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A position-sensitive germanium detector for gamma-ray astronomy

The critical problem in high-resolution cosmic gamma-ray spectroscopy in the energy range from 0.02 to 10 MeV is the limited spectral sensitivity of the detectors used. This results from the small effective area of the detectors and the high background noise due to induced radioactivity and scattering in the detectors' high-energy particle environment. The effective area can be increased by increasing the number of detectors, but this becomes prohibitive because of the size and expense of the resulting instrument. We have taken a new approach: a segmented large-volume germanium gamma-ray detector which can effectively discriminate against internal background yet maintain the high spectral resolution and efficiency of conventional coaxial Ge detectors. To verify this concept, a planar detector divided into two segments has been fabricated and laboratory measurements agree well with Monte Carlo calculations. A large coaxial detector which will be divided into five segments is being built using the techniques developed for the planar detector. Monte Carlo calculations show that the sensitivity (minimum detectable flux) of the segmented coaxial detector is a factor of 2-3 better than conventional detectors because of the reduction in the internal background.

Varnell, L. S.

Characteristics of capacitor-type micrometeoroid flux detectors when impacted with simulated micrometeoroids

A series of impact tests are described and data presented which characterize the operation of the capacitor-type micrometeoroid flux detectors used on the Meteoroid Technology Satellite (MTS). Capacitor-type detectors with silicon dioxide dielectric thickness of 0.4 and 1.0 microns were tested in the micrometeoroid impact simulator at the Langley Research Center, a 4-MV Van de Graaff electrostatic accelerator. The carbonyl iron projectiles were from 0.5 to 5.0 microns in diameter with velocities from 4 to 10.0 km/sec. The detector bias voltage was varied from -20 to -60 V; some tests were at detector temperatures of 90 C to -100 C; and the angle of impact varied from 0 deg to 75 deg from the normal to the detector. These tests showed that: (1) the detector operation is reliable when the bias voltage is greater than 30 V; (2) after an impact the detector returns to its original condition with an insignificant loss of active area; and (3) the sensitivity of the detector is inversely proportional to the detector thickness. The test results suggest a theoretical model in which the signal is an arc triggered by the impacting projectile, and the detector bias voltage must be high enough to insure that an arc will form.

Kassel, P. C., Jr.

A novel electron tunneling infrared detector

The pneumatic infrared detector, originally developed by Golay in the late 1940s, uses the thermal expansion of one cm(exp 3) of xenon at room temperature to detect the heat deposited by infrared radiation. This detector was limited by thermal fluctuations within a 10 Hz bandwidth, but suffered from long thermal time constants and a fragile structure. Nevertheless, it represents the most sensitive room temperature detector currently available in the long wavelength infrared (LWIR). Fabrication of this type of detector on smaller scales has been limited by the lack of a suitably sensitive transducer. Researchers designed a detector based on this principle, but which is constructed entirely from micromachined silicon, and uses a vacuum tunneling transducer to detect the expansion of the trapped gas. Because this detector is fabricated using micromachining techniques, miniaturization and integration into one and two-dimensional arrays is feasible. The extreme sensitivity of vacuum tunneling to changes in electrode separation will allow a prototype of this detector to operate in the limit of thermal fluctuations over a 10 kHz bandwidth. A calculation of the predicted response and noise of the prototype is presented with the general formalism of thermal detectors. At present, most of the components of the prototype have been fabricated and tested independently. In particular, a characterization of the micromachined electron tunneling transducer has been carried out. The measured noise in the tunnel current is within a decade of the limit imposed by shot noise, and well below the requirements for the operation of an infrared detector with the predicted sensitivity. Assembly and characterization of the prototype infrared detector will be carried out promptly.

Kenny, T. W.

Plural-wavelength flame detector that discriminates between direct and reflected radiation

A flame detector employs a plurality of wavelength selective radiation detectors and a digital signal processor programmed to analyze each of the detector signals, and determine whether radiation is received directly from a small flame source that warrants generation of an alarm. The processor's algorithm employs a normalized cross-correlation analysis of the detector signals to discriminate between radiation received directly from a flame and radiation received from a reflection of a flame to insure that reflections will not trigger an alarm. In addition, the algorithm employs a Fast Fourier Transform (FFT) frequency spectrum analysis of one of the detector signals to discriminate between flames of different sizes. In a specific application, the detector incorporates two infrared (IR) detectors and one ultraviolet (UV) detector for discriminating between a directly sensed small hydrogen flame, and reflections from a large hydrogen flame. The signals generated by each of the detectors are sampled and digitized for analysis by the digital signal processor, preferably 250 times a second. A sliding time window of approximately 30 seconds of detector data is created using FIFO memories.

