Abstract

High-resolution adaptive-optical systems with thousands to millions of pixels will most likely have to employ serial- or matrix-addressed spatial light modulators (e.g., microelectromechanical-system-on-VLSI spatial light modulators). We compare parallel gradient descent adaptive-optics algorithms with serial gradient descent algorithms running on serially addressed modulators. While serial algorithms have previously been shown to require more iterations than parallel algorithms, we show that, because of the limitations of the databus, each serial iteration of the algorithm on a serial modulator requires significantly less time to complete than a parallel iteration, thereby favoring the serial algorithm when time to convergence is used as the performance metric. Thus, such high-resolution serially addressed devices are generally better matched to the serial-update wavefront correction algorithm owing to the data load penalty imposed by the bandwidth-limited databus of these modulators.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  11. A. Gehner, M. Wildenhain, H. Neumann, J. Knobbe, and O. Komenda, "MEMS analog light processing--an enabling technology for adaptive optical phase control," Proc. SPIE 6113, 1-15 (2006).
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    [CrossRef]
  13. M. Ealey and J. Trauger, "High-density deformable mirrors to enable coronographic planet detection," Proc. SPIE 5166, 172-179 (2003).
    [CrossRef]
  14. J. Werfel, X. Xie, and H. S. Seung, "Learning curves for stochastic gradient descent in linear feedforward networks," in Advances in Neural Information Processing Systems (MIT Press, 2004).
  15. J. Alspector, R. Meir, B. Yuhas, A. Jayakumar, and D. Lippe, "A study of parallel perturbative gradient descent," in Advances in Neural Information Processing Systems (MIT Press, 1994), pp. 803-810.
  16. G. Cauwenberghs, "A fast stochastic error-descent algorithm for supervised learning and optimization," in Advances in Neural Information Processing Systems (Morgan Kaufmann, 1992), pp. 244-251.
  17. J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2007).

2006 (3)

A. Gehner, M. Wildenhain, H. Neumann, J. Knobbe, and O. Komenda, "MEMS analog light processing--an enabling technology for adaptive optical phase control," Proc. SPIE 6113, 1-15 (2006).

C. Ting, A. Rayankula, M. Giles, and P. Furth, "Closed-loop adaptive optics using a CMOS image quality metric sensor," Proc. SPIE 6306, 63060C (2006).
[CrossRef]

S. Zommer, E. N. Ribak, S. G. Lipson, and J. Adler, "Simulated annealing in ocular adaptive optics," Opt. Lett. 31, 939-941 (2006).
[CrossRef] [PubMed]

2004 (1)

S. Serati, K. Bauchert, and P. Millett, "Development of large-array spatial light modulators," Proc. SPIE 5362, 119-127 (2004).
[CrossRef]

2003 (1)

M. Ealey and J. Trauger, "High-density deformable mirrors to enable coronographic planet detection," Proc. SPIE 5166, 172-179 (2003).
[CrossRef]

2001 (1)

V. Shrauger and C. Warde, "Development of a high-speed high-fill-factor phase-only spatial light modulator," Proc. SPIE 4291, 101-108 (2001).
[CrossRef]

2000 (1)

1998 (2)

1997 (3)

Adler, J.

Alspector, J.

J. Alspector, R. Meir, B. Yuhas, A. Jayakumar, and D. Lippe, "A study of parallel perturbative gradient descent," in Advances in Neural Information Processing Systems (MIT Press, 1994), pp. 803-810.

Bauchert, K.

S. Serati, K. Bauchert, and P. Millett, "Development of large-array spatial light modulators," Proc. SPIE 5362, 119-127 (2004).
[CrossRef]

Carhart, G. W.

Cauwenberghs, G.

Cohen, M.

Ealey, M.

M. Ealey and J. Trauger, "High-density deformable mirrors to enable coronographic planet detection," Proc. SPIE 5166, 172-179 (2003).
[CrossRef]

Furth, P.

C. Ting, A. Rayankula, M. Giles, and P. Furth, "Closed-loop adaptive optics using a CMOS image quality metric sensor," Proc. SPIE 6306, 63060C (2006).
[CrossRef]

Gehner, A.

A. Gehner, M. Wildenhain, H. Neumann, J. Knobbe, and O. Komenda, "MEMS analog light processing--an enabling technology for adaptive optical phase control," Proc. SPIE 6113, 1-15 (2006).

Giles, M.

C. Ting, A. Rayankula, M. Giles, and P. Furth, "Closed-loop adaptive optics using a CMOS image quality metric sensor," Proc. SPIE 6306, 63060C (2006).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2007).

