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The current and voltage fluctuations in a normal tunnel junction are calculated from microscopic theory. The power spectrum can deviate from the familiar Johnson-Nyquist form when the self-capacitance of the junction is small, at low temperatures permitting experimental verification. The deviation reflects the discrete nature of the charge transfer across the junction and should be present in a wide class of similar systems.
This paper provides a detailed description of the data reduction and analysis procedures that have been employed in our previous studies of spatial fluctuation of the cosmic infrared background (CIB) using deep Spitzer Infrared Array Camera observations. The self-calibration we apply removes a strong instrumental signal from the fluctuations that would otherwise corrupt the results. The procedures and results for masking bright sources and modeling faint sources down to levels set by the instrumental noise are presented. Various tests are performed to demonstrate that the resulting power spectra of these fields are not dominated by instrumental or procedural effects. These tests indicate that the large-scale ([greater, similar]30') fluctuations that remain in the deepest fields are not directly related to the galaxies that are bright enough to be individually detected. We provide the parameterization of these power spectra in terms of separate instrument noise, shot noise, and power-law components. We discuss the relationship between fluctuations measured at different wavelengths and depths, and the relations between constraints on the mean intensity of the CIB and its fluctuation spectrum. Consistent with growing evidence that the [approx]1-5 [mu]m mean intensity of the CIB may not be as far above the integrated emission of resolved galaxies as has been reported in some analyses of DIRBE and IRTS observations, our measurements of spatial fluctuations of the CIB intensity indicate the mean emission from the objects producing the fluctuations is quite low ([greater, similar]1 nW m-2 sr-1 at 3-5 [mu]m), and thus consistent with current [gamma]-ray absorption constraints. The source of the fluctuations may be high-z Population III objects, or a more local component of very low luminosity objects with clustering properties that differ from the resolved galaxies. Finally, we discuss the prospects of the upcoming space-based surveys to directly measure the epochs inhabited by the populations producing these source-subtracted CIB fluctuations, and to isolate the individual fluxes of these populations.
The various sources of noise which are often encountered in magneto-optical readout systems are analyzed. Although the focus is on magneto-optics, most sources of noise are common among the various optical recording systems and one can easily adapt the results to other media and systems. A description of the magneto-optical readout system under consideration is given, and the standard methods and the relevant terminology of signal and noise measurement are described. The characteristics of thermal noise, which originates in the electronic circuitry of the readout system, are described. The most fundamental of all sources of noise, the shot noise, is considered, and a detailed account of its statistical properties is given. Shot noise, which is due to random fluctuations in photon arrival times, is an ever-present noise in optical detection. Since the performance of magneto-optical recording devices in use today is approaching the limit imposed by the shot noise, it is important that the reader have a good grasp of this particular source of noise. A model for the laser noise is described, and measurement results which yield numerical values for the strength of the laser power fluctuations are presented. Spatial variations of the disk reflectivity and random depolarization phenomena also contribute to the overall level of noise in readout; these and related issues are treated. Numerical simulation results describing some of the more frequently encountered sources of noise which accompany the recorded waveform itself, namely, jitter noise and signal-amplitude fluctuation noise are presented.
Single-slope analog-to-digital converters (ADCs) are particularly useful for onchip digitization in focal plane arrays (FPAs) because of their inherent monotonicity, relative simplicity, and efficiency for column-parallel applications, but they are comparatively slow. Squareroot encoding can allow the number of code values to be reduced without loss of signal-to-noise ratio (SNR) by keeping the quantization noise just below the signal shot noise. This encoding can be implemented directly by using a quadratic ramp. The reduction in the number of code values can substantially increase the quantization speed. However, in an FPA, the fixed pattern noise (FPN) limits the use of small quantization steps at low signal levels. If the zero-point is adjusted so that the lowest column is onscale, the other columns, including those at the center of the distribution, will be pushed up the ramp where the quantization noise is higher. Additionally, the finite frequency response of the ramp buffer amplifier and the comparator distort the shape of the ramp, so that the effective ramp value at the time the comparator trips differs from the intended value, resulting in errors. Allowing increased settling time decreases the quantization speed, while increasing the bandwidth increases the noise. The FPN problem is solved by breaking the ramp into two portions, with some fraction of the available code values allocated to a linear ramp and the remainder to a quadratic ramp. To avoid large transients, both the value and the slope of the linear and quadratic portions should be equal where they join. The span of the linear portion must cover the minimum offset, but not necessarily the maximum, since the fraction of the pixels above the upper limit will still be correctly quantized, albeit with increased quantization noise. The required linear span, maximum signal and ratio of quantization noise to shot noise at high signal, along with the continuity requirement, determines the number of code values that must be allocated to each portion. The distortion problem is solved by using a lookup table to convert captured code values back to signal levels. The values in this table will be similar to the intended ramp value, but with a correction for the finite bandwidth effects. Continuous-time comparators are used, and their bandwidth is set below the step rate, which smoothes the ramp and reduces the noise. No settling time is needed, as would be the case for clocked comparators, but the low bandwidth enhances the distortion of the non-linear portion. This is corrected by use of a return lookup table, which differs from the one used to generate the ramp. The return lookup table is obtained by calibrating against a stepped precision DC reference. This results in a residual non-linearity well below the quantization noise. This method can also compensate for differential non-linearity (DNL) in the DAC used to generate the ramp. The use of a ramp with a combination of linear and quadratic portions for a single-slope ADC is novel. The number of steps is minimized by keeping the step size just below the photon shot noise. This in turn maximizes the speed of the conversion. High resolution is maintained by keeping small quantization steps at low signals, and noise is minimized by allowing the lowest analog bandwidth, all without increasing the quantization noise. A calibrated return lookup table allows the system to maintain excellent linearity.
