The reconstruction of an in-line Fraunhofer (far-field) hologram is re-examined, and an analytical solution of the intensity distribution throughout the entire reconstructed image is presented. The solution bridges the gap between previously documented solutions which are limited to the plane-of-focus image and distant out-of-focus images. The analysis is motivated by a particle velocity measurement technique which attempts to distinguish the focussed image by photographic thresholding. The general methodology is presented for objects of one- and two-dimensional cross-section. Specific results are presented for the single exposure holograms of a long wire and a small particle of circular cross-section. The one-dimensional solution is verified experimentally. The results show precisely how the Fresnel diffraction term creates peaks in the intensity distribution, both upstream and downstream of the focussed image. This characteristic limits the resolution of methods which use thresholding as a means of distinguishing focussed images from their out-of-focus neighbors.
|Original language||English (US)|
|Number of pages||6|
|Journal||Applied Physics B Photophysics and Laser Chemistry|
|State||Published - Apr 1 1991|