Full complex modulation using liquid-crystal televisions

Complex amplitude modulated holographic display system based on polarization grating

We propose a holographic display system for complex amplitude modulation (CAM) using a phase-only spatial light modulator (SLM) and two polarization gratings (PG). The two sub-holograms of the complex-amplitude computed generated hologram (CGH) are loaded in different regions of SLM. Two diffractive components couple in space after longitudinal migration from the double PGs, and finally interfered through the line polarizer. The influence of the system error on the reconstructed image quality is analyzed, which provides a theoretical assessment for adding pre-compensation to CGH to compensate the system error. Moreover, on the base of the proposed system, a large depth of field and enlarged display area display is realized and the real-time display can be achieved because of the analytical complex-amplitude computed generated hologram. The optical experimental results show that the proposed system has high energy efficiency, and can provide high-quality holographic display with a large depth of field and enlarged display area.

Review of computer-generated hologram algorithms for color dynamic holographic three-dimensional display

Holographic three-dimensional display is an important display technique because it can provide all depth information of a real or virtual scene without any special eyewear. In recent years, with the development of computer and optoelectronic technology, computer-generated holograms have attracted extensive attention and developed as the most promising method to realize holographic display. However, some bottlenecks still restrict the development of computer-generated holograms, such as heavy computation burden, low image quality, and the complicated system of color holographic display. To overcome these problems, numerous algorithms have been investigated with the aim of color dynamic holographic three-dimensional display. In this review, we will explain the essence of various computer-generated hologram algorithms and provide some insights for future research.

Complex spatial light modulation capability of a dual layer in-plane switching liquid crystal panel

Complex spatial light modulator (SLM), which can simultaneously control the amplitude and phase of light waves, is a key technology for wide-range of wave-optic technologies including holographic three-dimensional displays. This paper presents a flat panel complex spatial light modulator that consists of dual in-plane switching liquid crystal panels with double-degrees of freedom of voltage inputs. The proposed architecture features single-pixel level complex light modulation enabling complex light modulation in entire free space, which is most contrast to conventional macro-pixel based complex modulation techniques. Its complex light modulation capability is verified with theoretical simulation and experimental characterization, and a three-dimensional holographic image reconstruction without conjugate noise. It is believed that the proposed flat panel complex SLM can be an essential device for a wide range of advanced wave optic technologies.

Uniform and efficient beam shaping for high-energy lasers

Phase-only beam shaping with liquid crystal on silicon spatial light modulators (SLM) allows modulating the wavefront dynamically and generating arbitrary intensity patterns with high efficiency. Since this method cannot take control of all degrees of freedom, a speckle pattern appears and drastically impairs the outcome. There are several methods to overcome this issue including algorithms which directly control phase and amplitude, but they suffer from low efficiency. Methods using two SLMs yield excellent results but they are usually limited in the applicable energy due to damage to the SLM's backplane. We present a method which makes use of two SLMs and simultaneously gives way for high-energy laser applications. The algorithm and setup are designed to keep the fluence on the SLMs low by distributing the light over a large area. This provides stability against misalignment and facilitates experimental feasibility while keeping high efficiency.

High spatial resolution pixel synthesis structure for full-complex amplitude modulation with twisted nematic LCD

Various optics applications require a low-cost twisted nematic LCD that can modulate phase and amplitude independently. We propose a high spatial resolution light-synthesis structure that achieves full-complex amplitude modulation with a twisted nematic LCD. The synthesis structure uses two sparse lateral-shift pixel arrays for the x direction and four sparse lateral-shift pixel arrays for the y direction. The structure recreates an image with two superpixels formed from pairs of adjacent pixels in both directions, and as a result, the spatial resolution is only halved in both directions, which yields an appropriate image quality for the synthesis technique. In experiments, we demonstrate the precise control of amplitude and phase using a twisted nematic LCD.

