Phase-only modulation using a twisted nematic liquid crystal television

Iterative Phase-Only Hologram Generation Based on the Perceived Image Quality

Image quality metrics are a critical element in the iterative Fourier transform algorithms (IFTAs) for the computer generation of phase-only holograms. Conventional image quality metrics such as root-mean-squared error (RMSE) are sensitive to image content and unable to reflect the perceived image quality accurately. This would have a significant impact on the calculation speed and the quality of the generated hologram. In this work, the structure similarity (SSIM) was proposed as an image quality metric in IFTAs due to its ability to predict the perceived image quality in the presence of the white Gaussian noise and its independence on the image content. This would enable IFTAs to terminate when further iterations would no longer lead to improvement in the perceived image quality. As a result, up to 75% of unnecessary iterations were eliminated by the use of SSIM as the image quality metric.

General theory of asymmetrical polarization-dependent optics in functional material-doped 90° twisted nematic liquid crystals

General theory, which can completely describe the asymmetrical optics in a functional material (FM)-doped 90° twisted nematic liquid crystals (TNLCs), is proposed using Cayley-Hamilton theorem and Jones calculus. The FMs, whose shape and size are similar to those of the adopted NLCs, can be aligned along the long axes of the NLCs. The FMs discussed herein are dichroic dye (DD) and polymer. The experimental results of asymmetrical transmission in DD-doped 90° TNLCs are consistent with the theoretical calculation. Such asymmetrical characterization can be further used in the current applications based on 90° TNLCs in all fields to obtain new potential functions.

Optimizing the diffraction efficiency of SLM-based holography with respect to the fringing field effect

The fringing field effect of liquid-crystal displays causes a crosstalk between neighboring pixels, so that a desired sharp phase edge gets blurred. This blurring effect influences the diffraction efficiency of holograms, which are displayed on the spatial light modulator (SLM). In this paper, we show two different simulation models for the SLM, one based on the measured subpixel Jones matrices of the SLM and the other based on a direction-dependent convolution model. Using these models we optimize different blazed gratings written in the SLM according to their diffraction efficiency followed by an experimental verification.

Spatial Light Interference Microscopy (SLIM) using twisted-nematic liquid-crystal modulation

We report the use of a twisted nematic liquid-crystal spatial light modulator (TNLC-SLM) for quantitative phase imaging. The experimental setup is a new implementation of the SLIM principle, which is a phase shifting, white light method for quantitative phase imaging. The approach is based on switching between the phase and amplitude modulation modes of the SLM. Our system is able to deliver a 0.99 nm spatial and 1.33 nm temporal pathlength sensitivity while retaining the optical transverse resolution. The system is implemented as an additional module mounted to a conventional microscope, which makes the system very easy to deploy and integrate with other imaging modalities.

Improvement of the performance of the twisted-nematic liquid-crystal display as a phase modulator

A twisted-nematic liquid-crystal display (TN-LCD) placed between two linear polarizers (P) generally produces coupled intensity and phase modulations. For the purpose of phase-only modulation, quarter-wave plates (QWPs) are often used in front of or behind the LCD. In this paper, we demonstrate theoretically and experimentally the QWPs' effect on the modulation properties of the TN-LCD based on the general Jones matrix descriptions for all the devices, which circumvents the inconvenience of the traditional method on the basis of the TN-LCD's internal parameters. We prove that the phase modulation depth of the TN-LCD can be further increased in the configuration of P1-QWP1-LCD-QWP2-P2 with each component properly oriented, provided that the mean intensity transmission is decreased to a lower level. By observing the diffracted patterns of the Ronchi phase grating or blazed grating addressed onto the TN-LCD, we verify the validity of the proposed method. Improved reconstructed image quality from the kinoform loaded on the TN-LCD is obtained in this configuration. This approach is valuable when the TN-LCD is employed as a phase modulator, especially for the modern, thinner TN-LCD.

Full-field phase modulation characterization of liquid-crystal spatial light modulator using digital holography

A direct quantitative phase measurement method to characterize intrinsic phase modulation from an entire active area of transmissive twisted-nematic liquid-crystal spatial light modulator (TN-LCSLM) is presented using digital holography (DH). The change in birefringence of liquid crystal material with respect to addressed gray scale produces phase modulation of wavefront transmitted through TN-LCSLM. Existing methods for phase modulation characterization of LCSLM mainly provides point measurement on its total active region. In this paper, the DH method is evolved to extract quantitative phase information of an entire active area from a single digital hologram formed using the complex wavefront transmitted through TN-LCSLM.

