The new technical field of electro-holography is essentially the marriage between holography and digital computational technologies. Holography is used to create 3-D images by recording and reproducing optical wavefronts. The conception of holography began less than 50 years ago[1],[2], and was applied to the recording and subsequent reconstruction of 3-D images beginning only 30 years ago with the arrival of the laser[3]. Optical holographic imaging[4] is a two-step process. Generally, a rigid object is illuminated with a coherent beam of light. A mutually coherent reference beam is aligned to interfere with the light scattered from the object. The resulting microscopic interference pattern (fringe pattern or simply fringe) is recorded in a high-resolution light-sensitive medium such as photographic film. Once developed, this recorded fringe diffracts an illuminating light beam to form a 3-D image that can look identical to the original object. The fringe pattern diffracts lights because its feature size is generally on the order of the wavelength of visible light (about 0.5 mm). Because of this microscopic resolution, the fringe pattern contains an enormous amount of information - roughly ten million resolvable features per square millimeter.
As early as 1964 researchers began to consider the computation, transmission, and use of holographic fringes to create images that were synthetic and perhaps dynamic[21]. These researchers encountered the fundamental problems inherent to computational holography: both the computation and display of holographic images are difficult due to the large amount of information contained in a fringe pattern. Roughly ten million samples per square millimeter are required to compute a discretized (sampled) fringe that matches the resolution (diffractive power) of an optically made hologram. The possibility of computing a ten-billion-sample fringe pattern at a rate of once per second was impossible, and the possibility of modulating a beam of light with such a fringe pattern was beyond any spatial light modulation technologies available at that time. For decades, the enormous size of a holographic fringe prohibited and discouraged the pursuit of real-time electronic 3-D holographic imaging.
In 1989, researchers at the MIT Media Laboratory Spatial Imaging Group created the first display system capable of producing real-time 3-D holographic images[50]. The images were small but were made possible by information reduction strategies that lowered the number of fringe samples to only 2 MB - the minimum necessary to create an image the size of a golf ball. A modulation scheme based on time-multiplexing an acousto-optic modulator was used to modulate a beam of light with the 2-MB of discretized computed holographic fringe pattern. Computation of the 2-MB fringe pattern still required several minutes for simple images using traditional computation methods that imitated the optical creation of holographic fringes. Speed was limited by two factors: (1) the huge number of samples in the discretized fringe, and (2) the complexity of the physical simulation of light propagation used to calculate each sample value. As display size increased, the amount of information increased too, roughly proportional to the image volume (i.e., the volume occupied by the 3-D image). To achieve interactive holographic computation, a new type of approach would have to be invented. That new approach - called "diffraction-specific computation" - is the subject of this dissertation.
This thesis concentrates on the generation of holographic fringes using a new method called diffraction-specific computation. The architecture of diffraction-specific computation is directed by two primary goals: (1) to produce fringes at a faster rate and (2) to enable holographic encoding schemes to reduce the bandwidth required to display holographic images. Traditional computing methods achieved neither of these goals. Traditional computation imitated the interference occurring in the optical generation of fringes. In contrast, diffraction-specific computation is based on only the diffraction that occurs during the reconstruction of a holographic image. The diffraction-specific approach is a better match to holovideo since the purpose of a real-time holographic display is to generate 3-D images through the modulation and subsequent diffraction of light. The research described in this dissertation demonstrates that moving from interference-based methods and toward diffraction-specific methods increased fringe computation speed.
The application of diffraction-specific computation provides a means for encoding fringes to make the most efficient use of computational power and electronic and optical bandwidth. Holographic fringes contain far less usable information than is intimated by a simple measure of bandwidth. Roughly ten million samples per square millimeter is required whether the fringe pattern represents a simple object or a complex scene, and whether the holographic image is to be viewed through a microscope or by the less acute human visual system (HVS). However, this observation alone does not provide instruction for the reduction or compression of fringe bandwidth. The development of holographic encoding begins by taking a closer look at the nature of holographic fringes. Diffraction-specific fringes are no longer strictly physical but are synthetically generated by specifying more deliberately their diffractive purpose. This specification leads to a more efficient use of holographic channel capacity. This dissertation documents a progression from interference-based computation towards diffraction specific fringes, from physical fringes to synthetic fringes, from inefficient use of channel capacity to a reduction in required bandwidth. Ultimately, the information-reduction strategies born of the diffraction-specific approach should allow for the design and construction of more information-efficient holographic displays.
A glossary of terms and abbreviations is included in Appendix A. Some of the analytical basis for diffraction-specific computation is discussed Appendix B, "Spectral Decomposition of Diffracted Light." Computational support for diffraction-specific computation is described in Appendix C, "Computation of Synthetic Basis Fringes."