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In this work we provide a simple experimental method to measure and evaluate the pixel crosstalk in phase-only liquid-crystal displays caused by the fringing field effect. The technique is a reverse engineering method that does not require information about the microscopic physical parameters of the liquid-crystal material or details of the fabrication and electronics of the display. Instead, it is based on the overall effect on the diffraction efficiency of displayed binary phase gratings as a function of the addressed gray level. We show how the efficiency of the zero (DC) and first diffraction orders provides valuable information enough to identify and quantify the pixel crosstalk. The technique is demonstrated with a modern phase-only liquid-crystal on silicon (LCOS) spatial light modulator (SLM), illustrating the limitations that this effect imposes to the spatial resolution of the device and providing quantitative measurement of the impact on the diffraction efficiency.

In this work we present a new method to optically obtain the convolution / correlation between two functions. The technique is based on obtaining higher powers of a properly designed phase-only hologram. The approach combines some of the advantages of the classical 4f and the JFTC correlator systems. These higher powers of the hologram transmission function can be obtained easily using a spatial light modulator (SLM) with an extended phase modulation of various cycles of 2π radians. SLMs with such extended phase modulation present useful unusual diffraction properties that can be exploited to surpass some limits of SLM technology. In this case we exploit them to obtain higher order optical correlation terms. Computational simulations and experimental results agree with theory.

When encoding diffractive lenses onto a spatial light modulator (SLM), there is a Nyquist limit to the smallest focal length that can be formed. When this limit is surpassed, a two-dimensional array of lenslets is formed. There have been very few discussions on the performance of these lenslets. In this work, we focus on the phase distribution of these lenses in the array. We show that, for certain values of the focal length, the lenslets are all in perfect phase. We show that this situation happens for a total number of N / 4 different discrete equidistant sub-Nyquist focal lengths, where N × N is the number of pixels in the SLM. We find other distances in between where the array is composed of two sets of lenslets with a relative π phase among them. Finally, we illustrate these phase distributions in the application to generate an array of vortex producing lenses. We expect that these results might be useful for high-accuracy interferometric or multiple imaging where this phase must be exactly the same for each replica.

In standard phase spatial light modulators (SLM), showing a phase modulation of 2π radians, there is a limit to the shortest focal length of an encoded lens. This Nyquist focal length limit is caused by the aliasing originated by the SLM pixelated structure. In this work we show that SLMs with very large phase modulation (in our case about five cycles of 2π radians) can be used to surpass this effect and efficiently encode lenses with focal lengths much lower than the Nyquist limit. We include experimental results showing that this limit is reduced by a factor of about 1/10.

We present a new type of optical convolver / optical correlator capable of encoding higher orders. The technique is based on obtaining higher powers of a properly designed hologram. This can be obtained in two ways. First, we can recalculate higher orders of the amplitude and phase hologram in a standard spatial light modulator (SLM). More easily, we can utilize a phase-only hologram and exploit the properties of an SLM with extended phase modulation range. Experimental results agree with theory in both cases.

We reexamine a simple technique for encoding complex amplitude information onto a phase-only spatial light modulator (SLM). The basis for the approach is to spatially vary the diffraction efficiency of a two-dimensional checkerboard binary phase diffraction grating where the period for the Nyquist grating is two pixels. As the phase depth of this 2D grating changes spatially, the amount of light diffracted into the zero order can be controlled. Unwanted information is encoded onto the first diffraction orders and is directed away from the center. This process uses a very simple coding algorithm to generate a complex beam reconstruction on-axis and allows exploiting the full spatial resolution for encoding amplitude. However, its experimental realization with the current liquid-crystal on silicon (LCOS) technology is strongly affected by the limitations imposed by the fringing effect in these devices. We provide experimental evidence of how this effect impacts the efficiency of diffraction gratings displayed on the SLM. We then show how it affects the encoding technique, both in the near field and in the Fourier transform domain, where the limitations imposed by the fringing effect are clearly visible in the form of a focused peak. These results provide evidence of the usefulness of the technique but also about the limitations imposed by the current LCOS technology, which do not allow fully exploiting their high resolution. Finally, we discuss the performance of these newer LCOS devices compared to other SLMs.

