Holographic Method Research Articles

Photoalignment of sub-micrometer periodic liquid crystal polarization grating by using the optical imprinting method.

Photoalignment of liquid crystal polarization grating based on optical imprinting is a promising technique for polarization grating mass production. However, when the period of the optical imprinting grating is in the sub-micrometer level, the zero-order energy from the master grating will become high, and it will strongly affect the photoalignment quality. This paper proposes a double-twisted polarization grating structure to eliminate the zero-order disturbance of master grating and gives the design method. Based on the designed results, a master grating was prepared, and the optically imprinted photoalignment of polarization grating with a period of 0.5μm was fabricated. This method has the advantages of high efficiency and significantly greater environmental tolerance than the traditional polarization holographic photoalignment methods. It has the potential to be used for large-area polarization holographic gratings production.

Computer-Generated Holography Methods for Data Page Reconstruction Using Phase-Only Medium

Achievements in the field of high-speed spatial modulation electrooptic components provide the possibility to create perspective optical-digital diffractive systems for information storage and processing that outperform modern electronic counterparts by utilizing throughput, energy efficiency, and reliability. This work presents a study of computer-generated holography methods that allow the formation of spatially-modulated information signals (data pages) with high accuracy using phase-only spatial light modulators. Computer-generated Fourier hologram fringe patterns were formed using bipolar intensity and double-phase coding. Numerical and experimental results of both methods’ implementation are compared. It was determined that bipolar intensity holograms provide higher data density on the data page if complex digital modulation methods such as multilevel amplitude and phase or quadrature modulation are used to represent data points. Double-phase coding can offer perspective for multilevel amplitude or multilevel intensity modulated data page reconstruction; however, exact control of phase modulation characteristics is required to obtain high reconstruction quality.

Compact reconstruction of a Fourier hologram for a 3D object by scaling compensation.

The Fourier holographic projection method is compact and computationally fast. However, since the magnification of the displayed image increases with the diffraction distance, this method cannot be used directly to display multi-plane three-dimensional (3D) scenes. We propose a holographic 3D projection method of Fourier holograms by scaling compensation to offset the magnification during optical reconstruction. To achieve a compact system, the proposed method is also used to reconstruct 3D virtual images with Fourier holograms. Different from traditional Fourier holographic displays, images are reconstructed behind a spatial light modulator (SLM) so that the observation position can be placed close to the SLM. The effectiveness of the method and the flexibility of combining it with other methods are confirmed by simulations and experiments. Therefore, our method could have potential applications in the augmented reality (AR) and virtual reality (VR) fields.

Повышение пространственного разрешения цифровых голограмм с помощью одномерного субпиксельного сканирования

The article considers the issue of increasing the spatial resolution during the registration of digital holograms. In practice, discretization is carried out by measuring signal samples using sensors with a certain finite aperture. The resolution is determined by the size of the aperture area over which the averaging takes place. The resolution enhancement method is based on the sampling equation for signals obtained by the subpixel shift method using generalized functions. A subpixel shift is carried out using a spatial shift by a value less than the element of resolution. Apertures of various shapes are used, for example, elliptical, diamond-shaped, hexagonal, but rectangular apertures are most commonly used. The discretization equation involves the use of a two-dimensional aperture function. Below is a way to increase the resolution when using a one-dimensional function. This can be done based on the structure of the holographic signal. In this case, you can use a subpixel shift in only one direction. Digital holography is distinguished by the fact that photodetector matrices which have a spatial resolution much lower than photographic media used in traditional holography methods are used to register the signal,. Therefore, digital holography uses optical schemes with small angles between interfering beams. However, certain restrictions are imposed on the shape of the objects under study. If the objects have a shape that is significantly different from a flat one, it is necessary to use traditional schemes. The article presents mathematical modeling of the resolution enhancement method based on the recovery of signals from a real hologram obtained in the usual way. The increase in resolution is achieved using a one-dimensional subpixel shift. The use of a one-dimensional subpixel shift makes it possible to significantly simplify the optical scheme of the holographic setup.

