Abstract

A novel method nicknamed ELASTIC is proposed for the alignment of multiple-aperture telescopes, in particular segmented telescopes. It only needs the acquisition of two diversity images of an unresolved source, and is based on the computation of a modified, frequency-shifted, cross-spectrum. It provides a polychromatic large-range tip/tilt estimation with the existing hardware and an inexpensive noniterative unsupervised algorithm. Its performance is studied and optimized by means of simulations. They show that with 5000 photoelectrons/subaperture/frame and 1024×1024 pixel images, residues are within the capture range of interferometric phasing algorithms such as phase diversity. The closed-loop alignment of a 6-subaperture mirror provides an experimental demonstration of the effectiveness of the method.

© 2017 Optical Society of America

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References

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2016 (2)

M. D. Perrin, D. S. Acton, C.-P. Lajoie, J. S. Knight, M. D. Lallo, M. Allen, W. Baggett, E. Barker, T. Comeau, E. Coppock, B. H. Dean, G. Hartig, W. L. Hayden, M. Jordan, A. Jurling, T. Kulp, J. Long, M. W. McElwain, L. Meza, E. P. Nelan, R. Soummer, J. Stansberry, C. Stark, R. Telfer, A. L. Welsh, T. P. Zielinski, and N. T. Zimmerman, “Preparing for JWST wavefront sensing and control operations,” Proc. SPIE 9904, 99040F (2016).
[Crossref]

M. Sauvage, J. Amiaux, J. Austin, M. Bello, G. Bianucci, S. Chesné, O. Citterio, C. Collette, S. Correia, G. A. Durand, S. Molinari, G. Pareschi, Y. Penfornis, G. Sironi, G. Valsecchi, S. Verpoort, and U. Wittrock, “A development roadmap for critical technologies needed for TALC: a deployable 20m annular space telescope,” Proc. SPIE 9904, 99041L (2016).
[Crossref]

2015 (2)

M. R. Bolcar, K. Balasubramanian, M. Clampin, J. Crooke, L. Feinberg, M. Postman, M. Quijada, B. Rauscher, D. Redding, N. Rioux, S. Shaklan, H. P. Stahl, C. Stahle, and H. Thronson, “Technology development for the Advanced Technology Large Aperture Space Telescope (ATLAST) as a candidate large UV-Optical-Infrared (LUVOIR) surveyor,” Proc. SPIE 9602, 960209 (2015).
[Crossref]

R. E. Carlisle and D. S. Acton, “Demonstration of extended capture range for James Webb Space Telescope phase retrieval,” Appl. Opt. 54, 6454–6460 (2015).
[Crossref]

2014 (2)

A. S. Jurling and J. R. Fienup, “Applications of algorithmic differentiation to phase retrieval algorithms,” J. Opt. Soc. Am. A 31, 1348–1359 (2014).
[Crossref]

G. Moretto, J. R. Kuhn, E. Thiébaut, M. Langlois, S. V. Berdyugina, C. Harlingten, and D. Halliday, “New strategies for an extremely large telescope dedicated to extremely high contrast: the Colossus project,” Proc. SPIE 9145, 91451L (2014).
[Crossref]

2012 (1)

D. S. Acton, J. S. Knight, A. Contos, S. Grimaldi, J. Terry, P. Lightsey, A. Barto, B. League, B. Dean, J. S. Smith, C. Bowers, D. Aronstein, L. Feinberg, W. Hayden, T. Comeau, R. Soummer, E. Elliott, M. Perrin, and C. W. Starr, “Wavefront sensing and controls for the James webb space telescope,” Proc. SPIE 8442, 84422H (2012).
[Crossref]

2011 (1)

2009 (1)

2008 (2)

F. Baron, I. Mocoeur, F. Cassaing, and L. M. Mugnier, “Unambiguous phase retrieval as a cophasing sensor for phased array telescopes: derivation of an analytical estimator,” J. Opt. Soc. Am. A 25, 1000–1015 (2008).
[Crossref]

S. Meimon, E. Delavaquerie, F. Cassaing, T. Fusco, L. M. Mugnier, and V. Michau, “Phasing segmented telescopes with long-exposure phase diversity images,” Proc. SPIE 7012, 701214 (2008).
[Crossref]

2006 (4)

D. S. Acton, T. Towell, J. Schwenker, J. Swensen, D. Shields, E. Sabatke, L. Klingemann, A. R. Contos, B. Bauer, K. Hansen, P. D. Atcheson, D. Redding, F. Shi, S. Basinger, B. Dean, and L. Burns, “Demonstration of the James Webb Space Telescope commissioning on the JWST testbed telescope,” Proc. SPIE 6265, 62650R (2006).
[Crossref]

B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, “Phase retrieval algorithm for JWST flight and testbed telescope,” Proc. SPIE 6265, 626511 (2006).
[Crossref]

I. Mocœur, F. Cassaing, F. Baron, L. Mugnier, S. Hofer, and H. Thiele, “Darwin fringe sensor: experimental results on the BRISE bench,” Proc. SPIE 6268, 62682B (2006).
[Crossref]

F. Cassaing, B. Sorrente, L. Mugnier, G. Rousset, V. Michau, I. Mocœur, and F. Baron, “BRISE: a multipurpose bench for cophasing sensors,” Proc. SPIE 6268, 62683A (2006).
[Crossref]

2003 (1)

L. H. Lee, G. Vasudevan, and E. H. Smith, “Point-by-point approach to phase-diverse phase retrieval,” Proc. SPIE 4850, 441–452 (2003).
[Crossref]

2000 (1)

D. A. Carrara, B. J. Thelen, and R. G. Paxman, “Aberration correction of segmented-aperture telescopes by using phase diversity,” Proc. SPIE 4123, 56–63 (2000).
[Crossref]

1998 (1)

D. C. Redding, S. A. Basinger, A. E. Lowman, A. Kissil, P. Y. Bely, R. Burg, R. G. Lyon, G. E. Mosier, M. Femiano, M. E. Wilson, R. G. Schunk, L. D. Craig, D. N. Jacobson, J. M. Rakoczy, and J. B. Hadaway, “Wavefront sensing and control for a next generation space telescope,” Proc. SPIE 3356, 758–772 (1998).
[Crossref]

1988 (2)

1987 (1)

1982 (1)

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 215829 (1982).
[Crossref]

1976 (1)

1974 (1)

K. T. Knox and B. J. Thompson, “Recovery of images from atmospherically degraded short-exposure photographs,” Astrophys. J. 193, L45–L48 (1974).
[Crossref]

Acton, D. S.

M. D. Perrin, D. S. Acton, C.-P. Lajoie, J. S. Knight, M. D. Lallo, M. Allen, W. Baggett, E. Barker, T. Comeau, E. Coppock, B. H. Dean, G. Hartig, W. L. Hayden, M. Jordan, A. Jurling, T. Kulp, J. Long, M. W. McElwain, L. Meza, E. P. Nelan, R. Soummer, J. Stansberry, C. Stark, R. Telfer, A. L. Welsh, T. P. Zielinski, and N. T. Zimmerman, “Preparing for JWST wavefront sensing and control operations,” Proc. SPIE 9904, 99040F (2016).
[Crossref]

R. E. Carlisle and D. S. Acton, “Demonstration of extended capture range for James Webb Space Telescope phase retrieval,” Appl. Opt. 54, 6454–6460 (2015).
[Crossref]

D. S. Acton, J. S. Knight, A. Contos, S. Grimaldi, J. Terry, P. Lightsey, A. Barto, B. League, B. Dean, J. S. Smith, C. Bowers, D. Aronstein, L. Feinberg, W. Hayden, T. Comeau, R. Soummer, E. Elliott, M. Perrin, and C. W. Starr, “Wavefront sensing and controls for the James webb space telescope,” Proc. SPIE 8442, 84422H (2012).
[Crossref]

D. S. Acton, T. Towell, J. Schwenker, J. Swensen, D. Shields, E. Sabatke, L. Klingemann, A. R. Contos, B. Bauer, K. Hansen, P. D. Atcheson, D. Redding, F. Shi, S. Basinger, B. Dean, and L. Burns, “Demonstration of the James Webb Space Telescope commissioning on the JWST testbed telescope,” Proc. SPIE 6265, 62650R (2006).
[Crossref]

B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, “Phase retrieval algorithm for JWST flight and testbed telescope,” Proc. SPIE 6265, 626511 (2006).
[Crossref]

Agnetta, G.

G. Pareschi, G. Agnetta, L. Antonelli, D. Bastieri, G. Bellassai, M. Belluso, C. Bigongiari, S. Billotta, B. Biondo, and G. Bonanno, et al., “The dual-mirror small size telescope for the Cherenkov Telescope Array,” arXiv:1307.4962 (2013).

Alis, C.

M. Mesrine, E. Thomas, S. Garin, P. Blanc, C. Alis, F. Cassaing, and D. Laubier, “High resolution Earth observation form Geostationary orbit by optical aperture synthesys,” in Sixth International Conference on Space Optics (ESA-CNES, ESA/ESTEC Noordwijk, 2006).

Allen, M.

M. D. Perrin, D. S. Acton, C.-P. Lajoie, J. S. Knight, M. D. Lallo, M. Allen, W. Baggett, E. Barker, T. Comeau, E. Coppock, B. H. Dean, G. Hartig, W. L. Hayden, M. Jordan, A. Jurling, T. Kulp, J. Long, M. W. McElwain, L. Meza, E. P. Nelan, R. Soummer, J. Stansberry, C. Stark, R. Telfer, A. L. Welsh, T. P. Zielinski, and N. T. Zimmerman, “Preparing for JWST wavefront sensing and control operations,” Proc. SPIE 9904, 99040F (2016).
[Crossref]

Amiaux, J.

