Reference Wave Research Articles

The reference window for reduced perturbation of the reference wave in electrical biasing off-axis electron holography

The perturbation of the reference wave due to electric stray fields represents a major challenge in quantitative electron holographic investigations. By introducing a focused-ion-beam-milled rectangular hole, the reference window, in an area of nearly constant electrostatic potential of the sample, this perturbation can be significantly reduced. The edge of the window forms a closed conducting loop, acting similarly to a Faraday cage, shielding the influence of the stray field on the reference wave to some extent. In this work, the shielding effect of the reference window is systematically investigated by comparing electron holograms of an electrically biased coplanar capacitor, as a well-known reference sample, with finite element simulations. It is shown that the introduction of the reference window into electrical biasing samples both suppresses unknown lateral phase distortions substantially and in addition improves the agreement of the experimentally observed phase slope with that expected by simulation significantly, particularly for small object-reference wave distances. Consequently, a slight adjustment of the sample geometry results in an improved reproducibility of electron holographic electrical biasing experiments, which is a significant step towards quantitative evaluation.

Orthogonality of polarization superposition based on polarization holography.

We propose a polarization superposition orthogonal theory based on tensor polarization holography. Based on this theory, the holographic multiplexing capability can be improved measurably. The orthogonality of polarization waves is characterized by the null reconstruction in polarization holography, achieved through the superposition of multiple basic polarization reference waves. This paper analyzes the orthogonality of linear polarization wave superposition and circular polarization wave superposition using the tensor polarization holography theory. Using the polarized holography multiplexing technique, we experimentally verify the orthogonality of polarization wave superposition. Our experimental results align with the theoretical analysis, indicating potential applications in polarization encoding and decoding by this theory, thereby diversifying optical encryption technology Additionally, we demonstrate that polarization superposition orthogonality holds significant promise for optical control technology.

High-accuracy ultrasonic measurement of oil film thickness in sliding bearings considering surface thin coating

Focusing on the difficulty and inaccuracy of separating reflected waves from overlapping echoes caused by coating when measuring the oil film thickness of coated sliding bearings using ultrasonic. This paper proposes a pseudo reflection coefficient (PRC) constructed using the overall reflected wave and reference wave. And a robust PRC model is constructed to simultaneously calculate the oil film and coating thickness. Acoustic simulations verify the accuracy of the method and reveal that the PRC model has better stability. Application experiments are conducted on an actual aviation fuel gear pump. The good consistency between theory and experiment has demonstrated the effectiveness of the method. In addition, the elastic deformation of the bearing is derived based on the minimum oil film thickness.

Numerical Investigation of the Quantum Inverse Algorithm on Small Molecules.

We evaluate the accuracy of the quantum inverse (Q-Inv) algorithm, in which the multiplication of Ĥ-k to the reference wave function is replaced by the Fourier transformed multiplication of e-iλĤ, as a function of the integration parameters and the iteration power k for various systems, including H2, LiH, BeH2 and the notorious H4 molecule at square geometry. We further consider the possibility of employing the Gaussian-quadrature rule as an alternate integration method and compared it to the results employing trapezoidal integration. The Q-Inv algorithm is compared to the inverse iteration method using the Ĥ-1 inverse (I-Iter) and the exact inverse by lower-upper decomposition. Energy values are evaluated as the expectation values of the Hamiltonian. Results suggest that the Q-Inv method provides lower energy results than the I-Iter method up to a certain k, after which the energy increases due to errors in the numerical integration that are dependent on the integration interval. A combined Gaussian-quadrature and trapezoidal integration method proved to be more effective at reaching convergence while decreasing the number of operations. For systems like H4, in which the Q-Inv cannot reach the expected error threshold, we propose a combination of Q-Inv and I-Iter methods to further decrease the error with k at lower computational cost. Finally, we summarize the recommended procedure when treating unknown systems.

