Abstract

The Zernike phase contrast method is a novel technique to phase the primary mirrors of segmented telescopes. It has been tested on-sky on a unit telescope of the Very Large Telescope with a segmented mirror conjugated to the primary mirror to emulate a segmented telescope. The theoretical background of this sensor and the algorithm used to retrieve the piston, tip, and tilt information are described. The performance of the sensor as a function of parameters such as star magnitude, seeing, and integration time is discussed. The phasing accuracy has always been below 15nm root mean square wavefront error under normal conditions of operation and the limiting star magnitude achieved on-sky with this sensor is 15.7 in the red, which would be sufficient to phase segmented telescopes in closed-loop during observations.

© 2010 Optical Society of America

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  4. N. Yaitskova, “Adaptive optics correction of segment aberration,” J. Opt. Soc. Am. A 26, 59–71 (2009).
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  6. R. Mazzoleni, F. Gonte, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack-Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
    [CrossRef]
  7. F. Gonte, C. Araujo, R. Bourtembourg, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, R. Mazzoleni, L. Noethe, I. Surdej, N. Yaitskova, R. Wilhelm, B. Luong, E. Pinna, S. Chueca, and A. Vigan, “Active Phasing Experiment: preliminary results and prospects,” Proc. SPIE 7012, 70120Z (2008).
    [CrossRef]
  8. E. Pinna, S. Esposito, A. Puglisi, F. Pieralli, R. M. Myers, L. Busoni, A. Tozzi, and P. Stefanini, “Phase ambiguity solution with the Pyramid Phasing Sensor,” Proc. SPIE 6267, 62672Y (2006).
    [CrossRef]
  9. L. Montoya, M. Reyes, A. Schumacher, and E. Hernandez, “DIPSI: the diffraction image phase sensing for APE,” Proc. SPIE 6267, 626732 (2006).
    [CrossRef]
  10. K. Dohlen, “Phase masks in astronomy from the Mach-Zehnder interferometer to coronographs,” in Astronomy with High Contrast Imaging II Instrumentation for Coronagraphy and Nulling Interferometry, Vol. 12 of EAS Publications Series (European Astronomical Society, 2004), pp. 33–44.
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    [CrossRef]
  12. A. Vigan, K. Dohlen, I. Surdej, N. Yaitskova, and F. Y. J. Gonte, “On-sky results of the ZEUS phasing sensor, closed-loop measurement precision in the context of multi-wavelength measurements,” Proc. SPIE 7733, 7733-187 (2010).
  13. F. Gonte, C. Dupuy, B. Luong, C. Frank, R. Brast, and B. Sedghi, “Active hexagonally segmented mirror to investigate new optical phasing technologies for segmented telescopes,” Appl. Opt. 48, 6392–6399 (2009).
    [CrossRef] [PubMed]
  14. R. Wilhelm, B. Luong, A. Courteville, S. Estival, F. Gont, and N. Schuhler, “Dual-wavelength low-coherence instantaneous phase-shifting interferometer to measure the shape of a segmented mirror with subnanometer precision,” Appl. Opt. 47, 5473–5491 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
  16. K. Dohlen, M. Langlois, P. Lanzoni, S. Mazzanti, A. Vigan, L. Montoya, E. Hernandez, M. Reyes, I. Surdej, and N. Yaitskova, “ZEUS: a cophasing sensor based on the Zernike phase contrast method,” Proc. SPIE 6267, 626734 (2006).
    [CrossRef]
  17. I. Surdej, H. Lorch, L. Noethe, N. Yaitskova, and R. Karban, “Pattern recognition and signal analysis in a Mach-Zehnder type phasing sensor,” Proc. SPIE 6696, 66960L (2007).
    [CrossRef]
  18. S. Chueca, M. Reyes, A. Schumacher, and L. Montoya, “DIPSI: measure of the tip-tilt with a diffraction image phase sensing instrument,” Proc. SPIE 7012, 701213 (2008).
    [CrossRef]
  19. M. G. Lofdahl and H. Eriksson, “Resolving piston ambiguities when phasing a segmented mirror,” Proc. SPIE 4013, 774–782(2000).
    [CrossRef]

2010 (1)

A. Vigan, K. Dohlen, I. Surdej, N. Yaitskova, and F. Y. J. Gonte, “On-sky results of the ZEUS phasing sensor, closed-loop measurement precision in the context of multi-wavelength measurements,” Proc. SPIE 7733, 7733-187 (2010).

2009 (2)

2008 (7)

P. Alvarez, J. M. Rodríguez Espinosa, F. J. Castro López-Tarruella, M. Pi, P. Hammersley, L. Cavaller, B. Siegel, J. Molgo, J. Pancorbo, R. Ascanio, G. Prieto, and J. Calvo, “The GTC project: under commissioning,” Proc. SPIE 7012, 701202 (2008).
[CrossRef]

J. Nelson and G. H. Sanders, “The status of the Thirty Meter Telescope project,” Proc. SPIE 7012, 70121A (2008).
[CrossRef]

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

R. Mazzoleni, F. Gonte, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack-Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

F. Gonte, C. Araujo, R. Bourtembourg, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, R. Mazzoleni, L. Noethe, I. Surdej, N. Yaitskova, R. Wilhelm, B. Luong, E. Pinna, S. Chueca, and A. Vigan, “Active Phasing Experiment: preliminary results and prospects,” Proc. SPIE 7012, 70120Z (2008).
[CrossRef]

R. Wilhelm, B. Luong, A. Courteville, S. Estival, F. Gont, and N. Schuhler, “Dual-wavelength low-coherence instantaneous phase-shifting interferometer to measure the shape of a segmented mirror with subnanometer precision,” Appl. Opt. 47, 5473–5491 (2008).
[CrossRef] [PubMed]

