Abstract

The pyramid sensor (PS) is an interesting alternative to the Shack-Hartmann wavefront sensor (SH WFS) for astronomical Adaptive Optics (AO) because of its potential advantages in sensitivity and applicability to novel wavefront sensing schemes. The PS uses a pyramidal prism to perform a knife-edge test in two dimensions simultaneously and relies on modulating the position of the prism to increase the linear dynamic range. It has been suggested that this could also be accomplished by a static diffusing element. We test this idea and show that the diffuser produces a modulation effect. We compare the results of our PS to a SH WFS measuring spatial and temporal properties of real turbulence produced in the lab with a hot-air turbulence generator.

© 2009 Optical Society of America

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2006 (1)

2004 (5)

C. Vérinaud, "On the nature of the measurements provided by a pyramid wave-front sensor," Opt. Commun. 233, 27-38 (2004).

J. B. Costa, M. Feldt, K. Wagner, P. Bizenberger, S. Hippler, H. Baumeister, M. Stumpf, R. Ragazzoni, S. Esposito, and T. Henning, "Status report of PYRAMIR: a near-infrared pyramid wavefront sensor for ALFA," Proc. SPIE 5490, 1189-1199 (2004).

J. B. Costa, M. Stumpf, and M. Feldt, "Testing a nonmodulated pyramid wavefront sensor," Proc. SPIE 5490, 1304-1314 (2004).

R. Clare and R. Lane, "Comparison of wavefront sensing with the Shack-Hartmann and pyramid sensors," Proc. SPIE 5490, 1211-1222 (2004).

C. Innocenti and A. Consortini, "Estimate of characteristics scales of atmospheric turbulence by thin beams: comparison between the von Karman and Hill-Andrews models," J. Mod. Opt. 51, 333-342 (2004).

2003 (4)

J. B. Costa, R. Ragazzoni, A. Ghedina, M. Carbillet, C. V’erinaud, M. Feldt, S. Esposito, E. Puga, and J. Farinato, "Is there need of any modulation in the pyramid wavefront sensor?" Proc. SPIE 4839, 288-298 (2003).

O. Keskin, L. Jolissaint, C. Bradley, S. Dost, and I. Sharf, "Hot-air turbulence generator for multiconjugate adaptive optics," Proc. SPIE 5162, pp. 49-57 (2003).

A. Ghedina, M. Cecconi, R. Ragazzoni, J. Farinato, A. Baruffolo, G. Crimi, E. Diolaiti, S. Esposito, L. Fini, M. Ghigo, E. Marchetti, T. Niero, and A. Puglisi, "On Sky Test of the PyramidWavefront Sensor," Proc. SPIE 4839, 869-877 (2003).

J. B. Costa, S. Hippler, M. Feldt, S. Esposito, R. Ragazzoni, P. Bizenberger, E. Puga, and T. F. E. Henning, "PYRAMIR: a near-infrared pyramid wavefront sensor for the Calar Alto adaptive optics system," Proc. SPIE 4839, 280-287 (2003).

2002 (2)

R. Ragazzoni, E. Diolaiti, J. Farinato, E. Fedrigo, E. Marchetti, M. Tordi, and D. Kirkman, "Multiple field of view layer-oriented adaptive optics. Nearly whole sky coverage on 8 m class telescopes and beyond," Astron. Astrophys. 396, 731-744 (2002).

R. Ragazzoni, E. Diolaiti, and E. Vernet, "A pyramid wavefront sensor with no dynamic modulation," Opt. Commun. 208, 51-60 (2002).

2001 (2)

E. Diolaiti, R. Ragazzoni, and M. Tordi, "Closed loop performance of a layer-oriented multi-conjugate adaptive optics system," Astron. Astrophys. 372, 710-718 (2001).

S. Esposito and A. Riccardi, "Pyramid Wavefront Sensor behavior in partial correction Adaptive Optic systems," Astron. Astrophys. 369, L9-L12 (2001).

2000 (4)

R. Ragazzoni, J. Farinato, and E. Marchetti, "Adaptive optics for 100-m-class telescopes: new challenges require new solutions," Proc. SPIE 4007, 1076-1087 (2000).

S. Esposito, O. Feeney, and A. Riccardi, "Laboratory test of a pyramid wavefront sensor," Proc. SPIE 4007, 416-422 (2000).

R. Ragazzoni, A. Ghedina, A. Baruffolo, E. Marchetti, J. Farinato, T. Niero, G. Crimi, and M. Ghigo, "Testing the pyramid wavefront sensor on the sky," Proc. SPIE 4007, 423-430 (2000).

S. Esposito, A. Riccardi, and O. Feeney, "Closed-loop performance of pyramid wavefront sensor," Proc. SPIE 4034, 184-189 (2000).

1999 (1)

R. Ragazzoni and J. Farinato, "Sensitivity of a pyramidic Wave Front sensor in closed loop Adaptive Optics," Astron. Astrophys. 350, L23-L26 (1999).

1998 (2)

A. Riccardi, N. Bindi, R. Ragazzoni, S. Esposito, and P. Stefanini, "Laboratory characterization of a Foucault-like wavefront sensor for adaptive optics," Proc. SPIE 3353, 941-951 (1998).

A. Fuchs, M. Tallon, and J. Vernin, "Focusing on a Turbulent Layer: Principle of the "Generalized SCIDAR,"Publ. Astron. Soc. Pac. 110, 86-91 (1998).

1997 (1)

1996 (1)

R. Ragazzoni, "Pupil plane wavefront sensing with an oscillating prism," J. Mod. Opt. 43, 289-293 (1996).

1995 (1)

P. Pugh, D. Lobb, D. Walker and T. Williams, "Pupil-imaging wavefront gradient sensor," Proc. SPIE 2534, 312-317 (1995).

1993 (1)

J. M. Beckers, "Adaptive optics for astronomy - Principles, performance, and applications," Annu. Rev. Astron. Astrophys. 31, 13-62 (1993).