Extended phase modulation depth in twisted nematic liquid crystal displays

We show how the phase modulation depth in twisted nematic liquid crystal displays (TNLCDs) can be increased dramatically by selecting a polarization configuration with a reduced mean intensity transmission. This phenomenon, which we have validated with various devices, is shown here for a device that presents a phase-only modulation only slightly over π radians in our classical rotated eigenvector configuration, but it is capable of producing close to a 2π phase depth for a configuration with 5% mean intensity transmission. A quantitative explanation is presented by means of a phasor analysis of the TNLCD eigenvector projections over input and output polarization states. The proposed technique can be a very useful solution in modern TNLCDs that have a very thin liquid crystal layer and a reduced maximum achievable phase modulation.

Jones-matrix models for twisted-nematic liquid-crystal devices

Twisted-nematic liquid-crystal devices having high spatial resolution are suitable for spatial light modulators. Phase-modulation characteristics of the devices have been widely studied, but the phase delay calculated using a conventional Jones-matrix model is slightly different from that measured using an interferometer. We propose a modified model whose matrix components are described by angular parameters that are related to the distribution of twist and tilt angles inside the liquid-crystal layer through differential equations. The model is used to simulate phase-modulation characteristics, and the result agrees well with the experimentally measured phase delay.

Unique measurement of the parameters of a twisted-nematic liquid-crystal display

The parameters of a twisted-nematic liquid-crystal display (TN-LCD) are measured with no ambiguity when we measure the intensity transmittance of a system that simply consists of a TN-LCD, two polarizers, a quarter-wave plate, and a monochromatic beam. First we show analytically that the director angle can have a 90 degree ambiguity and the twist angle of the liquid-crystal molecules a 180 degree ambiguity. Then we uniquely measure the parameters by fitting the theoretical predictions to the intensity transmittance measured with and without the quarter-wave plate and by using the quasi local-adiabatic condition. The birefringence of the TN-LCD is measured next as a function of the applied voltage. We design a phase spatial light modulator by using the measured parameters and measure the phase delay of the output beam to excellent agreement with the theoretical prediction.

Phase calibration of spatially nonuniform spatial light modulators

A new 512 x 512 pixel phase-only spatial light modulator (SLM) has been found to deviate from being flat by several wavelengths. Also, the retardation of the SLM relative to voltage varies across the device by as much as 0.25 wavelength. The birefringence of each pixel as a function of address voltage is measured from the intensity of the SLM between crossed polarizers. To these responses are added a reference spatial phase measured by phase shifting interferometry for a single address voltage. Fits to the measured data facilitate the compensation of the SLM to a root-mean-square wave-front error of 0.06 wavelength. The application of these corrections to flatten the full aperture of the SLM sharpens the focal plane spot and reduces the distortion of computer-designed diffraction patterns.

Tunable phase-only optical filters with a uniaxial crystal

A novel method of fabricating phase-only optical filters that is based on the properties of a uniaxial crystal is proposed. With these optical filters, the phase differences are tunable among the different filter zones. Many focal patterns can be obtained if these optical filters are placed in front of a lens; furthermore, these optical filters can also be used to make up for the distortions in fabrications in which they were used only as untunable optical filters.

Hyperresolving phase-only filters with an optically addressable liquid crystal spatial light modulator

Hyperresolving (sometimes called 'superresolving' or 'ultraresolving') phase-only filters can be generated using an optically addressable liquid crystal spatial light modulator. This approach avoids the problems of low efficiency, and coupling between amplitude and phase modulation, that arise when using conventional liquid crystal modulators. When addressed by a programmed light intensity distribution, it allows filters to be changed rapidly to modify the response of a system or permit the investigation of different filter designs. In this paper we present experimental hyperresolved images obtained using an optically addressable parallel-aligned nematic LCD with two zone Toraldo type phase-only filters. The images are compared with theoretical predictions.