S. Chueca, M. Reyes, A. Schumacher, and L. Montoya, “DIPSI: measure of the tip-tilt with a diffraction image phase sensing instrument,” Proc. SPIE 7012, 701213 (2008).
[CrossRef]

2007 (1)

I. Surdej, H. Lorch, L. Noethe, N. Yaitskova, and R. Karban, “Pattern recognition and signal analysis in a Mach-Zehnder type phasing sensor,” Proc. SPIE 6696, 66960L (2007).
[CrossRef]

2006 (4)

K. Dohlen, M. Langlois, P. Lanzoni, S. Mazzanti, A. Vigan, L. Montoya, E. Hernandez, M. Reyes, I. Surdej, and N. Yaitskova, “ZEUS: a cophasing sensor based on the Zernike phase contrast method,” Proc. SPIE 6267, 626734 (2006).
[CrossRef]

E. Pinna, S. Esposito, A. Puglisi, F. Pieralli, R. M. Myers, L. Busoni, A. Tozzi, and P. Stefanini, “Phase ambiguity solution with the Pyramid Phasing Sensor,” Proc. SPIE 6267, 62672Y (2006).
[CrossRef]

L. Montoya, M. Reyes, A. Schumacher, and E. Hernandez, “DIPSI: the diffraction image phase sensing for APE,” Proc. SPIE 6267, 626732 (2006).
[CrossRef]

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The Active Phasing Experiment: Part 1. Concept and objectives,” Proc. SPIE 6267, 62672Z (2006).
[CrossRef]

2005 (1)

2000 (1)

M. G. Lofdahl and H. Eriksson, “Resolving piston ambiguities when phasing a segmented mirror,” Proc. SPIE 4013, 774–782(2000).
[CrossRef]

1998 (1)

Alvarez, P.

P. Alvarez, J. M. Rodríguez Espinosa, F. J. Castro López-Tarruella, M. Pi, P. Hammersley, L. Cavaller, B. Siegel, J. Molgo, J. Pancorbo, R. Ascanio, G. Prieto, and J. Calvo, “The GTC project: under commissioning,” Proc. SPIE 7012, 701202 (2008).
[CrossRef]

Araujo, C.

R. Mazzoleni, F. Gonte, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack-Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

F. Gonte, C. Araujo, R. Bourtembourg, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, R. Mazzoleni, L. Noethe, I. Surdej, N. Yaitskova, R. Wilhelm, B. Luong, E. Pinna, S. Chueca, and A. Vigan, “Active Phasing Experiment: preliminary results and prospects,” Proc. SPIE 7012, 70120Z (2008).
[CrossRef]

Ascanio, R.

P. Alvarez, J. M. Rodríguez Espinosa, F. J. Castro López-Tarruella, M. Pi, P. Hammersley, L. Cavaller, B. Siegel, J. Molgo, J. Pancorbo, R. Ascanio, G. Prieto, and J. Calvo, “The GTC project: under commissioning,” Proc. SPIE 7012, 701202 (2008).
[CrossRef]

Bourtembourg, R.

F. Gonte, C. Araujo, R. Bourtembourg, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, R. Mazzoleni, L. Noethe, I. Surdej, N. Yaitskova, R. Wilhelm, B. Luong, E. Pinna, S. Chueca, and A. Vigan, “Active Phasing Experiment: preliminary results and prospects,” Proc. SPIE 7012, 70120Z (2008).
[CrossRef]

Brast, R.

F. Gonte, C. Dupuy, B. Luong, C. Frank, R. Brast, and B. Sedghi, “Active hexagonally segmented mirror to investigate new optical phasing technologies for segmented telescopes,” Appl. Opt. 48, 6392–6399 (2009).
[CrossRef] [PubMed]

F. Gonte, C. Araujo, R. Bourtembourg, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, R. Mazzoleni, L. Noethe, I. Surdej, N. Yaitskova, R. Wilhelm, B. Luong, E. Pinna, S. Chueca, and A. Vigan, “Active Phasing Experiment: preliminary results and prospects,” Proc. SPIE 7012, 70120Z (2008).
[CrossRef]

R. Mazzoleni, F. Gonte, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack-Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

Busoni, L.

E. Pinna, S. Esposito, A. Puglisi, F. Pieralli, R. M. Myers, L. Busoni, A. Tozzi, and P. Stefanini, “Phase ambiguity solution with the Pyramid Phasing Sensor,” Proc. SPIE 6267, 62672Y (2006).
[CrossRef]

Calvo, J.

P. Alvarez, J. M. Rodríguez Espinosa, F. J. Castro López-Tarruella, M. Pi, P. Hammersley, L. Cavaller, B. Siegel, J. Molgo, J. Pancorbo, R. Ascanio, G. Prieto, and J. Calvo, “The GTC project: under commissioning,” Proc. SPIE 7012, 701202 (2008).
[CrossRef]

Castro López-Tarruella, F. J.

P. Alvarez, J. M. Rodríguez Espinosa, F. J. Castro López-Tarruella, M. Pi, P. Hammersley, L. Cavaller, B. Siegel, J. Molgo, J. Pancorbo, R. Ascanio, G. Prieto, and J. Calvo, “The GTC project: under commissioning,” Proc. SPIE 7012, 701202 (2008).
[CrossRef]

Cavaller, L.

P. Alvarez, J. M. Rodríguez Espinosa, F. J. Castro López-Tarruella, M. Pi, P. Hammersley, L. Cavaller, B. Siegel, J. Molgo, J. Pancorbo, R. Ascanio, G. Prieto, and J. Calvo, “The GTC project: under commissioning,” Proc. SPIE 7012, 701202 (2008).
[CrossRef]

Chanan, G.

