Abstract
The Christiansen filter that is realized by odd smooth cylindrical lenses is analyzed in detail. Several popular filtering functions are discussed. The corresponding lens profile functions are obtained by an inverse scattering theory, which enables the filter to synthesize a desired prescribed response function. This kind of Christiansen filter has a passband narrower than that of the traditional Christiansen filter. Three Christiansen filters centered at 545 nm with full width at half-maximum of 2 nm are synthesized, and the approach to a better suppression of halos from the main transmission peak of the filters is presented in a systematic way.
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