Optimization of narrow optical spectral filters for nonparallel monochromatic radiation

This paper delineates a method of determining the design criteria for narrow optical passband filters used in the reception of nonparallel modulated monochromatic radiation. The analysis results in straightforward mathematical expressions for calculating the filter width and design center wavelength which maximize the signal-to-noise ratio. Two cases are considered: (a) the filter is designed to have a maximum transmission (for normal incidence) at the incident wavelength, but with the spectral width optimized, and (b) both the design wavelength and the spectral width are optimized. It is shown that the voltage signal-to-noise ratio for case (b) is 2((1/2)) that of case (a). Numerical examples are calculated.