M. Sauvage, J. Amiaux, J. Austin, M. Bello, G. Bianucci, S. Chesné, O. Citterio, C. Collette, S. Correia, G. A. Durand, S. Molinari, G. Pareschi, Y. Penfornis, G. Sironi, G. Valsecchi, S. Verpoort, and U. Wittrock, “A development roadmap for critical technologies needed for TALC: a deployable 20m annular space telescope,” Proc. SPIE 9904, 99041L (2016).
[Crossref]

Antonelli, L.

G. Pareschi, G. Agnetta, L. Antonelli, D. Bastieri, G. Bellassai, M. Belluso, C. Bigongiari, S. Billotta, B. Biondo, and G. Bonanno, et al., “The dual-mirror small size telescope for the Cherenkov Telescope Array,” arXiv:1307.4962 (2013).

Aronstein, D.

D. S. Acton, J. S. Knight, A. Contos, S. Grimaldi, J. Terry, P. Lightsey, A. Barto, B. League, B. Dean, J. S. Smith, C. Bowers, D. Aronstein, L. Feinberg, W. Hayden, T. Comeau, R. Soummer, E. Elliott, M. Perrin, and C. W. Starr, “Wavefront sensing and controls for the James webb space telescope,” Proc. SPIE 8442, 84422H (2012).
[Crossref]

Aronstein, D. L.

B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, “Phase retrieval algorithm for JWST flight and testbed telescope,” Proc. SPIE 6265, 626511 (2006).
[Crossref]

Atcheson, P. D.

D. S. Acton, T. Towell, J. Schwenker, J. Swensen, D. Shields, E. Sabatke, L. Klingemann, A. R. Contos, B. Bauer, K. Hansen, P. D. Atcheson, D. Redding, F. Shi, S. Basinger, B. Dean, and L. Burns, “Demonstration of the James Webb Space Telescope commissioning on the JWST testbed telescope,” Proc. SPIE 6265, 62650R (2006).
[Crossref]

Austin, J.

M. Sauvage, J. Amiaux, J. Austin, M. Bello, G. Bianucci, S. Chesné, O. Citterio, C. Collette, S. Correia, G. A. Durand, S. Molinari, G. Pareschi, Y. Penfornis, G. Sironi, G. Valsecchi, S. Verpoort, and U. Wittrock, “A development roadmap for critical technologies needed for TALC: a deployable 20m annular space telescope,” Proc. SPIE 9904, 99041L (2016).
[Crossref]

Baggett, W.

M. D. Perrin, D. S. Acton, C.-P. Lajoie, J. S. Knight, M. D. Lallo, M. Allen, W. Baggett, E. Barker, T. Comeau, E. Coppock, B. H. Dean, G. Hartig, W. L. Hayden, M. Jordan, A. Jurling, T. Kulp, J. Long, M. W. McElwain, L. Meza, E. P. Nelan, R. Soummer, J. Stansberry, C. Stark, R. Telfer, A. L. Welsh, T. P. Zielinski, and N. T. Zimmerman, “Preparing for JWST wavefront sensing and control operations,” Proc. SPIE 9904, 99040F (2016).
[Crossref]

Balasubramanian, K.

M. R. Bolcar, K. Balasubramanian, M. Clampin, J. Crooke, L. Feinberg, M. Postman, M. Quijada, B. Rauscher, D. Redding, N. Rioux, S. Shaklan, H. P. Stahl, C. Stahle, and H. Thronson, “Technology development for the Advanced Technology Large Aperture Space Telescope (ATLAST) as a candidate large UV-Optical-Infrared (LUVOIR) surveyor,” Proc. SPIE 9602, 960209 (2015).
[Crossref]

Barker, E.

M. D. Perrin, D. S. Acton, C.-P. Lajoie, J. S. Knight, M. D. Lallo, M. Allen, W. Baggett, E. Barker, T. Comeau, E. Coppock, B. H. Dean, G. Hartig, W. L. Hayden, M. Jordan, A. Jurling, T. Kulp, J. Long, M. W. McElwain, L. Meza, E. P. Nelan, R. Soummer, J. Stansberry, C. Stark, R. Telfer, A. L. Welsh, T. P. Zielinski, and N. T. Zimmerman, “Preparing for JWST wavefront sensing and control operations,” Proc. SPIE 9904, 99040F (2016).
[Crossref]

Baron, F.

F. Baron, I. Mocoeur, F. Cassaing, and L. M. Mugnier, “Unambiguous phase retrieval as a cophasing sensor for phased array telescopes: derivation of an analytical estimator,” J. Opt. Soc. Am. A 25, 1000–1015 (2008).
[Crossref]

I. Mocœur, F. Cassaing, F. Baron, L. Mugnier, S. Hofer, and H. Thiele, “Darwin fringe sensor: experimental results on the BRISE bench,” Proc. SPIE 6268, 62682B (2006).
[Crossref]

F. Cassaing, B. Sorrente, L. Mugnier, G. Rousset, V. Michau, I. Mocœur, and F. Baron, “BRISE: a multipurpose bench for cophasing sensors,” Proc. SPIE 6268, 62683A (2006).
[Crossref]

L. Mugnier, F. Cassaing, B. Sorrente, F. Baron, M.-T. Velluet, V. Michau, and G. Rousset, “Multiple-aperture optical telescopes: some key issues for earth observation from a GEO orbit,” in 5th International Conference on Space Optics, CNES/ESA (ESA, 2004), vol. SP-554, pp. 181–187.

Barto, A.

D. S. Acton, J. S. Knight, A. Contos, S. Grimaldi, J. Terry, P. Lightsey, A. Barto, B. League, B. Dean, J. S. Smith, C. Bowers, D. Aronstein, L. Feinberg, W. Hayden, T. Comeau, R. Soummer, E. Elliott, M. Perrin, and C. W. Starr, “Wavefront sensing and controls for the James webb space telescope,” Proc. SPIE 8442, 84422H (2012).
[Crossref]

Basinger, S.

D. S. Acton, T. Towell, J. Schwenker, J. Swensen, D. Shields, E. Sabatke, L. Klingemann, A. R. Contos, B. Bauer, K. Hansen, P. D. Atcheson, D. Redding, F. Shi, S. Basinger, B. Dean, and L. Burns, “Demonstration of the James Webb Space Telescope commissioning on the JWST testbed telescope,” Proc. SPIE 6265, 62650R (2006).
[Crossref]

Basinger, S. A.

D. C. Redding, S. A. Basinger, A. E. Lowman, A. Kissil, P. Y. Bely, R. Burg, R. G. Lyon, G. E. Mosier, M. Femiano, M. E. Wilson, R. G. Schunk, L. D. Craig, D. N. Jacobson, J. M. Rakoczy, and J. B. Hadaway, “Wavefront sensing and control for a next generation space telescope,” Proc. SPIE 3356, 758–772 (1998).
[Crossref]

Bastieri, D.

G. Pareschi, G. Agnetta, L. Antonelli, D. Bastieri, G. Bellassai, M. Belluso, C. Bigongiari, S. Billotta, B. Biondo, and G. Bonanno, et al., “The dual-mirror small size telescope for the Cherenkov Telescope Array,” arXiv:1307.4962 (2013).

Bauer, B.

D. S. Acton, T. Towell, J. Schwenker, J. Swensen, D. Shields, E. Sabatke, L. Klingemann, A. R. Contos, B. Bauer, K. Hansen, P. D. Atcheson, D. Redding, F. Shi, S. Basinger, B. Dean, and L. Burns, “Demonstration of the James Webb Space Telescope commissioning on the JWST testbed telescope,” Proc. SPIE 6265, 62650R (2006).
[Crossref]

Bellassai, G.

G. Pareschi, G. Agnetta, L. Antonelli, D. Bastieri, G. Bellassai, M. Belluso, C. Bigongiari, S. Billotta, B. Biondo, and G. Bonanno, et al., “The dual-mirror small size telescope for the Cherenkov Telescope Array,” arXiv:1307.4962 (2013).

Bello, M.

M. Sauvage, J. Amiaux, J. Austin, M. Bello, G. Bianucci, S. Chesné, O. Citterio, C. Collette, S. Correia, G. A. Durand, S. Molinari, G. Pareschi, Y. Penfornis, G. Sironi, G. Valsecchi, S. Verpoort, and U. Wittrock, “A development roadmap for critical technologies needed for TALC: a deployable 20m annular space telescope,” Proc. SPIE 9904, 99041L (2016).
[Crossref]

Belluso, M.

G. Pareschi, G. Agnetta, L. Antonelli, D. Bastieri, G. Bellassai, M. Belluso, C. Bigongiari, S. Billotta, B. Biondo, and G. Bonanno, et al., “The dual-mirror small size telescope for the Cherenkov Telescope Array,” arXiv:1307.4962 (2013).

Bely, P. Y.

D. C. Redding, S. A. Basinger, A. E. Lowman, A. Kissil, P. Y. Bely, R. Burg, R. G. Lyon, G. E. Mosier, M. Femiano, M. E. Wilson, R. G. Schunk, L. D. Craig, D. N. Jacobson, J. M. Rakoczy, and J. B. Hadaway, “Wavefront sensing and control for a next generation space telescope,” Proc. SPIE 3356, 758–772 (1998).
[Crossref]

Berdyugina, S. V.

G. Moretto, J. R. Kuhn, E. Thiébaut, M. Langlois, S. V. Berdyugina, C. Harlingten, and D. Halliday, “New strategies for an extremely large telescope dedicated to extremely high contrast: the Colossus project,” Proc. SPIE 9145, 91451L (2014).
[Crossref]

Bianucci, G.

M. Sauvage, J. Amiaux, J. Austin, M. Bello, G. Bianucci, S. Chesné, O. Citterio, C. Collette, S. Correia, G. A. Durand, S. Molinari, G. Pareschi, Y. Penfornis, G. Sironi, G. Valsecchi, S. Verpoort, and U. Wittrock, “A development roadmap for critical technologies needed for TALC: a deployable 20m annular space telescope,” Proc. SPIE 9904, 99041L (2016).
[Crossref]

Bierhaus, E.

