQD(R+DTQD)CTQD)))＝0 (24)；
step 3.2, estimating the adaptive optics system state vector
Figure BDA0003018592710000122
Comprises the following steps:
Figure BDA0003018592710000123
the step 4 specifically comprises the following steps:
the state feedback process of the linear quadratic Gaussian controller of the adaptive optical system obtained by combining the formula (25) and the formula (22) is as follows:
Figure BDA0003018592710000124
then, the final control voltage u (k) of the deformable mirror is obtained by solving the equation (26).
The invention uses the incident wavefront information to calculate by adopting an LQG method to obtain the optimal control voltage of the deformable mirror, and changes the optical path of light wave propagation by controlling the deformable mirror to be in a conjugate state with the incident wavefront, thereby achieving the effect of compensating and correcting the distorted wavefront.

Claims (1)

1. The self-adaptive distorted wavefront correction method based on the LQG is characterized by comprising a laser (1), wherein a deformable mirror (2) is arranged along the propagation direction of light waves emitted by the laser (1), the deformable mirror (2) reflects the light waves emitted by the laser (1), a beam splitter (3) is sequentially arranged along the direction of the reflected light waves, the reflected light waves are split into two light waves by the beam splitter (3), a focusing lens (4) and a CCD camera (5) are sequentially arranged in the propagation direction of one light wave, a self-adaptive optical system is arranged in the propagation direction of the other light wave, the self-adaptive optical system comprises a wavefront sensor (6) arranged in the propagation direction of the light waves, and the wavefront sensor (6) is sequentially connected with a digital filter (7) and an optical system through electric signals, Wavefront restorer (8), wavefront controller (9), D/A digital-to-analog converter (10) and high-voltage amplifier (11), high-voltage amplifier (11) still through electric signal connection distorting lens (2), specifically do: the laser device (1) generates distortion due to the influence of atmospheric turbulence in the transmission process of emitted light waves, residual aberration of distortion waves to be corrected is split through the splitting prism (3) after being reflected by the distorting lens (2), one light wave continuously transmits along a straight line and passes through the focusing lens (4) and the CCD camera (5), the CCD camera (5) images incident light waves, the other light wave sequentially obtains light wave slope information through the wavefront sensor (6), then the digital filter (7) performs digital filtering preprocessing, wavefront restoration is performed through the wavefront restorer (8), then distorted wavefront aberration data are provided for the wavefront controller (9), the wavefront controller (9) calculates the driving voltage required by the distorting lens (2) through an LQG method according to the distorted wavefront aberration data, then the digital driving voltage signals obtained through calculation are converted into analog driving voltage signals through the D/A digital-to-analog converter (10), and then the analog driving voltage signals are controlled through the high-voltage amplifier (11) The distortion mirror (2) changes the mirror surface structure, changes the transmission optical path of the incident beam, realizes the correction of the distorted wave signal, and finally achieves the purpose of correcting the distorted incident beam wave;
the LQG method is implemented according to the following steps:
step 1, establishing a self-adaptive optical system model according to a linear quadratic Gaussian control theory, and obtaining a state space equation of the self-adaptive optical system; the method specifically comprises the following steps:
step 1.1, estimating each processing link of the adaptive optics system as a function form:
frequency domain function H of a wavefront sensor (6)W(s) is:
Figure FDA0003456582140000021
applying the frequency domain function H of the digital filter (7)F(s) is:
Figure FDA0003456582140000022
frequency domain function H of wave front restorer (8)L(s) is:
Figure FDA0003456582140000023
frequency domain function H of wave front controller (9)C(s) is:
Figure FDA0003456582140000024
frequency domain function H of D/A digital-to-analog converter (10)Z(s) is:
Figure FDA0003456582140000025
frequency domain function H of a high voltage amplifier (11)H(s) is:
Figure FDA0003456582140000026
frequency domain function H of deformable mirror (2)D(s) is:
Figure FDA0003456582140000027
then the frequency domain open loop function estimated by each processing link of the adaptive optical control system is:
Figure FDA0003456582140000028
wherein T is the sampling period of the wavefront sensor (6) and τ1Time delay, τ, for sampling of the wavefront sensor (6)2Is the delay time of the digital filter (7) < tau >3Is the delay time of the wave front restorer (8) < tau >4Is the delay time of the wave front controller (9) < tau >5Is the delay time of the D/A digital-to-analog converter (10), tau6Is the delay time of the high-voltage amplifier (11), tau7Is the delay time of the deformable mirror (2), and s is the complex frequency;
counting:
τ＝τ1+τ2+τ3+τ4+τ5+τ6+τ7 (9)
the formula (9) is substituted for the formula (8) to obtain
Figure FDA0003456582140000031
E in the formula (10)τsExpanding according to Taylor series to obtain:
Figure FDA0003456582140000032
since the delay time τ is small, therefore:
eτs≈1+τs (12)
the formula (12) is substituted for the formula (10) to obtain
Figure FDA0003456582140000033
Then the frequency domain closed loop function estimated by each processing link of the adaptive optical control system is:
Figure FDA0003456582140000034
step 1.2, solving a state space equation of the adaptive optical system, specifically:
output vector of adaptive optics:
y(k)＝M(φW(k+1)-φM(k+1))+w(k) (15)
where M is the influence matrix of the adaptive optics system on the processing of the incident wave signal, i.e. M is the matrix
Figure FDA0003456582140000035
φW(k +1) is the phase of the incident wavefront, phiM(k +1) is the wavefront phase generated by the deformable mirror, w (k) is the measurement noise, and k is the discrete time length;
u(k+1)＝(φW(k+1)-φM(k+1)) (17)
wherein, the wave front phase of the incident light wave is:
φW(k+1)＝FφW(k)+v(k) (18)
wherein F is a diagonal matrix and v (k) is process noise;
by substituting formula (17) for formula (15)
y(k)＝M(u(k+1))+w(k) (19)
The adaptive optics system state space model can be obtained according to the equations (18) and (19), and the state space equation expression of the adaptive optics system is as follows:
Figure FDA0003456582140000041
wherein (A, B, C, D) is an adaptive optics system state space matrix, x (k) is an adaptive optics system n-dimensional state vector, y (k) is an adaptive optics system l-dimensional output vector, u (k) is an adaptive optics system m-dimensional input vector, w (k) is measurement noise, wherein,
Figure FDA0003456582140000042
step 2, selecting minimized residual wave front as a linear quadratic performance index of the adaptive optical system according to the state space equation of the adaptive optical system obtained in the step 1; the linear quadratic performance index J of the adaptive optical system is as follows:
Figure FDA0003456582140000043
wherein phi isM(k +1) is the compensation wavefront, phi, generated by the control deformable mirrorW(k +1) is the incident wavefront collected by the wavefront sensor, Q, R is the weighting matrix, and N is the time length;
according to the principle of the linear quadratic state regulator, it is required to generate a control vector u (k) such that the state vector x (k) always keeps the value of equation (21) at a minimum;
step 3, estimating a state vector of the adaptive optics system according to the state space equation of the adaptive optics system obtained in the step 2
Figure FDA0003456582140000051
The method specifically comprises the following steps:
step 3.1, obtaining the optimal solution of equation (21) through iteration as:
u(k)＝Kx(k+1)/k (22)
the state feedback gain of the adaptive optics system is as follows:
K＝(R+DTQD)-1(BP+(CT+DTQD)) (23)
in equation (23), P is a solution of an algebraic ricati equation, and is obtained by solving the following equation:
P(A-B(R+DTQD)-1BTP+(CTQC-(CTQC-CTQD(R+DTQD)CTQD)))＝0 (24)；
step 3.2, estimating the adaptive optics system state vector
Figure FDA0003456582140000052
Comprises the following steps:
Figure FDA0003456582140000053
step 4, completing the design of the LQG controller of the adaptive optical system according to the parameters obtained in the step 1-3, and calculating the final driving voltage u (k) of the deformable mirror, specifically:
the state feedback process of the linear quadratic Gaussian controller of the adaptive optical system obtained by combining the formula (25) and the formula (22) is as follows:
Figure FDA0003456582140000054
then, the final control voltage u (k) of the deformable mirror is obtained by solving the equation (26).
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101266334A (en) * 2008-05-07 2008-09-17 北京理工大学 Wavefront-free detector self-adapting optical system based on random paralleling gradient descent algorithm
CN103211575A (en) * 2013-03-06 2013-07-24 南京航空航天大学 Control method for human eye aberration correction
CN103901617A (en) * 2014-04-17 2014-07-02 淮海工学院 Wavefront detection-free adaptive optical system based on model
CN107843982A (en) * 2017-12-01 2018-03-27 长春理工大学 Based on real-time phase difference technology without Wavefront detecting adaptive optics system

