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Ray matrices are a powerful tool for the analysis of optical systems. This technique is modified to include a diffractive optical element within the optical system. Several research applications are discussed, including optical Fourier transforms and imaging with diffractive optical elements.
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We report a multiple imaging capability of replicated binary Fresnel phase-encoded lenses written on programmable spatial light modulators (SLMs). These lenses produce a large number (up to 9 x 9) of equally intense replica images from either an external object or from a pattern which is encoded onto the SLM along with the phase-encoded lens. Theoretical details and experimental results using the magnetooptic spatial light modulator are presented.
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We report the use of two-dimensional, binary phase-only diffraction gratings written on a programmable magnetooptic spatial light modulator to interconnect optically an input laser beam to multiple output locations. We show that we can achieve programmable weighted interconnects between the source and two output locations as well as a fan-out capability to as many as 128 separate output locations.
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We report the writing of Fresnel phase-encoded lenses onto programmable spatial light modulators (SLM's). When the product of the phase-encoded lens and the two-dimensional Fourier transform of a desired output spatial pattern is written onto the SLM, the desired spatial pattern is focused at programmable distances from the SLM. More importantly the inverted version of the desired pattern normally produced is encoded onto a diverging beam and is not imaged. Theoretical analysis and experimental results using the magneto-optic SLM are presented.
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We describe a technique for reducing false signals from optical correlators using binary phase-only filters (BPOF's). Since the impulse-response function of the BPOF contains both the target object and the inverted version of it, the output consists of the correlation of the input object with both of these objects. In our research a Fresnel phase plate lens is encoded onto the BPOF. As a result the correlation with the desired target is on a converging beam, and the correlation with the undesired inverted image of the target is on a diverging beam. Experimental results show that these filters reject inverted input objects.
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We have previously reported a technique for suppressing one of the two first-order diffracted beams from binary phase-only gratings written onto spatial light modulators by writing the cosine and sine filters onto separate halves of a spatial light modulator. We report the use of this phase-encoding technique for constructing binary approximations to continuous phase-only filters for use in optical correlators. Computer simulations of these filters are given. These results show that our new filters do not recognize inverted occurrences of the input object in contrast to binary phase-only filters made using previous techniques. In addition, these filters yield a greatly improved SNR over earlier types of filters.
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We report a technique for reducing the edge-enhanced impulse response from binary phase-only filters (BPOFs). In this technique, the object used to make the filter is multiplied by a random binary pattern. Then the BPOF is constructed. Experimental details are presented.
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We show that image-coding filters can be easily constructed using the binary phase-only filter and implemented using the Semetex magneto-optic spatial light modulator, and experimental results are presented.
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We present a technique for obtaining improved performance of programmable binary phase-only spatial masks written onto spatial light modulators by suppressing one of the two first-order diffracted beams through spatial dispersion. Theoretical and experimental performance studies are presented showing the results of writing diffraction gratings on the magnetooptic spatial light modulator using this new technique. The method works well, although it is extremely sensitive to the optical quality of all the components.
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The Hughes liquid crystal light valve (LCLV) has been evaluated for its applicability in writing and reading binary phase-only filters (BPOFs) in optical correlators. Experimental measurements of relevant performance characteristics of the LCLV as well as experimental results demonstrating its use for reconstructing BPOF's are reported. We also find that this device allows a significant optical system throughput. In addition, we discuss generation of the BPOF with a MacIntosh computer system.
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Theoretical studies of the multiplexing capabilities of binary phase-only filters (BPOF) for use in optical correlator systems are presented. We show that the BPOF has an inherent capability for simultaneously recognizing an object and an inverted version of the object. More complex multiplexing capabilities are examined including (1) use of a BPOF made from eight rotated versions of a letter to recognize any of the rotated input letters, (2) use of a BPOF made using the fifty-two letters of the alphabet (upper and lower case) to recognize any one letter, and (3) use of a BPOF made from a complex sentence to pick out a desired word. Finally, we present additional information on the generation of the BPOF using a MacIntosh computer system.
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We describe a multichannel correlator/convolver architecture utilizing an acoustooptic light modulator for the 1-D input channel and a magnetooptic spatial light modulator (MOSLM) for the second 2-D parallel channel. The MOSLM allows greater parallelism to be implemented into this correlator/convolver design than was previously reported. We demonstrate the implementation of 24 parallel channels with a 48 x 48 device. We present experimental data and discuss ways of increasing the number of parallel channels using commercially available MOSLMs and other previously discussed techniques such as frequency multiplexing. We show that over 2000 parallel channels are possible at 32-bit accuracy. A technique for obtaining a limited gray scale is also discussed.
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Theoretical studies of the performance capabilities of binary phase-only filters (BPOFs), constructed using both Fourier and Hartley transforms, are presented. A thorough analysis of the Fourier BPOF is given. We show that, although BPOFs constructed using Fourier transforms perform well in optical correlator systems, they are also subject to additional noise sources and have the possibility of generating large false correlation signals. We then present an analysis of BPOFs constructed using the Hartley transform. We show that BPOFs made using the Hartley transform provide superior false correlation rejection and more uniformly sized correlation signals for heavily multiplexed BPOFs, compared with those made using the Fourier transform. We also present a technique for constructing Hartley BPOFs. Therefore, although it is well known that the quality of the correlation signal depends on the object, this work demonstrates that the quality of the correlation signal can also depend on the technique used in the synthesis of the BPOF.
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The potential of the extremely inexpensive Radio Shack liquid-crystal television (LCTV) as a two-dimensional spatial light modulator has been investigated. The LCTV modulates the transmission of coherent or incoherent light and can either be electronically addressed through a microcomputer or optically addressed with a TV camera. We have measured the transmission characteristics of the device, examined its diffraction pattern, and tested its use as an input device for an optical correlator. We have discovered that, with proper modifications, it has potential for optical-data-processing applications.