Spherical crown holographic display with planar SLM

Spherical holography can expand the viewing angle, while the unavailability of spherical spatial light modulators (SLM) and the huge sampling number are challenges for spherical holography. In this paper, we propose a spherical crown holographic display method based on planar SLM. First by analyzing the diffraction formula of concentric spheres, the relationship between it and the plane diffraction is found. Then it is proposed that a spherical hologram loaded on a commercial planar SLM can reproduce the target object correctly with a reasonable number of sampling points. The method can be combined with spatiotemporal multiplexing and curved multiplexing to further expand the viewing angle and information capacity, respectively. It provides a new perspective for spherical holography, and has broad prospects in the field of 3D holographic display.

Fractional Fourier-transform filtering and reconstruction in off-axis digital holographic imaging.

An off-axis digital holographic reconstruction method with fractional Fourier transform domain filtering is proposed. The theoretical expression and analysis of the characteristics of fractional-transform-domain filtering are given. It is proven that the filtering in a lower fractional-order transform domain can utilize more high-frequency components than that in a conventional Fourier transform domain under the same size of filtering regions. In simulation and experiment, the results demonstrate that the reconstruction imaging resolution can be improved by filtering in the fractional Fourier transform domain. The presented fractional Fourier transform filtering reconstruction provides a novel (to our knowlede) optional way for off-axis holographic imaging.

Statefinder diagnosis for Barrow agegraphic dark energy

Here, by employing a Barrow entropy and the standard holographic method at a cosmic framework, we formulate Barrow agegraphic dark energy (BADE), taking the Universe age as an IR cutoff scale in a flat FLRW Universe. For evaluation of statefinder parameters in [Formula: see text] and [Formula: see text] planes, trajectories have been plotted for BADE and discovered that for various values of [Formula: see text], the model exhibits both the behavior of Chaplygin gas and quintessence. Moreover, as a supplement to the statefinder study, we looked at the BADE model without interaction in the plane [Formula: see text], which might offer us a dynamic study using the energy density BADE parameter [Formula: see text] and [Formula: see text], as per VI-[Formula: see text]CDM observational data without interaction from Planck 2018 results.

An equivalent source method for holographic visualization of acoustic sources in an apertured enclosure based on exterior measurements

Most acoustical holography techniques are developed to visualize sound sources or reconstruct sound field in a free-space environment, where no boundary reflected or scattered sound are present. However, in some engineering applications, a sound scatter is an inseparable part of source mechanism. For example, for a centrifugal fan, the aerodynamic noise sources are the turbulent pressure inside the fan shell, but the source distribution is significantly altered if the fan shell is removed. Thus, in order to visualize the sources inside the fan shell by holography methods based on exterior sound measurements, the measurements need to be performed with the presence of the shell (which is a sound scatter). This obviously violates the free-space assumption for most acoustical holography methods. In this work, traditional free-space equivalent source methods are extended to visualize acoustic sources situated in an enclosure with openings based on sound measurements exterior to the enclosure. The key step is to replace the free-space Green’s function used in traditional equivalent source methods by a Green’s function that satisfies the boundary condition of the apertured enclosure. Simulations are performed to prove the concept of the proposed acoustical holography method.

Numerical modeling of the 2D hologram of the low-frequency moving source by using horizontal antenna in a shallow water waveguide

The 2D holographic signal processing method by using a horizontal linear antenna (HLA) in shallow water is considered in the paper. The offered method of moving broad band source sound field hologram formation by using HLA is based on holographic signal processing of each element of HLA. The sound source moving in shallow water waveguide creates a stable interference pattern (interferogram) in the frequency-time domain on each HLA element. The 2D-FT (2D Fourier Transformation) of the interferogram is antenna element hologram (AEH). AEH allows to coherently accumulate the sound intensity of the interferogram in a small area as focal spots for each HLA element. It is shown in paper that the focal spots localization in AEH of HLA depends upon the source range, velocity, and motion direction [S. Pereselkov and V. Kuz’kin, JASA 151(2), 666–676). The output HLA hologram is formed by superposition AEH. Relationship between focal spot coordinates on the HLA hologram and the source range, velocity, and motion direction are derived in the paper. The results of the numerical experiment of HLA hologram formation for low-frequency (100–400 Hz) sound field of source moving in shallow water are presented. The results presented in the paper significantly expand the efficiency of interferometric signal processing in shallow water. [This study was supported by RFBR 19-29-06075, МК-4846.2022.4.]

