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Unitary control of partially coherent waves. II. Transmission or reflection
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Parallel performance of "Synchrotron Radiation Workshop" code: partially coherent calculations for storage rings and time-dependent calculations for XFELs
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Polarization tracking of a partially coherent signal using a double loop
We consider the problem of simultaneously estimating the phase and polarization angles of a linearly polarized electromagnetic wave. The solution of this problem has applications to space communications and ionospheric probing. The nonlinear stochastic characteristics of a cross-coupled double-loop implementation for the tracker are evaluated using the multidimensional Fokker-Planck equation. The exact stationary probability density is found for a special case of equal signal-to-noise ratio (SNR) in the two loops. The stationary probability density is obtained for a general class of double loops when the two loop bandwidths differ greatly.
The effect of partial coherence in receiving system noise temperature on array gain for telemetry and radio frequency carrier reception for receiving systems with unequal predetection signal-to-noise ratios
Signal to noise ratio improvement realized by arraying receiving systems or stations for coherent reception is reduced when some portion of the predetection noise is coherent in the array. This effect for arrayed receiving systems with unequal apertures including expected performance for selected planets of the solar system within the array beamwidth is examined.
Modelling the SIR-B image response to partially coherent seas
A mathematical model of transient seas modulated by coherent swells is developed as a Rayleigh-Poisson random process subject to deterministic correlations of scattering sites, as they appear in a time window defined by a SAR's range-Doppler measurements of the surface coordinates. This model of SAR response to sea surface dynamics is discussed as a Fourier domain predictor/corrector of a dynamic motion blur.
Partially coherent scattering in stellar chromospheres. II - The first-order escape probability method. III - A second-order escape probability method
Approximate analytic expressions are derived for resonance-line wing diagnostics, accounting for frequency redistribution effects, for homogeneous slabs, and slabs with a constant Planck function gradient. Resonance-line emission profiles from a simplified conceptual standpoint are described in order to elucidate the basic physical parameters of the line-forming layers prior to the performance of detailed numerical calculations. An approximate analytic expression is derived for the dependence on stellar surface gravity of the location of the Ca II and Mg II resonance-line profile peaks. An approximate radiative transfer equation using generalized second-order escape probabilities, applicable even in the presence of nearly coherent scattering in the damping wings of resonance lines, is derived. Approximate analytic solutions that can be applied in special regimes and achieve good agreement with accurate numerical results are found.
Stochastic Modeling and Generation of Partially Polarized or Partially Coherent Electromagnetic Waves
Many new Earth remote-sensing instruments are embracing both the advantages and added complexity that result from interferometric or fully polarimetric operation. To increase instrument understanding and functionality a model of the signals these instruments measure is presented. A stochastic model is used as it recognizes the non-deterministic nature of any real-world measurements while also providing a tractable mathematical framework. A stationary, Gaussian-distributed model structure is proposed. Temporal and spectral correlation measures provide a statistical description of the physical properties of coherence and polarization-state. From this relationship the model is mathematically defined. The model is shown to be unique for any set of physical parameters. A method of realizing the model (necessary for applications such as synthetic calibration-signal generation) is given and computer simulation results are presented. The signals are constructed using the output of a multi-input multi-output linear filter system, driven with white noise.
Paths of Partial Coherence: Jim Wyant’s Influence on my Profession Career
Writing a tribute paper is fraught with peril. While it is supposed to be about the other’s impact upon your life, in really it cannot help but be all about the author. Back in 2012, after my initial reluctance, the paper I wrote for the Bill Wolfe tribute[1]was so cathartic, that I had to write one for Jim Wyant–to add a chapter to my story, to explain how a path of successes and failures have lead me to the present, and in the process to exorcise more ghosts from my subconscious. While our relationship is complicated, it has always been respectful. In many regards, Jim Wyant may be one of the most important people helping me reach my potential. I am NOT ‘A’ Wyant Student. I am ‘a’ Wyant student. I took three classes from Jim: Interference and Diffraction, Holography and Optical Testing. As a result of those classes, I found something that I loved, something at which I was good, something that became apart of me–I found my technical bliss. And beyond the classroom, my professional career has been inescapably connected with Jim Wyant.
