X - Interference and diffraction with partially coherent light

Summary

Introduction

So far we have been mainly concerned with monochromatic light produced by a point source. Light from a real physical source is never strictly monochromatic, since even the sharpest spectral line has a finite width. Moreover, a physical source is not a point source, but has a finite extension, consisting of very many elementary radiators (atoms). The disturbance produced by such a source may be expressed, according to Fourier's theorem, as the sum of strictly monochromatic and therefore infinitely long wave trains. The elementary monochromatic theory is essentially concerned with a single component of this Fourier representation.

In a monochromatic wave field the amplitude of the vibrations at any point P is constant, while the phase varies linearly with time. This is no longer the case in a wave field produced by a real source: the amplitude and phase undergo irregular fluctuations, the rapidity of which depends essentially on the effective width Δv of the spectrum. The complex amplitude remains substantially constant only during a time interval Δt which is small compared to the reciprocal of the effective spectral width Δv; in such a time interval the change of the relative phase of any two Fourier components is much less than 2π and the addition of such components represents a disturbance which in this time interval behaves like a monochromatic wave with the mean frequency; however, this is not true for a longer time interval. The characteristic time Δt = 1/Δv is of the order of the coherence time introduced in §7.5.8.