Investigation of branch-point density using traditional wave-optics techniques

Jeffrey R. Beck; Mark F. Spencer; Jeremy P. Bos; Terry Brennan

doi:10.1117/12.2319871

18 September 2018 Investigation of branch-point density using traditional wave-optics techniques

Jeffrey R. Beck, Mark F. Spencer, Jeremy P. Bos, Terry Brennan

Proceedings Volume 10772, Unconventional and Indirect Imaging, Image Reconstruction, and Wavefront Sensing 2018; 1077206 (2018) https://doi.org/10.1117/12.2319871
Event: SPIE Optical Engineering + Applications, 2018, San Diego, California, United States

Abstract

This study uses traditional wave-optics techniques, such as the split-step beam propagation method with angular-spectrum propagation, to explore the number of branch points as a function of the numerical grid size (i.e., the branch-point density) with increasing strengths of turbulence. To help quantify the strength of the turbulence, the analysis makes use of the log-amplitude variance for a spherical wave. Given a point-source beacon and horizontal-propagation paths, this parameter gives a straightforward gauge for the amount of scintillation, and therefore the number of branch points in the phase function. As such, the goal throughout is to investigate the branch-point density in terms of a two-step process. The first step is to increase the numerical grid size to have an ever increasing number of grid points for a given instance of turbulence; particularly, with a log-amplitude variance for a spherical wave above 0.25, because this is where branch points start to arise in the phase function. In turn, the second step is to utilize a Monte-Carlo averaging scheme with the resultant branch-point density for many instances of turbulence and turbulence strengths. Using this two-step process, the initial results show that the branch-point density grows without bound. Such results seem unphysical and could have direct implications for wave-optics studies that involve wavefront sensing in the presence of deep turbulence.

Conference Presentation

Citation Download Citation

Jeffrey R. Beck, Mark F. Spencer, Jeremy P. Bos, and Terry Brennan "Investigation of branch-point density using traditional wave-optics techniques", Proc. SPIE 10772, Unconventional and Indirect Imaging, Image Reconstruction, and Wavefront Sensing 2018, 1077206 (18 September 2018); https://doi.org/10.1117/12.2319871

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