Abstract

A new wavefront sensorless adaptive optics method is presented that can accurately correct for time-varying aberrations using a single focal plane image at each sample instance. The linear relation between the mean square of the aberration gradient and the change in second moment of the image forms the basis of the presented method. The new algorithm results in significant improvements when an accurate model of the aberration’s temporal dynamics is known, by applying a Kalman filter and optimal control. Moreover, where existing wavefront sensorless adaptive optics methods update all modes sequentially, the information of the Kalman filter is used to select and update the modes that are expected to give the greatest improvement in performance. The performance is analyzed in a simulation of an adaptive optics system for atmospheric turbulence. The results show that the new method is able to correct for the aberration more accurately for higher wind speeds and higher noise levels than existing algorithms.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (4)

C. E. Carrizo, R. M. Calvo, and A. Belmonte, “Intensity-based adaptive optics with sequential optimization for laser communications,” Opt. Express 26, 16044–16053 (2018).
[Crossref]

X. He, X. Zhao, S. Cui, and H. Gu, “A rapid hybrid wave front correction algorithm for sensor-less adaptive optics in free space optical communication,” Opt. Commun. 429, 127–137 (2018).
[Crossref]

R. Doelman, N. H. Thao, and M. Verhaegen, “Solving large-scale general phase retrieval problems via a sequence of convex relaxations,” J. Opt. Soc. Am. A 35, 1410–1419 (2018).
[Crossref]

W. Lianghua, P. Yang, W. Shuai, L. Wenjing, C. Shanqiu, and B. Xu, “A high speed model-based approach for wavefront sensorless adaptive optics systems,” Opt. Laser Technol. 99, 124–132 (2018).
[Crossref]

2017 (1)

2015 (3)

2014 (1)

R. Conan and C. Correia, “Object-oriented MATLAB adaptive optics toolbox,” Proc. SPIE 9148, 91486C (2014).
[Crossref]

2011 (1)

2008 (1)

K. Hinnen, M. Verhaegen, and N. Doelman, “A data-driven H2-optimal control approach for adaptive optics,” IEEE Trans. Control Syst. Technol. 16, 381–395 (2008).
[Crossref]

2007 (1)

2006 (2)

2000 (1)

Adler, J.

Ao, M.

Belmonte, A.

Calvo, R. M.

Carhart, G. W.

Carrizo, C. E.

Cauwenberghs, G.

Chapman, H. N.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Process. Mag. 32, 87–109 (2015).
[Crossref]

Cohen, M.

Cohen, O.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Process. Mag. 32, 87–109 (2015).
[Crossref]

Conan, J.-M.

Conan, R.

R. Conan and C. Correia, “Object-oriented MATLAB adaptive optics toolbox,” Proc. SPIE 9148, 91486C (2014).
[Crossref]

Correia, C.

R. Conan and C. Correia, “Object-oriented MATLAB adaptive optics toolbox,” Proc. SPIE 9148, 91486C (2014).
[Crossref]

Cui, S.

X. He, X. Zhao, S. Cui, and H. Gu, “A rapid hybrid wave front correction algorithm for sensor-less adaptive optics in free space optical communication,” Opt. Commun. 429, 127–137 (2018).
[Crossref]

De Lesegno, P. V.

Doelman, N.

K. Hinnen, M. Verhaegen, and N. Doelman, “A data-driven H2-optimal control approach for adaptive optics,” IEEE Trans. Control Syst. Technol. 16, 381–395 (2008).
[Crossref]

Doelman, R.

Eldar, Y. C.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Process. Mag. 32, 87–109 (2015).
[Crossref]

Gu, H.

X. He, X. Zhao, S. Cui, and H. Gu, “A rapid hybrid wave front correction algorithm for sensor-less adaptive optics in free space optical communication,” Opt. Commun. 429, 127–137 (2018).
[Crossref]

He, X.

X. He, X. Zhao, S. Cui, and H. Gu, “A rapid hybrid wave front correction algorithm for sensor-less adaptive optics in free space optical communication,” Opt. Commun. 429, 127–137 (2018).
[Crossref]

Hinnen, K.

