Low Photon Count Research Articles

Analysis of Energy Spectra with Low Photon Counts via Bayesian Posterior Simulation

Over the past 10 years Bayesian methods have rapidly grown more popular as several computationally intensive statistical algorithms have become feasible with increased computer power. In this paper, we begin with a general description of the Bayesian paradigm for statistical inference and the various state-of-the-art model fitting techniques that we employ (e.g., Gibbs sampler and Metropolis- Hastings). These algorithms are very flexible and can be used to fit models that account for the highly hierarchical structure inherent in the collection of high-quality spectra and thus can keep pace with the accelerating progress of new space telescope designs. The methods we develop, which will soon be available in the CIAO software package, explicitly model photon arrivals as a Poisson process and, thus, have no difficulty with high resolution low count X-ray and gamma-ray data. We expect these methods to be useful not only for the recently launched Chandra X-ray observatory and XMM but also new generation telescopes such as Constellation X, GLAST, etc. In the context of two examples (Quasar S5 0014+813 and Hybrid-Chromosphere Supergiant Star alpha TrA) we illustrate a new highly structured model and how Bayesian posterior sampling can be used to compute estimates, error bars, and credible intervals for the various model parameters.

CHEST WALL THICKNESS MEASUREMENTS OF THE LLNL PHANTOM FOR SMALL AREA GERMANIUM DETECTOR COUNTING

The Lawrence Livermore National Laboratory (LLNL) phantom was developed to calibrate lung counting systems that are used to estimate plutonium and other low energy photon emitting radionuclides deposited in the lung. Originally, low energy photon counting systems consisted of sodium iodide or phoswich detectors, but they have been largely replaced by smaller germanium detector arrays. The average chest wall thicknesses of the LLNL phantom's torso plate and its overlay plates provided by the manufacturer refer to the regions covered by phoswich detectors; however, germanium detectors are of a different size and are placed in different locations on the phantom's torso plate. Previous work has shown that the manufacturer's data were not applicable for large area germanium detectors. The lung counting system at the Korea Atomic Energy Institute (KAERI) is a small area germanium detector array. Although the detectors are placed within the phoswich circles, only about 25% of the area is covered by the detectors. The LLNL phantom at KAERI has been examined to determine if the manufacturer's data are valid or if new chest wall thickness values must be determined. This paper presents chest wall thickness data for the LLNL phantom with and without its B-series overlay plates at 17 keV, 60 keV, 200 keV, and 1,500 keV and shows that these values are different from the manufacturer's values.

The Sun as an X‐Ray Star. I. Deriving the Emission Measure Distribution versus Temperature of the Whole Solar Corona from theYohkoh/Soft X‐Ray Telescope Data

The scope of this work is to obtain the emission measure distributions versus temperature, EM(T ), of the whole solar corona from Yohkoh Soft X-ray Telescope images. As discussed in Paper II, the EM(T ) is our starting point for studying the Sun as an X-ray star. To this purpose, we need to extract as much information as possible from the Yohkoh/SXT data covering the whole range of the Yohkoh/SXT tem- perature sensitivity, i.e., 5.5 log T (K) 8. In particular at low photon counts and temperatures below 106 K, errors on the temperature and emission measure determination are expected to be large. To this end, we have made an extensive set of simulations to explore the nominal performance of the entire system (instrument and data analysis system) in the determination of the plasma temperature and emis- sion measure at low, intermediate, and high photon counts per pixel. We have shown that low-count data with a number of photons per pixel are aUected by large errors and lead to the deriva- n phot 10 tion of an unrealistic EM(T ) characterized by a steep negative slope. As a result, we have devised an analysis method that minimizes the instrumental and statistical eUects on the determination of EM(T ) and allows us to determine the global coronal EM(T ). As a —rst application to real SXT data, we have derived the EM(T ) of the Sun close to the maximum of the solar cycle, a challenging case. The low- temperature part is in agreement with analogous studies made in the UV band, and it shows a well- de—ned maximum at T D 2 MK. Subject headings: Sun: activitySun: coronaSun: X-rays, gamma rays