We report on the interference between the double rings generated by the Fourier transform of a binary diffractive axicon. These two rings have the same size and correspond to the ± 1 diffracted order beams. The interference condition between both rings can be easily changed by adding a constant phase bias, resulting in a central ring that is either dark or bright. Additionally, this interference condition can be changed along the ring and can be easily tuned, thus allowing greater flexibility. We present experimental results obtained with a binary π-phase liquid-crystal spatial light modulator. These patterns might find applications in optical trapping systems, where the bright or dark regions could trap particles whose refractive index is either higher or lower than the medium.

We have been investigating the angular spectrum method for analysis of single-mode and multimode optical fibers. The justification is simple because the approach requires less computational time than other methods because it is heavily dependent on the fast Fourier transform. This method should become much more important as new approaches are being studied for higher data rate transmission. We examine two basic components in the application of this technique to propagation of light in optical fibers – an absorbing layer at the outer radius and design of the interface between the cord and cladding of the optical fiber.

In this work, we present the realization of a high-phase diffractive axicon. For that purpose, we use a spatial light modulator that exhibits 10π phase modulation. We compare the results with standard diffractive axicons that exhibit 2π phase modulation. We show that high-phase modulation axicons generate Bessel beams with a shorter range and a smaller radius than standard axicons with the same period. We also find that the higher phase modulation regime provides improved diffraction efficiency since fringing effects are reduced. Therefore, dynamic control of Bessel beams is presented, controlled through the phase modulation dynamic range.

We present a holographic projection system based on the encoding of computer-generated holograms onto a spatial light modulator. We show how the size, location, and polarization state of the output can be controlled electronically, without physically moving any element. Experimental results are included in all cases

We examine single-mode optical fiber transmission using the angular spectrum method. We find excellent agreement with the theoretical solutions for the cylindrical single-mode optical fiber. Next, we examine fiber coupler configurations with 1×2, 1×3, and 1×5 designs. The input within the central fiber core is broadcast equally into the surrounding fiber cores and then returns with propagation distances as expected. Then we examine supermode theory for the 1×3 case. The initial energy is sent into different combinations of fiber cores where their phase relationship governs the output. Surprisingly, we find evidence of an unexpected mode in some of the multicore designs. We expect these results might be useful for exploration of more complicated fiber core arrays. However, computational times are short using this algorithm.

We encode q-plates where the angular orientation of the principal axis is varied spatially with a nonstandard distribution. In the usual q-plate design, the orientation of the optical axis depends linearly on the azimuthal angle. In this work, we examine cases where this azimuthal dependence is nonlinear. We consider two cases: first, where the principal axis distribution is like an inverse-tangent function of the azimuth; and second, where it displays linear and flat segments. This last case is proposed as a new method for encoding binary data into the azimuthal lobes of the vector beam. We encode these patterns using a spatial light modulator system that allows new and exotic q-plate designs without the difficulty of fabricating individual plates. Experimental results are presented.

Vector beams where the polarization state is spatially dependent are being examined as new optical communication channels. We demonstrate a vector beam spectrum analyzer capable of simultaneously determining the topological charge and the state of polarization of an input vector beam. We encode a two-dimensional polarization diffraction grating that generates six different q-plate channels from -3 to +3 in the horizontal direction, and each is split in the vertical direction into the six polarization channels at the cardinal points of the corresponding higher-order Poincare sphere. The horizontal q-plate grating is a optimized phase-only grating that produces harmonics of a given input q-plate having a charge of +1 all of which have equal strengths. The vertical polarization grating is specially designed to produce 6 orders where the amplitude and phase of each order can be independently controlled. Different gratings are required for the horizontal and vertical polarizations to create the desired polarization states in each diffracted order. Consequently, we generate 36 different channels in parallel. We demonstrate this polarization diffraction element using a single phase-only liquid-crystal spatial light modulator in a reflective optical architecture. Details are given regarding experimental details on this process. Finally, we demonstrate that this system can act as a vector beam polarization state spectrum analyzer allowing both the topological charge and the polarization state of the input vector beam to be simultaneously determined in a single experiment.

Liquid crystal displays allow the easy implementation of diffractive optical elements. However, the shortest focal lengths for lenses are limited by Nyquist conditions. In this work, we show that focal lengths much lower than this Nyquist limit can be encoded onto devices having a large phase-dynamic range. Experimental results are included with a display showing 10π phase modulation reducing the Nyquist limit by a factor of about 1/10.

