Effect Of Shot Noise Research Articles

Source anisotropies and pulsar timing arrays

Pulsar timing arrays (PTAs) hunt for gravitational waves (GWs) by searching for the correlations that GWs induce in the time-of-arrival residuals from different pulsars. If the GW sources are of astrophysical origin, then they are located at discrete points on the sky. However, PTA data are often modeled, and subsequently analyzed, via a “standard Gaussian ensemble.” That ensemble is obtained in the limit of an infinite density of vanishingly weak, Poisson-distributed sources. In this paper, we move away from that ensemble, to study the effects of two types of “source anisotropy.” The first (a), which is often called “shot noise,” arises because there are N discrete GW sources at specific sky locations. The second (b) arises because the GW source positions are not a Poisson process, for example, because galaxy locations are clustered. Here, we quantify the impact of (a) and (b) on the mean and variance of the pulsar-averaged Hellings and Downs correlation. For conventional PTA sources, we show that the effects of shot noise (a) are much larger than the effects of clustering (b). Published by the American Physical Society 2024

Quantum Algorithms for the Variational Optimization of Correlated Electronic States with Stochastic Reconfiguration and the Linear Method.

Solving the electronic Schrodinger equation for strongly correlated ground states is a long-standing challenge. We present quantum algorithms for the variational optimization of wave functions correlated by products of unitary operators, such as Local Unitary Cluster Jastrow (LUCJ) ansatzes, using stochastic reconfiguration (SR) and the linear method (LM). While an implementation on classical computing hardware would require exponentially growing compute cost, the cost (number of circuits and shots) of our quantum algorithms is polynomial in system size. We find that classical simulations of optimization with the linear method consistently find lower energy solutions than with the L-BFGS-B optimizer across the dissociation curves of the notoriously difficult N2 and C2 dimers; LUCJ predictions of the ground-state energies deviate from exact diagonalization by 1 kcal/mol or less at all points on the potential energy curve. While we do characterize the effect of shot noise on the LM optimization, these noiseless results highlight the critical but often overlooked role that optimization techniques must play in attacking the electronic structure problem (on both classical and quantum hardware), for which even mean-field optimization is formally NP hard. We also discuss the challenge of obtaining smooth curves in these strongly correlated regimes, and propose a number of quantum-friendly solutions ranging from symmetry-projected ansatz forms to a symmetry-constrained optimization algorithm.

Reduced Density Matrix Formulation of Quantum Linear Response.

The prediction of spectral properties via linear response (LR) theory is an important tool in quantum chemistry for understanding photoinduced processes in molecular systems. With the advances of quantum computing, we recently adapted this method for near-term quantum hardware using a truncated active space approximation with orbital rotation, named quantum linear response (qLR). In an effort to reduce the classic cost of this hybrid approach, we here derive and implement a reduced density matrix (RDM) driven approach of qLR. This allows for the calculation of spectral properties of moderately sized molecules with much larger basis sets than so far possible. We report qLR results for benzene and R-methyloxirane with a cc-pVTZ basis set and study the effect of shot noise on the valence and oxygen K-edge absorption spectra of H2O in the cc-pVTZ basis.

Scatterometric defect measurements – uncertainty assessment by means of a virtual instrument and a statistical analysis

Defects in nanostructured surfaces have to be detected in or close to the manufacturing process in the production environment. For this purpose, scatterometry promises a non-contact approach with in-process capability. However, the achievable measurement uncertainty with a scatterometric measurement principle is difficult to assess by means of experiments. Especially for nano-surfaces with stochastic features, a large sample size is required. In addition, the influence of the natural uncertainty due to the inherent surface stochastics, which causes an ultimate uncertainty limit, remains hidden. Therefore, a virtual experimentation in combination with a statistical evaluation is proposed for the uncertainty assessment of scatterometric defect measurements of nanostructured surface. One virtual experiment calculates the scattered light distribution from a randomized modelled surface. For the uncertainty assessment, (a) multiple defective surfaces with the same defect grade are modelled, (b) the surfaces’ scattered light distributions are simulated, (c) the signal processing is applied for obtaining the virtual measurement results of the defect grade, and (d) the uncertainty is determined. The proposed virtual method is realized and demonstrated for defective ZnO nanograss surfaces, where the vacancy of nanograss is the studied defect as an example. As central results for the exemplarily studied defect grade measurement, the determined achievable mean uncertainty due to the nanostructure randomness is 3.2%, and the effect of the detector shot noise is negligibly small. Furthermore, the proposed method is universally applicable for any type of nanostructure/defect, and for any scatterometric principle, to clarify the respective potential for the reliable detection of nanostructure defects.

