Photon-starved Regime Research Articles

Single-pixel compressive imaging via single photon counting

Single-pixel compressive imaging reconstructs a target scene with many pixels by using a single-pixel detector to measure the power variations as small sequences of sampling patterns are applied. While it boasts remarkable capabilities, its practical applications remain a challenge in the photon-starved regime where signal-to-noise is low. To address this challenge, we propose to combine quantum parametric mode sorting (QPMS) and deep neural networks (DNN) to overcome low signal-to-noise for faithful image construction. We benchmark our approach in a telecom-LiDAR system against that using direct photon counting detection. Our results show that with only 25 sampling patterns (corresponding compression ratio ∼0.043%), QPMS plus DNN give structural similarity index measure and peak signal-to-noise ratio on average above 22 dB and 0.9, respectively, much higher than those with direct detection (DD). The details of our targets from QPMS are more clearly compared with from DD. Notably, such high performance is sustained even in the presence of 500 times stronger in-band background noise, while DD fails. The high efficiency and robust noise rejection promise potential applications in various fields, especially in photon-starving scenarios.

Free-space coupled, large-active-area superconducting microstrip single-photon detector for photon-counting time-of-flight imaging

Numerous applications at the photon-starved regime require a free-space coupling single-photon detector with a large active area, low dark count rate (DCR), and superior time resolutions. Here, we developed a superconducting microstrip single-photon detector (SMSPD), with a large active area of 260 µm in diameter, a DCR of ∼5kcps, and a low time jitter of ∼171ps, operated at a near-infrared of 1550 nm and a temperature of ∼2.0K. As a demonstration, we applied the detector to a single-pixel galvanometer scanning system and successfully reconstructed the object information in depth and intensity using a time-correlated photon counting technology.

Optimized receiver design for entanglement-assisted communication using BPSK.

The use of pre-shared entanglement in entanglement-assisted communication offers a superior alternative to classical communication, especially in the photon-starved regime and highly noisy environments. In this paper, we analyze the performance of several low-complexity receivers that use optical parametric amplifiers. The simulations demonstrate that receivers employing an entanglement-assisted scheme with phase-shift-keying modulation can outperform classical capacities. We present a 2x2 optical hybrid receiver for entanglement-assisted communication and show that it has a roughly 10% lower error probability compared to previously proposed optical parametric amplifier-based receivers for more than 10 modes. However, the capacity of the optical parametric amplifier-based receiver exceeds the Holevo capacity and the capacities of the optical phase conjugate receiver and 2x2 optical hybrid receiver in the case of a single mode. The numerical findings indicate that surpassing the Holevo and Homodyne capacities does not require a large number of signal-idler modes. Furthermore, we find that using unequal priors for BPSK provides roughly three times the information rate advantage over equal priors.

Photon-starved snapshot holography

Digital holography (DH) is a powerful imaging modality that is capable of capturing the object wavefront information, making it very valuable for diverse scientific research applications. Generally, it requires ample illumination to enable good fringe visibility and a sufficient signal-to-noise ratio. As such, in situations such as probing live cells with minimal light interaction and high-speed volumetric tracking in flow cytometry, the holograms generated with a limited photon budget suffer from poor pattern visibility. While it is possible to make use of photon-counting detectors to improve the hologram quality, the long recording procedure coupled with the need for mechanical scanning means that real-time extremely low-light holographic imaging remains a formidable challenge. Here, we develop a snapshot DH that can operate at an ultra-low photon level (less than one photon per pixel). This is achieved by leveraging a quanta image sensor to capture a stack of binary holographic frames and then computationally reconstructing the wavefront through integrating the mathematical imaging model and the data-driven processing, an approach that we termed PSHoloNet. The robustness and versatility of our DH system are demonstrated on both synthetic and experimental holograms with two common DH tasks, namely particle volumetric reconstruction and phase imaging. Our results demonstrate that it is possible to expand DH to the photon-starved regime, and our method will enable more advanced holography applications in various scientific imaging systems.

Intensity-guided depth image estimation in long-range lidar

Long-range lidar systems usually record large but extremely sparse data cubes. It is a great challenge to estimate accurate depth images of the photon-starved regime with fewer memory requirements and lower computational complexity. An intensity-guided method is introduced to estimate the depth image by using temporal-spatial correlation of the reflected signals. Multi-scale superpixels and fast time-domain windows are established in the preprocessing step, leading to smaller data cubes with reduced empty and noisy pixels. To strike a balance between smoothness and preserving sharp edges, the fast-converging alternating direction method of multipliers (ADMM) is used in the modified cost function to estimate depth images. Experimental results show that the proposed method yields better depth estimates than other state-of-the-art methods, especially for long-rang targets of field experiments with a low signal return level of ∼1 photon per pixel.