Multimode optical fibers are gaining increased interest for higher data rate transmissions. In this work, we examine the propagation of beams in multimode optical fibers using the angular spectrum method for several values for the propagation constant V. We prepare a sequence of 4096 images over 200,000 steps, each representing a wavelength within the fiber. We perform a one-dimensional Fourier transform of these data and obtain the propagation constant for each transmitted mode. We then obtain the electric field profile for each transmitted mode. We find excellent agreement with weakly guided mode theory. This work represents another step in the use of this algorithm for analyzing more complicated optical fiber structures.

In this work we report on our achievements in generating switchable and arbitrary vector beams by means of q-plates. Two kind of q-plates are considered: i) a physical prototype from Citizen Co. and ii) a virtual device that is encoded onto a spatial light modulator (SLM). In both cases experimental and analytical results within the Jones formalism are shown. The performance of a segmented and tunable liquid crystal q-plate prototype is characterized at visible and telecommunications wavelengths, and the generation of first-order vector beams is probed. By using a reflective geometry and tuning the q-plate at half-wave or at quarter-wave retardance, it is shown how the device can operate either as a q-plate with double order. Finally, we show the generation of arbitrary programmable integer and fractional vector beams by encoding a q-plate onto a SLM based system. The system is based on a double-pass configuration that consecutively modulates the vertical and the horizontal polarization components of light using a transmissive LCoS display. Therefore, new and exotic q-plate designs can be analyzed prior to their fabrication.

The robustness of the polarization spatial distribution of vector beams upon propagation is crucial for a number of applications, including optical communications and materials processing. This study has been commonly centered on Gouy phase effects on focused vector beams. In this work, we present a theoretical and experimental analysis of the Gouy phase's effects on the propagation of pure and hybrid vector beams. Experimental results at various axial planes, before and past the focus, are obtained by using a simplified liquid-crystal spatial light modulator-based optical system that allows the easy generation of these beams. Furthermore, a new alternative optical set-up that is devoid of moving elements is demonstrated, which simplifies this study. We experimentally verify the differences between pure and hybrid vector beams upon propagation. While the first ones remain stable, hybrid vector beams show Gouy phase effects that demonstrate an optical activity where the local polarization states rotate by an angle that depends on the propagation distance. Experimental results agree with the theory.

A holographic projection system based on the encoding of computer-generated holograms onto a spatial light modulator is discussed. We show how the size, location, and polarization state of the output can be controlled completely electronically, without physically moving any element in the system. It is finally shown that the system is capable to produce optical logical operations by superimposing two different images encoded onto orthogonal polarization states. We show how these images can be added or subtracted, giving a polarization-based logic system. Experimental results are included in all cases.

We create a series of vortex beams consisting of positive and negative topological charges and develop a geometry where they interfere creating azimuthal multiple-beam interference effects. Usually the combination of two beams with opposite charges creates an azimuthal two-beam interference effect where the intensity varies sinusoidally with azimuthal angle. We combine several of these beams to create patterns where the interference becomes more sharply defined in the azimuthal direction and where destructive interference eliminates some of the intensity peaks. The process is complicated by the fact that the radii of the different vortex beams depend on the topological charge and the focal length of the Fourier lens. We generate a series of patterns where the different charges are focused with different focal lengths such that their radii agree. However to encode these, we encode patterns from the lower charges that have been Fresnel diffracted to the plane of the highest charge. These complicated patterns are encoded onto a liquid crystal display (LCD). Experimental results agree well with theory.

In this paper the fast Fresnel diffraction algorithm is reviewed and applied to some novel applications. The algorithm (also named the convolution or angular spectrum method) is a very powerful numerical technique that has been employed in the calculation of diffraction patterns. It utilizes two Fourier transform operations, thus becoming computationally much faster than the conventional approach. We analyze the practical implementation with spatial light modulators (SLM). First, the ray matrix approach is applied to derive and reexamine this computational technique. This approach easily allows us to find explicit expressions for the maximum and minimum distances over which the algorithm is accurate. Then, we describe the practical implementation of this algorithm to encode Fresnel propagated masks onto a SLM. We discuss the limitations caused by the Nyquist limit. Finally, we apply the technique to create an experimental virtual optical beam propagator system. This system uses one SLM and allows the experimental study of the beam propagation without physically moving any element. This laboratory propagator system can be extremely useful to build compact optical architectures or to emulate beam propagation without misalignments caused by moving elements in the experimental system. As examples, we design holograms capable of producing different patterns at different distances, and we can change the effective plane of observation by changing the encoded propagation. The technique can find applications in many different contexts, including the analysis of propagation dynamics of nondiffracting beams, and Airy beams.