1992 (1)

L. C. Andrews, "An analystical model for the refractive index power spectrum and its application to optical scintillations in the atmosphere," J. Mod. Opt. 39, 1849-1853 (1992).

1991 (1)

1989 (1)

J. M. Beckers, "Detailed compensation of atmospheric seeing using multiconjugate adaptive optics," Proc.SPIE 1114, 215-217 (1989).

1976 (1)

1948 (2)

E. H. Linfoot, "On the theory of the Zonal Foucault Test," Mon. Not. R. Astron. Soc. 108, 428-445 (1948).

E. H. Linfoot, "On the Interpretation of the Foucault Test," Proc. R. Soc. London. Series A, Math. Phys. Scie. 193, 248-259 (1948).

1946 (1)

E. H. Linfoot, "A Contribution to the Theory of the Foucault Test," Proc. R. Soc. London Ser. A, Math. Phys. Scie. 186, 72-99 (1946).

1917 (1)

Rayleigh, "On methods for detecting small optical retardations, and on the theory of Foucault’s test," Philos. Mag. 33, 161-178 (1917).

Andrews, L. C.

L. C. Andrews, "An analystical model for the refractive index power spectrum and its application to optical scintillations in the atmosphere," J. Mod. Opt. 39, 1849-1853 (1992).

Baruffolo, A.

A. Ghedina, M. Cecconi, R. Ragazzoni, J. Farinato, A. Baruffolo, G. Crimi, E. Diolaiti, S. Esposito, L. Fini, M. Ghigo, E. Marchetti, T. Niero, and A. Puglisi, "On Sky Test of the PyramidWavefront Sensor," Proc. SPIE 4839, 869-877 (2003).

R. Ragazzoni, A. Ghedina, A. Baruffolo, E. Marchetti, J. Farinato, T. Niero, G. Crimi, and M. Ghigo, "Testing the pyramid wavefront sensor on the sky," Proc. SPIE 4007, 423-430 (2000).

Baumeister, H.

J. B. Costa, M. Feldt, K. Wagner, P. Bizenberger, S. Hippler, H. Baumeister, M. Stumpf, R. Ragazzoni, S. Esposito, and T. Henning, "Status report of PYRAMIR: a near-infrared pyramid wavefront sensor for ALFA," Proc. SPIE 5490, 1189-1199 (2004).

Beckers, J. M.

J. M. Beckers, "Adaptive optics for astronomy - Principles, performance, and applications," Annu. Rev. Astron. Astrophys. 31, 13-62 (1993).

J. M. Beckers, "Detailed compensation of atmospheric seeing using multiconjugate adaptive optics," Proc.SPIE 1114, 215-217 (1989).

Bindi, N.

A. Riccardi, N. Bindi, R. Ragazzoni, S. Esposito, and P. Stefanini, "Laboratory characterization of a Foucault-like wavefront sensor for adaptive optics," Proc. SPIE 3353, 941-951 (1998).

Bizenberger, P.

J. B. Costa, M. Feldt, K. Wagner, P. Bizenberger, S. Hippler, H. Baumeister, M. Stumpf, R. Ragazzoni, S. Esposito, and T. Henning, "Status report of PYRAMIR: a near-infrared pyramid wavefront sensor for ALFA," Proc. SPIE 5490, 1189-1199 (2004).

J. B. Costa, S. Hippler, M. Feldt, S. Esposito, R. Ragazzoni, P. Bizenberger, E. Puga, and T. F. E. Henning, "PYRAMIR: a near-infrared pyramid wavefront sensor for the Calar Alto adaptive optics system," Proc. SPIE 4839, 280-287 (2003).

Bradley, C.

O. Keskin, L. Jolissaint, and C. Bradley, "Hot-air optical turbulence generator for the testing of adaptive optics systems: principles and characterization," Appl. Opt. 45, 4888-4897 (2006).
[PubMed]

O. Keskin, L. Jolissaint, C. Bradley, S. Dost, and I. Sharf, "Hot-air turbulence generator for multiconjugate adaptive optics," Proc. SPIE 5162, pp. 49-57 (2003).

Carbillet, M.

J. B. Costa, R. Ragazzoni, A. Ghedina, M. Carbillet, C. V’erinaud, M. Feldt, S. Esposito, E. Puga, and J. Farinato, "Is there need of any modulation in the pyramid wavefront sensor?" Proc. SPIE 4839, 288-298 (2003).

Cecconi, M.

A. Ghedina, M. Cecconi, R. Ragazzoni, J. Farinato, A. Baruffolo, G. Crimi, E. Diolaiti, S. Esposito, L. Fini, M. Ghigo, E. Marchetti, T. Niero, and A. Puglisi, "On Sky Test of the PyramidWavefront Sensor," Proc. SPIE 4839, 869-877 (2003).

Clare, R.

R. Clare and R. Lane, "Comparison of wavefront sensing with the Shack-Hartmann and pyramid sensors," Proc. SPIE 5490, 1211-1222 (2004).

Consortini, A.

C. Innocenti and A. Consortini, "Estimate of characteristics scales of atmospheric turbulence by thin beams: comparison between the von Karman and Hill-Andrews models," J. Mod. Opt. 51, 333-342 (2004).

Costa, J. B.

J. B. Costa, M. Stumpf, and M. Feldt, "Testing a nonmodulated pyramid wavefront sensor," Proc. SPIE 5490, 1304-1314 (2004).

