This paper was presented at by Mark Lucente at the International Symposium on 3-D Imaging and Holography in Osaka, Japan, Nov. 1994.
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The new technical field of electro-holography is essentially the marriage between holography and digital computational technologies. Holography [1] is used to create 3-D images by recording and reproducing optical wavefronts. To reconstruct an image, the recorded interference pattern modulates an illuminating beam of light. The modulated light diffracts and reconstructs a 3-D replica of the wavefront that was scattered from the object scene. Optical wavefront reconstruction makes the image appear to be physically present and tangible.
A holographic fringe pattern ("fringe") diffracts lights because its feature size is generally on the order of the wavelength of visible light (about 0.5 micrometer). Because of this microscopic resolution, the fringe pattern contains an enormous amount of information - roughly ten million resolvable features per square millimeter. Early on, researchers [2] began to consider the computation, transmission, and use of holographic fringes to create images that were synthetic and perhaps dynamic. 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 sample count 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[3] created the first display system capable of producing real-time 3-D holographic images. 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).
In this paper we describe the advances in holographic display systems and in holographic computation that made possible the interactive display of 3-D holographic images. We describe our most recent holovideo display, capable of producing images that occupy a volume approximately equivalent to a 100-mm-edge cube. We describe computational techniques have increased speeds by over two orders of magnitude compared to traditional approaches.
p = 4/lambda sin(theta/2) (1).Since a horizontal-parallax-only (HPO) CGH contains only a single vertical perspective (i.e., the viewing zone is vertically limited to a single location), spatial frequencies are low (~10 lp/mm) in the vertical dimension. The vertical image resolution is the number of hololines. (A hololine is a single horizontal line of the fringe). Eliminating vertical parallax reduces CGH information content by at least a factor of 100 by reducing the vertical spatial frequency content from roughly 1000 to roughly 10 lp/mm. Essentially, the 2-D holographic pattern representing an HPO 3-D image can be thought of as a vertical array of 1-D holograms or hololines[5]. Each hololine diffracts light to a single horizontal plane to form image points describing a horizontal slice of the image. Therefore, one hololine should contain contributions only from points that lie on a single horizontal slice of the object.
Consider the typical holographic set-up in the following illustration. Light scattered from the object, Eo, interferes with reference light, Er. (Optical wavefronts are represented by mutually coherent, identically polarized, spatially varying complex time-harmonic electric field scalars.) The total electric field incident on the hologram is the interference of the light from the entire object and the reference light, Eo + Er. The total interference fringe intensity is
I_T = | Eo + Er |^2 (2).A real-time holographic display uses the computed fringes to modulate a beam of light and produce an image. The heart of a holographic display is the spatial light modulator (SLM) used to modulate light with a computed fringe pattern. Ideally, a holographic SLM must display over 100 gigasamples. Current SLMs, however, can provide up to only 10 megasamples. Examples of SLMs include the flat-panel liquid-crystal display (LCD) and the magneto-optic SLM. These SLMs are capable of displaying a very small CGH pattern in real time. Early researchers employed a magneto-optic SLM[6], an LCD SLM[7], or a deformable mirror device (DMD)[8]. More recent work employed LCDs with higher pixel counts[9,10], but the images were still very small and essentially two-dimensional.
In 1993, we demonstrated a 36-MB 18-channel display system[14]. The increased size of the image volume and of the viewing zone created a very convincing 3-D image. In addition to an increase in channel parallelism, this system employed a novel multi-mirror horizontal scanning system composed of six galvanometric scanners. Each 19.5-mm-wide mirror was scanned in virtually perfect synchrony, essentially functioning as a 120-mm-wide Fresnel mirror. A system of 18 2-MB framebuffers provided the 18 signals to a pair of cross-fired AOMs, necessary to provide a bidirectional Scophony geometry that made use of both the forward and the backward mirror scans.
The following table summarizes the important parameters of holovideo display systems developed by the MIT Spatial Imaging Group:
Display creation date 1989 1991 1993 Size of fringe 2 MB 6 MB 36 MB Number of channels 1 3 18 Viewing zone 15 degrees 15 degrees 30 degrees Color red full color red Samples/hololine 32 K 32 K 256 K Hololine scan rate 2290 KHz 2750 KHz 150 KHz Total number of hololines 64 64 x 3 144 Image volume 36x24x50 mm 36x24x50 mm 150x75x150 mm width x height x depthDevelopment of the 36-MB system demonstrated that the scanned-AOM approach can be scaled up by increasing the degree of parallelism (i.e., the number of channels) in the system. As the sample count of the hologram increases, however, rapid fringe computation becomes more important.
