Rakesh Kumar and Sudhakar Prasad, (Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM)
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 to overcome this limitation, one that uses 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 [1], the subdivision of a circular pupil aperture into M Fresnel zones, with the mth zone having an outer radius proportional to m and impressing a spiral phase profile of form m? on the light wave, where ? is the azimuthal angle coordinate measured from a fixed x axis (the dislocation line), yields a PSF that rotates with defocus while keeping its shape and size. Physically speaking, a nonzero defocus of a point source means a quadratic optical phase in the pupil that, because of the square-root dependence of the zone radius on the zone number, increases on average by the same amount from one zone to the next. This uniformly incrementing phase yields, in effect, a rotation of the dislocation line, and thus a rotated PSF. Since the zone-to-zone phase increment depends linearly on defocus to first order, the PSF rotates uniformly with changing defocus. For an M-zone pupil, a complete rotation of the PSF occurs when the defocus-induced phase at the pupil edge changes by M waves. Our recent simulations of reconstructions from image data for 3D image scenes comprised of point sources at different focal depths have shown remarkable robustness of our rotating-PSF approach to achieve good transverse and longitudinal resolution even for moderate SNR. Additionally, the work seeks to clarify an important theoretical issue about 3D imaging, namely the detailed nature of the interplay between transverse and longitudinal resolutions, including 3D generalizations of the space-bandwidth product (SBP) and its dependence on image noise. An underlying transport equation, which we shall derive and analyze, describes the trade-off between the transverse and longitudinal blur processes in a manner analogous to the diffractive spreading of a light beam that is transversely confined. This work has immediate applications for space-based surveillance, particularly for 3D mapping and tracking of space debris flying in the vicinity of important AF space assets. Working with a well corrected conventional imager, our 3D computational imager can acquire with high sensitivity and speed an extended focal volume in which individual objects of interest can be subsequently probed and imaged with high resolution over smaller 2D field segments. [1] S. Prasad, Rotating Point Spread Function by Pupil Phase Engineering, Opt. Lett., vol. 38, pp. 585-587 (2013)
Date of Conference: September 10-13, 2013
Track: Adaptive Optics