Fundamental properties of spatial light modulators for Fourier transform applications

The operation of 2-D Fourier tTransform has been the foundation of most of the coherent optical processors developed. Two prominent examples are the tilted-plane optical processor for SAR data and the Fourier plane image correlator/processor. In all of these cases the processing throughput of the system is limited by the space-bandwidth product and the frame-time of the input (spatial light modulators - SLMs) and output (detector arrays) transducers (typically 512 x 512 at 30 frames/s). The passive optical elements (e.g. lenses) are, however, capable of handling much larger size images (4000 × 4000). In this paper we describe a system design that uses several discrete SLMs and combines their outputs coherently to optically synthesize a much larger size image that can then be processed in parallel by the Fourier transform-based optical processor. The output (power spectrum or correlation) can be similarly split optical and detected by several separate detector arrays. We call this concept "Optical MOSAIC Processors" since it is similar to puting several individual tiles together to cover a large area. The combining of the subimages in the input and splitting them in the output can be accomplished using prisms/gratings and mirrors or via coherent fiber bundles. The randomization of the optical wavefront in the input can be corrected via a phase correcting hologram. In this paper we will describe several promising designs and outline potential applications.

Liquid crystal on silicon (LCoS) spatial light modulators (SLMs) are versatile scientific tools relevant to an increasingly wide variety of research and technological applications including digital holography, wavefront correction, optical tweezing, and non-mechanical beam steering to name a few. Since SLMs are used in a multitude of different ways, some aspects of device performance (e.g., response time) are crucial to certain applications while being irrelevant to others. In this work we couple our standard SLMs with a thermo-electric cooler, allowing for tunability of the device operating temperature from 0° to 75 °C. We show that there is an inherent tradeoff between the liquid crystal response time and the phase stability of an SLM, and that the operating temperature offers a means of controlling this tradeoff. Furthermore, this paper aims to provide the reader with a brief but thorough explanation of SLM operating principles and device structure, defines the performance metrics of the SLM, and provides a methodology for measuring the specifications. By allowing control over the SLM operating temperature and detailing how temperature affects device functionality, SLM users are afforded greater experimental flexibility and will be better able to tailor the performance of their device for the given project or application at hand.

The behavior of a binary, spatial light modulator (SLM) in both the input and Fourier planes of a coherent optical correlator system is investigated using both a computer model and a working laboratory correlator. The computer model, based upon the fast Fourier transform, simulates the effect of the SLMs in the system and permits the examination of such parameters as input noise and shifts and their effect upon the theoretical output. The experimental correlator contains a SLM in the input plane operating in the binary amplitude mode and a SLM in the Fourier plane operating in the binary phase-only mode. The output of the system is compared to the model and analyzed. Significant performance results obtained with the computer model are also examined.

We present a general analytical treatment of optical correlation in correlators that use pixellated spatial light modulators with transmissive (or reflective) dead zones in both the input and filter planes. The active areas of the pixels modulate the light intensity while the dead zones transmit (or reflect) all of the light. Our model can predict the changes in the correlation peak and the signal-to-noise ratio with changes in dead zones, calculated in Part I [Appl. Opt. 32, 6527(1993)] from computer simulations. This model is also a general one: It applies to correlators in which one spatial light modulator contaions only opaque dead zones while the other contains only transmissive dead zones; it also applies to the case in which any one spatial light modulator contains both opaque and transmissive dead zones.

We investigate the possibility of using a real-axis spatial light modulator (SLM) to realize complex-amplitude modulation with full coverage over the unit circle. The real-axis SLM produces a pixelated bipolar-amplitude wavefront. Each pixel is basically a spatial pulse width with the signal information being carried by the pulse's amplitude. Data streams generated in this manner have real and imaginary components due to the relative even and odd symmetry of the pulse amplitude modulation. When the pulse rate is twice the minimum Nyquist rate for band-limited amplitude modulation, it is possible to resolve the signal into its quadrature phase components (real and imaginary terms). By changing the relative amplitude of these quadrature phase terms, any value within the complex plane is accessible. Since the SLM does not have any optical gain, coverage is limited to the unit circle in the complex plane.

