Low Photon Count Research Articles

Bayesian electron density determination from sparse and noisy single-molecule X-ray scattering images.

Single molecule x-ray scattering experiments using free-electron lasers hold the potential to resolve biomolecular structures and structural ensembles. However, molecular electron density determination has so far not been achieved because of low photon counts, high noise levels, and low hit rates. Most approaches therefore focus on large specimen like entire viruses, which scatter sufficiently many photons to allow orientation determination of each image. Small specimens like proteins, however, scatter too few photons for the molecular orientations to be determined. Here, we present a rigorous Bayesian approach to overcome these limitations, additionally taking into account intensity fluctuations, beam polarization, irregular detector shapes, incoherent scattering, and background scattering. We demonstrate using synthetic scattering images that electron density determination of small proteins is possible in this extreme high noise Poisson regime. Tests on published virus data achieved the detector-limited resolution of 9 nm, using only 0.01% of the available photons per image.

Deep Learning‐Based Variational Autoencoder for Classification of Quantum and Classical States of Light

AbstractAdvancements in optical quantum technologies have been enabled by the generation, manipulation, and characterization of light, with identification based on its photon statistics. However, characterizing light and its sources through single photon measurements requires efficient detectors and longer measurement times to obtain high‐quality photon statistics. Here, a deep learning‐based variational autoencoder (VAE) method is introduced for classifying single photon added coherent state (SPACS), single photon added thermal state (SPATS), and mixed states between coherent and SPACS as well as between thermal and SPATS of light. The semi‐supervised learning‐based VAE efficiently maps the photon statistics features of light to a lower dimension, enabling quasi‐instantaneous classification with low average photon counts. The proposed VAE method is robust and maintains classification accuracy in the presence of losses inherent in an experiment, such as finite collection efficiency, non‐unity quantum efficiency, finite number of detectors, etc. Additionally, leveraging the transfer learning capabilities of VAE enables successful classification of data of any quality using a single trained model. It is envisioned that such a deep learning methodology will enable better classification of quantum light and light sources even in poor detection.

Investigating deep learning strategies for fast denoising of 5D cardiac photon-counting micro-CT images


Photon-counting detectors (PCDs) for CT imaging use energy thresholds to simultaneously acquire projections at multiple energies, making them suitable for spectral imaging and material decomposition. Unfortunately, setting multiple energy thresholds results in noisy analytical reconstructions due to low photon counts in high-energy bins. Iterative reconstruction provides high quality photon-counting CT (PCCT) images but requires enormous computation time for 5D (3D + energy + time) in vivo cardiac imaging. 

Approach. 
We recently introduced UnetU, a deep learning (DL) approach that accurately denoises axial slices from 4D (3D + energy) PCCT reconstructions at various acquisition settings. In this study, we explore UnetU configurations for 5D cardiac PCCT denoising, focusing on singular value decomposition (SVD) modifications along the energy and time dimensions and alternate network architectures such as 3D U-net, FastDVDNet, and Swin Transformer UNet. We compare our networks to multi-energy non-local means (ME NLM), an established PCCT denoising algorithm. 

Main results. 
Our evaluation, using real mouse data and the digital MOBY phantom, revealed that all DL methods were more than 16 times faster than iterative reconstruction. DL denoising with SVD along the energy dimension was most effective, consistently providing low root mean square error and spatio-temporal reduced reference entropic difference, alongside strong qualitative agreement with iterative reconstruction. This superiority was attributed to lower effective rank along the energy dimension than the time dimension in 5D cardiac PCCT reconstructions. ME NLM sometimes outperformed DL with time SVD or time and energy SVD, but lagged behind iterative reconstruction and DL with energy SVD. Among alternate DL architectures with energy SVD, none consistently outperformed UnetU Energy (2D). 

Significance. 
Our study establishes UnetU Energy as an accurate and efficient method for 5D cardiac PCCT denoising, offering a 32-fold speed increase from iterative reconstruction. This advancement sets a new benchmark for DL applications in cardiovascular imaging.