We present an experimental multichannel polarization imaging system based on a polarization diffraction grating (PDG). The PDG simultaneously creates six diffraction orders, each having a different polarization state. For this proof-of-concept experiment, we encoded the PDG onto a parallel-aligned liquid-crystal spatial light modulator (LCSLM), using a double-pass optical architecture. We use a birefringent object where the top is covered with a retardation film and the bottom is isotropic. We show experimental results, where we simultaneously produce six images of this birefringent object, each with a different polarization state. The proposed technique can produce a single-shot imaging polarimeter.

In this work, we present a method to generate a 3D lattice of vortex beams. We apply phase look-up tables (LUTs) designed to generate gratings having an arbitrary content of diffraction orders. This phase LUT can be applied to a variety of diffraction optical elements, such as linear phase gratings, blazed diffractive lenses, and spiral phase patterns. We concentrate on combinations of all of these to create 3D structures of vortex beams. In particular, we generate all of these elements in the first output quadrant and eliminate the zero-order diffraction that often unavoidably accompanies these patterns. We discuss different ways of producing these 3D vortex gratings, and how the various output beams are related to the arithmetic of the 3D distribution of topological charges. Experimental results are provided by means of a liquid crystal spatial light modulator.

There is great interest in Airy beams because they appear to propagate in a curved path. These beams are usually generated by inserting a cubic phase mask onto the input plane of a Fourier transform system. Here, we utilize a fast Fresnel diffraction algorithm to easily derive both the propagation dynamics and the Gouy phase shift for these beams. The trajectories of these beams can be modified by adding additional linear and quadratic phase terms onto the cubic phase mask. Finally, we have rewritten the equations regarding the propagating Airy beams completely in laboratory coordinates for use by experimentalists. Experimental results are included. We expect that these results will be of great importance in applications of Airy beams.

Diffraction gratings produce a number of diffraction orders, which relative intensity is directly related to the grating profile. Continuous blazed phase-only gratings have the greatest efficiency onto a single first order [1], but they are difficult to fabricate. In more common binary amplitude or binary phase gratings, numerous diffracted harmonic orders are produced [2]. Dammann gratings are of interest because they produce equal intensities in a given number of selected orders [3]. They are designed by subdividing each grating period into regions with phases 0 or π radians. In order to increase their efficiency, different studies were conducted in the field of the so called fan-out arrays, extensively developed in the late 80’s [4]. More recently, Romero and Dickey further extended and provided a general framework for the design of optimal fan-out phase elements [5,6], by extending a previous study on the optimal triplicator [7]. The method provides an analytical optimal solution for designing a grating with a set of target diffraction orders. The calculation involves optimization of two numerical variables for each target order, and results in a single function that generates a periodic diffraction grating with continuous phase modulation levels.

We demonstrate encoding of positive and negative Fresnel diffraction onto a spatial light modulator. This allows the capability to study a propagating beam without moving the detector plane

We generate cylindrically polarized and more complicated variations of polarized light beams using a liquid crystal spatial light modulator and a double-pass architecture by adding additional linear and quadratic phase shifts to the two circular polarization components

In this work we describe techniques for the generation of vortex beams, including vortex generating diffraction gratings and diffractive lenses, as well as some possible applications in optical image processing. We then analyze the description of radially polarized beams in terms of superposition of such vortex beams. We present some methods for the production of radially polarized light, that include patterned linear polarizers, specially designed liquid crystal devices and spatial light modulators (SLMs). We analyze the manipulation of this radial polarization by means of wave-plates, in order to obtain other non-standard spatially variant polarized light beams. Theoretical analysis are presented based on the Jones matrix theory, and experimental results are included for all cases.