J. T. Pitman, A. Duncan, D. Stubbs, R. D. Sigler, R. L. Kendrick, E. H. Smith, J. E. Mason, G. Delory, J. H. Lipps, M. Manga, J. R. Graham, I. de Pater, S. Reiboldt, E. Bierhaus, J. B. Dalton, J. R. Fienup, and J. W. Yu, “Remote sensing space science enabled by the multiple instrument distributed aperture sensor (midas) concept,” in Optical Science and Technology, the SPIE 49th Annual Meeting (International Society for Optics and Photonics, 2004), pp. 301–310.

Bigongiari, C.

G. Pareschi, G. Agnetta, L. Antonelli, D. Bastieri, G. Bellassai, M. Belluso, C. Bigongiari, S. Billotta, B. Biondo, and G. Bonanno, et al., “The dual-mirror small size telescope for the Cherenkov Telescope Array,” arXiv:1307.4962 (2013).

Billotta, S.

G. Pareschi, G. Agnetta, L. Antonelli, D. Bastieri, G. Bellassai, M. Belluso, C. Bigongiari, S. Billotta, B. Biondo, and G. Bonanno, et al., “The dual-mirror small size telescope for the Cherenkov Telescope Array,” arXiv:1307.4962 (2013).

Biondo, B.

G. Pareschi, G. Agnetta, L. Antonelli, D. Bastieri, G. Bellassai, M. Belluso, C. Bigongiari, S. Billotta, B. Biondo, and G. Bonanno, et al., “The dual-mirror small size telescope for the Cherenkov Telescope Array,” arXiv:1307.4962 (2013).

Blanc, A.

L. M. Mugnier, A. Blanc, and J. Idier, Phase Diversity: A Technique for Wave-Front Sensing and for Diffraction-Limited Imaging (Elsevier, 2006), pp. 1–76.

Blanc, P.

M. Mesrine, E. Thomas, S. Garin, P. Blanc, C. Alis, F. Cassaing, and D. Laubier, “High resolution Earth observation form Geostationary orbit by optical aperture synthesys,” in Sixth International Conference on Space Optics (ESA-CNES, ESA/ESTEC Noordwijk, 2006).

Bolcar, M. R.

M. R. Bolcar, K. Balasubramanian, M. Clampin, J. Crooke, L. Feinberg, M. Postman, M. Quijada, B. Rauscher, D. Redding, N. Rioux, S. Shaklan, H. P. Stahl, C. Stahle, and H. Thronson, “Technology development for the Advanced Technology Large Aperture Space Telescope (ATLAST) as a candidate large UV-Optical-Infrared (LUVOIR) surveyor,” Proc. SPIE 9602, 960209 (2015).
[Crossref]

Bonanno, G.

G. Pareschi, G. Agnetta, L. Antonelli, D. Bastieri, G. Bellassai, M. Belluso, C. Bigongiari, S. Billotta, B. Biondo, and G. Bonanno, et al., “The dual-mirror small size telescope for the Cherenkov Telescope Array,” arXiv:1307.4962 (2013).

Bonnefois, A.

S. Vievard, F. Cassaing, A. Bonnefois, L. Mugnier, and J. Montri, “Real-time alignment and co-phasing of multi-aperture systems using phase diversity,” in SPIE Astronomical Telescopes+ Instrumentation (International Society for Optics and Photonics, 2016), pp. 99062Q.

Bowers, C.

D. S. Acton, J. S. Knight, A. Contos, S. Grimaldi, J. Terry, P. Lightsey, A. Barto, B. League, B. Dean, J. S. Smith, C. Bowers, D. Aronstein, L. Feinberg, W. Hayden, T. Comeau, R. Soummer, E. Elliott, M. Perrin, and C. W. Starr, “Wavefront sensing and controls for the James webb space telescope,” Proc. SPIE 8442, 84422H (2012).
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Burg, R.

D. C. Redding, S. A. Basinger, A. E. Lowman, A. Kissil, P. Y. Bely, R. Burg, R. G. Lyon, G. E. Mosier, M. Femiano, M. E. Wilson, R. G. Schunk, L. D. Craig, D. N. Jacobson, J. M. Rakoczy, and J. B. Hadaway, “Wavefront sensing and control for a next generation space telescope,” Proc. SPIE 3356, 758–772 (1998).
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Burns, L.

D. S. Acton, T. Towell, J. Schwenker, J. Swensen, D. Shields, E. Sabatke, L. Klingemann, A. R. Contos, B. Bauer, K. Hansen, P. D. Atcheson, D. Redding, F. Shi, S. Basinger, B. Dean, and L. Burns, “Demonstration of the James Webb Space Telescope commissioning on the JWST testbed telescope,” Proc. SPIE 6265, 62650R (2006).
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Carlisle, R. E.

Carrara, D. A.

D. A. Carrara, B. J. Thelen, and R. G. Paxman, “Aberration correction of segmented-aperture telescopes by using phase diversity,” Proc. SPIE 4123, 56–63 (2000).
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Cassaing, F.

I. Mocœur, L. M. Mugnier, and F. Cassaing, “Analytical solution to the phase-diversity problem for real-time wavefront sensing,” Opt. Lett. 34, 3487–3489 (2009).
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S. Meimon, E. Delavaquerie, F. Cassaing, T. Fusco, L. M. Mugnier, and V. Michau, “Phasing segmented telescopes with long-exposure phase diversity images,” Proc. SPIE 7012, 701214 (2008).
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F. Baron, I. Mocoeur, F. Cassaing, and L. M. Mugnier, “Unambiguous phase retrieval as a cophasing sensor for phased array telescopes: derivation of an analytical estimator,” J. Opt. Soc. Am. A 25, 1000–1015 (2008).
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I. Mocœur, F. Cassaing, F. Baron, L. Mugnier, S. Hofer, and H. Thiele, “Darwin fringe sensor: experimental results on the BRISE bench,” Proc. SPIE 6268, 62682B (2006).
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F. Cassaing, B. Sorrente, L. Mugnier, G. Rousset, V. Michau, I. Mocœur, and F. Baron, “BRISE: a multipurpose bench for cophasing sensors,” Proc. SPIE 6268, 62683A (2006).
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L. Mugnier, F. Cassaing, B. Sorrente, F. Baron, M.-T. Velluet, V. Michau, and G. Rousset, “Multiple-aperture optical telescopes: some key issues for earth observation from a GEO orbit,” in 5th International Conference on Space Optics, CNES/ESA (ESA, 2004), vol. SP-554, pp. 181–187.

M. Mesrine, E. Thomas, S. Garin, P. Blanc, C. Alis, F. Cassaing, and D. Laubier, “High resolution Earth observation form Geostationary orbit by optical aperture synthesys,” in Sixth International Conference on Space Optics (ESA-CNES, ESA/ESTEC Noordwijk, 2006).

S. Vievard, F. Cassaing, A. Bonnefois, L. Mugnier, and J. Montri, “Real-time alignment and co-phasing of multi-aperture systems using phase diversity,” in SPIE Astronomical Telescopes+ Instrumentation (International Society for Optics and Photonics, 2016), pp. 99062Q.

Chesné, S.

M. Sauvage, J. Amiaux, J. Austin, M. Bello, G. Bianucci, S. Chesné, O. Citterio, C. Collette, S. Correia, G. A. Durand, S. Molinari, G. Pareschi, Y. Penfornis, G. Sironi, G. Valsecchi, S. Verpoort, and U. Wittrock, “A development roadmap for critical technologies needed for TALC: a deployable 20m annular space telescope,” Proc. SPIE 9904, 99041L (2016).
[Crossref]

Citterio, O.

M. Sauvage, J. Amiaux, J. Austin, M. Bello, G. Bianucci, S. Chesné, O. Citterio, C. Collette, S. Correia, G. A. Durand, S. Molinari, G. Pareschi, Y. Penfornis, G. Sironi, G. Valsecchi, S. Verpoort, and U. Wittrock, “A development roadmap for critical technologies needed for TALC: a deployable 20m annular space telescope,” Proc. SPIE 9904, 99041L (2016).
[Crossref]

Clampin, M.

M. R. Bolcar, K. Balasubramanian, M. Clampin, J. Crooke, L. Feinberg, M. Postman, M. Quijada, B. Rauscher, D. Redding, N. Rioux, S. Shaklan, H. P. Stahl, C. Stahle, and H. Thronson, “Technology development for the Advanced Technology Large Aperture Space Telescope (ATLAST) as a candidate large UV-Optical-Infrared (LUVOIR) surveyor,” Proc. SPIE 9602, 960209 (2015).
[Crossref]

Collette, C.

M. Sauvage, J. Amiaux, J. Austin, M. Bello, G. Bianucci, S. Chesné, O. Citterio, C. Collette, S. Correia, G. A. Durand, S. Molinari, G. Pareschi, Y. Penfornis, G. Sironi, G. Valsecchi, S. Verpoort, and U. Wittrock, “A development roadmap for critical technologies needed for TALC: a deployable 20m annular space telescope,” Proc. SPIE 9904, 99041L (2016).
[Crossref]

Comeau, T.

M. D. Perrin, D. S. Acton, C.-P. Lajoie, J. S. Knight, M. D. Lallo, M. Allen, W. Baggett, E. Barker, T. Comeau, E. Coppock, B. H. Dean, G. Hartig, W. L. Hayden, M. Jordan, A. Jurling, T. Kulp, J. Long, M. W. McElwain, L. Meza, E. P. Nelan, R. Soummer, J. Stansberry, C. Stark, R. Telfer, A. L. Welsh, T. P. Zielinski, and N. T. Zimmerman, “Preparing for JWST wavefront sensing and control operations,” Proc. SPIE 9904, 99040F (2016).
[Crossref]

D. S. Acton, J. S. Knight, A. Contos, S. Grimaldi, J. Terry, P. Lightsey, A. Barto, B. League, B. Dean, J. S. Smith, C. Bowers, D. Aronstein, L. Feinberg, W. Hayden, T. Comeau, R. Soummer, E. Elliott, M. Perrin, and C. W. Starr, “Wavefront sensing and controls for the James webb space telescope,” Proc. SPIE 8442, 84422H (2012).
[Crossref]

Contos, A.

