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

Dynamic Phase and Polarization Modulation Using Two-Beam Parallel Coding for Optical Storage in Transparent Materials

In this paper, we propose and experimentally demonstrate a parallel coding and two-beam combining approach for the simultaneous implementation of dynamically generating holographic patterns at their arbitrary linear polarization states. Two orthogonal input beams are parallelly and independently encoded with the same target image information but there is different amplitude information by using two-phase computer-generated holograms (CGH) on two Liquid-Crystal-on-Silicon-Spatial-Light Modulators (LCOS SLMs). Two modulated beams are then considered as two polarization components and are spatially superposed to form the target polarization state. The final linear vector beam is created by the spatial superposition of the two base beams, capable of controlling the vector angle through the phase depth of the phase-only CGHs. Meanwhile, the combined holographic patterns can be freely encoded by the holograms of two vector components. Thus, this allows us to tailor the optical fields endowed with arbitrary holographic patterns and the linear polarization states at the same time. This method provides a more promising approach for laser data writing generation systems in the next-generation optical data storage technology in transparent materials.

Calibration of the pixel crosstalk in spatial light modulators for 4f pulse shaping

The targeted shaping of femtosecond pulses in 4f pulse shapers is complicated by, among other factors, the crosstalk between adjacent pixels of a spatial light modulator (SLM). Current methods for the crosstalk evaluation require setting up a different experiment, which is highly inconvenient. Here, we propose a simple procedure to extract the pixel crosstalk within the standard SLM calibration used in pulse shaping. The calibration is based on an analysis of the contrast of a periodic modulation in the spectra induced via SLM. We demonstrate the calibration procedure on a liquid-crystal-based SLM and show that we attain a constant crosstalk effect represented by a Gaussian function with σ=1.0 pix over a broad operational range of the SLM.

Liquid Crystal Devices for Beam Steering Applications

Liquid crystals are valuable materials for applications in beam steering devices. In this paper, an overview of the use of liquid crystals in the field of adaptive optics specifically for beam steering and lensing devices is presented. The paper introduces the properties of liquid crystals that have made them useful in this field followed by a more detailed discussion of specific liquid crystal devices that act as switchable optical components of refractive and diffractive types. The relative advantages and disadvantages of the different devices and techniques are summarised.

StainedView: Variable-Intensity Light-Attenuation Display with Cascaded Spatial Color Filtering for Improved Color Fidelity

We present StainedView, an optical see-through display that spatially filters the spectral distribution of light to form an image with improved color fidelity. Existing light-attenuation displays have limited color fidelity and contrast, resulting in a degraded appearance of virtual images. To use these displays to present virtual images that are more consistent with the real world, we require three things: intensity modulation of incoming light, spatial color filtering with narrower bandwidth, and appropriate light modulation for incoming light with an arbitrary spectral distribution. In StainedView, we address the three requirements by cascading two phase-only spatial light modulators (PSLMs), a digital micromirror device, and polarization optics to control both light intensity and spectrum distribution. We show that our design has a 1.8 times wider color gamut fidelity (75.8% fulfillment of sRGB color space) compared to the existing single-PSLM approach (41.4%) under a reference white light. We demonstrated the design with a proof-of-concept display system. We further introduce our optics design and pixel-selection algorithm for the given light input, evaluate the spatial color filter, and discuss the limitation of the current prototype.

Binary multi-order diffraction optical elements with variable fill factor for the formation and detection of optical vortices of arbitrary order

In this paper we consider the calculation of binary diffraction optical elements (DOEs) for the formation and detection of optical vortices of arbitrary order. The synthesis of binary DOEs is based on a combination of the method of carrier spatial frequencies and binary coding with a variable fill factor. Unlike various methods of multiplication, the method of carrier spatial frequencies is characterized by great flexibility and versatility. It allows us to not only form the given field distributions in arbitrary diffraction orders, but also to give them arbitrary weight ratio (energy distribution in orders). As a rule, such universality leads to the need to form a complex amplitude-phase distribution in the input plane. To avoid this, in this paper it is proposed to use binary coding with a variable level. The effect of such coding is studied in detail both theoretically and numerically. It is shown that the level variation makes it possible to change the set of the observed diffraction orders. The positions and orders of the optical vortices formed are uniquely determined by the values of the carrying spatial frequencies and the topological charges of the vortices in the basic order. The results can be useful in optical communications.

