Arbitrary Coherence Research Articles

Combination of Fourier transform Jones matrix and beam coherence polarization matrix: Application to a double polarizer rectangular aperture

In this work, we extend the Fourier transform Jones (FTJ) matrix approach to handle input scalar fields with spatially variant transverse profiles. Additionally, we integrate the FTJ matrix with the beam coherence-polarization (BCP) matrix, suitable for describing partially coherent and partially polarized light. This approach is particularly effective when the polarization diffractive optical element is illuminated with a quasi-monochromatic paraxial scalar field with transverse spatial coherence, but with any degree of polarization and transverse profile. We apply the method to a meaningful example: a rectangular aperture with orthogonal polarizers on each half, illuminated with uniform randomly polarized light. We provide experimental validation using a randomly polarized He-Ne laser and a specially fabricated double polarizer mask. Furthermore, by placing a polarizer behind the polarization diffractive optical element, we generate a scalar beam with spatial incoherence across two distinct zones, suggesting the potential use of randomly polarized lasers with binary patterned polarizers to encode arbitrary binary coherence functions.

A coherence-improved and mass-balanced inflow turbulence generation method for large eddy simulation

Realistic inflow turbulence is crucial in large eddy simulations for obtaining accurate results. In this paper, an improved inflow turbulence generation method is proposed, called the coherence-improved and mass-balanced random flow generation (CMRFG) method. First, a study of the effect of the inlet mass-balanced condition is presented. Subsequently, the proposed method is explicitly deduced to satisfy arbitrary spatial coherence functions and the mass-balanced condition, so the generated turbulent fields effectively preserve the original turbulence characteristics, eliminating the need for additional inlet mass flux corrections. Meanwhile, the novel method retains the advantages of the previous method, satisfying arbitrary turbulence intensities, temporal spectra, temporal correlations, and spatial correlation coefficients. Additionally, the proposed method also ensures compliance with the divergence-free condition and Taylor's frozen hypothesis, which are essential for accurate flow field development. Finally, large eddy simulations of both homogeneous isotropic and anisotropic turbulent fields demonstrate that the turbulent fields generated by CMRFG closely align with experimental results and exhibit no artificial pressure fluctuations within the computational domain.

Coherence and the merging of relational classes in self-organizing networks: Extending Relational Density Theory

We extended prior work on Relational Density Theory (Belisle & Dixon, 2020a,b) by evaluating the role of pre-experimental coherence among relational classes on the development of merged classes. Distance was modelled geometrically using a multidimensional scaling procedure. Phases 1 and 2 were identical across the participants and Phase 3 differed based on group assignment. In phase 1, we examined the pre-experimental relatedness of 12 arbitrary symbols and 4 known textual words (SALT, PEPPER, KING, QUEEN). Non-coherence was observed between the arbitrary symbols and coherence between the known words (SALT=PEPPER, KING=QUEEN). In phase 2, we established 4, 4-member equivalence classes using a linear training arrangement, where each class included 3 arbitrary symbols and 1 known word. Separation of the classes within the geometric space was observed. In Phase 3, for half of the participants, we attempted to establish a class merger between 2 members of each coherent class (Coherence condition; salt = pepper and king = queen). For the other participants, we attempted to establish a class merger between 2 members of each non-coherent class (Non-coherence condition; king = pepper and queen = salt). Results support the successful merger of the merged coherence class but not the merged non-coherence class. Results have implications for relational self-organization in the establishment of complex combined networks.

Methodology to identify the marketing strategies that affect the purchasing moment: TRAPPOLA

La creciente globalización, el consumismo y la rivalidad entre las empresas han influido a lo largo del tiempo en la generación de estrategias de mercadeo para prevalecer, por medio del análisis de los comportamientos humanos. Por ello, a partir de una revisión de literatura de estos aspectos, se diseñó una metodología constructivista llamada “Trappola”, que permite, a través de una situación de consumo enfocada en estrategias de mercadeo, que los participantes vivencien el principio de la economía conductual, que se basa en la idea de que las personas no son completamente racionales, sino también previsiblemente irracionales. Es decir, que su irracionalidad se produce siempre del mismo modo una y otra vez. Por ende, el objetivo de aprendizaje gira en torno a reconocer métodos como el efecto señuelo, efecto anclaje, coherencia arbitraria, gregarismo o efecto arrastre, efecto del coste cero, marketing emocional y efecto de la expectativa o efecto Pigmalión. Por último, se concluye que el comportamiento humano al ser predecible permite que las estrategias de marketing se cumplan en gran medida al momento de efectuar una compra.