The recent successes of the Galileo solid-state imaging (SSI) experiment at the Moon and Gaspra show the utility of multispectral imaging of planetary objects. 'Clementine' is the planetary community's 'code name' for the SDIO (Space Defense Initiative Organization), mission to the Moon and the asteroid Geographos. This mission is designed as a long term stressing test on sensors and space systems developed for SDIO. In the course of this test Clementine will obtain science data using a varied and powerful array of remote sensing instruments which were developed by or for Lawrence Livermore National Laboratory in Livermore, California. Clementine carries five cameras, one for navigation and four for science experiments. In addition, a laser ranger is included which will serve as a laser altimeter. The Clementine cameras cover a wider range of spatial resolutions and wavelength range than did Galileo and are almost ideally suited to mapping of mafic rock types as are present on the Moon and expected at Geographos. Calibration of the cameras will occur at the sensor calibration laboratory at LLNL. In flight calibrations, using standard stars and other standards should improve the stated accuracies. Signal-to-noise ratios (SNRs) include the following noise sources: shot noise, calibration error, digitization noise, readout noise, and frame transfer noise (where applicable). The achieved SNRs are a balance between detector saturation and acceptable image smear. The 'worst' case uses the longest possible integration times.
We describe a new Fabry-Perot spectrometer that is optimized for the detection of extended, low-surface-brightness line emission from 1.4 to 2.4 microns. The instrument combines high throughput and high sensitivity, yet limits the background radiation falling on the detector. The instrument has a single 20 sec - 200 sec beam and a resolving power lambda/delta(lambda) approximately 2500. The system is background shot-noise limited in the K window and limited by a combination of read noise, dark-current shot noise, and fluctuations in the OH airglow lines in the H window. We present sample data of some of the lowest-surface-brightness H2 line emission in the near infrared obtained to date.
Arm locking is a technique that has been proposed for reducing laser frequency fluctuations in the Laser Interferometer Space Antenna (LISA). a gravitational-wave observatory sensitive' in the milliHertz frequency band. Arm locking takes advantage of the geometric stability of the triangular constellation of three spacecraft that comprise LISA to provide a frequency reference with a stability in the LISA measurement band that exceeds that available from a standard reference such as an optical cavity or molecular absorption line. We have implemented a time-domain simulation of arm locking including the expected limiting noise sources (shot noise, clock noise. spacecraft jitter noise. and residual laser frequency noise). The effect of imperfect a priori knowledge of the LISA heterodyne frequencies and associated "pulling" of an arm locked laser is included. We find that our implementation meets requirements both on the noise and dynamic range of the laser frequency.
One of the major sources of noise in a direct detection optical communication receiver is the shot noise due to the quantum nature of the photodetector. The shot noise is signal dependent and is neither Gaussian nor wide sense stationary. When a photomultiplier tube (PMT) or an avalanche photodiode (APD) is used, there is also a multiplicative excess noise due to the randomness of the internal photodetector gain. Generally speaking, the radio frequency (RF) communication theory cannot be applied to direct detection optical communication systems because noise in RF communication systems is usually additive and Gaussian. A receiver structure which is mathematically optimal for signal dependent shot noise is derived. Several suboptimal receiver structures are discussed and compared with the optimal receiver. The objective is to find a receiver structure which is easy to implement and gives close to optimal performance.
Observation of squeezed noise, 5 +/- 0.3 dB below the shot noise level, generated with pulses in a fiber ring interferometer is reported. The interferometric geometry is used to separate the pump pulse from the squeezed vacuum radiation. A portion of the pump is reused as the local oscillator in a homodyne detection. The pump fluctuations are successfully subtracted and shot noise limited performance is achieved at low frequencies (35-85 KHz). A possible utilization of the generated squeezed vacuum in improving a fiber gyro's signal to noise ratio is discussed.