Quantum-limited discrimination of laser light and thermal light.

Understanding the fundamental sensitivity limit of an optical sensor requires a full quantum mechanical description of the sensing task. In this work, we calculate the fundamental (quantum) limit for discriminating between pure laser light and thermal noise in a photon-starved regime. The Helstrom bound for discrimination error probability for single mode measurement is computed along with error probability bounds for direct detection, coherent homodyne detection and the Kennedy receiver. A generalized Kennedy (GK) receiver is shown to closely approach the Helstrom limit. We present an experimental demonstration of this sensing task and demonstrate a 15.4 dB improvement in discrimination sensitivity over direct detection using a GK receiver and an improvement of 19.4% in error probability over coherent detection.

Quantum Limits in Optical Communications

This tutorial reviews the Holevo capacity limit as a universal tool to analyze the ultimate transmission rates in a variety of optical communication scenarios, ranging from conventional optically amplified fiber links to free-space communication with power-limited optical signals. The canonical additive white Gaussian noise model is used to describe the propagation of the optical signal. The Holevo limit exceeds substantially the standard Shannon limit when the power spectral density of noise acquired in the course of propagation is small compared to the energy of a single photon at the carrier frequency per unit time-bandwidth area. General results are illustrated with a discussion of efficient communication strategies in the photon-starved regime.

Expectation-Maximization Based Approach to 3D Reconstruction From Single-Waveform Multispectral Lidar Data

In this article, we present a novel Bayesian approach for estimating spectral and range profiles from single-photon Lidar waveforms associated with single surfaces in the photon-limited regime. In contrast to classical multispectral Lidar signals, we consider a single Lidar waveform per pixel, whereby a single detector is used to acquire information simultaneously at multiple wavelengths. A new observation model based on a mixture of distributions is developed. It relates the unknown parameters of interest to the observed waveforms containing information from multiple wavelengths. Adopting a Bayesian approach, several prior models are investigated and a stochastic Expectation-Maximization algorithm is proposed to estimate the spectral and depth profiles. The reconstruction performance and computational complexity of our approach are assessed, for different prior models, through a series of experiments using synthetic and real data under different observation scenarios. The results obtained demonstrate a significant speed-up (up to 100 times faster for four bands) without significant degradation of the reconstruction performance when compared to existing methods in the photon-starved regime.

Monte Carlo simulations of relativistic radiation-mediated shocks: II. photon-starved regime

ABSTRACT Radiation-mediated shocks (RMS) play a key role in shaping the early emission observed in many transients. In most cases, e.g. shock breakout in supernovae, llGRBs, and neutron star mergers, the upstream plasma is devoid of radiation, and the photons that ultimately reach the observer are generated predominantly inside and downstream of the shock. Predicting the observed spectrum requires detailed calculations of the shock structure and thermodynamic state that account properly for the shock microphysics. We present results of self-consistent Monte Carlo simulations of photon-starved RMS, which yield the shock structure and emission for a broad range of shock velocities, from subrelativistic (βsh = 0.1) to highly relativistic (Γsh = 20). Our simulations confirm that in relativistic RMS the immediate downstream temperature is regulated by exponential pair creation, ranging from 50 keV at βsh = 0.5–200 keV at Γsh = 20. At lower velocities, the temperature becomes sensitive to the shock velocity, with kT ∼ 0.5 keV at βsh = 0.1. We also confirm that in relativistic shocks the opacity is completely dominated by newly created pairs, which has important implications for the breakout physics. We find the transition to pair dominance to occur at βsh = 0.5 roughly. In all cases examined, the spectrum below the νFν peak has been found to be substantially softer than the Planck distribution. This has important implications for the optical emission in fast and relativistic breakouts, and their detection. The applications to GRB 060218 and GRB 170817A are discussed.

Learning Non-Local Spatial Correlations To Restore Sparse 3D Single-Photon Data.

This paper presents a new algorithm for the learning of spatial correlation and non-local restoration of single-photon 3-Dimensional Lidar images acquired in the photon starved regime (fewer or less than one photon per pixel) or with a reduced number of scanned spatial points (pixels). The algorithm alternates between three steps: (i) extract multi-scale information, (ii) build a robust graph of non-local spatial correlations between pixels, and (iii) the restoration of depth and reflectivity images. A non-uniform sampling approach, which assigns larger patches to homogeneous regions and smaller ones to heterogeneous regions, is adopted to reduce the computational cost associated with the graph. The restoration of the 3D images is achieved by minimizing a cost function accounting for the multi-scale information and the non-local spatial correlation between patches. This minimization problem is efficiently solved using the alternating direction method of multipliers (ADMM) that presents fast convergence properties. Various results based on simulated and real Lidar data show the benefits of the proposed algorithm that improves the quality of the estimated depth and reflectivity images, especially in the photon-starved regime or when containing a reduced number of spatial points.