Generating large field of view en-face projection images from intra-acquisition motion compensated volumetric optical coherence tomography data.

A technique to generate large field of view projection maps of arbitrary optical coherence tomography (OCT) data is described. The technique is divided into two stages - an image acquisition stage that features a simple to use fast and robust retinal tracker to get motion free retinal OCT volume scans - and a stitching stage where OCT data from different retinal locations is first registered against a reference image using a custom pyramid-based approach and finally stitched together into one seamless large field of view (FOV) image. The method is applied to data recorded with a polarization sensitive OCT instrument in healthy subjects and glaucoma patients. The tracking and stitching accuracies are quantified, and finally, large FOV images of retinal nerve fiber layer retardation that contain the arcuate nerve fiber bundles from the optic nerve head to the raphe are demonstrated.

The Arbitrary Coherence Effect and Decision Making

In Behavioral Economics, “arbitrary coherence” is when an arbitrary, randomly chosen number, influences the amount purchasers are willing to pay for a product. Arbitrary coherence is similar to anchoring which marketers sometimes use to help set optimal prices. This paper examines how the arbitrary coherence effect influences individual decision making.

Matrix algorithm for 3D nonparaxial optical field modeling under arbitrary spatial coherence.

Nonparaxial modeling of optical field propagation at distances comparable to the wavelength and under arbitrary spatial coherence is crucial for micro- and nano-optics. Fourier and Fresnel transform-based algorithms are unable to simulate it accurately because of their paraxial approach. A nonparaxial matrix algorithm, supported by the theoretical model that characterizes the optical field and the setup configuration in terms of sets of real and virtual point emitters, is capable of simulating the 3D optical field distribution in the volume delimited by the input and the output planes placed at a very short distance from each other by using experimental data as entries. The algorithm outcomes are accurate predictions of the power spectrum of interference and diffraction experiments. Simulations of specific experimental situations, including speckle phenomena, illustrate the algorithm's capabilities.

Scattering concentration bounds: brightness theorems for waves

The brightness theorem---brightness is nonincreasing in passive systems---is a foundational conservation law, with applications ranging from photovoltaics to displays, yet it is restricted to the field of ray optics. For general linear wave scattering, we show that power per scattering channel generalizes brightness, and we derive power-concentration bounds for systems of arbitrary coherence. The bounds motivate a concept of "wave \'{e}tendue" as a measure of incoherence among the scattering-channel amplitudes, and which is given by the rank of an appropriate density matrix. The bounds apply to nonreciprocal systems that are of increasing interest, and we demonstrate their applicability to maximal control in nanophotonics, for metasurfaces and waveguide junctions. Through inverse design, we discover metasurface elements operating near the theoretical limits.

Volumetric non-local-means based speckle reduction for optical coherence tomography.

We present a novel tomographic non-local-means based despeckling technique, TNode, for optical coherence tomography. TNode is built upon a weighting similarity criterion derived for speckle in a three-dimensional similarity window. We present an implementation using a two-dimensional search window, enabling the despeckling of volumes in the presence of motion artifacts, and an implementation using a three-dimensional window with improved performance in motion-free volumes. We show that our technique provides effective speckle reduction, comparable with B-scan compounding or out-of-plane averaging, while preserving isotropic resolution, even to the level of speckle-sized structures. We demonstrate its superior despeckling performance in a phantom data set, and in an ophthalmic data set we show that small, speckle-sized retinal vessels are clearly preserved in intensity images en-face and in two orthogonal, cross-sectional views. TNode does not rely on dictionaries or segmentation and therefore can readily be applied to arbitrary optical coherence tomography volumes. We show that despeckled esophageal volumes exhibit improved image quality and detail, even in the presence of significant motion artifacts.

Maximizing Young fringe visibility with a universal SU2 polarization gadget.

When a Young interferometer is fed by a general electromagnetic field, the fringe visibility may change upon insertion of an anisotropic optical element over one of the interferometer pinholes. The maximum visibility that the fringes may exhibit in this way is theoretically known, but no direct experimental check seems to be available. Here we discuss the scheme of an experimental test. In particular, maximum fringe visibility is obtained with a three-component universal SU2 polarization gadget for arbitrary coherence features of the illuminating field. Confirming results obtained with a suitable experimental setup are presented.

