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.
Guizar-Sicairos
Manuel
M
The Institute of Optics, University of Rochester, Rochester, New York 14627, USA. mguizar@optics.rochester.edu
Fienup
James R
JR
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