K. Hinnen, M. Verhaegen, and N. Doelman, “A data-driven H2-optimal control approach for adaptive optics,” IEEE Trans. Control Syst. Technol. 16, 381–395 (2008).
[Crossref]

Jia, J.

Jiang, W.

Kangjian, Y.

Kulcsár, C.

Lianghua, W.

W. Lianghua, P. Yang, W. Shuai, L. Wenjing, C. Shanqiu, and B. Xu, “A high speed model-based approach for wavefront sensorless adaptive optics systems,” Opt. Laser Technol. 99, 124–132 (2018).
[Crossref]

W. Lianghua, P. Yang, Y. Kangjian, C. Shanqiu, W. Shuai, L. Wenjing, and B. Xu, “Synchronous model-based approach for wavefront sensorless adaptive optics system,” Opt. Express 25, 20584–20597 (2017).
[Crossref]

Linhai, H.

Lipson, S.

Liu, Y.

Miao, J.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Process. Mag. 32, 87–109 (2015).
[Crossref]

Petit, C.

Rao, C.

Raynaud, H.-F.

Ribak, E.

Segev, M.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Process. Mag. 32, 87–109 (2015).
[Crossref]

Shanqiu, C.

W. Lianghua, P. Yang, W. Shuai, L. Wenjing, C. Shanqiu, and B. Xu, “A high speed model-based approach for wavefront sensorless adaptive optics systems,” Opt. Laser Technol. 99, 124–132 (2018).
[Crossref]

W. Lianghua, P. Yang, Y. Kangjian, C. Shanqiu, W. Shuai, L. Wenjing, and B. Xu, “Synchronous model-based approach for wavefront sensorless adaptive optics system,” Opt. Express 25, 20584–20597 (2017).
[Crossref]

Shechtman, Y.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Process. Mag. 32, 87–109 (2015).
[Crossref]

Shuai, W.

W. Lianghua, P. Yang, W. Shuai, L. Wenjing, C. Shanqiu, and B. Xu, “A high speed model-based approach for wavefront sensorless adaptive optics systems,” Opt. Laser Technol. 99, 124–132 (2018).
[Crossref]

W. Lianghua, P. Yang, Y. Kangjian, C. Shanqiu, W. Shuai, L. Wenjing, and B. Xu, “Synchronous model-based approach for wavefront sensorless adaptive optics system,” Opt. Express 25, 20584–20597 (2017).
[Crossref]

Soloviev, O.

Thao, N. H.

Verdult, V.

M. Verhaegen and V. Verdult, Filtering and System Identification: A Least Squares Approach (Cambridge University, 2007).

Verhaegen, M.

R. Doelman, N. H. Thao, and M. Verhaegen, “Solving large-scale general phase retrieval problems via a sequence of convex relaxations,” J. Opt. Soc. Am. A 35, 1410–1419 (2018).
[Crossref]

H. Yang, O. Soloviev, and M. Verhaegen, “Model-based wavefront sensorless adaptive optics system for large aberrations and extended objects,” Opt. Express 23, 24587–24601 (2015).
[Crossref]

K. Hinnen, M. Verhaegen, and N. Doelman, “A data-driven H2-optimal control approach for adaptive optics,” IEEE Trans. Control Syst. Technol. 16, 381–395 (2008).
[Crossref]

M. Verhaegen and V. Verdult, Filtering and System Identification: A Least Squares Approach (Cambridge University, 2007).

Vorontsov, M. A.

Wang, M.

Wenjing, L.

W. Lianghua, P. Yang, W. Shuai, L. Wenjing, C. Shanqiu, and B. Xu, “A high speed model-based approach for wavefront sensorless adaptive optics systems,” Opt. Laser Technol. 99, 124–132 (2018).
[Crossref]

W. Lianghua, P. Yang, Y. Kangjian, C. Shanqiu, W. Shuai, L. Wenjing, and B. Xu, “Synchronous model-based approach for wavefront sensorless adaptive optics system,” Opt. Express 25, 20584–20597 (2017).
[Crossref]

Xu, B.

