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

Genetic algorithm for the response of arbitrarily twisted nematic liquid crystals to an applied field

When an external field is applied across a liquid-crystal cell, the twist and tilt distributions cannot be calculated analytically and must be extracted numerically. In the standard approach, the Euler-Lagrange equations are derived from the minimization of the free energy of the system and then solved via finite-difference methods, often implemented in commercial software. These tools iterate from initial solutions that are compatible with the boundary conditions, providing limited to no flexibility for customization. Here we present a genetic algorithm that outputs fast and accurate solutions to the integral form of the equations. In our approach, the evolutionary routine is sequentially applied at each position within the bulk of the cell, thus overcoming the necessity of assuming trial solutions. The full range of twist angles from -90^{∘} to 90^{∘} is considered. In this way, the predictions of our routine strongly support the experimentally observed polarization transformations of light incident on different spatially varying twisted nematic liquid-crystal cells, patterned with different topologies on the two alignment layers.

Neural étendue expander for ultra-wide-angle high-fidelity holographic display

Holographic displays can generate light fields by dynamically modulating the wavefront of a coherent beam of light using a spatial light modulator, promising rich virtual and augmented reality applications. However, the limited spatial resolution of existing dynamic spatial light modulators imposes a tight bound on the diffraction angle. As a result, modern holographic displays possess low étendue, which is the product of the display area and the maximum solid angle of diffracted light. The low étendue forces a sacrifice of either the field-of-view (FOV) or the display size. In this work, we lift this limitation by presenting neural étendue expanders. This new breed of optical elements, which is learned from a natural image dataset, enables higher diffraction angles for ultra-wide FOV while maintaining both a compact form factor and the fidelity of displayed contents to human viewers. With neural étendue expanders, we experimentally achieve 64 × étendue expansion of natural images in full color, expanding the FOV by an order of magnitude horizontally and vertically, with high-fidelity reconstruction quality (measured in PSNR) over 29 dB on retinal-resolution images.

High fidelity laser beam shaping using liquid crystal on silicon spatial light modulators as diffractive neural networks

Spatial light modulators (SLMs) based on liquid crystal on silicon (LCoS) are powerful tools for laser beam shaping as they can be used to dynamically create almost arbitrary intensity distributions. However, laser beam shaping with LCoS-SLMs often suffers from beam shaping artifacts in part caused by unconsidered properties of the LCoS devices: astigmatism that stems from the non-normal incidence of the laser beam on the SLM and the effect commonly referred to as the '0-th diffraction order' that is caused by both the crosstalk between neighboring pixels and the direct reflection at the cover glass of the SLM. We here present a method to consider and compensate for these inherent properties of LCoS devices by treating the SLM as a diffractive neural network.

Sparse holographic imaging for an integrated augmented reality near-eye display

Diffraction is the main physical effect involved in the imaging process of holographic displays. In the application of near-eye displays, it generates physical limits that constrain the field of view of the devices. In this contribution, we evaluate experimentally an alternative approach for a holographic display based mainly on refraction. This unconventional imaging process, based on sparse aperture imaging, could lead to integrated near-eye displays through retinal projection, with a larger field of view. We introduce for this evaluation an in-house holographic printer that allows the recording of holographic pixel distributions at a microscopic scale. We show how these microholograms can encode angular information that overcomes the diffraction limit and could alleviate the space bandwidth constraint usually associated with conventional display design.

Accurate holographic light potentials using pixel crosstalk modelling

Arbitrary light potentials have proven to be a valuable and versatile tool in many quantum information and quantum simulation experiments with ultracold atoms. Using a phase-modulating spatial light modulator (SLM), we generate arbitrary light potentials holographically with measured efficiencies between 15 and 40% and an accuracy of [Formula: see text] root-mean-squared error. Key to the high accuracy is the modelling of pixel crosstalk of the SLM on a sub-pixel scale which is relevant especially for large light potentials. We employ conjugate gradient minimisation to calculate the SLM phase pattern for a given target light potential after measuring the intensity and wavefront at the SLM. Further, we use camera feedback to reduce experimental errors, we remove optical vortices and investigate the difference between the angular spectrum method and the Fourier transform to simulate the propagation of light. Using a combination of all these techniques, we achieved more accurate and efficient light potentials compared to previous studies, and generated a series of potentials relevant for cold atom experiments.