Chueca, S.

F. Gonte, C. Araujo, R. Bourtembourg, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, R. Mazzoleni, L. Noethe, I. Surdej, N. Yaitskova, R. Wilhelm, B. Luong, E. Pinna, S. Chueca, and A. Vigan, “Active Phasing Experiment: preliminary results and prospects,” Proc. SPIE 7012, 70120Z (2008).
[CrossRef]

S. Chueca, M. Reyes, A. Schumacher, and L. Montoya, “DIPSI: measure of the tip-tilt with a diffraction image phase sensing instrument,” Proc. SPIE 7012, 701213 (2008).
[CrossRef]

Courteville, A.

Dekens, F.

Derie, F.

R. Mazzoleni, F. Gonte, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack-Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

F. Gonte, C. Araujo, R. Bourtembourg, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, R. Mazzoleni, L. Noethe, I. Surdej, N. Yaitskova, R. Wilhelm, B. Luong, E. Pinna, S. Chueca, and A. Vigan, “Active Phasing Experiment: preliminary results and prospects,” Proc. SPIE 7012, 70120Z (2008).
[CrossRef]

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The Active Phasing Experiment: Part 1. Concept and objectives,” Proc. SPIE 6267, 62672Z (2006).
[CrossRef]

Dierickx, P.

Dohlen, K.

A. Vigan, K. Dohlen, I. Surdej, N. Yaitskova, and F. Y. J. Gonte, “On-sky results of the ZEUS phasing sensor, closed-loop measurement precision in the context of multi-wavelength measurements,” Proc. SPIE 7733, 7733-187 (2010).

K. Dohlen, M. Langlois, P. Lanzoni, S. Mazzanti, A. Vigan, L. Montoya, E. Hernandez, M. Reyes, I. Surdej, and N. Yaitskova, “ZEUS: a cophasing sensor based on the Zernike phase contrast method,” Proc. SPIE 6267, 626734 (2006).
[CrossRef]

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The Active Phasing Experiment: Part 1. Concept and objectives,” Proc. SPIE 6267, 62672Z (2006).
[CrossRef]

N. Yaitskova, K. Dohlen, P. Dierickx, and L. Montoya, “Mach–Zehnder interferometer for piston and tip-tilt sensing in segmented telescopes: theory and analytical treatment,” J. Opt. Soc. Am. A 22, 1093–1105 (2005).
[CrossRef]

K. Dohlen, “Phase masks in astronomy from the Mach-Zehnder interferometer to coronographs,” in Astronomy with High Contrast Imaging II Instrumentation for Coronagraphy and Nulling Interferometry, Vol. 12 of EAS Publications Series (European Astronomical Society, 2004), pp. 33–44.

Duhoux, P.

F. Gonte, C. Araujo, R. Bourtembourg, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, R. Mazzoleni, L. Noethe, I. Surdej, N. Yaitskova, R. Wilhelm, B. Luong, E. Pinna, S. Chueca, and A. Vigan, “Active Phasing Experiment: preliminary results and prospects,” Proc. SPIE 7012, 70120Z (2008).
[CrossRef]

R. Mazzoleni, F. Gonte, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack-Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

Dupuy, C.

F. Gonte, C. Dupuy, B. Luong, C. Frank, R. Brast, and B. Sedghi, “Active hexagonally segmented mirror to investigate new optical phasing technologies for segmented telescopes,” Appl. Opt. 48, 6392–6399 (2009).
[CrossRef] [PubMed]

R. Mazzoleni, F. Gonte, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack-Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

F. Gonte, C. Araujo, R. Bourtembourg, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, R. Mazzoleni, L. Noethe, I. Surdej, N. Yaitskova, R. Wilhelm, B. Luong, E. Pinna, S. Chueca, and A. Vigan, “Active Phasing Experiment: preliminary results and prospects,” Proc. SPIE 7012, 70120Z (2008).
[CrossRef]

Eriksson, H.

M. G. Lofdahl and H. Eriksson, “Resolving piston ambiguities when phasing a segmented mirror,” Proc. SPIE 4013, 774–782(2000).
[CrossRef]

Esposito, S.

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The Active Phasing Experiment: Part 1. Concept and objectives,” Proc. SPIE 6267, 62672Z (2006).
[CrossRef]

E. Pinna, S. Esposito, A. Puglisi, F. Pieralli, R. M. Myers, L. Busoni, A. Tozzi, and P. Stefanini, “Phase ambiguity solution with the Pyramid Phasing Sensor,” Proc. SPIE 6267, 62672Y (2006).
[CrossRef]

Estival, S.

Frank, C.

F. Gonte, C. Dupuy, B. Luong, C. Frank, R. Brast, and B. Sedghi, “Active hexagonally segmented mirror to investigate new optical phasing technologies for segmented telescopes,” Appl. Opt. 48, 6392–6399 (2009).
[CrossRef] [PubMed]

F. Gonte, C. Araujo, R. Bourtembourg, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, R. Mazzoleni, L. Noethe, I. Surdej, N. Yaitskova, R. Wilhelm, B. Luong, E. Pinna, S. Chueca, and A. Vigan, “Active Phasing Experiment: preliminary results and prospects,” Proc. SPIE 7012, 70120Z (2008).
[CrossRef]

R. Mazzoleni, F. Gonte, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack-Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

Gilmozzi, R.

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

Gont, F.

Gonte, F.

