Phase-only modulation of a twisted nematic liquid-crystal TV by use of the eigenpolarization states

Mueller matrix imaging microscope using dual continuously rotating anisotropic mirrors

We demonstrate calibration and operation of a Mueller matrix imaging microscope using dual continuously rotating anisotropic mirrors for polarization state generation and analysis. The mirrors contain highly spatially coherent nanostructure slanted columnar titanium thin films deposited onto optically thick titanium layers on quartz substrates. The first mirror acts as polarization state image generator and the second mirror acts as polarization state image detector. The instrument is calibrated using samples consisting of laterally homogeneous properties such as straight-through-air, a clear aperture linear polarizer, and a clear aperture linear retarder waveplate. Mueller matrix images are determined for spatially varying anisotropic samples consisting of a commercially available (Thorlabs) birefringent resolution target and a spatially patterned titanium slanted columnar thin film deposited onto a glass substrate. Calibration and operation are demonstrated at a single wavelength (530 nm) only, while, in principle, the instrument can operate regardless of wavelength. We refer to this imaging ellipsometry configuration as rotating-anisotropic-mirror-sample-rotating-anisotropic-mirror ellipsometry (RAM-S-RAM-E).

Holographic contact lens display that provides focusable images for eyes

In this paper, we propose a holographic image generation technique for contact lens displays. The proposed technique employs a phase-only spatial light modulator (SLM), a holographic optical element (HOE) backlight, and a polarizer. The proposed holographic technique can generate 3D images apart from the contact lens displays. Therefore, the eyes can focus on the 3D images while simultaneously observing the real scene through the phase-only SLM and the HOE backlight, which provides see-through capability. A bench-top experimental system was constructed to verify the far-distance image generation capability and see-through function.

Single-shot wavelength-selective quantitative phase microscopy by partial aperture imaging and polarization-phase-division multiplexing

We propose a single-shot wavelength-selective quantitative phase microscopy by annular white-light illumination, polarization-phase-division, and parallel phase-shifting. Compared to conventional multi-wavelength incoherence digital holography, the proposed microscopy presents the following merits: no switching of illumination or mechanical scanning, high spatiotemporal phase sensitivity, and single-shot reconstruction at each wavelength. Experiments validate these characteristics by quantitative phase imaging of gratings, cells, and tissues.

Universal phase-only spatial light modulators

Universal phase-only spatial light modulators (UP-SLMs) are proposed and demonstrated by simulation and experiment. UP-SLMs, which consist of unitarily coupled electrically controllable wave plates, convert the optically anisotropic properties of the paired two wave plates into an effective single isotropic phase plate and can be realized with electrically tunable birefringence materials such as uniaxial liquid crystals (LCs). The universal approaches are applicable to any uniaxial anisotropic materials based cells, any LC cell operation modes and any incident light polarization states. Further the UP-SLMs are experimentally demonstrated even with commercial LCD panels having low geometrical rotational symmetry. These UP-SLMs will play significant roles in wave optics, communications, information displays, digital holography, quantum optics and quantum information technology by harnessing their unique capacity of modulating the only phase of linearly, circularly, elliptically, azimuthally, radially and even randomly polarized light.

Characterization, design, and optimization of a two-pass twisted nematic liquid crystal spatial light modulator system for arbitrary complex modulation

Arbitrary two-dimensional complex modulation of an optical field is a powerful tool for coherent optical systems. No single spatial light modulator (SLM) offers true arbitrary complex modulation, but they can be combined in order to achieve this. In this work, two sides of a twisted nematic (TN) liquid crystal SLM are used sequentially to implement different arbitrary modulation schemes. In order to fully explore and exploit the rich modulation behavior offered by a TN device, a generalized Jones matrix approach is used. A method for in situ characterization of the SLM inside the two-pass system is demonstrated, where each side of the SLM is independently characterized. This characterization data is then used to design appropriate polarizer configurations to implement arbitrary complex modulation schemes (albeit without 100% efficiency). Finally, an in situ optimization technique that corrects states by applying a translation in the complex plane is demonstrated. This technique can correct both for variations across the SLM and bulk changes in the SLM behavior due to the changing temperature.

Holographic projection with field-dependent aberration correction

We present an algorithm for the computation of computer-generated holograms projecting arbitrary patterns through optical reconstruction systems with strong field-dependent aberrations. The algorithm is based on a modification of the iterative Fourier transform algorithm. Aberrations are specified using Zernike polynomials. The trade-off between reconstruction error and diffraction efficiency can be altered using a simple constant within the algorithm. We show first experimental results for the correction of the reconstruction through a strongly aberrated Fourier system.