Attosecond two-color x-ray free-electron lasers with dual chirp-taper configuration and bunching inheritance

Attosecond x-ray pulses play a crucial role in the study of ultrafast phenomena occurring within inner and valence electrons. To achieve attosecond time-resolution studies and gain control over electronic wave functions, it is crucial to develop techniques capable of generating and synchronizing two-color x-ray pulses at the attosecond scale. In this paper, we present a novel approach for generating attosecond pulse pairs using a dual chirp-taper free-electron laser with bunching inheritance. An electron beam with a sinusoidal energy chirp, introduced by the external laser, passes through the main undulator and afterburner, both with tapers. Two-color x-ray pulses are generated from the main undulator and the afterburner, respectively, with temporal separations of several femtoseconds and energy separations of tens of electron volts. Notably, the afterburner is much shorter than the main undulator due to the bunching inheritance, which reduces the distance between two source points and alleviates the beamline focusing requirements of the two-color pulses. A comprehensive stability analysis is conducted in this paper, considering the individual effects of shot noise from self-amplified spontaneous emission and carrier-envelope phase jitter of the few-cycle laser. The results show that the radiation from the afterburner exhibits excellent stability in the proposed scheme, which is beneficial for x-ray pump-probe experiments. The proposed scheme opens up new possibilities for attosecond science enabled by x-ray attosecond pump-probe techniques and coherent control of ultrafast electronic wave packets in quantum systems. Published by the American Physical Society 2024

Simulation of shot noise effects in the EIC strong hadron cooling accelerator using real number of electrons

In the electron ion collider design, in order to achieve the peak luminosity 1034/cm 2/s with a reasonable lifetime, an efficient coherent electron cooling scheme was proposed to reduce the hadron beam emittance growth. Such a cooling scheme requires a good electron beam quality with a small energy spread. However, the shot noise in the electron beam through the accelerator might be amplified due to the microbunching instability and degrades the electron beam quality in the modulator section of the strong hadron cooling channel and correspondingly cooling rate. In this study, we report on self-consistent simulations of these effects using a real number of electrons to capture the details of shot noise and analysis of the shot noise growth through the accelerator.

Analyzing the effect of shot noise in indirect Time-of-Flight cameras

Continuous wave indirect Time-of-Flight cameras obtain depth images by emitting a modulated continuous light wave and measuring the delay of the received signal. In this paper we generalize the estimation of the effect of the shot noise when obtaining the phase delay with an arbitrary number of points in the Discrete Fourier Transform, extending and generalizing the analysis done in previous works for the case of four points. For that particular case, we compare our analysis with the state of art. Moreover, we extend the error model using a second order approximation in the error propagation analysis, which provides more accurate estimations according to the Montecarlo simulation experiments. The analysis, based on both analytical and numerical methods, shows that the phase error is, in general, related to the exposure time and weakly to the number of points in the Discrete Fourier Transform. It also depends on the background illumination level, on the amplitude of the received signal, and, when using a three point DFT, on the distance to the objects.

Estimation of atmospheric refractive index structure constant using an InGaAs/InP single-photon detector.

Remote sensing of atmospheric refractive index structure constant ($\boldsymbol{C}_{\boldsymbol{n}}^2$) using lidar incorporating a single-photon detector (SPD) is proposed. The influence of turbulence on the fiber coupling efficiency with different fiber modes is analyzed. $\boldsymbol{C}_{\boldsymbol{n}}^2$ can be derived from the ratio of the backscattering signals counted on single-mode and multimode fiber-coupling channels of the SPD. In the experiment, by eliminating the shot noise effect on the fluctuation of the ratio, the lowest coupling ratio is used to retrieve $\boldsymbol{C}_{\boldsymbol{n}}^2$ and demonstrated by comparing to the results measured from a large aperture scintillometer (LAS). Good agreement between results from the LAS and the lidar is achieved. The correlation coefficients are 0.90, 0.89, and 0.89, under three different weather conditions.

High-efficiency single-photon compressed sensing imaging based on the best choice scheme.