Detection method for the complex amplitude of a signal beam with intensity and phase modulation using the transport of intensity equation for holographic data storage

Holographic data storage (HDS), in which both the amplitude and the phase of a signal beam are modulated, has been extensively studied with the goal of increasing its storage capacity. To detect such modulation during data retrieval, it is necessary to acquire the complex amplitude of the signal beam. In this study, we focus on the transport of intensity equation (TIE) method, which allows us to detect the phase distribution of the light wave quantitatively without using interferometry, contributing to miniaturization of the optical system and improvement of the vibration tolerance of HDS. We discuss the conditions of the modulation phase distribution of the signal beam required for accurate phase detection and propose a method to estimate and eliminate the noise that frequently appears in the phase distribution detected by the TIE method.

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.

Multilevel recording of complex amplitude data pages in a holographic data storage system using digital holography

A holographic data storage system using digital holography is proposed to record and retrieve multilevel complex amplitude data pages. Digital holographic techniques are capable of modulating and detecting complex amplitude distribution using current electronic devices. These techniques allow the development of a simple, compact, and stable holographic storage system that mainly consists of a single phase-only spatial light modulator and an image sensor. As a proof-of-principle experiment, complex amplitude data pages with binary amplitude and four-level phase are recorded and retrieved. Experimental results show the feasibility of the proposed holographic data storage system.

Linear phase encoding for holographic data storage with a single phase-only spatial light modulator

A linear phase encoding is presented for realizing a compact and simple holographic data storage system with a single spatial light modulator (SLM). This encoding method makes it possible to modulate a complex amplitude distribution with a single phase-only SLM in a holographic storage system. In addition, an undesired light due to the imperfection of an SLM can be removed by spatial frequency filtering with a Nyquist aperture. The linear phase encoding is introduced to coaxial holographic data storage. The generation of a signal beam using linear phase encoding is experimentally verified in an interferometer. In a coaxial holographic data storage system, single data recording, shift selectivity, and shift multiplexed recording are experimentally demonstrated.

Principle and characteristics of 3D display based on random source constructive interference

The paper discusses the principle and characteristics of 3D display based on random source constructive interference (RSCI). The voxels of discrete 3D images are formed in the air via constructive interference of spherical light waves emitted by point light sources (PLSs) that are arranged at random positions to depress high order diffraction. The PLSs might be created by two liquid crystal panels sandwiched between two micro-lens arrays. The point spread function of the system revealed that it is able to reconstruct voxels with diffraction limited resolution over a large field width and depth. The high resolution was confirmed by the experiments. Theoretical analyses also shows that the system could provide a 3D image contrast and gray levels no less than that in liquid crystal panels. Compared with 2D display, it needs only additional depth information, which brings only about 30% data increment.

Digital phase conjugate mirror by parallel arrangement of two phase-only spatial light modulators

In a conventional digital phase conjugation system, only the phase of an input light is time-reversed. This deteriorates phase conjugation fidelity and restricts application fields to specific cases only when the input light has uniformly-distributed scattered wavefront. To overcome these difficulties, we present a digital phase conjugate mirror based on parallel alignment of two phase-only spatial light modulators (SLMs), in which both amplitude and phase of the input light can be time-reversed. Experimental result showed that, in the phase conjugation through a holographic diffuser with diffusion angle of 0.5 degree, background noises decrease to 65% by our digital phase conjugation mirror.

Super-resolution with complex masks using a phase-only LCD

Two methods to achieve super-resolution with complex masks displayed in one-phase-only liquid crystal display (LCD) are described. The first method decomposes the complex mask into two phase-only elements with a posterior recombination using an interferometer, and the second method simultaneously encodes the amplitude and the phase by modulating the amplitude of the carrier phase. Experimental results are presented using a liquid crystal on silicon spatial light modulator under reflection.