D. S. Acton, J. S. Knight, A. Contos, S. Grimaldi, J. Terry, P. Lightsey, A. Barto, B. League, B. Dean, J. S. Smith, C. Bowers, D. Aronstein, L. Feinberg, W. Hayden, T. Comeau, R. Soummer, E. Elliott, M. Perrin, and C. W. Starr, “Wavefront sensing and controls for the James webb space telescope,” Proc. SPIE 8442, 84422H (2012).
[Crossref]

Contos, A. R.

D. S. Acton, T. Towell, J. Schwenker, J. Swensen, D. Shields, E. Sabatke, L. Klingemann, A. R. Contos, B. Bauer, K. Hansen, P. D. Atcheson, D. Redding, F. Shi, S. Basinger, B. Dean, and L. Burns, “Demonstration of the James Webb Space Telescope commissioning on the JWST testbed telescope,” Proc. SPIE 6265, 62650R (2006).
[Crossref]

Coppock, E.

M. D. Perrin, D. S. Acton, C.-P. Lajoie, J. S. Knight, M. D. Lallo, M. Allen, W. Baggett, E. Barker, T. Comeau, E. Coppock, B. H. Dean, G. Hartig, W. L. Hayden, M. Jordan, A. Jurling, T. Kulp, J. Long, M. W. McElwain, L. Meza, E. P. Nelan, R. Soummer, J. Stansberry, C. Stark, R. Telfer, A. L. Welsh, T. P. Zielinski, and N. T. Zimmerman, “Preparing for JWST wavefront sensing and control operations,” Proc. SPIE 9904, 99040F (2016).
[Crossref]

Correia, S.

M. Sauvage, J. Amiaux, J. Austin, M. Bello, G. Bianucci, S. Chesné, O. Citterio, C. Collette, S. Correia, G. A. Durand, S. Molinari, G. Pareschi, Y. Penfornis, G. Sironi, G. Valsecchi, S. Verpoort, and U. Wittrock, “A development roadmap for critical technologies needed for TALC: a deployable 20m annular space telescope,” Proc. SPIE 9904, 99041L (2016).
[Crossref]

Craig, L. D.

D. C. Redding, S. A. Basinger, A. E. Lowman, A. Kissil, P. Y. Bely, R. Burg, R. G. Lyon, G. E. Mosier, M. Femiano, M. E. Wilson, R. G. Schunk, L. D. Craig, D. N. Jacobson, J. M. Rakoczy, and J. B. Hadaway, “Wavefront sensing and control for a next generation space telescope,” Proc. SPIE 3356, 758–772 (1998).
[Crossref]

Crooke, J.

M. R. Bolcar, K. Balasubramanian, M. Clampin, J. Crooke, L. Feinberg, M. Postman, M. Quijada, B. Rauscher, D. Redding, N. Rioux, S. Shaklan, H. P. Stahl, C. Stahle, and H. Thronson, “Technology development for the Advanced Technology Large Aperture Space Telescope (ATLAST) as a candidate large UV-Optical-Infrared (LUVOIR) surveyor,” Proc. SPIE 9602, 960209 (2015).
[Crossref]

Dalton, J. B.

J. T. Pitman, A. Duncan, D. Stubbs, R. D. Sigler, R. L. Kendrick, E. H. Smith, J. E. Mason, G. Delory, J. H. Lipps, M. Manga, J. R. Graham, I. de Pater, S. Reiboldt, E. Bierhaus, J. B. Dalton, J. R. Fienup, and J. W. Yu, “Remote sensing space science enabled by the multiple instrument distributed aperture sensor (midas) concept,” in Optical Science and Technology, the SPIE 49th Annual Meeting (International Society for Optics and Photonics, 2004), pp. 301–310.

de Pater, I.

J. T. Pitman, A. Duncan, D. Stubbs, R. D. Sigler, R. L. Kendrick, E. H. Smith, J. E. Mason, G. Delory, J. H. Lipps, M. Manga, J. R. Graham, I. de Pater, S. Reiboldt, E. Bierhaus, J. B. Dalton, J. R. Fienup, and J. W. Yu, “Remote sensing space science enabled by the multiple instrument distributed aperture sensor (midas) concept,” in Optical Science and Technology, the SPIE 49th Annual Meeting (International Society for Optics and Photonics, 2004), pp. 301–310.

Dean, B.

D. S. Acton, J. S. Knight, A. Contos, S. Grimaldi, J. Terry, P. Lightsey, A. Barto, B. League, B. Dean, J. S. Smith, C. Bowers, D. Aronstein, L. Feinberg, W. Hayden, T. Comeau, R. Soummer, E. Elliott, M. Perrin, and C. W. Starr, “Wavefront sensing and controls for the James webb space telescope,” Proc. SPIE 8442, 84422H (2012).
[Crossref]

D. S. Acton, T. Towell, J. Schwenker, J. Swensen, D. Shields, E. Sabatke, L. Klingemann, A. R. Contos, B. Bauer, K. Hansen, P. D. Atcheson, D. Redding, F. Shi, S. Basinger, B. Dean, and L. Burns, “Demonstration of the James Webb Space Telescope commissioning on the JWST testbed telescope,” Proc. SPIE 6265, 62650R (2006).
[Crossref]

Dean, B. H.

M. D. Perrin, D. S. Acton, C.-P. Lajoie, J. S. Knight, M. D. Lallo, M. Allen, W. Baggett, E. Barker, T. Comeau, E. Coppock, B. H. Dean, G. Hartig, W. L. Hayden, M. Jordan, A. Jurling, T. Kulp, J. Long, M. W. McElwain, L. Meza, E. P. Nelan, R. Soummer, J. Stansberry, C. Stark, R. Telfer, A. L. Welsh, T. P. Zielinski, and N. T. Zimmerman, “Preparing for JWST wavefront sensing and control operations,” Proc. SPIE 9904, 99040F (2016).
[Crossref]

B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, “Phase retrieval algorithm for JWST flight and testbed telescope,” Proc. SPIE 6265, 626511 (2006).
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Delavaquerie, E.

S. Meimon, E. Delavaquerie, F. Cassaing, T. Fusco, L. M. Mugnier, and V. Michau, “Phasing segmented telescopes with long-exposure phase diversity images,” Proc. SPIE 7012, 701214 (2008).
[Crossref]

Delory, G.

J. T. Pitman, A. Duncan, D. Stubbs, R. D. Sigler, R. L. Kendrick, E. H. Smith, J. E. Mason, G. Delory, J. H. Lipps, M. Manga, J. R. Graham, I. de Pater, S. Reiboldt, E. Bierhaus, J. B. Dalton, J. R. Fienup, and J. W. Yu, “Remote sensing space science enabled by the multiple instrument distributed aperture sensor (midas) concept,” in Optical Science and Technology, the SPIE 49th Annual Meeting (International Society for Optics and Photonics, 2004), pp. 301–310.

Duncan, A.

J. T. Pitman, A. Duncan, D. Stubbs, R. D. Sigler, R. L. Kendrick, E. H. Smith, J. E. Mason, G. Delory, J. H. Lipps, M. Manga, J. R. Graham, I. de Pater, S. Reiboldt, E. Bierhaus, J. B. Dalton, J. R. Fienup, and J. W. Yu, “Remote sensing space science enabled by the multiple instrument distributed aperture sensor (midas) concept,” in Optical Science and Technology, the SPIE 49th Annual Meeting (International Society for Optics and Photonics, 2004), pp. 301–310.

Durand, G. A.

M. Sauvage, J. Amiaux, J. Austin, M. Bello, G. Bianucci, S. Chesné, O. Citterio, C. Collette, S. Correia, G. A. Durand, S. Molinari, G. Pareschi, Y. Penfornis, G. Sironi, G. Valsecchi, S. Verpoort, and U. Wittrock, “A development roadmap for critical technologies needed for TALC: a deployable 20m annular space telescope,” Proc. SPIE 9904, 99041L (2016).
[Crossref]

Elliott, E.

D. S. Acton, J. S. Knight, A. Contos, S. Grimaldi, J. Terry, P. Lightsey, A. Barto, B. League, B. Dean, J. S. Smith, C. Bowers, D. Aronstein, L. Feinberg, W. Hayden, T. Comeau, R. Soummer, E. Elliott, M. Perrin, and C. W. Starr, “Wavefront sensing and controls for the James webb space telescope,” Proc. SPIE 8442, 84422H (2012).
[Crossref]

Feinberg, L.

M. R. Bolcar, K. Balasubramanian, M. Clampin, J. Crooke, L. Feinberg, M. Postman, M. Quijada, B. Rauscher, D. Redding, N. Rioux, S. Shaklan, H. P. Stahl, C. Stahle, and H. Thronson, “Technology development for the Advanced Technology Large Aperture Space Telescope (ATLAST) as a candidate large UV-Optical-Infrared (LUVOIR) surveyor,” Proc. SPIE 9602, 960209 (2015).
[Crossref]

D. S. Acton, J. S. Knight, A. Contos, S. Grimaldi, J. Terry, P. Lightsey, A. Barto, B. League, B. Dean, J. S. Smith, C. Bowers, D. Aronstein, L. Feinberg, W. Hayden, T. Comeau, R. Soummer, E. Elliott, M. Perrin, and C. W. Starr, “Wavefront sensing and controls for the James webb space telescope,” Proc. SPIE 8442, 84422H (2012).
[Crossref]

Femiano, M.

