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<p>This dissertation describes two computational sensors that were used to demonstrate
applications of generalized sampling of the optical field. The first sensor was an
incoherent imaging system designed for compressive measurement of the power spectral
density in the scene (spectral imaging). The other sensor was an interferometer used
to compressively measure the mutual intensity of the optical field (coherence imaging)
for imaging through turbulence. Each sensor made anisomorphic measurements of the
optical signal of interest and digital post-processing of these measurements was required
to recover the signal. The optical hardware and post-processing software were co-designed
to permit acquisition of the signal of interest with sub-Nyquist rate sampling, given
the prior information that the signal is sparse or compressible in some basis.</p>
<p>Compressive spectral imaging was achieved by a coded aperture snapshot spectral
imager (CASSI), which used a coded aperture and a dispersive element to modulate the
optical field and capture a 2D projection of the 3D spectral image of the scene in
a snapshot. Prior information of the scene, such as piecewise smoothness of objects
in the scene, could be enforced by numerical estimation algorithms to recover an estimate
of the spectral image from the snapshot measurement.</p>
<p>Hypothesizing that turbulence between the scene and CASSI would introduce spectral
diversity of the point spread function, CASSI's snapshot spectral imaging capability
could be used to image objects in the scene through the turbulence. However, no turbulence-induced
spectral diversity of the point spread function was observed experimentally. Thus,
coherence functions, which are multi-dimensional functions that completely determine
optical fields observed by intensity detectors, were considered. These functions have
previously been used to image through turbulence after extensive and time-consuming
sampling of such functions. Thus, compressive coherence imaging was attempted as an
alternative means of imaging through turbulence.</p>
<p>Compressive coherence imaging was demonstrated by using a rotational shear interferometer
to measure just a 2D subset of the 4D mutual intensity, a coherence function that
captures the optical field correlation between all the pairs of points in the aperture.
By imposing a sparsity constraint on the possible distribution of objects in the scene,
both the object distribution and the isoplanatic phase distortion induced by the turbulence
could be estimated with the small number of measurements made by the interferometer.</p>
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