Kinoform using an electrically controlled birefringent liquid-crystal spatial light modulator

Lithography-free IR polarization converters via orthogonal in-plane phonons in α-MoO3 flakes

Exploiting polaritons in natural vdW materials has been successful in achieving extreme light confinement and low-loss optical devices and enabling simplified device integration. Recently, α-MoO₃ has been reported as a semiconducting biaxial vdW material capable of sustaining naturally orthogonal in-plane phonon polariton modes in IR. In this study, we investigate the polarization-dependent optical characteristics of cavities formed using α-MoO₃ to extend the degrees of freedom in the design of IR photonic components exploiting the in-plane anisotropy of this material. Polarization-dependent absorption over 80% in a multilayer Fabry-Perot structure with α-MoO₃ is reported without the need for nanoscale fabrication on the α-MoO₃. We observe coupling between the α-MoO₃ optical phonons and the Fabry-Perot cavity resonances. Using cross-polarized reflectance spectroscopy we show that the strong birefringence results in 15% of the total power converted into the orthogonal polarization with respect to incident wave. These findings can open new avenues in the quest for polarization filters and low-loss, integrated planar IR photonics and in dictating polarization control.

Scalable micromesh-digital spatial light modulators

Digital spatial light modulators (SLMs) with small pitch comparable to the wavelength of illuminating light and large physical dimension comparable to consumer displays are highly demanding for realizing realistic digital holography but are impractical due to various technical issues. Previously we proposed the way to overcome these hurdles by scalable SLM-micromesh (μM) heterostructures utilizing large scale consumer displays and passive binary amplitude μMs (AMs). However, a few drawbacks with these heterostructures are identified such as their low power efficiency due to the blocking of light beam diffracted from the SLM by the opaque part of the AM and the brightest zeroth order diffraction beam causing the lower power efficiency at higher diffraction orders. Thus in this paper, we employed scalable binary phase micromeshes (PMs) instead of AMs in the scalable heterostructures. This is able to minimize the power loss and to diminish the zeroth order diffraction beam simultaneously without requiring any time consuming steps. As a result, this allows full utilization of large scale consumer displays for scalable digital holography by employing scalable SLM-μM heterostructures with negligible power loss.

Enhancing the quality of reconstructed 3D objects by using point clusters

A novel algorithm for constructing computer-generated holograms using point clusters is presented. This method exploits the precalculated triangular meshes used in previous research and can reconstruct less noisy 3D objects. In addition, the high-speed property of a ferroelectric liquid crystal spatial light modulator is utilized to enhance the reconstruction quality. All 3D holograms generated in this paper are based on Fresnel propagation; thus, the Fresnel plane is treated as a vital element in producing the hologram. A GeForce GTX 770 graphics card with 2 GB memory was used to achieve parallel high-speed hologram generation.

Fast precalculated triangular mesh algorithm for 3D binary computer-generated holograms

A new method for constructing computer-generated holograms using a precalculated triangular mesh is presented. The speed of calculation can be increased dramatically by exploiting both the precalculated base triangle and GPU parallel computing. Unlike algorithms using point-based sources, this method can reconstruct a more vivid 3D object instead of a "hollow image." In addition, there is no need to do a fast Fourier transform for each 3D element every time. A ferroelectric liquid crystal spatial light modulator is used to display the binary hologram within our experiment and the hologram of a base right triangle is produced by utilizing just a one-step Fourier transform in the 2D case, which can be expanded to the 3D case by multiplying by a suitable Fresnel phase plane. All 3D holograms generated in this paper are based on Fresnel propagation; thus, the Fresnel plane is treated as a vital element in producing the hologram. A GeForce GTX 770 graphics card with 2 GB memory is used to achieve parallel computing.

Hybrid holographic microscopy free of conjugate and zero-order images

The true image area that can be used for recording microscopic objects in hybrid holographic microscopy can be increased by elimination of the conjugate image and the zero-order image. We therefore added two shutters and one phase modulator to the electro-optical holographic recording system so that we could change the recording parameters and evaluate four methods of eliminating the conjugate image and the zero-order image. We found that the methods that use only the phase modulator require the recording of fewer holograms than do the methods that use the shutters and also provide reconstructed images that are less noisy.