Stereo Jones Matrix Holography with Longitudinal Polarization Transformation

AbstractMetasurfaces have exhibited powerful abilities for manipulating multiple fundamental properties of light including amplitude, phase, polarization, and so on. However, these strategies are commonly concentrated on the modulations at a single transverse plane of output light. The spatial evolutions of these properties, especially the polarizations along longitudinal direction, are rarely investigated. Here, a stereo Jones matrix holography method is presented for understanding the spatial evolution including polarization, amplitude, and phase variations along the longitudinal direction. Stereo holographic algorithms in matrix framework are developed to generate multiplane and even continuously varied vectorial holographic images that exhibit distinct polarization states at each transverse plane. This method provides a benchmark of longitudinal polarization transformations as well as beam modulations by simply using a single planar metasurface without extra burdens on optical path. In addition, the obtained propagation‐dependent features can favor the realizing of on‐demand transverse and longitudinal spatial evolution from the perspective of the holographic method. Furthermore, it may also promote the development of related areas including polarization‐switchable devices, optical trapping, microscopy, laser processing, etc.

Orbital Angular Momentum Multiplexing Holography for Data Storage

In the letter, we propose a holographic data storage method based on orbital angular momentum (OAM). In the proposed method, the OAM holography by discovering strong OAM selectivity in the spatial-frequency domain without a theoretical helical mode index limit is used to label different data pages. Each data page’s points and intensity levels are used to store the information. The data page can be reconstructed by using an OAM reading beam with an inverse helical mode illuminating the OAM-recording hologram. To further increase the density, different OAM-recording holograms are multiplexed. The experimental results show that we can store and read out the data by using the OAM hologram, and the density can be greatly improved by using the OAM-multiplexing hologram.

Breaking of Wavelength-Dependence in Holographic Wavefront Sensors Using Spatial-Spectral Filtering.

Nowadays, wavefront sensors are widely used to control the shape of the wavefront and detect aberrations of the complex field amplitude in various fields of physics. However, almost all of the existing wavefront sensors work only with quasi-monochromatic radiation. Some of the methods and approaches applied to work with polychromatic radiation impose certain restrictions. However, the contemporary methods of computer and digital holography allow implementing a holographic wavefront sensor that operates with polychromatic radiation. This paper presents a study related to the analysis and evaluation of the error in the operation of holographic wavefront sensors with such radiation.

Experimental Results of Double Near-filed Holography method for a commercial Product

In my laboratory, the new localization method, Double Near-field Acoustic Holography (DNAH) method is being Developed. This method is developed to overcome the limit of acoustic holography methods, that the acoustic holography methods cannot measure low frequency noise precisely. In former presentations, the numerical simulation results, and basic experimental results are reported. In these presentations, it is verified that the DNAH method has good resolution for low frequency sound sources. But they are carried out for simple sound source(s), simulated point source(s). In this presentation, the experimental results for a commercial product will be presented. From these results, it is verified that the DNAH method has good resolution for low frequency noise of a commercial product between 10Hz and 200Hz, and the DNAH method has enough resolution for low frequency sound localization.

Machine learning aided near-field acoustic holography based on equivalent source method.

In recent times, equivalent source method-based near-field acoustic holography methods have been extensively applied in sound source localization and characterization. The most commonly used equivalent sources are spherical harmonics. In a non-reverberant environment with no reflections, these equivalent sources could be the best choice since spherical harmonics are derived for the Sommerfeld boundary condition. However, these methods are not the best fit for reverberating environments. In such cases, a new relationship can be calculated between the field weights and the measured pressure with enough training examples. The proposed machine learning models include linear regression (LR) with adaptive moment estimation (Adam), LR with limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), and multi-layer perceptron with one and two hidden layers. These methods are tested for multiple monopoles and vibrating plate simulations in a room with different wall absorption coefficients. The data-driven methods are also studied on loudspeakers numerically and experimentally in a free field environment. The results from these methods are compared with the results of one norm convex optimization (L1CVX). LR with L-BFGS performed the best among all the methods studied and performed better than L1CVX for less absorption coefficient for geometrically separable sources. LR with L-BFGS also has much faster inference times.

