Optical path difference analysis of ultra-rapid-scanning imaging interferometer

A new method to deduce the optical path difference of a kind of ultra-rapid-scanning imaging spectrometer is provided. The process of the derivation is elaborated, and the ultimate formula is given. The formula of the optical path difference is recalculated by setting several related parameters. The curves of optical path difference are presented. They are given by changing one of those parameters with other parameters at fixed values. The contributions of the parameters is compared and discussed. The design of this kind of ultra-rapid-scanning imaging interferometer and the recovery of the interferogram to spectrogram should base on the optical path difference formula.