Propagation of partially spatially coherent laser beams in instantaneous Kerr media
The propagation of intense, partially spatially coherent laser beams in a medium with instantaneous third-order susceptibility is studied analytically and numerically. For sufficiently high power relative to that required for nonlinear self-focusing, the propagation initially proceeds in two stages. In the first stage, spatial coherence builds up, and in the second stage, the number of speckles reduces. Once the degree of coherence is sufficiently high, whole-beam self-focusing occurs. The beam power is mostly confined within the initial spot radius. Two analytical approaches for describing the evolution of the beam are presented. The method of moments leads to an analytical solution for the rms spot radius that is in excellent agreement with simulations. This method does not require any knowledge of the field statistics beyond the initial conditions and provides no information about the evolution of the individual speckles. The other approach employs a self-similar solution for the second-order coherence function of the field and assumes that the fourth-order coherence function is factorizable and obeys complex circular Gaussian random statistics. The latter method also leads to an analytical expression for the spot radius, but its predictions for the qualitative evolution of the speckles disagree with wave-optics simulations.
Phase-Sensitive Coherence and the Classical-Quantum Boundary in Ghost Imaging
The theory of partial coherence has a long and storied history in classical statistical optics. the vast majority of this work addresses fields that are statistically stationary in time, hence their complex envelopes only have phase-insensitive correlations. The quantum optics of squeezed-state generation, however, depends on nonlinear interactions producing baseband field operators with phase-insensitive and phase-sensitive correlations. Utilizing quantum light to enhance imaging has been a topic of considerable current interest, much of it involving biphotons, i.e., streams of entangled-photon pairs. Biphotons have been employed for quantum versions of optical coherence tomography, ghost imaging, holography, and lithography. However, their seemingly quantum features have been mimicked with classical-sate light, questioning wherein lies the classical-quantum boundary. We have shown, for the case of Gaussian-state light, that this boundary is intimately connected to the theory of phase-sensitive partial coherence. Here we present that theory, contrasting it with the familiar case of phase-insensitive partial coherence, and use it to elucidate the classical-quantum boundary of ghost imaging. We show, both theoretically and experimentally, that classical phase-sensitive light produces ghost imaging most closely mimicking those obtained in biphotons, and we derived the spatial resolution, image contrast, and signal-to-noise ratio of a standoff-sensing ghost imager, taking into account target-induced speckle.
Wave optics simulations for new soft x-ray beamlines at NSLS-II
In this work, we performed fully- and partially-coherent synchrotron emission and propagation simulations with the "Synchrotron Radiation Workshop" computer code to analyze the performance of two soft X-ray beamlines under development at the National Synchrotron Light Source II: Soft X-ray Nanoprobe (SXN), and Angle-Resolved Photoemission Spectroscopy (ARPES) and Resonant Inelastic X-ray Scattering (RIXS) Imaging (ARI). The SXN beamline intends to provide high flux and high spatial resolution coherent soft X-ray imaging capabilities using both zone plate and lensless coherent imaging techniques. The ARI beamline aims to perform high flux ARPES and RIXS experiments with a focal spot size at the sample approaching 100 nm using highly-demagnifying mirrors in Kirkpatrick-Baez geometry. To accurately calculate the resolution and the degree of X-ray coherence provided by the two state-of-the-art beamlines, partial coherence effects are required to be taken into account in wave optics simulations for these two beamlines. In this talk, beamline performance parameters such as spot size, degree of coherence, flux, and energy resolution at the sample are presented. The effects of mirror surface slope errors on beamline performance were studied and some suggestions for further optimization are discussed.
Efficient end-to-end simulation of time-dependent coherent X-ray scattering experiments
Physical optics simulations for beamlines and experiments allow users to test experiment feasibility and optimize beamline settings ahead of beam time in order to optimize valuable beam time at synchrotron light sources like NSLS-II. Further, such simulations also help to develop and test experimental data processing methods and software in advance. The Synchrotron Radiation Workshop ( SRW ) software package supports such complex simulations. We demonstrate how recent developments in SRW significantly improve the efficiency of physical optics simulations, such as end-to-end simulations of time-dependent X-ray photon correlation spectroscopy experiments with partially coherent undulator radiation (UR). The molecular dynamics simulation code LAMMPS was chosen to model the sample: a solution of silica nanoparticles in water at room temperature. Real-space distributions of nanoparticles produced by LAMMPS were imported into SRW and used to simulate scattering patterns of partially coherent hard X-ray UR from such a sample at the detector. The partially coherent UR illuminating the sample can be represented by a set of orthogonal coherent modes obtained by simulation of emission and propagation of this radiation through the coherent hard X-ray (CHX) scattering beamline followed by a coherent-mode decomposition. GPU acceleration is added for several key functions of SRW used in propagation from sample to detector, further improving the speed of the calculations. The accuracy of this simulation is benchmarked by comparison with experimental data.
