Quantum theory of an optical maser. 3 - Theory of photoelectron counting statistics
Photoelectron counting statistics produced by fully quantum mechanical laser
Lamb, W. E., Jr.↗
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Dynamical computation of photon correlations and counting statistics
Dynamical computation of photon correlations and counting statistics
PHOTON↗
Quantum theory of an optical maser. III - Theory of photoelectron counting statistics.
Quantum mechanics method for obtaining photocount distribution from optical maser photoelectron counting statistics
Lamb, W. E., Jr.↗
Interpretation of gamma-ray burst source count statistics
Ever since the discovery of gamma-ray bursts, the so-called log N-log S relation has been used for determination of their distances and distribution. This task has not been straightforward because of varying thresholds for the detection of bursts. Most of the current analyses of these data are couched in terms of ambiguous distributions, such as the distribution of Cp/Clim, the ratio of peak to threshold photon count rates, or the distribution of V/Vmax = (Cp/Clim) exp -3/2. It is shown that these distributions are not always a true reflection of the log N-log S relation. Some kind of deconvolution is required for obtaining the true log N-log S. Therefore, care is required in the interpretation of results of such analyses. A new method of analysis of these data is described, whereby the bivariate distribution of Cp and Clim is obtained directly from the data.
Petrosian, Vahe↗
The flat fielding and achievable signal-to-noise of the MAMA detectors
The Space Telescope Imaging Spectrograph (STIS) was designed to achieve a signal-to-noise (S/N) of at least 100:1 per resolution element. Multi-Anode Microchannel Arrays (MAMA) observations during Servicing Mission Orbital Verification (SMOV) confirm that this specification can be met. From analysis of a single spectrum of GD153, with counting statistics of approximately 165 a S/N of approximately 125 is achieved per spectral resolution element in the far ultraviolet (FUV) over the spectral range of 1280A to 1455A. Co-adding spectra of GRW+7OD5824 to increase the counting statistics to approximately 300 yields a S/N of approximately 190 per spectral resolution element over the region extending from 1347A to 1480A in the FUV. In the near ultraviolet (NUV), a single spectrum of GRW+7OD5824 with counting statistics of approximately 200 yields a S/N of approximately 150 per spectral resolution element over the spectral region extending from 2167 to 2520A. Details of the flat field construction, the spectral extraction, and the definition of a spectral resolution element will be described in the text.
Kaiser, Mary Elizabeth↗
Elemental Composition Variations for Large Dusty and Rocky Regions on Mars Using Gamma-Ray Data from the Mars Odyssey Gamma-Ray Spectrometer
The Gamma-Ray Spectrometer (GRS) on the Mars Odyssey spacecraft has been mapping the elemental composition of the surface materials since June 2002. To study elemental composition variations on the martian surface, seven large regions of Mars were selected: three very dusty ones and four mainly rocky ones. Large regions were used to get good counting statistics on as many gamma-ray peaks as possible from spectrum accumulated by the GRS experiment on Mars Odyssey, including elements with poor counting statistics. Data from TES were used to help select these regions. Gamma-ray peaks for several elements were analyzed. Some results and trends are reported.
Evans, L. G.↗
The role of high resolution observations in determining energy release and transport processes
With present observations from the Solar Maximum Mission, we are seeing a very selective sample of spatially large flares in the soft part (10 to 50 keV) of the hard X-ray spectrum. The spatial resolution is at best 5600 km with a corresponding time resolution of 4.5 s for adequate count statistics. This resolution gives rise to the following problems: We cannot resolve the minor radii of the loops involved or tell where and how the energy release occurs. The manner in which loops interact and the relationship between the soft and hard or approx 00 keV) parts of hard X-rays remains elusive. We cannot see how energy propagates in most cases. Thus it is desirable to determine the minimum increase in spatial and temporal resolution required to solve these problems. Spatially we need to resolve the minor radius of a small loop which is about 800 km or 1 arc s. Upper limits to observed speeds of conduction fronts and shocks are approx km/s with theoretical limits running about a factor of 2 higher. Thus, a compatible minimum time resolution is in the range of 0.2 to 0.4 s. With these spatial and temporal resolutions, sufficient count statistics are required to go up to approx 120 keV with a sufficient number of energy bands to obtain spectra.