Polarization eigenstates for twisted-nematic liquid-crystal displays

We derive theoretical expressions for the eigenvalues and the eigenvectors for a twisted-nematic liquid-crystal display (LCD) as a function of the twist angle and the birefringence by use of the Jones-matrix formalism. These polarization eigenvectors are of particular interest for phase-only transmission because they propagate unchanged through the display. We find that the eigenvectors are elliptically polarized and that the ellipticity changes as a function of the birefringence of the LCD (which is proportional to the external voltage applied to the display). We can define an average eigenvector over a desired range for the applied voltage. We show, using Jones matrices, how this average eigenvector can be generated using a quarter-wave plate and a linear polarizer having appropriate orientation angles. Using this average eigenvector, we show that superior phase-only operation can be obtained over a given operating range for the LCD compared with other approaches.

Object-binarized phase-only matched filtering with dual liquid-crystal spatial light modulators

A real-time optical processing system with dual liquid-crystal spatial light modulators is constructed and used as both an amplitude-input device and a multilevel phase-only filter. Fourier analysis is given to show the performance of light efficiency, signal-to-noise ratio, and discrimination capability with the binarization of gray objects. The ratio of the dc power spectrum to the power spectra for input objects is introduced to incorporate the power spectrum into discrimination-capability evaluation. A numerical calculation is performed for gray-level and binarized amplitude-phase correlations. Improvement of the performance criteria has been achieved for an amplitude in a binary mode to a phase correlator. The higher the threshold level of the binarized objects is, the better performance criteria are produced. The effect of illumination over an input object on the autocorrelation maximum is experimentally investigated. Experimental results are presented to support the calculations.

Interlacing technique approach for the synthesis of kinoforms

An interlacing technique algorithm is proposed for the synthesis of kinoforms. The conventional iterative methods are quite powerful for optimizing kinoforms, but there is still a large reconstruction error for a quantized kinoform. We suggest the use of a number of subkinoforms interlaced together to synthesize a multikinoform for reconstructing the desired image. The idea of our interlacing technique is to increase the size of a kinoform to reduce the reconstruction error. The first subkinoform is generated from the desired image. Other subkinoforms are generated from the error images between the desired image and the image reconstructed from the previous subkinoforms. A theoretical analysis shows that the reconstruction error will be reduced as the number of subkinoforms is increased. Simulation results show that our interlacing method can reduce the reconstruction error more than do the conventional iterative methods and that the reconstructed image can be improved.

Reconfigurable lens with an electro-optical learning system

An electro-optical system is proposed to control a reconfigurable lens that is a combination of a physical lens and a two-dimensional liquid-crystal phase modulator. The functions of an imaging system employing the reconfigurable lens can be controlled by a change in the phase distribution of the modulator. A computer changes the phase distribution and evaluates the image of an optical system. This process is iteratively performed on the basis of the simulated-annealing algorithm to optimize the phase distribution. We demonstrate control of a point-spread function and the correction of imaging properties degraded by defocusing or phase objects. The corrected imaging properties are even better than the original ones.

Phase retrieval of recorded kinoform transmittance and estimation of the phase-recording curve characteristic

Methods are presented for recovering, by the use of the basic Gerchberg-Saxton algorithm, the complex-valued transmittance of a recorded kinoform and for estimating the phase-recording curve characteristic of a kinoform-fabrication system by comparison of the phase to be recorded with that actually recorded. Related issues considered here are the shift of the central sampling point from the optical axis in the Fourier-image domain, a kinoform phase sequence suitable for estimating the curve characteristic, the initial estimate of the iterative algorithm, and the influence of errors in the measurement of the kinoform or of the Fourier-image amplitude. Results of an optical experiment with a fabrication system including a photographic process are discussed and shown to confirm the effectiveness of the proposed methods.