Jayakumar, A.

J. Alspector, R. Meir, B. Yuhas, A. Jayakumar, and D. Lippe, "A study of parallel perturbative gradient descent," in Advances in Neural Information Processing Systems (MIT Press, 1994), pp. 803-810.

Kalogeropoulos, T. E.

T. E. Kalogeropoulos, Y. G. Saridakis, and M. S. Zakynthinaki, "Improved stochastic optimization algorithms for adaptive optics," Comput. Phys. Commun. 99, 255-269 (1997).
[CrossRef]

Knobbe, J.

A. Gehner, M. Wildenhain, H. Neumann, J. Knobbe, and O. Komenda, "MEMS analog light processing--an enabling technology for adaptive optical phase control," Proc. SPIE 6113, 1-15 (2006).

Komenda, O.

A. Gehner, M. Wildenhain, H. Neumann, J. Knobbe, and O. Komenda, "MEMS analog light processing--an enabling technology for adaptive optical phase control," Proc. SPIE 6113, 1-15 (2006).

Lippe, D.

J. Alspector, R. Meir, B. Yuhas, A. Jayakumar, and D. Lippe, "A study of parallel perturbative gradient descent," in Advances in Neural Information Processing Systems (MIT Press, 1994), pp. 803-810.

Lipson, S. G.

Meir, R.

J. Alspector, R. Meir, B. Yuhas, A. Jayakumar, and D. Lippe, "A study of parallel perturbative gradient descent," in Advances in Neural Information Processing Systems (MIT Press, 1994), pp. 803-810.

Millett, P.

S. Serati, K. Bauchert, and P. Millett, "Development of large-array spatial light modulators," Proc. SPIE 5362, 119-127 (2004).
[CrossRef]

Neumann, H.

A. Gehner, M. Wildenhain, H. Neumann, J. Knobbe, and O. Komenda, "MEMS analog light processing--an enabling technology for adaptive optical phase control," Proc. SPIE 6113, 1-15 (2006).

Pruidze, D. V.

Rayankula, A.

C. Ting, A. Rayankula, M. Giles, and P. Furth, "Closed-loop adaptive optics using a CMOS image quality metric sensor," Proc. SPIE 6306, 63060C (2006).
[CrossRef]

Ribak, E. N.

Ricklin, J. C.

Saridakis, Y. G.

T. E. Kalogeropoulos, Y. G. Saridakis, and M. S. Zakynthinaki, "Improved stochastic optimization algorithms for adaptive optics," Comput. Phys. Commun. 99, 255-269 (1997).
[CrossRef]

Serati, S.

S. Serati, K. Bauchert, and P. Millett, "Development of large-array spatial light modulators," Proc. SPIE 5362, 119-127 (2004).
[CrossRef]

Seung, H. S.

J. Werfel, X. Xie, and H. S. Seung, "Learning curves for stochastic gradient descent in linear feedforward networks," in Advances in Neural Information Processing Systems (MIT Press, 2004).

Shrauger, V.

V. Shrauger and C. Warde, "Development of a high-speed high-fill-factor phase-only spatial light modulator," Proc. SPIE 4291, 101-108 (2001).
[CrossRef]

Sivokon, V. P.

Ting, C.

C. Ting, A. Rayankula, M. Giles, and P. Furth, "Closed-loop adaptive optics using a CMOS image quality metric sensor," Proc. SPIE 6306, 63060C (2006).
[CrossRef]

Trauger, J.

M. Ealey and J. Trauger, "High-density deformable mirrors to enable coronographic planet detection," Proc. SPIE 5166, 172-179 (2003).
[CrossRef]

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics (Academic, 1991).

Voelz, D. G.

Voronstsov, M. A.

Vorontsov, M. A.

Warde, C.

V. Shrauger and C. Warde, "Development of a high-speed high-fill-factor phase-only spatial light modulator," Proc. SPIE 4291, 101-108 (2001).
[CrossRef]

Werfel, J.

J. Werfel, X. Xie, and H. S. Seung, "Learning curves for stochastic gradient descent in linear feedforward networks," in Advances in Neural Information Processing Systems (MIT Press, 2004).

Wildenhain, M.

A. Gehner, M. Wildenhain, H. Neumann, J. Knobbe, and O. Komenda, "MEMS analog light processing--an enabling technology for adaptive optical phase control," Proc. SPIE 6113, 1-15 (2006).

Xie, X.

J. Werfel, X. Xie, and H. S. Seung, "Learning curves for stochastic gradient descent in linear feedforward networks," in Advances in Neural Information Processing Systems (MIT Press, 2004).

