On the representation of a continuous stochastic intensity by Poisson shot noise
Poisson shot noise process relationship with continuous stochastic intensity as sample function
Gagliardi, R. M.↗
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Sub-Shot Noise Power Source for Microelectronics
Low-current, high-impedance microelectronic devices can be affected by electric current shot noise more than they are affected by Nyquist noise, even at room temperature. An approach to implementing a sub-shot noise current source for powering such devices is based on direct conversion of amplitude-squeezed light to photocurrent. The phenomenon of optical squeezing allows for the optical measurements below the fundamental shot noise limit, which would be impossible in the domain of classical optics. This becomes possible by affecting the statistical properties of photons in an optical mode, which can be considered as a case of information encoding. Once encoded, the information describing the photon (or any other elementary excitations) statistics can be also transmitted. In fact, it is such information transduction from optics to an electronics circuit, via photoelectric effect, that has allowed the observation of the optical squeezing. It is very difficult, if not technically impossible, to directly measure the statistical distribution of optical photons except at extremely low light level. The photoelectric current, on the other hand, can be easily analyzed using RF spectrum analyzers. Once it was observed that the photocurrent noise generated by a tested light source in question is below the shot noise limit (e.g. produced by a coherent light beam), it was concluded that the light source in question possess the property of amplitude squeezing. The main novelty of this technology is to turn this well-known information transduction approach around. Instead of studying the statistical property of an optical mode by measuring the photoelectron statistics, an amplitude-squeezed light source and a high-efficiency linear photodiode are used to generate photocurrent with sub-Poissonian electron statistics. By powering microelectronic devices with this current source, their performance can be improved, especially their noise parameters. Therefore, a room-temperature sub-shot noise current source can be built that will be beneficial for a very broad range of low-power, low-noise electronic instruments and applications, both cryogenic and room-temperature. Taking advantage of recent demonstrations of the squeezed light sources based on optical micro-disks, this sub-shot noise current source can be made compatible with the size/power requirements specific of the electronic devices it will support.
Strekalov, Dmitry V.↗
Effect of Electronic Shot Noise on Dynamic Measurements using Optical Techniques: Examples from Rayleigh Scattering and Unsteady PSP
Electronic shot noise is an unavoidable reality in all optical techniques that depend on measuring light intensity. For steady-state, time-averaged measurements the impact of shot noise can be easily reduced by increasing the exposure time, or by averaging over multiple-exposures. That is not the case for unsteady measurements, where time histories of light intensity variations need to be created either by high-speed photography (unsteady PSP) or via photoelectron counting (spectrally resolved Rayleigh scattering) over short time durations using a photo-multiplier tube (PMT) and photon counting electronics. Electronic shot noise introduces a fixed amount of random error, which can overwhelm the light intensity variation caused by turbulent fluctuations. Spectrum computed from such time series shows a fixed noise floor that is independent of the number of data points in the time series. For a fixed optical system, where the collected power of the luminescent light (uPSP), or the scattered light (Rayleigh) is fixed, one needs to resort to special techniques to obtain enough signal-to noise ratio (SNR). For the uPSP application it is shown that averaging of the adjacent pixels improves SNR; although this may lead to a sacrifice of spatial resolution. A second means is to increase the exposure time, which leads to a lowering of the frequency range. For the Rayleigh application, improvements of SNR can be achieved via two different cross-correlation based approaches. The first involves measuring the light intensity using two PMTs using short, contiguous gates; thereby, creating two time-series of data. The second one involves collecting one long time-series of data using one set of measurement device, followed by an odd-even splitting into two time series. When the two time-series are cross-correlated, and a power spectrum is calculated, a significant reduction in the shot noise floor can be achieved. Examples from measurements of density and velocity fluctuations spectra from two different Rayleigh setup are presented to demonstrate the process.
uPSP↗
Unsteady Pressure-Sensitive-Paint Shot Noise Reduction
In the study of unsteady Pressure-Sensitive Paint (uPSP) image data sets, pixel intensity values collected by Phantom cameras from multiple perspectives are used to calculate the surface pressure of an experimental model. This paper focuses on mitigation of shot noise which is introduced into the image data set by the cameras. Shot noise impacts the quality of data collected, increasing the system error in its pressure value calculations. This paper characterises statistical methods to reduce shot noise within experimental data by taking an average or weighted average across an area of pixels of their respective counts. Each combined-pixel has a higher total effective intensity value and therefore exhibits reduced noise throughout its time history. This is demonstrated by calculating the standard deviations of the combined pixel values through time, which decrease as the combined pixel area increases. Finally, these methods are compared across experimental wind tunnel conditions to examine their effectiveness at different Mach numbers. Ultimately, the results are used to recommend a blur filter type and size which will be applied to the raw image data prior to processing, as well as a minimum camera resolution for future experiments. Downstream of the filter application, the software to convert the 2D image data sets into surface pressure readings on a 3D grid use a ratio of decimation that assigns multiple pixels to each 3D grid node. This decimation ratio will also be aligned with the size of the blur filter, resulting in a more manageable data set size and compromised spatial resolution. Combined with the effect of the blur filter, the resulting pixel intensity readings will exhibit significantly reduced shot noise, reducing the magnitude of uncertainty and error in the final calculated pressure. For future tests, the camera spatial resolution must be sufficient to capture small flow and model features even after the recommended blur filter is applied. The image data set is taken from a uPSP experiment of the Space Launch System Block 1 cargo vehicle model in September 2019.
