Deconvolving optical sensor image distortion using Hermite functions

Henry Berger; Edmundo Simental

doi:10.1117/12.366275

27 October 1999 Deconvolving optical sensor image distortion using Hermite functions

Henry Berger, Edmundo Simental

Proceedings Volume 3753, Imaging Spectrometry V; (1999) https://doi.org/10.1117/12.366275
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

Optical systems associated with imaging sensors and instruments typically distort the 'true' or object image, I(x), in a manner usually characterized by their point spread function (PSF). Determining I(x) from the measured image data, M(z), using the convolutional relation with the PSF is called deconvolution. This paper proposes what appears to be a new deconvolution technique by taking advantage of a remarkable coincidence. It is that for most optical systems of interest here the PSF is Gaussian, which is a zeroth order Hermite function. By expressing I(x) in an orthogonal representation using Hermite functions, which are to be distinguished from Hermite polynomials, the convolution integral can be evaluated exactly in analytical form, perhaps for the first time for the general case. This, in turn, leads to simple, precise linear relations between the coefficients of the Hermite representation of I(x) and that of M(x); while avoiding the common problem of division of noisy data by small quantities. The coefficients in those linear equations have precise values obtained from the nature of Hermite function interrelations rather than measured data. These values of I(x) may be more useful than M(x) as the initial iterate in the iteration techniques commonly used for deconvolution.

Citation Download Citation

Henry Berger and Edmundo Simental "Deconvolving optical sensor image distortion using Hermite functions", Proc. SPIE 3753, Imaging Spectrometry V, (27 October 1999); https://doi.org/10.1117/12.366275

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KEYWORDS

Point spread functions

Deconvolution

Convolution

Fourier transforms

Optical sensors

Image sensors

Distortion

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