Hall, Gregory H.

Superconducting Detectors Come of Age, or Ready to Leave the Lab

Cryogenically cooled superconducting detectors have become essential tools for a wide range of measurement applications, ranging from quantum limited heterodyne detection in the millimeter range to direct searches for dark matter with superconducting phonon detectors operating at 20 mK. Superconducting detectors have several fundamental and practical advantages which have resulted in their rapid adoption by experimenters. Their excellent performance arises in part from reductions in noise resulting from their low operating temperatures, but unique superconducting properties provide a wide range of mechanisms for detection. For example, the steep dependence of resistance with temperature on the superconductor normal transition provides a sensitive thermometer for calorimetric and bolometric applications. Parametric changes in the properties of superconducting resonators provide a mechanism for high sensitivity detection of submillil.neter photons. From a practical point of view, the use of superconducting detectors has grown rapidly because many of these devices couple well to SQUID amplifiers, which are easily integrated with the detectors. These SQUID-based amplifiers and multiplexers have matured with the detectors; they are convenient to use, and have excellent noise performance. The first generation of fully integrated large-scale superconducting detection systems is now being deployed. Improved understanding of the operation of these detectors, combined with rapidly improving fabrication techniques, is quickly expanding the capability of these detectors. I will review the development and application of superconductor-based detectors, the ultimate limits to their performance, and consider prospects for their future applications. Continued advances promise to enable important new measurements in physics, and with appropriate advances in cryogenic infrastn~cturem, ay result in the use of these detectors in everyday monitoring applications.

Moseley, Samuel H.

Microwave Kinetic Inductance Detector with Selective Polarization Coupling

A conventional low-noise detector requires a technique to both absorb incident power and convert it to an electrical signal at cryogenic temperatures. This innovation combines low-noise detector and readout functionality into one device while maintaining high absorption, controlled polarization sensitivity, and broadband detection capability. The resulting far-infrared detectors can be read out with a simple approach, which is compact and minimizes thermal loading. The proposed microwave kinetic inductance detector (MKID) consists of three basic elements. The first is the absorptive section in which the incident power is coupled to a superconducting resonator at far-infrared frequency above its superconducting critical frequency (where superconductor becomes normal conductor). This absorber's shape effectively absorbs signals in the desired polarization state and is resonant at the radio frequency (RF) used for readout of the device. Control over the metal film used in the absorber allows realization of structures with either a 50% broadband or 100% resonance absorptance over a 30% fractional bandwidth. The second element is a microwave resonator - which is realized from the thin metal films used to make the absorber as transmission lines - whose resonance frequency changes due to a variation in its kinetic inductance. The resonator's kinetic inductance is a function of the power absorbed by the device. A low-loss dielectric (mono-crystalline silicon) is used in a parallel-plate transmission line structure to realize the desired superconducting resonators. There is negligible coupling among the adjacent elements used to define the polarization sensitivity of each detector. The final component of the device is a microwave transmission line, which is coupled to the resonator, and allows detection of changes in resonance frequency for each detector in the focal plane array. The spiral shape of the detector's absorber allows incident power with two polarizations to couple to the detector equally. A stepped impedance resonator was used that allows the incident power absorbed in the detecting membrane area to be uniformly distributed in the detector's transmission line at the RF readout frequency. This maximizes the sensitivity of the detector. The signal is read out via a frequency multiplexing technique that requires a minimum number of interface transmission lines for readout. This reduces the packaging complexity and coupling to the device's thermal environment.