Rapid terahertz beam profiling and antenna characterization with phase-shifting holography

In this paper we investigate the application of phase-shifting digital holography for the real-time characterization of electromagnetic sources in the THz frequency range. We use an off-the-shelf terahertz detector array composed of 64×64\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$64 \ imes 64$$\\end{document} power-sensitive pixels, over an area of 96mm×96mm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$96\\,\\hbox {mm} \ imes 96\\,\\hbox {mm}$$\\end{document}, to record intensity interferograms cast between the coherent radiation emitted from a reference source and an unknown antenna under test. This approach parallelizes the acquisition process with respect to conventional near-field point scanning methods, reducing the measurement time by orders of magnitude. In our system, the measurement time is limited only by the refresh rate of the detector array and the speed of a delay line stage that is used to phase-shift the reference wave. As a proof-of-principle demonstration, we map the 2D near-field distribution and estimate the far-field radiation pattern emitted by a plano-convex PTFE spherical lens antenna illuminated by a diagonal horn at 290 GHz frequency with ∼1Hz\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim \\,1\\,\\hbox {Hz}$$\\end{document} refresh rate.

Bragg Matching when Multiplexing Volume Holograms

In this work, we analyzed the influence of Bragg matching on the recording and reconstruction of animated holograms on thick media. It is shown that in order to prevent overlapping of images reconstructed from different holograms on a CCD-type receiving device (charge-coupled device), it is very important that two requirements are met, or at least one of them: when restoring an animated hologram, the reference beam usually overlaps several holograms, however, only one reconstructed image should fall on the CCD, the one that we want to read from the hologram we need; the reference beam falls on an area where several holograms are recorded, however, only one hologram we need is restored, i.e. the restoration circuit is built in such a way that the reference beam has the ability to filter out unnecessary images. This sampling capability is specified by changing the characteristics of the reconstruction wave relative to the characteristics of the recording reference wave. These include changes in the angle of incidence, phase characteristics of the wave, wavelength, etc. Restoration with other characteristics leads to a sharp decrease in the diffraction efficiency of the hologram to negligible values.

Demonstration of chirped pulse phase-shifting digital holography for capturing the sequence of ultrafast optical wavefronts

We experimentally demonstrate chirped pulse phase-shifting digital holography. This method, recently proposed, allows for capturing the sequence of ultrafast optical wavefronts with picosecond time resolution in a single-shot manner. In our experiment, we recorded two object pulses with a time separation of 1.67 ps using 35-fs-width optical pulses, employing a diffractive optical element and a bandpass filter, on a single polarization camera simultaneously. We reconstructed both the intensity and phase images of these object pulses using modified calculations that account for corrections in the polarization states of the reference waves, thereby improving the quality of the reconstructed images.

Object alignment in spatially multiplexed holograms applied to polarization sensing.

The paper presents a new algorithm for object alignment in digital holography with multiple spherical reference waves. The algorithm was applied to polarization sensing with two orthogonally polarized reference waves. A novel holographic setup was built using a diffraction grating to generate two symmetric reference waves, keeping the setup simple and highly adjustable. The angles of rotation of the polarizing elements were calculated with mean absolute errors of 0.71° and 2.96° based on intensity and phase measurements, respectively. The same algorithm can be applied to any digital holographic measurement with multiple spherical reference waves.