Dual Stage Bionic Spatial Convolutional Restoration Model for Image De-noising and De-mosaicking

The first two important steps in the pipeline for processing picture signals are de-noising and de-mosaicking. The joint solution of the highly uncertain inverse problem of de-noising and de-mosaicking has garnered increased attention in research today. It is difficult to restore high-quality images from raw data in low light because of a variety of disturbances brought on by a low photon count and a complex image signal processing scheme. Even if some restoration and improvement techniques have been used, they might not work in harsh situations, including raw data imaging with brief exposure. Therefore, this research focuses on developing a de-mosaicking and de-noising model with effective end to end manner outcomes. Initially, the pre-processing is conducted using Gaussian filtering to eliminate artifacts from the input image, thereby enhancing the image quality. Then, the proposed method incorporates an Enhanced Spatial Convolutional Residual Net (EnConvResNet) for image de-mosaicking and an Adaptive U-net restoration model for image de-noising. An enhanced gazelle optimization (EnGa) algorithm is used to fine-tune the hyper-parameters of the model in order to maximize its performance and improve its generalization capacity. The proposed method accomplished peak signal to noise ratio (PSNR) and structural similarity index measure (SSIM) of 46.65 and 98.89, respectively.

Detectability of hemodynamic oscillations in cerebral cortex through functional near-infrared spectroscopy: a simulation study.

We explore the feasibility of using time-domain (TD) and continuous-wave (CW) functional near-infrared spectroscopy (fNIRS) to monitor brain hemodynamic oscillations during resting-state activity in humans, a phenomenon that is of increasing interest in the scientific and medical community and appears to be crucial to advancing the understanding of both healthy and pathological brain functioning. Our general object is to maximize fNIRS sensitivity to brain resting-state oscillations. More specifically, we aim to define comprehensive guidelines for optimizing main operational parameters in fNIRS measurements [average photon count rate, measurement length, sampling frequency, and source-detector distance (SSD)]. In addition, we compare TD and CW fNIRS performance for the detection and localization of oscillations. A series of synthetic TD and CW fNIRS signals were generated by exploiting the solution of the diffusion equation for two different geometries of the probed medium: a homogeneous medium and a bilayer medium. Known and periodical perturbations of the concentrations of oxy- and deoxy-hemoglobin were imposed in the medium, determining changes in its optical properties. The homogeneous slab model was used to determine the effect of multiple measurement parameters on fNIRS sensitivity to oscillatory phenomena, and the bilayer model was used to evaluate and compare the abilities of TD and CW fNIRS in detecting and isolating oscillations occurring at different depths. For TD fNIRS, two approaches to enhance depth-selectivity were evaluated: first, a time-windowing of the photon distribution of time-of-flight was performed, and then, the time-dependent mean partial pathlength (TMPP) method was used to retrieve the hemoglobin concentrations in the medium. In the homogeneous medium case, the sensitivity of TD and CW fNIRS to periodical perturbations of the optical properties increases proportionally with the average photon count rate, the measurement length, and the sampling frequency and approximatively with the square of the SSD. In the bilayer medium case, the time-windowing method can detect and correctly localize the presence of oscillatory components in the TD fNIRS signal, even in the presence of very low photon count rates. The TMPP method demonstrates how to correctly retrieve the periodical variation of hemoglobin at different depths from the TD fNIRS signal acquired at a single SSD. For CW fNIRS, measurements taken at typical SSDs used for short-separation channel regression show notable sensitivity to oscillations occurring in the deep layer, challenging the assumptions underlying this correction method when the focus is on analyzing oscillatory phenomena. We demonstrated that the TD fNIRS technique allows for the detection and depth-localization of periodical fluctuations of the hemoglobin concentrations within the probed medium using an acquisition at a single SSD, offering an alternative to multi-distance CW fNIRS setups. Moreover, we offered some valuable guidelines that can assist researchers in defining optimal experimental protocols for fNIRS studies.

Symmetry-Breaking Charge Separation Mediated Triplet Population in a Perylenediimide Trimer at the Single-Molecule Level.

Herein, we demonstrate triplet excited-state population in a conformationally rigid perylenediimide trimer (PDI-T) via intramolecular symmetry-breaking charge separation (SB-CS) at the single-molecule level. The single-molecule fluorescence intensity trajectories of PDI-T in nonpolar polystyrene matrix (ε = 2.60) exhibit prolonged fluorescence with infrequent dark states, representing the triplet and/or the charge transfer states. In contrast, in a poly(vinyl alcohol) matrix (ε = 7.80), erratic blinking dynamics resulting in low photon counts were observed, corroborating the feasibility of charge separation in a polar environment. In agreement with the single-molecule measurements, transient absorption spectroscopy of PDI-T reveals ultrafast SB-CS (τCS < 5 ps) in polar tetrahydrofuran (ε = 7.58) and acetone (ε = 20.70), with the population of the triplet excited-state through charge recombination. The current investigation shows the utility of rigid and weakly coupled molecular constructs in controlling triplet generation and SB-CS for potential applications in optoelectronic devices.