Developments in SRW Code and Sirepo Framework Supporting Simulation of Time-Dependent Coherent X-ray Scattering Experiments
Physical optics simulations for beamlines and experiments are essential for the effective use of synchrotron light source facilities such as NSLS-II at BNL. The SRW software package supports such source-to-detector simulations for coherent X-ray scattering and imaging experiments through its Python interface and Sirepo browser-based graphical user interface. This allows one to define custom sample models, assess the feasibility of an experiment, and estimate most appropriate beamline settings before using valuable beamtime. We discuss the recent use of general-purpose GPU resources and coherent mode decomposition algorithms in SRW to accelerate physical optics simulations with partially coherent X-rays. To illustrate these new capabilities, we describe simulations of typical time series of partially coherent scattering images used in X-ray Photon Correlation Spectroscopy (XPCS) experiments; aiming to characterize the nanoscale dynamics of a disordered sample, representing a solution of nanoparticles undergoing Brownian diffusion.
Design considerations for optical heterodyne receivers: A review
The current state of knowledge concerning optical heterodyne receivers is reviewed. Following a discussion of noise processes in the heterodyne receiver and the manner in which sensitivity is increased through time integration of the detected signal, an expression for the mean square signal current is derived by mixing a coherent local oscillator with a partially coherent, quasimonochromatic source. Then the manner in which the IF signal calculation can be transferred to any convenient plane in the optical front end of the receiver is demonstrated. Using these techniques, a relatively simple equation is obtained for the coherently detected signal from an extended incoherent source and applied to the heterodyne detection of an extended thermal source and to the backscatter lidar problem where the antenna patterns of both the transmitter beam and heterodyne receiver must be taken into account. Finally, the detection of a coherent source is considered and, in particular, a distant point source such as a star or laser transmitter in a long range heterodyne communications system is discussed.
Respiratory modulation of human autonomic rhythms
We studied the influence of three types of breathing [spontaneous, frequency controlled (0.25 Hz), and hyperventilation with 100% oxygen] and apnea on R-R interval, photoplethysmographic arterial pressure, and muscle sympathetic rhythms in nine healthy young adults. We integrated fast Fourier transform power spectra over low (0.05-0.15 Hz) and respiratory (0.15-0.3 Hz) frequencies; estimated vagal baroreceptor-cardiac reflex gain at low frequencies with cross-spectral techniques; and used partial coherence analysis to remove the influence of breathing from the R-R interval, systolic pressure, and muscle sympathetic nerve spectra. Coherence among signals varied as functions of both frequency and time. Partialization abolished the coherence among these signals at respiratory but not at low frequencies. The mode of breathing did not influence low-frequency oscillations, and they persisted during apnea. Our study documents the independence of low-frequency rhythms from respiratory activity and suggests that the close correlations that may exist among arterial pressures, R-R intervals, and muscle sympathetic nerve activity at respiratory frequencies result from the influence of respiration on these measures rather than from arterial baroreflex physiology. Most importantly, our results indicate that correlations among autonomic and hemodynamic rhythms vary over time and frequency, and, thus, are facultative rather than fixed.
Broadband X-ray ptychography using multi-wavelength algorithm
Ptychography is a rapidly developing scanning microscopy which is able to view the internal structures of samples at a high resolution beyond the illumination size. The achieved spatial resolution is theoretically dose-limited. A broadband source can provide much higher flux compared with a monochromatic source; however, it conflicts with the necessary coherence requirements of this coherent diffraction imaging technique. In this paper, a multi-wavelength reconstruction algorithm has been developed to deal with the broad bandwidth in ptychography. Compared with the latest development of mixed-state reconstruction approach, this multi-wavelength approach is more accurate in the physical model, and also considers the spot size variation as a function of energy due to the chromatic focusing optics. Therefore, this method has been proved in both simulation and experiment to significantly improve the reconstruction when the source bandwidth, illumination size and scan step size increase. It is worth mentioning that the accurate and detailed information of the energy spectrum for the incident beam is not required in advance for the proposed method. Further, we combine multi-wavelength and mixed-state approaches to jointly solve temporal and spatial partial coherence in ptychography so that it can handle various disadvantageous experimental effects. The significant relaxation in coherence requirements by our approaches allows the use of high-flux broadband X-ray sources for high-efficient and high-resolution ptychographic imaging.
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.