Model-based compensation of pixel crosstalk in liquid crystal spatial light modulators

Spatial light modulators (SLMs) based on liquid crystals are widely used for wavefront shaping. Their large number of pixels allows one to create complex wavefronts. The crosstalk between neighboring pixels, also known as fringing field effect, however, can lead to strong deviations. The realized wavefront may deviate significantly from the prediction based on the idealized assumption that the response across a pixel is uniform and independent of its neighbors. Detailed numerical simulations of the SLM response based on a full 3D physical model accurately match the measured response and properly model the pixel crosstalk. The full model is then used to validate a simplified model that enables much faster crosstalk evaluation and pattern optimization beyond standard performance. General conclusions on how to minimize crosstalk in liquid crystal on silicon (LCoS) SLM systems are derived, as well as a readily accessible estimation of the amount of fringing in a given SLM.

Non-invasive correction of thermally induced wavefront aberrations of spatial light modulator in holographic projection

Holographic phase-only projection technique utilizing spatial light modulators (SLM) as an active element may be intended to work in environments in which the temperature changes with time, such as outdoors or automotive applications. In order to achieve maximum possible resolution, the thermally induced aberrations of the SLM must be corrected in real time. We present the results of non-invasive determination of the SLM aberrations in holographic image projection, caused mostly by thermal strains of SLM, with the use of one fixed camera detector and iterative phase retrieval. We show real-time wavefront correction leading to experimentally proven, diffraction-limited image quality in a wide range of SLM temperatures.

Optically addressed modulator for tunable spatial polarization control

We present an optically addressed non-pixelated spatial light modulator. The system is based on reversible photoalignment of a LC cell using a red light sensitive novel azobenzene photoalignment layer. It is an electrode-free device that manipulates the liquid crystal orientation and consequently the polarization via light without artifacts caused by electrodes. The capability to miniaturize the spatial light modulator allows the integration into a microscope objective. This includes a miniaturized 200 channel optical addressing system based on a VCSEL array and hybrid refractive-diffractive beam shapers. As an application example, the utilization as a microscope objective integrated analog phase contrast modulator is shown.

Optimization of a spatial light modulator driven by digital video interface graphics to generate holographic optical traps

We propose a method to optimize spatial light modulators (SLMs) driven by digital video interface graphics in a holographic optical tweezers system. A method analogous to that used to optimize LCD televisions is used to optimize the properties of the graphics card through a diffraction-based experiment and develop a lookup table for the SLM. The optimization allows the SLM to function with its full phase modulation depth with improved diffraction efficiency. Further, we propose a simple and robust method to correct for the spatially varying phase response of the SLM to enhance its diffraction efficiency. The optimization results in an improvement of uniformity in the intensity and quality of the trap spots.

High precision wavefront control in point spread function engineering for single emitter localization

Point spread function (PSF) engineering is used in single emitter localization to measure the emitter position in 3D and possibly other parameters such as the emission color or dipole orientation as well. Advanced PSF models such as spline fits to experimental PSFs or the vectorial PSF model can be used in the corresponding localization algorithms in order to model the intricate spot shape and deformations correctly. The complexity of the optical architecture and fit model makes PSF engineering approaches particularly sensitive to optical aberrations. Here, we present a calibration and alignment protocol for fluorescence microscopes equipped with a spatial light modulator (SLM) with the goal of establishing a wavefront error well below the diffraction limit for optimum application of complex engineered PSFs. We achieve high-precision wavefront control, to a level below 20 mλ wavefront aberration over a 30 minute time window after the calibration procedure, using a separate light path for calibrating the pixel-to-pixel variations of the SLM, and alignment of the SLM with respect to the optical axis and Fourier plane within 3 μm (x/y) and 100 μm (z) error. Aberrations are retrieved from a fit of the vectorial PSF model to a bead z-stack and compensated with a residual wavefront error comparable to the error of the SLM calibration step. This well-calibrated and corrected setup makes it possible to create complex '3D+λ' PSFs that fit very well to the vectorial PSF model. Proof-of-principle bead experiments show precisions below 10 nm in x, y, and λ, and below 20 nm in z over an axial range of 1 μm with 2000 signal photons and 12 background photons.

