Wavefront synthesis and reconstruction: Direct binary search holograms and synthetic aperture radar
Abstract
Computer-generated binary holograms can perform complex waveshaping functions that are beyond the capability of ordinary refractive optical elements. An iterative procedure for the synthesis of computer-generated holograms (CGH's) is investigated that consists of a direct binary search (DBS) for the element configuration that minimizes the error between the actual and desired reconstructed wavefronts. Although DBS CGH's have low reconstruction error and high diffraction efficiency, images reconstructed from DBS holograms suffer from leakage noise due to parts of the diffraction pattern that are not controlled by the algorithm. The statistics of the nonhomogeneous leakage noise are analyzed under the assumption of independent, identically-distributed addressable hologram cell transmittances. The severity of the leakage noise is compared to the representation-related error caused by the finite resolution and binary transmittance of the medium used to realize the CGH. Except for a cross artifact due to a nonzero mean hologram transmittance, the leakage is found to exhibit speckle-like unity contrast. Due to the computational complexity of the DBS algorithm, it has been limited to synthesis of CGH's with a relatively small number of addressable cells. To ameliorate this disadvantage, a fast algorithm is developed that recursively computes the error measure to be minimized. For complex amplitude-based error, the required computation for an L point CGH is reduced by a factor of $\rm\sqrt{L/log\sb2\/L}$. The fast intensity-based algorithm is substantially more complicated; and modifications are considered to make the algorithm more efficient. An acceleration technique that attempts increase the rate of convergence of DBS is also investigated. Spotlight-mode synthetic aperture radar provides measurements in a limited annular sector of the two-dimensional spatial Fourier transform of the complex reflectance function of a spatially limited terrain patch. A maximum likelihood estimate of the reflectance magnitude based on the measured data is derived under the assumption of independent, uniformly distributed reflectance phase. The expectation-maximization (EM) algorithm is employed to solve the nonlinear likelihood function; and it yields a computationally efficient iterative estimator.
Degree
Ph.D.
Advisors
Allebach, Purdue University.
Subject Area
Electrical engineering|Optics
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