International audience; We report a method to generate phase-only diffractive beam splitters allowing asymmetry of the target diffracted orders, as well as providing a tailored phase difference between the diffracted orders. We apply a well-established design method that requires the determination of a set of numerical parameters, and avoids the use of image iterative algorithms. As a result, a phase lookup table is determined that can be used for any situation where a first-order (blazed) diffractive element is modified to produce higher or- ders with desired intensity and/or phase relation. As examples, we demonstrate the phase difference control on triplicators, as well as on other generalized diffractive elements like bifocal Fresnel lenses and phase masks for the generation of vortex beams. Results are experimentally demonstrated by en- codingthe calculated phasepattern onto parallel-aligned liquid crystalspatial light modulators. © 2013 Optical Society of America

Abruptly focusing Airy beams have previously been generated using a radial cubic phase pattern that represents the Fourier transform of the Airy beam. The Fourier transform of this pattern is formed using a system length of 2f, where f is the focal length of the Fourier transform lens. In this work, we directly generate these abruptly focusing Airy beams using a 3/2 radial phase pattern encoded onto a liquid crystal display. The resulting optical system is much shorter. In addition, we can easily produce vortex patterns at the focal point of these beams. Experimental results match theoretical predictions.

International audience; We present a simple method to check the exact realization of a radially polarized light beam by means of a vortex-sensing diffraction grating. The use of this grating easily allows the determination of the topological charges included in each of the two circular polarization components of the incident beam. Therefore a pure radially polarized beam can be easily distinguished from a pseudo-radially polarized beam. Experimental results are presented with radial beams generated with two different devices: a patterned radial polarizer and a specially designed liquid crystal device.

Vector beams, usually generated using q-plates, are of interest because their polarization state varies spatially. In general, the q-plate performance is examined by illuminating the device and detecting the output beam with polarization states on the 6 cardinal points on the zero-order Poincaré sphere, requiring a total of 36 separate measurements. In this work we present a powerful technique to generate arbitrary vector beams in parallel, thus reducing the number of measurements required. We begin with a programmable polarization diffraction grating capable to generate an arbitrary number of diffraction orders with defined polarization states selected at will. Then we combine this grating with a segmented q-plate device with q = 1/2 value. Using this combination, the parallel generation of six arbitrary first-order vector beams is achieved in a single shot. Therefore, the analysis of these beams can be greatly reduced.

Anderson localization has been previously demonstrated both theoretically and experimentally for transmission of a Gaussian beam through long distances in an optical fiber consisting of a random array of smaller fibers, each having either a higher or lower refractive index. However, the computational times were extremely long. We show how to simulate these results using a fast Fresnel diffraction algorithm. In each iteration of this approach, the light passes through a phase mask, undergoes Fresnel diffraction over a small distance, and then passes through the same phase mask. We also show results where we use a binary amplitude mask at the input that selectively illuminates either the higher or the lower index fibers. Additionally, we examine imaging of various sized objects through these fibers. In all cases, our results are consistent with other computational methods and experimental results, but with a much reduced computational time.

We generate nondiffracting vector beams where the charge and the polarization state vary with the propagation distance. We use reflective geometry where a parallel-aligned spatial light modulator is used to spatially modulate two orthogonal linear polarizations. We encode spiral phases with equal charge but with opposite signs onto the two polarization directions to encode a vector beam and add two axicon phases. Both the charge and the phase shift between the two axicons can be varied along the focus line. We provide experimental results that demonstrate both features.

We generate programmable vector beams with arbitrary q-plates encoded using a spatial light modulator system. Consequently, we can analyze new and exotic q-plate designs without the difficulty of fabricating individual plates. We show experimental results for positive and negative integer and new fractional vector beam values.

We report the generation of continuous phase masks designed to generate a set of target diffraction orders with defined relative intensity weights. We apply a previously reported analytic calculation that requires resolving a single equation with a set of parameters defining the target diffraction orders. Then the same phase map is extended to other phase patterns such as vortex generating/sensing gratings. Results are demonstrated experimentally with a parallel-aligned spatial light modulator.

In this work we apply the Dammann grating concept to generate an equal-intensity square array of Bessel quasi-free diffraction beams that diverge from a common center. We generate a binary phase mask that combines the axicon phase with the phase of a Dammann grating. The procedure can be extended to include vortex spiral phases that generate an array of optical pipes. Experimental results are provided by means of a twisted nematic liquid crystal display operating as a binary π phase spatial light modulator.

