Photon Counting Statistics Research Articles

Galactic Center excess at the highest energies: Morphology and photon-count statistics

Galactic Center excess at the highest energies: Morphology and photon-count statistics

Maximum-A-Posteriori Estimation of Retinal Oxygen Tension Based on Photon Counting Statistics.

The regularization of retinal oxygen tension estimation was previously proposed with an assumption that phosphorescence intensity images are corrupted by additive Gaussian noise. Based on this assumption, a regularized least-squares estimate has been shown to be better than a conventional least-squares estimation. However, this assumption is inconsistent with the acquisition process of phosphorescence intensity images acquired using an intensified charge-coupled device camera. Almost the entire acquisition process is governed by the natural aspects of photons. Therefore, a method based on photon counting statistics is more appropriate. In this study, we propose a regularized oxygen tension estimation method based on photon counting statistics and a phosphorescence lifetime imaging model.

Modular GAN: positron emission tomography image reconstruction using two generative adversarial networks.

The reconstruction of PET images involves converting sinograms, which represent the measured counts of radioactive emissions using detector rings encircling the patient, into meaningful images. However, the quality of PET data acquisition is impacted by physical factors, photon count statistics and detector characteristics, which affect the signal-to-noise ratio, resolution and quantitative accuracy of the resulting images. To address these influences, correction methods have been developed to mitigate each of these issues separately. Recently, generative adversarial networks (GANs) based on machine learning have shown promise in learning the complex mapping between acquired PET data and reconstructed tomographic images. This study aims to investigate the properties of training images that contribute to GAN performance when non-clinical images are used for training. Additionally, we describe a method to correct common PET imaging artefacts without relying on patient-specific anatomical images. The modular GAN framework includes two GANs. Module 1, resembling Pix2pix architecture, is trained on non-clinical sinogram-image pairs. Training data are optimised by considering image properties defined by metrics. The second module utilises adaptive instance normalisation and style embedding to enhance the quality of images from Module 1. Additional perceptual and patch-based loss functions are employed in training both modules. The performance of the new framework was compared with that of existing methods, (filtered backprojection (FBP) and ordered subset expectation maximisation (OSEM) without and with point spread function (OSEM-PSF)) with respect to correction for attenuation, patient motion and noise in simulated, NEMA phantom and human imaging data. Evaluation metrics included structural similarity (SSIM), peak-signal-to-noise ratio (PSNR), relative root mean squared error (rRMSE) for simulated data, and contrast-to-noise ratio (CNR) for NEMA phantom and human data. For simulated test data, the performance of the proposed framework was both qualitatively and quantitatively superior to that of FBP and OSEM. In the presence of noise, Module 1 generated images with a SSIM of 0.48 and higher. These images exhibited coarse structures that were subsequently refined by Module 2, yielding images with an SSIM higher than 0.71 (at least 22% higher than OSEM). The proposed method was robust against noise and motion. For NEMA phantoms, it achieved higher CNR values than OSEM. For human images, the CNR in brain regions was significantly higher than that of FBP and OSEM (p < 0.05, paired t-test). The CNR of images reconstructed with OSEM-PSF was similar to those reconstructed using the proposed method. The proposed image reconstruction method can produce PET images with artefact correction.

The Statistical Uncertainties on X-Ray Flux and Spectral Parameters from Chandra ACIS-I Observations of Faint Sources: Application to the Cygnus OB2 Association

We investigate the uncertainties of fitted X-ray model parameters and fluxes for relatively faint Chandra ACIS-I source spectra. Monte Carlo (MC) simulations are employed to construct a large set of 150,000 fake X-ray spectra in the low photon count statistics regime (from 10 to 350 net counts) using the XSPEC spectral model-fitting package. The simulations employed both absorbed thermal (APEC) and nonthermal (power-law) models, in concert with the Chandra ACIS-I instrument response and interstellar absorption. Simulated X-ray spectra were fit assuming a wide set of different input parameters and C-statistic minimization criteria to avoid numerical artifacts in the accepted solutions. Results provide an error estimate for each parameter (absorption, N H, plasma temperature, kT, or power-law slope, Γ, and flux) and for different background contamination levels. The distributions of these errors are studied as a function of the 1σ quantiles, and we show how these correlate with different model parameters, net counts in the spectra, and relative background level. Maps of uncertainty in terms of the 1σ quantiles for parameters and flux are computed as a function of spectrum net counts. We find very good agreement between our estimated X-ray spectral parameter and flux uncertainties and those recovered from spectral fitting for a subset of the X-ray sources detected in the Chandra Cygnus OB2 Legacy Survey diagnosed to be association members and that have between 20 and 350 net counts. Our method can provide uncertainties for spectral parameters whenever formal X-ray spectral fits cannot be well constrained, or are unavailable, and predictions useful for computing Chandra ACIS-I exposure times for observation planning.

