Abstract
We propose an algorithm for absolute phase retrieval from multiwavelength noisy phase coded diffraction patterns. A lensless optical system is considered with a set of successive single wavelength experiments (wavelength-division setup). The phase masks are applied for modulation of the multiwavelength object wavefronts. The algorithm uses the forward/backward propagation for coherent light beams and sparsely encoding wavefronts, which leads to the complex-domain block-matching three-dimensional filtering. The key-element of the algorithm is an original aggregation of the multiwavelength object wavefronts for high-dynamic-range absolute phase reconstruction. Simulation tests demonstrate that the developed approach leads to the effective solutions explicitly using the sparsity for noise suppression and high-accuracy object absolute phase reconstruction from noisy data.
Highlights
We consider lensless diffraction imaging where information on the object phase and amplitude in question is given by intensities of phase-coded diffraction patterns
Where us;λ is a wavefront propagated to the sensor plane, Ps;λ;dfg is an image formation operator, i.e., the propagation operator from the object to the sensor plane, including in particular random phase masks used for wavefront modulation, d is a propagation distance, ys;λ is the intensity of the wavefront at the sensor plane, and zs;λ are noisy observations as defined by the generator Gfg of the random variables corresponding to ys;λ, and S is a number of experiments
We show that the proposed multiwavelength wavelength division (WD) algorithm is quite successful and is able to reconstruct the absolute phase even from very noisy data
Summary
We consider lensless diffraction imaging where information on the object phase and amplitude in question is given by intensities of phase-coded diffraction patterns. The Gerchberg–Saxton (GS) algorithms[6,7] are from the most popular in the field of phase retrieval These iterative algorithms originally proposed the noiseless data use, alternating projection between the complex-valued object uo and complex-valued wavefronts us at the sensor plane. The multiwavelength phase retrieval is much less studied as compared with the standard single-wavelength formulation These works by the principle of measurements can be separated into two groups. The phase unwrapping algorithms for two-dimensional (2-D) images with simultaneous processing of multiple noisy complexexponent observations have been developed based on the maximum-likelihood techniques.[18]. Katkovnik et al.: Multiwavelength surface contouring from phase-coded noisy diffraction patterns: wavelength-division optical setup Another group of the techniques uses amplitudes or intensities (powers) as measurements. These formulations are from the class of the multiwavelength phase retrieval problems, e.g., Refs.
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