F. Gonte, C. Dupuy, B. Luong, C. Frank, R. Brast, and B. Sedghi, “Active hexagonally segmented mirror to investigate new optical phasing technologies for segmented telescopes,” Appl. Opt. 48, 6392–6399 (2009).
[CrossRef] [PubMed]

R. Mazzoleni, F. Gonte, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack-Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

F. Gonte, C. Araujo, R. Bourtembourg, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, R. Mazzoleni, L. Noethe, I. Surdej, N. Yaitskova, R. Wilhelm, B. Luong, E. Pinna, S. Chueca, and A. Vigan, “Active Phasing Experiment: preliminary results and prospects,” Proc. SPIE 7012, 70120Z (2008).
[CrossRef]

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The Active Phasing Experiment: Part 1. Concept and objectives,” Proc. SPIE 6267, 62672Z (2006).
[CrossRef]

Gonte, F. Y. J.

A. Vigan, K. Dohlen, I. Surdej, N. Yaitskova, and F. Y. J. Gonte, “On-sky results of the ZEUS phasing sensor, closed-loop measurement precision in the context of multi-wavelength measurements,” Proc. SPIE 7733, 7733-187 (2010).

Hammersley, P.

P. Alvarez, J. M. Rodríguez Espinosa, F. J. Castro López-Tarruella, M. Pi, P. Hammersley, L. Cavaller, B. Siegel, J. Molgo, J. Pancorbo, R. Ascanio, G. Prieto, and J. Calvo, “The GTC project: under commissioning,” Proc. SPIE 7012, 701202 (2008).
[CrossRef]

Hernandez, E.

L. Montoya, M. Reyes, A. Schumacher, and E. Hernandez, “DIPSI: the diffraction image phase sensing for APE,” Proc. SPIE 6267, 626732 (2006).
[CrossRef]

K. Dohlen, M. Langlois, P. Lanzoni, S. Mazzanti, A. Vigan, L. Montoya, E. Hernandez, M. Reyes, I. Surdej, and N. Yaitskova, “ZEUS: a cophasing sensor based on the Zernike phase contrast method,” Proc. SPIE 6267, 626734 (2006).
[CrossRef]

Karban, R.

F. Gonte, C. Araujo, R. Bourtembourg, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, R. Mazzoleni, L. Noethe, I. Surdej, N. Yaitskova, R. Wilhelm, B. Luong, E. Pinna, S. Chueca, and A. Vigan, “Active Phasing Experiment: preliminary results and prospects,” Proc. SPIE 7012, 70120Z (2008).
[CrossRef]

R. Mazzoleni, F. Gonte, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack-Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

I. Surdej, H. Lorch, L. Noethe, N. Yaitskova, and R. Karban, “Pattern recognition and signal analysis in a Mach-Zehnder type phasing sensor,” Proc. SPIE 6696, 66960L (2007).
[CrossRef]

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The Active Phasing Experiment: Part 1. Concept and objectives,” Proc. SPIE 6267, 62672Z (2006).
[CrossRef]

Kirkman, D.

Langlois, M.

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The Active Phasing Experiment: Part 1. Concept and objectives,” Proc. SPIE 6267, 62672Z (2006).
[CrossRef]

K. Dohlen, M. Langlois, P. Lanzoni, S. Mazzanti, A. Vigan, L. Montoya, E. Hernandez, M. Reyes, I. Surdej, and N. Yaitskova, “ZEUS: a cophasing sensor based on the Zernike phase contrast method,” Proc. SPIE 6267, 626734 (2006).
[CrossRef]

Lanzoni, P.

K. Dohlen, M. Langlois, P. Lanzoni, S. Mazzanti, A. Vigan, L. Montoya, E. Hernandez, M. Reyes, I. Surdej, and N. Yaitskova, “ZEUS: a cophasing sensor based on the Zernike phase contrast method,” Proc. SPIE 6267, 626734 (2006).
[CrossRef]

Lofdahl, M. G.

M. G. Lofdahl and H. Eriksson, “Resolving piston ambiguities when phasing a segmented mirror,” Proc. SPIE 4013, 774–782(2000).
[CrossRef]

Lorch, H.

I. Surdej, H. Lorch, L. Noethe, N. Yaitskova, and R. Karban, “Pattern recognition and signal analysis in a Mach-Zehnder type phasing sensor,” Proc. SPIE 6696, 66960L (2007).
[CrossRef]

Luong, B.

Mast, T.

Mazzanti, S.

K. Dohlen, M. Langlois, P. Lanzoni, S. Mazzanti, A. Vigan, L. Montoya, E. Hernandez, M. Reyes, I. Surdej, and N. Yaitskova, “ZEUS: a cophasing sensor based on the Zernike phase contrast method,” Proc. SPIE 6267, 626734 (2006).
[CrossRef]

Mazzoleni, R.

R. Mazzoleni, F. Gonte, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack-Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

F. Gonte, C. Araujo, R. Bourtembourg, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, R. Mazzoleni, L. Noethe, I. Surdej, N. Yaitskova, R. Wilhelm, B. Luong, E. Pinna, S. Chueca, and A. Vigan, “Active Phasing Experiment: preliminary results and prospects,” Proc. SPIE 7012, 70120Z (2008).
[CrossRef]

Michaels, S.

Molgo, J.

P. Alvarez, J. M. Rodríguez Espinosa, F. J. Castro López-Tarruella, M. Pi, P. Hammersley, L. Cavaller, B. Siegel, J. Molgo, J. Pancorbo, R. Ascanio, G. Prieto, and J. Calvo, “The GTC project: under commissioning,” Proc. SPIE 7012, 701202 (2008).
[CrossRef]

Montoya, L.