Three-dimensional single-photon imaging through obscurants.

We investigate the depth imaging of objects through various densities of different obscurants (water fog, glycol-based vapor, and incendiary smoke) using a time-correlated single-photon detection system which had an operating wavelength of 1550 nm and an average optical output power of approximately 1.5 mW. It consisted of a monostatic scanning transceiver unit used in conjunction with a picosecond laser source and an individual Peltier-cooled InGaAs/InP single-photon avalanche diode (SPAD) detector. We acquired depth and intensity data of targets imaged through distances of up to 24 meters for the different obscurants. We compare several statistical algorithms which reconstruct both the depth and intensity images for short data acquisition times, including very low signal returns in the photon-starved regime.

Wavelength-time coding for multispectral 3D imaging using single-photon LiDAR.

Single-photon multispectral light detection and ranging (LiDAR) approaches have emerged as a route to color reconstruction and enhanced target identification in photon-starved imaging scenarios. In this paper, we present a three-dimensional imaging system based on a time-of-flight approach which is capable of simultaneous multispectral measurements using only one single-photon detector. Unlike other techniques, this approach does not require a wavelength router in the receiver channel. By observing multiple wavelengths at each spatial location, or per pixel (four discrete visible wavelengths are used in this work), we can obtain a single waveform with wavelength-to-time mapped peaks. The time-mapped peaks are created by the known chromatic group delay dispersion in the laser source's optical fiber, resulting in temporal separations between these peaks being in the region of 200 to 1000 ps, in this case. A multispectral single waveform algorithm was proposed to fit these multiple peaked LiDAR waveforms, and then reconstruct the color (spectral response) and depth profiles for the entire image. To the best of our knowledge, this is the first dedicated computational method operating in the photon-starved regime capable of discriminating multiple peaks associated with different wavelengths in a single pixel waveform and reconstructing spectral responses and depth.

Holographic wavefront sensor for fast defocus measurement

Abstract Atmospheric effects significantly influence the propagation of light. Conventional adaptive optics systems, based on Shack-Hartmann sensors (SHS), work well for vertical-path propagation. However, for more challenging scenarios like horizontal-path imaging or free-space laser communications through extended-volume turbulence and strong scintillation, the bandwidth of SHS is insufficient. A promising alternative is the holographic wavefront sensor (HWFS). Our paper deals with some dependencies and limitations of the HWFS. First, we show that the sensitivity of the HWFS is highly dependent on the detector size. The smaller the detector, the more sensitive is the sensor. This has consequences in the photon-starved regime, which would naturally occur when the sensor is operated at the intended MHz speed. Second, we show that uncorrected (or residual) tip/tilt has a large impact on the accuracy of the measurement. We present experimental results of measuring an important and also easily correctable aberration, defocus, with the HWFS.

Inside-out or outside-in: the topology of reionization in the photon-starved regime suggested by Lyα forest data

We use a set of seminumerical simulations based on the Zel'dovich approximation, the friends-of-friends algorithm and excursion set formalism to generate reionization maps of high dynamic range with a range of assumptions regarding the distribution and luminosity of ionizing sources and the spatial distribution of sinks for the ionizing radiation. We find that ignoring the inhomogeneous spatial distribution of regions of high gas density where recombinations are important - as is often done in studies of this kind - can lead to misleading conclusions regarding the topology of reionization, especially if reionization occurs in the photon-starved regime suggested by Lya forest data. The inhomogeneous spatial distribution of recombinations significantly reduces the mean-free path of ionizing photons and the typical size of coherently ionized regions. Reionization proceeds then much more as an outside-in process. Low-density regions far from ionizing sources become ionized before regions of high gas density not hosting sources of ionizing radiation. The spatial distribution of sinks of ionization radiation also significantly affects the shape and amplitude of the power spectrum of fluctuations of 21 cm emission. The slope of the 21 cm power spectrum as measured by upcoming 21 cm experiments should be able to distinguish to what extent the topology of reionization proceeds outside-in or inside-out, while the evolution of the amplitude of the power spectrum with increasing ionized mass fraction should be sensitive to the spatial distribution and the luminosity of ionizing sources.