Abstract

A phased sparse aperture system provides an economic solution to get high resolution images with less volume and weight. The crucial point of such systems is adaptive correction of piston, that is, a close-loop control aiming at stabilizing the optical path differences within a fraction of the wavelength. In this paper, we present an autonomous phasing approach using stochastic parallel gradient descent algorithm through optimization of image quality. The synthetic system can be phased by iteratively commanding piston actuators without any additional optics. Simulations are first performed to test the validity. Then experimental results based on a binocular telescope testbed are presented, showing that our proposed close-loop control of piston correction doesn’t only work with both laser and white-light point sources, but also with an extended object.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (2)

2016 (3)

2015 (1)

2014 (1)

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

2012 (1)

M. Clampin, “Status of the James Webb Space Telescope observatory,” Proc. SPIE 8442, 84422A (2012).
[Crossref]

2011 (1)

H. Yang and X. Li, “Comparison of several stochastic parallel optimization algorithms for adaptive optics system without a wavefront sensor,” Opt. Laser Technol. 43(3), 630–635 (2011).
[Crossref]

2010 (1)

2009 (1)

2008 (1)

R. Gilmozzi and J. Spyromilio, “The 42m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[Crossref]

2006 (1)

2003 (1)

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, and S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiment on NGST’s wavefront control testbed,” Proc. SPIE 4850, 318–328 (2003).
[Crossref]

2000 (1)

1998 (2)

1988 (1)

1984 (1)

J. S. Fender, “Synthetic apertures: an overview,” Proc. SPIE 440, 2–7 (1984).
[Crossref]

1979 (1)

R. A. Gonsalves and R. Chidlaw, “Wavefront sensing by phase retrieval,” Proc. SPIE 207, 32–39 (1979).
[Crossref]

1974 (1)

R. A. Muller and A. Buffington, “Real-time correction of atmospherically degraded telescope images through image sharpening,” J. Opt. Soc. Am. A. 64(9), 1200–1210 (1974).
[Crossref]

Aubrun, J.-N.

Basinger, S. A.

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, and S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiment on NGST’s wavefront control testbed,” Proc. SPIE 4850, 318–328 (2003).
[Crossref]

Bell, R.

Bellanger, C.

Benson, L.

Benson, R.

Bouchez, A. H.

Bowers, C. W.

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, and S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiment on NGST’s wavefront control testbed,” Proc. SPIE 4850, 318–328 (2003).
[Crossref]

Brace, D.

Breakwell, J.

Buffington, A.

R. A. Muller and A. Buffington, “Real-time correction of atmospherically degraded telescope images through image sharpening,” J. Opt. Soc. Am. A. 64(9), 1200–1210 (1974).
[Crossref]

Burns, L. A.

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, and S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiment on NGST’s wavefront control testbed,” Proc. SPIE 4850, 318–328 (2003).
[Crossref]

Burriesci, L.

Byler, E.

Camp, J.

Chanan, G.

Chidlaw, R.

R. A. Gonsalves and R. Chidlaw, “Wavefront sensing by phase retrieval,” Proc. SPIE 207, 32–39 (1979).
[Crossref]

Clampin, M.

M. Clampin, “Status of the James Webb Space Telescope observatory,” Proc. SPIE 8442, 84422A (2012).
[Crossref]

Clausse, J. M.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Cross, G.

Cuneo, P.

Dali Ali, W.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

de Leon, E.

Dean, P.

Dekens, F.

Deprez, M.

Digumerthi, R.

Dong, L.

Duncan, A.

Farley, J.

Fender, J. S.

J. S. Fender, “Synthetic apertures: an overview,” Proc. SPIE 440, 2–7 (1984).
[Crossref]

Fienup, J. R.

Gilmozzi, R.

R. Gilmozzi and J. Spyromilio, “The 42m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[Crossref]

Girard, P.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Gleichman, K.

Gong, C.

Gonsalves, R. A.

R. A. Gonsalves and R. Chidlaw, “Wavefront sensing by phase retrieval,” Proc. SPIE 207, 32–39 (1979).
[Crossref]

Green, A.

Hamilton, H. H.

He, X.

Henault, F.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Herman, B.

Hill, J. M.

Jiang, J.

Jiang, W.

Kendrick, R. L.

Kirkman, D.

Lauraitis, K.

Li, X.

H. Yang and X. Li, “Comparison of several stochastic parallel optimization algorithms for adaptive optics system without a wavefront sensor,” Opt. Laser Technol. 43(3), 630–635 (2011).
[Crossref]

H. Yang, X. Li, C. Gong, and W. Jiang, “Restoration of turbulence-degraded extended object using the stochastic parallel gradient descent algorithm: numerical simulation,” Opt. Express 17(5), 3052–3062 (2009).
[Crossref] [PubMed]

Lombard, L.

Lorell, K.

Lowman, A. E.

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, and S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiment on NGST’s wavefront control testbed,” Proc. SPIE 4850, 318–328 (2003).
[Crossref]

Ma, H.

Marcotto, A.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Martin, R.

Mast, T.

Matosian, K.

Mauclert, N.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

McLeod, B. A.

Meilland, A.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Michaels, S.

Mourard, D.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Muench, T.

Muller, R. A.

R. A. Muller and A. Buffington, “Real-time correction of atmospherically degraded telescope images through image sharpening,” J. Opt. Soc. Am. A. 64(9), 1200–1210 (1974).
[Crossref]

Nelson, J.

Ni, M.

Ohara, C.

Ohara, C. M.

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, and S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiment on NGST’s wavefront control testbed,” Proc. SPIE 4850, 318–328 (2003).
[Crossref]

Palmer, A.

