Photon Counting Process Research Articles

3D visualization in turbid water using optimal photon counting and a GAT-based peplography method

Peplography is a three-dimensional (3D) approach for the visualization of targets in environments characterized by heavy scattering. It detects ballistic photons and subsequently generates a 3D image using integral imaging, where the expected number of ballistic photons is set arbitrarily. However, it affects the robustness of the method and accuracy in the analysis of results. Therefore, we propose a method to determine the optimal number of ballistic photons based on the maximum entropy of the photon counting image. Because accuracy in visualizing 3D targets may be compromised due to extraneous photons and fluctuations in photon intensity, we also address this challenge by integrating the generalized Anscombe transformation (GAT) with the conventional peplography technique. The noise caused by an image sensor during image acquisition can be modeled as a Poisson–Gaussian noise, and the photon counting process can be modeled as a Poisson process. Addressing such noise indirectly involves applying the GAT to the reconstructed image to stabilize its variance, denoising the stabilized data with a Gaussian denoising algorithm (i.e., non-local means filtering), and subsequently applying an exact unbiased inverse GAT to the denoised data. Experimental validation is conducted through experiments, with comparisons to conventional peplography, wavelet peplography, and a few standard dehazing and machine learning methods. Various image quality metrics such as correlation, structural similarity, the peak signal-to-noise ratio, and the natural image quality evaluator are used to demonstrate the superiority of the proposed method over conventional ones.

A Review on Low-Dose Emission Tomography Post-Reconstruction Denoising with Neural Network Approaches.

Low-dose emission tomography (ET) plays a crucial role in medical imaging, enabling the acquisition of functional information for various biological processes while minimizing the patient dose. However, the inherent randomness in the photon counting process is a source of noise which is amplified low-dose ET. This review article provides an overview of existing post-processing techniques, with an emphasis on deep neural network (NN) approaches. Furthermore, we explore future directions in the field of NN-based low-dose ET. This comprehensive examination sheds light on the potential of deep learning in enhancing the quality and resolution of low-dose ET images, ultimately advancing the field of medical imaging.

FLASH LiDAR SINGLE PHOTON IMAGING OVER 50 KM

Abstract. In order to demonstrate the feasibility of single-photon imaging of flash lidar in the permanent shadow area of the moon, a set of space-based single-photon imaging system is designed, including the lidar based on VCSEL array, the optical emitting system based on the uniform beam shaping meta-lens using propagation phase and geometric phase joint control method, the two-axis three-mirror optical receiving system, and the single-photon detector array based on photon counting mode. According to the heavy-tailed pulse laser function, Poisson statistical filtering theory and Monte Carlo simulation method, the echo photon number, the photon counting process, the ranging accuracy and the intensity image are simulated in the condition of 50 km detection distance by setting different of the object reflectivity, the repetition times and the gating interval time. The results show that according to the parameter settings in this paper, the number of echo photons is as low as about 10-4 orders. However, the photon counting waveform can better restore the transmission waveform. The setting of the repetition number and the gating interval time should not only consider the missing detection phenomenon, but also consider the noise accumulation. When the repetition number is 2000 and the gate number is 200, the ranging accuracy can reach 0.075m, and the imaging in the crater without light is realized.

Uncertainty analysis of gamma-ray densitometry applied for gas flow modulation technique in bubble columns

The gas flow modulation technique is a recently proposed approach for measuring the axial gas dispersion coefficient in bubble columns. This study presents a quantitative analysis of the experimental uncertainty associated with gamma-ray densitometry and ensemble-averaging of the data. The considered uncertainty sources are the statistics of the photon counting process, a mismatch between the modelled and the real radiation propagation due to the spatial extent of the detector, and a potential mismatch between modulation and sampling frequencies. The analysis is based on a numerical gamma-ray propagation model and a Monte Carlo approach to account for statistical uncertainty. The proposed algorithm supports the selection of an optimal total scanning time based on detector size, modulation parameters, involved fluids and column and source parameters. The analysis reveals that a mismatch between the modulation and sampling frequencies is most critical while the impact of the other considered uncertainty sources is rather marginal.

Statistics of electron-multiplying charge-coupled devices

Electron-multiplying charge-coupled devices are efficient imaging devices for low-surface-brightness ultraviolet astronomy from space. The large amplification allows photon counting (PC), the detection of events versus nonevents. This paper provides the statistics of the observation process, the photon-counting process, the amplification process, and the compression. The expression for the signal-to-noise of PC is written in terms of the polygamma function. The optimal exposure time is a function of the clock-induced charge. The exact distribution of amplification process is a simple-to-compute powered matrix. The optimal cutoff for comparing to the read noise is close to a strong function of the read noise and a weak function of the electron-multiplying gain and photon rate. A formula gives the expected compression rate.

