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A fast partial Fourier transform (FPFT) for data compression and filtering

Proceedings of SPIE - The International Society for Optical Engineering

Smith, Mark W.

A discrete Fourier transform (DFT) or the closely related discrete cosine transform (DCT) is often employed as part of a data compression scheme. This paper presents a fast partial Fourier transform (FPFT) algorithm that is useful for calculating a subset of M Fourier transform coefficients for a data set comprised of N points (M < N). This algorithm reduces to the standard DFT when M = 1 and it reduces to the radix-2, decimation-in-time FFT when M = N and N is a power of 2. The DFT requires on the order of MN complex floating point multiplications to calculate M coefficients for N data points, a complete FFT requires on the order of (N/2)log2N multiplications independent of M, and the new FPFT algorithm requires on the order of (N/2)log2M + N multiplications. The FPFT algorithm introduced in this paper could be readily adapted to parallel processing. In addition to data compression, the FPFT algorithm described in this paper might be useful for very narrow band filter operations that pass only a small number of non-zero frequency coefficients such that M ≪ N. © 2010 Copyright SPIE - The International Society for Optical Engineering.

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Adaptive optics and phase diversity imaging for responsive space applications

Smith, Mark W.; Wick, David V.

The combination of phase diversity and adaptive optics offers great flexibility. Phase diverse images can be used to diagnose aberrations and then provide feedback control to the optics to correct the aberrations. Alternatively, phase diversity can be used to partially compensate for aberrations during post-detection image processing. The adaptive optic can produce simple defocus or more complex types of phase diversity. This report presents an analysis, based on numerical simulations, of the efficiency of different modes of phase diversity with respect to compensating for specific aberrations during post-processing. It also comments on the efficiency of post-processing versus direct aberration correction. The construction of a bench top optical system that uses a membrane mirror as an active optic is described. The results of characterization tests performed on the bench top optical system are presented. The work described in this report was conducted to explore the use of adaptive optics and phase diversity imaging for responsive space applications.

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14 Results
14 Results