A hybrid correlation system incorporates an optical correlator, spatial light modulators(SLM), digital cameras and a computer. Spatial light modulators and cameras are used to dynamically update the input and the spatial filter. The hybrid correlation system integrates the parallel processing capability of the optical correlator and the flexibility of the digital system. It can be used as a high-speed multi-function information processor. This paper focuses on the design and fabrication of a hybrid optical correlator and how it is used as an intelligent instrument. We address the issues of rigorous requirements for filter registration and matched filtering by proposing practical approaches. We include the analysis and use of intensity filters based on commercial SLMs for real-time pattern recognition. We present the engineering details of a specific hybrid optical correlator for applications to the real-time identification of an aircraft.

Diffractive optical element (DOE) design techniques can be applied to the generation of pattern recognition filters for optical correlators, in which case the spatial light modulator (SLM) in the filler plane is thought of as a real-time DOE. The designer must first select the desired complex pattern recognition filter and then apply DOE design techniques to map the fully complex function onto the limited dynamic range SLM. To illustrate the procedure, we apply the techniques to the problem of implementing a matched filter with limited dynamic range Fourier plane SLM’s. We use computer simulations to evaluate the effectiveness of the technique. We quantify the performance by measuring the mean squared error between the ideal matched output and output from quantized filters. Numerical simulations indicate that the DOE method yields a significant improvement over direct quantization. The improvement in mean squared error comes, however, at the expense of light efficiency. The DOE technique has been applied to design of matched filters with binary phase, ternary phase, and phase-only SLM’s for coherent as well as incoherent optical correlators. The additional phase freedom in the incoherent design results in improved performance, but incoherent systems are limited to correlation with real positive reference scenes. A proof-of-principle laboratory experiment has been constructed to complement the numerical simulations.

The traditional joint transform correlator (JTC) uses two spatial light modulators (SLMs); one to display an input scene, the other to display a filter. Each SLM requires separate transform lenses and addressing beams, as well as separate cameras to detect the Fourier transform (FT) of the scene it displays. The use of two SLMs can rapidly become expensive in terms of cost and space. The single modulator implementation of the joint transform correlator may alleviate this apparent redundancy in architecture. In the single modulator configuration the input scene and filter are alternately displayed on one SLM and addressed by a single path of light. While the SLM displays the input scene the transform plane camera detects the FT of the input scene. This is the joint transform filter. The input scene is then replaced by the filter on the SLM. While the filter is being addressed, the transform plane camera is detecting the resulting correlation signal. A driver circuit has been constructed which will multiplex the input scene and the filter onto the SLM. In addition, a demultiplexer is provided to route the filter and correlation signal, as detected by the transform plane camera, onto two separate video lines.

The use of a binary, magneto-optic spatial light modulator as an input device and as a spatial filter in a VanderLugt correlator is investigated. The statistics of the correlation that is obtained when the input image or the spatial filter is thresholded are estimated. Optical correlation using the magneto-optic device at the input and Fourier planes of a VanderLugt correlator is demonstrated experimentally.

Various nonlinear mapping techniques have been investigated for exploiting the restrictive characteristics of available spatial light modulators (e.g., phase-only or binary phase-only) and/or to modify the performance of coherent optical correlators. The phasewith- constrained-magnitude filter (PCMF) is a practical complex spatial filter realizable with today’s technology. It relies on the coupling between magnitude and phase transmittance exhibited by certain types of spatial light modulators. It requires relatively little computational effort to implement, and its performance has been shown to compare quite favorably with that of phase-only filters. In this paper we review the basic PCMF concept and show how performance of the PCMF can be improved by modifying the basic PCMF algorithm in two ways: (1) by setting the magnitude transmittance of the spatial light modulator to its lowest achievable value for a chosen set of low spatial frequency components and (2) by adjusting the values of the desired spatial frequency distribution relative to the available dynamic range of the spatial light modulator. The second method, in particular, can be used to make the PCMF perform more like an inverse filter or more like a matched filter, depending on the desired results.