A Machine Learning Enhanced Approach for Automated Sunquake Detection in Acoustic Emission Maps

Sunquakes are seismic emissions visible on the solar surface, associated with some solar flares. Although discovered in 1998, they have only recently become a more commonly detected phenomenon. Despite the availability of several manual detection guidelines, to our knowledge, the astrophysical data produced for sunquakes is new to the field of machine learning. Detecting sunquakes is a daunting task for human operators, and this work aims to ease and, if possible, to improve their detection. Thus, we introduce a dataset constructed from acoustic egression-power maps of solar active regions obtained for Solar Cycles 23 and 24 using the holography method. We then present a pedagogical approach to the application of machine-learning representation methods for sunquake detection using autoencoders, contrastive learning, object detection and recurrent techniques, which we enhance by introducing several custom, domain-specific data augmentation transformations. We address the main challenges of the automated sunquake-detection task, namely the very high noise patterns in and outside the active region shadow and the extreme class imbalance given by the limited number of frames that present sunquake signatures. With our trained models, we find temporal and spatial locations of peculiar acoustic emission and qualitatively associate them to eruptive and high energy emission. While noting that these models are still in a prototype stage, and there is much room for improvement in metrics and bias levels, we hypothesize that their agreement on example use cases has the potential to enable detection of weak solar acoustic manifestations.

DMD-based pure-phase superpixel method for digital holography

In this work, we implement a pure-phase superpixel (PPSP) method with a digital micromirror device (DMD). Here the DMD acts in an unconventional mode, i.e. as a phase-only modulator with hundreds of phase levels. An iterative Fourier transform algorithm is adapted to the DMD with high quality in a 2f-configuration without filters. When using 1600 × 1600 DMD pixels, the simulations show that the PPSP method in combination with the mixed-region amplitude freedom algorithm reduces the root-mean-square error by at least 33.5% compared with the conventional amplitude and phase modulation methods, and provides higher efficiency by 7.3%.

Holographic Back-Projection Method for Calibration of Fully Digital Polarimetric Phased Array Radar

Phased Array Radar (PAR) technology is rapidly rising as a candidate for future weather radars because it can provide focused, high-quality meteorological observations. Due to the need for precise measurements of polarimetric weather variables, it is desired that the radar simultaneously transmits and receives linearly polarized horizontal (H) and vertical (V) fields through beams that are well matched in gain and shape at every pointing direction. These scanning characteristics are difficult to achieve, especially with current methods such as the “park and probe” calibration, because the radiation patterns of PAR antennas are inherently dependent on their pointing direction. Thus, polarimetric array calibration is critical to produce matched H/V copolar antenna patterns. In this article, we present a polarimetric antenna calibration procedure for the fully-digital PARs based on the holographic back-projection of electric fields. The fully digital S-band Horus radar is used to implement and evaluate the proposed calibration method. First, near-field measurements of a fully active Horus antenna panel are back-projected onto the plane of the array to derive the copolar magnitude and phase of the H/V fields radiated by each antenna element. Then, digital calibration parameters are produced from back-projected fields to compensate for excitation differences and produce uniform radiation at the plane of the array. The performance of the back-projection calibration method is evaluated for broadside and for electronically scanned angles and compared to the more conventional park and probe calibration method. A robustness analysis is conducted using simulations to evaluate the impact of excitation amplitude and phase errors that could result from practical near-field environments and amplifier performance degradation. Preliminary results show that through precise digital calibration based on back-projected fields, beam matching can be significantly improved to achieve the desired polarimetric calibration levels. For electronically steered beams, back-projection calibration can reduce H/V beam mismatch biases by approximately 25%, from 0.34 dB to 0.08 dB. This improves measurement accuracy of fully digital PARs by mitigating antenna-induced biases in meteorological estimates.