Smith, D. F.↗
Numerical least-square method for resolving complex pulse height spectra
Linear least-square method resolves complex pulse height spectra, allowing for calculation of relative intensity, of statistical variance based on counting statistics of the correlation between library components, and of the goodness-of-fit chi square. Some applications are to gamma-ray, X ray, and charged-particle spectroscopy.
Schmadebeck, R.↗
Photon counting and Laguerre detection.
In this correspondence maximum-likelihood binary detection theory is applied to an incoherent optical system model employing photodetectors governed by Laguerre counting statistics. It is shown that a maximum-likelihood Laguerre detector corresponds to a count comparison over each signaling interval. Laguerre error probabilities are presented and compared with those for Poisson counting.
Gagliardi, R. M.↗
Comparison of spherical double probe electric field measurements with plasma bulk flows in plasmas having densities less than 1 cm-3
For a three-hour period in the magnetotail over which plasma density varied from less than 0.1 to about 1/cu cm, comparisons of ISEE-1 spherical double probe (dawn to dusk) electric field measurements and ISEE-2 plasma flows (converted to electric fields) show the zero lag cross correlation coefficient between 768 second averages of the two data sets to have been 0.93. A statistical relative uncertainty between pairs of points in the two data sets, estimated by only including counting statistics in the plasma measurement and time variations of the observed electric field over the measurement interval, is able to account for at least 75 percent of the deviations between the two data sets. In agreement with simple Langmuir probe theory, it has been found that the spacecraft potential measured over the three-hour interval by the double probe instrument varied as the log of the product of the plasma density and the square root of the electron temperature.
Mozer, F. S.↗
Avalanche photodiode photon counting receivers for space-borne lidars
Avalanche photodiodes (APD) are studied for uses as photon counting detectors in spaceborne lidars. Non-breakdown APD photon counters, in which the APD's are biased below the breakdown point, are shown to outperform: (1) conventional APD photon counters biased above the breakdown point; (2) conventional APD photon counters biased above the breakdown point; and (3) APD's in analog mode when the received optical signal is extremely weak. Non-breakdown APD photon counters were shown experimentally to achieve an effective photon counting quantum efficiency of 5.0 percent at lambda = 820 nm with a dead time of 15 ns and a dark count rate of 7000/s which agreed with the theoretically predicted values. The interarrival times of the counts followed an exponential distribution and the counting statistics appeared to follow a Poisson distribution with no after pulsing. It is predicted that the effective photon counting quantum efficiency can be improved to 18.7 percent at lambda = 820 nm and 1.46 percent at lambda = 1060 nm with a dead time of a few nanoseconds by using more advanced commercially available electronic components.
Sun, Xiaoli↗
A scanning defect mapping system for semiconductor characterization
We have developed an optical scanning system that generates maps of the spatial distributions of defects in single and polycrystalline silicon wafers. This instrument, called Scanning Defect Mapping System, utilizes differences in the scattering characteristics of dislocation etch pits and grain boundaries from a defect-etched sample to identify and count them. This system simultaneously operates in the dislocation mode and the grain boundary (GB) mode. In the 'dislocation mode,' the optical scattering from the etch pits is used to statistically count dislocations, while ignoring the GB's. Likewise, in the 'grain boundary mode' the system only recognizes the local scattering from the GB's to generate grain boundary distributions. The information generated by this instrument is valuable for material quality control, identifying mechanisms of defect generation and the nature of thermal stresses during the crystal growth, and the solar cell process design.
Sopori, Bushnan L.↗
Mercurian crater-filling classes constrain the emplacement process of the intercrater plains material
The multivariate method for statistical analysis of crater-filling classes, as presently applied to craters of more than 10-km diameter on Mercury, is noted to be superior to current techniques due to the obviation of any amalgamation of data from regions with different histories in order to arrive at the pertinent counting statistics. In this application to the Mercury intercrater plains, the process responsible for emplacement is constrained to be one that leaves the crater class distribution unaltered from that observed on the densely cratered terrain. The analysis explicitly eliminates the viability of the pulse emplacement of volcanics or basin ejecta.