Wollack, Edward

Snowballs in Euclid and WFIRST Detectors

Snowballs are transient events observed in HgCdTe detectors with a sudden increase of charge in a few pixels. They appear between consecutive reads of the detector, after which the affected pixels return to their normal behavior. The origin of the snowballs is unknown, but it was speculated that they could be the result of alpha decay of naturally radioactive contaminants in the detectors, but a cosmic ray origin cannot be ruled out. Even though previous studies predicted a low rate of occurrence of these events, and consequently, a minimal impact on science, it is interesting to investigate the cause or causes that may generate snowballs and their impact in detectors designed for future missions. We searched for the presence of snowballs in the dark current data in Euclid and Wide Field Infrared Survey Telescope (WFIRST) detectors tested in the Detector Characterization Laboratory at Goddard Space Flight Center. Our investigation shows that for Euclid and WFIRST detectors, there are snowballs that appear only one time, and others that repeat in the same spatial localization. For Euclid detectors, there is a correlation between the snowballs that repeat and bad pixels in the operational masks (pixels that do not fulfill the requirements to pass spectroscopy noise, photometry noise, quantum efficiency, and/or linearity). The rate of occurrence for a snowball event is about 0.9 snowballs/hr. in Euclid detectors (for the ones that do not have associated bad pixels in the mask), and about 0.7 snowballs/hr. in PV3 Full Array Lot WFIRST detectors.

Astronomy

NIAC Phase-2 Final Report for Astrophysics and Technical Lab Studies of a Solar Neutrino Spacecraft Detector

The Sun provides all the energy that our planet needs for life and has been doing so for five billion years. Understanding our Sun and its interior is one of the major goals of the NASA Science program. Still this is a very difficult task because very little makes it directly out of the Sun’s interior. The energy we see today, that warms the Earth, was made 50,000 to 80,000 years ago and is only now coming to the surface to make light. However, neutrinos penetrate matter almost without interaction and make it to Earth in only eight minutes from creation. Since neutrinos interact only weakly they are hard to detect; never-the-less within the last ten years neutrino detectors on Earth have started to reliably detect neutrinos from the fusion reactions in the interior of the Sun and scientists have started to use this information to investigate the Sun’s nuclear furnace. Changes in solar neutrino flux make it advantageous to take a neutrino detector into space since the solar neutrino intensity changes dramatically as the inverse square of the distance from the Sun, by five orders of magnitude when going from the Earth to the Sun. Launch of a neutrino detector into space toward the Sun will: a) aim to significantly increase the neutrino flux 10,000x allowing for a smaller detector which improves detector energy resolution and performance, b) attempt to completely eliminate background terrestrial neutrino sources for improved measurement accuracy, and c) conduct unique science experiments near the Sun not achievable with much larger detectors on the Earth. NASA's interest in deep space exploration has been a key factor in its unmanned spacecraft development and launch of exploration science satellites and spacecraft. NASA has done exceptional experiments in space where science benefits from the unique platform of spacecraft that provides unprecedented views. For example, the Hubble Space Telescope is really a small and very common instrument, but when it is put into an orbit high above the Earth, it becomes one of the most powerful optical observatories man has ever made. Moving neutrino observations to space is the next obvious step. The concept of putting a neutrino detector in close orbit of the sun is completely unexplored and innovative. Its scientific return is to vastly enhance the understanding of the solar interior which is a NASA major goal as stated in the decadal survey. Preliminary calculations show that such a spacecraft if properly shielded, can operate in this environment both taking data of neutrino interactions which can be distinguished from random background rates of solar Electromagnetic emissions, Galactic charged cosmic-ray, and gamma-rays by using a double pulsed signature. The NIAC Phase-1 simulations have shown this idea to be very successful in eliminating background and identifying the neutrino interaction signal, hence this spacecraft detector concept once demonstrated to be Technical Readiness Level 7 and flight mission-ready would enable a whole new type of mission to explore and study our Sun, in details that could neither be done with the largest neutrino detectors on Earth nor other types of space-craft measurements that are not using neutrino detection. Our goal in this NIAC Phase-2 was to take the detector simulation ideas and construct a prototype for testing in the lab with tagged sources to evaluate and demonstrate that the performance in the simulations are borne out by a prototype.