Photon-counting-based underwater wireless optical communication employing orbital angular momentum multiplexing.

Underwater wireless optical communication (UWOC) is a critical technology for underwater communication, providing high speed, low latency, and security advantages. However, the strong attenuation in the water channel still limits the UWOC systems and their performances require further improvement. In this study, an orbital angular momentum (OAM) multiplexing UWOC system that uses photon-counting detection is experimentally demonstrated. By employing a single-photon counting module to receive photon signals, we analyze the bit error rate (BER) and photon-counting statistics by building a theoretical model that fits the real system, and demodulate the OAM states in single photon level and implement signal processing using field programmable gate array (FPGA) programming. Based on these modules, a 2-OAM multiplexed UWOC link is established over a water channel of 9 m. By using on-off keying modulation and 2-pulse position modulation, we achieve a BER of 1.26×10-3 with data rate of 20Mbps and 3.17×10-4 with data rate of 10Mbps respectively, which below the forward error correction (FEC) threshold of 3.8×10-3. The total transmission loss is 37 dB under an emission power of 0.5 mW, which is equivalent to the attenuation of 283 m Jerlov I type seawater from the perspective of energy loss. Our verified communication scheme will benefit the development of long-range and high-capacity UWOC.

Squeezed state generation using cryogenic InP HEMT nonlinearity

This study focuses on generating and manipulating squeezed states with two external oscillators coupled by an InP HEMT operating at cryogenic temperatures. First, the small-signal nonlinear model of the transistor at high frequency at 5 K is analyzed using quantum theory, and the related Lagrangian is theoretically derived. Subsequently, the total quantum Hamiltonian of the system is derived using Legendre transformation. The Hamiltonian of the system includes linear and nonlinear terms by which the effects on the time evolution of the states are studied. The main result shows that the squeezed state can be generated owing to the transistor’s nonlinearity; more importantly, it can be manipulated by some specific terms introduced in the nonlinear Hamiltonian. In fact, the nonlinearity of the transistors induces some effects, such as capacitance, inductance, and second-order transconductance, by which the properties of the external oscillators are changed. These changes may lead to squeezing or manipulating the parameters related to squeezing in the oscillators. In addition, it is theoretically derived that the circuit can generate two-mode squeezing. Finally, second-order correlation (photon counting statistics) is studied, and the results demonstrate that the designed circuit exhibits antibunching, where the quadrature operator shows squeezing behavior.

Photon counting probabilities of the output field for a single-photon input

In this paper, photon-counting statistics for an output field of a single-photon wave packet interacting with a quantum system was derived. The problem was formulated using a collision model with a bidirectional field approximated by two sequences of qubits. It was shown that the collision model formulated for the light with the temporal correlations allows deriving formulae for quantum trajectories in an effective and intuitive way. Starting from the discrete in-time evolution of the composed system, we determined the conditional and unconditional evolution of the quantum system, provided a physical interpretation of quantum trajectories, and determined the analytical formulae for the exclusive probability densities for the reflected and transmitted fields. Finally, our results were applied to a two-level atom, and we also determined analytical expressions for probability densities of arrival times of the successive counts.