Ultrasound guided I–125 permanent prostate implants: seed calibration and radiation exposure levels

Purpose: (1) To present data on I–125 seed calibration in a clinical setting so that reasonable tolerance levels can be set for the discrepancy in seed strength between manufacturer specified value and institution measured value; (2) To present data on measured exposure rates and estimate radiation exposure levels associated with I–125 prostate implants.Methods and Materials: Ten percent of each batch for 50 batches of I–125 seeds were calibrated using an HDR 1000 PLUS well chamber with a single source holder. Exposure rates due to I–125 were measured by survey meters with a scintillation probe designed for low energy photon counting, as well as a survey meter of the ionization chamber type. Exposure rates of an unshielded I–125 seed, a needle loaded with three seeds, and 54 prostate implant patients immediately after the implant were obtained.Results: Compared to the manufacturer stated midrange seed strength for a batch of seeds, the average seed strength of sampled seeds had maximum deviations of ±8%, however for 45 out of 50 batches the deviation was less than ±5%. Measured single seed strength deviated up to ±12% from the manufacturer stated midrange value, and between −11% to 7% from the mean of the sampled batch. The exposure rate of a 1.39×107 Bq (0.375 mCi) unshielded I–125 seed was about 1.548×10−8C/kgh (0.06 mR/h) at 1 m, and 1.29×10−6C/kgh (5 mR/h) at 10 cm. For a needle loaded with three seeds, the exposure rate was 1.29×10−8C/kgh (0.05 mR/h) at the handle, and 1.29×10−7C/kgh (0.5 mR/h) along the shaft. For patients implanted with I–125 seeds in the prostate, the average exposure rate was 3.61×10−8C/kgh (0.14 mR/h) at 1m, and 4.13×10−7C/kgh (1.6 mR/h) at the pelvis surface.Conclusions: For the mean seed strength a first action level should be set at a deviation of at least 5% deviation from the manufacturer stated midrange value. For individual seeds, a first action level set at 10% deviation from the manufacturer stated midrange value seems reasonable. A person performing I–125 seed calibration or seed loading could receive up to 0.5 mSv (50 mR) per case to the hands. In the first year following an I–125 prostate implant, the spouse of the patient could receive slightly over 1mSv from the I–125 in the patient. A co-worker should not receive more than 0.5 mSv from the patient.

Chest wall thickness measurements of the LLNL and JAERI torso phantoms for germanium detector counting. Lawrence Livermore National Laboratory and Japanese Atomic Energy Research Institute.

The Lawrence Livermore National Laboratory and Japanese Atomic Energy Research Institute torso phantoms were developed to calibrate lung counting systems that are used to estimate plutonium and other radionuclides deposited in the lung. Originally, low energy photon counting systems consisted of phoswich detectors. The average chest wall thicknesses and individual measurement points of the Lawrence Livermore National Laboratory phantom and its overlay plates in the regions covered by these detectors were provided by the manufacturer. Germanium detectors are of a different size and are placed in different locations on the phantom so that the manufacturer's data are no longer applicable for the locations of the germanium detectors on the phantom. The Human Monitoring Laboratory has re-evaluated the chest wall thickness of both the Lawrence Livermore National Laboratory and Japanese Atomic Energy Research Institute phantoms and their overlay plates for its germanium lung counting system. The measurements were made in the upper right, lower right, upper left, and lower left positions on the phantom's torso plate above the lungs. The effective chest wall thicknesses (17 keV) for the Lawrence Livermore National Laboratory torso plate are 1.46 cm, 1.43 cm, 1.66 cm, 1.48 cm, respectively. The manufacturer's quoted average effective chest wall thickness for a pair of phoswich detectors is 1.63 cm. The measured effective chest wall thicknesses (17 keV) for the JAERI's torso plate are 1.76 cm, 2.15 cm, 1.79 cm, 2.15 cm, respectively. The manufacturer's quoted average chest wall thickness for an unspecified region of the chest is 1.50 cm. This paper presents effective chest wall thickness data for the phantoms with and without their overlay plates at 17 keV, 60 keV, 200 keV and 1,500 keV. The uncertainties involved in determining the effective chest wall thickness have shown that there is no significant difference between the effective chest wall thickness and the physical chest wall thickness.