With single-photon sensitivity and picosecond resolution, single-photon imaging technology is an ideal solution for extreme conditions and ultra-long distance imaging. However, the current single-photon imaging technology has the problem of slow imaging speed and poor quality caused by the quantum shot noise and the fluctuation of background noise. In this work, an efficient single-photon compressed sensing imaging scheme is proposed, in which a new mask is designed by the Principal Component Analysis algorithm and the Bit-plane Decomposition algorithm. By considering the effects of quantum shot noise, dark count on imaging, the number of masks is optimized to ensure high-quality single-photon compressed sensing imaging with different average photon counts. The imaging speed and quality are greatly improved compared with the commonly used Hadamard scheme. In the experiment, a 64 × 64 pixels' image is obtained with only 50 masks, the sampling compression rate reaches 1.22%, and the sampling speed increases by 81 times. The simulation and experimental results demonstrated that the proposed scheme will effectively promote the application of single-photon imaging in practical scenarios.

SHIMM: a versatile seeing monitor for astronomy

ABSTRACTCharacterization of atmospheric optical turbulence is crucial for the design and operation of modern ground-based optical telescopes. In particular, the effective application of adaptive optics correction on large and extremely large telescopes relies on a detailed knowledge of the prevailing atmospheric conditions, including the vertical profile of the optical turbulence strength and the atmospheric coherence time-scale. The Differential Image Motion Monitor (DIMM) has been employed as a facility seeing monitor at many astronomical observing sites across the world for several decades, providing a reliable estimate of the seeing angle. Here, we present the Shack–Hartmann Image Motion Monitor (SHIMM), which is a development of the DIMM instrument, in that it exploits differential image motion measurements of bright target stars. However, the SHIMM employs a Shack–Hartmann wavefront sensor in place of the two-hole aperture mask utilized by the DIMM. This allows the SHIMM to provide an estimate of the seeing, unbiased by shot noise or scintillation effects. The SHIMM also produces a low-resolution (three-layer) measure of the vertical turbulence profile, as well as an estimate of the coherence time-scale. The SHIMM is designed as a low-cost, portable instrument. It is comprised of off-the-shelf components so that it is easy to duplicate and well suited for comparisons of atmospheric conditions within and between different observing sites. Here, the SHIMM design and methodology for estimating key atmospheric parameters will be presented, as well as initial field test results with comparisons to the Stereo-SCIntillation Detection And Ranging instrument.

3D compressive imaging system with a single photon-counting detector.

For photon-counting based compressive imaging systems, it is difficult to obtain 3D image with intensity and depth information precisely due to the dead time and shot noise effect of photon-counting detectors. In this study, we design and achieve a 3D compressive imaging system using a single photon-counting detector. To overcome the radiometric distortion arising from the dead time and shot noise, considering the response mechanism of photon-counting detectors, a Bayesian posterior model is derived and a Reversible jump Markov chain Monte Carlo (RJMCMC)-based method is proposed to iteratively obtain model parameters. Experimental and simulation results indicate that the 3D image of targets can be effectively and accurately reconstructed with a smaller number of repeated illuminations and no longer restricted by the photon flux conditions (i.e., breaking through the upper limit of the received signal level). The proposed Bayesian RJMCMC-based radiometric correction method is not only beneficial to single-photon 3D compressive imaging system, but also to any other photon-counting based systems, e.g., photon-counting lidars. In addition, limiting condition of recovering the actual photon number for photon-counting imaging or lidar systems is also quantitatively analyzed, which is of great significance to the system scheme design.

Shot Noise Analysis for Differential Sampling in Indirect Time of Flight Cameras

Continuous wave Time of Flight cameras obtain depth images by emitting a modulated continuous light wave and measuring the delay of the received signal. One of the main sources of error is shot noise. In this letter we analyze and provide insights about the effect of shot noise when obtaining the phase delay with a new architecture, based on differentiating the phase integrations in the analog domain, and using any number of points in the calculation of the Discrete Fourier Transform (DFT). One of the main findings is that the error depends on the integration time regardless the number of points in the DFT used to calculate the phase offset. Simulated experiments are provided which support the proposed theoretical analysis.

Channel Estimation in Visible Light Communication Systems: The Effect of Input Signal-Dependent Noise

Visible light communication (VLC) has been proposed as a promising way for next generation wireless communication networks to mitigate the scarcity of the radio frequency (RF) spectrum, and has consequently attracted much attention. This paper introduces a single-input single-output (SISO) VLC system under the joint effects of statistical random channel and signal-dependent shot noise (SDSN). Moreover, it estimates the channel of the considered system using maximum likelihood (ML), least square (LS), linear minimum mean square error (LMMSE), maximum posteriori probability (MAP) and minimum mean square error (MMSE) estimators. Furthermore, a Bayesian Cramér-Rao lower bound (BCRLB) is derived for the proposed system and it is compared to the mean square error (MSE) of the proposed estimators. The problem of unknown SDSN factor, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\zeta ^{2}$</tex-math></inline-formula> , at the receiver side is discussed and two solutions are investigated. The receiver of a VLC system under SDSN and random channel gain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$h$</tex-math></inline-formula> is designed and its BER is studied. Finally, Monte Carlo simulation results of the proposed estimators, which show the dramatic effect of the SDSN on the considered system, are provided. In particular, the presence of noise variance, as well as the SDSN factor, causes an increase in the MSE of the system, while increasing the power reinforces the system performance.

