Tolerances For Layer Thicknesses in Dielectric Multilayer Coatings and Interference Filters

A theory is developed for dielectric multilayer coatings in which the layers depart from calculated thickness. The theory is applied to alternating systems of quarter wave layers of ZnS and MgF(2). The effects of thickness errors are: (1) A shift of the wavelength at which maximum reflectance occurs; and (2) a change in phase shift upon reflection. The magnitude of these effects, and also their dependence on various parameters, are determined. Statistical tolerances for layer thicknesses are computed for given tolerances on the multilayer performance. The accuracy required for producing dielectric interference filters is up to about 40 times higher than the accuracy sufficient for the production of dielectric mirrors and beam splitters. Various techniques of experimentally controlling film thicknesses, and their accuracies, are discussed. The production of mirrors and beam splitters deviating from theoretical maximum reflectance by only 1 percent seems to be possible with Dufour’s simple single photocell method of monitoring film thicknesses. With more precise methods, such as those developed by Giacomo and Jacquinot, or Traub, the production of interference filters appears to be possible to within plus or minus one half their half widths.