D. C. Redding, S. A. Basinger, A. E. Lowman, A. Kissil, P. Y. Bely, R. Burg, R. G. Lyon, G. E. Mosier, M. Femiano, M. E. Wilson, R. G. Schunk, L. D. Craig, D. N. Jacobson, J. M. Rakoczy, and J. B. Hadaway, “Wavefront sensing and control for a next generation space telescope,” Proc. SPIE 3356, 758–772 (1998).
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Fienup, J. R.

A. S. Jurling and J. R. Fienup, “Applications of algorithmic differentiation to phase retrieval algorithms,” J. Opt. Soc. Am. A 31, 1348–1359 (2014).
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R. G. Paxman and J. R. Fienup, “Optical misalignment sensing and image reconstruction using phase diversity,” J. Opt. Soc. Am. A 5, 914–923 (1988).
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J. T. Pitman, A. Duncan, D. Stubbs, R. D. Sigler, R. L. Kendrick, E. H. Smith, J. E. Mason, G. Delory, J. H. Lipps, M. Manga, J. R. Graham, I. de Pater, S. Reiboldt, E. Bierhaus, J. B. Dalton, J. R. Fienup, and J. W. Yu, “Remote sensing space science enabled by the multiple instrument distributed aperture sensor (midas) concept,” in Optical Science and Technology, the SPIE 49th Annual Meeting (International Society for Optics and Photonics, 2004), pp. 301–310.

Fontanella, J. C.

Fusco, T.

S. Meimon, E. Delavaquerie, F. Cassaing, T. Fusco, L. M. Mugnier, and V. Michau, “Phasing segmented telescopes with long-exposure phase diversity images,” Proc. SPIE 7012, 701214 (2008).
[Crossref]

Garin, S.

M. Mesrine, E. Thomas, S. Garin, P. Blanc, C. Alis, F. Cassaing, and D. Laubier, “High resolution Earth observation form Geostationary orbit by optical aperture synthesys,” in Sixth International Conference on Space Optics (ESA-CNES, ESA/ESTEC Noordwijk, 2006).

Gonsalves, R. A.

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 215829 (1982).
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Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company, 2005).

Graham, J. R.

J. T. Pitman, A. Duncan, D. Stubbs, R. D. Sigler, R. L. Kendrick, E. H. Smith, J. E. Mason, G. Delory, J. H. Lipps, M. Manga, J. R. Graham, I. de Pater, S. Reiboldt, E. Bierhaus, J. B. Dalton, J. R. Fienup, and J. W. Yu, “Remote sensing space science enabled by the multiple instrument distributed aperture sensor (midas) concept,” in Optical Science and Technology, the SPIE 49th Annual Meeting (International Society for Optics and Photonics, 2004), pp. 301–310.

Grimaldi, S.

D. S. Acton, J. S. Knight, A. Contos, S. Grimaldi, J. Terry, P. Lightsey, A. Barto, B. League, B. Dean, J. S. Smith, C. Bowers, D. Aronstein, L. Feinberg, W. Hayden, T. Comeau, R. Soummer, E. Elliott, M. Perrin, and C. W. Starr, “Wavefront sensing and controls for the James webb space telescope,” Proc. SPIE 8442, 84422H (2012).
[Crossref]

Hadaway, J. B.

D. C. Redding, S. A. Basinger, A. E. Lowman, A. Kissil, P. Y. Bely, R. Burg, R. G. Lyon, G. E. Mosier, M. Femiano, M. E. Wilson, R. G. Schunk, L. D. Craig, D. N. Jacobson, J. M. Rakoczy, and J. B. Hadaway, “Wavefront sensing and control for a next generation space telescope,” Proc. SPIE 3356, 758–772 (1998).
[Crossref]

Halliday, D.

G. Moretto, J. R. Kuhn, E. Thiébaut, M. Langlois, S. V. Berdyugina, C. Harlingten, and D. Halliday, “New strategies for an extremely large telescope dedicated to extremely high contrast: the Colossus project,” Proc. SPIE 9145, 91451L (2014).
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M. D. Perrin, D. S. Acton, C.-P. Lajoie, J. S. Knight, M. D. Lallo, M. Allen, W. Baggett, E. Barker, T. Comeau, E. Coppock, B. H. Dean, G. Hartig, W. L. Hayden, M. Jordan, A. Jurling, T. Kulp, J. Long, M. W. McElwain, L. Meza, E. P. Nelan, R. Soummer, J. Stansberry, C. Stark, R. Telfer, A. L. Welsh, T. P. Zielinski, and N. T. Zimmerman, “Preparing for JWST wavefront sensing and control operations,” Proc. SPIE 9904, 99040F (2016).
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M. D. Perrin, D. S. Acton, C.-P. Lajoie, J. S. Knight, M. D. Lallo, M. Allen, W. Baggett, E. Barker, T. Comeau, E. Coppock, B. H. Dean, G. Hartig, W. L. Hayden, M. Jordan, A. Jurling, T. Kulp, J. Long, M. W. McElwain, L. Meza, E. P. Nelan, R. Soummer, J. Stansberry, C. Stark, R. Telfer, A. L. Welsh, T. P. Zielinski, and N. T. Zimmerman, “Preparing for JWST wavefront sensing and control operations,” Proc. SPIE 9904, 99040F (2016).
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J. T. Pitman, A. Duncan, D. Stubbs, R. D. Sigler, R. L. Kendrick, E. H. Smith, J. E. Mason, G. Delory, J. H. Lipps, M. Manga, J. R. Graham, I. de Pater, S. Reiboldt, E. Bierhaus, J. B. Dalton, J. R. Fienup, and J. W. Yu, “Remote sensing space science enabled by the multiple instrument distributed aperture sensor (midas) concept,” in Optical Science and Technology, the SPIE 49th Annual Meeting (International Society for Optics and Photonics, 2004), pp. 301–310.

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M. D. Perrin, D. S. Acton, C.-P. Lajoie, J. S. Knight, M. D. Lallo, M. Allen, W. Baggett, E. Barker, T. Comeau, E. Coppock, B. H. Dean, G. Hartig, W. L. Hayden, M. Jordan, A. Jurling, T. Kulp, J. Long, M. W. McElwain, L. Meza, E. P. Nelan, R. Soummer, J. Stansberry, C. Stark, R. Telfer, A. L. Welsh, T. P. Zielinski, and N. T. Zimmerman, “Preparing for JWST wavefront sensing and control operations,” Proc. SPIE 9904, 99040F (2016).
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F. Cassaing, B. Sorrente, L. Mugnier, G. Rousset, V. Michau, I. Mocœur, and F. Baron, “BRISE: a multipurpose bench for cophasing sensors,” Proc. SPIE 6268, 62683A (2006).
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G. Moretto, J. R. Kuhn, E. Thiébaut, M. Langlois, S. V. Berdyugina, C. Harlingten, and D. Halliday, “New strategies for an extremely large telescope dedicated to extremely high contrast: the Colossus project,” Proc. SPIE 9145, 91451L (2014).
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M. R. Bolcar, K. Balasubramanian, M. Clampin, J. Crooke, L. Feinberg, M. Postman, M. Quijada, B. Rauscher, D. Redding, N. Rioux, S. Shaklan, H. P. Stahl, C. Stahle, and H. Thronson, “Technology development for the Advanced Technology Large Aperture Space Telescope (ATLAST) as a candidate large UV-Optical-Infrared (LUVOIR) surveyor,” Proc. SPIE 9602, 960209 (2015).
[Crossref]

Rakoczy, J. M.

D. C. Redding, S. A. Basinger, A. E. Lowman, A. Kissil, P. Y. Bely, R. Burg, R. G. Lyon, G. E. Mosier, M. Femiano, M. E. Wilson, R. G. Schunk, L. D. Craig, D. N. Jacobson, J. M. Rakoczy, and J. B. Hadaway, “Wavefront sensing and control for a next generation space telescope,” Proc. SPIE 3356, 758–772 (1998).
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Rauscher, B.

M. R. Bolcar, K. Balasubramanian, M. Clampin, J. Crooke, L. Feinberg, M. Postman, M. Quijada, B. Rauscher, D. Redding, N. Rioux, S. Shaklan, H. P. Stahl, C. Stahle, and H. Thronson, “Technology development for the Advanced Technology Large Aperture Space Telescope (ATLAST) as a candidate large UV-Optical-Infrared (LUVOIR) surveyor,” Proc. SPIE 9602, 960209 (2015).
[Crossref]

Redding, D.

M. R. Bolcar, K. Balasubramanian, M. Clampin, J. Crooke, L. Feinberg, M. Postman, M. Quijada, B. Rauscher, D. Redding, N. Rioux, S. Shaklan, H. P. Stahl, C. Stahle, and H. Thronson, “Technology development for the Advanced Technology Large Aperture Space Telescope (ATLAST) as a candidate large UV-Optical-Infrared (LUVOIR) surveyor,” Proc. SPIE 9602, 960209 (2015).
[Crossref]

D. S. Acton, T. Towell, J. Schwenker, J. Swensen, D. Shields, E. Sabatke, L. Klingemann, A. R. Contos, B. Bauer, K. Hansen, P. D. Atcheson, D. Redding, F. Shi, S. Basinger, B. Dean, and L. Burns, “Demonstration of the James Webb Space Telescope commissioning on the JWST testbed telescope,” Proc. SPIE 6265, 62650R (2006).
[Crossref]

Redding, D. C.

D. C. Redding, S. A. Basinger, A. E. Lowman, A. Kissil, P. Y. Bely, R. Burg, R. G. Lyon, G. E. Mosier, M. Femiano, M. E. Wilson, R. G. Schunk, L. D. Craig, D. N. Jacobson, J. M. Rakoczy, and J. B. Hadaway, “Wavefront sensing and control for a next generation space telescope,” Proc. SPIE 3356, 758–772 (1998).
[Crossref]

Reiboldt, S.

