Phase calibration and applications of a liquid-crystal spatial light modulator

Simple and fast calibration method for phase-only spatial light modulators

Phase-only spatial light modulators (SLMs) are widely used to engineer the phase of light in various applications. However, liquid-crystal-on-silicon SLMs have undesirable spatial variations in phase response and optical flatness across the SLM panel, which must be compensated for accurate phase control. Here, we introduce a simple and fast way to simultaneously extract these two types of SLM nonuniformities at single-pixel resolution using Twyman-Green interferometry without a piezoelectric transducer. By modulating the interference intensity via the SLM gray level, our approach requires N times fewer interferograms than typical N-step phase shift interferometry (PSI), while providing flatness correction as accurate as PSI. In practice, our calibration method works well with as few as 18 interferograms, which can be quickly acquired without concern for phase drift. We detail the calibration procedure and discuss the performance of our calibration.

Adaptable Shack-Hartmann wavefront sensor with diffractive lenslet arrays to mitigate the effects of scintillation

Adaptive optics systems are used to compensate for distortions of the wavefront of light induced by turbulence in the atmosphere. Shack-Hartmann wavefront sensors are used to measure this wavefront distortion before correction. However, in turbulence conditions where strong scintillation (intensity fluctuation) is present, these sensors show considerably worse performance. This is partly because the lenslet arrays of the sensor are designed without regard to scintillation and are not adaptable to changes in turbulence strength. Therefore, we have developed an adaptable Shack-Hartmann wavefront sensor that can flexibly exchange its lenslet array by relying on diffractive lenses displayed on a spatial light modulator instead of utilizing a physical microlens array. This paper presents the principle of the sensor, the design of a deterministic turbulence simulation test-bed, and an analysis how different lenslet arrays perform in scintillation conditions. Our experiments with different turbulence conditions showed that it is advantageous to increase the lenslet size when scintillation is present. The residual phase variance for an array with 24 lenslets was up to 71% lower than for a 112 lenslet array. This shows that the measurement error of focal spots has a strong influence on the performance of a Shack-Hartmann wavefront sensor and that in many cases it makes sense to increase the lenslet size. With our adaptable wavefront sensor such changes in lenslet configurations can be done very quickly and flexibly.

Phase-only modulation with two vertical aligned liquid crystal devices

Spatial Light Modulators (SLMs) are widely used in several fields of optics such as adaptive optics. SLMs based on Liquid Crystal (LC) devices allow a dynamic and easy representation of two-dimensional phase maps. A drawback of these devices is their elevated cost, preventing a massive use of the technology. We present a more affordable approach based on the serial arrangement of vertical aligned LC devices, with characteristics of phase modulation similar to a widely used parallel aligned LC device. We discuss the peculiarities of the approach, the performance and some potential areas of applications.

Self-referenced multiple-beam interferometric method for robust phase calibration of spatial light modulator

Phase-only liquid crystal spatial light modulator has wide ranging applications that require accurate phase retardance. The phase calibration of the spatial light modulator is therefore of vital importance. Available self-referenced calibration methods face the challenges of high time consumption, low efficiency, and low stability against the conditions. A self-referenced multiple-beam interferometric method is proposed to derive the global grayscale-phase response. As is presented theoretically and experimentally, the proposed method reduces the measuring time and improves the calibration efficiency by encoding multiple fringes in a single hologram. Results also show that the method is equally accurate when compared with traditional two-beam interferometric method, whereas providing a greater robustness against measuring errors since the standard deviation is only 56% of that of the traditional method.

Spatial light modulator phase calibration based on spatial mode projection

Spatial light modulators (SLMs), which are devices used to manipulate the phase of an incident wave front, are prolific in fields such as optical trapping, dynamic diffractive optical elements, and display technology. Of the many challenges inherent to using SLMs, one of the most ubiquitous is the calibration of the device's phase-shifting mechanism. In this paper, we present a new SLM calibration method based on spatial mode projection. We also implement a data processing technique to our data to generate accurate look-up tables from our calibration curves. We then evaluate the success of our method by propagating Laguerre-Gauss beams with computer-generated holograms. Our results show that the qualitative analysis of modes propagated using the SLM is a viable method of assessing performance. On the whole, we show that spatial mode projection provides clear performance improvements in the SLM's phase-modulating capabilities.