Pseudorandom phase-only encoding of real-time spatial light modulators

We previously proposed a method of mapping full-complex spatial modulations into phase-only modulations. The Fourier transform of the encoded modulations approximates that of the original complex modulations. The amplitude of each pixel is encoded by the property that the amplitude of a random-phasor sum is reduced corresponding to its standard deviation. Pseudorandom encoding is designed for phase-only spatial light modulators that produce 360° phase shifts. Because such devices are rare, experiments are performed with a 326°modulator composed of two In Focus model TVT6000 liquid-crystal displays. Qualitative agreement with theory is achieved despite several nonideal properties of the modulator.

Liquid-crystal point-diffraction interferometer for wave-front measurements

A new instrument, the liquid-crystal point-diffraction interferometer (LCPDI), is developed for the measurement of phase objects. This instrument maintains the compact, robust design of Linnik's point-diffraction interferometer and adds to it a phase-stepping capability for quantitative interferogram analysis. The result is a compact, simple to align, environmentally insensitive interferometer capable of accurately measuring optical wave fronts with very high data density and with automated data reduction. We describe the theory and design of the LCPDI. A focus shift was measured with the LCPDI, and the results are compared with theoretical results.

Programmable multiple-level phase modulation that uses ferroelectric liquid-crystal spatial light modulators

We present a novel method of producing arbitrarily valued binary phase-only modulation from a commercially available ferroelectric liquid-crystal spatial light modulator that is used in conjunction with simple polarization components. By cascading of such stages, modulators with four and eight equally spaced phase levels are constructed with 128 × 128 pixels. Near-diffraction-limited performance, when stopped down to 64 × 64 pixels, is reported in producing simple diffraction patterns and when used to generate asymmetric spot arrays in the Fourier plane of a lens.

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.

Speckle-noise reduction on kinoform reconstruction using a phase-only spatial light modulator

Random-phase distributions that are statistically independent individually are used for computing kinoforms. These uncorrelated kinoforms are recorded and read out sequentially by a phase-only liquid-crystal spatial light modulator, and reconstructed images with well-developed speckles are added. The fidelity of the resultant image to an original is improved as the number of additions increases. The dependence of the speckle contrast on the initial random phase and the influence of the liquid-crystal spatial light modulator's display performance on the image quality are discussed.

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

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

Quantized phase optimization of two-dimensional Fourier kinoforms by a genetic algorithm

We have developed a phase optimization method of a quantized kinoform by a genetic algorithm. Because the genetic algorithm inherently deals with discrete values, the quantized phase of the kinoform can be easily estimated. The two-dimensional Fourier kinoform can utilize effectively the periodicity of the discrete Fourier transform in the genetic algorithm. This condition enables us to perform the crossover process that is one of the processes in genetic algorithm without a spatial bandwidth of the kinoform. The optimization has been performed successfully in computer simulation. The optically reconstructed image agrees well with the theoretical one.

Subharmonic focal-length intensities formed by Fresnel lenses

Binary Fresnel lenses produce focused spots at subharmonics of the principal focal length of the lens. The intensities of these focal spots can be controlled by variation of the relative widths of the rings of the Fresnel lens compared with the spacings between the rings. Theory is presented and experimentalverification is provided with Fresnel lenses written onto the magneto-optic spatial light modulator.

Approximating fully complex spatial modulation with pseudorandom phase-only modulation

Any desired diffraction pattern can be produced in the Fourier plane by the specification of a corresponding input-plane transparency. Complex-valued transmittance is generally required, but in practice phase-only transmittance is used. Many design procedures use numerically intensive, constrained optimization. We instead introduce a noniterative procedure that directly translates the desired but unavailable complex transparency into an appropriate phase transparency. At each pixel the value of phase is pseudorandomly selected from a random distribution whose standard deviation is specified by the desired amplitude. We also derive statistical expressions and use them to evaluate the approximation errors between the desired and achieved diffraction patterns.