Raman lidar at 355 nm using low dead time photon counting for atmospheric aerosol measurements.

Photon counting is an effective way to enhance the dynamic range of the data acquisition system (DAQ) in Raman lidars. However, there exists a deficiency of relatively high dead times among current options, which necessitates an additional calibration procedure for the nonlinearity of the photon counting signal, thus leading to unanticipated errors. A field programmable gate array (FPGA)-based photon counting module has been proposed and implemented in a Raman lidar, offering two operational channels. Through observational experiments, it was determined that this module has an overall dead time of 1.13ns taking advantage of the high-speed amplifier/discriminator pair and the logic design, a significant improvement compared to the 4.35ns of a commercially used Licel transient recorder within the same counting rate range. This notably low dead time implies that its output maintains sufficient linearity even at substantially high counting rates. As a result, the need for a dead time calibration procedure prior to signal integration with the analog signal is eliminated, reducing uncertainty in the final integrated signal, and even in the retrieval result. The backscattering result of the comparison between this module and a transient recorder indicates that a more precise performance can be acquired benefiting from this hardware upgrading.

Real-Time Low-Light Imaging in Space Based on the Fusion of Spatial and Frequency Domains

Due to the low photon count in space imaging and the performance bottlenecks of edge computing devices, there is a need for a practical low-light imaging solution that maintains satisfactory recovery while offering lower network latency, reduced memory usage, fewer model parameters, and fewer operation counts. Therefore, we propose a real-time deep learning framework for low-light imaging. Leveraging the parallel processing capabilities of the hardware, we perform the parallel processing of the image data from the original sensor across branches with different dimensionalities. The high-dimensional branch conducts high-dimensional feature learning in the spatial domain, while the mid-dimensional and low-dimensional branches perform pixel-level and global feature learning through the fusion of the spatial and frequency domains. This approach ensures a lightweight network model while significantly improving the quality and speed of image recovery. To adaptively adjust the image based on brightness and avoid the loss of detailed pixel feature information, we introduce an adaptive balancing module, thereby greatly enhancing the effectiveness of the model. Finally, through validation on the SID dataset and our own low-light satellite dataset, we demonstrate that this method can significantly improve image recovery speed while ensuring image recovery quality.

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.

Guided block matching and 4-D transform domain filter projection denoising method for dynamic PET image reconstruction

PurposeDynamic PET is an essential tool in oncology due to its ability to visualize and quantify radiotracer uptake, which has the potential to improve imaging quality. However, image noise caused by a low photon count in dynamic PET is more significant than in static PET. This study aims to develop a novel denoising method, namely the Guided Block Matching and 4-D Transform Domain Filter (GBM4D) projection, to enhance dynamic PET image reconstruction.MethodsThe sinogram was first transformed using the Anscombe method, then denoised using a combination of hard thresholding and Wiener filtering. Each denoising step involved guided block matching and grouping, collaborative filtering, and weighted averaging. The guided block matching was performed on accumulated PET sinograms to prevent mismatching due to low photon counts. The performance of the proposed denoising method (GBM4D) was compared to other methods such as wavelet, total variation, non-local means, and BM3D using computer simulations on the Shepp–Logan and digital brain phantoms. The denoising methods were also applied to real patient data for evaluation.ResultsIn all phantom studies, GBM4D outperformed other denoising methods in all time frames based on the structural similarity and peak signal-to-noise ratio. Moreover, GBM4D yielded the lowest root mean square error in the time-activity curve of all tissues and produced the highest image quality when applied to real patient data.ConclusionGBM4D demonstrates excellent denoising and edge-preserving capabilities, as validated through qualitative and quantitative assessments of both temporal and spatial denoising performance.

Time-Resolved Line Shapes of Single Quantum Emitters via Machine Learned Photon Correlations.