We present a method to generate complete arbitrary spatially variant polarization modulation of a light beam by means of a parallel aligned nematic liquid crystal spatial light modulator (SLM). We first analyze the polarization modulation properties in a transmission mode. We encode diffraction gratings onto the SLM and show how to achieve partial polarization control of the zero order transmitted light. We then extend the technique to a double modulation scheme, which is implemented using a single SLM divided in two areas in a reflective configuration. The polarization states of the transmitted beam from the first pass through the first area are rotated using two passes through a quarter wave plate. The beam then passes through the second area of the SLM where additional polarization information can be encoded. By combining previously reported techniques, we can achieve complete amplitude, phase and polarization control for the diffracted light that allows the creation of arbitrary diffractive optical elements including polarization control. Theoretical analysis based on the Jones matrix formalism, as well as excellent experimental results are presented.

We show that the output from wave front coding systems depends critically upon the optical imaging system. Our analysis is based on results using nondiffracting accelerated Airy beams and we show computational results.

We show that the output from wavefront coding systems depends critically upon the optical imaging system. Our analysis is based on results using nondiffracting accelerated Airy beams. We review the similarities and critical differences between various optical systems and show computational results. We suggest new directions for improving the performance of these wavefront coding masks.

The Fraunhofer diffraction pattern from a partially blocked spiral phase plate (SPP) produces a partial vortex output pattern that is rotated by 90 degrees compared with the input. The rotation direction depends on whether the angular phase pattern increases in the clockwise or counterclockwise direction. In this work, we present an explanation of this effect based on careful examination of classical diffraction theory and show new experimental results. This approach is very convenient for easily determining the sign of the vortex charge.

We demonstrate the creation of a three dimensional (3D) lattice of focus spots using a 3D Dammann grating structure. Such a 3D lattice of focus spots can be used for probing 3D structures or for creating 3D photonic crystal structures in optically sensitive media. Experimental results are included where the patterns are encoded onto a programmable liquid crystal display. We demonstrate the generation of five planar arrays each having 6×6 points surrounding another set of four planar arrays each having 5×5 points with a single pattern.

Vortex sensing diffraction gratings can analyze the sign and charge value of an incident vortex beam. They allow vortex spectral analysis of fractional vortex beams as well as the output from segmented spiral phase plates.

A 3D lattice of equally intense focus spots can be created using a 3D Dammann structure. We show 4 planar arrays each having 4x4 points using a single pattern.

Optical vortices can be easily generated using a multilevel spiral phase plate (SPP). However the quality of the generated vortex beam depends on the number of phase segments. We review the theory for this multilevel SPP using a Fourier expansion of integer topological charged vortices. We then experimentally examine the validity of this expansion using a fabricated Dammann vortex diffraction grating spectrum analyzer. The Dammann vortex diffraction grating is fabricated using SU-8 photoresist on glass substrate and yields uniform diffraction efficiency across a desired number of diffracted orders. Experimental results show the extra angular harmonics of a multilevel SPP and agree with the theory.

Nondiffracting beams are useful for alignment applications because the size of the beam does not change as the beam propagates. In this research we report a technique that allows for distance measurements with nondiffracting beams. With our approach a diffractive optical element is designed that generates two off-axis, tilted, nondiffracting Bessel function beams. These beams intersect at a desired distance from the input plane, producing interference. We generate these Bessel function arrays with a programmable spatial light modulator allowing external control over the intersection distance.

Nondiffracting beams are of interest for optical metrology applications because the size and shape of the beams do not change as the beams propagate. We have created a generating pattern consisting of a linear combination of two nondiffracting patterns. This pattern forms a nondiffracting interference pattern that appears as a circular array of nondiffracting spots. More complicated multiplexed arrays are also constructed that simultaneously yield two different nondiffracting patterns. We generate these Bessel function arrays with a programmable spatial light modulator. Such arrays would be useful for angular alignment and for optical interconnection applications.

Nondiffracting beams are of interest for optical metrology applications because the size of the beam does not change as the beam propagates. However, accuracy can be increased if the diameter of the beam is smaller. One technique for accomplishing this is to use the dark axial intensity profile associated with a higher-order nondiffracting Bessel function beam. We generate these higher-order Bessel function beams with a programmable spatial light modulator. We study the intensity patterns and the phase dependence of these nondiffracting beams. In addition, we examine interference effects caused by recording these patterns onto a binary spatial light modulator.