Resolution of Maximum Entropy Method-Derived Posterior Conformational Ensembles of a Flexible System Probed by FRET and Molecular Dynamics Simulations

Maximum entropy methods (MEMs) determine posterior distributions by combining experimental data with prior information. MEMs are frequently used to reconstruct conformational ensembles of molecular systems for experimental information and initial molecular ensembles. We performed time-resolved Förster resonance energy transfer (FRET) experiments to probe the interdye distance distributions of the lipase-specific foldase Lif in the apo state, which likely has highly flexible, disordered, and/or ordered structural elements. Distance distributions estimated from ensembles of molecular dynamics (MD) simulations serve as prior information, and FRET experiments, analyzed within a Bayesian framework to recover distance distributions, are used for optimization. We tested priors obtained by MD with different force fields (FFs) tailored to ordered (FF99SB, FF14SB, and FF19SB) and disordered proteins (IDPSFF and FF99SBdisp). We obtained five substantially different posterior ensembles. As in our FRET experiments the noise is characterized by photon counting statistics, for a validated dye model, MEM can quantify consistencies between experiment and prior or posterior ensembles. However, posterior populations of conformations are uncorrelated to structural similarities for individual structures selected from different prior ensembles. Therefore, we assessed MEM simulating varying priors in synthetic experiments with known target ensembles. We found that (i) the prior and experimental information must be carefully balanced for optimal posterior ensembles to minimize perturbations of populations by overfitting and (ii) only ensemble-integrated quantities like inter-residue distance distributions or density maps can be reliably obtained but not ensembles of atomistic structures. This is because MEM optimizes ensembles but not individual structures. This result for a highly flexible system suggests that structurally varying priors calculated from varying prior ensembles, e.g., generated with different FFs, may serve as an ad hoc estimate for MEM reconstruction robustness.

Redshift prediction ofFermi-LAT gamma-ray sources usingcatboostgradient boosting decision trees

ABSTRACTThe determination of distance is fundamental in astrophysics. Gamma-ray sources are poorly characterized in this sense, as the limited angular resolution and poor photon-count statistics in gamma-ray astronomy makes it difficult to associate them to a multiwavelength object with known redshift. Taking the 1794 active galactic nuclei (AGNs) with known redshift from the Fermi-LAT latest AGN catalogue, 4LAC–DR3, we employ machine learning techniques to predict the distance of the rest of AGNs based on their spectral and spatial properties. The state-of-the-art catboost algorithm reaches an average 0.56 R2 score with 0.46 root-mean-squared error, predicting an average redshift value of zavg = 0.63, with a maximum zmax = 1.97. We use the shap explainer package to gain insights into the variables influence on the outcome, and also study the extragalactic background light implications. In a second part, we use this regression model to predict the redshift of the unassociated sample of the latest LAT point-source catalogue, 4FGL–DR3, using the results of a previous paper to determine the possible AGNs within them.

Quantum statistical theory for an exciton-polariton condensate: Fluctuations and coherence

A full quantum theory beyond the mean-field regime is developed for an exciton-polariton condensate, for a complete understanding of quantum fluctuations. We find an analytical solution for the polariton density matrix, showing the nonlinearity causing fast relaxation correlated with the pump so as to yield the quantum condensation above threshold. Increasing the pump intensity, a nonequilibrium phase transition towards the condensation of the lower polaritons emerges, with a statistics transiting from a thermal, through a super-Poissonian, and towards a nonclassical distribution; the latter two possess off-diagonal long-range order but the last one is beyond. The results signify the role of dark states for polariton fluctuations, and lead to a nonclassical counting statistics of emitted photons, which elaborates the role of the key parameters, e.g., pump, detuning, and temperature.

Engineering nonclassical SU(1,1) coherent states of light by multiphoton excitation

Quantum optical systems with nonclassical features play a vital role in the physical implementation of a large variety of quantum technologies, such as quantum metrology, quantum information processing, and quantum computation protocols, and hence are important to exploit the quantum advantage. In this work, we construct a general class of nonclassical coherent states (CSs) of light and present a scheme to enhance their nonclassicality by multiphoton excitation. In particular, using various optical realizations of Lie algebra, we construct CSs of light following Barut-Girardello formalism and then perform the multiphoton discrete excitation on these continuous-variable optical CSs. We investigate the nonclassical features by analyzing the photon-counting probability distribution, Mandel parameter, quadrature squeezing, and Wigner quasi-probability distribution. Our numerical results show that, for a particular set of parametric values, these multiphoton excited states exhibit sub-Poisson photon-counting statistics, quadrature squeezing, and negativity of Wigner distribution, which are indicators of nonclassicality. Moreover, it is shown that the nonclassical nature of these states gets enhanced as the photon-excitation number increases.