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.

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.

Dynamic holography using pixelated light modulators

Dynamic holography using spatial light modulators is a very flexible technique that offers various new applications compared to static holography. We give an overview on the technical background of dynamic holography focusing on pixelated spatial light modulators and their technical restrictions, and we present a selection of the numerous applications of dynamic holography.

The minimum Euclidean distance principle applied to improve the modulation diffraction efficiency in digitally controlled spatial light modulators

Digital addressing of the electrical signal in spatial light modulators, as it is the case in present liquid crystal on silicon (LCoS) displays, may lead to temporal phase fluctuations in the optical beam. In diffractive optics applications a reduction in the modulation diffraction efficiency may be expected. Experimental work is done characterizing the fluctuations amplitude and phase depth for three different digital addressing sequences. We propose a diffractive model to evaluate the modulation diffraction efficiency of phase diffractive optical elements (DOEs) in the presence of phase fluctuations. Best results are obtained for the most stable electrical sequence even though its phase depth is as small as 280 degrees . The results show good agreement with the numerical calculation given by the model.

Direct calibration of a spatial light modulator by lateral shearing interferometry

A new interferometric technique is described to measure the complex modulation curve of a spatial light modulator. Based on a lateral shear imaging interferometer, it enables the amplitude and phase modulation for several modulation levels to be displayed simultaneously in a single interferogram. As an example of the power of this technique a heuristic optimization of input and output elliptical polarization states for a mostly-phase operation mode was obtained within a few minutes for a commercial twisted-nematic liquid crystal display.

Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics

In this paper we provide evidence of the temporal fluctuations of the phase modulation property of a liquid crystal on silicon (LCoS) display, and we analyze its effect when the device is used for displaying a diffractive optical element. We use a commercial twisted nematic LCoS display configured to produce a phase-only modulation, and we provide time resolved measurements of the diffraction efficiency that show rapid fluctuations of the phase modulation, in the millisecond order. We analyze how these fluctuations have to be considered in two typical methods for the characterization of the phase modulation: two beam interference and diffraction from a binary grating. We finally provide experimental results on the use of this device for displaying a computer generated hologram. A reduction of the modulation diffraction efficiency results from the phase modulation fluctuation.

Hologram optimization for SLM-based reconstruction with regard to polarization effects

We report on first results obtained with two modified hologram optimization algorithms. These algorithms take into account the complex modulation characteristic of the spatial light modulators employed for hologram reconstruction. To this end the Jones matrices of the modulator as well as all other components of the setup are used within a modified direct binary search and an iterative Fourier transform algorithm. Geometrical phase effects are included in the optimization. Elimination of the analyzer behind the spatial light modulator is possible by that approach and for typical setups using twisted-nematic liquid crystal modulators an enhanced overall diffraction efficiency is achieved. Possible applications are the comparative digital holography and optical tweezers. Experimental results for the reconstructions of holograms with a Holoeye LC-R 3000 modulator are presented.

Time-resolved Mueller matrix analysis of a liquid crystal on silicon display

We present a full polarimetric characterization of a liquid crystal on silicon (LCoS) display, with time resolution measurements below the frame period of the device. This time-resolved analysis shows evidence of temporal fluctuations in the millisecond range in the state of polarization of the beam reflected by the display. We demonstrate that light reflected by the display is maintained fully polarized, but these temporal fluctuations result in an effective depolarization effect when detectors with long time integration intervals are used in the characterization of the display.

Mueller-Stokes characterization and optimization of a liquid crystal on silicon display showing depolarization

In this paper we characterize the polarimetric properties of a liquid crystal on silicon display (LCoS), including depolarization and diattenuation which are usually not considered when applying the LCoS in diffractive or adaptive optics. On one hand, we have found that the LCoS generates a certain degree (that can be larger than a 10%) of depolarized light, which depends on the addressed gray level and on the incident state of polarization (SOP), and can not be ignored in the above mentioned applications. The main origin of the depolarized light is related with temporal fluctuations of the SOP of the light reflected by the LCoS. The Mueller matrix of the LCoS is measured as a function of the gray level, which enables for a numerical optimization of the intensity modulation configurations. In particular we look for maximum intensity contrast modulation or for constant intensity modulation. By means of a heuristic approach we show that, using elliptically polarized light, amplitude-mostly or phase-mostly modulation can be obtained at a wavelength of 633 nm.

