Steven C. Gustafson

Implementation of hexagonal micromirror arrays as phase-mostly spatial light modulators

Hexagonal micromirror arrays and associated test structures have been fabricated using a commercial surface-micromachining process. The hexagonal micromirrors are 50 micrometers across and are arranged in a hexagonal array of 127 mirrors with 75 micrometers center-to-center spacing between nearest micromirrors. Each micromirror is supported by three flexure hinges, each of which surrounds one third of the micromirror perimeter. Each micromirror in the array can be displaced independently through a vertical distance of over 1 micrometers by a voltage applied to an underlying address electrode. The flexures and other highly diffracting or poorly reflecting areas can be covered by a statinary reflecting plate with holes that expose the moving micromirrors. These micromirror arrays function as efficient phase-mostly spatial light modulators. Applications for these micro-opto-electro-mechanical systems include optical processing, coherent beam shaping, and adaptive optics. This design has several important advantages. First, the hexagonal micromirror and array geometries maximize the active surface area of the array. Second, the use of three flexures instead of four, as is typical for square phase-mostly micromirrors, lowers the required drive voltage. Third, the reflecting cover plate ensures that light efficiency is maximized and that a substantial stationary coherent reference plane is provided. Design considerations for fabricating the arrays in commercial surface mciromachining processes are discussed. The deflection versus voltage behavior of the hexagonal micromirror is determined analytically and experimentally. Test results are used to design the next generation array.

Multiperspective autostereoscopic display

We present a design for a 3D display system that is simultaneously autostereoscopic (no viewer eyewear is required), multiperspective or look-around (horizontal parallax is achieved without head tracking), raster-filled (all pixels have gray scale), and dynamic (live or real-time scenes may be displayed). This system will enable the demonstration of improved pilot performance and situation awareness due to multiperspective (i.e., look-around) viewing capability. The system uses twenty separate small liquid crystal televisions (LCTVs) with corresponding perspective views projected onto a pupil-forming screen consisting of a Fresnel lens and a pair of crossed lenticular arrays. The system will provide design data necessary for the development of a more compact and optically efficient system that uses digital micromirror devices instead of LCTVs.

Interferometric characterization of the flexure-beam micromirror device

The flexure-beam micromirror device (FBMD) developed by Texas Instruments, Inc., is presently being considered for use in communication and imaging systems. This device consists of thousands of individually addressable micromirror elements with phase-mostly responses, greater than 70% active area, and response times of 10 microseconds. Accurate determination of individual mirror element amplitude and phase responses versus address voltage is important for understanding the effect this device will have in the various applications. an experimental setup based on a laser microscopic interferometric technique was used to precisely map the surface displacement of individual mirror elements as a function of address voltage. The test structure consisted of an 8 X 8 array of 25 X 25 micrometers square flexure-beam elements. A phase response of greater than 2(pi) radians at a wavelength of 632.8 nm was observed for address voltages ranging from 0 to 5.8 V. The phase versus voltage relationship is shown to be nonlinear.

Convolver-based optical systolic processing architectures

Optical systolic processors perform rapid parallel multiplications of vector and matrix elements. These multiplications may be performed by convolving the digits of individual numbers. Current transducers (particularly acousto-optic cells) make time-domain convolution the method of choice. A time-domain convolver can operate in time-integrating or space-integrating modes. These two modes can be considered as variations of a basic multiplier unit. Starting with the basic multiplier, four matrix-vector and two matrix-matrix multipliers can be derived. Some of these processors are new, and some have been previously identified. Within this unifying framework the perfor-mance of all these processors may be analyzed, and design trade-offs may be identified.

Microactuated mirrors for beam steering

The design, fabrication, and potential performance of micro- actuated mirrors for beam steering are considered. Micro- actuators are by definition small devices that implement small displacements; they typically function using either electrostatic attraction or thermal expansion and are much smaller and less expensive than voice coil, piezoelectric stack, and related macro-actuators. Mirrors for use with micro-actuators may consist of rigid optically flat plates, continuous deformable membranes of facesheets, or arrays of elements with many possible element shapes, spacings, and displacement patterns. In general, the number of potentially practical micro-actuated mirror designs for beam steering increases as angular range, aperture size, steering speed, optical quality, and optical power requirements decrease.

Micromirror arrays for coherent beam steering and phase control

Micromirror arrays have been designed, fabricated, and tested that can steer coherent beams and that can simultaneously implement continuous phase control for beam shaping or aberration correction. A typical micromirror consists of a polysilicon plate (metalized for reflection) that is less than 100 microns in maximum dimension. Each micromirror is suspended a few microns above a polysilicon electrode by flexure hinges, and potentials of less than 50 volts applied to the electrodes displace the micromirrors over continuous ranges. Applications for arrays of these micromirrors include adaptive optics, active optical interconnections, and laser radar and communications.

Micromirror arrays for active optical aberration control

Micromirror arrays are being developed that can have up to tens of thousands of micromirror elements, each as small as 20 microns on a side, each spaced relative to neighbors so that optical efficiency exceeds 90 percent, and each individually controlled with response times as small as 10 microseconds for piston-like phase-mostly displacements that cover more than one- half optical wavelength. These arrays may be well suited for active aberration control of the focused coherent beams used in many applications, including optical disk storage, optical scanning, and laser radar systems. Active aberration control requires determination of the voltage supplied to the micromirror array elements so that constructive and destructive interference in light reflected from many elements yields the desired result. This paper discussed an approach in which the voltages are determined off-line by simulated annealing optimization and stored for real-time use.

Optimal reconstruction of missing-pixel images

A basis-function technique for reconstructing images with missing pixels is described. This technique yields optimal reconstructed image smoothness in that each basis-function width is maximized consistent with an acceptable level of computational effort.

Flexure-beam micromirror spatial light modulator devices for acquisition, tracking, and pointing

The new flexure-beam micromirror (FBM) spatial light modulator devices developed by Texas Instruments Inc. have characteristics that enable superior acquisition, tracking, and pointing in communications and other applications. FBM devices can have tens of thousands of square micromirror elements, each as small as 20 microns on a side, each spaced relative to neighbors so that optical efficiency exceeds 90 percent, and each individually controlled with response times as small as 10 microseconds for piston-like motions that cover more than one-half optical wavelength. These devices may enable order-of-magnitude improvements in space-bandwidth product, efficiency, and speed relative to other spatial light modulator devices that could be used to generate arbitrary coherent light patterns in real time. However, the amplitude and phase of each mirror element cannot be specified separately because there is only one control voltage for each element. This issue can be addressed by adjusting the control voltages so that constructive and destructive interference in the coherent light reflected from many elements produces the desired far field coherent light pattern. Appropriate control voltages are best determined using a robust software optimization procedure such as simulated annealing. Simulated annealing yields excellent results, but it is not real time (it may require hours of execution time on workstation-class computers). An approach that permits real-time applications stores control voltages determined off-line by simulated annealing that produce key desired far field coherent light beam shapes. These stored results are then used as training data for radial basis function neural networks that interpolate in real time between the training cases.

Design of a real-time unskeletonized autostereoscopic display system enabled by new technology

The design of a 3D display system that is simultaneously autostereoscopic, look-around, raster-filled, and dynamic and that is enabled by new digital micromirror device technology is discussed.