Yuhas, B.

J. Alspector, R. Meir, B. Yuhas, A. Jayakumar, and D. Lippe, "A study of parallel perturbative gradient descent," in Advances in Neural Information Processing Systems (MIT Press, 1994), pp. 803-810.

Zakynthinaki, M. S.

T. E. Kalogeropoulos, Y. G. Saridakis, and M. S. Zakynthinaki, "Improved stochastic optimization algorithms for adaptive optics," Comput. Phys. Commun. 99, 255-269 (1997).
[CrossRef]

Zommer, S.

Appl. Opt. (1)

Comput. Phys. Commun. (1)

T. E. Kalogeropoulos, Y. G. Saridakis, and M. S. Zakynthinaki, "Improved stochastic optimization algorithms for adaptive optics," Comput. Phys. Commun. 99, 255-269 (1997).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Lett. (2)

Proc. SPIE (5)

C. Ting, A. Rayankula, M. Giles, and P. Furth, "Closed-loop adaptive optics using a CMOS image quality metric sensor," Proc. SPIE 6306, 63060C (2006).
[CrossRef]

V. Shrauger and C. Warde, "Development of a high-speed high-fill-factor phase-only spatial light modulator," Proc. SPIE 4291, 101-108 (2001).
[CrossRef]

A. Gehner, M. Wildenhain, H. Neumann, J. Knobbe, and O. Komenda, "MEMS analog light processing--an enabling technology for adaptive optical phase control," Proc. SPIE 6113, 1-15 (2006).

S. Serati, K. Bauchert, and P. Millett, "Development of large-array spatial light modulators," Proc. SPIE 5362, 119-127 (2004).
[CrossRef]

M. Ealey and J. Trauger, "High-density deformable mirrors to enable coronographic planet detection," Proc. SPIE 5166, 172-179 (2003).
[CrossRef]

Other (5)

J. Werfel, X. Xie, and H. S. Seung, "Learning curves for stochastic gradient descent in linear feedforward networks," in Advances in Neural Information Processing Systems (MIT Press, 2004).

J. Alspector, R. Meir, B. Yuhas, A. Jayakumar, and D. Lippe, "A study of parallel perturbative gradient descent," in Advances in Neural Information Processing Systems (MIT Press, 1994), pp. 803-810.

G. Cauwenberghs, "A fast stochastic error-descent algorithm for supervised learning and optimization," in Advances in Neural Information Processing Systems (Morgan Kaufmann, 1992), pp. 244-251.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2007).

R. K. Tyson, Principles of Adaptive Optics (Academic, 1991).

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Figures (4)

Fig. 1
Fig. 1

Simplified adaptive-optical phase compensation setup for Strehl ratio optimization, which corresponds with our simulation.

Fig. 2
Fig. 2

M × N array of wavefront modulators employing a raster-addressing architecture.

Fig. 3
Fig. 3

(Color online) Number of signal lines required for three wavefront modulator addressing schemes: direct addressed, matrix addressed, and rasterized-matrix addressed.

Fig. 4
Fig. 4

(Color online) TTC required for 80% Strehl ratio convergence for a stochastic serial gradient descent algorithm using one perturbation per iteration on a serially addressed modulator using a 32   MHz pixel clock.

Tables (1)

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Table 1 Comparison of Simulations of Stochastic Gradient Descent Algorithms on a Serially Addressed Modulator with 576 Elements a

Equations (13)

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TTC p = l Q p ( m , n ) [ t c p ( m , n ) + t pix m n k ] .
TTC p l Q p ( m , n ) t pix m n k .
TTC s = l Q s ( m , n ) [ t c s + t pix ] .
TTC s l Q s ( m , n ) t pix .
I ( f x , f y ) 1 λ 2 F 2 | { U ¯ m ( x , y ) } | 2 ,
U ¯ m ( x , y ) = A e j W ( x , y ) e j M ( x , y ) P ( x , y ) = A e j T ( x , y ) P ( x , y ) ,
P ( x , y ) = { 1 , | x | L x 2 , | y | L y 2 0 , otherwise .
I ( f x , f y ) A 2 λ 2 F 2 | { e j T ( x , y ) } [ ( sin ( π f x L x ) π f x L x ) ( sin ( π f y L y ) π f y L y ) ] | 2 ,
M = { e j M i , j } , i = 1 m ; j = 1 n ,
W = { e j W i , j } ,
T = { e j T i , j } = { e j ( W i , j + T i , j ) } ,
M i , j s = M i , j s + ϕ ,
M i , j s +1 = M i , j s + Δ I η ϕ ( 1 I s I max ) ,

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