Photon-counting statistics-based support vector machine with multi-mode photon illumination for quantum imaging

We propose a photon-counting-statistics-based imaging process for quantum imaging where background photon noise can be distinguished and eliminated by photon mode estimation from the multi-mode Bose–Einstein distribution. Photon-counting statistics show multi-mode behavior in a practical, low-cost single-photon-level quantum imaging system with a short coherence time and a long measurement time interval. Different mode numbers in photon-counting probability distributions from single-photon illumination and background photon noise can be classified by a machine learning technique such as a support vector machine (SVM). The proposed photon-counting statistics-based support vector machine (PSSVM) learns the difference in the photon-counting distribution of each pixel to distinguish between photons from the source and the background photon noise to improve the image quality. We demonstrated quantum imaging of a binary-image object with photon illumination from a spontaneous parametric down-conversion (SPDC) source. The experiment results show that the PSSVM applied quantum image improves a peak signal-to-noise ratio (PSNR) gain of 2.89dB and a structural similarity index measure (SSIM) gain of 27.7% compared to the conventional direct single-photon imaging.

Threshold switching strategy for unambiguous state discrimination of quadrature phase-shift-keying coherent states under thermal noise.

Quantum-enhanced measurement technologies can unambiguously discriminate coherent states with accuracy beyond the classical heterodyne measurement. However, typical quantum-enhanced measurement scheme is vulnerable to the thermal noise, which will change the photon counting statistics of the coherent state. This paper presents a threshold-switching strategy that can discriminate quadrature phase-shift-keying coherent states with performance surpassing the typical quantum-enhanced scheme. In our scheme, photon number resolving detectors are used to switch the value of the threshold, which can mitigate the influence of thermal noise and other imperfections. Simulation results show that our scheme unambiguously discriminates the signal states with higher correct probability and the same error ratio compared with the typical scheme. Besides, this scheme can reduce the error ratio simultaneously for thermal noise N ≤ 0.2. The paper demonstrations that quantum-enhanced measurement with the threshold-switching strategy can adapt to different thermal noises by switching the value of the threshold under situations of different thermal noises and signal states.

New Solar Flare Calcium Abundances with No Surprises: Results from the Solar Maximum Mission Bent Crystal Spectrometer

The calcium abundance in flare plasmas is estimated using X-ray spectra from the Solar Maximum Mission Bent Crystal Spectrometer (BCS) during the decays of 194 flares (Geostationary Operational Environmental Satellite, GOES, classifications from B6.4 to X13) occurring between 1980 and 1989. Previous work by Sylwester et al. found that the abundance varied from flare to flare. That analysis is improved on here using updated instrument parameters and by including all calcium lines viewed by the BCS instead of only the resonance line, so greatly enhancing the photon count statistics. The abundance variations are confirmed with the average abundance, A(Ca) (expressed logarithmically with A(H) = 12), equal to 6.77 ± 0.20 for 194 flares (141 of which are new in this study). This range corresponds to factors of between 1.7 and 7.2 larger than the photospheric abundance, and so our results are in line with a “first ionization potential” (FIP) effect whereby low-FIP elements like Ca (FIP = 6.11 eV) have enhanced coronal abundances. The Ca flare abundance is uncorrelated with solar activity indices, but weak correlations are suggested with GOES flare class and duration (larger A(Ca) for smaller and shorter flares). The ponderomotive force theory of Laming explaining the FIP effect gives a range of parameters within which our estimates of A(Ca) agree with the theory. However, this then gives rise to disagreements with previous estimates of the flare silicon and sulfur abundances, although those of argon and iron are in good agreement. Small adjustments of the theory may thus be necessary.