Efficient tensor approach for propagation of beams of arbitrary shape and coherence through atmospheric turbulence

A tensor approach to simulate and predict the transverse intensity and distribution of a two-point correlation of beams of arbitrary shape and coherence through atmospheric turbulence has been derived on the basis of the extended Huygens–Fresnel principle. The validity of this approach is verified by comparing the reconstructed intensity and second-order correlation of symmetric points in the output plane of a Gaussian Schell-model beam with calculated results from analytic formulae. An example illustrates how this tensor approach can be applied to beams blocked by finite apertures in the atmospheric propagation. Our approach provides an efficient and universal numerical model to manage the turbulent propagation of various optical sources. This approach can be useful in long-distance imaging and optical communication.

Quantum networks: topology and spectral characterization

To utilize a scalable quantum network and perform a quantum state transfer within distant arbitrary nodes, coherence and control of the dynamics of couplings between the information units must be achieved as a prerequisite ingredient for quantum information processing within a hierarchical structure. Graph theoretic approach provides a powerful tool for the characterization of quantum networks with non-trivial clustering properties. By encoding the topological features of the underlying quantum graphs, relations between the quantum complexity measures are presented revealing the intricate links between a quantum and a classical networks dynamics.

Angular random walk limited by Rayleigh backscattering in resonator fiber optic gyros.

This paper is concerned with the angular random walk (ARW) limited by Rayleigh backscattering in the resonator fiber optic gyro (RFOG) with a light source of arbitrary temporal coherence. First, a model of Rayleigh backscattering noise in RFOGs is established to predict the fluctuation characteristics of backscattered intensity and interference intensity. Next, the formula for the ARW limited by Rayleigh backscattering is derived, and the requirement of carrier suppression level is calculated to make sure the ARW is limited by the detector's shot noise rather than Rayleigh scattering noise. Finally, the influences of the cavity length, the linewidth, and the finesse on the ARW limited by Rayleigh backscattering are investigated. The results predict that the influence of the cavity length L and the laser linewidth ΔυL on the ARW is dominantly related to the factor e-2πΔυLneL/c, and under the finesse 88, the best ARW is obtained when there is a relation L·ΔυL≈4×105 m·Hz.

Distributed stress and temperature sensing based on Rayleigh scattering of low-coherence light

A novel arrangement for fiber optic distributed stress and temperature sensing based on the Rayleigh scattering spectra correlation method is proposed. The principal feature of the arrangement is usage of low-coherence light in probe pulses, which ensures a wide dynamic range for measurements at moderate sensitivity. Such a characteristic corresponds to performance specifications for infrastructure monitoring systems. A theory of optical time domain reflectometry for arbitrary coherence light is developed describing the contrast in reflectograms and Rayleigh scattering spectra properties. The experimental setup uses a wideband source of light pulses and an electronically controlled micro-electro-mechanical system optical filter for wavelength tuning. Temperature change experiments show root mean square (RMS) noise levels of 0.13 °C, 0.24 °C and 0.3 °C for fiber lengths of 2 km, 8 km and 25 km, respectively, at a spatial resolution of about 1 m (for 10 min data collection). As much as 2000 µstrain dynamic range is demonstrated in the stress measurement experiment while the noise level (RMS error) is estimated to be 2 µstrain. Our experimental results are compared with the theory and a satisfactory match is demonstrated.

Interaction description of light propagation

The interaction between real and virtual point emitters is presented as the propagation principle of light under arbitrary spatial coherence. It is supported on a geometrical interpretation of the two-point correlation and the introduction of the geometrical potential. This principle and the spectrum of classes of point emitters constitute a complete theoretical model that offers a unified phenomenological framework for interference and diffraction not only of light but also of single particles, which is not possible in the conventional formalism based on the wave superposition principle.

Potentials of radial partially coherent beams in free-space optical communication: a numerical investigation.