Lucy Tang↗
Unsteady Pressure-Sensitive Paint (UPSP) Shot Noise Reduction
In the study of unsteady Pressure-Sensitive Paint (uPSP) image data sets, pixel intensity values collected by Phantom cameras from multiple perspectives are used to calculate the surface pressure of an experimental model. This paper focuses on mitigation of shot noise which is introduced into the image data set by the cameras. Shot noise impacts the quality of data collected, increasing the system error in its pressure value calculations. This paper characterises statistical methods to reduce shot noise within experimental data by taking an average or weighted average across an area of pixels of their respective counts. Each combined-pixel has a higher total effective intensity value and therefore exhibits reduced noise throughout its time history. This is demonstrated by calculating the standard deviations of the combined pixel values through time, which decrease as the combined pixel area increases. Finally, these methods are compared across experimental wind tunnel conditions to examine their effectiveness at different Mach numbers. Ultimately, the results are used to recommend a blur filter type and size which will be applied to the raw image data prior to processing, as well as a minimum camera resolution for future experiments. Downstream of the filter application, the software to convert the 2D image data sets into surface pressure readings on a 3D grid use a ratio of decimation that assigns multiple pixels to each 3D grid node. This decimation ratio will also be aligned with the size of the blur filter, resulting in a more manageable data set size and compromised spatial resolution. Combined with the effect of the blur filter, the resulting pixel intensity readings will exhibit significantly reduced shot noise, reducing the magnitude of uncertainty and error in the final calculated pressure. For future tests, the camera spatial resolution must be sufficient to capture small flow and model features even after the recommended blur filter is applied. The image data set is taken from a uPSP experiment of the Space Launch System Block 1 cargo vehicle model in September 2019.
Lucy Tang↗
Shot noise limits to sensitivity of optical interferometry
By arguing that the limiting noise is the photoelectron shot noise, we show that the sensitivity of image synthesis by an ideal optical interferometer is independent of the details of beam-splitting and recombination. The signal-to-noise ratio of the synthesized image is proportional to the square root of the total number of photoelectrons detected by the entire array. For non-ideal interferometers, which are forced to employ a closure-phase method of indirect inference of the visibility data, essentially the same result holds for strong sources, but at weak light levels beam-splitting degrades sensitivity.
Prasad, Sudhakar↗
Shot noise in the Lagrangian one-dimensional model
Shot noise in one-dimensional planar Lagrangian computer simulation of electron diode
DIODE↗
Shot noise limited detection of OH using the technique of laser induced fluorescence
Nearly shot-noise limited detection of OH using the technique of laser-induced fluorescence is reported. A LIDAR configuration is used to excite fluorescence in a large volume and a narrow-bandwidth interference filter provides spectral discrimination. This arrangement alleviates the effect of ozone interference and facilitates image processing at relatively close distances. The detection limit is determined mainly by the shot-noise of the solar background. Ground-based measurements in Dearborn indicate a detection limit of better than 1 x 10 to the 6th power OH/cubic cm over a forty-minute acquisition period. Under favorable conditions, a comparable detection limit was also observed for airborne measurements.
Bakalyar, D. M.↗
Estimating Random Errors Due to Shot Noise in Backscatter Lidar Observations
In this paper, we discuss the estimation of random errors due to shot noise in backscatter lidar observations that use either photomultiplier tube (PMT) or avalanche photodiode (APD) detectors. The statistical characteristics of photodetection are reviewed, and photon count distributions of solar background signals and laser backscatter signals are examined using airborne lidar observations at 532 nm using a photon-counting mode APD. Both distributions appear to be Poisson, indicating that the arrival at the photodetector of photons for these signals is a Poisson stochastic process. For Poisson-distributed signals, a proportional, one-to-one relationship is known to exist between the mean of a distribution and its variance. Although the multiplied photocurrent no longer follows a strict Poisson distribution in analog-mode APD and PMT detectors, the proportionality still exists between the mean and the variance of the multiplied photocurrent. We make use of this relationship by introducing the noise scale factor (NSF), which quantifies the constant of proportionality that exists between the root-mean-square of the random noise in a measurement and the square root of the mean signal. Using the NSF to estimate random errors in lidar measurements due to shot noise provides a significant advantage over the conventional error estimation techniques, in that with the NSF uncertainties can be reliably calculated from/for a single data sample. Methods for evaluating the NSF are presented. Algorithms to compute the NSF are developed for the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) lidar and tested using data from the Lidar In-space Technology Experiment (LITE). OCIS Codes:
Liu, Zhaoyan↗
Effects of photon bunching on shot noise in photoelectric detection.