Spatial filters for complex wavefront modulation

In this paper we propose a method to generate independent and simultaneous phase and amplitude modulation by a phase-only spatial light modulator and Fourier filtering. The incident light is modulated by a suitable phase pattern containing high spatial frequencies. The modulated light is transmitted through a 4f optical system having an appropriate spatial filter in the Fourier plane in order to synthesize the expected complex modulated wavefront on the output of the system. We propose a simple method to generate spatial filters applicable for the phase-only to complex modulated wavefront conversion. We analyze the quality of the output image related to the ideal wavefront using the proposed filters. We show that more efficient complex modulation can be realized by the proposed method than by the earlier solutions.

Full-range, complex spatial light modulator for real-time holography

We demonstrate a full-range complex and transmissive spatial light modulator (SLM) for simultaneous and independent amplitude and phase modulation of an input wave field. Arbitrary scalar complex optical fields are generated by stacking a pixelated liquid crystal display operating in phase-only (2π) modulation with passive polarization-sensitive components. The principle is based on optical combining the light fields of two neighboring phase-only modulating pixels, which were made orthogonally polarized by a structured half-wave plate, then passing through a birefringent plate to laterally shift one of the beams collinear to the other, and finally bringing to interference by a linear polarizer. Complex modulation by the proposed SLM is experimentally verified in monochrome green operation.

Full-complex amplitude modulation with binary spatial light modulators

Imperfections and nonrobust behavior of practical multilevel spatial light modulators (SLMs) degrade the performance of many proposed full-complex amplitude modulation schemes. We consider the use of more robust binary SLMs for this purpose. We propose a generic method, by which, out of K binary (or 1 bit) SLMs of size M×N, we effectively create a new 2(K)-level (or K bit) SLM of size M×N. The method is a generalization of the well-known concepts of bit plane representation and decomposition for ordinary gray scale digital images and relies on forming a properly weighted superposition of binary SLMs. When K is sufficiently large, the effective SLM can be regarded as a full-complex one. Our method is as efficient as possible from an information theoretical perspective. A 4f system is discussed as a possible optical implementation. This 4f system also provides a means for eliminating the undesirable higher diffraction orders. The components of the 4f system can easily be customized for different production technologies.

Novel real-time joint-transform correlation by use of acousto-optic heterodyning

To replace the film recording aspect of performing optical correlation, conventional real-time joint-transform correlation (JTC) optical systems make use of a spatial light modulator (SLM) located in the Fourier plane to record the joint-transform power spectrum (JPS) to achieve real-time processing. The use of an SLM in the Fourier plane, however, is a major drawback in these systems because SLMs are limited in resolution, phase uniformity, and contrast ratio, which are, therefore, not desirable for robust applications. We propose a hybrid (optical/electronic) processing technique to achieve real-time joint-transform correlation. The technique employs acousto-optic heterodyning scanning. The proposed real-time JTC system does not require an SLM at the Fourier plane as in other real-time JTC systems. This departure from the conventional scheme is extremely important as the proposed approach does not depend on SLM issues. We develop the theory of the technique and substantiate it with experimental results.

Effects of indented interframe cross talk in charge-coupled device detection of discrete displays

By considering CCD detection as a spatiotemporal sampling process and considering electronically addressed liquid-crystal display's (LCD's) and cathode ray tube (CRT) display's as discrete displays, we investigate the frame-grabbing process for CCD detection of discrete displays by using CRT-CCD and LCD-CCD models. Because of the nature of the timing for pixel addressing in the CRT, line addressing in the LCD, and frame transfer in the CCD, it is found that CCD frames suffer from indented interframe cross talk of the displayed input frames. This indented cross talk occurs regardless of whether a synchronizing signal is utilized. Cross talk typically takes place between two or three input frames. Indented interframe cross talk does not affect CCD detection for frame refreshing. However, cross talk increases as the interframe difference between successive displayed input frames increases.

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.