All-optical image processing with a supranonlinear dye-doped liquid-crystal film

We demonstrate a dynamic all-optical image-intensity-inversion technique that uses self- and mutual-phase-modulation effects with a highly nonlinear nematic liquid-crystal film placed in an intermediate focal plane. This process requires submilliwatt optical power, responds in a few milliseconds, and can be realized over a very broad spectral range.

Measurement of the phase modulation of liquid-crystal televisions by a noninterferometric technique

A simple method of measuring the phase-modulation properties of liquid-crystal televisions (LCTV's) that vary with the driving gray-scale level is presented. The theoretical derivation of the method is described. Compared with previous methods of measuring the phase shifts of LCTV's, this technique is noninterferometric and very simple. The experimental results of a LCTV are shown.

Nonlinear filtering for recognition of phase-encoded images

We investigate the use of Fourier plane nonlinear filtering for phase-encoded images. We investigate the performance of the nonlinear joint transform correlator and the nonlinearly transformed matched filter for phase-encoded images with different types of input noise. We use the peak-to-output-energy ratio, peak-to-sidelobe ratio, and discrimination ratio as the metrics for measuring the performances. We mathematically analyze the peak-to-output-energy ratio of the nonlinearly transformed matched filter for phase-encoded images with spatially nonoverlapping white noise. Computer simulations are provided to show the performance improvements of the nonlinear filtering techniques for the phase-encoded images. In comparison with linear filtering techniques, we find that the nonlinear filtering techniques substantially improve the performance metrics. From the computer-simulation results it can be seen that the nonlinear joint transform correlator performs better than the nonlinearly transformed matched filter in detecting phase-encoded targets in the presence of different types of noise, such as additive overlapping white noise, spatially nonoverlapping white background noise, spatially nonoverlapping colored background noise, and nontarget objects.

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.

Complex amplitude modulation by use of liquid-crystal spatial light modulators

We propose to study the conditions for implementation of complex amplitude modulation on standard liquid-crystal spatial light modulators when illuminated by polarized light. The spatial light modulators are used in a conventional configuration, i.e., the voltage is applied parallel to the wave-front propagation direction. The most commonly used liquid-crystal materials are compared and their usefulness in some general applications discussed. Their specificities with respect to different modulation types and application requirements are briefly described. Typical characteristics such as response time, modulation range, and wavelength insensitivity are also discussed. Finally, as an illustration, a first attempt at nomenclature is proposed for the case of a linearly polarized light.

Performance of a phase-transformed input joint transform correlator

Conventionally a detected image is represented by an intensity array owing to the square-law nature of most detectors. However, this does not mean that we have to restrict ourselves to using intensity images for the correlation process. Transforming intensity images into phase images before correlation, which can be easily realized by a phase-modulation spatial light modulator, offers an alternative approach for high-performance pattern recognition. A phase-transformed input joint transform correlator is investigated in detail in terms of pattern discriminability, detection efficiency, and noise robustness. We show that the phase-transformed joint transform correlator has higher pattern discriminability and detection efficiency than the conventional joint transform correlator, and it also offers a better trade-off between the pattern discriminability and noise tolerance. A proof-of-concept experiment is also provided.

Color encoding for polychromatic single-channel optical pattern recognition

The common multichannel system for recognizing colored images is replaced by a color-encoded single-channel system. Amethod inspired by the Munsell color system is used for encoding the different colors as phase and amplitude functions. It is shown that for many practical cases the phase information part of the color code is sufficient for obtaining good results. An implementation based on a liquid-crystal television panel that works in a phase-modulation mode is suggested. Computer simulations that demonstrate the capabilities of the suggested method are given as well as a comparison with previously published multichannel performance.

Multilayer associative memory and its hybrid optical implementation

We propose a multilayer associative memory with a winner-take-all operation on the inner product between an input and stored exemplars. The winner-take-all operation is performed by a unit-step operation with an adaptive-threshold strategy. We show that the multilayer-associative-memory unit-step operation with an adaptive-threshold strategy has a high noise immunity and a large storage capacity, and it is also capable of extending to a gray-level associative memory with a phase-representation technique. A hybrid optical implementation with a proof-of-concept experiment is also provided.