Yang, H.

Yang, P.

Yang, Q.

Zhao, J.

Zhao, X.

X. He, X. Zhao, S. Cui, and H. Gu, “A rapid hybrid wave front correction algorithm for sensor-less adaptive optics in free space optical communication,” Opt. Commun. 429, 127–137 (2018).
[Crossref]

Zommer, S.

IEEE Signal Process. Mag. (1)

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Process. Mag. 32, 87–109 (2015).
[Crossref]

IEEE Trans. Control Syst. Technol. (1)

K. Hinnen, M. Verhaegen, and N. Doelman, “A data-driven H2-optimal control approach for adaptive optics,” IEEE Trans. Control Syst. Technol. 16, 381–395 (2008).
[Crossref]

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

X. He, X. Zhao, S. Cui, and H. Gu, “A rapid hybrid wave front correction algorithm for sensor-less adaptive optics in free space optical communication,” Opt. Commun. 429, 127–137 (2018).
[Crossref]

Opt. Express (6)

Opt. Laser Technol. (1)

W. Lianghua, P. Yang, W. Shuai, L. Wenjing, C. Shanqiu, and B. Xu, “A high speed model-based approach for wavefront sensorless adaptive optics systems,” Opt. Laser Technol. 99, 124–132 (2018).
[Crossref]

Opt. Lett. (2)

Proc. SPIE (1)

R. Conan and C. Correia, “Object-oriented MATLAB adaptive optics toolbox,” Proc. SPIE 9148, 91486C (2014).
[Crossref]

Other (2)

O. Soloviev, “Optimal basis for modal sensorless adaptive optics,” arXiv:1707.08489 (2017).

M. Verhaegen and V. Verdult, Filtering and System Identification: A Least Squares Approach (Cambridge University, 2007).

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Figures (8)

Fig. 1.
Fig. 1. Schematic representation of a WFSless adaptive optics setup.
Fig. 2.
Fig. 2. Schematic representation of the processes in one output sample time from $kT$ until $(k+1)T$ . The lines indicate the computation of the element in the box at its end, using the element(s) in the box where it originates. Equation numbers are added to indicate which relation is used.
Fig. 3.
Fig. 3. Actuator placement for ${m_1}=7$ . The $m=37$ active actuator centers are represented by solid squares. This center serves as the local origin of this actuators’ influence function [i.e., ${\chi_1}={\chi_2}=0$ in Eq. (34)].
Fig. 4.
Fig. 4. Results for varying the wind speed. The other simulation parameters are given in Table 2. “Dynamic SM” represents the method presented in this paper, and “Static SM” is the existing method presented in [14]. The boxes indicate the 25th and 75th percentiles of the results in the Monte Carlo simulation, and the lines are drawn through the medians. (a) Mean Strehl ratio. (b) Mean second moment of the PSF.
Fig. 5.
Fig. 5. Results of the new algorithm for different values of $p$ . (a)  $p$ is varied while all the other parameters are kept at their standard values given in Table 2. The presentation of the results is similar to Fig. 4. (b) Influence of the wind speed on the best choice of $p$ ; only the median Strehl ratios over the Monte Carlo simulations are shown.
Fig. 6.
Fig. 6. Example of the most often selected actuators by the method described in Section 3.D. The simulation parameters equal the standard values in Table 2 with $N=1000$ sample times, and the configuration of the DM is as in Fig. 3. The color scale displays how many times this actuator was chosen to be part of the subset ${\cal I}$ .
Fig. 7.
Fig. 7. Strehl ratio for different values of the Fried parameter ${r_0}$ . The presentation of the results is similar to Fig. 4. The line indicated by “DM optimal” displays the maximum possible performance of the DM for each turbulence strength.
Fig. 8.
Fig. 8. Strehl ratios for different measurement noise values. The presentation of the results is similar to Fig. 4.

Tables (2)

Tables Icon

Table 1. Table of Notations

Tables Icon

Table 2. Simulation Parameters a

Equations (34)

Equations on this page are rendered with MathJax. Learn more.