Photon counting statistics with imperfect detectors

Measurement of photon statistics is an important tool for the verification of quantum properties of light. Due to the various imperfections of real single photon detectors, the observed statistics of photon counts deviates from the underlying statistics of photons. Here we analyze statistical properties of coherent states, and investigate a connection between Poissonian distribution of photons and sub-Poissonian distribution of photon counts due to the detector dead-time corrections. We derive a functional dependence between the mean number of photons and the mean number of photon counts, as well as connection between higher-order statistical moments, for the pulsed or continuous wave coherent light sources, and confirm the results by numerical simulations.

Trace-element XAFS sensitivity: a stress test for a new XRF multi-detector.

X-ray absorption fine-structure (XAFS) spectroscopy can assess the chemical speciation of the elements providing their coordination and oxidation state, information generally hidden to other techniques. In the case of trace elements, achieving a good quality XAFS signal poses several challenges, as it requires high photon flux, counting statistics and detector linearity. Here, a new multi-element X-ray fluorescence detector is presented, specifically designed to probe the chemical speciation of trace 3d elements down to the p.p.m. range. The potentialities of the detector are presented through a case study: the speciation of ultra-diluted elements (Fe, Mn and Cr) in geological rocks from a calcareous formation related to the dispersal processes from Ontong (Java) volcanism (mid-Cretaceous). Trace-elements speciation is crucial in evaluating the impact of geogenic and anthropogenic harmful metals on the environment, and to evaluate the risks to human health and ecosystems. These results show that the new detector is suitable for collecting spectra of 3d elements in trace amounts in a calcareous matrix. The data quality is high enough that quantitative data analysis could be performed to determine their chemical speciation.

Influence of light source and detector’s imperfections on the photon counting statistics

Photon counting provides a valuable tool for measuring quantum properties of light. Unavoidable imperfections of photon detectors lead to discrepancies between the statistics of photons and statistics of photon counts. Here we consider dead-time corrections and influence of intensity fluctuations for simulated Poissonian statistics of photo counts for the pulsed or continuous wave coherent light sources. We analyse dependence between the statistical moments of corrected distribution and the mean photon number, dead-time, and level of intensity fluctuations.

A generalized Euler probability distribution

From a new class of q-deformed coherent states we introduce a generalization of the Euler probability distribution for which the main statistical parameters are obtained explicitly. As application, we discuss the corresponding photon counting statistics with respect to all parameters labeling the coherent states under consideration.

Quantum dynamics of a f-deformed cavity-field beyond the rotating wave approximation

The aim of this study is to investigate dynamical properties of a two-mode f-deformed cavity- field ‎coupled to an effective two-level atom with and without the rotating wave approximation. The first ‎section discusses the theoretical model of the interaction between a two-mode cavity-field and an ‎effective two-level atom within the framework of an f-DJCM without the rotating wave ‎approximation. After that, we obtain the reduced density matrix of the cavity-field with and without ‎the rotating-wave approximation. Then, we have investigated the effect of the counter-rotating ‎terms on temporal evolution of various non-classical properties of the cavity-field, i.e., photon-‎counting statistics, the cross correlation between the modes of the field, and the quantum ‎fluctuations of the quadrature components. Particularly, we compare the numerical result for three ‎different values of the deformation parameter q (q=1, q=1.1, q=0.9) with and without applying the rotating ‎wave approximation. By using of the numerical method, we concluded that even under the ‎condition in which the RWA is considered to be valid, there are the significant effects of virtual-‎photon field on the photon-counting statistics, the cross correlation between the modes of the ‎field, and the quantum fluctuations of the quadrature components‎.

Universality of photon counting below a local bifurcation threshold

At a bifurcation point, a small change of a parameter causes a qualitative change in the system. Quantum fluctuations wash out this abrupt transition and enable the emission of quantized energy, which we term photons, below the classical bifurcation threshold. Close to the bifurcation point, the resulting photon counting statistics is determined by the instability. We propose a generic method to derive a characteristic function of photon counting close to a bifurcation threshold that only depends on the dynamics and the type of bifurcation, based on the universality of the Martin-Siggia-Rose action. We provide explicit expressions for the cusp catastrophe without conservation laws. Moreover, we propose an experimental setup using driven Josephson junctions that exhibits both a fold and a pitchfork bifurcation behavior close to a cusp catastrophe.