Super-compact shearography based on a single diffractive optical element with 3-in-1 phase mask

This Letter communicates a new, to the best of our knowledge, designing framework of shearography. The three elementary functional parts of quantitative shearography, namely imaging, shearing, and phase shifting, are integrated into a single diffractive optical element (DOE), named a 3-in-1 phase mask. The idea breaks through the conventional designing routine of shearography, and converts it from the combination of individual optical elements to the spatial manipulation of phase. The slicing, splicing, and alternating strategy is proposed to generate the 3-in-1 phase mask from a given number of sequenced Fresnel lenses and a modified echelle grating. The operating component is merely a DOE, which renders the optics naturally coaxial. The delivered shearography system enjoys a super-compact configuration, a high level of robustness and stability, and the potential for implementing outside optics laboratories. Crucial system parameters, e.g., shear amount, shear direction, working distance, can be readily shifted on call by re-making the 3-in-1 phase mask. The future of the present idea is in its shape and seems promising with lithography, micromachining, and metasurfaces.

Diffraction characteristics of orthogonal gratings analysis based on a spatial light modulator

The diffraction characteristics of orthogonal gratings with variable duty cycles and phase modulation depths are analyzed by using a spatial light modulator. The calculation methods of the transmission function, far-field diffraction light field, and diffraction efficiency of orthogonal gratings are deduced in theory. Meanwhile, the influences of the duty cycle and phase modulation depth on the diffraction characteristics of the orthogonal grating are discussed. The simulation and experimental results verify the correctness of the theoretical derivation. This method can be widely used in the fields of an optical vortex array, laser parallel processing, optical computing, optical communication, and optoelectronic hybrid processing.

Diffractive optical system design by cascaded propagation

Modern design of complex optical systems relies heavily on computational tools. These frequently use geometrical optics as well as Fourier optics. Fourier optics is typically used for designing thin diffractive elements, placed in the system's aperture, generating a shift-invariant Point Spread Function (PSF). A major bottleneck in applying Fourier Optics in many cases of interest, e.g. when dealing with multiple, or out-of-aperture elements, comes from numerical complexity. In this work, we propose and implement an efficient and differentiable propagation model based on the Collins integral, which enables the optimization of diffractive optical systems with unprecedented design freedom using backpropagation. We demonstrate the applicability of our method, numerically and experimentally, by engineering shift-variant PSFs via thin plate elements placed in arbitrary planes inside complex imaging systems, performing cascaded optimization of multiple planes, and designing optimal machine-vision systems by deep learning.

Advanced liquid crystal devices for augmented reality and virtual reality displays: principles and applications

Liquid crystal displays (LCDs) and photonic devices play a pivotal role to augmented reality (AR) and virtual reality (VR). The recently emerging high-dynamic-range (HDR) mini-LED backlit LCDs significantly boost the image quality and brightness and reduce the power consumption for VR displays. Such a light engine is particularly attractive for compensating the optical loss of pancake structure to achieve compact and lightweight VR headsets. On the other hand, high-resolution-density, and high-brightness liquid-crystal-on-silicon (LCoS) is a promising image source for the see-through AR displays, especially under high ambient lighting conditions. Meanwhile, the high-speed LCoS spatial light modulators open a new door for holographic displays and focal surface displays. Finally, the ultrathin planar diffractive LC optical elements, such as geometric phase LC grating and lens, have found useful applications in AR and VR for enhancing resolution, widening field-of-view, suppressing chromatic aberrations, creating multiplanes to overcome the vergence-accommodation conflict, and dynamic pupil steering to achieve gaze-matched Maxwellian displays, just to name a few. The operation principles, potential applications, and future challenges of these advanced LC devices will be discussed.

