Abstract
We consider a computational superresolution inverse diffraction problem for phase retrieval from phase-coded intensity observations. The optical setup includes a thin lens and a spatial light modulator for phase coding. The designed algorithm is targeted on an optimal solution for Poissonian noisy observations. One of the essential instruments of this design is a complex-domain sparsity applied for complex-valued object (phase and amplitude) to be reconstructed. Simulation experiments demonstrate that good quality imaging can be achieved for high-level of the superresolution with a factor of 32, which means that the pixel of the reconstructed object is 32 times smaller than the sensor’s pixel. This superresolution corresponds to the object pixel as small as a quarter of the wavelength.
Highlights
In modern science and technology, phase and wavefield imaging are popular and well-established techniques for highaccuracy measuring, recording, and reconstructing of two(2-D) and three-dimensional (3-D) objects
Phase measurements are exploited in microscopy and coherent tomography
The superresolution sparse phase and amplitude reconstruction (SR-SPAR) algorithm proposed in this paper is designed for superresolution phase/amplitude imaging, which is optimal for Poissonian observations
Summary
In modern science and technology, phase and wavefield imaging are popular and well-established techniques for highaccuracy measuring, recording, and reconstructing of two(2-D) and three-dimensional (3-D) objects. Reconstruction of the complex-valued object uo (phase and amplitude) from noiseless or noisy observations is phase retrieval problem. Let the absolute value jusj of us be given and the phase of us is unknown Is it possible to reconstruct the phase of us and in this way the original uo from the amplitude of FT jusj? Defocusing of the registered images is one of the popular instruments to get a sufficient phase diversity.[5,6,7,8] In a recent development, a spatial light modulator (SLM) is exploited for defocusing Random phase modulation of the wavefront is another tool to achieve a desirable phase diversity It results in observations known as coded diffraction patterns The phase modulation is able to dramatically change the diffraction pattern of Pfuog by redistribution of the observed intensities from low to high frequencies
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