Efficient compensation of Zernike modes and eye aberration patterns using low-cost spatial light modulators

Off-the-shelf spatial light modulators (SLMs) like those commonly included in video projection devices have been seldom used for the compensation of eye aberrations, mainly due to the relatively low dynamic range of the phase retardation that can be introduced at each pixel. They present, however, some interesting features, such as high spatial resolution, easy handling, wide availability, and low cost. We describe an efficient four-level phase encoding scheme that allows us to use conventional SLMs for compensating optical aberrations as those typically found in human eyes. Experimental results are obtained with artificial eyes aberrated by refractive phase plates introducing either single Zernike terms or complex eye aberration patterns. This proof-of-concept is a step toward the use of low-cost, general purpose SLMs for the compensation of eye aberrations.

Diffractive optical elements designed for highly precise far-field generation in the presence of artifacts typical for pixelated spatial light modulators

Diffractive optical elements (DOEs) realized by spatial light modulators (SLMs) often have features that distinguish them from most conventional, static DOEs: strong coupling between phase and amplitude modulation, a modulation versus steering parameter characteristic that may not be precisely known (and may vary with, e.g., temperature), and deadspace effects and interpixel cross talk. For an optimal function of the DOE, e.g. as a multiple-beam splitter, the DOE design must account for these artifacts. We present an iterative design method in which the optimal setting of each SLM pixel is carefully chosen by considering the SLM artifacts and the design targets. For instance, the deadspace-interpixel effects are modeled by dividing the pixel to be optimized, and its nearest neighbors, into a number of subareas, each with its unique response and far-field contribution. Besides the customary intensity control, the design targets can also include phase control of the optical field in one or more of the beams in the beam splitter. We show how this can be used to cancel a strong unwanted zeroth-order beam, which results from using a slightly incorrect modulation characteristic for the SLM, by purposely sending a beam in the same direction but with the opposite phase. All the designs have been implemented on the 256 x 256 central pixels of a reflective liquid crystal on silicon SLM with a selected input polarization state and a direction of transmission axis of the output polarizer such that for the available different pixel settings a phase modulation of ~2pi rad could be obtained, accompanied by an intensity modulation depth as high as >95%.

Polarimetric characterization of liquid-crystal-on-silicon panels

Mueller matrix imaging polarimetry of liquid-crystal-on-silicon (LCoS) panels provides detailed information useful for the diagnosis of LCoS problems and to understand the interaction of LCoS panels with other projector components. Data reduction methods are presented for the analysis of LCoS Mueller matrix images yielding contrast ratio, efficiency, spatial uniformity, and the calculation of optimum trim retarders. The effects of nonideal retardance, retardance orientation, and depolarization on LCoS system performance are described. The white-state and dark-state Mueller matrix images of an example LCoS panel are analyzed in terms of LCoS performance metrics typical for red-green-blue wavelengths of 470, 550, and 640 nm. Variations of retardance, retardance orientation, and depolarization are shown to have different effects on contrast ratio, efficiency, and brightness. Thus Mueller matrix images can diagnose LCoS problems in a way different from radiometric testing. The calculation of optimum trim retarders in the presence of spatial variations is discussed. The relationship of the LCoS retardance in single-pass (from front to back) to the double-pass retardance (from entrance to exit) is established and used to clarify coordinate system issues related to Mueller matrices for reflection devices.

Adaptive correction to the speckle correlation fringes by using a twisted-nematic liquid-crystal display

An innovative technique for reducing speckle noise and improving the intensity profile of the speckle correlation fringes is presented. The method is based on reducing the range of the modulation intensity values of the speckle interference pattern. After the fringe pattern is corrected adaptively at each pixel, a simple morphological filtering of the fringes is sufficient to obtain smoothed fringes. The concept is presented both analytically and by simulation by using computer-generated speckle patterns. The experimental verification is performed by using an amplitude-only spatial light modulator (SLM) in a conventional electronic speckle pattern interferometry setup. The optical arrangement for tuning a commercially available LCD array for amplitude-only behavior is described. The method of feedback to the LCD SLM to modulate the intensity of the reference beam in order to reduce the modulation intensity values is explained, and the resulting fringe pattern and increase in the signal-to-noise ratio are discussed.

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.

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.

Complex encoding of rotation-invariant filters onto a single phase-only spatial light modulator

The accuracy and flexibility of the technique proposed by Davis et al. [Appl. Opt. 35, 2488 (1996)] for the encoding of the amplitude and the phase of a filter onto a single liquid-crystal spatial light modulator operating in a phase-only regime has been exploited to implement several filter designs in a convergent optical correlator. We have selected some filters, that given their mathematical structure showing some degree of rotational invariance, or having a parameter to regulate their behavior, require amore precise encoding. We present correlation results of outstanding quality for various rotationally invariant filter designs that have never been previously implemented with a real-time optical correlator.