Patru, F.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Paxman, R.

Paxman, R. G.

Petrone, P.

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, and S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiment on NGST’s wavefront control testbed,” Proc. SPIE 4850, 318–328 (2003).
[Crossref]

Primot, J.

Qi, B.

Redding, D. C.

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, and S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiment on NGST’s wavefront control testbed,” Proc. SPIE 4850, 318–328 (2003).
[Crossref]

Ren, G.

Roseman, D.

Russell, S.

Schweiger, P.

Shi, F.

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, and S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiment on NGST’s wavefront control testbed,” Proc. SPIE 4850, 318–328 (2003).
[Crossref]

Sigler, R.

Simar, J. F.

Sivokon, V. P.

Smith, J.

Spyromilio, J.

R. Gilmozzi and J. Spyromilio, “The 42m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[Crossref]

Stockman, Y.

Stone, R.

Stubbs, D.

Surdej, J.

Swietek, G.

Tan, Y.

Tarmoul, N.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Thatcher, J.

Tischhauser, C.

Troy, M.

van Dam, M. A.

Vorontsov, M. A.

Wattellier, B.

Wong, H.

Xie, Z.

Yang, H.

H. Yang and X. Li, “Comparison of several stochastic parallel optimization algorithms for adaptive optics system without a wavefront sensor,” Opt. Laser Technol. 43(3), 630–635 (2011).
[Crossref]

H. Yang, X. Li, C. Gong, and W. Jiang, “Restoration of turbulence-degraded extended object using the stochastic parallel gradient descent algorithm: numerical simulation,” Opt. Express 17(5), 3052–3062 (2009).
[Crossref] [PubMed]

Zarifis, V.

Zeng, Q.

Zhao, W.

Appl. Opt. (6)

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

J. Opt. Soc. Am. A. (1)

R. A. Muller and A. Buffington, “Real-time correction of atmospherically degraded telescope images through image sharpening,” J. Opt. Soc. Am. A. 64(9), 1200–1210 (1974).
[Crossref]

Mon. Not. R. Astron. Soc. (1)

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Opt. Express (4)

Opt. Laser Technol. (1)

H. Yang and X. Li, “Comparison of several stochastic parallel optimization algorithms for adaptive optics system without a wavefront sensor,” Opt. Laser Technol. 43(3), 630–635 (2011).
[Crossref]

Opt. Lett. (1)

Proc. SPIE (5)

J. S. Fender, “Synthetic apertures: an overview,” Proc. SPIE 440, 2–7 (1984).
[Crossref]

M. Clampin, “Status of the James Webb Space Telescope observatory,” Proc. SPIE 8442, 84422A (2012).
[Crossref]

R. Gilmozzi and J. Spyromilio, “The 42m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[Crossref]

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, and S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiment on NGST’s wavefront control testbed,” Proc. SPIE 4850, 318–328 (2003).
[Crossref]

R. A. Gonsalves and R. Chidlaw, “Wavefront sensing by phase retrieval,” Proc. SPIE 207, 32–39 (1979).
[Crossref]

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Figures (10)

Fig. 1
Fig. 1 The relation curves between the PSF sharpness metrics and pistons using 4 candidate definition functions.
Fig. 2
Fig. 2 Flowchart of SPGD phasing algorithm.
Fig. 3
Fig. 3 Simulation setup. (a) The USAF 1951 resolution test chart used as an extended object. (b) The four aperture configuration. (c) The loaded piston errors [200, 300, 400] nm.
Fig. 4
Fig. 4 Results of simulation. (a) The evolution of the sharpness metric as SPGD algorithm proceeds. (b) The residual piston errors [12, 4, 16] nm after close-loop control. The images without (c) and with (d) piston correction. (e) The trace lines of the same sets of bars of (c) and (d) marked with blue and red dotted lines, respectively.
Fig. 5
Fig. 5 The evolutions of the sharpness metrics generated by SPGD algorithm using different update gains.
Fig. 6
Fig. 6 The optical configuration of the binocular telescope testbed. The piston actuator (the lower right), is composed of a pyramidal mirror and a coupled motorized translation stage. The high-precision one (PI’s product, E-727) can achieve a spatial resolution of 1 nm.
Fig. 7
Fig. 7 Experimental phasing results with a laser source. (a) The evolution of the sharpness metric as SPGD algorithm proceeds. The images without (b) and with (c) piston correction.
Fig. 8
Fig. 8 Experimental phasing results with a white-light source. (a) The evolution of the sharpness metric as SPGD algorithm proceeds. The images without (b) and with (c) piston correction.
Fig. 9
Fig. 9 The spectrums of the images without (a) and with (b) piston correction (log scale).
Fig. 10
Fig. 10 Experimental phasing results with an extended object. The images without (a) and with (b) piston correction. (c) The evolution of the sharpness metric as SPGD algorithm proceeds. (d) The trace lines of (a) and (b) marked with blue and red dotted lines, respectively.

Tables (1)

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Table 1 Different candidate image sharpness metrics

Equations (9)

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

I(x,y)=o(x,y)h(x,y)+n(x,y)
h(x,y,λ)= | FT( P(u,v,λ) ) | 2
P(u,v,λ)=p(u u 1 ,v v 1 )+ n=2 N p(u u n ,v v n ) exp( 2πi λ OP D n )
h(x,y)= λ 1 λ M h(x,y,λ)s(λ) dλ
OPD ' n =OP D n m n
w( u,v,t )= n=1 N m n ( t ) S n ( u,v )
S n ( u,v )= 2π λ p(u u n ,v v n )
m n (k+1) = m n (k) +γδ J (k) δ m n (k)
δJ=J( m+δm )J( mδm )

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