Phase Diverse Phase Retrieval for Microscopy: Comparison of Gaussian and Poisson Approaches

Phase diversity is a widefield aberration correction method that uses multiple images to estimate the phase aberration at the pupil plane of an imaging system by solving an optimization problem. This estimated aberration can then be used to deconvolve the aberrated image or to reacquire it with aberration corrections applied to a deformable mirror. The optimization problem for aberration estimation has been formulated for both Gaussian and Poisson noise models but the Poisson model has never been studied in microscopy nor compared with the Gaussian model. Here, the Gaussian- and Poisson-based estimation algorithms are implemented and compared for widefield microscopy in simulation. The Poisson algorithm is found to match or outperform the Gaussian algorithm in a variety of situations, and converges in a similar or decreased amount of time. The Gaussian algorithm does perform better in low-light regimes when image noise is dominated by additive Gaussian noise. The Poisson algorithm is also found to be more robust to the effects of spatially variant aberration and phase noise. Finally, the relative advantages of re-acquisition with aberration correction and deconvolution with aberrated point spread functions are compared.

Tomographic Muon Imaging of the Great Pyramid of Giza

The pyramids of the Giza plateau have fascinated visitors since ancient times and are the last of the Seven Wonders of the ancient world still standing. It has been half a century since Luiz Alvarez and his team used cosmic-ray muon imaging to look for hidden chambers in Khafres Pyramid. Advances in instrumentation for High-Energy Physics (HEP) allowed a new survey, ScanPyramids, to make important new discoveries at the Great Pyramid (Khufu) utilizing the same basic technique that the Alvarez team used, but now with modern instrumentation. The Exploring the Great Pyramid Mission plans to field a very-large muon telescope system that will be transformational with respect to the field of cosmic-ray muon imaging. We plan to field a telescope system that has upwards of 100 times the sensitivity of the equipment that has recently been used at the Great Pyramid, will image muons from nearly all angles and will, for the first time, produce a true tomographic image of such a large structure.