The solution of the multilayer filter is obtained as a boundary value problem. A recursion formula is developed, which, applied once for each layer gives the reflected beam. A graphical means for determining the unknown quantity in the recursion formula has been shown to apply to dielectric layers.
The solution has been used to explain an irregular fringe shift in the reflected pattern from an interferometer, one of whose plates has a uniform wedge of dielectric deposited on it. It is shown that this irregular shifting of the fringes with thickness of the dielectric must be considered if interferometric determinations of index of refraction are to be made.
This method of determining the reflected beam has also been applied in finding the transmission characteristics of the frustrated total reflection filter. It is found that the width of the transmission band which, theoretically, could be arbitrarily small without loss of peak transmission, is limited by the uniformity in the thickness of the spacer layer.
HARRY D. POLSTER, "Reflection from a Multilayer Filter," J. Opt. Soc. Am. 39, 1038-1041 (1949)