Estimates of beat to beat handling of activator calcium using measurements of [Ca2+]i in aequorin loaded ferret cardiac muscle.

The aims were (1) to measure simultaneously and on a beat to beat basis intracellular calcium concentration ([Ca2+]i) transients and force transients in isolated ferret cardiac trabeculae; (2) to obtain and compare independent estimates of the recirculating fraction of Ca2+ using the [Ca2+]i data and the force data (recirculating fraction is the fraction of activator Ca2+ taken up by the sarcoplasmic reticulum in each beat and, in the steady state twitch, the fraction of activator Ca2+ released by the sarcoplasmic reticulum); and (3) to estimate the amount of Ca2+ that returns to the sarcoplasmic reticulum and the amount that, during steady state contractions, enters the cytosol, presumably from the extracellular compartment, with each beat. Eight trabeculae were mounted in the myograph. The servo-controlled muscle length was 98% of the length at which developed force was maximal. A modified technique was used for chemical loading of aequorin, and a new method for computer controlled low level photon counting, storage, calibration, and analysis. [Ca2+]i transients and force transients were simultaneously recorded during potentiated beats, together with their respective decays toward control steady state [Ca2+]i transients and force transients. A modified test of postextrasystolic potentiation achieved with a brief train of rapid pacing followed by a pause was used to evoke the potentiated beats. At 2.0 mM extracellular Ca2+ ([Ca2+]o), resting [Ca2+]i was 283(SD 77) nM. The resting tension was 1.6(0.3) g.mm-2. The steady state [Ca2+]i transient and the peak potentiated [Ca2+]i transient averaged 992(165) and 1290(154) nM respectively. The corresponding tensions were 4.0(1.9) and 8.7(3.1) g.mm-2 respectively. The recirculating fraction of Ca2+ calculated from the dissipation of the potentiated [Ca2+]i transient averaged 45(4)%. This recirculating fraction was indistinguishable from the one calculated with another method from the decay of the force potentiation. This is the first study to estimate the recirculating fraction of activator Ca2+ using measurements of [Ca2+]i. The results indicate that over a wide range of [Ca2+]i and tensions the Ca(2+)-force relationship is well approximated by a straight line. At 2.0 mM [Ca2+]o it appears that some 450 nM of Ca2+ recirculates and that a similar amount per steady state beat enters the cytosol, probably from the extracellular compartment.

Beat-to-beat measurements of [Ca2+]i and force in ferret cardiac muscle after chemical loading of aequorin

This communication reports the development of a modified procedure for chemical loading of aequorin in small multicellular cardiac preparations, with special emphasis directed toward the implementation of a new method for computer-controlled low-photon counting and digital processing and analysis of the data to obtain intracellular Ca2+ concentration ([Ca2+]i). In eight ferret right ventricular trabeculae, we measured the mechanical performance and found that, at 1.25 mM extracellular Ca2+ concentration ([Ca2+]o), resting tension, developed tension, and time to peak tension were unchanged by the loading procedure. Estimated resting and peak systolic [Ca2+]i were 299 +/- 65 and 766 +/- 131 nM, respectively. Thirty minutes after raising the [Ca2+]o to 5 mM, there was a robust increase in mechanical performance, with peak systolic [Ca2+]i averaging 1,218 +/- 222 nM. The diastolic [Ca2+]i remained unchanged. In four other trabeculae, exposure to a low-Na(+)-containing superfusate demonstrated a remarkable beat-to-beat correspondence of increases in diastolic [Ca2+]i and resting tensions. The same beat-to-beat concordance was also observed between the rapidly changing amplitudes of peak [Ca2+]i and developed tension. In additional experiments, simultaneous recordings of [Ca2+]i and force transients were obtained during rapid pace pause maneuvers. These studies showed distinct and quantifiable fluctuations of [Ca2+]i in a 1:1 relation to the mechanical record to a frequency of at approximately 300 beats/min. These results demonstrate that beat-to-beat measurements of [Ca2+]i and tension transients can be obtained with good resolution in multicellular cardiac preparations.

