Image Distortion in Reconstructions from Phase-Only Holograms

Metherell has proposed and demonstrated a method of acoustical holography which retains only the phase information in the acoustic waves scattered by an object [1]. Spatial amplitude variations of the object beam are disregarded. This type of hologram is of particular interest in computer holography since the amount of data used in the processing is reduced by half. Experiments performed by Metherell and colleagues have shown that such a “phase-only” hologram can, in fact, produce a good reproduction of simple objects. Although there is little evidence of image distortion in Metherell's experimental results, one might expect that some form of distortion would be introduced by the process.

This paper shows mathematically that for the particular case of Fraunhofer holograms, the image will exhibit a strong accentuation of intensity in regions having components of high spatial frequency (edges, etc.). For many purposes, this form of distortion is not detrimental because it results in little loss of resolution. Additionally, there can be a periodic nature to the reconstruction since the hologram exhibits a grating-like structure.

Using a digital computer we have also made a study of the reconstructed image of a back-irradiated slit where the system dimensions are comparable to those used in Metherell's experiments. The theoretical images obtained in this way show a type of distortion which is similar, but less pronounced, than that found in the Fraunhofer phase-only holograms; that is, the intensity is greatly increased in the region of the edge.