Nonuniformly correlated partially coherent beams (PCBs) have extraordinary propagation properties, making it possible to further improve the performance of free-space optical communications. In this paper, a series of PCBs with varying degrees of coherence in the radial direction, academically called radial partially coherent beams (RPCBs), are considered. RPCBs with arbitrary coherence distributions can be created by adjusting the amplitude profile of a spatial modulation function imposed on a uniformly correlated phase screen. Since RPCBs cannot be well characterized by the coherence length, a modulation depth factor is introduced as an indicator of the overall distribution of coherence. By wave optics simulation, free-space and atmospheric propagation properties of RPCBs with (inverse) Gaussian and super-Gaussian coherence distributions are examined in comparison with conventional Gaussian Schell-model beams. Furthermore, the impacts of varying central coherent areas are studied. Simulation results reveal that under comparable overall coherence, beams with a highly coherent core and a less coherent margin exhibit a smaller beam spread and greater on-axis intensity, which is mainly due to the self-focusing phenomenon right after the beam exits the transmitter. Particularly, those RPCBs with super-Gaussian coherence distributions will repeatedly focus during propagation, resulting in even greater intensities. Additionally, RPCBs also have a considerable ability to reduce scintillation. And it is demonstrated that those properties have made RPCBs very effective in improving the mean signal-to-noise ratio of small optical receivers, especially in relatively short, weakly fluctuating links.

Random sources for rotating spectral densities.

The propagating modes of a wide-sense stationary Schell-like source with arbitrary coherence state and a twist factor are determined. This suggests a convenient practical method for modeling novel classes of twisted partially coherent beam-like fields. The first example discusses the previously introduced twisted anisotropic Gaussian Schell-model source and verifies the feasibility of this method. As a second example, we introduce a new type of twisted partially coherent beam in which a radiated flat-top average intensity pattern remains invariant in shape (but not size) while it twists around the axis upon propagation.

Wavenumber–frequency deconvolution of aeroacoustic microphone phased array data of arbitrary coherence

Deconvolution of aeroacoustic data acquired with microphone phased arrays is a computationally challenging task for distributed sources with arbitrary coherence. A new technique for performing such deconvolution is proposed. This technique relies on analysis of the array data in the wavenumber–frequency domain, allowing for fast convolution and reduced storage requirements when compared to traditional coherent deconvolution. A positive semidefinite constraint for the iterative deconvolution procedure is implemented and shows improved behavior in terms of quantifiable convergence metrics when compared to a standalone covariance inequality constraint. A series of simulations validates the method׳s ability to resolve coherence and phase angle relationships between partially coherent sources, as well as determines convergence criteria for deconvolution analysis. Simulations for point sources near the microphone phased array show potential for handling such data in the wavenumber–frequency domain. In particular, a physics-based integration boundary calculation is described, and can successfully isolate sources and track the appropriate integration bounds with and without the presence of flow. Magnitude and phase relationships between multiple sources are successfully extracted. Limitations of the deconvolution technique are determined from the simulations, particularly in the context of a simulated acoustic field in a closed test section wind tunnel with strong boundary layer contamination. A final application to a trailing edge noise experiment conducted in an open-jet wind tunnel matches best estimates of acoustic levels from traditional calculation methods and qualitatively assesses the coherence characteristics of the trailing edge noise source.

Optimal Detection of Faded Pilot Signal in MIMO Channels with Applications in Cognitive Radio Systems

Multiple transmit and receive antenna arrays can be used to form MIMO systems to improve spectrum sensing cycle of recently proposed cognitive radio (CRs) systems by utilizing diversity and/or multiplexing techniques. This paper designs an optimal spectrum detection for multiple antenna CR with a multiple antenna primary user as a backhand licensed network while the primary network protocol uses preamble or pilot signal. The MIMO channel between the primary and secondary users is modeled by Rayleigh distribution with arbitrary coherence time which is proper for slow to fast fading environments. In this situation, optimal detector is presented and closed-form expressions for probability of detection and false alarm are derived. Analytical and simulation results demonstrate that the performance of the proposed scheme outperforms other existing suboptimal detectors.

Experimental generation of an optical field with arbitrary spatial coherence properties

We describe an experimental technique for generating a quasi-monochromatic field with any arbitrary spatial coherence properties that can be described by the cross-spectral density function, W(r1,r2). This is done by using a dynamic binary amplitude grating generated by a digital micromirror device to rapidly alternate between a set of coherent fields, creating an incoherent mix of modes that represent the coherent mode decomposition of the desired W(r1,r2). This method was then demonstrated experimentally by interfering two plane waves and then spatially varying the coherence between them. It is then shown that this creates an interference pattern between the two beams whose fringe visibility varies spatially in an arbitrary and prescribed way.