J. B. Costa, M. Feldt, K. Wagner, P. Bizenberger, S. Hippler, H. Baumeister, M. Stumpf, R. Ragazzoni, S. Esposito, and T. Henning, "Status report of PYRAMIR: a near-infrared pyramid wavefront sensor for ALFA," Proc. SPIE 5490, 1189-1199 (2004).

J. B. Costa, S. Hippler, M. Feldt, S. Esposito, R. Ragazzoni, P. Bizenberger, E. Puga, and T. F. E. Henning, "PYRAMIR: a near-infrared pyramid wavefront sensor for the Calar Alto adaptive optics system," Proc. SPIE 4839, 280-287 (2003).

J. B. Costa, R. Ragazzoni, A. Ghedina, M. Carbillet, C. V’erinaud, M. Feldt, S. Esposito, E. Puga, and J. Farinato, "Is there need of any modulation in the pyramid wavefront sensor?" Proc. SPIE 4839, 288-298 (2003).

Crimi, G.

A. Ghedina, M. Cecconi, R. Ragazzoni, J. Farinato, A. Baruffolo, G. Crimi, E. Diolaiti, S. Esposito, L. Fini, M. Ghigo, E. Marchetti, T. Niero, and A. Puglisi, "On Sky Test of the PyramidWavefront Sensor," Proc. SPIE 4839, 869-877 (2003).

R. Ragazzoni, A. Ghedina, A. Baruffolo, E. Marchetti, J. Farinato, T. Niero, G. Crimi, and M. Ghigo, "Testing the pyramid wavefront sensor on the sky," Proc. SPIE 4007, 423-430 (2000).

Diolaiti, E.

A. Ghedina, M. Cecconi, R. Ragazzoni, J. Farinato, A. Baruffolo, G. Crimi, E. Diolaiti, S. Esposito, L. Fini, M. Ghigo, E. Marchetti, T. Niero, and A. Puglisi, "On Sky Test of the PyramidWavefront Sensor," Proc. SPIE 4839, 869-877 (2003).

R. Ragazzoni, E. Diolaiti, J. Farinato, E. Fedrigo, E. Marchetti, M. Tordi, and D. Kirkman, "Multiple field of view layer-oriented adaptive optics. Nearly whole sky coverage on 8 m class telescopes and beyond," Astron. Astrophys. 396, 731-744 (2002).

R. Ragazzoni, E. Diolaiti, and E. Vernet, "A pyramid wavefront sensor with no dynamic modulation," Opt. Commun. 208, 51-60 (2002).

E. Diolaiti, R. Ragazzoni, and M. Tordi, "Closed loop performance of a layer-oriented multi-conjugate adaptive optics system," Astron. Astrophys. 372, 710-718 (2001).

Dost, S.

O. Keskin, L. Jolissaint, C. Bradley, S. Dost, and I. Sharf, "Hot-air turbulence generator for multiconjugate adaptive optics," Proc. SPIE 5162, pp. 49-57 (2003).

Esposito, S.

J. B. Costa, M. Feldt, K. Wagner, P. Bizenberger, S. Hippler, H. Baumeister, M. Stumpf, R. Ragazzoni, S. Esposito, and T. Henning, "Status report of PYRAMIR: a near-infrared pyramid wavefront sensor for ALFA," Proc. SPIE 5490, 1189-1199 (2004).

J. B. Costa, S. Hippler, M. Feldt, S. Esposito, R. Ragazzoni, P. Bizenberger, E. Puga, and T. F. E. Henning, "PYRAMIR: a near-infrared pyramid wavefront sensor for the Calar Alto adaptive optics system," Proc. SPIE 4839, 280-287 (2003).

A. Ghedina, M. Cecconi, R. Ragazzoni, J. Farinato, A. Baruffolo, G. Crimi, E. Diolaiti, S. Esposito, L. Fini, M. Ghigo, E. Marchetti, T. Niero, and A. Puglisi, "On Sky Test of the PyramidWavefront Sensor," Proc. SPIE 4839, 869-877 (2003).

S. Esposito and A. Riccardi, "Pyramid Wavefront Sensor behavior in partial correction Adaptive Optic systems," Astron. Astrophys. 369, L9-L12 (2001).

S. Esposito, A. Riccardi, and O. Feeney, "Closed-loop performance of pyramid wavefront sensor," Proc. SPIE 4034, 184-189 (2000).

S. Esposito, O. Feeney, and A. Riccardi, "Laboratory test of a pyramid wavefront sensor," Proc. SPIE 4007, 416-422 (2000).

A. Riccardi, N. Bindi, R. Ragazzoni, S. Esposito, and P. Stefanini, "Laboratory characterization of a Foucault-like wavefront sensor for adaptive optics," Proc. SPIE 3353, 941-951 (1998).

Farinato, J.

A. Ghedina, M. Cecconi, R. Ragazzoni, J. Farinato, A. Baruffolo, G. Crimi, E. Diolaiti, S. Esposito, L. Fini, M. Ghigo, E. Marchetti, T. Niero, and A. Puglisi, "On Sky Test of the PyramidWavefront Sensor," Proc. SPIE 4839, 869-877 (2003).

R. Ragazzoni, E. Diolaiti, J. Farinato, E. Fedrigo, E. Marchetti, M. Tordi, and D. Kirkman, "Multiple field of view layer-oriented adaptive optics. Nearly whole sky coverage on 8 m class telescopes and beyond," Astron. Astrophys. 396, 731-744 (2002).

R. Ragazzoni, J. Farinato, and E. Marchetti, "Adaptive optics for 100-m-class telescopes: new challenges require new solutions," Proc. SPIE 4007, 1076-1087 (2000).

R. Ragazzoni, A. Ghedina, A. Baruffolo, E. Marchetti, J. Farinato, T. Niero, G. Crimi, and M. Ghigo, "Testing the pyramid wavefront sensor on the sky," Proc. SPIE 4007, 423-430 (2000).