Solid-state single-photon emitters (SPEs) are quantum light sources that combine atomlike optical properties with solid-state integration and fabrication capabilities. SPEs are hindered by spectral diffusion, where the emitter's surrounding environment induces random energy fluctuations. Timescales of spectral diffusion span nanoseconds to minutes and require probing single emitters to remove ensemble averaging. Photon correlation Fourier spectroscopy (PCFS) can be used to measure time-resolved single emitter line shapes, but is hindered by poor signal-to-noise ratio in the measured correlation functions at early times due to low photon counts. Here, we develop a framework to simulate PCFS correlation functions directly from diffusing spectra that match well with experimental data for single colloidal quantum dots. We use these simulated datasets to train a deep ensemble autoencoder machine learning model that outputs accurate, noiseless, and probabilistic reconstructions of the noisy correlations. Using this model, we obtain reconstructed time-resolved single dot emission line shapes at timescales as low as 10ns, which are otherwise completely obscured by noise. This enables PCFS to extract optical coherence times on the same timescales as Hong-Ou-Mandel two-photon interference, but with the advantage of providing spectral information in addition to estimates of photon indistinguishability. Our machine learning approach is broadly applicable to different photon correlation spectroscopy techniques and SPE systems, offering an enhanced tool for probing single emitter line shapes on previously inaccessible timescales.

CASPI: collaborative photon processing for active single-photon imaging

Image sensors capable of capturing individual photons have made tremendous progress in recent years. However, this technology faces a major limitation. Because they capture scene information at the individual photon level, the raw data is sparse and noisy. Here we propose CASPI: Collaborative Photon Processing for Active Single-Photon Imaging, a technology-agnostic, application-agnostic, and training-free photon processing pipeline for emerging high-resolution single-photon cameras. By collaboratively exploiting both local and non-local correlations in the spatio-temporal photon data cubes, CASPI estimates scene properties reliably even under very challenging lighting conditions. We demonstrate the versatility of CASPI with two applications: LiDAR imaging over a wide range of photon flux levels, from a sub-photon to high ambient regimes, and live-cell autofluorescence FLIM in low photon count regimes. We envision CASPI as a basic building block of general-purpose photon processing units that will be implemented on-chip in future single-photon cameras.

Plasmonic-Enhanced Bright Single Spin Defects in Silicon Carbide Membranes.

Optically addressable spin defects in silicon carbide (SiC) have emerged as attractable platforms for various quantum technologies. However, the low photon count rate significantly limits their applications. We strongly enhanced the brightness by 7 times and spin-control strength by 14 times of single divacancy defects in 4H-SiC membranes using a surface plasmon generated by gold film coplanar waveguides. The mechanism of the plasmonic-enhanced effect is further studied by tuning the distance between single defects and the surface of the gold film. A three-energy-level model is used to determine the corresponding transition rates consistent with the enhanced brightness of single defects. Lifetime measurements also verified the coupling between defects and surface plasmons. Our scheme is low-cost, without complicated microfabrication and delicate structures, which is applicable for other spin defects in different materials. This work would promote developing spin-defect-based quantum applications in mature SiC materials.

Design and Fabrication of High-Efficiency, Low-Power, and Low-Leakage Si-Avalanche Photodiodes for Low-Light Sensing.

Since the advent of impact ionization and its application in avalanche photodiodes (APD), numerous application goals have contributed to steady improvements over several decades. The characteristic high operating voltages and the need for thick absorber layers (π-layers) in the Si-APDs pose complicated design and operational challenges in complementary metal oxide semiconductor integration of APDs. In this work, we have designed a sub-10 V operable Si-APD and epitaxially grown the stack on a semiconductor-on-insulator substrate with a submicron thin π-layer, and we fabricated the devices with integrated photon-trapping microholes (PTMH) to enhance photon absorption. The fabricated APDs show a substantially low prebreakdown leakage current density of ∼50 nA/mm2. The devices exhibit a consistent ∼8.0 V breakdown voltage with a multiplication gain of 296.2 under 850 nm illumination wavelength. We report a ∼5× increase in the EQE at 850 nm by introducing the PTMH into the device. The enhancement in the EQE is evenly distributed across the entire wavelength range (640-1100 nm). The EQE of the devices without PTMH (flat devices) undergo a notable oscillation caused by the resonance at specific wavelengths and show a strong dependency on the angle of incidence. This characteristic dependency is significantly circumvented by introducing the PTMH into the APD. The devices exhibit a significantly low off-state power consumption of 0.41 μW/mm2 and stand fairly well against the state-of-the-art literature. Such high efficiency, low leakage, low breakdown voltage, and extremely low-power Si-APD can be easily incorporated into the existing CMOS foundry line and enable on-chip, high-speed, and low-photon count detection on a large scale.