Neutrino

Calibration of a broadband x-ray crystal spectrometer using a continuum x-ray source and photon-counting detectors

We report measurements of sensitivity of a broadband (≃20–30 keV) x-ray crystal spectrometer using a bremsstrahlung continuum x-ray source and several detectors, including an energy-discriminating photon-counting point detector (Si drift diode, Amptek Inc.), imaging hybrid photon-counting detectors (Eiger2-Si and Eiger2-CdTe, DECTRIS Ltd.), and image plates (SR type). Sensitivity is defined as a ratio of the crystal-reflected energy-position-dispersed spectrum measured by a given detector to the incident non-dispersed spectrum measured using the energy-discriminating point detector. The sensitivity derived from data measured exclusively by the point detector is considered detector-independent and serves as a reference. The sensitivities derived from data collected with the hybrid photon-counting detectors were matched to the reference using a scale factor of 1.05. The image plate-derived sensitivities required a scale factor of 1.16 to match the reference. Furthermore, the resulting mismatch in the shapes of all measured scaled sensitivities in the range of the spectrometer was ≲±10%, while the mismatch between the shapes of the sensitivities corresponding to the Si-based detectors was ≲±2.5%.

Crystal optics

Fine-tuning machine-learned particle-flow reconstruction for new detector geometries in future colliders

We demonstrate transfer learning capabilities in a machine-learned algorithm trained for particle-flow reconstruction in high energy particle colliders. This paper presents a cross-detector fine-tuning study, where we initially pretrain the model on a large full simulation dataset from one detector design, and subsequently fine-tune the model on a sample with a different collider and detector design. Specifically, we use the Compact Linear Collider detector (CLICdet) model for the initial training set and demonstrate successful knowledge transfer to the CLIC-like detector (CLD) proposed for the Future Circular Collider in electron-positron mode. We show that with an order of magnitude less samples from the second dataset, we can achieve the same performance as a costly training from scratch, across particle-level and event-level performance metrics, including jet and missing transverse momentum resolution. Furthermore, we find that the fine-tuned model achieves comparable performance to the traditional rule-based particle-flow approach on event-level metrics after training on 100,000 CLD events, whereas a model trained from scratch requires at least 1 million CLD events to achieve similar reconstruction performance. To our knowledge, this represents the first full-simulation cross-detector transfer learning study for particle-flow reconstruction. These findings offer valuable insights towards building large foundation models that can be fine-tuned across different detector designs and geometries, helping to accelerate the development cycle for new detectors and opening the door to rapid detector design and optimization using machine learning.

43 PARTICLE ACCELERATORS

Single channel PICOSEC Micromegas detector with improved time resolution

This paper presents design guidelines and the experimental verification of a single-channel PICOSEC Micromegas (MM) detector with an improved time resolution. The design encompasses the detector board, vessel, auxiliary mechanical parts, and electrical connectivity for high voltage (HV) and signals, focusing on improving the stability, reducing noise, and ensuring signal integrity to optimize timing performance. A notable feature is the simple and fast reassembly procedure, facilitating quick replacement of the detector internal components that allows for an efficient measurement strategy involving different detector components. The paper also examines the influence of parasitic capacitance and inductance on the output signal integrity. To validate the design, a prototype assembly and three interchangeable detector boards with varying readout pad diameters were manufactured. Detectors were initially tested in the laboratory. Finally, the timing performance of the detectors with different pad sizes was verified using 150 GeV muons. Notably, a record time resolution for a PICOSEC Micromegas detector technology with a CsI photocathode of 12.5 ± 0.8 ps was achieved for a detector with 10 mm diameter readout pad size.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND

A new neutron time-of-flight detector for yield and ion-temperature measurements in DT implosions on OMEGA

A new neutron time-of-flight (nTOF) detector for yield and ion-temperature measurements in deuterium–tritium (DT) implosions was designed, installed, and calibrated on the OMEGA Laser System. This detector was installed at θ = 46.8° from the vertical and φ = 84.9°, previously a region without other detectors, in order to decrease the uncertainty of low-mode asymmetry measurements by six other nTOF detectors. The new nTOF detector uses the “PMT only” concept [Glebov et al., Rev. Sci. Instrum. 92, 013509 (2021)] and consists of a Photek photomultiplier tube (PMT)-110 in a thin aluminum housing. There is no lead shielding in front of the PMT to allow measurements of the x-ray instrument response function of the detector. The detector is installed in the OMEGA H2-port line of sight at 9.3 m from the target chamber center in the OMEGA Target Bay and is called the H2 nTOF detector. The H2 nTOF measures DT yields in the 1 × 10 13 to 3 × 10 14 range and ion temperatures from 2 to 12 keV. H2 nTOF reduced the hotspot flow uncertainty in the z-direction from ±10 to ±8 km/s, and the uncertainty in the anisotropic flow axis from σ θ = ±26° to ±13° and σ φ = ±25° to ±21°. Here, the design details, performance, and calibration results of the H2 nTOF detector in DT implosions on OMEGA will be presented.