Multilevel phase- and amplitude-encoded modified-filter synthetic-discriminant-function filters

The performance of the modified-filter synthetic-discriminant-function (MfSDF) filter with multilevel phase and amplitude (MLAP) constraints is investigated with various in-plane rotated images from an in-class Bradley armored personnel carrier vehicle and an out-of-class Abram MI tank; this is of interest because of the commercial availability of liquid-crystal televisions, which are able to encode the gray-level amplitude and/or the discrete multilevel phase information. The evaluation is performed to explain better the image-distortion range that can be covered effectively by MLAP/MfSDF filters. The results show that the MLAP/MfSDF filter offers much-improved correlator system performance with a greater allowable image-distortion range while maintaining 100% discrimination between in-class and out-ofclass images; furthermore, it shows an improved ability to accommodate the input image noise when compared with the MfSDF filter with a binary phase-only constraint. Thus the MLAP/MfSDF can be implemented effectively by a hybrid optical/digital correlator system to track a vehicle or a tank dynamically as it moves along a random trajectory across the input field.

Phase-encoded input joint transform correlator with improved pattern discriminability

The concept of using phase-encoded input representation in a joint transform correlator is presented, in which we show that the phase-encoded input joint transform correlator is an optimal filtering system that improves detection efficiency and pattern discriminability.

Real-time binary phase holograms on a reflective ferroelectric liquid-crystal spatial light modulator

A ferroelectric liquid-crystal spatial light modulator with an active silicon backplane is used to implement reconfigurable reflective phase holograms. Optical results are presented for an optimized computergenerated Fourier hologram.

Spherical aberration correction using a liquid-crystal spatial-light modulator in off-axis electron holography

One can correct spherical aberration in a transmission electron microscope by using a newly developed aberration-correction method involving off-axis electron holography. In this method, a liquid-crystal spatial-light modulator (LC SLM) is employed during the holographic reconstruction step to compensate for spherical aberration. Application of this method to high-resolution off-axis electron holograms of fine gold particles is presented. The phase distribution of the corrected object wave is visualized by the Zernike phase-contrast method carried out with the same LC SLM.

Diffraction efficiency analysis of a parallel-aligned nematic-liquid-crystal spatial light modulator

An optically addressed parallel-aligned nematic-liquid-crystal spatial light modulator is developed for applications in optical information processing and interferometry. Its performance, including diffraction efficiency, is measured, and a theoretical analysis of diffraction efficiency is performed. A comparison between the experimental results and the theoretical analysis shows good agreement. The diffraction efficiency of near-sinusoidal gratings written on the device is of the order of 30%, which is close to theoretical maximum.

Real-time electron-holographic interference microscopy with a liquid-crystal spatial light modulator

An electron-holographic interference microscope that produces a time-sequential interference micrograph at a TV rate is developed. In this system, the electron off-axis hologram detected with a TV camera is transferred to a liquid-crystal spatial light modulator as a video signal. The liquid-crystal spatial light modulator can function as a thin amplitude hologram or a thin phase hologram. Time-sequential interference micrograph is obtained at a TV rate by superimposition of a plane reference wave onto the reconstructed object wave. Experimental results for observing a dynamic domain-wall motion in thin Permalloy film are demonstrated.

Experiments on a multichannel holographic optical switch with the use of a liquid-crystal display

A new configuration of holographic switches is proposed and verified for multichannel optical switching. Experimental 1 x 64 and 2 x 32 switching is achieved by using real-time binary phase-only holograms generated by a twisted nematic liquid-crystal display. This holographic free-space switching is applicable to photonic switching systems and optical interconnections.

Spatial-light-modulator-based electro-optical imaging system

We describe a novel electro-optical system that can image objects over a long range of distance without involving any mechanical movement.

Generation of programmable coherent source arrays using spatial light modulators

We demonstrate and characterize arrays of coherent focused spots generated by writing multiple Fresnel zone plates on optically and electrically addressed modulators. The programmable parameters of the array are its size (number of generated spots) and the transmissivity and focal length of each lens. As expected, phase modulators have a better conversion efficiency than amplitude modulators do.

Using the hybrid modulating properties of liquid crystal television

The phase modulating capabilities of a commercially available liquid crystal television (LCTV) have been investigated and applied to the joint transform optical correlator architecture. Operating the LCTV in a phase modulating mode requires a much smaller coherent light source while still producing a good joint transform power spectrum and good correlation signals.