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Deming RW. Chromotomography for a rotating-prism instrument using backprojection, then filtering. Opt Lett. 2006;31(15):2281-3doi: 10.1364/ol.31.002281.
Deming, R. W. (2006). Chromotomography for a rotating-prism instrument using backprojection, then filtering. Optics letters, 31(15), 2281-3. https://doi.org/10.1364/ol.31.002281
Deming, Ross W. "Chromotomography for a rotating-prism instrument using backprojection, then filtering." Optics letters vol. 31,15 (2006): 2281-3. doi: https://doi.org/10.1364/ol.31.002281
Deming RW. Chromotomography for a rotating-prism instrument using backprojection, then filtering. Opt Lett. 2006 Aug 01;31(15):2281-3. doi: 10.1364/ol.31.002281. PMID: 16832459.
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Opt Lett. 2006 Aug 01;31(15):2281-3. doi: 10.1364/ol.31.002281.

Chromotomography for a rotating-prism instrument using backprojection, then filtering.

Optics letters

Ross W Deming

Affiliations

  1. Anteon Corporation, 5100 Springfield Pike, Suite 509, Dayton, Ohio 45431, USA. [email protected]

PMID: 16832459 DOI: 10.1364/ol.31.002281

Abstract

A simple closed-form solution is derived for reconstructing a 3D spatial-chromatic image cube from a set of chromatically dispersed 2D image frames. The algorithm is tailored for a particular instrument in which the dispersion element is a matching set of mechanically rotated direct vision prisms positioned between a lens and a focal plane array. By using a linear operator formalism to derive the Tikhonov-regularized pseudoinverse operator, it is found that the unique minimum-norm solution is obtained by applying the adjoint operator, followed by 1D filtering with respect to the chromatic variable. Thus the filtering and backprojection (adjoint) steps are applied in reverse order relative to an existing method. Computational efficiency is provided by use of the fast Fourier transform in the filtering step.

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