R. Ragazzoni and J. Farinato, "Sensitivity of a pyramidic Wave Front sensor in closed loop Adaptive Optics," Astron. Astrophys. 350, L23-L26 (1999).

Fedrigo, E.

R. Ragazzoni, E. Diolaiti, J. Farinato, E. Fedrigo, E. Marchetti, M. Tordi, and D. Kirkman, "Multiple field of view layer-oriented adaptive optics. Nearly whole sky coverage on 8 m class telescopes and beyond," Astron. Astrophys. 396, 731-744 (2002).

Feeney, O.

S. Esposito, O. Feeney, and A. Riccardi, "Laboratory test of a pyramid wavefront sensor," Proc. SPIE 4007, 416-422 (2000).

S. Esposito, A. Riccardi, and O. Feeney, "Closed-loop performance of pyramid wavefront sensor," Proc. SPIE 4034, 184-189 (2000).

Feldt, M.

J. B. Costa, M. Feldt, K. Wagner, P. Bizenberger, S. Hippler, H. Baumeister, M. Stumpf, R. Ragazzoni, S. Esposito, and T. Henning, "Status report of PYRAMIR: a near-infrared pyramid wavefront sensor for ALFA," Proc. SPIE 5490, 1189-1199 (2004).

J. B. Costa, M. Stumpf, and M. Feldt, "Testing a nonmodulated pyramid wavefront sensor," Proc. SPIE 5490, 1304-1314 (2004).

J. B. Costa, S. Hippler, M. Feldt, S. Esposito, R. Ragazzoni, P. Bizenberger, E. Puga, and T. F. E. Henning, "PYRAMIR: a near-infrared pyramid wavefront sensor for the Calar Alto adaptive optics system," Proc. SPIE 4839, 280-287 (2003).

Fini, L.

A. Ghedina, M. Cecconi, R. Ragazzoni, J. Farinato, A. Baruffolo, G. Crimi, E. Diolaiti, S. Esposito, L. Fini, M. Ghigo, E. Marchetti, T. Niero, and A. Puglisi, "On Sky Test of the PyramidWavefront Sensor," Proc. SPIE 4839, 869-877 (2003).

Fuchs, A.

A. Fuchs, M. Tallon, and J. Vernin, "Focusing on a Turbulent Layer: Principle of the "Generalized SCIDAR,"Publ. Astron. Soc. Pac. 110, 86-91 (1998).

Ghedina, A.

J. B. Costa, R. Ragazzoni, A. Ghedina, M. Carbillet, C. V’erinaud, M. Feldt, S. Esposito, E. Puga, and J. Farinato, "Is there need of any modulation in the pyramid wavefront sensor?" Proc. SPIE 4839, 288-298 (2003).

A. Ghedina, M. Cecconi, R. Ragazzoni, J. Farinato, A. Baruffolo, G. Crimi, E. Diolaiti, S. Esposito, L. Fini, M. Ghigo, E. Marchetti, T. Niero, and A. Puglisi, "On Sky Test of the PyramidWavefront Sensor," Proc. SPIE 4839, 869-877 (2003).

R. Ragazzoni, A. Ghedina, A. Baruffolo, E. Marchetti, J. Farinato, T. Niero, G. Crimi, and M. Ghigo, "Testing the pyramid wavefront sensor on the sky," Proc. SPIE 4007, 423-430 (2000).

Ghigo, M.

A. Ghedina, M. Cecconi, R. Ragazzoni, J. Farinato, A. Baruffolo, G. Crimi, E. Diolaiti, S. Esposito, L. Fini, M. Ghigo, E. Marchetti, T. Niero, and A. Puglisi, "On Sky Test of the PyramidWavefront Sensor," Proc. SPIE 4839, 869-877 (2003).

R. Ragazzoni, A. Ghedina, A. Baruffolo, E. Marchetti, J. Farinato, T. Niero, G. Crimi, and M. Ghigo, "Testing the pyramid wavefront sensor on the sky," Proc. SPIE 4007, 423-430 (2000).

Henning, T.

J. B. Costa, M. Feldt, K. Wagner, P. Bizenberger, S. Hippler, H. Baumeister, M. Stumpf, R. Ragazzoni, S. Esposito, and T. Henning, "Status report of PYRAMIR: a near-infrared pyramid wavefront sensor for ALFA," Proc. SPIE 5490, 1189-1199 (2004).

Henning, T. F. E.

J. B. Costa, S. Hippler, M. Feldt, S. Esposito, R. Ragazzoni, P. Bizenberger, E. Puga, and T. F. E. Henning, "PYRAMIR: a near-infrared pyramid wavefront sensor for the Calar Alto adaptive optics system," Proc. SPIE 4839, 280-287 (2003).

Hippler, S.

J. B. Costa, M. Feldt, K. Wagner, P. Bizenberger, S. Hippler, H. Baumeister, M. Stumpf, R. Ragazzoni, S. Esposito, and T. Henning, "Status report of PYRAMIR: a near-infrared pyramid wavefront sensor for ALFA," Proc. SPIE 5490, 1189-1199 (2004).

J. B. Costa, S. Hippler, M. Feldt, S. Esposito, R. Ragazzoni, P. Bizenberger, E. Puga, and T. F. E. Henning, "PYRAMIR: a near-infrared pyramid wavefront sensor for the Calar Alto adaptive optics system," Proc. SPIE 4839, 280-287 (2003).

Innocenti, C.

C. Innocenti and A. Consortini, "Estimate of characteristics scales of atmospheric turbulence by thin beams: comparison between the von Karman and Hill-Andrews models," J. Mod. Opt. 51, 333-342 (2004).

Jolissaint, L.