Double-slit holography—a single-shot lensless imaging technique

In this study, we propose a new method for single-shot, high-resolution lensless imaging called double-slit holography. This technique combines the properties of in-line and off-axis holography in one single-shot measurement using the simplest double-slit device: a plate with two apertures. In double-slit holography, a plane wave illuminates the two apertures giving rise to two spherical waves. While diffraction of one spherical wave from a sample positioned behind the first aperture (the object aperture) provides the object wave, the other spherical wave diffracted from the second (reference) aperture provides the reference wave. The resulting interference pattern in the far-field (hologram) combines the properties of an in-line (or Gabor-type) hologram and an off-axis hologram due to the added reference wave from the second aperture. Both the object and reference waves have the same intensity, which ensures high contrast of the hologram. Due to the off-axis scheme, the amplitude and phase distributions of the sample can be directly reconstructed from the hologram, and the twin image can be easily separated. Due to the object wave being the same as in-line holography with a spherical wave, imaging at different magnifications is similarly done by simply adjusting the aperture-to-sample distance. The resolution of the reconstructed object is given by the numerical aperture of the optical setup and the diameter of the reference aperture. It is shown both by theory and simulations that the resolution of the reconstructed object depends on the diameter of the reference wave aperture but does not depend on the diameter of the object aperture. Light optical proof-of-concept experiments are provided. The proposed method can be particularly practical for X-rays, where optical elements such as beam splitters are not available and conventional off-axis holography schemes cannot be realised.

Fractional Fourier-transform off-axis digital holographic imaging

A fractional Fourier-transform digital holographic imaging method with resolution enhancement features is presented. In an optical configuration, an extended fractional Fourier-transform optical setup is set in the object arm of an off-axis digital holographic recording system to record a fractional Fourier-transform hologram via the optical interference of the fractional Fourier-transform wavefront of an object wave with a reference wave. For reconstruction imaging, the reconstruction approach for fractional Fourier-transform holograms is given. In the experiment, the fractional Fourier-transform digital holograms are recorded under the different recording parameters, and their amplitude images are effectively reconstructed. The imaging results demonstrate that the reconstruction-imaging resolution of fractional-order Fourier-transform holograms is obviously enhanced compared to that of conventional image-plane holograms. The presented fractional Fourier-transform digital holographic imaging with resolution enhancement and optical configuration flexibility provides, to our knowledge, a novel way for off-axis digital holographic imaging.

Tensor-Free Holographic Metasurface Leaky-Wave Multi-Beam Antennas with Tailorable Gain and Polarization.

Recently, the community has seen a rise in interest and development regarding holographic antennas. The planar hologram is made of subwavelength metal patches printed on a grounded dielectric board, constituting flat metasurfaces. When a known reference wave is launched, the hologram produces a pencil beam towards a prescribed direction. Most earlier works on such antennas have considered only a single beam. For the few later ones that studied multiple beams, they were achieved either by having each beam taken care of by a distinct frequency or by partitioning the hologram, thereby depriving each beam of the directivity it could have had it not shared the holographic aperture with other beams. There have been recent studies related to the use of tensor surface impedance concepts for the synthesis of holograms which have attained control over the polarizations and intensities of the beams. However, this approach is complicated, tedious, and time-consuming. In this paper, we present a method for designing a planar holographic leaky-wave multi-beam metasurface antenna, of which each simultaneous beam radiating at the same frequency towards any designated direction has a tailorable amplitude, phase, and polarization, all without hologram partitioning. Most importantly, this antenna is exempted from the need for the cumbersome technique of tensor impedance. Such features of beam configurability are useful in selective multiple-target applications that require differential gain and polarization control among the various beams. Only a single source is needed, which is another benefit. In addition, effective methods to mitigate sidelobes are also proposed here. Designs by simulations according to the method are herein validated with measurements performed on fabricated prototypes.

Deformation measurement by digital speckle pattern interferometry using holographically recorded object in LiNbO3 as a reference

A new method, to the best of our knowledge, in digital speckle pattern interferometry is introduced. It depends on extending the applicability of using LiNbO3 crystal as a holographic recording medium for the evaluation of the difference in displacement between two similar objects (master and test), and displaying the comparison result in the form of an interference pattern. The method is a two-stage process. In the first stage, two states (un-displaced and displaced states) of the master object are recorded in a LiNbO3 crystal using the usual holographic arrangement. In the second stage, various phase stepping algorithms are applied, using the reconstructed wavefronts of the master object as a holographic optical element to produce a reference wave field in the comparison process. Recording and analysis of the difference correlation fringes are performed using the phase wrapping algorithm and real experiment.