Performance analysis and experimental verification of SPAD receivers without photon counting for optical wireless communications

Single photon avalanche diode (SPAD) attracts increasing interests to realize photon-sensitive receivers for optical wireless communications (OWC). In SPAD receivers, the bit information is extracted by photon counting process, which will increase the burden of data processing and storage. To remove complex photon counting process, we propose a scheme of letting recording pulses pass through low-pass finite impulse response (FIR) filter to realize a SPAD receiver without photon counting. Based on the SPAD operation principles, the Monte-Carlo model of SPAD-based OWC system is built and verified with experimental results. Moreover, based on the signal-dependent noise model, a simple and accurate signal estimation and decision algorithm is developed to demodulate the low-pass signal. On this basis, the system error performance under different operation conditions is investigated. The results indicate that utilizing the proposed algorithm, the system error performance is improved 1- to 3-orders of magnitude better than conventional algorithm, which depends on additive Gaussian noise model.

Multi-frame super-resolution reconstruction based on mixed Poisson–Gaussian noise

In this paper, a non-blind multi-frame super-resolution (SR) model based on mixed Poisson–Gaussian noise (MPGSR) is proposed. Poisson noise arises from the stochastic nature of the photon-counting process. Readout noise and reset noise inherent to the readout circuitry can be modeled by an additive Gaussian noise. Therefore, a mixed Poisson–Gaussian noise model is more appropriate for real imaging system. Instead of deriving the data fidelity term from the perspective of error norms and the corresponding influence functions, we address the multi-frame SR problem based on a statistical noise model. The derived objective function is decomposed into sub-functions and solved by the alternating direction method of multipliers (ADMM) algorithm which allows using techniques of constrained optimization. The validation of the proposed MPGSR was performed quantitatively and qualitatively on natural and X-ray images. In comparison to the optimization-based and learning-based state-of-the-art methods, we have demonstrated the feasibility of MPGSR and the significance of applying a more appropriate noise model on the SR image reconstruction.

Probabilistic Graphical Models for Dynamic PET: A Novel Approach to Direct Parametric Map Estimation and Image Reconstruction.

In the context of dynamic emission tomography, the conventional processing pipeline consists of independent image reconstruction of single-time frames, followed by the application of a suitable kinetic model to time-activity curves (TACs) at the voxel or region-of-interest level. Direct 4D positron emission tomography (PET) reconstruction, by contrast, seeks to move beyond this scheme and incorporate information from multiple time frames within the reconstruction task. Established direct methods are based on a deterministic description of voxelwise TACs, captured by the chosen kinetic model, considering the photon counting process the only source of uncertainty. In this paper, we introduce a new probabilistic modeling strategy based on the key assumption that activity time course would be subject to uncertainty even if the parameters of the underlying dynamic process are known. This leads to a hierarchical model that we formulate using the formalism of probabilistic graphical modeling. The inference is addressed using a new iterative algorithm, in which kinetic modeling results are treated as prior expectation of activity time course, rather than as a deterministic match, making it possible to control the trade-off between a data-driven and a model-driven reconstruction. The proposed method is flexible to an arbitrary choice of (linear and nonlinear) kinetic models, it enables the inclusion of arbitrary (sub)differentiable priors for parametric maps, and it is simple to implement. Computer simulations and an application to a real-patient scan show how the proposed method is able to generalize over conventional indirect and direct approaches, providing a bridge between them by properly tuning the impact of the kinetic modeling step on image reconstruction.

A fitting model of the pixel response to monochromatic X-rays in photon counting detectors

We present a simple fitting model for the pixel response to monochromatic X-rays in single photon counting pixelated detectors that takes into account the 2D effects of the charge sharing and of the electronic noise on the photon counting process. It is based only on geometrical and physical parameters such as the pixel size, the charge cloud size at the pixel depth and the total electronic noise of the front-end circuitry. The equations describing the pixel point spread function and the integral pulse height spectrum are derived preserving the genuine 2D nature of the charge collection process. The fitting performances of the model has been assessed on a set of experimental integral pulse height spectra measured with an IBEX photon counting ASIC bonded to a 450μm thick Silicon sensor with 75μm×75μm pixel size, irradiated with monochromatic X-rays in the energy range 6–12.4 keV, with excellent agreement between model and measurement. The actual contributions of the charge sharing and of the electronic noise are identified and estimated. As a possible consequence, the model can be used to predict precisely the behavior of photon counting detection systems as a function of the design parameters.

