Rakesh Kumar and Sudhakar Prasad, (Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM)
https://doi.org/10.64861/MSST3987
Keywords: Space Situational Awareness, SSA, Adaptive Optics, Imaging
Abstract:
For a clear, well corrected imaging aperture in space, the point-spread function (PSF) in its Gaussian image plane has the conventional, diffraction-limited, tightly focused Airy form. Away from that plane, the PSF broadens rapidly, however, resulting in a loss of sensitivity and transverse resolution that makes such a traditional best-optics approach untenable for rapid 3D image acquisition. One must scan in focus to maintain high sensitivity and resolution as one acquires image data, slice by slice, from a 3D volume with reduced efficiency. In this paper we describe a computational-imaging approach [1] to overcome this limitation. We propose the use of pupil-phase engineering to fashion a PSF that, although not as tight as the Airy spot, maintains its shape and size while rotating uniformly with changing defocus over many waves of defocus phase at the pupil edge. As one of us has shown recently [2], dividing a circular pupil aperture into L Fresnel zones, with the lth zone having an outer radius proportional to ?l, and impressing a spiral phase profile of form l? on the light wave, where ? is the azimuthal angle coordinate measured from a fixed x axis (the dislocation line) in the pupil plane, yields a PSF that rotates with defocus while keeping its shape and size. Our PSF rotation concept is quite different from that employed by Piestun and collaborators [3] in which combine an appropriate selected subset of Gauss-Laguerre modes, followed by pupil-phase optimization, to create a doublehelix rotating PSF pattern with high power throughput. This work preceded work by a different group [4] of a very similar flavor except that the double helix was dispensed with, by a different pupil-phase optimization strategy, in favor of a single-helix, or corkscrew, PSF. Much like the work presented here, because of its single-lobe structure the corkscrew PSF leads to less confusion in the image obtained for a relatively crowded field of point sources. The present paper explores detailed properties of our rotating-PSF design, including a theoretical analysis of the trade-offs between transverse and longitudinal resolutions, simulation of image data for 3D scenes based on such a PSF and optimization based algorithms for their recovery, and more general design related issues. We shall derive an underlying conservation law that both controls the transverse-longitudinal trade-off and might suggest still more general design strategies with better rotational shape invariance.
Date of Conference: September 10-13, 2013
Track: Adaptive Optics