S. Chueca, M. Reyes, A. Schumacher, and L. Montoya, “DIPSI: measure of the tip-tilt with a diffraction image phase sensing instrument,” Proc. SPIE 7012, 701213 (2008).
[CrossRef]

K. Dohlen, M. Langlois, P. Lanzoni, S. Mazzanti, A. Vigan, L. Montoya, E. Hernandez, M. Reyes, I. Surdej, and N. Yaitskova, “ZEUS: a cophasing sensor based on the Zernike phase contrast method,” Proc. SPIE 6267, 626734 (2006).
[CrossRef]

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The Active Phasing Experiment: Part 1. Concept and objectives,” Proc. SPIE 6267, 62672Z (2006).
[CrossRef]

L. Montoya, M. Reyes, A. Schumacher, and E. Hernandez, “DIPSI: the diffraction image phase sensing for APE,” Proc. SPIE 6267, 626732 (2006).
[CrossRef]

N. Yaitskova, K. Dohlen, P. Dierickx, and L. Montoya, “Mach–Zehnder interferometer for piston and tip-tilt sensing in segmented telescopes: theory and analytical treatment,” J. Opt. Soc. Am. A 22, 1093–1105 (2005).
[CrossRef]

Myers, R. M.

E. Pinna, S. Esposito, A. Puglisi, F. Pieralli, R. M. Myers, L. Busoni, A. Tozzi, and P. Stefanini, “Phase ambiguity solution with the Pyramid Phasing Sensor,” Proc. SPIE 6267, 62672Y (2006).
[CrossRef]

Nelson, J.

Noethe, L.

R. Mazzoleni, F. Gonte, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack-Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

F. Gonte, C. Araujo, R. Bourtembourg, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, R. Mazzoleni, L. Noethe, I. Surdej, N. Yaitskova, R. Wilhelm, B. Luong, E. Pinna, S. Chueca, and A. Vigan, “Active Phasing Experiment: preliminary results and prospects,” Proc. SPIE 7012, 70120Z (2008).
[CrossRef]

I. Surdej, H. Lorch, L. Noethe, N. Yaitskova, and R. Karban, “Pattern recognition and signal analysis in a Mach-Zehnder type phasing sensor,” Proc. SPIE 6696, 66960L (2007).
[CrossRef]

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The Active Phasing Experiment: Part 1. Concept and objectives,” Proc. SPIE 6267, 62672Z (2006).
[CrossRef]

Pancorbo, J.

P. Alvarez, J. M. Rodríguez Espinosa, F. J. Castro López-Tarruella, M. Pi, P. Hammersley, L. Cavaller, B. Siegel, J. Molgo, J. Pancorbo, R. Ascanio, G. Prieto, and J. Calvo, “The GTC project: under commissioning,” Proc. SPIE 7012, 701202 (2008).
[CrossRef]

Pi, M.

P. Alvarez, J. M. Rodríguez Espinosa, F. J. Castro López-Tarruella, M. Pi, P. Hammersley, L. Cavaller, B. Siegel, J. Molgo, J. Pancorbo, R. Ascanio, G. Prieto, and J. Calvo, “The GTC project: under commissioning,” Proc. SPIE 7012, 701202 (2008).
[CrossRef]

Pieralli, F.

E. Pinna, S. Esposito, A. Puglisi, F. Pieralli, R. M. Myers, L. Busoni, A. Tozzi, and P. Stefanini, “Phase ambiguity solution with the Pyramid Phasing Sensor,” Proc. SPIE 6267, 62672Y (2006).
[CrossRef]

Pinna, E.

F. Gonte, C. Araujo, R. Bourtembourg, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, R. Mazzoleni, L. Noethe, I. Surdej, N. Yaitskova, R. Wilhelm, B. Luong, E. Pinna, S. Chueca, and A. Vigan, “Active Phasing Experiment: preliminary results and prospects,” Proc. SPIE 7012, 70120Z (2008).
[CrossRef]

E. Pinna, S. Esposito, A. Puglisi, F. Pieralli, R. M. Myers, L. Busoni, A. Tozzi, and P. Stefanini, “Phase ambiguity solution with the Pyramid Phasing Sensor,” Proc. SPIE 6267, 62672Y (2006).
[CrossRef]

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The Active Phasing Experiment: Part 1. Concept and objectives,” Proc. SPIE 6267, 62672Z (2006).
[CrossRef]

Prieto, G.

P. Alvarez, J. M. Rodríguez Espinosa, F. J. Castro López-Tarruella, M. Pi, P. Hammersley, L. Cavaller, B. Siegel, J. Molgo, J. Pancorbo, R. Ascanio, G. Prieto, and J. Calvo, “The GTC project: under commissioning,” Proc. SPIE 7012, 701202 (2008).
[CrossRef]

Puglisi, A.

E. Pinna, S. Esposito, A. Puglisi, F. Pieralli, R. M. Myers, L. Busoni, A. Tozzi, and P. Stefanini, “Phase ambiguity solution with the Pyramid Phasing Sensor,” Proc. SPIE 6267, 62672Y (2006).
[CrossRef]

Reyes, M.

S. Chueca, M. Reyes, A. Schumacher, and L. Montoya, “DIPSI: measure of the tip-tilt with a diffraction image phase sensing instrument,” Proc. SPIE 7012, 701213 (2008).
[CrossRef]

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The Active Phasing Experiment: Part 1. Concept and objectives,” Proc. SPIE 6267, 62672Z (2006).
[CrossRef]

K. Dohlen, M. Langlois, P. Lanzoni, S. Mazzanti, A. Vigan, L. Montoya, E. Hernandez, M. Reyes, I. Surdej, and N. Yaitskova, “ZEUS: a cophasing sensor based on the Zernike phase contrast method,” Proc. SPIE 6267, 626734 (2006).
[CrossRef]

L. Montoya, M. Reyes, A. Schumacher, and E. Hernandez, “DIPSI: the diffraction image phase sensing for APE,” Proc. SPIE 6267, 626732 (2006).
[CrossRef]

Rodríguez Espinosa, J. M.