Belavkin filter for mixture of quadrature and photon counting process with some control techniques

The Belavkin filter for the H-P Schrodinger equation is derived when the measurement process consists of a mixture of quantum Brownian motions and conservation/Poisson process. Higher-order powers of the measurement noise differentials appear in the Belavkin dynamics. For simulation, we use a second-order truncation. Control of the Belavkin filtered state by infinitesimal unitary operators is achieved in order to reduce the noise effects in the Belavkin filter equation. This is carried out along the lines of Luc Bouten. Various optimization criteria for control are described like state tracking and Lindblad noise removal.

Problemy korekcji w hybrydowych pikselowych detektorach promieniowania X

X-ray imaging is widely used in medicine in classic radiography, X-ray computed tomography and structural characterization of materials. X-ray detectors working in single photon counting mode, which register and process each photon separately, become more and more popular due to the possibility of imaging contrast enhancement. This paper presents problems of nonuniformity in imaging using this type of pixel X-ray detectors and methods of its correction. (Correction in hybrid pixel X-ray detectors). Slowa kluczowe: detekcja promieniowania X, hybrydowe detektory promieniowania, detektory pikselowe, algorytmy korekcji

Statistical Based Impulsive Noise Removal in Digital Radiography

A new filter to restore radiographic images corrupted by impulsive noise is proposed. It is based on a switching scheme where all the pulses are first detected and then corrected through a median filter. The pulse detector is based on the hypothesis that the major contribution to image noise is given by the photon counting process, with some pixels corrupted by impulsive noise. Such statistics is described by an adequate mixture model. The filter is also able to reliably estimate the sensor gain. Its operation has been verified on both synthetic and real images; the experimental results demonstrate the superiority of the proposed approach in comparison with more traditional methods.

Statistical Analysis of Sodium Doppler Wind–Temperature Lidar Measurements of Vertical Heat Flux

Abstract A statistical study is presented of the errors in sodium Doppler lidar measurements of wind and temperature in the mesosphere that arise from the statistics of the photon-counting process that is inherent in the technique. The authors use data from the Colorado State University (CSU) sodium Doppler wind-temperature lidar, acquired at a midlatitude site, to define the statistics of the lidar measurements in different seasons under both daytime and nighttime conditions. The CSU lidar measurements are scaled, based on a 35-cm-diameter receiver telescope, to the use of large-aperture telescopes (i.e., 1-, 1.8-, and 3.5-m diameters). The expected biases in vertical heat flux measurements at a resolution of 480 m and 150 s are determined and compared to Gardner and Yang’s reported geophysical values of 2.3 K m s−1. A cross-correlation coefficient of 2%–7% between the lidar wind and temperature estimates is found. It is also found that the biases vary from −4 × 10−3 K m s−1 for wintertime measurements at night with a 3.5-m telescope to −61 K m s−1 for summertime measurements at midday with a 1-m telescope. During winter, at night, the three telescope systems yield biases in their heat flux measurements that are less than 10% of the reported value of the heat flux; and during summer, at night, the 1.8- and 3.5-m systems yield biases in their heat flux measurements that are less than 10% of the geophysical value. While during winter at midday the 3.5-m system yields biases in their heat flux measurements that are less than 10% of the geophysical value, during summer at midday all of the systems yield flux biases that are greater than the geophysical value of the heat flux. The results are discussed in terms of current lidar measurements and proposed measurements at high-latitude sites.

Multispectral fluorescence lifetime imaging by TCSPC

We present a fluorescence lifetime imaging technique with simultaneous spectral and temporal resolution. The technique is fully compatible with the commonly used multiphoton microscopes and nondescanned (direct) detection. An image of the back-aperture of the microscope lens is projected on the input of a fiber bundle. The input of the fiber bundle is circular, and the output is flattened to match the input slit of a spectrograph. The spectrum at the output of the spectrograph is projected on a 16-anode PMT module. For each detected photon, the encoding logics of the PMT module deliver a timing pulse and the number of the PMT channel in which the photon was detected. The photons are accumulated by a multidimensional time-correlated single photon counting (TCSPC) process. The recording process builds up a four-dimensional photon distribution over the times of the photons in the excitation pulse period, the wavelengths of the photons, and the coordinates of the scan area. The method delivers a near-ideal counting efficiency and is capable of resolving double-exponential decay functions. We demonstrate the performance of the technique for autofluorescence imaging of tissue.