A computer interfaced, 5000 X 7500 picture element, 20,000 X 30,000 addressable position, spatial light modulator (SLM) system for ultra high resolution optical processing applications is described. The system consists of a host computer such as an IBM PC, electronics and optics with beam position feedback to rapidly and precisely scan a focussed laser beam over the writing area of the SLM, and an erasable, editable, SLM with nonvolatile storage of the image written by the scan system. Because the image is stored by the SLM, no periodic electronic refresh is required. The resolution and information content achieved by this SLM system is higher than that of professional quality color film. Potential applications include optical correlation, optical processing of photographic quality information, electronic holography and optical computing.

We have designed and constructed a small number of prototype spatial light modulators (SLMs) based on a pixel array of 512 x512. The digital CMOS backplane allows fast writing of binary data onto the FLC layer for optical readout. We anticipate the use of the design in coherent applications such as optical correlators and programmable holograms as well as incoherent applications such as miniature displays.

Engineering implementation of a hybrid optical correlator using SLMs

The effectiveness of utilizing spatial light modulators (SLMs), developed at Sanders, for reducing some of the critical bottlenecks inherent within the Hyperspectral Imaging (HSI) chain will be presented. Specifically, the more common classification, detection, and endmember selection algorithm used in HSI, which are suitable for optical implementation, are presented here. These algorithms were reformulated for implementation on a compact Vander- Lugt correlator based on Sanders' multi-level quantum well (MQW) spatial light modulator (SLM). Sanders devices are GaAs Fabry-Perot vertical cavity multiple quantum well (MQW) SLMs consisting of MQW optical chips flip-chip bonded to Si/CMOS driver circuitry. Details of the reformation of Pixel Purity Index, an endmember selection algorithm, to the optical correlator is presented as well as a projection of its performance based on software simulations. In addition, hardware results are presented for Spectral Angle Mapper based on a Vander-Lugt implementation using Sanders 128 X 128 binary SLMs. An opto-electronic hyperspectral workstation accelerator is proposed which is based on a Vander-Lugt correlator using Sanders' MQW-SLMs and FPGA- based compute nodes and has the capability of 6.4 Million 1D correlations per second for HSI endmember selection, classification and detection.

Mueller–Stokes polarimetry is emerging as a prominent noninvasive imaging technique to study the structural characteristics of an anisotropic medium. Spatial light modulator (SLM) is a programmable liquid crystal device (LCD), which is used to modulate the amplitude, phase, and polarization of light. The compact design and cumbrous manufacturing process of SLM requires its polarimetric calibration prior to its utilization for various applications. In this study, we experimentally demonstrate Mueller–Stokes imaging of a reflective-type SLM (Holoeye, LCR-720) to calibrate its polarization modulation characteristics with respect to its dynamic gray value range (0–255) at different spatial locations of SLM screen. Mueller matrices at 18 different gray values of SLM at an interval of 15, that is, at gray values 0, 15, 30, up to 255 have been experimentally measured using an improvised Mueller matrix imaging polarimeter (MMIP). Crucial polarimetric characteristics, that is, diattenuation, polarizance, state of polarization (SOP), depolarization, and retardance have been estimated with respect to the gray value range of SLM. Significant polarization modulation characteristics [diattenuation (0.08–0.3), polarizance (0.02–0.2), and retardance (0 to π)] have been determined for the SLM. These results indicate that the SLM exhibits spatially variable depolarizing nature and hence it is not perfectly homogeneous in structure. Therefore, it is expected that the outcomes of this study would be helpful for exploring the applicability of Mueller–Stokes polarimetry in advancement of LC technology.