P. Alvarez, J. M. Rodríguez Espinosa, F. J. Castro López-Tarruella, M. Pi, P. Hammersley, L. Cavaller, B. Siegel, J. Molgo, J. Pancorbo, R. Ascanio, G. Prieto, and J. Calvo, “The GTC project: under commissioning,” Proc. SPIE 7012, 701202 (2008).
[CrossRef]

Sanders, G. H.

J. Nelson and G. H. Sanders, “The status of the Thirty Meter Telescope project,” Proc. SPIE 7012, 70121A (2008).
[CrossRef]

Schuhler, N.

Schumacher, A.

S. Chueca, M. Reyes, A. Schumacher, and L. Montoya, “DIPSI: measure of the tip-tilt with a diffraction image phase sensing instrument,” Proc. SPIE 7012, 701213 (2008).
[CrossRef]

L. Montoya, M. Reyes, A. Schumacher, and E. Hernandez, “DIPSI: the diffraction image phase sensing for APE,” Proc. SPIE 6267, 626732 (2006).
[CrossRef]

Sedghi, B.

Siegel, B.

P. Alvarez, J. M. Rodríguez Espinosa, F. J. Castro López-Tarruella, M. Pi, P. Hammersley, L. Cavaller, B. Siegel, J. Molgo, J. Pancorbo, R. Ascanio, G. Prieto, and J. Calvo, “The GTC project: under commissioning,” Proc. SPIE 7012, 701202 (2008).
[CrossRef]

Spyromilio, J.

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

Stefanini, P.

E. Pinna, S. Esposito, A. Puglisi, F. Pieralli, R. M. Myers, L. Busoni, A. Tozzi, and P. Stefanini, “Phase ambiguity solution with the Pyramid Phasing Sensor,” Proc. SPIE 6267, 62672Y (2006).
[CrossRef]

Surdej, I.

A. Vigan, K. Dohlen, I. Surdej, N. Yaitskova, and F. Y. J. Gonte, “On-sky results of the ZEUS phasing sensor, closed-loop measurement precision in the context of multi-wavelength measurements,” Proc. SPIE 7733, 7733-187 (2010).

F. Gonte, C. Araujo, R. Bourtembourg, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, R. Mazzoleni, L. Noethe, I. Surdej, N. Yaitskova, R. Wilhelm, B. Luong, E. Pinna, S. Chueca, and A. Vigan, “Active Phasing Experiment: preliminary results and prospects,” Proc. SPIE 7012, 70120Z (2008).
[CrossRef]

R. Mazzoleni, F. Gonte, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack-Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

I. Surdej, H. Lorch, L. Noethe, N. Yaitskova, and R. Karban, “Pattern recognition and signal analysis in a Mach-Zehnder type phasing sensor,” Proc. SPIE 6696, 66960L (2007).
[CrossRef]

K. Dohlen, M. Langlois, P. Lanzoni, S. Mazzanti, A. Vigan, L. Montoya, E. Hernandez, M. Reyes, I. Surdej, and N. Yaitskova, “ZEUS: a cophasing sensor based on the Zernike phase contrast method,” Proc. SPIE 6267, 626734 (2006).
[CrossRef]

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The Active Phasing Experiment: Part 1. Concept and objectives,” Proc. SPIE 6267, 62672Z (2006).
[CrossRef]

Terrett, D.

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The Active Phasing Experiment: Part 1. Concept and objectives,” Proc. SPIE 6267, 62672Z (2006).
[CrossRef]

Tozzi, A.

E. Pinna, S. Esposito, A. Puglisi, F. Pieralli, R. M. Myers, L. Busoni, A. Tozzi, and P. Stefanini, “Phase ambiguity solution with the Pyramid Phasing Sensor,” Proc. SPIE 6267, 62672Y (2006).
[CrossRef]

Troy, M.

Vigan, A.

A. Vigan, K. Dohlen, I. Surdej, N. Yaitskova, and F. Y. J. Gonte, “On-sky results of the ZEUS phasing sensor, closed-loop measurement precision in the context of multi-wavelength measurements,” Proc. SPIE 7733, 7733-187 (2010).

F. Gonte, C. Araujo, R. Bourtembourg, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, R. Mazzoleni, L. Noethe, I. Surdej, N. Yaitskova, R. Wilhelm, B. Luong, E. Pinna, S. Chueca, and A. Vigan, “Active Phasing Experiment: preliminary results and prospects,” Proc. SPIE 7012, 70120Z (2008).
[CrossRef]

K. Dohlen, M. Langlois, P. Lanzoni, S. Mazzanti, A. Vigan, L. Montoya, E. Hernandez, M. Reyes, I. Surdej, and N. Yaitskova, “ZEUS: a cophasing sensor based on the Zernike phase contrast method,” Proc. SPIE 6267, 626734 (2006).
[CrossRef]

Wilhelm, R.

R. Wilhelm, B. Luong, A. Courteville, S. Estival, F. Gont, and N. Schuhler, “Dual-wavelength low-coherence instantaneous phase-shifting interferometer to measure the shape of a segmented mirror with subnanometer precision,” Appl. Opt. 47, 5473–5491 (2008).
[CrossRef] [PubMed]

F. Gonte, C. Araujo, R. Bourtembourg, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, R. Mazzoleni, L. Noethe, I. Surdej, N. Yaitskova, R. Wilhelm, B. Luong, E. Pinna, S. Chueca, and A. Vigan, “Active Phasing Experiment: preliminary results and prospects,” Proc. SPIE 7012, 70120Z (2008).
[CrossRef]

Yaitskova, N.