Woronow, Alex↗
Detection and Estimation of an Optical Image by Photon-Counting Techniques
Statistical description of a photoelectric detector is given. The photosensitive surface of the detector is divided into many small areas, and the moment generating function of the photo-counting statistic is derived for large time-bandwidth product. The detection of a specified optical image in the presence of the background light by using the hypothesis test is discussed. The ideal detector based on the likelihood ratio from a set of numbers of photoelectrons ejected from many small areas of the photosensitive surface is studied and compared with the threshold detector and a simple detector which is based on the likelihood ratio by counting the total number of photoelectrons from a finite area of the surface. The intensity of the image is assumed to be Gaussian distributed spatially against the uniformly distributed background light. The numerical approximation by the method of steepest descent is used, and the calculations of the reliabilities for the detectors are carried out by a digital computer.
Wang, Lily Lee↗
Results on the energy dependence of cosmic ray charge composition
Measurements using a balloon-borne ionization spectrometer on the differential energy spectra of the heavy nuclei of the galactic cosmic radiation are reported. The spectra of individual elements up to oxygen and groups of nuclei up through iron were measured up to almost 100 GeV/nucleon. The energy spectrum of the secondary nuclei, B+N, is steeper than that of the primary nuclei, C+O, by gamma = 0.21 + or - .09 in agreement with other authors. The spectral shapes found are reasonably well represented by single power laws between 2 and 60 GeV/nucleon. Data are consistent with the decrease in the secondary to primary ratio found by others above 20 GeV/nucleon, but it shows no evidence for any sudden change in this ratio within counting statistics. The most dramatic finding is that the spectrum of the iron nuclei is flatter than that of the carbon and oxygen nuclei by 0.57 + or - 0.14 of a power. The experimental techniques for charge and energy determination are presented and corrections due to nuclear disintegration and losses of energy out the bottom of the spectrometer are discussed.
Balasubrahmanyan, V. K.↗
Short-term time variability of Cygnus X-1. II
A complete theory for shot-noise analysis is presented. The theory takes into account the effects of counting statistics, time resolution, and finite observing times on the autocorrelation function and on the moments of data assumed to consist of shot noise plus a steady component. When applied to X-ray observations of Cyg X-1 in the high and low states, the results provide evidence that both the typical correlation time (about 0.5 s) and the fraction of flux in shots (about 30%) are constant, independent of the state. The rate of occurrence of the shots may also be constant at approximately one shot per second, a possibility which, if verified, would imply that the principal difference in time variability in the two states is the amplitude of the shots. We also suggest that the occasionally observed large flares may possibly be just the rare superposition of several shots.
Sutherland, P. G.↗
The distribution of titanium on the lunar surface
Titanium concentrations derived from the lunar-orbiting gamma-ray experiment on Apollo 15 and 16 by analyzing a spectral interval in which the titanium signal is relatively enhanced are presented. Landing site soil values provide the reference for a regression curve from which Ti concentrations in 137 regions of adequate counting statistics are calculated. Mare Tranquillitatis contains the highest, and Mare Crisium the lowest Ti concentration, and regional values in the western maria range from 1.1% to 4.1%. Highland Ti concentrations suggest a north-south symmetry which is not consistent with previously reported Fe and Th results. Comparisons with telescopic spectral reflectance studies of the maria do not show complete agreement and suggest that effects due to Fe may not have been fully removed from the reflectance data.
Metzger, A. E.↗
Current NASA studies for a Far Ultraviolent Spectrographic Explorer (FUSE)
The NASA plans for FUSE, a satellite which obtains spectra with resolutions between 100,000 and 100 in the spectral regions from 912 to 1216A and 100 to 912A, are outlined. Scientific problems which can be tackled by FUSE, but not by IUE or the Space Telescope, are discussed. A grazing incidence echelle and a hybrid echelle design are presented. They have high throughput, large simultaneous spectral range, and low background photon counting statistics. The satellite operational organization is similar to that of IUE.
Linsky, J.↗