Progress in Phase Calibration for Liquid Crystal Spatial Light Modulators

Phase-only Spatial Light Modulator (SLM) is one of the most widely used devices for phase modulation. It has been successfully applied in the field with requirements of precision phase modulation such as holographic display, optical tweezers, lithography, etc. However, due to the limitations in the manufacturing process, the grayscale-phase response could be different for every single SLM device, even varying on sections of an SLM panel. A diverse array of calibration methods have been proposed and could be sorted into two categories: the interferometric phase calibration methods and the diffractive phase calibration methods. The principles of phase-only SLM are introduced. The main phase calibration methods are discussed and reviewed. The advantages of these methods are analyzed and compared. The potential methods for different applications are suggested.

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.

Characterization of Spatial Light Modulator Based on the Phase in Fourier Domain of the Hologram and Its Applications in Coherent Imaging

Although digital holography is used widely at present, the information contained in the digital hologram is still underutilized. For example, the phase values of the Fourier spectra of the hologram are seldom used directly. In this paper, we take full advantage of them for characterizing the phase modulation of a spatial light modulator (SLM). Incident plane light beam is divided into two beams, one of which passes the SLM and interferes with the other one. If an image with a single grey scale loads on the SLM, theoretical analysis proves that the phase of the Fourier spectra of the obtained hologram contains the added phase and a constant part relative to the optical distance. By subtracting the phase for the image with the grey scale of 0 from that for the image with other grey scales, the phase modulation can be characterized. Simulative and experimental results validate that the method is effective. The SLM after characterization is successfully used for coherent imaging, which reconfirms that this method is exact in practice. When compared to the traditional method, the new method is much faster and more convenient.

Characterizing a spatial light modulator using ptychography

Ptychography is used to characterize the phase response of a spatial light modulator (SLM). We use the technique to measure and correct the optical curvature and the gamma curve of the device. Ptychography's unique ability to extend field of view is then employed to test performance by mapping the phase profile generated by a test image to subpixel resolution over the entire active region of the SLM.

Interferometric method for phase calibration in liquid crystal spatial light modulators using a self-generated diffraction-grating

An auto-referenced interferometric method for calibrating phase modulation of parallel-aligned liquid crystal (PAL) spatial light modulators (SLM) is described. The method is experimentally straightforward, robust, and requires solely of a collimated beam, with no need of additional optics. This method uses the SLM itself to create a tilted plane wave and a reference wave which mutually interfere. These waves are codified by means of a binary diffraction grating and a uniformly distributed gray level area (piston) into the SLM surface. Phase shift for each gray level addressed to the piston section can then be evaluated. Phase modulation on the SLM can also be retrieved with the proposed method over spatially resolved portions of the surface. Phase information obtained with this novel method is compared to other well established calibration procedures, requiring extra elements and more elaborated optical set-ups. The results show a good agreement with previous methods. The advantages of the new method include high mechanical stability, faster performance, and a significantly easier practical implementation.

Nonlinear dynamic phase response calibration by digital holographic microscopy

An accurate phase characterization method by digital holographic microscopy for spatial light modulators (SLMs) is proposed. This method permits high precision measurement for individual SLM pixels. Based on this method, the nonlinear dynamic phase response of the SLM is analyzed and calibrated in two steps: the global phase calibration and the local phase calibration. After the calibrations, both the phase modulation deficiency and the sharp phase jump of the 26-step grating are optimized. The root mean square error of the phase grating is reduced from 1.6319 to 0.2132 rad. The accurate phase distribution control may find various applications concerning high-resolution and high-accuracy wavefront modulation.

Calibration of spatial light modulators suffering from spatially varying phase response

We present a method for converting the desired phase values of a hologram to the correct pixel addressing values of a spatial light modulator (SLM), taking into account detailed spatial variations in the phase response of the SLM. In addition to thickness variations in the liquid crystal layer of the SLM, we also show that these variations in phase response can be caused by a non-uniform electric drive scheme in the SLM or by local heating caused by the incident laser beam. We demonstrate that the use of a global look-up table (LUT), even in combination with a spatially varying scale factor, generally does not yield sufficiently accurate conversion for applications requiring highly controllable output fields, such as holographic optical trapping (HOT). We therefore propose a method where the pixel addressing values are given by a three-dimensional polynomial, with two of the variables being the (x, y)-positions of the pixels, and the third their desired phase values. The coefficients of the polynomial are determined by measuring the phase response in 8 × 8 sub-sections of the SLM surface; the degree of the polynomial is optimized so that the polynomial expression nearly replicates the measurement in the measurement points, while still showing a good interpolation behavior in between. The polynomial evaluation increases the total computation time for hologram generation by only a few percent. Compared to conventional phase conversion methods, for an SLM with varying phase response, we found that the proposed method increases the control of the trap intensities in HOT, and efficiently prevents the appearance of strong unwanted 0th order diffraction that commonly occurs in SLM systems.