I ( ζ , ϕ ) = | F ( A ( χ ) e i ϕ ( χ ) ) | 2 ,
z ( ϕ ) = R 2 I ( ζ , ϕ ) | ζ | 2 d ζ .
R 2 ( I ( ζ , ϕ ) I ( ζ , 0 ) ) | ζ | 2 d ζ = 1 4 π 2 R 2 A 2 ( χ ) | ϕ ( χ ) | 2 d χ ,
z ( ϕ ) z ( 0 ) = c 0 ϕ 2 2 ,
ϕ ~ ( χ ) = ϕ ( χ ) + ϕ ( χ ) ,
ϕ ( χ ) = j = 1 m u j E j ( χ ) ,
ϕ j ( χ ) : = β E j ( χ ) + ϕ ( χ ) .
S i j = R 2 ( E i χ 1 E j χ 1 + E i χ 2 E j χ 2 ) d χ 1 d χ 2 ,
s i = R 2 ( E i χ 1 ) 2 + ( E i χ 2 ) 2 d χ 1 d χ 2 ,
y m = Δ [ z ( ϕ 1 ) z ( ϕ ) z ( ϕ m ) z ( ϕ ) ] = C m u + y m , 0 ,
u = C m 1 ( y m y m , 0 ) .
ϕ j ( χ , t + j T i ) = β E j ( χ ) + ϕ ( χ , t + j T i ) .
S = U Σ U T ,
u d = C d 1 ( y d , m y d , 0 ) ,
x = B u .
ϕ = E u = E B 1 x .
x t ( k T i + T i ) = A f x t ( k T i ) + w f ( k T i ) ,
x t ( k T + T ) = A x t ( k T ) + w ( k T ) ,
x m ( k T i ) = B u ( k T i T i ) ,
x ( k T i ) = x t ( k T i ) + x m ( k T i ) .
y ( k T ) = Δ [ z ( ϕ I 1 ( k T ( p 1 ) T i ) ) z ( ϕ ( k T p T i ) ) z ( ϕ I p ( k T ) ) z ( ϕ ( k T p T i ) ) ] = C ( k T ) x ( k T ) + y 0 ( k T ) + v ( k T ) ,
x ( k T + T ) = A x ( k T ) + B u ( k T ) A B u ( k T T ) + w ( k T ) ,
y ( k T ) = C ( k T ) x ( k T ) + y 0 ( k T ) + v ( k T ) .
x ^ ( k T | k T ) = x ^ ( k T | k T T ) + K ( k T ) ( y ( k T ) C ( k T ) x ^ ( k T | k T T ) y 0 ( k T ) ) ,
x ^ ( k T + T | k T ) = A ( x ^ ( k T | k T ) B u ( k T T i ) ) + B u ( k T + p T i ) .
x ^ ( k T + ( j + 1 ) T i | k T ) = A f ( x ^ ( k T + j T i | k T ) B u ( k T + ( j 1 ) T i ) ) + B u ( k T + j T i )
min u ( k T + ( j 1 ) T i ) x ^ ( k T + j T i | k T ) 2 2 , j = 1 , 2 , , p + 1.
x ^ ( k T + j T i | k T ) = 0 f o r j = 1 , 2 , , p + 1 ,
u ( k T ) = B 1 A f ( x ^ ( k T | k T ) B u ( k T T i ) ) ,
u ( k T + j T i ) = B 1 A f B u ( k T + ( j 1 ) T i ) f o r j = 1 , , p 1 ,
u ( k T + p T i ) = B 1 A ( x ^ ( k T | k T ) B u ( k T T i ) ) .
x ^ ( k T | k T ) = K ( k T ) ( y ( k T ) y 0 ( k T ) ) .
P ( k T + j T i | k T ) : = E [ ( x ( k T + j T i ) x ^ ( k T + j T i | k T ) ) ( x ( k T + j T i ) x ^ ( k T + j T i | k T ) ) T ] ,
E i ( χ ) = e ln ( λ ) ( ( χ 1 2 + χ 2 2 ) / d ) 2 ,

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