Feasible optimal deformable mirror shaping algorithm for high-contrast imaging

The Princeton University Terrestrial Planet Finder (TPF) group has been working on a novel method for direct imaging of extra solar planets using a shaped-pupil coronagraph. The entrance pupil of the coronagraph is optimized to have a point spread function (PSF) that provides the suppression level needed at the angular separation required for detection of extra solar planets. When integration time is to be minimized, the photon count at the planet location in the image plane is a Poisson distributed random process. The ultimate limitation of these high-dynamic-range imaging systems comes from scattering due to imperfections in the optical surfaces of the collecting system. The first step in correcting the wavefront errors is the estimation of the phase aberrations. The phase aberration caused by these imperfections is assumed to be a sum of two-dimensional sinusoidal functions. Assuming one uses a deformable mirror to correct these aberrations, we propose an algorithm that optimally decreases the scattering level in specified localized areas in the image plane independent of the choice of influence function of the deformable mirror.

[1]  Joseph M. Geary,et al.  Introduction to Wavefront Sensors , 1995 .

[2]  Garth D. Illingworth,et al.  Hubble's Science Legacy: Future Optical/Ultraviolet Astronomy from Space , 2003 .

[3]  J. Schneider,et al.  The study of extrasolar planets : methods of detection, first discoveries and future perspectives , 1999 .

[4]  R. Gerchberg.  A practical algorithm for the determination of phase from image and diffraction plane pictures , 1972 .

[5]  Aharon Levi,et al.  Image restoration by the method of generalized projections with application to restoration from magnitude , 1984 .

[6]  Ulrich Hopp,et al.  THE ASTRONOMICAL SOCIETY OF THE PACIFIC. , 1916, Science.

[7]  Philippe Réfrégier,et al.  Maximum-likelihood estimation of an astronomical image from a sequence at low photon levels , 1998 .

[8]  Robert K. Tyson.  Introduction to Adaptive Optics , 2000 .

[9]  William J. Borucki,et al.  A SEARCH FOR EARTH-SIZED PLANETS IN HABITABLE ZONES USING PHOTOMETRY , 1996 .

[10]  R. Paul Butler,et al.  Two New Planets from the Anglo-Australian Planet Search , 2001 .

[11]  Gautam Vasisht,et al.  Astrometry with the Keck Interferometer , 1998, Astronomical Telescopes and Instrumentation.

[12]  D. Spergel.  A New Pupil for Detecting Extrasolar Planets , 2001, astro-ph/0101142.

[13]  B. Lyot.  The study of the solar corona and prominences without eclipses (George Darwin Lecture, 1939) , 1939 .

[14]  R. Vanderbei,et al.  Extrasolar Planet Finding via Optimal Apodized-Pupil and Shaped-Pupil Coronagraphs , 2003 .

[15]  J R Fienup,et al.  Phase retrieval algorithms: a comparison. , 1982, Applied optics.

[16]  R. Vanderbei,et al.  Spiderweb Masks for High-Contrast Imaging , 2003, astro-ph/0303049.

[17]  M. Shao,et al.  HIGH-DYNAMIC-RANGE IMAGING USING A DEFORMABLE MIRROR FOR SPACE CORONOGRAPHY , 1995, astro-ph/9502042.

[18]  David Charbonneau,et al.  Hubble Space Telescope Time-Series Photometry of the Transiting Planet of HD?209458 , 2001 .

[19]  James V. Burke,et al.  Optical Wavefront Reconstruction: Theory and Numerical Methods , 2002, SIAM Rev..

[20]  F. Roddier,et al.  The Nulling Stellar Coronagraph: Laboratory Tests and Performance Evaluation , 1999 .

[21]  J Shamir,et al.  Wave-front analysis using Fresnel lens arrays. , 1995, Optics letters.