Importance profiles. Visualization of atomic basis set requirements

Recent developments in fully numerical methods promise interesting opportunities for new, compact atomic orbital (AO) basis sets that maximize the overlap to fully numerical reference wave functions, following the pioneering work of Richardson and coworkers from the early 1960s. Motivated by this technique, we suggest a way to visualize the importance of AO basis functions employing fully numerical wave functions computed at the complete basis set limit: the importance of a normalized AO basis function |α⟩ centered on some nucleus can be visualized by projecting |α⟩ on the set of numerically represented occupied orbitals |ψi⟩ as I0(α)=∑i⟨α|ψi⟩⟨ψi|α⟩ . Choosing α to be a continuous parameter describing the AO basis, such as the exponent of a Gaussian-type orbital or Slater-type orbital basis function, one is then able to visualize the importance of various functions. The proposed visualization I0(α) has the important property 0⩽I0(α)⩽1 which allows unambiguous interpretation. We also propose a straightforward generalization of the importance profile for polyatomic applications I(α) , in which the importance of a test function |α⟩ is measured as the increase in projection from the atomic minimal basis. We exemplify the methods with importance profiles computed for atoms from the first three rows, and for a set of chemically diverse diatomic molecules. We find that the importance profile offers a way to visualize the atomic basis set requirements for a given system in an a priori manner, provided that a fully numerical reference wave function is available.

Deep neural networks for crack detection inside structures

Crack detection is a long-standing topic in structural health monitoring. Conventional damage detection techniques rely on intensive, time-consuming, resource-intensive intervention. The current trend of crack detection emphasizes using deep neural networks to build an automated pipeline from measured signals to damaged areas. This work focuses on the seismic-wave-based technique of crack detection for plate structures. Previous work proposed an encoder–decoder network to extract crack-related wave patterns from measured wave signals and predict crack existence on the plate. We extend previous work with extensive experiments on different network components and a data preprocessing strategy. The proposed methods are tested on an expanded crack detection dataset. We found that a robust backbone network, such as Densely Connected Convolutional Network (DenseNet) can effectively extract the features characterizing cracks of wave signals, and by using the reference wave field for normalization, the accuracy of detecting small cracks can be further improved.

0th-Order Diffraction Light Removal using Two Holograms with Different Polarization Reference Waves in Digital Holography

0th-Order Diffraction Light Removal using Two Holograms with Different Polarization Reference Waves in Digital Holography

Capturing the electron-electron cusp with the coupling-constant averaged exchange-correlation hole: A case study for Hooke's atoms.

In density-functional theory, the exchange-correlation (XC) energy can be defined exactly through the coupling-constant (λ) averaged XC hole n̄xc(r,r'), representing the probability depletion of finding an electron at r' due to an electron at r. Accurate knowledge of n̄xc(r,r') has been crucial for developing XC energy density-functional approximations and understanding their performance for molecules and materials. However, there are very few systems for which accurate XC holes have been calculated since this requires evaluating the one- and two-particle reduced density matrices for a reference wave function over a range of λ while the electron density remains fixed at the physical (λ = 1) density. Although the coupled-cluster singles and doubles (CCSD) method can yield exact results for a two-electron system in the complete basis set limit, it cannot capture the electron-electron cusp using finite basis sets. Focusing on Hooke's atom as a two-electron model system for which certain analytic solutions are known, we examine the effect of this cusp error on the XC hole calculated using CCSD. The Lieb functional is calculated at a range of coupling constants to determine the λ-integrated XC hole. Our results indicate that, for Hooke's atoms, the error introduced by the description of the electron-electron cusp using Gaussian basis sets at the CCSD level is negligible compared to the basis set incompleteness error. The system-, angle-, and coupling-constant-averaged XC holes are also calculated and provide a benchmark against which the Perdew-Burke-Ernzerhof and local density approximation XC hole models are assessed.

