Mark E. Lucente

Interactive computation of holograms using a look-up table

Several methods of increasing the speed and simplicity of the computation of off-axis transmission holograms are presented, with applications to the real-time display ofholographic images. The bipolar intensity approach allows for the real-valued linear summation of interference fringes, a factor of 2 speed increase, and the elimination of image noise caused by object self-interference. An order of magnitude speed increase is obtained through the use of a precomputed look-up table containing a large array of elemental interference patterns corresponding to point source contributions from each of the possible locations in image space. Results achieved using a data-parallelsupercomputer to compute horizontal-parallaxonly holographic patterns containing six megasamples indicate that an image comprised of 10,000 points with arbitrary brightness (gray scale) can be computed in under 1 s. Implemented on a common workstation, the look-up table approach increases computation speed by a factor of 43.

Rendering interactive holographic images

We present a method for computing holographic patterns for the generation of three-dimensional (3-D) holographic images at interactive speeds. We used this method to render holograms on a conventional computer graphics workstation. The framebuffer system supplied signals directly to a real-time holographic (“holovideo”) display. We developed an efficient algorithm for computing an image-plane stereogram, a type of hologram that allowed for several computational simplifications. The rendering algorithm generated the holographic pattern by compositing a sequence of view images that were rendered using a recentering shear-camera geometry. Computational efficiencies of our rendering method allowed the workstation to calculate a 6-megabyte holographic pattern in under 2 seconds, over 100 times faster than traditional computing methods. Data-transfer time was negligible. Holovideo displays are ideal for numerous 3-D visualization applications, and promise to provide 3-D images with extreme realism. Although the focus of this work was on fast computation for holovideo, the computed holograms can be displayed using other holographic media. We present our method for generating holographic patterns, preceded by a background section containing an introduction to optical and computational holography and holographic displays.

Electronic display system for computational holography

We present an electro-optical apparatus capable of displaying a computer generated hologram (CGH) in real time. The CGH is calculated by a supercomputer, read from a fast frame buffer, and transmitted to a high-bandwidth acousto-optic modulator (AOM). Coherent light is modulated by the AOM and optically processed to produce a three-dimensional image with horizontal parallax.

Color images with the MIT holographic video display

The MIT holographic video display can be converted to color by illuminating the 3 acoustic channels of the acousto-optic modulator (AOM) with laser light corresponding to the red, green, and blue parts of the visible spectrum. The wavelengths selected are 633 nm (red), 532 nm (green), and 442 nm (blue). Since the AOM is operated in the Bragg regime, each wavelength is diffracted over a different angular range, resulting in a final image in which the three color primaries do not overlap. This situation can be corrected by shifting the diffracted spatial frequencies with an holographic optical element (HOE). This HOE consisting of a single grating is placed right after the AOM in the optical setup. Calculation of the required spatial frequency for the HOE must take into account the optical activity of the TeO2 crystal used in the AOM. The HOE introduces distortions in the final image, but these are so small as to be visually negligible. The final images are of a good quality and exhibit excellent color registration. The horizontal view zone, however, diminishes for the shorter wavelengths.

Advances in holographic video

We discuss recent developments in the MIT electronic holography display. These include the use of multiple galvanometric scanners as the horizontal scanning element, two 18-channel acousto-optic modulators (AOMs) working in tandem, and a bank of custom-designed high- bandwidth framebuffers. We also describe some recent progress on computational issues.

Real-time holographic display: improvements using a multichannel acousto-optic modulator and holographic optical elements

Any practical holographic display device relying on the MIT synthetic aperture approach will require time-bandwidth products far exceeding those available with single channel acousto- optic modulators (AOMs). A solution to this problem is to use a multichannel AOM, thus making use of the parallelism inherent in optical systems. It is now technically feasible to accommodate a large number of acoustic channels on a single crystal with a corresponding improvement in image characteristics. The vertical view zone also becomes a significant problem for any large size display since each horizontal scan line is visible only from a narrow angle in the vertical direction. Using holographic optical elements (HOEs) alleviates this limitation in two ways: First, the interline spacing can be adjusted easily with HOEs. Second, it is possible to manufacture an HOE which will act as a one-dimensional diffuser. Placing such an HOE in the vertical focus plane of the display increases the view zone by diffusing each line in the vertical direction, but leaves the horizontal image content unaltered.

Computational holographic bandwidth compression

A novel technique to compute holographic fringe patterns for real-time display is described. Hogelvector holographic bandwidth compression, a diffraction-specific approach, treats a fringe as discretized in space and spatial frequency. By undersampling fringe spectra, hogel-vector encoding achieves a compression ratio of 16:1 with an acceptably small loss in image resolution. Hogel-vector bandwidth compression achieves interactive rates of holographic computation for real-time three-dimensional electro-holographic (holovideo) displays. Total computation time for typical three-dimensional images is reduced by a factor of over 70 to 4.0 seconds per 36-MB holographic fringe and under 1.0 seconds for a 6-MB full-color image. Analysis focuses on the trade-offs among compression ratio, image fidelity, and image depth. Hogel-vector bandwidth compression matches information content to the human visual system, achieving “visualbandwidth holography.” Holovideo may now be applied to visualization, entertainment, and information.

Hardware architecture for rapid generation of electro-holographic fringe patterns

This report describe the hardware architecture and software implementation of a hologram computing system developed at the MIT Media Laboratory. The hologram computing employs specialized stream-processing hardware embedded in the Cheops Image Processing system--a compact, block data-flow parallel processor. A superposition stream processor performs weighted summations of arbitrary 1D basis functions. A two-step holographic computation method--called Hogel-Vector encoding--utilizes the stream processors computational power. An array of encoded hogel vectors, generated from a 3D scene description, is rapidly decoded using the processor. The resulting 36-megabyte holographic pattern is transferred to frame- buffers and then fed to a real-time electro-holographic display, producing 3D holographic images. System performance is sufficient to generate an image volume approximately 100 mm per side in 3 seconds. The architecture is scalable over a limited range in both display size and computational power. The limitations on system scalability will be identified and solutions proposed.

Compact prototype one-step Ultragram printer

We describe a prototype reduced-size holographic stereogram printer capable of producing scalable, Ultragram-format hardcopy output. An analysis of the resolution requirements for high quality stereogram output with respect to the printing method and printer components is presented. A holographic optical element is combined with a pseudorandom band-limited diffuser to focus the spatially modulated object beam and provide Fourier-plane broadening, thus improving image quality. We analyze issues of image preparation time and integration of image rendering and exposure control to optimize system resource requirements.

New approaches to holographic video

Recent advances in both the computation and display of holographic images have enabled several firsts. Interactive display of images is now possible using the bipolar intensity computation method and a fast look-up table approach to fringe pattern generation. Full-color images have been generated by computing and displaying three color component images (red, green, and blue). Using parallelism to scale up the first generation system, images as large as 80 mm in all three dimensions have been displayed. The combination of multi-channel acousto-optic modulators and fast horizontal scanning continue to provide the basis of an effective real-time holographic display system.