A. Vigan, K. Dohlen, I. Surdej, N. Yaitskova, and F. Y. J. Gonte, “On-sky results of the ZEUS phasing sensor, closed-loop measurement precision in the context of multi-wavelength measurements,” Proc. SPIE 7733, 7733-187 (2010).

N. Yaitskova, “Adaptive optics correction of segment aberration,” J. Opt. Soc. Am. A 26, 59–71 (2009).
[CrossRef]

R. Mazzoleni, F. Gonte, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack-Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

F. Gonte, C. Araujo, R. Bourtembourg, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, R. Mazzoleni, L. Noethe, I. Surdej, N. Yaitskova, R. Wilhelm, B. Luong, E. Pinna, S. Chueca, and A. Vigan, “Active Phasing Experiment: preliminary results and prospects,” Proc. SPIE 7012, 70120Z (2008).
[CrossRef]

I. Surdej, H. Lorch, L. Noethe, N. Yaitskova, and R. Karban, “Pattern recognition and signal analysis in a Mach-Zehnder type phasing sensor,” Proc. SPIE 6696, 66960L (2007).
[CrossRef]

K. Dohlen, M. Langlois, P. Lanzoni, S. Mazzanti, A. Vigan, L. Montoya, E. Hernandez, M. Reyes, I. Surdej, and N. Yaitskova, “ZEUS: a cophasing sensor based on the Zernike phase contrast method,” Proc. SPIE 6267, 626734 (2006).
[CrossRef]

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The Active Phasing Experiment: Part 1. Concept and objectives,” Proc. SPIE 6267, 62672Z (2006).
[CrossRef]

N. Yaitskova, K. Dohlen, P. Dierickx, and L. Montoya, “Mach–Zehnder interferometer for piston and tip-tilt sensing in segmented telescopes: theory and analytical treatment,” J. Opt. Soc. Am. A 22, 1093–1105 (2005).
[CrossRef]

Appl. Opt. (3)

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

Proc. SPIE (13)

K. Dohlen, M. Langlois, P. Lanzoni, S. Mazzanti, A. Vigan, L. Montoya, E. Hernandez, M. Reyes, I. Surdej, and N. Yaitskova, “ZEUS: a cophasing sensor based on the Zernike phase contrast method,” Proc. SPIE 6267, 626734 (2006).
[CrossRef]

I. Surdej, H. Lorch, L. Noethe, N. Yaitskova, and R. Karban, “Pattern recognition and signal analysis in a Mach-Zehnder type phasing sensor,” Proc. SPIE 6696, 66960L (2007).
[CrossRef]

S. Chueca, M. Reyes, A. Schumacher, and L. Montoya, “DIPSI: measure of the tip-tilt with a diffraction image phase sensing instrument,” Proc. SPIE 7012, 701213 (2008).
[CrossRef]

M. G. Lofdahl and H. Eriksson, “Resolving piston ambiguities when phasing a segmented mirror,” Proc. SPIE 4013, 774–782(2000).
[CrossRef]

R. Mazzoleni, F. Gonte, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack-Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

F. Gonte, C. Araujo, R. Bourtembourg, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, R. Mazzoleni, L. Noethe, I. Surdej, N. Yaitskova, R. Wilhelm, B. Luong, E. Pinna, S. Chueca, and A. Vigan, “Active Phasing Experiment: preliminary results and prospects,” Proc. SPIE 7012, 70120Z (2008).
[CrossRef]

E. Pinna, S. Esposito, A. Puglisi, F. Pieralli, R. M. Myers, L. Busoni, A. Tozzi, and P. Stefanini, “Phase ambiguity solution with the Pyramid Phasing Sensor,” Proc. SPIE 6267, 62672Y (2006).
[CrossRef]

L. Montoya, M. Reyes, A. Schumacher, and E. Hernandez, “DIPSI: the diffraction image phase sensing for APE,” Proc. SPIE 6267, 626732 (2006).
[CrossRef]

P. Alvarez, J. M. Rodríguez Espinosa, F. J. Castro López-Tarruella, M. Pi, P. Hammersley, L. Cavaller, B. Siegel, J. Molgo, J. Pancorbo, R. Ascanio, G. Prieto, and J. Calvo, “The GTC project: under commissioning,” Proc. SPIE 7012, 701202 (2008).
[CrossRef]

J. Nelson and G. H. Sanders, “The status of the Thirty Meter Telescope project,” Proc. SPIE 7012, 70121A (2008).
[CrossRef]

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

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The Active Phasing Experiment: Part 1. Concept and objectives,” Proc. SPIE 6267, 62672Z (2006).
[CrossRef]

A. Vigan, K. Dohlen, I. Surdej, N. Yaitskova, and F. Y. J. Gonte, “On-sky results of the ZEUS phasing sensor, closed-loop measurement precision in the context of multi-wavelength measurements,” Proc. SPIE 7733, 7733-187 (2010).

Other (1)

K. Dohlen, “Phase masks in astronomy from the Mach-Zehnder interferometer to coronographs,” in Astronomy with High Contrast Imaging II Instrumentation for Coronagraphy and Nulling Interferometry, Vol. 12 of EAS Publications Series (European Astronomical Society, 2004), pp. 33–44.

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Figures (12)

Fig. 1
Fig. 1

Zernike phasing sensor layout. After the filtering of the incoming wavefront U 1 by the phase mask in the focal plane, the pupil is reimaged in the detector plane, U 2 , after a pupil reimaging lens of focal length f.

Fig. 2
Fig. 2

The phase mask consists of a cylindrical pellet, etched within a substrate, with a depth corresponding to the OPD and with a diameter noted as phase mask diameter in the figure.