J. T. Pitman, A. Duncan, D. Stubbs, R. D. Sigler, R. L. Kendrick, E. H. Smith, J. E. Mason, G. Delory, J. H. Lipps, M. Manga, J. R. Graham, I. de Pater, S. Reiboldt, E. Bierhaus, J. B. Dalton, J. R. Fienup, and J. W. Yu, “Remote sensing space science enabled by the multiple instrument distributed aperture sensor (midas) concept,” in Optical Science and Technology, the SPIE 49th Annual Meeting (International Society for Optics and Photonics, 2004), pp. 301–310.

Rioux, N.

M. R. Bolcar, K. Balasubramanian, M. Clampin, J. Crooke, L. Feinberg, M. Postman, M. Quijada, B. Rauscher, D. Redding, N. Rioux, S. Shaklan, H. P. Stahl, C. Stahle, and H. Thronson, “Technology development for the Advanced Technology Large Aperture Space Telescope (ATLAST) as a candidate large UV-Optical-Infrared (LUVOIR) surveyor,” Proc. SPIE 9602, 960209 (2015).
[Crossref]

Roddier, F.

F. Roddier, “Interferometric imaging in optical astronomy,” Phys. Rep. 170, 97–166 (1988).
[Crossref]

Roggemann, M. C.

M. C. Roggemann, B. M. Welsh, and B. R. Hunt, Imaging through Turbulence (CRC Press, 1996).

Rousset, G.

F. Cassaing, B. Sorrente, L. Mugnier, G. Rousset, V. Michau, I. Mocœur, and F. Baron, “BRISE: a multipurpose bench for cophasing sensors,” Proc. SPIE 6268, 62683A (2006).
[Crossref]

L. Mugnier, F. Cassaing, B. Sorrente, F. Baron, M.-T. Velluet, V. Michau, and G. Rousset, “Multiple-aperture optical telescopes: some key issues for earth observation from a GEO orbit,” in 5th International Conference on Space Optics, CNES/ESA (ESA, 2004), vol. SP-554, pp. 181–187.

Sabatke, E.

D. S. Acton, T. Towell, J. Schwenker, J. Swensen, D. Shields, E. Sabatke, L. Klingemann, A. R. Contos, B. Bauer, K. Hansen, P. D. Atcheson, D. Redding, F. Shi, S. Basinger, B. Dean, and L. Burns, “Demonstration of the James Webb Space Telescope commissioning on the JWST testbed telescope,” Proc. SPIE 6265, 62650R (2006).
[Crossref]

Sauvage, M.

M. Sauvage, J. Amiaux, J. Austin, M. Bello, G. Bianucci, S. Chesné, O. Citterio, C. Collette, S. Correia, G. A. Durand, S. Molinari, G. Pareschi, Y. Penfornis, G. Sironi, G. Valsecchi, S. Verpoort, and U. Wittrock, “A development roadmap for critical technologies needed for TALC: a deployable 20m annular space telescope,” Proc. SPIE 9904, 99041L (2016).
[Crossref]

Schunk, R. G.

D. C. Redding, S. A. Basinger, A. E. Lowman, A. Kissil, P. Y. Bely, R. Burg, R. G. Lyon, G. E. Mosier, M. Femiano, M. E. Wilson, R. G. Schunk, L. D. Craig, D. N. Jacobson, J. M. Rakoczy, and J. B. Hadaway, “Wavefront sensing and control for a next generation space telescope,” Proc. SPIE 3356, 758–772 (1998).
[Crossref]

Schwenker, J.

D. S. Acton, T. Towell, J. Schwenker, J. Swensen, D. Shields, E. Sabatke, L. Klingemann, A. R. Contos, B. Bauer, K. Hansen, P. D. Atcheson, D. Redding, F. Shi, S. Basinger, B. Dean, and L. Burns, “Demonstration of the James Webb Space Telescope commissioning on the JWST testbed telescope,” Proc. SPIE 6265, 62650R (2006).
[Crossref]

Sève, A.

Shaklan, S.

M. R. Bolcar, K. Balasubramanian, M. Clampin, J. Crooke, L. Feinberg, M. Postman, M. Quijada, B. Rauscher, D. Redding, N. Rioux, S. Shaklan, H. P. Stahl, C. Stahle, and H. Thronson, “Technology development for the Advanced Technology Large Aperture Space Telescope (ATLAST) as a candidate large UV-Optical-Infrared (LUVOIR) surveyor,” Proc. SPIE 9602, 960209 (2015).
[Crossref]

Shi, F.

D. S. Acton, T. Towell, J. Schwenker, J. Swensen, D. Shields, E. Sabatke, L. Klingemann, A. R. Contos, B. Bauer, K. Hansen, P. D. Atcheson, D. Redding, F. Shi, S. Basinger, B. Dean, and L. Burns, “Demonstration of the James Webb Space Telescope commissioning on the JWST testbed telescope,” Proc. SPIE 6265, 62650R (2006).
[Crossref]

Shields, D.

D. S. Acton, T. Towell, J. Schwenker, J. Swensen, D. Shields, E. Sabatke, L. Klingemann, A. R. Contos, B. Bauer, K. Hansen, P. D. Atcheson, D. Redding, F. Shi, S. Basinger, B. Dean, and L. Burns, “Demonstration of the James Webb Space Telescope commissioning on the JWST testbed telescope,” Proc. SPIE 6265, 62650R (2006).
[Crossref]

Shiri, R.

B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, “Phase retrieval algorithm for JWST flight and testbed telescope,” Proc. SPIE 6265, 626511 (2006).
[Crossref]

Sigler, R. D.

J. T. Pitman, A. Duncan, D. Stubbs, R. D. Sigler, R. L. Kendrick, E. H. Smith, J. E. Mason, G. Delory, J. H. Lipps, M. Manga, J. R. Graham, I. de Pater, S. Reiboldt, E. Bierhaus, J. B. Dalton, J. R. Fienup, and J. W. Yu, “Remote sensing space science enabled by the multiple instrument distributed aperture sensor (midas) concept,” in Optical Science and Technology, the SPIE 49th Annual Meeting (International Society for Optics and Photonics, 2004), pp. 301–310.

Sironi, G.

M. Sauvage, J. Amiaux, J. Austin, M. Bello, G. Bianucci, S. Chesné, O. Citterio, C. Collette, S. Correia, G. A. Durand, S. Molinari, G. Pareschi, Y. Penfornis, G. Sironi, G. Valsecchi, S. Verpoort, and U. Wittrock, “A development roadmap for critical technologies needed for TALC: a deployable 20m annular space telescope,” Proc. SPIE 9904, 99041L (2016).
[Crossref]

Smith, E. H.

L. H. Lee, G. Vasudevan, and E. H. Smith, “Point-by-point approach to phase-diverse phase retrieval,” Proc. SPIE 4850, 441–452 (2003).
[Crossref]

J. T. Pitman, A. Duncan, D. Stubbs, R. D. Sigler, R. L. Kendrick, E. H. Smith, J. E. Mason, G. Delory, J. H. Lipps, M. Manga, J. R. Graham, I. de Pater, S. Reiboldt, E. Bierhaus, J. B. Dalton, J. R. Fienup, and J. W. Yu, “Remote sensing space science enabled by the multiple instrument distributed aperture sensor (midas) concept,” in Optical Science and Technology, the SPIE 49th Annual Meeting (International Society for Optics and Photonics, 2004), pp. 301–310.

Smith, J. S.

D. S. Acton, J. S. Knight, A. Contos, S. Grimaldi, J. Terry, P. Lightsey, A. Barto, B. League, B. Dean, J. S. Smith, C. Bowers, D. Aronstein, L. Feinberg, W. Hayden, T. Comeau, R. Soummer, E. Elliott, M. Perrin, and C. W. Starr, “Wavefront sensing and controls for the James webb space telescope,” Proc. SPIE 8442, 84422H (2012).
[Crossref]

B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, “Phase retrieval algorithm for JWST flight and testbed telescope,” Proc. SPIE 6265, 626511 (2006).
[Crossref]

Sorrente, B.

F. Cassaing, B. Sorrente, L. Mugnier, G. Rousset, V. Michau, I. Mocœur, and F. Baron, “BRISE: a multipurpose bench for cophasing sensors,” Proc. SPIE 6268, 62683A (2006).
[Crossref]

L. Mugnier, F. Cassaing, B. Sorrente, F. Baron, M.-T. Velluet, V. Michau, and G. Rousset, “Multiple-aperture optical telescopes: some key issues for earth observation from a GEO orbit,” in 5th International Conference on Space Optics, CNES/ESA (ESA, 2004), vol. SP-554, pp. 181–187.

Soummer, R.

M. D. Perrin, D. S. Acton, C.-P. Lajoie, J. S. Knight, M. D. Lallo, M. Allen, W. Baggett, E. Barker, T. Comeau, E. Coppock, B. H. Dean, G. Hartig, W. L. Hayden, M. Jordan, A. Jurling, T. Kulp, J. Long, M. W. McElwain, L. Meza, E. P. Nelan, R. Soummer, J. Stansberry, C. Stark, R. Telfer, A. L. Welsh, T. P. Zielinski, and N. T. Zimmerman, “Preparing for JWST wavefront sensing and control operations,” Proc. SPIE 9904, 99040F (2016).
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D. S. Acton, J. S. Knight, A. Contos, S. Grimaldi, J. Terry, P. Lightsey, A. Barto, B. League, B. Dean, J. S. Smith, C. Bowers, D. Aronstein, L. Feinberg, W. Hayden, T. Comeau, R. Soummer, E. Elliott, M. Perrin, and C. W. Starr, “Wavefront sensing and controls for the James webb space telescope,” Proc. SPIE 8442, 84422H (2012).
[Crossref]

Stahl, H. P.

