Phase-only Spatial Light Modulator Research Articles

Simulating multilevel diffractive optical elements on a spatial light modulator.

Multilevel diffractive optical elements (DOEs) offer a solution to approximate complex diffractive phase profiles in a stepwise manner. However, while much attention has focused on efficiency, the impact on modal content in the context of structured light has, to our best knowledge, remained unexplored. Here, we outline a simple theory that accounts for efficiency and modal purity in arbitrary structured light produced by multilevel DOEs. We make use of a phase-only spatial light modulator as a "testbed" to experimentally implement various multileveled diffractive profiles, including orbital angular momentum beams, Bessel beams, and Airy beams, outlining the subsequent efficiency and purity both theoretically and experimentally, confirming that a low number of multilevel steps can produce modes of high fidelity. Our work will be useful to those wishing to digitally evaluate modal effects from DOEs prior to physical fabrication.

Complex-amplitude Fourier single-pixel imaging via coherent structured illumination

We propose a method of complex-amplitude Fourier single-pixel imaging (CFSI) with coherent structured illumination to acquire both the amplitude and phase of an object. In the proposed method, an object is illustrated by a series of coherent structured light fields, which are generated by a phase-only spatial light modulator, the complex Fourier spectrum of the object can be acquired sequentially by a single-pixel photodetector. Then the desired complex-amplitude image can be retrieved directly by applying an inverse Fourier transform. We experimentally implemented this CFSI with several different types of objects. The experimental results show that the proposed method provides a promising complex-amplitude imaging approach with high quality and a stable configuration. Thus, it might find broad applications in optical metrology and biomedical science.

Hybrid diffractive optics design via hardware-in-the-loop methodology for achromatic extended-depth-of-field imaging.

End-to-end optimization of diffractive optical elements (DOEs) profile through a digital differentiable model combined with computational imaging have gained an increasing attention in emerging applications due to the compactness of resultant physical setups. Despite recent works have shown the potential of this methodology to design optics, its performance in physical setups is still limited and affected by manufacturing artefacts of DOE, mismatch between simulated and resultant experimental point spread functions, and calibration errors. Additionally, the computational burden of the digital differentiable model to effectively design the DOE is increasing, thus limiting the size of the DOE that can be designed. To overcome the above mentioned limitations, a co-design of hybrid optics and image reconstruction algorithm is produced following the end-to-end hardware-in-the-loop strategy, using for optimization a convolutional neural network equipped with quantitative and qualitative loss functions. The optics of the imaging system consists on the phase-only spatial light modulator (SLM) as DOE and refractive lens. SLM phase-pattern is optimized by applying the Hardware-in-the-loop technique, which helps to eliminate the mismatch between numerical modelling and physical reality of image formation as light propagation is not numerically modelled but is physically done. Comparison with compound multi-lens optics of a last generation smartphone and a mirrorless commercial cameras show that the proposed system is advanced in all-in-focus sharp imaging for a depth range 0.4-1.9 m.

Flattop Beam Shaping Using Hybrid Gratings

A new method of laser beam shaping with hybrid gratings is presented. The hybrid gratings consist of a blazed grating and a gradient binary grating. The blazed grating is used to separate the incident Gaussian beam into zero order and nonzero diffraction orders. A filter is used to block the nonzero order beams and obtain the zero orders with the desired shape. The gradient binary grating is used to improve the energy distribution of the inside area of the geometric shape. A phase hologram designed with the desired shape and hybrid gratings, is loaded on a phase-only spatial light modulation to achieve arbitrary geometric flattop shapes with high uniformity. Squared and hexagonal shaping experiments demonstrated that the presented method can convert a Gaussian beam into a flattop beam with steepness edge and high uniformity. Experimental results show that the beam non-uniformity is less than 0.037.

Experimental study on phase conjecture based on two-dimensional image and carrying three-dimensional image with mist in electro-holographic reconstruction

A method is proposed for phase conjecture based on the intensity curve of a two-dimensional (2D) image by computing a polynomial equation. The intensity values of the 2D image, which represents the distance between the image detectors and the three-dimensional (3D) scene is converted to phase information by our method. The results of numerical calculation with phase conjecture are analyzed. And what’s more, the numerical reconstruction results with phase information obtained as initial phase factors of a complex object for Fresnel kinoform and dynamic pseudorandom-phase tomographic computer holography(DPP-TCH) are compared. The peak signal-to-noise ratio (PSNR) and correlation coefficient (CC) between the reconstructed images and original object are analyzed. An experimental system is designed for photoelectric holographic reconstruction based on phase-only liquid crystal spatial light modulator (LC-SLM) and mist screen. The electro-optical experimental results indicate that suppressed the speckle noise 3D images that can be observed with naked eye have been obtained.