Traditionally, computational holography[4] was slow due to two fundamental properties of fringe patterns: (1) the enormous number of samples required to represent microscopic features, and (2) the computational complexity associated with the physical simulation of light propagation and interference. A typical full-parallax hologram 100 mm 100 mm in size has a sample count (also called space-bandwidth product or SBWP or simply "bandwidth") of over 100 gigasamples of information. A larger image requires a proportionally larger number of samples. Several techniques have been used to reduce information content to a manageable size. The elimination of vertical parallax[15] provided great savings in display complexity and computational requirements[12] without greatly compromising the overall display performance.
Recalling Equation 2, the expression for total intensity in an interference pattern expands to
I_T = |Eo|^2 + |Er|^2 + 2 Re{ Eo Er* } (3). object reference useful self- bias fringes inter- ferenceThe total intensity is a real physical light distribution comprising three components.
As discussed in the references by Lucente[15,16], the expression for the bipolar intensity (in Equation 3) was simplified to involve only real-valued arithmetic, resulting in a computation speed increase of a factor of 2.0. There are many advantages to the use of bipolar intensity computation. There is no object self-interference noise. There is no reference bias - in fact there is no need to specify the reference beam intensity - resulting in a more efficient use of the available dynamic range of the fringe pattern. The most interesting advantage of the bipolar intensity method is that linear summation of elemental fringes is possible, with each elemental fringe representing a single image element. Real-valued summation enables the efficient use of precomputed elemental fringes, an approach which, when implemented on a supercomputer, achieved CGH computation at interactive rates[16].
Bipolar intensity implemented with precomputed elemental fringes allowed for the first ever interactive display of holographic images in 1990. Even though the interactively generated images were small, this early work demonstrated the power of linear summation and the possibility of generating a fringe as a linear combination of precomputed fringes provided. These two concepts provided guidance for the recent development of an entirely new approach to fringe computation: "diffraction-specific computation."
The application of diffraction-specific computation provided a means for encoding fringes to make the most efficient use of computational power and electronic and optical bandwidth[17]. Holographic fringes contain far less usable information than is intimated by a simple measure of bandwidth. The limited acuity of the human visual system (HVS) cannot utilize the extremely high image resolution provided by optical holograms.
Lucente[17] recently reported the development and implementation of diffraction-specific fringe computation and its adjunct holographic encoding schemes (called "fringelet encoding" and "hogel-vector encoding"). These holographic encoding schemes achieved compression ratios of 16 and higher. Holographic encoding adds a predictable amount of image blur. The analysis of diffraction-specific computation revealed an important three-way trade-off between compression ratio, image fidelity, and image depth. The decreased image resolution (increased point spread) that was introduced into holographic images due to encoding was imperceptible to the human visual system under certain conditions. A compression ratio of 16 was achieved (using either encoding method) with an acceptably small loss in image resolution. Total computation time is reduced by a factor of over 100 to less than 7.0 seconds per 36-MB holographic fringe using the fringelet encoding method implemented on a standard serial workstation. Diffraction-specific computation more efficiently matches the information content of holographic fringes to the capabilities of the human visual system.
The "Connection Machine" supercomputer was manufactured by Thinking Machines, Inc., Cambridge, MA, USA.
The authors gratefully acknowledge the support of researchers in the MIT Spatial Imaging Group and in the MIT Media Laboratory: Carlton J. Sparrell, Wendy J. Plesniak, Michael Halle, Shawn Becker, John Watlington, V. Michael Bove, Jr., Brett Granger, Michael Klug, Tinsley Galyean, Ravikanth Pappu, John D. Sutter, Derrick Arias, Jeff Breidenbach. Thanks also to Professor Tomas A. Arias and Dr. Shuguang Zhang.
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[16] Mark Lucente, "Interactive computation of holograms using a look-up table," Journal of Electronic Imaging, vol. 2, #1, pp. 28-34, Jan 1993.
[17] Mark Lucente, "Diffraction-Specific Fringe Computation for Electro-Holography," Ph. D. Thesis, Dept. of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Sept. 1994.
In his work, Dr. Lucente combines a knowledge of optics, spatial light modulation, computation, visual perception, and communication systems to develop electro-holography into a practical medium. His earlier work involved the application of lasers to high-bandwidth optical communication systems and 3-D imaging systems, and to the study of device physics.