Stochastic optimal phase retrieval algorithm for high-contrast imaging

The Princeton University Terrestrial Planet Finder (TPF) 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. Its parameters are estimated using a global search with a genetic algorithm and a local optimization with the BFGS quasi-Newton method with a mixed quadratic and cubic line search procedure.

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

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

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

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

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

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

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

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

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

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

[11]  W. Traub,et al.  A Coronagraph with a Band-limited Mask for Finding Terrestrial Planets , 2002, astro-ph/0203455.

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

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

[14]  E. Hecht.  Optics 4th Edition , 1998 .

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

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

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

[18]  R. Paul Butler,et al.  Planets Orbiting Other Suns , 2000 .

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

[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.

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

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