Only-train-electrical-to-optical-conversion (OTEOC): simple diffractive neural networks with optical readout.

Machine learning hardware based on optical diffraction is emerging as a new computing platform with high throughput and low latency. The current all-optical diffractive deep neural networks often suffer from complex optical configuration, lack of efficient optical nonlinear activation, and critical alignment between optical layers for system integration. The opto-electronic diffractive neural networks can partially address these issues by shifting some computation load, e.g., nonlinear activation and adaptive training, to the electronic domain. However, these hybrid networks require extra optical-to-electrical conversion that inevitably slows the overall process down. Here, we propose a simple opto-electronic diffractive neural network with just one optical layer enabled by a standard phase-only spatial light modulator. The proposed system can classify images by optical readout and does not need to collect the light distribution for subsequent electronic computation. The nonlinear function is intrinsically integrated in the essential encoding process from the electronic input to the modulated wavefront of light. Thanks to its simplicity, the system can reach high classification accuracy without calibration and can be reconfigured by updating the weights without changing or moving any physical component. We believe this technology brings diffractive neural networks a step closer to building realistic optics-based neurocomputers.

Phase-Shifting Common-Path Polarization Self-Interferometry for Evaluating the Reconstruction of Holograms Displayed on a Phase-Only Display

In this work we apply a phase-shifting interferometry (PSI) to evaluate the reconstruction of complex-valued holograms displayed onto a phase-only spatial light modulator (SLM). The interferometer is vibration-free since it uses a common-path polarization arrangement based on the SLM itself, which is used simultaneously to display the hologram and to apply the phase-shifting values. The change from the hologram display configuration to the interferometer configuration involves only a rotation of a polarizer. The continuous phase modulation provided by the SLM allows using PSI with arbitrary phase bias values. Several examples are demonstrated by generating different combinations of modes with an efficient on-axis hologram encoding technique.

Compact generation of robust Airy beam pattern with spatial coherence engineering.

We present a class of partially coherent light sources having Airy-type amplitude and Airy-correlated spatial coherence. We show that the light beam generated by such sources can preserve the Airy beam pattern well during its propagation from source to far field. We demonstrate the robustness of the Airy beam pattern by introducing a hard aperture to largely block the beam source. We find that the coherence-induced Airy beam pattern can still be well reconstructed during propagation. We successfully synthesize such partially coherent source using the principle of complex random modes decomposition by using a single phase-only spatial light modulator. The proposed robust Airy beam pattern may find applications in information transmission through complex media.

Real-time complex light field generation through a multi-core fiber with deep learning

The generation of tailored complex light fields with multi-core fiber (MCF) lensless microendoscopes is widely used in biomedicine. However, the computer-generated holograms (CGHs) used for such applications are typically generated by iterative algorithms, which demand high computation effort, limiting advanced applications like fiber-optic cell manipulation. The random and discrete distribution of the fiber cores in an MCF induces strong spatial aliasing to the CGHs, hence, an approach that can rapidly generate tailored CGHs for MCFs is highly demanded. We demonstrate a novel deep neural network—CoreNet, providing accurate tailored CGHs generation for MCFs at a near video rate. The CoreNet is trained by unsupervised learning and speeds up the computation time by two magnitudes with high fidelity light field generation compared to the previously reported CGH algorithms for MCFs. Real-time generated tailored CGHs are on-the-fly loaded to the phase-only spatial light modulator (SLM) for near video-rate complex light fields generation through the MCF microendoscope. This paves the avenue for real-time cell rotation and several further applications that require real-time high-fidelity light delivery in biomedicine.

Generation of Higher-Order Hermite–Gaussian Modes via Cascaded Phase-Only Spatial Light Modulators

The spatial distribution of higher-order Hermite–Gaussian (HG) modes is more complicated than the fundamental mode, and the characteristics of different modes and their orthogonal characteristics have essential applications in the fields of measurement, imaging, and large-capacity communications. The main issue in future applications is how to efficiently generate higher-order HG modes. The spatial light modulator has high spatial resolution and excellent maneuverability, so it is a simple and effective way to generate higher-order HG modes. Here, the efficient generation of higher-order HG modes via cascaded spatial light modulators was experimentally investigated. For the HG90 mode, the conversion efficiency is 61%. The method with high conversion efficiency has promising application potentials in biophotonics, laser physics, and quantum information.

