Publications

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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.

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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Hadamard Transform Spectrometer (HTS) approaches share the multiplexing advantages found in Fourier transform spectrometers. Interest in Hadamard systems has been limited due to data storage/computational limitations and the inability to perform accurate high order masking in a reasonable amount of time. Advances in digital micro-mirror array (DMA) technology have opened the door to implementing an HTS for a variety of applications including fluorescent microscope imaging and Raman imaging. A Hadamard transform spectral imager (HTSI) for remote sensing offers a variety of unique capabilities in one package such as variable spectral and temporal resolution, no moving parts (other than the micro-mirrors) and vibration tolerance. Two approaches to for 2D HTS systems have been investigated in this LDRD. The first approach involves dispersing the incident light, encoding the dispersed light then recombining the light. This method is referred to as spectral encoding. The other method encodes the incident light then disperses the encoded light. The second technique is called spatial encoding. After creating optical designs for both methods the spatial encoding method was selected as the method that would be implemented because the optical design was less costly to implement.