Improving Electrophoretic Particle Motion Control in Electrophoretic Displays by Eliminating the Fringing Effect via Driving Waveform Design

Electrophoretic display is realized by controlling colored nanoparticles moving in micrometer spaces via electrophoresis. The quality of information display is therefore affected by the unsynchronized particle moving speed and the mismatched electric signal according to the crosstalk of the electric field and inhomogeneous material distribution. In this work, we analyzed the mechanism of a fringe phenomenon that affected the information display quality of electrophoretic displays (EPDs). Electrical driving waveforms (voltage signals) are designed to reduce the fringe phenomenon. By using the optimizing driving waveform, we proposed that the fringe phenomenon is quantified as gray value that can be diminished by 25.5, while keeping a response time of 200 ms.

Fiber-based lensless polarization holography for measuring Jones matrix parameters of polarization-sensitive materials

We report a fiber-based lensless holographic imaging system to realize a single-shot measurement of two dimensional (2-D) Jones matrix parameters of polarization-sensitive materials. In this system, a multi-source lensless off-axis Fresnel holographic recording geometry is adopted, and two optical fiber splitters are used to generate the multiple reference and illumination beams required for recording a four-channel angular-multiplexing polarization hologram (AMPH). Using this system and the method described in this paper, spatially resolved Jones matrix parameters of a polarization-sensitive material can be retrieved from one single-shot AMPH. We demonstrate the feasibility of the method by extracting a 2-D Jones matrix of a composite polarizer. Applications of the method to measure the Jones matrix maps of a stressed polymethyl methacrylate sample and a mica fragment are also presented. Benefit from the fiber-based and lensless off-axis holographic design, the system possesses a quite compact configuration, which provides a feasible approach for development of an integrated and portable system to measure Jones matrix parameters of polarization-sensitive materials.

Backplane aberration calibration of spatial light modulators using a phase-retrieval algorithm

The calibration and correction of backplane aberration of a liquid-crystal spatial light modulator (LCSLM) are important for its proper functioning. To simplify the calibration procedurally, we study a random-illumination-phase-retrieval-based method. Our method improves the convergence of the phase-retrieval-based calibration and reduces the calibration complexity. However, the cross talk of the LCSLM deteriorates the calibration performance. We determined the relationship between the probability density function of the random phases and the light-intensity pattern and proposed an algorithm to compensate for the cross talk. We conducted a series of simulations to test the performance of the above-mentioned algorithms. The results show that our algorithms are effective and outperform other methods.

Tilt-effect of holograms and images displayed on a spatial light modulator

We show that a liquid crystal spatial light modulator (LCOS-SLM) can be used to display amplitude images, or phase holograms, which change in a pre-determined way when the display is tilted, i.e. observed under different angles. This is similar to the tilt-effect (also called "latent image effect") known from various security elements ("kinegrams") on credit cards or bank notes. The effect is achieved without any specialized optical components, simply by using the large phase shifting capability of a "thick" SLM, which extends over several multiples of 2π, in combination with the angular dependence of the phase shift. For hologram projection one can use the fact that the phase of a monochromatic wave is only defined modulo 2π. Thus one can design a phase pattern extending over several multiples of 2π, which transforms at different readout angles into different 2π-wrapped phase structures, due to the angular dependence of the modulo 2π operation. These different beams then project different holograms at the respective readout angles. In amplitude modulation mode (with inserted polarizer) the intensity of each SLM pixel oscillates over several periods when tuning its control voltage. Since the oscillation period depends on the readout angle, it is possible to find a certain control voltage which produces two (or more) selectable gray levels at a corresponding number of pre-determined readout angles. This is done with all SLM pixels individually, thus constructing different images for the selected angles. We experimentally demonstrate the reconstruction of multiple (Fourier- and Fresnel-) holograms, and of different amplitude images, by readout of static diffractive patterns in a variable angular range between 0° and 60°.