Implementation of a non-zero-order joint-transform correlator by use of phase-shifting techniques

The implementation of non-zero-order joint-transform correlators (JTC's) is presented. The zero-order spectra (i.e., the autocorrelation power spectra) are removed from the joint-transform power spectrum by use of phase-shifting techniques by which the output diffraction and input spatial domain can more efficiently be utilized. Applications of the phase-shifting techniques to both conventional JTC's and phase-transformed input JTC's (PJTC's) are discussed. Compared with the conventional JTC, the PJTC has the advantages of higher light efficiency, a better signal-to-clutter ratio, and the simplicity to realize phase shifting. We anticipate that the proposed non-zero-order JTC's should have a significant impact on the future development of more efficient JTC's.

Intensity-only modulation for atmospheric scintillation correction by liquid-crystal spatial light modulators

We consider the use of a ferroelectric liquid-crystal spatial light modulator (FLC SLM) to control the transmittance of a telescope pupil to compensate for the effects of scintillation. Our aim here is to prove the necessary and physically interesting result that it is possible to control the intensity of light by use of FLC SLM without inducing further phase aberrations. Furthermore, we show that system errors have only a small effect on the phase of the transmitted beam.

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 calibration and applications of a liquid-crystal spatial light modulator

A simple phase-characterization method for spatial light modulators is proposed. The low-cost method permits high-precision measurement and provides data for the setting of the spatial-light-modulator operating point in the phase-modulation mode. The dynamic phase response is used to perform efficient kinoform recording. In order to record the kinoform, we modify the global iterative coding to compute phase holograms. Finally, modified phase-phase correlation is introduced. The phase-phase correlator permits sharper correlation peaks, better energy transmission, and higher discrimination than an amplitude-phase correlation. Optical experimental results are presented.

Nonlinear optical hit-miss transform for detection

Morphological processing involves nonlinear low-level image-processing operations that can be realized on optical processors. Amodified version of the hit-miss morphological transform is described for object detection. Simulation results and optical laboratory realizations are presented. Some of the simple filters required can be realized as ternary-phase-amplitude optical filters.

Application of position encoding to a complex joint transform correlator

Because a joint transform correlator can be used as a general optical signal processor, complex-impulse-response implementations in the spatial domain are often requested. We introduce a position-encoding technique with which complex-valued references for the joint transform correlator can be obtained with an amplitude-modulated spatial light modulator. A proof-of-concept experiment is also provided.

Recall of linear combinations of stored data pages based on phase-code multiplexing in volume holography

We describe a novel method for the recall of linear combinations of stored data pages in a volume holographic memory based on phase-code multiplexing. Recall is demonstrated by use of a compound phase-and-amplitude spatial light modulator in the reference beam path.

Multicriteria characterization of coding domains with optimal Fourier spatial light modulator filters

A multicriteria optimization method is introduced in order to find optimal filters for implementation on arbitrary spatial light modulators in the Fourier plane of an optical correlator. This method is applied to the trade-offs between noise robustness, sharpness of the correlation peak, and optical efficiency. A fast and simple algorithm is given in this case, which is independent of the particular form of the spatial light modulator coding constraint. It is used to characterize and to compare typical coding domains through the performances of their associated optimal filters.

Optimal realizable filters and the minimum Euclidean distance principle

Minimizing a Euclidean distance in the complex plane optimizes a wide class of correlation metrics for filters implemented on realistic devices. The algorithm searches over no more than two real scalars (gain and phase). It unifies a variety of previous solutions for special cases (e.g., a maximum signal-to-noise ratio with colored noise and a real filter and a maximum correlation intensity with no noise and a coupled filter). It extends optimal partial information filter theory to arbitrary spatial light modulators (fully complex, coupled, discrete, finite contrast ratio, and so forth), additive input noise (white or colored), spatially nonuniform filter modulators, and additive correlation detection noise (including signaldependent noise). An appendix summarizes the algorithm as it is implemented in available computer code.

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.

Tutorial survey of composite filter designs for optical correlators

A tutorial survey is presented of the many composite filter designs proposed for distortion-invariant optical pattern recognition. Remarks are made throughout regarding areas for further investigation.