Abstract

Digital filters for spectrometric applications are compared with the classical RC filter. Properties discussed include noise reduction, line shift, and conservation of line moments. For Gaussian and Lorentzian lines, signal deformation and change of half-width as a function of time constant and line width are calculated for several filter types. Using accuracy, sensitivity, and scan speed as criteria, it is shown that a fourth-order digital smoothing polynomial (DISPO) filter is better by typically 1 or even 2 orders of magnitude than the RC filter. Since a real time implementation of these filters is possible, they can directly replace RC filters in all spectrometric applications.

Polynomial filters of any degree

P. D. Willson and S. R. Polo
J. Opt. Soc. Am. 71(5) 599-603 (1981)

Least-Squares Polynomial Filtering of Images by Convolution

Peter A. Jansson
J. Opt. Soc. Am. 62(2) 195-198 (1972)

Restoration of noisy blurred images by a smoothing spline filter

M. J. Peyrovian and A. A. Sawchuk
Appl. Opt. 16(12) 3147-3153 (1977)

Phase unwrapping algorithm using polynomial phase approximation and linear Kalman filter

Rishikesh Kulkarni and Pramod Rastogi
Appl. Opt. 57(4) 702-708 (2018)

Christiansen filter realized by an odd smooth cylindrical lens

Jian Li, N. Goddard, and Kang Xie
J. Opt. Soc. Am. A 27(1) 100-108 (2010)