Laser fusion

First demonstration of a TES based cryogenic Li 2 MoO 4 detector for neutrinoless double beta decay search

Cryogenic calorimetric experiments to search for neutrinoless double-beta decay (0vββ) are highly competitive, scalable and versatile in isotope. The largest planned detector array, CUPID, is comprised of about 1500 individual Li 2 100 MoO 4 detector modules with a further scale up envisioned for a follow up experiment (CUPID-1T). In this article, we present a novel detector concept targeting this second stage with a low impedance TES based readout for the Li 2 MoO 4 absorber that is easily mass-produced and lends itself to a multiplexed readout. We present the detector design and results from a first prototype detector operated at the NEXUS shallow underground facility at Fermilab. The detector is a 2-cm-side cube with 21 g mass that is strongly thermally coupled to its readout chip to allow rise-times of ~0.5 ms. This design is more than one order of magnitude faster than present NTD based detectors and is hence expected to effectively mitigate backgrounds generated through the pile-up of two independent two neutrino decay events coinciding close in time. Together with a baseline resolution of 1.95 keV (FWHM) these performance parameters extrapolate to a background index from pile-up as low as 5 • 10 –6 counts/keV/kg/yr in CUPID size crystals. The detector was calibrated up to the MeV region showing sufficient dynamic range for 0vββ searches. In combination with a SuperCDMS HVeV detector this setup also allowed us to perform a precision measurement of the scintillation time constants of Li 2 MoO 4 , which showed a primary component with a fast O(20 μs) time scale. Similar content being viewe

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND

Advancing Detector R&D for High-Pressure Gaseous Argon TPCs in Precision Neutrino Physics

High-pressure gaseous argon time projection chambers (HPgTPCs) represent an emerging detector paradigm for neutrino physics, combining increased target density with the intrinsic tracking and low thresholds of gaseous detectors. This approach enables detailed reconstruction of exclusive final states, improved particle identification, and sensitivity to low-energy and rare processes — capabilities that are increasingly central to precision oscillation measurements and searches for beyond-the-Standard-Model signatures. This abstract presents an overview of ongoing detector R&D toward high-pressure gaseous argon TPC operation, with emphasis on micro-pattern gas detector (MPGD) charge amplification in argon-based mixtures. We report experimental characterization of triple-GEM structures at pressures relevant for neutrino applications, including studies of multiplication factor scaling, stability, and operational voltage envelopes across gas admixtures. Measurements performed at the TOAD and GORG test stands at Fermilab help define viable amplification and electronics noise regimes in conditions where higher density imposes stricter constraints on signal formation. These results provide essential input to the optimization of high-pressure gaseous argon detectors for future neutrino experiments, including near-detector concepts such as ND-GAr in DUNE Phase II near detector upgrade. More broadly, this program shows how dedicated detector R&D can expand the precision frontier in neutrino physics by enabling complementary reconstruction capabilities beyond conventional detectors.

McConnell, Brenna [Indiana U.] (ORCID:000900041138

High-spatial resolution and high-spectral resolution detector for use in the measurement of solar flare hard X-rays

In the areas of high spatial resolution, the evaluation of a hard X-ray detector with 65 micron spatial resolution for operation in the energy range from 30 to 400 keV is proposed. The basic detector is a thick large-area scintillator faceplate, composed of a matrix of high-density scintillating glass fibers, attached to a proximity type image intensifier tube with a resistive-anode digital readout system. Such a detector, combined with a coded-aperture mask, would be ideal for use as a modest-sized hard X-ray imaging instrument up to X-ray energies as high as several hundred keV. As an integral part of this study it was also proposed that several techniques be critically evaluated for X-ray image coding which could be used with this detector. In the area of high spectral resolution, it is proposed to evaluate two different types of detectors for use as X-ray spectrometers for solar flares: planar silicon detectors and high-purity germanium detectors (HPGe). Instruments utilizing these high-spatial-resolution detectors for hard X-ray imaging measurements from 30 to 400 keV and high-spectral-resolution detectors for measurements over a similar energy range would be ideally suited for making crucial solar flare observations during the upcoming maximum in the solar cycle.