O. Keskin, L. Jolissaint, and C. Bradley, "Hot-air optical turbulence generator for the testing of adaptive optics systems: principles and characterization," Appl. Opt. 45, 4888-4897 (2006).
[PubMed]

O. Keskin, L. Jolissaint, C. Bradley, S. Dost, and I. Sharf, "Hot-air turbulence generator for multiconjugate adaptive optics," Proc. SPIE 5162, pp. 49-57 (2003).

Keskin, O.

O. Keskin, L. Jolissaint, and C. Bradley, "Hot-air optical turbulence generator for the testing of adaptive optics systems: principles and characterization," Appl. Opt. 45, 4888-4897 (2006).
[PubMed]

O. Keskin, L. Jolissaint, C. Bradley, S. Dost, and I. Sharf, "Hot-air turbulence generator for multiconjugate adaptive optics," Proc. SPIE 5162, pp. 49-57 (2003).

Kirkman, D.

R. Ragazzoni, E. Diolaiti, J. Farinato, E. Fedrigo, E. Marchetti, M. Tordi, and D. Kirkman, "Multiple field of view layer-oriented adaptive optics. Nearly whole sky coverage on 8 m class telescopes and beyond," Astron. Astrophys. 396, 731-744 (2002).

Lane, R.

R. Clare and R. Lane, "Comparison of wavefront sensing with the Shack-Hartmann and pyramid sensors," Proc. SPIE 5490, 1211-1222 (2004).

Linfoot, E. H.

E. H. Linfoot, "On the theory of the Zonal Foucault Test," Mon. Not. R. Astron. Soc. 108, 428-445 (1948).

E. H. Linfoot, "On the Interpretation of the Foucault Test," Proc. R. Soc. London. Series A, Math. Phys. Scie. 193, 248-259 (1948).

E. H. Linfoot, "A Contribution to the Theory of the Foucault Test," Proc. R. Soc. London Ser. A, Math. Phys. Scie. 186, 72-99 (1946).

Lobb, D.

P. Pugh, D. Lobb, D. Walker and T. Williams, "Pupil-imaging wavefront gradient sensor," Proc. SPIE 2534, 312-317 (1995).

Marchetti, E.

A. Ghedina, M. Cecconi, R. Ragazzoni, J. Farinato, A. Baruffolo, G. Crimi, E. Diolaiti, S. Esposito, L. Fini, M. Ghigo, E. Marchetti, T. Niero, and A. Puglisi, "On Sky Test of the PyramidWavefront Sensor," Proc. SPIE 4839, 869-877 (2003).

R. Ragazzoni, E. Diolaiti, J. Farinato, E. Fedrigo, E. Marchetti, M. Tordi, and D. Kirkman, "Multiple field of view layer-oriented adaptive optics. Nearly whole sky coverage on 8 m class telescopes and beyond," Astron. Astrophys. 396, 731-744 (2002).

R. Ragazzoni, J. Farinato, and E. Marchetti, "Adaptive optics for 100-m-class telescopes: new challenges require new solutions," Proc. SPIE 4007, 1076-1087 (2000).

R. Ragazzoni, A. Ghedina, A. Baruffolo, E. Marchetti, J. Farinato, T. Niero, G. Crimi, and M. Ghigo, "Testing the pyramid wavefront sensor on the sky," Proc. SPIE 4007, 423-430 (2000).

Masciadri, E.

Niero, T.

A. Ghedina, M. Cecconi, R. Ragazzoni, J. Farinato, A. Baruffolo, G. Crimi, E. Diolaiti, S. Esposito, L. Fini, M. Ghigo, E. Marchetti, T. Niero, and A. Puglisi, "On Sky Test of the PyramidWavefront Sensor," Proc. SPIE 4839, 869-877 (2003).

R. Ragazzoni, A. Ghedina, A. Baruffolo, E. Marchetti, J. Farinato, T. Niero, G. Crimi, and M. Ghigo, "Testing the pyramid wavefront sensor on the sky," Proc. SPIE 4007, 423-430 (2000).

Noll, R. J.

Puga, E.

J. B. Costa, S. Hippler, M. Feldt, S. Esposito, R. Ragazzoni, P. Bizenberger, E. Puga, and T. F. E. Henning, "PYRAMIR: a near-infrared pyramid wavefront sensor for the Calar Alto adaptive optics system," Proc. SPIE 4839, 280-287 (2003).

Pugh, P.

P. Pugh, D. Lobb, D. Walker and T. Williams, "Pupil-imaging wavefront gradient sensor," Proc. SPIE 2534, 312-317 (1995).

Puglisi, A.

A. Ghedina, M. Cecconi, R. Ragazzoni, J. Farinato, A. Baruffolo, G. Crimi, E. Diolaiti, S. Esposito, L. Fini, M. Ghigo, E. Marchetti, T. Niero, and A. Puglisi, "On Sky Test of the PyramidWavefront Sensor," Proc. SPIE 4839, 869-877 (2003).

Ragazzoni, R.

J. B. Costa, M. Feldt, K. Wagner, P. Bizenberger, S. Hippler, H. Baumeister, M. Stumpf, R. Ragazzoni, S. Esposito, and T. Henning, "Status report of PYRAMIR: a near-infrared pyramid wavefront sensor for ALFA," Proc. SPIE 5490, 1189-1199 (2004).

J. B. Costa, R. Ragazzoni, A. Ghedina, M. Carbillet, C. V’erinaud, M. Feldt, S. Esposito, E. Puga, and J. Farinato, "Is there need of any modulation in the pyramid wavefront sensor?" Proc. SPIE 4839, 288-298 (2003).