Holographic method of neural network design

The paper presents a method for solving the problem of changing a full-connected neural network of direct propagation with a sigmoid activation function in the conditions of the emergence of a new class, with the ability to preserve the network to recognize already known classes and to classify objects of a new class. Such conditions generate a new neural network, which is trained on examples of all classes, including the new class. The learning process takes a long time and requires the selection of several parameters. The emergence of a new class in natural neural networks does not cause a transformation of the network structure, only the strength of connections between neurons changes. The network shows the properties of stability and plasticity at the same time. The authors draw attention to the analogy between neural networks and holograms in their ability to store information and form an image of a class in response to an input signal. Following the holographic analogy, the paper proposes a model of the wave nature of neural networks, which treats the network weights as a hologram and the input signal as a wave passing through a hologram. The construction of a new network is created with two neural networks, which are a combination of two holograms. The first hologram represents the original network, and the second is a new network with a similar structure, but it is trained to recognize one new class. The addition of the holograms of these neural networks implements the mechanisms of plasticity and stability in the model.

A forward reconstruction, holographic method to overcome the lens effect during 3D detection of semi-transparent, non-spherical particles.

Suspensions of semi-transparent particles such as polystyrene microparticles are commonly used as model systems in the study of micro-rheology, biology, and microfluidics. Holography is a valuable tool that allows one to obtain 3-D information for particle position and orientation, but forward reconstruction techniques often struggle to infer this information accurately for semi-transparent spheroids with an O(1) aspect ratio, since the lens effect from the particle introduces complex patterns. We propose a reconstruction method that uses image moment information to generate a mask over the sharp patterns from the lens effect and gives reasonable estimation of the 3-D position and orientation of the particle. The method proposed in this work uses the average particle geometry information to determine the process parameters and identify the appropriate detection zone. The average detection error for zc is less than 25% of the average particle thickness, and the average errors in the in-plane and out-of-plane orientations ϕ and θ are 2° and 4°, respectively. Our method provides comparable accuracy in the detection of the particle center of mass (xc, yc, zc) and in-plane orientation ϕ as a recent forward reconstruction method for semi-transparent particles proposed by Byeon et al. (H. Byeon, T. Go and S. J. Lee, Appl. Opt., 2016, 54, 2106-2112; H. Byeon, T. Go and S. J. Lee, Opt. Express, 2016, 24, 598-610). This method provides a clearly defined framework for identifying the particle's out-of-plane tilt angle θ. We finally demonstrate the applicability of the method to opaque, slender (aspect ratio AR ≫ 1) particles by analyzing the 3-D motion of E. coli cells from holographic video footage.

A Quad-Polarization Reconfigurable Fixed-Frequency Beam-Scanning Leaky-Wave Antenna Based on the Holographic Method for Millimeter-Wave Application

A quad-polarization reconfigurable fixed-frequency beam-scanning leaky-wave antenna (LWA) operating at millimeter-wave Ka-band is presented in this article. A low-loss groove gap waveguide (GGW) structure is employed for low-loss transmission and feeding, above which there locates a metal-covered superstrate. Two rows of inclined slots etched on the metal cover in a staggered arrangement operate as the radiated sources. A modified holographic method is presented, and the hologram can be manipulated by switching the states between “ON” and “OFF” of the p-i-n diodes, and hence the fixed-frequency beam-scanning property with polarization agility of four different polarization states can be realized, including horizontal polarization (HP), vertical polarization (VP), left-handed circular polarization (LHCP), and right-handed circular polarization (RHCP). Besides, measured results of the fabricated antenna are given to verify its performance. The measured peak gains at 30 GHz reach 11.3 dBi in the HP state, 13.0 dBi in the VP state, 11.5 dBic in the LHCP state, and 11.8 dBic in the RHCP state, respectively, with a beam-scanning range of 100° (from −50° to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm{50}^{\circ }$ </tex-math></inline-formula> ), showing good agreement with the simulated results.