Deletion of PsbM in Tobacco Alters the QB Site Properties and the Electron Flow within Photosystem II

Photosystem II, the oxygen-evolving complex of photosynthetic organisms, includes an intriguingly large number of low molecular weight polypeptides, including PsbM. Here we describe the first knock-out of psbM using a transplastomic, reverse genetics approach in a higher plant. Homoplastomic Delta psbM plants exhibit photoautotrophic growth. Biochemical, biophysical, and immunological analyses demonstrate that PsbM is not required for biogenesis of higher order photosystem II complexes. However, photosystem II is highly light-sensitive, and its activity is significantly decreased in Delta psbM, whereas kinetics of plastid protein synthesis, reassembly of photosystem II, and recovery of its activity are comparable with the wild type. Unlike wild type, phosphorylation of the reaction center proteins D1 and D2 is severely reduced, whereas the redox-controlled phosphorylation of photosystem II light-harvesting complex is reversely regulated in Delta psbM plants because of accumulation of reduced plastoquinone in the dark and a limited photosystem II-mediated electron transport in the light. Charge recombination in Delta psbM measured by thermoluminescence oscillations significantly differs from the 2/6 patterns in the wild type. A simulation program of thermoluminescence oscillations indicates a higher Q(B)/Q(-)(B) ratio in dark-adapted mutant thylakoids relative to the wild type. The interaction of the Q(A)/Q(B) sites estimated by shifts in the maximal thermoluminescence emission temperature of the Q band, induced by binding of different herbicides to the Q(B) site, is changed indicating alteration of the activation energy for back electron flow. We conclude that PsbM is primarily involved in the interaction of the redox components important for the electron flow within, outward, and backward to photosystem II.

A transmission scheme for PPM-OCDMA systems in which the transmitted symbols are embedded in the desired user's weighted positions

We propose a transmission scheme designed to increase the number of subscribers without degradation of the bit error probability in an embedded transmission method for optical code division multiple access (OCDMA) with pulse position modulation signaling (PPM). In the conventional scheme, the transmission symbols and their slot positions are embedded in the desired user's weighted positions in M-ary PPM-OCDMA. However, in the proposed scheme, only the transmission symbols are embedded in the desired user's weighted positions. We analyze the bit error rate (BER) of the proposed scheme for a Poisson photon counting process. We show that the proposed scheme can increase the number of simultaneous users compared to the conventional scheme while achieving a BER of ≤10−9 and keeping the information rate constant. © 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 89(10): 55–65, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.20224

Theory of single molecule line shapes of multichromophoric macromolecules

A theoretical framework is developed for the line shapes of the single molecule spectroscopy (SMS) of multichromophoric macromolecules by combining the Hamiltonian-based line shape theory with a kinetic equation formulation of single molecule photon counting processes. The theory allows a consistent treatment of two different line broadening mechanisms, one originating from the fast quantum dynamical degrees of freedom and the other originating from slow stochastic fluctuations that can be substantial within the SMS measurement time scale. A general expression is derived for the photon counting probability, which enables simulation of SMS line shape as an average over a renewal process and makes it possible to study the effects of radiation induced fluctuations. Then conditions are clarified under which the line shape reduces to a simple average over the distribution function of slow fluctuations. Model calculations for a bichromophoric system illustrate the subtle interplay between the fast and slow line broadening mechanisms.

A new measure of xenobiotic toxicity to the first-line human defence system from the time-resolved phagocyte luminescence

A new measure of toxicity based on stochastic modelling of single photon-counting processes, representing time-resolved phagocyte luminescence of xenobiotic-perturbed human neutrophils, has been constructed. The stochastic measure of toxicity has been verified by the QSAR method, and then compared and contrasted with the traditional toxicity measure used in bio- and chemiluminescent research. Phenol and benzene homologues were chosen as perturbers due to their importance from the viewpoint of ecotoxicology and occupational medicine.

Quantum jumps in hydrogenlike systems.

In this paper it is shown that the Lyman-$\alpha$ transition of a single hydrogen-like system driven by a laser exhibits macroscopic dark periods, provided there exists an additional constant electric field. We describe the photon-counting process under the condition that the polarization of the laser coincides with the direction of the constant electric field. The theoretical results are given for the example of $^4{He}^+$. We show that the emission behavior depends sensitively on the Lamb shift (W.E. Lamb, R.C. Retherford, Phys. Rev. 72, 241 (1947)) between the $2s_{1/2}$ and $2p_{1/2}$ energy levels. A possibly realizable measurement of the mean duration of the dark periods should give quantitative information about the above energy difference by using the proposed photon-counting process.

Electron counting probability

The probability distribution of n electrons being registered by an electron counter during a time t is calculated by using a model similar to the Srinivas and Davies model of photon counting processes. The result shows that whenever electron propagation is described by a free Hamiltonian, the statistics of the electron numbers recorded by the counter follows the sub-Poissonian distribution. This distribution is independent of the initial state of the electrons. The second-order coherence in the results of the two-counter measurement reflects the antibunching correlation of the electrons.