Micro-CT imaging of multiple K-edge elements using GaAs and CdTe photon counting detectors

Objective. To evaluate the performance of two photon-counting (PC) detectors based on different detector materials, gallium arsenide (GaAs) and cadmium telluride (CdTe), for PC micro-CT imaging of phantoms with multiple contrast materials. Another objective is to determine if combining these two detectors in the same micro-CT system can offer higher spectral performance and significant artifact reduction compared to a single detector system. Approach. We have constructed a dual-detector, micro-CT system equipped with two PCDs based on different detector materials: gallium arsenide (GaAs) and cadmium telluride (CdTe). We demonstrate the performance of these detectors for PC micro-CT imaging of phantoms with up to 5 contrast materials with K-edges spread across the x-ray spectrum ranging from iodine with a K-edge at 33.2 keV to bismuth with a K-edge at 90.5 keV. We also demonstrate the use of our system to image a mouse prepared with both iodine and bismuth contrast agents to target different biological systems. Main results. When using the same dose and scan parameters, GaAs shows increased low energy (<50 keV) spectral sensitivity and specificity compared to CdTe. However, GaAs performance at high energies suffers from spectral artifacts and has comparatively low photon counts indicating wasted radiation dose. We demonstrate that combining a GaAs-based and a CdTe-based PC detector in the same micro-CT system offers higher spectral performance and significant artifact reduction compared to a single detector system. Significance. More accurate PC micro-CT using a GaAs PCD alone or in combination with a CdTe PCD could serve for developing new contrast agents such as nanoparticles that show promise in the developing field of theranostics (therapy and diagnostics).

Deep-learning-based denoising of X-ray differential phase and dark-field images

PurposeStatistical photon noise has always been a common problem in X-ray multi-contrast imaging and significantly influenced the quality of retrieved differential phase and dark-field images. We intend to develop a deep learning-based denoising algorithm to reduce the noise of retrieved X-ray differential phase and dark-field images. MethodsA novel deep learning based image noise suppression algorithm (named DnCNN-P) is presented. We proposed two different denoising modes: Retrieval-Denoising mode (R-D mode) and Denoising-Retrieval mode (D-R mode). While the R-D mode denoises the retrieved images, the D-R mode denoises the raw phase stepping data. The two denoising modes are evaluated under different photon counts and visibilities. ResultsExperimental results show that with the algorithm DnCNN-P used, the D-R mode always exhibits a better noise reduction under diverse experimental conditions, even in the case of a low photon count and/or a low visibility. With a detected photon count of 1800 and a visibility of 0.3, compared to the differential phase images without denoising, the standard deviation is reduced by 89.1% and 16.4% in the D-R and R-D modes. Compared to the dark-field images without denoising, the standard deviation is reduced by 83.7% and 12.6% in the D-R and R-D modes, respectively.Conclusions.The novel supervised DnCNN-P algorithm can significantly reduce the noise in retrieved X-ray differential phase and dark-field images. We believe this novel algorithm can be a promising approach to improve the quality of X-ray differential phase and dark-field images, and therefore dose efficiency in future biomedical applications.

A proton-recoil track imaging system for fast neutrons: the RIPTIDE detector

Fast neutron detection is often based on the neutron-proton elastic scattering reaction: the ionization caused by recoil protons in a hydrogenous material constitutes the basic information for the design and development of a class of neutron detectors. Although experimental techniques have continuously improved, proton-recoil track imaging remains still at the frontier of n-detection systems, due to the high photon sensitivity required. Several state-of-the-art approaches for neutron tracking by using n-p single and double scattering — referred to as Recoil Proton Track Imaging (RPTI) — can be found in the literature. So far, they have showed limits in terms of detection efficiency, complexity, cost, and implementation. In order to address some of these deficiencies, we propose the design of RIPTIDE, a novel recoil-proton track imaging detector in which the light output produced by a fast scintillator is used to perform a complete reconstruction in space and time of the interaction events. The proposed idea is viable thanks to the dramatic advances in low noise and single photon counting achieved in the last decade by new scientific CMOS cameras as well as pixel sensors, like Timepix or MIMOSIS. In this contribution, we report the advances on the RIPTIDE concept: Geant4 Monte Carlo simulations, light collection tests as well as state-of-the-art approach to image readout, processing and fast analysis.