Spatially resolved phase-response calibration of liquid-crystal-based spatial light modulators

Methods for measuring and compensating the nonlinear electro-optical effect of transmissive, parallel-aligned liquid crystal (LC)-based spatial light modulators (SLMs) are presented. Particularly, the analysis is focused on the spatial nonuniformity of the voltage versus phase modulation characteristics for an active-matrix-driven, electrically controlled birefringence type LC-SLM. A high-quality reconstruction from phase-only modulating SLMs requires a well-calibrated phase addressing across the entire SLM panel. I discuss how the commonly inherent phase-response inhomogeneity of LC-SLM is characterized by purposeful localized measurement techniques. This phase-response inhomogeneity is efficiently compensated by utilizing a Legendre polynomial representation in combination with a remapping of an 8 bit gray level addressing. The calibration procedure is corroborated by measurement data. The LC-SLM's experimental demonstration finally verifies the resultant improvement in holographic imaging.

Extended viewing angle holographic display system with tilted SLMs in a circular configuration

This paper presents an extended viewing angle holographic display for reconstruction of real world objects in which the capture and display systems are decoupled. This is achieved by employing multiple tilted spatial light modulators (SLMs) arranged in a circular configuration. In order to prove the proper reconstruction and visual perception of holographic images the Wigner distribution function is employed. We describe both the capture system using a single static camera with a rotating object and a holographic display utilizing six tilted SLMs. The experimental results based on the reconstruction of computer generated and real world scenes are presented. The coherent noise removal procedure is described and implemented. The experiments prove the possibility to view images reconstructed in the display binocularly and with good quality.

Holographic display with tilted spatial light modulator

In this paper, we analyze a holographic display system utilizing a phase-only spatial light modulator (SLM) based on liquid crystal on silicon (LCoS). An LCoS SLM works in reflection, and, in some applications, it is convenient to use with an inclined illumination. Even with a highly inclined illumination, the holographic display is capable of good-quality image generation. We show that the key to obtain high-quality reconstructions is the tilt-dependent calibration and algorithms. Typically, an LCoS SLM is illuminated with a plane wave with normal wave vector. We use inclined illumination, which requires development of new algorithms and display characterization. In this paper we introduce two algorithms. The first one is designed to process a digital hologram captured in CCD normal configuration, so it can be displayed in SLM tilted geometry, while the second one is capable of synthetic hologram generation for tilted SLM configuration. The inclined geometry asymmetrically changes the field of view of a holographic display. The presented theoretical analysis of the aliasing effect provides a formula for the field of view as a function of SLM tilt. The incidence angle affects SLM performance. Both elements of SLM calibration, i.e., pixel phase response and wavefront aberrations, strongly depend on SLM tilt angle. The effect is discussed in this paper. All of the discussions are accompanied with experimental results.

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.

On resolution and viewing of holographic image generated by 3D holographic display

In the paper Wigner Distribution (WD) representation analysis of holographic display is presented. The display reconstructs holographic image by means of Spatial Light Modulator. Two major aspects are covered: imaging and viewing. Optically reconstructed images are characterized by low and spatially variant resolution. Utilizing WD representation we present a simple formula for resolution as a function of both coordinates: transverse and longitudinal. The analysis of an aliasing effect allows for meaningful extension of the field of view. All theoretical results are proven experimentally. The WD representation of angularly and spatially limited holographic image is extended to cover its visual perception as well. Angular resolution and field of view are theoretically examined. Both monocular and binocular perception are studied and illustrated experimentally.

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.