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Focusing of a Laser Beam Passed through a Moderately Scattering Medium Using Phase-Only Spatial Light Modulator

The rarely considered case of laser beam propagation and focusaing through the moderately scattering medium was researched. A phase-only spatial light modulator (SLM) with 1920×1080 pixel resolution was used to increase the efficiency of focusing of laser radiation propagated through the 5 mm layer of the scattering suspension of 1 µm polystyrene microbeads in distilled water with the concentration values ranging from 105 to 106 mm−3. A CCD camera with micro-objective was used to estimate the intensity distribution of the far-field focal spot. A Shack-Hartmann sensor was used to measure wavefront distortions. The conducted experimental research demonstrated the 8% increase in integral intensity and 16% decrease in diameter of the far-field focal spot due to the use of the SLM for laser beam focusing.

Enhance the delivery of light energy ultra-deep into turbid medium by controlling multiple scattering photons to travel in open channels

Multiple light scattering is considered as the major limitation for deep imaging and focusing in turbid media. In this paper, we present an innovative method to overcome this limitation and enhance the delivery of light energy ultra-deep into turbid media with significant improvement in focusing. Our method is based on a wide-field reflection matrix optical coherence tomography (RM-OCT). The time-reversal decomposition of the RM is calibrated with the Tikhonov regularization parameter in order to get more accurate reversal results deep inside the scattering sample. We propose a concept named model energy matrix, which provides a direct mapping of light energy distribution inside the scattering sample. To the best of our knowledge, it is the first time that a method to measure and quantify the distribution of beam intensity inside a scattering sample is demonstrated. By employing the inversion of RM to find the matched wavefront and shaping with a phase-only spatial light modulator, we succeeded in both focusing a beam deep (~9.6 times of scattering mean free path, SMFP) inside the sample and increasing the delivery of light energy by an order of magnitude at an ultra-deep (~14.4 SMFP) position. This technique provides a powerful tool to understand the propagation of photon in a scattering medium and opens a new way to focus light inside biological tissues.

An open source three-mirror laser scanning holographic two-photon lithography system.

Two-photon polymerization is a widely adopted technique for direct fabrication of 3D and 2D structures with sub-diffraction-limit features. Here we present an open-hardware, open-software custom design for a holographic multibeam two-photon polymerization system based on a phase-only spatial light modulator and a three-mirror scanhead. The use of three reflective surfaces, two of which scanning the phase-modulated image along the same axis, allows to overcome the loss of virtual conjugation within the large galvanometric mirrors pair needed to accommodate the holographic projection. This extends the writing field of view among which the hologram can be employed for multi-beam two-photon polymerization by a factor of ~2 on one axis (i.e. from ~200μm to ~400μm), with a voxel size of ~250nm × ~1050nm (lateral × axial size), and writing speed of three simultaneous beams of 2000 voxels/s, making our system a powerful and reliable tool for advanced micro and nano-fabrications on large area.

Polarimetric analysis of cross-talk phenomena induced by the pixelation in PA-LCoS devices

Liquid crystal on silicon (LCoS) microdisplays are an element commonly found in advanced photonic applications. Phase-only modulation and spatial light modulators (SLMs) use parallel-aligned LCoS (PA-LCoS) microdisplays due to their large resolution and small pixel size. However, the crosstalk between neighbouring pixels induces several phenomena, i.e. the smoothing of the electric field in the interpixel region known as fringing fields, out-of-plane reorientation of the liquid crystal director, and diffraction effects due to the finite pixel grid pattern. These effects degrade the performance in SLM applications. Therefore, a rigorous numerical analysis is carried out based on a full 3D model that estimates the LC director distribution of the PA-LCoS microdisplay through uniform applied voltages. Once the LC director distribution is known, a numerical finite-difference scheme simulates light propagation across the structure. Here, the impact of crosstalk is analysed from the polarimetric point of view for different pixel and interpixel sizes. It has been found that the finite-patterned pixel scheme induces the phenomena previously addressed, degrading the responses of the Stokes vector components S0, and S1 and also the degree of polarization (DOP). Furthermore, the impact over these parameters is generally inversely proportional to the fill factor. To isolate the influence of diffraction, out-of-plane, and fringing fields effects is challenging since all phenomena are mixed in both time and space, however we have found some useful trends.