Spline function approximation for velocimeter Doppler frequency measurement

A spline function approximation approach for measuring the Doppler spectral peak frequency in a laser Doppler velocimeter system is presented. The processor is designed for signal bursts with mean Doppler shift frequencies up to 100 MHz, input turbulence up to 20%, and photon counts as low as 300. The frequency-domain processor uses a bank of digital bandpass filters for the capture of the energy spectrum of each signal burst. The average values of the filter output energies, as a function of normalized frequency, are modeled as deterministic spline functions which are linearly weighted to evaluate the spectral peak location associated with the Doppler shift. The weighting coefficients are chosen to minimize the mean square error. Performance evaluation by simulation yields average errors in estimating mean Doppler frequencies within 0.5% for poor signal-to-noise conditions associated with a low photon count of 300 photons/burst. >

Optical Ranicon detectors for photon counting imaging. I

We discuss the design and development of Ranicon detectors for optical photon counting imaging on ground-based telescopes. The significant factors which determine the performance of these detectors are found to be the proximity focusing stage, the microchannel-plate stack (MCP), and the signal processing electronics. For applications in optical astronomy, the low photon counting efficiency typically found with optical MCP-based detectors, due to ion barrier films, presents an additional consideration. We review the performance of each stage of the Ranicon detector and the techniques for achieving optimal performance. A new approach to the signal processing electronics reduces nonlinearity, while achieving increased processing speeds and a position error corresponding to <21 μm FWHM. A significant improvement in detector performance is achieved with an advanced Ranicon incorporating a reduced proximity focusing gap and an unfilmed input plate in the MCP stack. The theoretical spatial resolution of both standard and advanced Ranicon designs is derived and compared to the experimentally determined values. For the advanced Ranicon, this spatial resolution is shown to be typically 40 μm FWHM at ∼650 nm. The point spread function of the Ranicon system is shown to be stationary over the active imaging area, principally due to the removal of nonlinearities and noise sources from the signal processing electronics.

Discriminative low energy photon counting for an evaluation of coherent and incoherent scattering by atmospheric environments

“Discriminative low energy photon counting” is proposed to evaluate coherent and incoherent scattering by atmospheric environments. Isotope X-ray sources with decay mode of E.C. and I.T. are chosen for the test sources of monochromatic X-rays. Distance-depending component of the discriminative counting ratio was involved in the incoherent scattering.

Enhancement of low energy photon intensity caused by coherent scattering with collimator

The low energy photon counting rate normalized to the source-detector geometry showed an enhancement in intensities, when the source was placed in the vicinity of the detector. Isotopic X-ray source of known output /93mNb,55Fe and49V/ was used. This enhancement is interpreted to be due, at least, to the occurrence of diffractional coherent scattering with the lead collimator.

Noise in Photon Correlation and Photon Structure Functions

Estimator variances of photon correlation and structure functions can be calculated exactly for gaussian-lorentzian light if the total experimental duration is large compared with the coherence time. For low photon count rates, the correlation function consistently shows the better noise performance. At high mean count rates, the structure function gives the faster estimate, particularly for the high-frequency part of the signal. This suggests the usefulness of photon structure functions for diffusion measurements on highly polydisperse systems.