Sagnac-interferometer-based characterization of spatial light modulators

A method for characterizing the phase response of spatial light modulators (SLMs) by using a Sagnac interferometer is proposed and demonstrated. The method represents an improvement over conventional diffraction-based or interferometric techniques by providing a simple and accurate phase measurement while taking advantage of the inherent phase stability of a Sagnac interferometer. As a demonstration, the phase response of a commercial liquid crystal on a silicon SLM is characterized and then linearized by using a programmable lookup table. The transverse phase profile over the SLM surface is also measured.

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.

Analysis of PVA/AA based photopolymers at the zero spatial frequency limit using interferometric methods

One of the problems associated with photopolymers as optical recording media is the thickness variation during the recording process. Different values of shrinkages or swelling are reported in the literature for photopolymers. Furthermore, these variations depend on the spatial frequencies of the gratings stored in the materials. Thickness variations can be measured using different methods: studying the deviation from the Bragg's angle for nonslanted gratings, using MicroXAM S/N 8038 interferometer, or by the thermomechanical analysis experiments. In a previous paper, we began the characterization of the properties of a polyvinyl alcohol/acrylamide based photopolymer at the lowest end of recorded spatial frequencies. In this work, we continue analyzing the thickness variations of these materials using a reflection interferometer. With this technique we are able to obtain the variations of the layers refractive index and, therefore, a direct estimation of the polymer refractive index.

Polarization-splitting common-path interferometer based on a zero-twist liquid crystal display

We present a compact optical polarization-splitting common-path interferometer based on a zero-twist liquid crystal display (LCD). The LCD is encoded with a diffraction grating pattern and illuminated with a polarization state with both horizontal and vertical components. The polarization component perpendicular to the director axis of the liquid crystal molecules is not affected by the LCD and forms the reference beam. However, the polarization component parallel to the director axis is diffracted at an angle determined by the period of the grating. By imposing an analyzer polarizer, these two beams create an interferogram that can either display retardance patterns encoded onto the LCD or analyze external birefringent optical elements. The programmability of the system allows new ways of increasing the utility of the interferograms. Experimental results are provided, including the visualization of optical vortices with different and opposite topological charges.

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.

Real-time interferometric characterization of a polyvinyl alcohol based photopolymer at the zero spatial frequency limit

We characterize the optical modulation properties of a polyvinyl alcohol/acrylamide (PVA/AA) photopolymer at the lowest end of recorded spatial frequencies. To achieve this goal we have constructed a double beam interferometer in combination with the setup to expose the recording material. This is a novel approach since usually holographic recording materials are only characterized at high spatial frequencies. Some benefits are provided by the approach we propose: a direct calculation of the properties of the material is possible, and on the other hand additional information can be obtained since the results are not influenced by diffusion processes. Furthermore, this characterization is needed to optimize the PVA/AA photopolymers for another range of applications, such as recording of diffractive optical elements, where very low spatial frequencies are recorded. Different PVA/AA compositions and layer thicknesses have been analyzed. We have found that, depending on the layer characteristics, we can achieve high values of the phase-shift modulation depth and enhance the sensitivity of the material.

Self-interferometric technique for visualization of phase patterns encoded onto a liquid-crystal display

We report a new self-interferometric technique for visualizing phase patterns that are encoded onto a phase-only liquid-crystal display (LCD). In our approach, the LCD generates both the desired object beam as well as the reference beam. Normally the phase patterns are encoded with a phase depth of 2pi radians, and all of the incident energy is diffracted into the first-order beam. However, by reducing this phase depth, we can generate an additional zero-order diffracted beam, which acts as the reference beam. We work at distances such that these two patterns spatially interfere, producing an interference pattern that displays the encoded phase pattern. This approach was used recently to display the phase vortices of helical Ince-Gaussian beams. Here we show additional experimental results and analyze the process.

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.

Modified minimum-distance criterion for blended random and nonrandom encoding

Two pixel-oriented methods for designing Fourier transform holograms--pseudorandom encoding and minimum-distance encoding-usually produce higher-fidelity reconstructions when combined than those produced by each method individually. In previous studies minimum-distance encoding was defined as the mapping from the desired complex value to the closest value produced by the modulator. This method is compared with a new minimum-distance criterion in which the desired complex value is mapped to the closest value that can be realized by pseudorandom encoding. Simulations and experimental measurements using quantized phase and amplitude modulators show that the modified approach to blended encoding produces more faithful reconstructions than those of the previous method.