Calibration of phase-only liquid-crystal spatial light modulators by diffractogram analysis

Phase-only spatial light modulator (SLM) is a key device for light manipulation. It is critical to calibrate the grayscale-phase response to the driving voltage of SLM, namely the look-up table (LUT), before use. The conventional calibration methods, which rely on interference, diffraction, or polarization to extract the phase, require extra optical devices and are sensitive to mechanical vibration, air turbulence, and systematic aberrations. To overcome these shortcomings, here we develop a novel method, which is based on the diffractogram analysis. By analyzing the intensity distribution of the diffractogram as a function of the specific SLM hologram, we identify both the global and the localized LUTs of SLM at high accuracy. Compared with the other ones, our method allows in-situ SLM calibration and is more tolerant to the exogenous factors.

The Error Analysis of the Complex Modulation for Flattop Focusing Beam Shaping

In order to obtain a focusing flattop beam with high uniformity, complex modulation is used to modulate the optical pupil function, and the beam shaping algorithm is designed with a single phase-only spatial light modulator (SLM). Actually, the wavefront aberrations introduced by each element reduce the uniformity of the shaped beam. In particular, the wavefront aberrations in different positions have different effects on this complex modulation algorithm. However, there is a lack of the corresponding error data and robustness analysis. Here, the error and robustness of the complex modulation algorithm are analyzed when different types of aberrations (defocus, astigmatism, and coma) exist in different positions of the shaping optical system, and the mixed area magnification-free (MRAF) algorithm is used as a reference for comparison. The results show that coma has the greatest effect on the beam shaping quality. It is also proved that the impact on the beam quality when there are aberrations in the laser and beam expansion system is greater than those in the SLM and the focusing lens for the complex modulation algorithm, which is different from the MRAF case.

Efficient wavefront sensorless adaptive optics based on large dynamic crosstalk-free holographic modal wavefront sensing.

The correction of wavefront sensorless adaptive optics (WFSless AO) can be significantly accelerated by using a holographic modal wavefront sensor (HMWFS). The HMWFS is realized by a computer-generated hologram (CGH) into which all aberration modes to be detected are encoded and only a single-shot image is required for simultaneous measurement of multiple modes. The conventional HMWFS suffers from a quite limited dynamic range and severe inter-modal crosstalk which deteriorates the sensing accuracy. We proposed a novel HMWFS with a large dynamic range and no crosstalk and validated its performance by simulation and experiment. In the improved HMWFS scheme, the aberration is represented by Lukosz modes whose gradients are orthogonal and the modal coefficients can be estimated independently. Instead of using a binary CGH in conventional HMWFS, a kinoform CGH with high diffraction efficiency is adopted in the improved HMWFS. The kinoform CGH is produced by a phase-only liquid-crystal spatial light modulator (LCSLM) which also serves as a wavefront corrector in our WFSless AO system.

Trade-Off Asymmetric Profile for Extended-Depth-of-Focus Ocular Lens

We explore the possibility of extending the depth of focus of an imaging lens with an asymmetric quartic phase-mask, while keeping the aberration within a relatively low level. This can be intended, for instance, for ophthalmic applications, where no further digital processing can take place, relying instead on the patient’s neural adaptation to their own aberrations. We propose a computational optimization method to derive the design-strength factor of the asymmetric profile. The numerical and experimental results are shown. The optical experiment was conducted by means of a modulo-2π phase-only spatial light modulator. The proposed combination of the asymmetric mask and the lens can be implemented in a single refractive element. An exemplary case of an extended-depth-of focus intraocular lens based on the proposed element is described and demonstrated with a numerical experiment.

High-Precision Calibration of Phase-Only Spatial Light Modulators

In the fields of optics and photonics, phase-only spatial light modulators (SLMs) play an increasingly important role in wave-front engineering. However, the SLMs are subject to wavefront distortion arising from the imperfection in the birefringence effect and physical structure of modulators. This paper presents a simple self-interference phase calibration method applicable to liquid-crystal SLM. We build an interferometric imaging system based on the Pancharatnam phase-shifting to measure the phase distribution of a light beam coming from SLMs. Two types of phase modulation errors of SLMs can be characterized in the measurement process: the erroneous gamma curve and shape aberration. The former belongs to dynamic phase distortion and is measured through a four-step Pancharatnam phase-shifting interference, which allows a one-shot recording of interference pattern via a polarization camera; the latter represents static phase distortion and is extracted from the interference between light waves coming from different regions of the SLM panel by using Zernike polynomial fitting. Our method has the advantages of high-precision pixel-wise phase correction and robustness against environmental disturbance and thus can facilitate the applications of SLM in optical field manipulation.