J. B. Costa, S. Hippler, M. Feldt, S. Esposito, R. Ragazzoni, P. Bizenberger, E. Puga, and T. F. E. Henning, "PYRAMIR: a near-infrared pyramid wavefront sensor for the Calar Alto adaptive optics system," Proc. SPIE 4839, 280-287 (2003).

A. Ghedina, M. Cecconi, R. Ragazzoni, J. Farinato, A. Baruffolo, G. Crimi, E. Diolaiti, S. Esposito, L. Fini, M. Ghigo, E. Marchetti, T. Niero, and A. Puglisi, "On Sky Test of the PyramidWavefront Sensor," Proc. SPIE 4839, 869-877 (2003).

R. Ragazzoni, E. Diolaiti, and E. Vernet, "A pyramid wavefront sensor with no dynamic modulation," Opt. Commun. 208, 51-60 (2002).

R. Ragazzoni, E. Diolaiti, J. Farinato, E. Fedrigo, E. Marchetti, M. Tordi, and D. Kirkman, "Multiple field of view layer-oriented adaptive optics. Nearly whole sky coverage on 8 m class telescopes and beyond," Astron. Astrophys. 396, 731-744 (2002).

E. Diolaiti, R. Ragazzoni, and M. Tordi, "Closed loop performance of a layer-oriented multi-conjugate adaptive optics system," Astron. Astrophys. 372, 710-718 (2001).

R. Ragazzoni, J. Farinato, and E. Marchetti, "Adaptive optics for 100-m-class telescopes: new challenges require new solutions," Proc. SPIE 4007, 1076-1087 (2000).

R. Ragazzoni, A. Ghedina, A. Baruffolo, E. Marchetti, J. Farinato, T. Niero, G. Crimi, and M. Ghigo, "Testing the pyramid wavefront sensor on the sky," Proc. SPIE 4007, 423-430 (2000).

R. Ragazzoni and J. Farinato, "Sensitivity of a pyramidic Wave Front sensor in closed loop Adaptive Optics," Astron. Astrophys. 350, L23-L26 (1999).

A. Riccardi, N. Bindi, R. Ragazzoni, S. Esposito, and P. Stefanini, "Laboratory characterization of a Foucault-like wavefront sensor for adaptive optics," Proc. SPIE 3353, 941-951 (1998).

R. Ragazzoni, "Pupil plane wavefront sensing with an oscillating prism," J. Mod. Opt. 43, 289-293 (1996).

Rayleigh,

Rayleigh, "On methods for detecting small optical retardations, and on the theory of Foucault’s test," Philos. Mag. 33, 161-178 (1917).

Riccardi, A.

S. Esposito and A. Riccardi, "Pyramid Wavefront Sensor behavior in partial correction Adaptive Optic systems," Astron. Astrophys. 369, L9-L12 (2001).

S. Esposito, A. Riccardi, and O. Feeney, "Closed-loop performance of pyramid wavefront sensor," Proc. SPIE 4034, 184-189 (2000).

S. Esposito, O. Feeney, and A. Riccardi, "Laboratory test of a pyramid wavefront sensor," Proc. SPIE 4007, 416-422 (2000).

A. Riccardi, N. Bindi, R. Ragazzoni, S. Esposito, and P. Stefanini, "Laboratory characterization of a Foucault-like wavefront sensor for adaptive optics," Proc. SPIE 3353, 941-951 (1998).

Sharf, I.

O. Keskin, L. Jolissaint, C. Bradley, S. Dost, and I. Sharf, "Hot-air turbulence generator for multiconjugate adaptive optics," Proc. SPIE 5162, pp. 49-57 (2003).

Stefanini, P.

A. Riccardi, N. Bindi, R. Ragazzoni, S. Esposito, and P. Stefanini, "Laboratory characterization of a Foucault-like wavefront sensor for adaptive optics," Proc. SPIE 3353, 941-951 (1998).

Stumpf, M.

J. B. Costa, M. Feldt, K. Wagner, P. Bizenberger, S. Hippler, H. Baumeister, M. Stumpf, R. Ragazzoni, S. Esposito, and T. Henning, "Status report of PYRAMIR: a near-infrared pyramid wavefront sensor for ALFA," Proc. SPIE 5490, 1189-1199 (2004).

J. B. Costa, M. Stumpf, and M. Feldt, "Testing a nonmodulated pyramid wavefront sensor," Proc. SPIE 5490, 1304-1314 (2004).

Tallon, M.

A. Fuchs, M. Tallon, and J. Vernin, "Focusing on a Turbulent Layer: Principle of the "Generalized SCIDAR,"Publ. Astron. Soc. Pac. 110, 86-91 (1998).

Tordi, M.

R. Ragazzoni, E. Diolaiti, J. Farinato, E. Fedrigo, E. Marchetti, M. Tordi, and D. Kirkman, "Multiple field of view layer-oriented adaptive optics. Nearly whole sky coverage on 8 m class telescopes and beyond," Astron. Astrophys. 396, 731-744 (2002).

E. Diolaiti, R. Ragazzoni, and M. Tordi, "Closed loop performance of a layer-oriented multi-conjugate adaptive optics system," Astron. Astrophys. 372, 710-718 (2001).

Vérinaud, C.

C. Vérinaud, "On the nature of the measurements provided by a pyramid wave-front sensor," Opt. Commun. 233, 27-38 (2004).

Vernet, E.

R. Ragazzoni, E. Diolaiti, and E. Vernet, "A pyramid wavefront sensor with no dynamic modulation," Opt. Commun. 208, 51-60 (2002).

Vernin, J.

A. Fuchs, M. Tallon, and J. Vernin, "Focusing on a Turbulent Layer: Principle of the "Generalized SCIDAR,"Publ. Astron. Soc. Pac. 110, 86-91 (1998).