High resolution 2D beam steerer made from cascaded 1D liquid crystal phase gratings

Optical beam steering (BS) has multiple applications in fields like target seeking and tracking, optical tweezers, billboard displays and many others. In this work, a two-dimensional beam deflector based on blaze gratings is presented. Phase-only 1D blaze gratings have been prepared using maskless Direct Laser Writing (DLW) resulting in high-resolution structures in indium-tin oxide (ITO) coated glass wafers. The device is composed of two identical 1D liquid crystal (LC) cells cascaded orthogonally back-to-back, with a resultant active area of 1.1 × 1.1 mm². The 1D cells have been prepared with 144 pixels each with a 7.5 µm pitch. The total 288 pixels are driven by a custom made 12-bit Pulse Width Modulation (PWM) electronic driver, allowing for an arbitrarily high resolution. The system performance is documented, and the efficiency of the system has been tested. A maximum diagonal steering angle of ± 3.42° was achieved.

Targeted generation of complex temporal pulse profiles

A targeted shaping of complex femtosecond pulse waveforms and their characterization is essential for many spectroscopic applications. A 4f pulse shaper combined with an advanced pulse characterization technique should, in the idealized case, serve this purpose for an arbitrary pulse shape. This is, however, violated in the real experiment by many imperfections and limitations. Although the complex waveform generation has been studied in-depth, the comparison of the effects of various experimental factors on the actual pulse shape has stayed out of focus so far. In this paper, we present an experimental study on the targeted generation and retrieval of complex pulses by using two commonly-used techniques: spatial-light-modulator (SLM)-based 4f pulse shaper and second-harmonic generation frequency-resolved optical gating (FROG) and cross-correlation FROG (XFROG). By combining FROG and XFROG traces, we analyze the pulses with SLM-adjusted complex random phases ranging from simple to very complex waveforms. We demonstrate that the combination of FROG and XFROG ensures highly consistent pulse retrieval, irrespective of the used retrieval algorithm. This enabled us to evaluate the role of various experimental factors on the agreement between the simulated and actual pulse shape. The factors included the SLM pixelation, SLM pixel crosstalk, finite laser focal spot in the pulse shaper, or interference fringes induced by the SLM. In particular, we observe that including the SLM pixelation and crosstalk effect significantly improved the pulse shaping simulation. We demonstrate that the complete simulation can faithfully reproduce the pulse shape. Nevertheless, even in this case, the intensity of individual peaks differs between the retrieved and simulated pulses, typically by 10–20% of the peak value, with the mean standard deviation of 5–9% of the maximum pulse intensity. We discuss the potential sources of remaining discrepancies between the theoretically expected and experimentally retrieved pulse.

Suppression of spurious image duplicates in Fourier holograms by pixel apodization of a spatial light modulator

Holographic projectors and near-eye displays are a promising technology with truly three-dimensional, natural viewing and excellent energetic efficiency. Spatial light modulators with periodic pixel matrices cause image duplicates, which distract the viewer and waste energy of the playback beam. We present the engineering of the far field intensity envelope, which suppresses higher-order image duplicates in the simplest possible optical setup by physically changing the shape of modulator pixels with attached apodizing masks. Numerical and experimental results show the limited number of perceived duplicates and better uniformity in off-axis projections for the price of compromised energetic efficiency due to amplitude masks.

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.

Uniform and efficient beam shaping for high-energy lasers

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

Adaptive optics enables aberration-free single-objective remote focusing for two-photon fluorescence microscopy

Two-photon fluorescence microscopy has been widely applied to three-dimensional (3D) imaging of complex samples. Remote focusing by controlling the divergence of excitation light is a common approach to scanning the focus axially. However, microscope objectives induce distortion to the wavefront of non-collimated excitation beams, leading to degraded imaging quality away from the natural focal plane. In this paper, using a liquid-crystal spatial light modulator to control the divergence of the excitation beam through a single objective, we systematically characterized the aberrations introduced by divergence control through microscope objectives of NA 0.45, 0.8, and 1.05. We used adaptive optics to correct the divergence-induced-aberrations and maintain diffraction-limited focal quality over up to 800-µm axial range. We further demonstrated aberration-free remote focusing for in vivo imaging of neurites and synapses in the mouse brain.