Speckle contrast of interfering fluorescence X-rays

With the development of X-ray free-electron lasers (XFELs), producing pulses of femtosecond durations comparable with the coherence times of X-ray fluorescence, it has become possible to observe intensity-intensity correlations due to the interference of emission from independent atoms. This has been used to compare durations of X-ray pulses and to measure the size of a focusedX-raybeam, for example. Here it is shown that it is also possible to observe the interference of fluorescence photons through the measurement of the speckle contrast of angle-resolved fluorescence patterns. Speckle contrast is often used as a measure of the degree of coherence of the incident beam or the fluctuations of the illuminated sample as determined from X-ray diffraction patterns formed by elastic scattering, rather than from fluorescence patterns as addressed here. Commonly used approaches to estimate speckle contrast were found to suffer when applied to XFEL-generated fluorescence patterns due to low photon counts and a significant variation of the excitation pulse energy from shot to shot. A new method to reliably estimate speckle contrast under such conditions, using a weighting scheme, is introduced. The method is demonstrated by comparing the speckle contrast of fluorescence observed with pulses of 3 fs to 15 fs duration.

Efficient Reconstruction of Low Photon Count Images from a High Speed Camera

Challenging imaging applications requiring ultra-short exposure times or imaging in photon-starved environments can acquire extremely low numbers of photons per pixel, (&lt;1 photon per pixel). Such photon-sparse images can require post-processing techniques to improve the retrieved image quality as defined quantitatively by metrics including the Structural Similarity Index Measure (SSIM) and Mean Squared Error (MSE) with respect to the ground truth. Bayesian retrodiction methods have been shown to improve estimation of the number of photons detected and spatial distributions in single-photon imaging applications. In this work, we demonstrate that at high frame rates (&gt;1 MHz) and low incident photon flux (&lt;1 photon per pixel), image post processing can provide better grayscale information and spatial fidelity of reconstructed images than simple frame averaging, with improvements in SSIM up to a factor of 3. Various other image post-processing techniques are also explored and some of which result in a similar quality of image reconstruction to Bayesian retrodiction, with lower computational load. Image reconstructions using Bayesian Retrodiction or bilateral filtering are of comparable quality to frame averaging, as measured by the Structural Similarity Index Measure, when using less than 40% of the photon flux.

The demographics of obscured AGN from X-ray spectroscopy guided by multiwavelength information

ABSTRACT A complete census of active galactic nuclei (AGNs) is a prerequisite for understanding the growth of supermassive black holes across cosmic time. A significant challenge towards this goal is the whereabouts of heavily obscured AGN that remain uncertain. This paper sets new constraints on the demographics of this population by developing a methodology that combines X-ray spectral information with priors derived from multiwavelength observations. We select X-ray AGN in the Chandra COSMOS Legacy survey and fit their $2.2\!-\!500\, \mu \mathrm{m}$ spectral energy distributions with galaxy and AGN templates to determine the mid-infrared ($6\, \mu \mathrm{m}$) luminosity of the AGN component. Empirical correlations between X-ray and $6\, \mu \mathrm{m}$ luminosities are then adopted to infer the intrinsic accretion luminosity at X-rays for individual AGN. This is used as prior information in our Bayesian X-ray spectral analysis to estimate physical properties, such as line-of-sight obscuration. Our approach breaks the degeneracies between accretion luminosity and obscuration that affect X-ray spectral analysis, particularly for the most heavily obscured (Compton-Thick) AGN with low photon counts X-ray spectra. The X-ray spectral results are then combined with the selection function of the Chandra COSMOS Legacy survey to derive the AGN space density and a Compton-Thick fraction of $21.0^{+16.1}_{-9.9}{{\ \rm per\ cent}}$ at redshifts z &amp;lt; 0.5. At higher redshift, our analysis suggests upper limits to the Compton-Thick AGN fraction of $\lesssim 40{{\ \rm per\ cent}}$. These estimates are at the low end of the range of values determined in the literature and underline the importance of multiwavelength approaches for tackling the challenge of heavily obscured AGN demographics.