Phase Shift Effects in Fringes of Equal Chromatic Order

Abstract

For the calculation of step heights or interferometer plate displacement three methods of analysis are discussed. A comprehensive expression is derived which requires knowledge of the phase shift on reflection. A simple expression, 2Δt = λ1Δλ/(λ0−λ1), is shown to be exact under certain conditions. Here Δt is the step height, Δλ the fringe shift, and λ0, λ1 are the wavelengths of adjacent fringes, λ0 > λ1. A method is introduced which does not require prior knowledge of the phase shift dispersion. For one set of fringes an arbitrary integer, N, is selected and the function τN(λ) is found by plotting Nλ0vs λ0, (N+1)λ1vs λ1, etc. For the set of shifted fringes the function τN′(λ) is found similarly by plotting Nλ0′ vs λ0′, etc., where the fringe at λ0′ has the same order number as that at λ0. It is shown that the vertical displacement between the two curves is a constant equal to twice the step height. Other uses of the tau function are described. If the tau function is linear with wavelength, the simple expression above can be used without error.