A Cryo-CMOS Oscillator With an Automatic Common-Mode Resonance Calibration for Quantum Computing Applications

This article presents a 4-to-5GHz LC oscillator operating at 4.2K for quantum computing applications. The phase noise (PN) specification of the oscillator is derived based on the control fidelity for a single-qubit operation. To reveal the substantial gap between the theoretical predictions and measurement results at cryogenic temperatures, a new PN expression for an oscillator is derived by considering the shot-noise effect. To reach the optimum performance of an LC oscillator, a common-mode (CM) resonance technique is implemented. Additionally, this work presents a digital calibration loop to adjust the CM frequency automatically at 4.2K, reducing the oscillator’s PN and thus improving the control fidelity. The calibration technique reduces the flicker corner of the oscillator over a wide temperature range (10 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> and 8 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> reduction at 300K and 4.2K, respectively). At 4.2K, our 0.15-mm2 oscillator consumes a 5-mW power and achieves a PN of −153.8dBc/Hz at a 10MHz offset, corresponding to a 200-dB FOM. The calibration circuits consume only a 0.4-mW power and 0.01-mm2 area.

Ghost projection. II. Beam shaping using realistic spatially random masks

Spatial light modulation is important for many scientific and industrial applications. The spatial light modulator and optical data projector both rely on precisely configurable optical elements to shape a light beam. Here we explore an image-projection approach which does not require a configurable beam-shaping element. We term this approach ghost projection on account of its conceptual relation to computational ghost imaging. Instead of a configurable beam shaping element, the method transversely displaces a single illuminated mask, such as a spatially-random screen, to create specified distributions of radiant exposure. The method has potential applicability to image projection employing a variety of radiation and matter wave fields, such as hard x rays, neutrons, muons, atomic beams and molecular beams. Building on our previous theoretical and computational studies, we here seek to understand the effects, sensitivity, and tolerance of some key experimental limitations of the method. Focusing on the case of hard x rays, we employ experimentally acquired masks to numerically study the deleterious effects of photon shot noise, inaccuracies in random-mask exposure time, and inaccuracies in mask positioning, as well as adapting to spatially non-uniform illumination. Understanding the influence of these factors will assist in optimizing experimental design and work towards achieving ghost projection in practice.

KiDS+VIKING+GAMA: Halo occupation distributions and correlations of satellite numbers with a new halo model of the galaxy-matter bispectrum for galaxy-galaxy-galaxy lensing

Context. Halo models and halo occupation distributions (HODs) are important tools to model the distribution of galaxies and matter. Aims. We present and assess a new method for constraining the parameters of HODs using the mean gravitational lensing shear around galaxy pairs, so-called galaxy-galaxy-galaxy lensing (G3L). In contrast to galaxy-galaxy lensing, G3L is also sensitive to the correlations between the per-halo numbers of galaxies from different populations. We employed our G3L halo model to probe these correlations and test the default hypothesis that they are negligible. Methods. We derived a halo model for G3L and validated it with realistic mock data from the Millennium Simulation and a semi-analytic galaxy model. Then, we analysed public data from the Kilo-Degree Survey (KiDS), the VISTA Infrared Kilo-Degree Galaxy Survey (VIKING) and data from the Galaxy And Mass Assembly Survey (GAMA) to infer the HODs of galaxies at z &lt; 0.5 in five different stellar mass bins between 108.5h−2 M⊙ and 1011.5h−2 M⊙ and two colours (red and blue), as well as correlations between satellite numbers. Results. The analysis accurately recovers the true HODs in the simulated data for all galaxy samples within the 68% credibility range. The model best fits agree with the observed G3L signal on the 95% confidence level. The inferred HODs vary significantly with colour and stellar mass. In particular, red galaxies prefer more massive halos ≳1012 M⊙, while blue galaxies are present in halos ≳1011 M⊙. There is strong evidence (&gt; 3σ) for a high correlation, increasing with halo mass, between the numbers of red and blue satellites and between galaxies with stellar masses below 1010 M⊙. Conclusions. Our G3L halo model accurately constrains galaxy HODs for lensing surveys of up to 103 deg2 and redshift below 0.5 probed here. Analyses of future surveys may need to include non-Poisson variances of satellite numbers or a revised model for central galaxies. Correlations between satellite numbers are ubiquitous between various galaxy samples and are relevant for halos with masses ≳1013 M⊙, that is, of galaxy-group scale and more massive. Possible causes of these correlations are the selection of similar galaxies in different samples, the survey flux limit, or physical mechanisms such as a fixed ratio between the satellite numbers of distinct populations. The decorrelation for halos with smaller masses is probably an effect of shot noise by low-occupancy halos. The inferred HODs can be used to complement galaxy-galaxy lensing or galaxy-clustering HOD studies or as input to cosmological analyses and improved mock galaxy catalogues.

