The addition of one or more partially reflecting mirrors to a traditional two-mirror Fabry–Perot interferometer results in a multimirror Fabry–Perot interferometer. A superposition of all possible multiple reflected beams is described with a general theory for multimirror interferometers, featuring matrices analogous to the theory of multilayer thin films. However, the parameters in the matrix elements are mirror reflection coefficients and spacings instead of the usual refractive indices and layer thicknesses of thin films. The transmission characteristics of two-, three-, and four-mirror Fabry–Perot optical filters are described. It is shown that a suitable choice of reflection coefficients results in transmission properties that can be described approximately with Butterworth profiles, which are known from network analysis of electrical circuits.
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