Motion-resolved, reference-free holographic imaging via spatiotemporally regularized inversion

Holography is a powerful technique that records the amplitude and phase of an optical field simultaneously, enabling a variety of applications such as label-free biomedical analysis and coherent diffraction imaging. Holographic recording without a reference wave has been long pursued because it obviates the high experimental requirements of conventional interferometric methods. However, due to the ill-posed nature of the underlying phase retrieval problem, reference-free holographic imaging is faced with an inherent tradeoff between imaging fidelity and temporal resolution. Here, we propose a general computational framework, termed spatiotemporally regularized inversion (STRIVER), to achieve motion-resolved, reference-free holographic imaging with high fidelity. Specifically, STRIVER leverages signal priors in the spatiotemporal domain to jointly eliminate phase ambiguities and motion artifacts, and, when combined with diversity measurement schemes, produces a physically reliable, time-resolved holographic video from a series of intensity-only measurements. We experimentally demonstrate STRIVER in near-field ptychography, where dynamic holographic imaging of freely swimming paramecia is performed at a framerate-limited speed of 112 fps. The proposed method can be potentially extended to other measurement schemes, spectral regimes, and computational imaging modalities, pushing the temporal resolution toward higher limits.

Rydberg electron stabilizes the charge localized state of the diamine cation

A previous controversial discussion regarding the interpretation of Rydberg spectra of gaseous dimethylpiperazine (DMP) as showing the co-existence of a localized and delocalized mixed-valent DMP+ radical cation is revisited. Here we show by high-level quantum-chemical calculations that an apparent barrier separating localized and delocalized DMP+ minima in previous multi-reference configuration-interaction (MRCI) calculations and in some other previous computations were due to unphysical curve crossings of the reference wave functions. These discontinuities on the surface are removed in state-averaged MRCI calculations and with some other, orthogonal high-level approaches, which do not provide a barrier and thus no localized minimum. We then proceed to show that in the actually observed Rydberg state of neutral DMP the 3s-type Rydberg electron binds more strongly to a localized positive charge distribution, generating a localized DMP* Rydberg-state minimum, which is absent for the DMP+ cation. This work presents a case where interactions of a Rydberg electron with the underlying cationic core alter molecular structure in a fundamental way.

Correction of phase drifts in two-wavelength digital holographic microscopy using secondary reference waves

We present a two-wavelength digital holographic microscopy setup for surface topography measurement with single-point illumination and a method for correction of unwanted phase drifts using secondary reference waves.

Towards reliable and efficient modeling of [Cu2O2]2+-based compound electronic structures with the partially fixed reference space protocols.

This work reports a computationally efficient approach for reliable modeling of complex electronic structures based on [Cu2O2]2+ moieties. Specifically, we explore the recently developed partially fixed reference space (PFRS) protocol to minimize the active space size, taking into account the double d-shell effects. We show that the ground-state electronic structure of the core [Cu2O2]2+ model system is dominated by the d9/d10 occupations. The PFRS-crafted active spaces are further used to generate the reference wave functions for the multi-reference coupled cluster, configuration interaction, and multi-reference perturbation theory calculations. Specifically, we demonstrate that the bare [Cu2O2]2+ core can be modeled qualitatively using active spaces as small as CAS(2,2)PFRS. To obtain quantitative agreement with the reference DMRG(32,62)CI calculations, the CAS(4,4) has to be used in conjunction with the MRCCSD correction on top of it. This reliable and computationally efficient protocol is further used to model the electronic structure and properties of ammonia coordinated [Cu2O2]2+ complexes. Finally, based on the large amount of available experimental data regarding the oxo-peroxo equilibrium of [Cu2O2]2+-based systems, it is possible to formulate educated guesses regarding the effect of each experimental variable over each d-occupancy-specific state. With a large sample size of d-occupancy-specific state dependence with ligands and solvents, it should be possible to propose new ligands with specific d-occupancy and, therefore, oxidative properties based on the d-occupancy energy gaps of relatively low-cost calculations.