Ignacio Moreno

Encoding amplitude information onto phase-only filters

We report a new, to our knowledge, technique for encoding amplitude information onto a phase-only filter with a single liquid-crystal spatial light modulator. In our approach we spatially modulate the phase that is encoded onto the filter and, consequently, spatially modify the diffraction efficiency of the filter. Light that is not diffracted into the first order is sent into the zero order, effectively allowing for amplitude modulation of either the first-order or the zero-order diffracted light. This technique has several applications in both optical pattern recognition and image processing, including amplitude modulation and inverse filters. Experimental results are included for the new technique.

Polarization eigenstates for twisted-nematic liquid-crystal displays

We derive theoretical expressions for the eigenvalues and the eigenvectors for a twisted-nematic liquid-crystal display (LCD) as a function of the twist angle and the birefringence by use of the Jones-matrix formalism. These polarization eigenvectors are of particular interest for phase-only transmission because they propagate unchanged through the display. We find that the eigenvectors are elliptically polarized and that the ellipticity changes as a function of the birefringence of the LCD (which is proportional to the external voltage applied to the display). We can define an average eigenvector over a desired range for the applied voltage. We show, using Jones matrices, how this average eigenvector can be generated using a quarter-wave plate and a linear polarizer having appropriate orientation angles. Using this average eigenvector, we show that superior phase-only operation can be obtained over a given operating range for the LCD compared with other approaches.

Modulation light efficiency of diffractive lenses displayed in a restricted phase-mostly modulation display.

We present an analysis of the diffraction efficiency of diffractive lenses displayed on spatial light modulators that depends on the modulation response of the display. An ideal display would produce continuous phase-only modulation, reaching a maximum phase-modulation depth of 2pi. We introduce the concept of modulation diffraction efficiency that accounts for the effect of nonlinearities only in the phase modulation of the display. We review a diffractive model with which to evaluate this modulation efficiency, including modulation defects such as nonlinear phase modulation, coupled amplitude modulation, phase quantization, and a limited modulation depth. We apply this diffractive model to Fresnel lenses and show that these modulation defects produce a lens multiplex effect. Finally we demonstrate that the application of a minimum Euclidean projection principle leads to high modulation diffraction efficiency even if the phase-modulation depth is much less than 2pi. We demonstrate that the modulation efficiency can exceed 90% for a modulation depth of 1.4pi and can exceed 40% (the equivalent for a binary phase element) for a modulation depth of only 0.7pi. Experimental results from use of a twisted nematic liquid-crystal display are presented to confirm these conclusions.

Anamorphic and spatial frequency dependent phase modulation on liquid crystal displays: optimization of the modulation diffraction efficiency

In this work we present experimental evidence of an anamorphic and spatial frequency dependent phase modulation in commercially available twisted nematic liquid crystal spatial light modulators. We have found that the phase modulation depth depends on the magnitude of the local spatial frequency component along the horizontal direction. Along the vertical direction the phase modulation depth does not depend on the spatial frequency. This phenomenon is related with the electronics driving the device and in no way related to liquid crystal physics. It causes a reduction of the optical efficiency of a diffractive optical element displayed onto this type of modulator. We present an algorithm to correct this effect and more efficiently display a diffractive optical element. We apply it to the particular case of a Fresnel lens. Experimental results that confirm the improvements in the efficiency of the displayed diffractive lens are presented.

Fully complex synthetic discriminant functions written onto phase-only modulators

Synthetic discriminant functions (SDFs) are an effective tool for pattern-recognition applications. However, their experimental implementation is difficult because of the difficulty in writing full complex modulation functions onto spatial light modulators (SLMs) with restricted coding domains. Iterative methods are required for the implementation of SDF filters in real SLMs. A great deal of experimental research has been done with phase-only filters because they can be successfully implemented with liquid-crystal SLMs. We have recently introduced a technique for encoding arbitrary amplitude information onto the phase-only filter, thus allowing us to encode an arbitrary complex function onto a phase-only SLM. We apply this technique to the generation of arbitrary complex SDF filters, thus avoiding the necessity of iterative algorithms. We examine the discrimination capabilities of fully complex SDF filters designed with different parameters and constraints. Experimental results obtained with liquid-crystal SLMs are included.

COLOR PATTERN RECOGNITION WITH CIRCULAR COMPONENT WHITENING

Polychromatic object recognition based on circular whitening preprocessing of red-green-blue components and multichannel matched filtering is described. Computer simulations and experimental results are provided to facilitate recognizing a color target among objects of similar shape but with different color contents. Experimental results are obtained with an optical correlator with two spatial light modulators, one to introduce the scene and the second one to introduce the filter.

Color component transformations for optical pattern recognition

Several elementwise component transformations performed over primary color image components (RGB) before optical multichannel correlations are proposed to improve real-time multispectral pattern recognition. The first transformation is deduced from the theory of the optimal filter for object location and recognition extended to multispectral images. Several modifications of this transformation are studied. We investigate these transformations in terms of noise robustness and discrimination capability. Computer simulation with noisy input images for various kinds of correlation filter are presented to illustrate improvement of color pattern recognition by using the proposed transformations. Experimental results are also presented.

REAL-TIME BINARY-AMPLITUDE PHASE-ONLY FILTERS

A real-time binary-amplitude phase-only filter (BAPOF) implemented in available phase-only modulators is presented. The BAPOF has an amplitude transmission equal to one only in a region of support, while the transmission is equal to zero in the complementary region. To implement zero transmission in a phase-only modulator we propose to add a linear phase to the region of support. In this way the correlation desired is obtained off axis. Computer simulations and experimental results obtained with this technique are given.

Twist angle determination in liquid crystal displays by location of local adiabatic points

In this work we present a method for the determination of the twist angle of an arbitrary twisted nematic liquid crystal spatial light modulator. The method is based on the location of local adiabatic points, i.e., situations in which the liquid crystal SLM acts only as a rotation device. For these cases, the rotation induced on the polarization of the incident beam is equal to the twist angle. Consequently, the twist angle can be determined with high precision. We show that local adiabatic regime may be achieved in two ways, either by changing the incident beam wavelength, or by applying a voltage to the electrodes of the display. However, the simple model that describes the SLM in the off-state, may break down when a voltage is applied to the display, and it may affect the local adiabatic behaviour. We present theoretical and experimental results.

Bessel function output from an optical correlator with a phase-only encoded inverse filter

We report on a technique for producing a Bessel function correlation output for an arbitrary input pattern. The central dark spot at the center of the Bessel function correlator output is narrower than the width of the normal correlation spot and can be extremely useful for locating the center of the correlation signal. The Bessel function is produced by convolution of the extremely sharp correlation produced by an inverse filter with the Bessel function and is encoded with a single phase-only liquid-crystal spatial light modulator. To encode amplitude information on the filter, we spatially modulate the phase encoded on the filter. Amplitude modulation is obtained by modulation of the diffraction efficiency of the phase grating. Experimental results are presented.