Aerial projection of three-dimensional motion pictures by electro-holography and parabolic mirrors

We demonstrate an aerial projection system for reconstructing 3D motion pictures based on holography. The system consists of an optical source, a spatial light modulator corresponding to a display and two parabolic mirrors. The spatial light modulator displays holograms calculated by computer and can reconstruct holographic motion pictures near the surface of the modulator. The two parabolic mirrors can project floating 3D images of the motion pictures formed by the spatial light modulator without mechanical scanning or rotating. In this demonstration, we used a phase-modulation-type spatial light modulator. The number of pixels and the pixel pitch of the modulator were 1,080 × 1,920 and 8.0 μm × 8.0 μm, respectively. The diameter, the height and the focal length of each parabolic mirror were 288 mm, 55 mm and 100 mm, respectively. We succeeded in aerially projecting 3D motion pictures of size ~2.5 mm³ by this system constructed by the modulator and mirrors. In addition, by applying a fast computational algorithm for holograms, we achieved hologram calculations at ~12 ms per hologram with 4 CPU cores.

Predictive capability of average Stokes polarimetry for simulation of phase multilevel elements onto LCoS devices

Parallel-aligned (PA) liquid-crystal on silicon (LCoS) microdisplays are especially appealing in a wide range of spatial light modulation applications since they enable phase-only operation. Recently we proposed a novel polarimetric method, based on Stokes polarimetry, enabling the characterization of their linear retardance and the magnitude of their associated phase fluctuations or flicker, exhibited by many LCoS devices. In this work we apply the calibrated values obtained with this technique to show their capability to predict the performance of spatially varying phase multilevel elements displayed onto the PA-LCoS device. Specifically we address a series of multilevel phase blazed gratings. We analyze both their average diffraction efficiency ("static" analysis) and its associated time fluctuation ("dynamic" analysis). Two different electrical configuration files with different degrees of flicker are applied in order to evaluate the actual influence of flicker on the expected performance of the diffractive optical elements addressed. We obtain a good agreement between simulation and experiment, thus demonstrating the predictive capability of the calibration provided by the average Stokes polarimetric technique. Additionally, it is obtained that for electrical configurations with less than 30° amplitude for the flicker retardance, they may not influence the performance of the blazed gratings. In general, we demonstrate that the influence of flicker greatly diminishes when the number of quantization levels in the optical element increases.

How to use a phase-only spatial light modulator as a color display

We demonstrate that a parallel aligned liquid crystal on silicon (PA-LCOS) spatial light modulator (SLM) without any attached color mask can be used as a full color display with white light illumination. The method is based on the wavelength dependence of the (voltage controlled) birefringence of the liquid crystal pixels. Modern SLMs offer a wide range over which the birefringence can be modulated, leading (in combination with a linear polarizer) to several intensity modulation periods of a reflected light wave as a function of the applied voltage. Because of dispersion, the oscillation period strongly depends on the wavelength. Thus each voltage applied to an SLM pixel corresponds to another reflected color spectrum. For SLMs with a sufficiently broad tuning range, one obtains a color palette (i.e., a "color lookup-table"), which allows one to display color images. An advantage over standard liquid crystal displays (LCDs), which use color masks in front of the individual pixels, is that the light efficiency and the display resolution are increased by a factor of three.

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.

LCD panel characterization by measuring full Jones matrix of individual pixels using polarization-sensitive digital holographic microscopy

We present measurements of the full Jones matrix of individual pixels in a liquid-crystal display (LCD) panel. Employing a polarization-sensitive digital holographic microscopy based on Mach-Zehnder interferometry, the complex amplitudes of the light passing through individual LCD pixels are precisely measured with respect to orthogonal bases of polarization states, from which the full Jones matrix components of individual pixels are obtained. We also measure the changes in the Jones matrix of individual LCD pixels with respect to an applied bias. In addition, the complex optical responses of a LCD panel with respect to arbitrary polarization states of incident light were characterized from the measured Jones matrix.