Phasor analysis of eigenvectors generated in liquid-crystal displays

We analyze optical systems for creating phase-only operation of a liquid-crystal display (LCD). We introduce a new formalism in which any input or output polarization state can be described in terms of a linear combination of the eigenvectors of the LCD. We use a phasor analysis to examine the linear combination of the eigenvectors and show how improved performance can be obtained with a new configuration. We experimentally compare the intensity and phase operation for two configurations with the same spatial light modulator and show the improved performance with the new configuration.

Secure optical storage that uses fully phase encryption

A secure holographic memory system that uses fully phase encryption is presented. Two-dimensional arrays of data are phase encoded. Each array is then transformed into a stationary white-noise-like pattern by use of a random-phase mask located at the input plane and another at the Fourier plane. This encrypted information is then stored holographically in a photorefractive LiNbO(3):Fe crystal. The original phase-encoded data can be recovered, by use of the two random-phase masks, with a phase-conjugate readout beam. This phase information can then be converted back to intensity information with an interferometer. Recording multiple images by use of angular multiplexing is demonstrated. The influence of a limited system bandwidth on the quality of reconstructed data is evaluated numerically. These computer simulation results show that a fully phase-based encryption system generally performs better than an amplitude-based encryption system when the system bandwidth is limited by a moderate amount.

Optical correlation by use of partial phase-only modulation with VGA liquid-crystal displays

The development of liquid-crystal panels for use in commercial equipment has been aimed at improving the pixel resolution and the display efficiency. These improvements have led to a reduction in the thickness of such devices, among other outcomes, that involves a loss in phase modulation. We propose a modification of the classical phase-only filter to permit displays in VGA liquid-crystal panels with a constant amplitude modulation and less than a 2pi phase modulation. The method was tested experimentally in an optical setup.

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.

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.

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.

Full-range, continuous, complex modulation by the use of two coupled-mode liquid-crystal televisions

Switchable, continuous, complex-amplitude modulation is demonstrated with two cascaded, twisted nematic liquid-crystal televisions (LCTV's), both operating in phase- and amplitude-coupled modulation modes. The condition for full-range complex modulation is that one of the LCTV's must provide a 2π-range phase modulation. A look-up table encoding method is proposed that permits the compensation of phase-amplitude coupling and nonlinearity in the two individual LCTV modulations. Experimental techniques for determining the LCTV-device parameters, for maximizing the phase-mostly modulation range and the amplitude-mostly modulation contrast, and for testing the complex-amplitude modulation are developed. Optical complex-amplitude Fresnel holograms are shown.

Phase-only joint-transform correlator: analysis and experimental results

An analysis of the popular joint-transform optical correlator is presented for architectures employing spatial light modulators that operate only on the phase of the coherent light. Experimental results are also presented, for simple scenes that produce analytic solutions, which support the analysis.

Optical wavelet transform by the phase-only joint-transform correlator

A method is presented that performs the optical wavelet transform with liquid-crystal televisions as spatial light modulators operating only on the phase of the incident coherent light. The architecture is the joint-transform correlator, and the wavelets and the image to be transformed are encoded in the input plane of the system. The mathematical formalism describing the adaptation of the joint-transform correlator to the wavelet transform is given and extended to the operation of the phase-only joint-transform correlator. A new wavelet is described for two-dimensional image processing, and experimental results are presented for optical wavelet transforms done in real time by use of this wavelet in the phase-only joint-transform-correlator architecture. The analysis is extended to multiwavelet (multispectral) analysis by the joint-transform correlator, and simulation results are given. Finally experimental results with the phase-only joint-transform correlator applied to multi-wavelet analysis are presented.

Programmable optical phase-mostly holograms with coupled-mode modulation liquid-crystal television

Commercial twisted nematic liquid-crystal television provides coupled phase and amplitude modulation. We propose a simple wedged shear plate interferometer for in situ measurement of its phase modulation and operating curve. For a given operating curve, the coupled-mode modulation holograms are designed with an iterative method. We adjust the operating curve by rotating the polarizer and analyzer to obtain the optimal operating curve. The phase-mostly holograms yield good-quality reconstructed images with the zero-order spot reduced to a minimum. Experimental results are shown.

Ternary phase and amplitude modulations using a twisted nematic liquid crystal spatial light modulator

Ternary phase and amplitude modulations that use a reflective mode, 45° twisted nematic liquid-crystal spatial-light modulator are demonstrated. This use offers a simple method for implementation of ternary phase-amplitude filters with high resolution, high optical efficiency, and fast response time.