Multiparameter tuning of surface-acoustic-wave filters.

An experimental methodology for tuning the frequency response of surface-acoustic-wave (SAW) filters after initial fabrication is demonstrated. The sensitivity of such a filter to perturbations in the length of individual electrodes of the interdigital transducer is determined from highly accurate swept-frequency measurements. Sensitivity measurements from several electrodes are then used to synthesize improved filter responses. Sensitivity measurements, measurement accuracy, and control of frequency-response sidelobes are demonstrated for devices fabricated on (YZ) lithium niobate. The tuning method provides predictions of improvement that closely match actual performance.

Electrostatic deposition of graphene.

Loose graphene sheets, one to a few atomic layers thick, are often observed on freshly cleaved HOPG surfaces. A straightforward technique using electrostatic attraction is demonstrated to transfer these graphene sheets to a selected substrate. Sheets from one to 22 layers thick have been transferred by this method. One sheet after initial deposition is measured by atomic force microscopy to be only an atomic layer thick (∼0.35 nm). A few weeks later, this height is seen to increase to ∼0.8 nm. Raman spectroscopy of a single layer sheet shows the emergence of an intense D band which dramatically decreases as the number of layers in the sheet increase. The intense D band in monolayer graphene is attributed to the graphene conforming to the roughness of the substrate. The disruption of the C-C bonds within the single graphene layer could also contribute to this intense D band as evidenced by the emergence of a new band at 1620 cm(-1).

Adaptive real-time architectures for phase-only correlation.

A video-rate correlator can be constructed with a phase-only spatial light modulator and a CCD camera. The phase of the Fourier transform of a signal and a reference image is determined by fringe-scanning interferometry. The two measured phase images are then subtracted. The optical Fourier transform of this difference produces the phase-only correlation response. This system can update both signal and reference images with live scenery. Currently, only the joint transform correlator has demonstrated this degree of adaptivity in real time. Physically compact versions of the correlator can be built with a single spatial light modulator and a Fourier-transform lens.

Deformable mirror device uses in frequency excision and optical switching.

A spatial light modulator is described which consists of a row of 1200 electrostatically deflectable mirror elements. This deformable mirror device is included in an acoustooptic spectrum analyzer and, as such, allows the removal of interfering signals from 333 frequency bands. Radiometric scans demonstrate the contrast and resolution possible with the device. Based on these results, the suitability of the device to frequency excisors and optical switches is considered.

Approximating fully complex spatial modulation with pseudorandom phase-only modulation.

Any desired diffraction pattern can be produced in the Fourier plane by the specification of a corresponding input-plane transparency. Complex-valued transmittance is generally required, but in practice phase-only transmittance is used. Many design procedures use numerically intensive, constrained optimization. We instead introduce a noniterative procedure that directly translates the desired but unavailable complex transparency into an appropriate phase transparency. At each pixel the value of phase is pseudorandomly selected from a random distribution whose standard deviation is specified by the desired amplitude. We also derive statistical expressions and use them to evaluate the approximation errors between the desired and achieved diffraction patterns.

Effects of systematic phase errors on phase-only correlation.

The performance of phase-only optical correlators is usually reduced if the filter-plane phase differs from that prescribed for the classical matched filter. Current spatial light modulators, which frequently produce less than 2π phase modulation, and interface circuits, which quantize or incorrectly amplify signals placed on the spatial light modulator, both can produce systematic phase errors. We examine these effects using a model of correlation-peak amplitude as a function of phase error. The correlation peak is reasonably approximated as the product of an average of unity-amplitude error phasors multiplied by the average amplitude across the filter plane. The trends predicted by this new model compare favorably with computer simulations that use gray-scale images.

Pseudorandom phase-only encoding of real-time spatial light modulators.

We previously proposed a method of mapping full-complex spatial modulations into phase-only modulations. The Fourier transform of the encoded modulations approximates that of the original complex modulations. The amplitude of each pixel is encoded by the property that the amplitude of a random-phasor sum is reduced corresponding to its standard deviation. Pseudorandom encoding is designed for phase-only spatial light modulators that produce 360° phase shifts. Because such devices are rare, experiments are performed with a 326°modulator composed of two In Focus model TVT6000 liquid-crystal displays. Qualitative agreement with theory is achieved despite several nonideal properties of the modulator.

Ternary pseudorandom encoding of Fourier transform holograms.

Pseudorandom encoding is a statistical method for designing Fourier transform holograms by mapping ideal complex-valued modulations onto spatial light modulators that are not fully complex. These algorithms are notable because their computational overhead is low and because the space-bandwidth product of the encoded signal is identical to the number of modulator pixels. All previous pseudorandom-encoding algorithms were developed for analog modulators. A less restrictive algorithm for quantized modulators is derived that permits fully complex ranges to be encoded with as few as three noncollinear modulation values that are separated by more than 180 degrees on the complex plane.

Pseudorandom encoding for real-valued ternary spatial light modulators.

Pseudorandom encoding with quantized real modulation values encodes only continuous real-valued functions. However, an arbitrary complex value can be represented if the desired value is first mapped to the closest real value realized by use of pseudorandom encoding. Examples of encoding real- and complex-valued functions illustrate performance improvements over conventional minimum distance mapping methods in reducing peak sidelobes and in improving the uniformity of spot arrays.

Modified minimum-distance criterion for blended random and nonrandom encoding.

Two pixel-oriented methods for designing Fourier transform holograms--pseudorandom encoding and minimum-distance encoding-usually produce higher-fidelity reconstructions when combined than those produced by each method individually. In previous studies minimum-distance encoding was defined as the mapping from the desired complex value to the closest value produced by the modulator. This method is compared with a new minimum-distance criterion in which the desired complex value is mapped to the closest value that can be realized by pseudorandom encoding. Simulations and experimental measurements using quantized phase and amplitude modulators show that the modified approach to blended encoding produces more faithful reconstructions than those of the previous method.

Random phase encoding of composite fully complex filters.

The mapping of complex-valued functions onto phase-only spatial light modulators is examined. Random phase encoding effectively adds amplitude control to the phase-only filter and can be used to trade off systematic errors of the phase-only filter for random errors. This is illustrated for the problem of recognizing a threedimensional object from arbitrary views. The complex-valued composite filters that constitute a filter bank design are encoded by phase-only and pseudorandom methods. The best recognition probabilities are achieved by blending the two methods so that only the smallest amplitudes are randomly encoded.

High-diffraction-efficiency pseudorandom encoding.

Pseudorandom encoding (PRE) is a statistics-based procedure in which a pure-phase spatial light modulator (SLM) can yield, on the average, the prescribed diffraction pattern specified by the user. We seek to combine PRE with the optimization of an aperture-based target function. The target function is a fully complex input transmittance, unrealizable by a phase-only SLM, that generates a prescribed light intensity. The optimization is done to increase the diffraction efficiency of the overall process. We compare three optimization methods-Monte Carlo simulation, a genetic algorithm, and a gradient search-for maximizing the diffraction efficiency of a spot-array generator. Calculated solutions are then encoded by PRE, and the resulting diffraction patterns are computer simulated. Details on the complexity of each procedure are furnished, as well as comparisons on the quality, such as uniformity of the output spot array.

Optical characteristics of a deformable-mirror spatial light modulator.

Some of the optical characteristics of a recently developed solid-state deformable-mirror spatial light modulator have been investigated. The device is composed of an array of 128 x 128 pixels, with each pixel consisting of four hinged reflective rectangular surfaces. Modulation at video frame rates has been achieved, providing real-time displays in coherent light, which may be useful for a variety of optical processing and computing applications.