M. R. Bolcar, K. Balasubramanian, M. Clampin, J. Crooke, L. Feinberg, M. Postman, M. Quijada, B. Rauscher, D. Redding, N. Rioux, S. Shaklan, H. P. Stahl, C. Stahle, and H. Thronson, “Technology development for the Advanced Technology Large Aperture Space Telescope (ATLAST) as a candidate large UV-Optical-Infrared (LUVOIR) surveyor,” Proc. SPIE 9602, 960209 (2015).
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Stahle, C.

M. R. Bolcar, K. Balasubramanian, M. Clampin, J. Crooke, L. Feinberg, M. Postman, M. Quijada, B. Rauscher, D. Redding, N. Rioux, S. Shaklan, H. P. Stahl, C. Stahle, and H. Thronson, “Technology development for the Advanced Technology Large Aperture Space Telescope (ATLAST) as a candidate large UV-Optical-Infrared (LUVOIR) surveyor,” Proc. SPIE 9602, 960209 (2015).
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Stansberry, J.

M. D. Perrin, D. S. Acton, C.-P. Lajoie, J. S. Knight, M. D. Lallo, M. Allen, W. Baggett, E. Barker, T. Comeau, E. Coppock, B. H. Dean, G. Hartig, W. L. Hayden, M. Jordan, A. Jurling, T. Kulp, J. Long, M. W. McElwain, L. Meza, E. P. Nelan, R. Soummer, J. Stansberry, C. Stark, R. Telfer, A. L. Welsh, T. P. Zielinski, and N. T. Zimmerman, “Preparing for JWST wavefront sensing and control operations,” Proc. SPIE 9904, 99040F (2016).
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Stark, C.

M. D. Perrin, D. S. Acton, C.-P. Lajoie, J. S. Knight, M. D. Lallo, M. Allen, W. Baggett, E. Barker, T. Comeau, E. Coppock, B. H. Dean, G. Hartig, W. L. Hayden, M. Jordan, A. Jurling, T. Kulp, J. Long, M. W. McElwain, L. Meza, E. P. Nelan, R. Soummer, J. Stansberry, C. Stark, R. Telfer, A. L. Welsh, T. P. Zielinski, and N. T. Zimmerman, “Preparing for JWST wavefront sensing and control operations,” Proc. SPIE 9904, 99040F (2016).
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Starr, C. W.

D. S. Acton, J. S. Knight, A. Contos, S. Grimaldi, J. Terry, P. Lightsey, A. Barto, B. League, B. Dean, J. S. Smith, C. Bowers, D. Aronstein, L. Feinberg, W. Hayden, T. Comeau, R. Soummer, E. Elliott, M. Perrin, and C. W. Starr, “Wavefront sensing and controls for the James webb space telescope,” Proc. SPIE 8442, 84422H (2012).
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Stubbs, D.

J. T. Pitman, A. Duncan, D. Stubbs, R. D. Sigler, R. L. Kendrick, E. H. Smith, J. E. Mason, G. Delory, J. H. Lipps, M. Manga, J. R. Graham, I. de Pater, S. Reiboldt, E. Bierhaus, J. B. Dalton, J. R. Fienup, and J. W. Yu, “Remote sensing space science enabled by the multiple instrument distributed aperture sensor (midas) concept,” in Optical Science and Technology, the SPIE 49th Annual Meeting (International Society for Optics and Photonics, 2004), pp. 301–310.

Swensen, J.

D. S. Acton, T. Towell, J. Schwenker, J. Swensen, D. Shields, E. Sabatke, L. Klingemann, A. R. Contos, B. Bauer, K. Hansen, P. D. Atcheson, D. Redding, F. Shi, S. Basinger, B. Dean, and L. Burns, “Demonstration of the James Webb Space Telescope commissioning on the JWST testbed telescope,” Proc. SPIE 6265, 62650R (2006).
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Telfer, R.

M. D. Perrin, D. S. Acton, C.-P. Lajoie, J. S. Knight, M. D. Lallo, M. Allen, W. Baggett, E. Barker, T. Comeau, E. Coppock, B. H. Dean, G. Hartig, W. L. Hayden, M. Jordan, A. Jurling, T. Kulp, J. Long, M. W. McElwain, L. Meza, E. P. Nelan, R. Soummer, J. Stansberry, C. Stark, R. Telfer, A. L. Welsh, T. P. Zielinski, and N. T. Zimmerman, “Preparing for JWST wavefront sensing and control operations,” Proc. SPIE 9904, 99040F (2016).
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Terry, J.

D. S. Acton, J. S. Knight, A. Contos, S. Grimaldi, J. Terry, P. Lightsey, A. Barto, B. League, B. Dean, J. S. Smith, C. Bowers, D. Aronstein, L. Feinberg, W. Hayden, T. Comeau, R. Soummer, E. Elliott, M. Perrin, and C. W. Starr, “Wavefront sensing and controls for the James webb space telescope,” Proc. SPIE 8442, 84422H (2012).
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D. A. Carrara, B. J. Thelen, and R. G. Paxman, “Aberration correction of segmented-aperture telescopes by using phase diversity,” Proc. SPIE 4123, 56–63 (2000).
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Thiébaut, E.

G. Moretto, J. R. Kuhn, E. Thiébaut, M. Langlois, S. V. Berdyugina, C. Harlingten, and D. Halliday, “New strategies for an extremely large telescope dedicated to extremely high contrast: the Colossus project,” Proc. SPIE 9145, 91451L (2014).
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Thiele, H.

I. Mocœur, F. Cassaing, F. Baron, L. Mugnier, S. Hofer, and H. Thiele, “Darwin fringe sensor: experimental results on the BRISE bench,” Proc. SPIE 6268, 62682B (2006).
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Thomas, E.

M. Mesrine, E. Thomas, S. Garin, P. Blanc, C. Alis, F. Cassaing, and D. Laubier, “High resolution Earth observation form Geostationary orbit by optical aperture synthesys,” in Sixth International Conference on Space Optics (ESA-CNES, ESA/ESTEC Noordwijk, 2006).

Thompson, B. J.

K. T. Knox and B. J. Thompson, “Recovery of images from atmospherically degraded short-exposure photographs,” Astrophys. J. 193, L45–L48 (1974).
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Thronson, H.

M. R. Bolcar, K. Balasubramanian, M. Clampin, J. Crooke, L. Feinberg, M. Postman, M. Quijada, B. Rauscher, D. Redding, N. Rioux, S. Shaklan, H. P. Stahl, C. Stahle, and H. Thronson, “Technology development for the Advanced Technology Large Aperture Space Telescope (ATLAST) as a candidate large UV-Optical-Infrared (LUVOIR) surveyor,” Proc. SPIE 9602, 960209 (2015).
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Thurman, S. T.

Towell, T.

D. S. Acton, T. Towell, J. Schwenker, J. Swensen, D. Shields, E. Sabatke, L. Klingemann, A. R. Contos, B. Bauer, K. Hansen, P. D. Atcheson, D. Redding, F. Shi, S. Basinger, B. Dean, and L. Burns, “Demonstration of the James Webb Space Telescope commissioning on the JWST testbed telescope,” Proc. SPIE 6265, 62650R (2006).
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Valsecchi, G.

M. Sauvage, J. Amiaux, J. Austin, M. Bello, G. Bianucci, S. Chesné, O. Citterio, C. Collette, S. Correia, G. A. Durand, S. Molinari, G. Pareschi, Y. Penfornis, G. Sironi, G. Valsecchi, S. Verpoort, and U. Wittrock, “A development roadmap for critical technologies needed for TALC: a deployable 20m annular space telescope,” Proc. SPIE 9904, 99041L (2016).
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Vasudevan, G.

L. H. Lee, G. Vasudevan, and E. H. Smith, “Point-by-point approach to phase-diverse phase retrieval,” Proc. SPIE 4850, 441–452 (2003).
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Velluet, M.-T.

L. Mugnier, F. Cassaing, B. Sorrente, F. Baron, M.-T. Velluet, V. Michau, and G. Rousset, “Multiple-aperture optical telescopes: some key issues for earth observation from a GEO orbit,” in 5th International Conference on Space Optics, CNES/ESA (ESA, 2004), vol. SP-554, pp. 181–187.

Verpoort, S.

M. Sauvage, J. Amiaux, J. Austin, M. Bello, G. Bianucci, S. Chesné, O. Citterio, C. Collette, S. Correia, G. A. Durand, S. Molinari, G. Pareschi, Y. Penfornis, G. Sironi, G. Valsecchi, S. Verpoort, and U. Wittrock, “A development roadmap for critical technologies needed for TALC: a deployable 20m annular space telescope,” Proc. SPIE 9904, 99041L (2016).
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Vievard, S.

S. Vievard, “Développement et validation d’un analyseur de surface d’onde en plan focal pour un instrument multi-pupille,” Ph.D. dissertation (Université Pierre et Marie Curie, 2017).

S. Vievard, F. Cassaing, A. Bonnefois, L. Mugnier, and J. Montri, “Real-time alignment and co-phasing of multi-aperture systems using phase diversity,” in SPIE Astronomical Telescopes+ Instrumentation (International Society for Optics and Photonics, 2016), pp. 99062Q.

Welsh, A. L.

M. D. Perrin, D. S. Acton, C.-P. Lajoie, J. S. Knight, M. D. Lallo, M. Allen, W. Baggett, E. Barker, T. Comeau, E. Coppock, B. H. Dean, G. Hartig, W. L. Hayden, M. Jordan, A. Jurling, T. Kulp, J. Long, M. W. McElwain, L. Meza, E. P. Nelan, R. Soummer, J. Stansberry, C. Stark, R. Telfer, A. L. Welsh, T. P. Zielinski, and N. T. Zimmerman, “Preparing for JWST wavefront sensing and control operations,” Proc. SPIE 9904, 99040F (2016).
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Welsh, B. M.

M. C. Roggemann, B. M. Welsh, and B. R. Hunt, Imaging through Turbulence (CRC Press, 1996).

Wilson, M. E.