E. Masciadri and J. Vernin, "Optical technique for inner-scale measurement: possible astronomical applications," Appl. Opt. 36, 1320-1327 (1997).
[PubMed]

Wagner, K.

J. B. Costa, M. Feldt, K. Wagner, P. Bizenberger, S. Hippler, H. Baumeister, M. Stumpf, R. Ragazzoni, S. Esposito, and T. Henning, "Status report of PYRAMIR: a near-infrared pyramid wavefront sensor for ALFA," Proc. SPIE 5490, 1189-1199 (2004).

Walker, D.

P. Pugh, D. Lobb, D. Walker and T. Williams, "Pupil-imaging wavefront gradient sensor," Proc. SPIE 2534, 312-317 (1995).

Williams, T.

P. Pugh, D. Lobb, D. Walker and T. Williams, "Pupil-imaging wavefront gradient sensor," Proc. SPIE 2534, 312-317 (1995).

Winker, D. M.

Annu. Rev. Astron. Astrophys. (1)

J. M. Beckers, "Adaptive optics for astronomy - Principles, performance, and applications," Annu. Rev. Astron. Astrophys. 31, 13-62 (1993).

Appl. Opt. (2)

Astron. Astrophys. (4)

R. Ragazzoni and J. Farinato, "Sensitivity of a pyramidic Wave Front sensor in closed loop Adaptive Optics," Astron. Astrophys. 350, L23-L26 (1999).

E. Diolaiti, R. Ragazzoni, and M. Tordi, "Closed loop performance of a layer-oriented multi-conjugate adaptive optics system," Astron. Astrophys. 372, 710-718 (2001).

R. Ragazzoni, E. Diolaiti, J. Farinato, E. Fedrigo, E. Marchetti, M. Tordi, and D. Kirkman, "Multiple field of view layer-oriented adaptive optics. Nearly whole sky coverage on 8 m class telescopes and beyond," Astron. Astrophys. 396, 731-744 (2002).

S. Esposito and A. Riccardi, "Pyramid Wavefront Sensor behavior in partial correction Adaptive Optic systems," Astron. Astrophys. 369, L9-L12 (2001).

J. Mod. Opt. (3)

R. Ragazzoni, "Pupil plane wavefront sensing with an oscillating prism," J. Mod. Opt. 43, 289-293 (1996).

C. Innocenti and A. Consortini, "Estimate of characteristics scales of atmospheric turbulence by thin beams: comparison between the von Karman and Hill-Andrews models," J. Mod. Opt. 51, 333-342 (2004).

L. C. Andrews, "An analystical model for the refractive index power spectrum and its application to optical scintillations in the atmosphere," J. Mod. Opt. 39, 1849-1853 (1992).

J. Opt. Soc. Am. (1)

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

Math. Phys. Scie. (2)

E. H. Linfoot, "A Contribution to the Theory of the Foucault Test," Proc. R. Soc. London Ser. A, Math. Phys. Scie. 186, 72-99 (1946).

E. H. Linfoot, "On the Interpretation of the Foucault Test," Proc. R. Soc. London. Series A, Math. Phys. Scie. 193, 248-259 (1948).

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

E. H. Linfoot, "On the theory of the Zonal Foucault Test," Mon. Not. R. Astron. Soc. 108, 428-445 (1948).

Opt. Commun. (2)

R. Ragazzoni, E. Diolaiti, and E. Vernet, "A pyramid wavefront sensor with no dynamic modulation," Opt. Commun. 208, 51-60 (2002).

C. Vérinaud, "On the nature of the measurements provided by a pyramid wave-front sensor," Opt. Commun. 233, 27-38 (2004).

Philos. Mag. (1)

Rayleigh, "On methods for detecting small optical retardations, and on the theory of Foucault’s test," Philos. Mag. 33, 161-178 (1917).

Proc. SPIE (13)

O. Keskin, L. Jolissaint, C. Bradley, S. Dost, and I. Sharf, "Hot-air turbulence generator for multiconjugate adaptive optics," Proc. SPIE 5162, pp. 49-57 (2003).

J. B. Costa, R. Ragazzoni, A. Ghedina, M. Carbillet, C. V’erinaud, M. Feldt, S. Esposito, E. Puga, and J. Farinato, "Is there need of any modulation in the pyramid wavefront sensor?" Proc. SPIE 4839, 288-298 (2003).

J. B. Costa, M. Stumpf, and M. Feldt, "Testing a nonmodulated pyramid wavefront sensor," Proc. SPIE 5490, 1304-1314 (2004).

P. Pugh, D. Lobb, D. Walker and T. Williams, "Pupil-imaging wavefront gradient sensor," Proc. SPIE 2534, 312-317 (1995).

R. Clare and R. Lane, "Comparison of wavefront sensing with the Shack-Hartmann and pyramid sensors," Proc. SPIE 5490, 1211-1222 (2004).

A. Riccardi, N. Bindi, R. Ragazzoni, S. Esposito, and P. Stefanini, "Laboratory characterization of a Foucault-like wavefront sensor for adaptive optics," Proc. SPIE 3353, 941-951 (1998).

S. Esposito, O. Feeney, and A. Riccardi, "Laboratory test of a pyramid wavefront sensor," Proc. SPIE 4007, 416-422 (2000).

R. Ragazzoni, A. Ghedina, A. Baruffolo, E. Marchetti, J. Farinato, T. Niero, G. Crimi, and M. Ghigo, "Testing the pyramid wavefront sensor on the sky," Proc. SPIE 4007, 423-430 (2000).

A. Ghedina, M. Cecconi, R. Ragazzoni, J. Farinato, A. Baruffolo, G. Crimi, E. Diolaiti, S. Esposito, L. Fini, M. Ghigo, E. Marchetti, T. Niero, and A. Puglisi, "On Sky Test of the PyramidWavefront Sensor," Proc. SPIE 4839, 869-877 (2003).