Photon bunching effects on shot noise power in photoelectric detection, noting case of superposed coherent and chaotic incident radiation
Lachs, G.↗
Sub-Poissonian light and photocurrent shot-noise suppression in closed opto-electronic loop
We examine experimentally photocurrent noise reduction in the opto-electronic closed loop. Photocurrent noise density 12.5 dB below the shot-noise was observed. So large suppression was not reached in previous experiments and cannot be explained in terms of an ordinary sub-Poissonian light in the loop. We propose the concept of anticorrelation state for the description of light in the loop.
Masalov, A. V.↗
Shot noise limited detection of OH using the technique of laser-induced fluorescence
Nearly shot-noise limited detection of OH using the technique of laser-induced fluorescence is reported. A LIDAR configuration is used to excite fluoresence in a large volume and a narrow-bandwidth interference filter provides spectral discrimination. This arrangement alleviates the effect of ozone interference and facilitates image processing at relatively close distances. The detection limit is determined mainly by the short-noise of the solar background. Ground-based measurements in Dearborn indicate a detection limit of better than 1 x 10 to the 6th power OH/cubic cm over a forty-minute acquisition period. Under favorable conditions, a comparable detection limit was also observed for airborne measurements.
Bakalyar, D. M.↗
Optical synchronization-phase locking with shot noise processes Interim technical report
Optical communication synchronization with phase lock tracking loop and analysis of shot noise processes
Gagliardi, R.↗
An upper limit on ultraviolet shot noise from Cygnus X-1
Rapid photometry of Cygnus X-1 through an ultraviolet filter centered on 0.35 micron has been obtained at 100-ms sampling intervals. The autocorrelation function of these data has been examined for shot noise analogous to the behavior of the X-ray light curve. The ultraviolet data are entirely consistent with white noise. Considering randomly occurring ultraviolet shots with the same duration (0.5 s) and average rate (1 per sec) as the X-ray shots, a 3-sigma upper limit on the ratio of optical to X-ray energies per shot is estimated to be 0.13, before the ultraviolet light is attenuated by interstellar dust. This limit is then generalized for shots of arbitrary duration and rate.
Duthie, J. G.↗
On the physical reality of the millisecond bursts in Cygnus X-1 - Bursts and shot noise
The method of data analysis used to interpret the millisecond temporal structure of Cyg X-1 is discussed. In particular, the effects produced by the shot-noise variability of this source, which occurs on time scales of about 0.5 s, are examined. Taking into account the recent discovery that only about 30% of the flux may be in the shots, it is found that spurious 'millisecond bursts' will be detected. A comparison of the properties of these bursts with currently published experimental data is performed.
Weisskopf, M. C.↗
Shot noise cross-correlation functions and cross spectra - Implications for models of QPO X-ray sources
The cross-correlation functions (CCFs) and cross spectra expected for quasi-periodic oscillation (QPO) shot noise models are calculated under various assumptions, and the results are compared to observations. Effects due to possible coherence of the QPO oscillations are included. General formulas for the cross spectrum, the cross-phase spectrum, and the time-delay spectrum for QPO shot models are calculated and discussed. It is shown that the CCFs, cross spectra, and power spectra observed for Cyg X-e2 imply that the spectrum of the shots evolves with time, with important implications for the interpretation of these functions as well as of observed average energy spectra. The possible origins for the observed hard lags are discussed, and some physical difficulties for the Comptonization model are described. Classes of physical models for QPO sources are briefly addressed, and it is concluded that models involving shot formation at the surface of neutron stars are favored by observation.
Shibazaki, N.↗
Discrimination of shot-noise-driven Poisson processes by external dead time - Application of radioluminescence from glass
Ways in which dead time can be used to constructively enhance or diminish the effects of point processes that display bunching in the shot-noise-driven doubly stochastic Poisson point process (SNDP) are discussed. Interrelations between photocount bunching arising in the SNDP and the antibunching character arising from dead-time effects are investigated. It is demonstrated that the dead-time-modified count mean and variance for an arbitrary doubly stochastic Poisson point process can be obtained from the Laplace transform of the single-fold and joint-moment-generating functions for the driving rate process. The theory is in good agreement with experimental values for radioluminescence radiation in fused silica, quartz, and glass, and the process has many applications in pulse, particle, and photon detection.
Saleh, B. E. A.↗
Shot-noise in resistive-diode mixers and the attenuator noise model
The representation of a pumped exponential diode, operating as a mixer, by an equivalent lossy network, is reexamined. It is shown that the model is correct provided the network has ports for all sideband frequencies at which (real) power flow can occur between the diode and its embedding. The temperature of the equivalent network is eta/2 times the physical temperature of the diode. The model is valid only if the series resistance and nonlinear capacitance of the diode are negligible. Expressions are derived for the input and output noise temperature and the noise-temperature ratio of ideal mixers. Some common beliefs concerning noise-figure and noise-temperature ratio are shown to be incorrect.
Kerr, A. R.↗