Computed Reconstructions from Phase-Only and Amplitude-Only Holograms

Abstract

We have analyzed several types of acoustical holograms similar to and including the phase-only hologram suggested by Metherell.¹ The analyses have involved three different diffraction regions: the Fraunhofer, Fresnel, and very-near-field. Each type of hologram studied is characterized by discarding some part of the information present in the wave scattered by the object and recording the portion that is left, thus allowing more efficient use of the recording medium. (For example, in the phase-only hologram the phase information in the scattered wave is retained, but the amplitude information is discarded.) The object investigated in each case was a long slit, thereby confining the analyses to one dimension.

In the cases involving the Fraunhofer region we assumed that the hologram was infinitely wide. Mathematically, the reconstructed image of a slit from a phase-only sideband Fraunhofer hologram of infinite extent is an infinite series of intense lines of light separated by a distance equal to the width of the slit. The two central lines can be regarded as defining the slit edges. The light intensity decreases, but does not drop to zero, between the two central lines. However, it does drop to zero halfway between all other pairs of the intense lines. The reconstructed image from an amplitude-only sideband Fraunhofer hologram bears little resemblance to the slit, although there is some geometric information present.

In the Fresnel and very-near-field regions the analyses were carried out on a digital computer. This was necessitated by having to use the Fresnel-Kirchhoff diffraction integral. Theoretical images were reconstructed for the phase-only, amplitude-only, and conventional holograms. The results indicated that the phase-only process introduces some degree of distortion. The higher spatial frequencies are emphasized and this leads to an exaggeration of edges, corners, etc. This may prove to be useful for many purposes, such as enhancement of object outlines. Also, the phase-only hologram has the advantage of eliminating some of the interfering noise present in the other types of holograms. The amplitude-only holograms seem to have little value in image reconstruction unless the hologram is recorded very close to the object.

Theoretical analysis showed that if the object beam and a bias signal were first added together in conventional fashion, but then only the phase were detected, it would be possible to almost duplicate the reconstruction capability of the conventional hologram. The size of the bias signal determines the degree of similarity in the two capabilities. This method has the same advantage as the phase-only process, i.e., only half of the data present must be recorded, and therefore the full dynamic range of the recording medium could be used more efficiently. Reconstruction data obtained from a computer study verified this similarity of image reconstruction.

This work supported in part by NIH Grant No. 1, RO1 GM 16474–01.