Desai, U. D.

HgCdTe for NASA EOS missions and detector uniformity benchmarks

Important NASA Earth Observing System (EOS) missions, Atmospheric Infrared Sounder (AIRS) and Moderate Resolution Imaging Spectrometer (MODIS-N), which require detector spectral response in the range of 14 to 17 microns at medium background flux levels and operation in the range of temperatures between 65 to 95 K, will be flown beginning in the next few years. Currently, a prime candidate detector technology for these missions is trapping-mode photoconductive HgCdTe devices. These devices can be tailored to the exact cutoff wavelengths required by those missions, and thus offer the performance advantages of an intrinsic detector which is ideally matched to the mission wavelength. Under the long wavelength-background-temperature conditions of these EOS missions, any detector will at best be thermal generation-recombination noise limited. Photoconductive devices are generally preferred under these circumstances, since at elevated temperatures their performance degrades with n(sub i) while for photovoltaic detectors performance degrades as n sub i(exp 2) n sub i is the intrinsic carrier concentration which is a function of alloy composition and temperature, but not doping. Very high performance trapping-mode photoconductive HgCdTe detectors have been developed which can be reproducibly fabricated. Detectivity (D asterisk) at 80K and 16 micron cutoff wavelength in excess of 10(exp 11) Jones has been measured for these devices. Power dissipation is at least two orders of magnitude less than conventional HgCdTe photoconductors - on the order of 0.12 W/cm(exp 2) compared with 12 W/cm(exp 2). EOS missions define thermal noise limited conditions for the long wavelength operating bands. Trapping-mode photoconductive HgCdTe detectors are linear under such conditions and responsivity is independent of background flux. At lower temperatures or high flux conditions in which background flux limits detector performance, trapping-mode detectors have a responsivity which varies with background flux. Internal calibration must be provided for radiometric measurements under the latter conditions (not an EOS mission concern). Liquid phase epitaxy is used to grow these HgCdTe device structures. This technique has been shown to give control of the cutoff wavelength on the order of 16 plus or minus 1 micron or less, both from run to run and across wafer dimensions of several centimeters on a side.

Norton, Paul R.

Characteristics of AlGaAs/GaAs multiple quantum well infrared detectors

Researchers fabricated and characterized several AlGaAs/GaAs multiple quantum well infrared detectors to evaluate the ultimate performance of these devices for low infrared background applications. The detectors were designed to have a single bound state in the quantum well and the first excited state in the continuum above the AlGaAs conduction band edge. The difference in energy between the two levels, as determined by the quantum well width and aluminum mole fraction in the barrier, was chosen such that peak absorption would occur near 8 microns. The initial structures studied comprised 50 periods with 40 A well widths and 300 A Al(0.28)Ga(0.72)As barriers. The performance of these detectors are summarized. To better interpret these results and design optimized detectors, researchers modeled both the detector noise and tunneling currents. The noise model correctly predicts that multiple quantum well detectors will, indeed, exhibit noise lower than full shot noise. The tunneling current model predicts the dark current versus bias for any choice of design parameters in a multiple quantum well detector. This model predicts a substantially reduced dark current (x 10(exp 04)) for samples with 400 A barriers. To evaluate structures with thicker barriers, researchers fabricated and characterized detectors with 400 A and 500 A barriers; a comparison of detector dark currents is shown. These results are consistent with the predictions of the dark current model.

Janousek, Bruce K.

GLAS 532nm Optical Detector

This report documents fabrication and testing of 532nm optical detectors. Testing procedures included 532nm quantum efficiency, detector gain, and photon counting performance, in particular, photon counting efficiency. 532nm quantum efficiency was measured to be 36% to 39% for the detectors fabricated. Detectors with a GaAs APD anode had measured gains of 12,000 to 15,000 maximum. Photon counting efficiency for the detector with an APD anode was measured to be approximately 80% with a detector gain of 11,000. Measurements made on an identical detector, not fabricated under this contract, had a photon counting efficiency exceeding 90% with a gain of 13,000. A formula is derived in which the photon counting efficiency is determined by the system preamp noise and the peak single photon pulse height which is proportional to detector gain. This formula agrees well with the measured results and indicates that a detector gain of 15,000 is sufficient to provide a counting efficiency of 99.6%.

LaRue, Ross A.