J. B. Costa, S. Hippler, M. Feldt, S. Esposito, R. Ragazzoni, P. Bizenberger, E. Puga, and T. F. E. Henning, "PYRAMIR: a near-infrared pyramid wavefront sensor for the Calar Alto adaptive optics system," Proc. SPIE 4839, 280-287 (2003).

J. B. Costa, M. Feldt, K. Wagner, P. Bizenberger, S. Hippler, H. Baumeister, M. Stumpf, R. Ragazzoni, S. Esposito, and T. Henning, "Status report of PYRAMIR: a near-infrared pyramid wavefront sensor for ALFA," Proc. SPIE 5490, 1189-1199 (2004).

R. Ragazzoni, J. Farinato, and E. Marchetti, "Adaptive optics for 100-m-class telescopes: new challenges require new solutions," Proc. SPIE 4007, 1076-1087 (2000).

S. Esposito, A. Riccardi, and O. Feeney, "Closed-loop performance of pyramid wavefront sensor," Proc. SPIE 4034, 184-189 (2000).

Proc.SPIE (1)

J. M. Beckers, "Detailed compensation of atmospheric seeing using multiconjugate adaptive optics," Proc.SPIE 1114, 215-217 (1989).

Publ. Astron. Soc. Pac. (1)

A. Fuchs, M. Tallon, and J. Vernin, "Focusing on a Turbulent Layer: Principle of the "Generalized SCIDAR,"Publ. Astron. Soc. Pac. 110, 86-91 (1998).

Other (4)

R. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic press, 1998).

D. Peter, M. Feldt, B. Dorner, T. Henning, S. Hippler, and J. Aceituno, "PYRAMIR: Calibration and Operation of a Pyramid Near-Infrared Wavefront Sensor," Publ. Astron. Soc. Pac.  120, 872-886 (2008). 0808.0137.

J. M. Beckers, "Increasing the Size of the Isoplanatic Patch with Multiconjugate Adaptive Optics," in Proceedings of a ESO Conference on Very Large Telescopes and their Instrumentation, held in Garching, March 21-24, 1988,Garching: European Southern Observatory, pp. 693-703 (1988).

R. Ragazzoni, "Adaptive optics for giant telescopes: NGS vs. LGS," in Proceedings of the Backaskog workshop on extremely large telescopes, pp. 175-180 (2000).

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Figures (7)

Fig. 1.
Fig. 1.

A schematic diagram of the PS implemented in 1d is shown. The prism spatially filters the electric field phasor of the aberrated beam in the focal plane while splitting the light into two beams. The images of the pupils are formed on the detector by a second lens. The signals are generated by the difference of the illumination in the top and bottom pupil, normalized to the total intensity.

Fig. 2.
Fig. 2.

A schematic diagram of the experimental setup is shown. Light from a fiber source is collimated and a tilt is introduced by the fold mirror. Using the beamsplitter the tilt was measured by the mini-Wavescope and the intensity in the re-imaged pupil of the PS was recorded. The turbulator was introduced into the setup by replacing the fold mirror and repositioning the source in line with the PS CCD.

Fig. 3.
Fig. 3.

This plot shows the fractional change in intensity in the re-imaged pupil of the PS recorded with the DALSA CCD. The x and y error bars are less than or equal to the size of the data points. The slope of calibration curve for the 0.5° diffuser is 1.62 ±0.03 millirad-1 and 0.89±0.01 millirad-1 for the 1.0° diffuser. The linearity of the tilt response demonstrates the modulation effect provided by the diffuser and the fact that the slope decreases when the modulation angle is increased illustrates that the sensitivity of the PS is inversely proportional to the modulation angle.

Fig. 4.
Fig. 4.

This plot shows the temporal power spectra of the tilt mode of the turbulence produced by the turbulator calculated using the mini-Wavescope and PS data at a temperature difference of ΔT ≈ 140°C. Fitting was performed to extract the knee frequency at the transition between the low frequency and high frequency regimes. This frequency is related to the effective wind speed, νeff , of the turbulator by equation 3.

Fig. 5.
Fig. 5.

In (a) the variances of the Zernike wavefront coefficient measured with the mini-Wavescope are shown. The results of Noll, 1976 were modified to included the attenuation of the inner and outer scale and the values for r 0, l 0, and L 0 were extracted by fitting the modified variances. Panel (b) shows the Zernike slope variances measured with the PS. Again fitting is used to obtain r 0, l 0, and L 0.

Fig. 6.
Fig. 6.

This plot shows the dependence of r 0 on ΔT observed with the mini-Wavescope and the PS. The lines represent power law fits to the data with a fitting function of the form r 0 = AΔT -b . The fit parameters are log(A) = 2.44 ±0.11 and b = 0.89 ±0.08 for the mini-Wavescope and log(A) = 2.36 ±0.13 and b = 0.91 ±0.09 for the PS. The exponent, b, agrees well between the two sensors meaning that both WFS’s measure the same trend in r 0 vs ΔT

Fig. 7.
Fig. 7.

The distribution of sensitivity values for the PS using a diffuser is shown in this histogram. The mean value is 1.76 mrad-1, close to the overall calibration constant of 1.62 mrad-1 from Fig. 3. The standard deviation is 0.9 mrad-1.

Equations (5)

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S ( x , y ) = U p + ( x , y ) 2 U p ( x , y ) 2 A 2
U p ± ( x , y ) = 1 2 E ( x , y ) i 2 π E ( x , t ) t x dx
S = { isgn ( f ) f > α λ α f f < α λ
f knee = 0.3 ν eff D
r 0 5 3 = 04234 ( 2 π λ ) 2 C N 2 Δ h

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