Effect of Signal-Dependent Shot Noise on Visible Light Positioning

This paper investigates the error bounds for position estimation in downlink visible light communication (VLC) systems. More precisely, we use Cramér-Rao lower bounds (CRLBs) to study the effect of signal-dependent shot noise (SDSN) on the error performance in visible light positioning. We consider synchronous, quasi-synchronous, and asynchronous visible light positioning (VLP) systems. The system performance is assessed based on the position estimation, and uses information from parameters relating to the time of arrival (TOA), time difference of arrival (TDOA), and received signal strength (RSS). The results demonstrate that SDSN has a negative impact on the error bounds in all considered scenarios. Moreover, the level of degradation observed is not uniform among all cases at higher SDSN levels.

Detectability of the Cross-Correlation between CMB Lensing and Stochastic GW Background from Compact Object Mergers

The anisotropies of the Stochastic Gravitational-Wave Background (SGWB), produced by merging compact binaries, constitute a possible new probe of the Large-Scale Structure (LSS). However, the significant shot noise contribution caused by the discreteness of the GW sources and the poor angular resolution of the instruments hampers the detection of the intrinsic anisotropies induced by the LSS. In this work, we investigate the potential of cross-correlating forthcoming high precision measurements of the SGWB energy density and the Cosmic Microwave Background (CMB) lensing convergence to mitigate the effect of shot noise. Combining a detailed model of stellar and galactic astrophysics with a novel framework to distribute the GW emitters in the sky, we compute the auto- and cross-correlation power spectra for the two cosmic fields, evaluate the shot noise contribution and predict the signal-to-noise ratio. The results of our analysis show that the SGWB energy density correlates significantly with the CMB lensing convergence and that the cross-correlation between these two cosmic fields reduces the impact of instrumental and shot noise. Unfortunately, the S/N is not high enough to detect the intrinsic SGWB anisotropies. Nevertheless, a network composed of both present and future generation GW interferometers, operating for at least 10 yrs, should be able to measure the shot noise contribution.

Effect of photon counting shot noise on total internal reflection microscopy.

Total internal reflection microscopy (TIRM) measures changes in the distance between a colloidal particle and a transparent substrate by measuring the scattering intensity of the particle illuminated by an evanescent wave. From the distribution of the recorded separation distances, the height-dependent effective potential φ(z) between the colloidal particle and the substrate can be measured. In this work, we show that spatial resolution with which TIRM can measure φ(z) is limited by the photon counting statistics of the scattered laser light. We develop a model to evaluate the effect of photon counting statistics on different potential profiles using Brownian dynamics simulations and experiments. Our results show that the effect of photon counting statistics depends on spatial gradients ∂φ/∂z of the potential, with the result that sharp features tend to be significantly blurred. We further establish the critical role of photon counting statistics and the intensity integration time τ in TIRM measurements, which is a trade-off between narrowing the width of the photon counting distribution and capturing the instantaneous position of the probe particle.

Distance Estimation in Visible Light Communications: The Case of Imperfect Synchronization and Signal-Dependent Noise

This paper investigates the error bounds for distance estimation in visible light communication (VLC) systems. More precisely, we study the effect of signal-dependent shot noise (SDSN) on the estimation error bounds for both synchronous and asynchronous systems. Moreover, a bi-directional synchronization protocol is exploited, which can mitigate the effects of clock-biasing between the transmitter and receiver. The results demonstrate that SDSN negatively affects the distance estimation bounds for all considered scenarios. Furthermore, the bi-directional distance estimation protocol outperforms the directional estimation techniques even in the case of perfect synchronization between the transmitter and receiver.