Accurate, Efficient and Rigorous Numerical Analysis of 3D H-PDLC Gratings

This work presents recent results derived from the rigorous modelling of holographic polymer-dispersed liquid crystal (H-PDLC) gratings. More precisely, the diffractive properties of transmission gratings are the focus of this research. This work extends previous analysis performed by the authors but includes new features and approaches. More precisely, full 3D numerical modelling was carried out in all analyses. Each H-PDLC sample was generated randomly by a set of ellipsoid geometry-based LC droplets. The liquid crystal (LC) director inside each droplet was computed by the minimisation of the Frank elastic free energy as a function of the applied electric field. The analysis carried out considered the effects of Frank elastic constants K11, K22 and K33; the anchoring strength W0; and even the saddle-splay constant K24. The external electric field induced an orientation of the LC director, modifying the optical anisotropy of the optical media. This effect was analysed using the 3D split-field finite-difference time-domain (SF-FDTD) method. In order to reduce the computational costs due to a full 3D tensorial analysis, a highly optimised method for high-performance computing solutions (HPC) was developed. The influences of the anchoring and voltage on the diffraction efficiencies were investigated, showing the potential of this approach.

Tunable mode-locked erbium-doped fiber laser based on a digital micro-mirror device

A tunable mode-locked erbium-doped fiber laser with a digital micro-mirror device (DMD) as the wavelength tuner and nonlinear amplifying loop mirror as the mode-locked device is proposed and experimentally demonstrated. The mode-locked pulse with the center wavelength of 1538-1565 nm continuously tunable is achieved. The average power of the output pulse is 1.028 mW, the pulse repetition frequency is 1.7 MHz, the pulse duration is 616 fs, and the single pulse energy is 0.6 nJ. By controlling the DMD, the center wavelength can be fine-tuned with the tuning accuracy of 0.07 nm. With the increase of the pump power, the traditional soliton pulse is transformed into a noise-like pulse (NLP), and the power of the NLP can reach 34 mW. This mode-locked process can work for a long time and is almost unaffected by the external environment. These results are very useful for applications where pulsed lasers with different wavelengths are needed.

VIPR: vectorial implementation of phase retrieval for fast and accurate microscopic pixel-wise pupil estimation

In microscopy, proper modeling of the image formation has a substantial effect on the precision and accuracy in localization experiments and facilitates the correction of aberrations in adaptive optics experiments. The observed images are subject to polarization effects, refractive index variations, and system specific constraints. Previously reported techniques have addressed these challenges by using complicated calibration samples, computationally heavy numerical algorithms, and various mathematical simplifications. In this work, we present a phase retrieval approach based on an analytical derivation of the vectorial diffraction model. Our method produces an accurate estimate of the system's phase information, without any prior knowledge about the aberrations, in under a minute.

Characterization of the spatially anamorphic phenomenon and temporal fluctuations in high-speed, ultra-high pixels-per-inch liquid crystal on silicon phase modulator

High-birefringence liquid crystal (LC) in ultrathin LCOS panels was adopted to prepare high phase precision (mSTD =λ/50) and phase accuracy (mAPAE% ∼8%) with suppressed pixel-level crosstalk effects. In conjunction with optimized digital driving scheme, the zero order light loss was found directly related to the phase accuracy error. Meanwhile, the world's fastest pure phase modulation LCOS with a response time of ∼0.87 ms at 45 °C was also achieved. The low-temporal flicker (P-P ∼2.0%) with high-speed LC responses was demonstrated by applying new digital driving scheme. Finally, the 4K2 K LCOS-SLM (∼7000 PPI) was evaluated its difficulties and opportunities.