Design of an optoelectronic cellular processing system with a reconfigurable holographic interconnect

The design of an optoelectronic parallel processing system is presented. In this system a reconfigurable computer-generated hologram is used to perform a shift-invariant optical interconnection operation. Scalability issues are investigated, and simple cellular processing operations are experimentally demonstrated.

Method of compensating for aberrations in electron holography by using a liquid-crystal spatial-light modulator

A method for correcting the aberration of an electron-objective lens during the holographic reconstruction stage is proposed. In this method, a liquid-crystal spatial-light modulator is used as a computercontrolled phase plate on the Fourier plane of an optical reconstruction system. The effective refractive index of the liquid crystals changes with the applied electric field because of the crystals's birefringence. Thus the phase of light passing through the liquid-crystal spatial-light modulator can be flexibly modulated to compensate for wave aberration. Experimental results on adjusting the focus of the image wave reconstructed from an electron-image hologram of magnesium oxide particles are presented.

Phase optimization of a kinoform by simulated annealing

The design of a kinoform by the use of simulated annealing is discussed. The simulated annealing process is applied to decrease the reconstruction noise and to adjust the phase distribution of the kinoform to the configuration of the recording device. A liquid-crystal spatial light modulator is used to display the kinoform. The reconstructed image of the optimized kinoform is found to be in good agreement with the computed image. Some experimental results obtained with a liquid-crystal spatial light modulator are presented. The phase quantization effect of the kinoform is discussed.

Real-time electron-holographic interference microscopy with a liquid-crystal spatial light modulator

An electron-holographic interference microscope that produces a time-sequential interference micrograph at a TV rate is developed. In this system, the electron off-axis hologram detected with a TV camera is transferred to a liquid-crystal spatial light modulator as a video signal. The liquid-crystal spatial light modulator can function as a thin amplitude hologram or a thin phase hologram. Time-sequential interference micrograph is obtained at a TV rate by superimposition of a plane reference wave onto the reconstructed object wave. Experimental results for observing a dynamic domain-wall motion in thin Permalloy film are demonstrated.

Optical on-axis imperfect phase-only correlator using liquid-crystal television

We present a VanderLugt-type optical phase-only correlator that uses the currently available liquidcrystal television. Theoretical and experimental results show that phase mismatching and phase and amplitude cross coupling of the liquid-crystal television can reduce the peak intensity to approximately 60%-70%. The imperfect phase-only filter yields on-axis correlation with high light efficiency and utilizes all the available space-bandwidth product of the liquid-crystal television.

Wave-front control using liquid-crystal devices

We report on complete wave-front control with amplitude- and phase-modulation liquid-crystal devices (LCD's). A twisted nematic device is used for amplitude modulation, and an electrically controlled birefringent device is used for phase modulation. Because the LCD's are optically coupled with afocal optics and are driven by individual LCD driver circuits, the amplitude and the phase can be controlled two dimensionally and independently. Complex amplitude data are calculated, and on-axis computergenerated holograms are directly recorded. Furthermore, we discuss LCD performance requirements for high-quality reconstruction.

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.

Iterative interlacing approach for synthesis of computer-generated holograms

An approach for optimizing computer-generated holograms is discussed. The approach can be summarized most generally as hierarchically designing a number of holograms to add up coherently to a single desired reconstruction. In the case of binary holograms, this approach results in the interlacing technique (IT) and the iterative interlacing technique (IIT). In the IT, a number of subholograms are designed and interlaced together to generate the total binary hologram. The first subhologram is designed to reconstruct the desired image. The succeeding subholograms are designed to correct the remaining error image. In the IIT, the remaining error image after the last subhologram is circulated back to the first subhologram, and the process is continued a number of sweeps until convergence. Both techniques can be used together with most computer-generated-hologram synthesis algorithms and result in a substantial reduction in reconstruction error as well as an increased speed of convergence in the case of iterative algorithms.

Anamorphic optical systems using programmable spatial light modulators

Anamorphic optical systems with different horizontal and vertical magnifications are constructed by using programmable anamorphic lenses written on a magneto-optic spatial light modulator.