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111290281A (en) * 2020-03-23 2020-06-16 中国科学院光电技术研究所 Wavefront control method based on ADRC-Smith algorithm

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101266334A (en) * 2008-05-07 2008-09-17 北京理工大学 Wavefront-free detector self-adapting optical system based on random paralleling gradient descent algorithm
CN103211575A (en) * 2013-03-06 2013-07-24 南京航空航天大学 Control method for human eye aberration correction
CN103901617A (en) * 2014-04-17 2014-07-02 淮海工学院 Wavefront detection-free adaptive optical system based on model
CN107843982A (en) * 2017-12-01 2018-03-27 长春理工大学 Based on real-time phase difference technology without Wavefront detecting adaptive optics system

Non-Patent Citations (6)

* Cited by examiner, † Cited by third party
Title
Linear Quadratic Gaussian Control Applied to WFAO Systems: Simulation and Experimental Results;Anne Costille;《European Journal of Control（Volume 17,Issue 3）》;20120731;第302–315页 *
LINEAR-QUADRATIC GAUSSIAN CONTROL OF A DEFORMABLE MIRROR ADAPTIVE OPTICS SYSTEM WITH TIME-DELAYED MEASUREMENTS;PASCHALL,RN and ANDERSON, DJ;《 APPLIED OPTICS 》;19931101;第6347-6358页 *
变形镜与液晶空间光调制器用于波前校正的对比研究;韩柯娜;《中国优秀硕士学位论文全文数据库 (信息科技辑)》;20190815;I135-219 *
基于线性二次高斯控制器的空间相机高频像差校正;陈家兴;《航天返回与遥感》;20210228;第1-8页 *
基于线性二次高斯控制的波前校正实验验证;林海奇;《中国激光》;20190715;第1-6页 *
天文望远镜大气湍流下优化控制技术研究;付强;《中国博士学位论文全文数据库 (基础科学辑)》;20141015;A004-6 *

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