D. C. Redding, S. A. Basinger, A. E. Lowman, A. Kissil, P. Y. Bely, R. Burg, R. G. Lyon, G. E. Mosier, M. Femiano, M. E. Wilson, R. G. Schunk, L. D. Craig, D. N. Jacobson, J. M. Rakoczy, and J. B. Hadaway, “Wavefront sensing and control for a next generation space telescope,” Proc. SPIE 3356, 758–772 (1998).
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Wittrock, U.

M. Sauvage, J. Amiaux, J. Austin, M. Bello, G. Bianucci, S. Chesné, O. Citterio, C. Collette, S. Correia, G. A. Durand, S. Molinari, G. Pareschi, Y. Penfornis, G. Sironi, G. Valsecchi, S. Verpoort, and U. Wittrock, “A development roadmap for critical technologies needed for TALC: a deployable 20m annular space telescope,” Proc. SPIE 9904, 99041L (2016).
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Yu, J. W.

J. T. Pitman, A. Duncan, D. Stubbs, R. D. Sigler, R. L. Kendrick, E. H. Smith, J. E. Mason, G. Delory, J. H. Lipps, M. Manga, J. R. Graham, I. de Pater, S. Reiboldt, E. Bierhaus, J. B. Dalton, J. R. Fienup, and J. W. Yu, “Remote sensing space science enabled by the multiple instrument distributed aperture sensor (midas) concept,” in Optical Science and Technology, the SPIE 49th Annual Meeting (International Society for Optics and Photonics, 2004), pp. 301–310.

Zielinski, T. P.

M. D. Perrin, D. S. Acton, C.-P. Lajoie, J. S. Knight, M. D. Lallo, M. Allen, W. Baggett, E. Barker, T. Comeau, E. Coppock, B. H. Dean, G. Hartig, W. L. Hayden, M. Jordan, A. Jurling, T. Kulp, J. Long, M. W. McElwain, L. Meza, E. P. Nelan, R. Soummer, J. Stansberry, C. Stark, R. Telfer, A. L. Welsh, T. P. Zielinski, and N. T. Zimmerman, “Preparing for JWST wavefront sensing and control operations,” Proc. SPIE 9904, 99040F (2016).
[Crossref]

Zimmerman, N. T.

M. D. Perrin, D. S. Acton, C.-P. Lajoie, J. S. Knight, M. D. Lallo, M. Allen, W. Baggett, E. Barker, T. Comeau, E. Coppock, B. H. Dean, G. Hartig, W. L. Hayden, M. Jordan, A. Jurling, T. Kulp, J. Long, M. W. McElwain, L. Meza, E. P. Nelan, R. Soummer, J. Stansberry, C. Stark, R. Telfer, A. L. Welsh, T. P. Zielinski, and N. T. Zimmerman, “Preparing for JWST wavefront sensing and control operations,” Proc. SPIE 9904, 99040F (2016).
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Appl. Opt. (1)

Astrophys. J. (1)

K. T. Knox and B. J. Thompson, “Recovery of images from atmospherically degraded short-exposure photographs,” Astrophys. J. 193, L45–L48 (1974).
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J. Opt. Soc. Am. (1)

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Phys. Rep. (1)

F. Roddier, “Interferometric imaging in optical astronomy,” Phys. Rep. 170, 97–166 (1988).
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Figures (16)

Fig. 1.
Fig. 1.

(top) Misaligned telescope. The segment tip/tilts induce sub-PSF shifts in the focal plane. An additional shift, specific to each subaperture, due to the diversity and denoted by an arrow on the diagram, appears in the defocused plane. (bottom) Aligned telescope. All the sub-PSFs are superimposed in the focal plane. In the defocused plane, the additional diversity-induced shift remains.

Fig. 2.
Fig. 2.

(top) From left to right: global defocus over the full aperture; facet defocus as piston/tip/tilt over each subaperture; pseudo-defocus as tip/tilt over each subaperture. (bottom left) Defocused image with a 10 rad amplitude. The sub-PSFs are sprawled. (bottom right) Pseudo-defocus or facet defocus with a 10 rad amplitude. The sub-PSFs’ sprawling is prevented because the facets are planar.

Fig. 3.
Fig. 3.

Columns from left to right: pupil, PSF, OTF modulus (logarithmic scale), and phase for a 3-subaperture configuration (see text and Appendix A for more details). (1) No aberration, coherent sub-PSFs; (2) tip/tilt aberrations on pupil 0, 1, and 2, coherent sub-PSFs; (3) tip/tilt aberrations on pupil 0, 1, and 2, incoherent sub-PSFs.

Fig. 4.
Fig. 4.

Illustration of ELASTIC. Line 1: two diversity images with a 3-aperture interferometer (left: focal plane with tip/tilt errors, right: with an added pseudo-defocus). Line 2: image correlation. The three autospots are inside the overplotted circle in the center, while the six interspots are scattered around. Line 3: modulus (left) and phase (right) of their cross-spectrum. Note: a sub-PSF 50% brighter in line 1 has a 225% brighter autospot in line 2.

Fig. 5.
Fig. 5.

Left column: standard cross-spectrum (bottom line) as the result of the product between one sub-PSF FT from one subaperture in the first diversity plane (line 1) with the conjugated sub-PSF FT of the same subaperture in the second diversity plane (line 2). Right column: frequency-shifted cross-spectrum (bottom line) as the result of the product between one sub-PSF FT from one subaperture in the first diversity plane (line 1) with the shifted and conjugated sub-PSF FT of the same (line 2). Each complex term has a modulus (thick line) and a phase that includes two components: the input tip/tilt (dashed line) and the diversity (here a pseudo-defocus, in dotted line).

Fig. 6.
Fig. 6.

18-subaperture pupil considered for simulations, sampled on a 512×512 pixel grid.

Fig. 7.
Fig. 7.

Sensor linearity for various shift amplitudes.

Fig. 8.
Fig. 8.

Line 1: image simulation with sub-PSFs in parking positions in the focal image (left) and in the pseudo defocused image (right). Line 2: image correlation; autospots in the circle are separated and isolated from the interspots.

Fig. 9.
Fig. 9.

Estimation RMSE versus diversity for various shifts δ.

Fig. 10.
Fig. 10.

Wavefront error in waves as a function of the image flux for δ=4, and for an 18-subaperture instrument.

Fig. 11.
Fig. 11.

(left) The active segmented mirror with 19 subapertures. (right) Simulation of the parking position in the focal plane with the six subapertures used (first corona).

Fig. 12.
Fig. 12.

Closed-loop sequence up to the parking position with a δ amplitude of 2 and a total flux of 3e7 photoelectrons per image. Columns are iteration number, focal images, and pseudo-defocused images.

Fig. 13.
Fig. 13.

Evolution of tip/tilt estimation versus the iteration number during the loop.

Fig. 14.
Fig. 14.

Experimental estimation RSME for different illumination conditions. Each point is computed with 50 outcomes.

Fig. 15.
Fig. 15.

Zoom of focal (left) and pseudo-defocused (right) PSF after final superimposition (128×128 pixel images).

Fig. 16.
Fig. 16.

Focal (left) and defocused (right) PSFs after phase diversity fine phasing algorithm (128×128 pixel images).

Tables (1)

Tables Icon

Table 1. Variation of Field Coverage with δ and Corresponding Maximum Aberration Coefficient amax in our Simulated Case

Equations (38)

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Π(u)={1for|u|1,0elsewhere,
pn,d=[ρnΠn,dexp(jk=132πak,nZk)]δcn,
Πn,d=Πexp[jΨn,d]andj2=1,
pd=n=1Napn,d.
sd(u)=(pdpd)(u)=pd(u)pd*(u+u)du.
sd(u)=n=1Nan=1Na[(pn,dpn,d)δ(cncn)](u).
sd(u)=n=1Naρn2Λn,d(u)exp[jk=234πak,nZk(u2)],
Λn,d=(Πexp[jΨn,d])(Πexp[jΨn,d]).
ns=λF2Rppix.
sd,q=n=1Naρn2Λn,d(nsqNp)exp[jk=234πaknZk(nsq2Np)].
δ2=(δ,0),δ3=(0,δ).
jm,q=s1,q×Δm[s2,q*],
jm,q=n=1Naρn4(Λn×Δm[Λn*])(nsqNp)×exp[jk=234πak,n(ZkΔm[Zk])(nsq2Np)].
(ZkΔm[Zk])(nsq2Np)=nsδNpδk,m,
jm,q=n=1Naρn4exp[j4πnsδNpam,n]n,m(nsqNp),
n,m=Λn×Δm[Λn*].
xm=[xm,1,,xm,Na]T,m{2,3},
xm,n=Δρn4exp[j4πnsδNpam,n],n{1,,Na}.
jm=Cmxm,
xm^=Cmjm.
{a^m,n=Np4πnsδArg(x^m,n),ρ^m,n=|x^m,n|1/4.
RMSE=1Nam,n(a^m,nam,n)2,
afield=Np8ns.
amax(δ)=2afieldδ=Np4nsδ.
a^m,nam,n+Np4πnsδIm(εnxm,n),
Z1(un)=1,(piston),
Z2(un)=2un,(tip),
Z3(un)=2vn,(tilt),
Z4(un)=3(2un21).(defocus).
r=rn+Rcn,
un=ΔrnR,u=ΔrB/2,
u=2RB(un+cn).
Z4(u)=3[24R2B2(un2+2un·cn+cn2)1],
=4R2B2Z4(un)+232R2B[cx,nB/2Z2(un)+cy,nB/2Z3(un)]+3[2R2B2/4cn2+4R2B21].
a2,n=234R2B2cx,nA4.
θ=kpppixF=2amλRam=Rθ2λ=kpRppix2λF=kp4ns,
A4=163B24R21P.
Δam=234R2B2(B2R)A4+14.

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