Numerical Computation of Phase from Amplitude at Optical Frequencies

Abstract

This paper presents phase tables for use in determining phase from amplitude or vice versa at optical and higher frequencies. The new tables, combined with tables previously published by the author, are believed to make possible the determination of phase from amplitude or vice versa of any minimum phase function occurring in any area of the physical sciences, and at any place in the frequency spectrum. The phase is determined by a summation process based on Bode's straight-line approximation method. The paper gives a brief historical background of the method, discusses the application of the numerical phase summation technique to optical and higher frequencies, describes the derivation of new tabulations useful at these frequencies, and gives quantitative examples of their use. A table expanding the existing tables of phase of a semi-infinite unit slope near f/f <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> equal to one is given. Additional tables of phase of a unit line segment and a new straight-line element, the unit wedge, are given. Finally, there is a brief discussion of the potential of the method in solving physical and engineering problems.