The Significance of Far-zone Coherence for Sources or Scatterers with Hidden Periodicity

Abstract

General expressions are derived for the far-zone intensity and degree of coherence of partially coherent radiation emanating from a periodic structure such as a diffraction grating. The case in which the source intensity distribution and degree of spatial coherence are both assumed gaussian in the absence of the periodic structure is treated explicitly for arbitrary ratios of beam waist to correlation length and periodicity. It is shown that when the source coherence is too weak to permit detection of the periodic structure from the far-zone angular intensity distribution, the periodicity may nevertheless be manifest in the corresponding angular distribution of the degree of coherence. Consequently interferometry and related methods offer in principle more sensitive means of detecting such structures.