CONTRIBUTIONS TO DIGITAL HOLOGRAPHY FOR THE THREE-DIMENSIONAL DISPLAY OF MEDICAL IMAGERY

In light of the growing presence and power of the digital computer in the radiology laboratory, a digital holographic approach to the 3-D display of medical image data is investigated. The fundamental concepts involve: producing the digital equivalent of an optical model of the data as a collection of parallel cross-sections; computing the complex Fresnel diffraction patterns (FDP) of the individual cross-sections at the hologram plane and, invoking linearity, summing them to yield the FDP of the 3-D model; modulating a high spatial frequency carrier with the FDP; and recording the resulting sample values on film. This holographic approach provides a volume filling, 3-D image, offering horizontal and vertical parallax, accommodation, and stereopsis. It is assumed that the digital data to be displayed has been processed to represent the pertinent information.; We model the data points as coherently radiating sources. If the holographic image subtends more than a few tenths of a degree the FDP must be sampled at typically 50 times the image sampling rate. Since the hologram forms the viewing window we must compute at least a factor of 50('2) more FDP sample points than image points to provide a reasonable look-around angle. The computation involved is the 2-D convolution of the coarsely sampled image cross-section and the 2-D quadratic phase function. We derive an algorithm which partitions this huge convolution into a multitude of manageable blocks, each of which can be independently computed with a single 2-D discrete Fourier transform. The advantages are savings in memory, computational costs, time and the suitability for parallel-processor-architecture computer implementation. The algorithm is experimentally verified by synthesizing a digital hologram based on the algorithm and viewing the reconstructed real and virtual images.; We also establish the mathematical framework for a new scanned digital holographic recorder. The amplitude and phase of the computed FDP samples control a scanning spatial light modulator modulating one of two interfering planes waves. The geometry is that of a reflection hologram so that the image can be viewed in white light. Another advantage of this recorder is that it and the computer must deal with only the baseband FDP and the film alone must resolve the wide-band interference pattern.