Fig. 3
Fig. 3

Theoretical signal profiles for different piston steps Δ p and phase masks. (a), (c) Δ p = 0 , Δ p = λ / 8 , Δ p = λ / 4 . (b), (d) Δ p = 3 λ / 8 , Δ p = λ / 2 . Both mask shapes are represented: the sidelobes of the signal are a signature of the sharp-edge phase mask [(a) and (b)]. The apodized phase mask is represented in (c) and (d).

Fig. 4
Fig. 4

Difference between IM measurements and OPS measurements. The IM measures the mean phase of the wavefront inside the segment and the OPS measures the phase at the intersegment edges. If the segments are not ideally flat, the IM and the OPS measure two different quantities.

Fig. 5
Fig. 5

Normalized images acquired on-sky with a filter centered on the 650 nm wavelength and with a bandwidth of 100 nm . The seeing conditions were around (a) 0.5 and (b) 1.2 . A phase mask of 1 diameter has been used in (a) and of 1.5 diameter in (b). The subaperture centered on a segment edge is used to extract the signal of the corresponding border. The two subapertures centered on one border shown in (b) are used to retrieve the relative tip–tilt between the segments.

Fig. 6
Fig. 6

Each of the following three sets contains the number of the border, the real piston step value, and the two measured piston steps obtained from the data in Figs. 5a, 5b. [24, 65.4 nm , (a) 39.8 nm , (b) 74.9 nm ], [59, 60.5 nm , (c) 54.8 nm , (d) 91.9 nm ], [99, 80 nm , (e) 66.4 nm , (f) 98.3 nm ].

Fig. 7
Fig. 7

Parameters (a) a 1 and (b) a 2 as a function of Δ p for three different borders with the 650 nm wavelength filter and a 100 nm bandwidth. Seeing conditions are around 1.5 and the 2 phase mask is used.

Fig. 8
Fig. 8

Closed-loop cycle obtained on-sky with a seeing of 0.5 and with the phase mask of diameter 1 .

Fig. 9
Fig. 9

Final accuracy as a function of the integration time for different seeing conditions.

Fig. 10
Fig. 10

Final accuracy as a function of the average number of counts per pixel for different seeing conditions, phase masks and integration time. (a) CCD configured with binning 1 × 1 . (b) CCD configured with binning 2 × 2 . The number of counts corresponds to the number of counts in the binning 1 × 1 case.

Fig. 11
Fig. 11

Dependence of the final accuracy for different seeing conditions on the diameter of the phase mask.

Fig. 12
Fig. 12

Final accuracy as a function of the seeing. The horizontal error bars represent the seeing variation during the closed-loop cycle measurements. The vertical error bars represent the stability of the loop. The curve represents the predicted dependence of the equation τ 2 + γ θ seeing 5 / 3 , where τ and γ are numerical coefficients. The encircled data have been acquired with a phase mask a = 1 and the rest of the points with a phase mask a = 1.5 .

Tables (1)

Tables Icon

Table 1 Final Accuracy and Limiting Star Magnitude

Equations (23)

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

b ( ρ ) = 1 + ( exp ( i ψ 0 ) 1 ) Π ( ρ ) ,
Π ( ρ ) = { 1 if | ρ | a 2 0 if | ρ | > a 2 .
U 2 ( r ) = U 1 ( r ) + ( exp ( i ψ 0 ) 1 ) 1 λ 2 U 1 ( r ) T ( r r ) d 2 r ,
T ( r ) = Π ( ρ ) exp ( i 2 π λ ρ · r ) d 2 ρ
= b 2 λ 2 4 π 2 J 1 ( b r ) ( b r ) ,
U 1 ( r ) = U 1 ( x ) = { exp ( i φ 1 ) = exp ( i 2 π λ p 1 ) if x < 0 exp ( i φ 2 ) = exp ( i 2 π λ p 2 ) if x > 0 ,
S ( x ) = | U 2 ( x ) | 2 = | U 1 ( x ) | 2 + 2 ( 1 cos ( ψ 0 ) ) U c * ( x ) U c ( x ) + 2 { U 1 * ( x ) U c ( x ) ( exp ( i ψ 0 ) 1 ) } ,
U c ( x ) = 1 λ U 1 ( x ) T ( x x ) d x .
S ( x ) = 1 + F ( x ) ,
F ( x ) = [ 1 f ( b | x | ) ] [ sign ( x ) sin ( ψ 0 ) sin ( Δ φ ) ] [ 1 f ( b | x | ) ] { f ( b | x | ) [ 1 cos ( ψ 0 ) ] [ 1 cos ( Δ φ ) ] } ,
f ( b x ) = 2 π Si ( b x ) = 2 π 0 b x sin ( t ) t d t .
Π ( ρ ) = exp ( ( ρ 0.6 a ) 2 ) .
T ( r ) = b 2 λ 2 π exp ( ( b r ) 2 ) ,
f ( b x ) = Φ ( b x ) = 2 b π 0 b x exp ( t 2 ) d t .
b b 1 + 1.24 ( θ seeing / a ) 2 .
Δ w = 253.5 λ c a [ 1 + 1.24 ( θ seeing / a ) 2 ] 1 / 2 g ,
I ¯ S = I ¯ S ( 1 + F ( x ) ) .
F ( x ) = I ¯ S I ¯ S I ¯ S = I S I S I S B 0 .
I i j N = I i j S I S I S B 0 .
I i j N = I i j S I i j ref I S B 0 .
F ( x ) = a 3 + a 4 ( x a 5 ) + [ 1 f ( u ) ] { a 2 f ( u ) ( 1 cos ( ψ 0 ) ) a 1 sign ( x a 5 ) sin ( ψ 0 ) } ,
{ a 1 = C 1 sin ( Δ φ ) a 2 = C 2 ( 1 cos ( Δ φ ) ) .
σ fa = τ 2 + γ θ seeing 5 / 3 ,

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