Coupled Amplitude Modulation Research Articles

Analysis of multiple internal reflections in a parallel aligned liquid crystal on silicon SLM.

Multiple internal reflection effects on the optical modulation of a commercial reflective parallel-aligned liquid-crystal on silicon (PAL-LCoS) spatial light modulator (SLM) are analyzed. The display is illuminated with different wavelengths and different angles of incidence. Non-negligible Fabry-Perot (FP) effect is observed due to the sandwiched LC layer structure. A simplified physical model that quantitatively accounts for the observed phenomena is proposed. It is shown how the expected pure phase modulation response is substantially modified in the following aspects: 1) a coupled amplitude modulation, 2) a non-linear behavior of the phase modulation, 3) some amount of unmodulated light, and 4) a reduction of the effective phase modulation as the angle of incidence increases. Finally, it is shown that multiple reflections can be useful since the effect of a displayed diffraction grating is doubled on a beam that is reflected twice through the LC layer, thus rendering gratings with doubled phase modulation depth.

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.

Genetic optimization of modulation characteristics for two twisted nematic liquid crystal spatial light modulators

A single twisted nematic liquid crystal spatial light modulator may suffer from coupled amplitude modulation and a phase modulation capability of less than 2π, although almost all panels can achieve π. Two twisted nematic liquid crystal panels can be combined in an optical system to produce a total phase modulation of at least 2π, and a minimal coupled amplitude modulation. A genetic algorithm is used to optimize the combined modulation characteristics of two liquid crystal panels in a multiplicative architecture. Simulation results and experimental verification are presented which show a substantial reduction in the combined amplitude modulation, and a total phase modulation of 2π.

Wavelength dependence of twisted nematic liquid crystal phase modulators

Many twisted nematic liquid crystal spatial light modulators suffer from limited phase modulation capability and coupled amplitude modulation. In particular, a phase modulation capability of less than 2 π radians is a severe limitation. Phase modulation is wavelength dependent. We examine the effect of changing the operating wavelength on the phase and amplitude modulation characteristics of a commercial liquid crystal spatial light modulator. Comparisons are made with a double pass configuration which can also increase the phase modulation capability.

Theory and optical implementation of the geometrical approach of multiple circular harmonic filters

The circular harmonic filter contains only one component of the image. Its discrimination capability has been questionable. The geometrical approach of multiple circular harmonic filters uses relative locations of the correlation peaks as the rotation-, shift-, and intensity-invariant features for pattern recognition. Each feature depends on the entire image. This approach has a good discrimination capability. Optical real-time implementation of the on-axis continuous phase-only circular harmonic filters by the use of a commercial liquid-crystal television is shown. A harmonic analysis shows that the phase-mostly filter can tolerate coupled amplitude modulation at the acceptable expense of the output signal-to-noise ratio. An optical experiment of the geometrical approach of multiple circular harmonic filters for a multiple-image input is described. The cross-correlation peaks between the individual filters and the clutter are eliminated, because they are not in good locations.

Optical on-axis real-time phase-dominant correlator using liquid crystal television

We use a commercially available liquid crystal television (LCTV) for encoding the on-axis phase-only filter (POF) in a real-time VanderLugt-type optical correlator. Diffraction theory, computer simulation, and optical experiments show that the coupled amplitude modulation and the phase mismatching in the LCTV yield a zero-order spot in the response of the POF and reduce the diffraction efficiency to about 60 to 70%. The correlation output of the filter is a superposition of the POF correlation peak and an image of the input. The filter, referred to as the phase-dominant filter, behaves like the POF with advantages of on-axis correlation, high light efficiency, and utilization of all the available space bandwidth product of the LCTV. Optical experimental results are shown.