Phase retrieval with transverse translation diversity: a nonlinear optimization approach.
We develop and test a nonlinear optimization algorithm for solving the problem of phase retrieval with transverse translation diversity, where the diverse far-field intensity measurements are taken after translating the object relative to a known illumination pattern. Analytical expressions for the gradient of a squared-error metric with respect to the object, illumination and translations allow joint optimization of the object and system parameters. This approach achieves superior reconstructions, with respect to a previously reported technique [H. M. L. Faulkner and J. M. Rodenburg, Phys. Rev. Lett. 93, 023903 (2004)], when the system parameters are inaccurately known or in the presence of noise. Applicability of this method for samples that are smaller than the illumination pattern is explored.
The Institute of Optics, University of Rochester, Rochester, New York 14627, USA. mguizar@optics.rochester.edu
Manuel
M
Guizar-Sicairos
James R
JR
Fienup
D000465:Algorithms; D016477:Artifacts; D005583:Fourier Analysis; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D016011:Normal Distribution; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D014965:X-Rays