Spatial tracking plays a very critical role in designing optical communication systems because of the small angular beamwidth associated with the optical signal. One possible solution for spatial tracking is to use a nutating mirror which dithers the incoming beam at a rate much higher than the mechanical disturbances. A power detector then senses the change in detected power as the signal is reflected off the nutating mirror. This signal is then correlated with the nutator driver signals to obtain estimates of the azimuth and elevation tracking signals to control the fast scanning mirrors. A theoretical analysis is performed for a spatial tracking system using a nutator disturbed by shot noise and mechanical vibrations. Contributions of shot noise and mechanical vibrations to the total tracking error variance are derived. Given the vibration spectrum and the expected signal power, there exists an optimal amplitude for the nutation which optimizes the receiver performance. The expected performance of a nutator based system is estimated based on the choice of nutation amplitude.
Shot noise places a practical limit on the spatial and temporal resolution of lidar photocount data. A 2-D signal-processing technique that utilizes spatial and temporal filtering to reduce shot noise and increase resolution is described. The technique is applied to sodium lidar data collected during the fall of 1979 over Urbana, Illinois. Temporal filtering is shown to enhance the spatial resolution of the sodium profiles significantly by reducing shot noise by more than 10 dB. The signal-processing technique is applicable to a wide variety of lidar data.
Shot-noise models provide a useful mathematical representation for some physical models for the quasi-periodic oscillations (QPOs) recently observed from several bright Galactic bulge and burst X-ray sources. Expressions are calculated for the first three moments for several versions of QPO shot-noise models that have appeared in the literature. It is shown that measurement of the third moment, together with measurement of the mean intensity and the power spectrum, can provide model-dependent constraints on important parameters of QPO shot-noise models, including the fraction of the X-ray intensity in shots and the shot rate. Under certain condtitions, a complete solution for all the shot-model parameters is possible.
An analysis is presented of the optical (0.44 micron) and radio flux density variations (4.8, 8.0, and 14.5 GHz) of the five best observed variable AGN, of which three are BL Lac objects and two are optically violent variable (OVV) quasars. For each object the nature of the variability at individual wavelengths is determined by using a structure function analysis and the autocorrelation function as calculated from the discrete correlation technique. Both techniques yield similar results, showing that the optical variations are similar for all objects and are a combination of flicker and shot noise. The radio variability is distinct, being described by shot noise (less variation at short times), with the two OVVs exhibiting the most extreme behavior. The time lag between the variations at the three radio frequencies and the optical flux is studied with the discrete cross-correlation function and the mean variance methods. It is concluded that the optical and radio emitting regions are physically related, exist on distinct time scales, and excite their synchrotron emitting plasmas differently.
The power spectrum of the relative intensity noise (RIN) of single-frequency diode-pumped Nd:YAG lasers is observed to be shot-noise limited at frequencies above 20 MHz for a photocurrent of up to 4.4 mA. Relaxation oscillations result in noise 60-70 dB above shot noise at a few hundred kHz. These relaxation oscillations have been suppressed using electronic feedback.
The purpose of this program was to demonstrate the potential of a fiber optic loop sensor for the measurement of electrically charged particle fluxes in space. The key elements of the sensor are a multiple turn loop of low birefringence, single mode fiber, with a laser diode light source, and a low noise optical receiver. The optical receiver is designed to be shot noise limited, with this being the limiting sensitivity factor for the sensor. The sensing element is the fiber optic loop. Under a magnetic field from an electric current flowing along the axis of the loop, there is a non-vanishing line integral along the fiber optic loop. This causes a net birefringence producing two states of polarization whose phase difference is correlated to magnetic field strength and thus, current in the optical receiver electronic processing. The objectives in this program were to develop a prototype laser diode powered fiber optic sensor. The performance specification of a minimum detectable current density of 1 (mu)amp/sq m-(radical)Hz, should be at the shot noise limit of the detection electronics. OPTRA has successfully built and tested a 3.2 m diameter loop with 137 turns of low birefringence optical fiber and achieved a minimum detectable current density of 5.4 x 10(exp-5) amps/(radical)Hz. If laboratory space considerations were not an issue, with the length of optical fiber available to us, we would have achieved a minimum detectable current density of 4 x 10(exp -7) amps/(radical)Hz.
Unsteady pressure-sensitive paint (uPSP) is a significant new technology for high spatial resolution measurement of complex dynamic surface pressure loading on a wind tunnel model, to better define flight vehicle buffet and aeroacoustic loads. Compared with the very sparse surface pressure measurements of traditional sensors, the pressure sensitivity of uPSP light reflectivity provides a visual measure of surface pressure fluctuations over a wide area illuminated by high intensity light, captured by a high-speed digital camera. Panda et al (AIAA Journal, May 2019) have shown good data is recoverable up to 10 kHz. In cases where available uPSP luminescence is low for a painted wind tunnel test model, significant noise levels have been observed primarily due to the discrete photon arrival variability of low intensity light (termed “shot noise”). In this case, uPSP measurements can exhibit unusually low signal to noise ratio (SNR of 0.1 or less). This paper will report on latest work to recover calibrated uPSP measurements which are noise free over a useful dynamic range of 10-15 dB. It will be shown how the distinct spatial correlations of both the shot noise and the underlying aeroacoustic surface pressure play an important role in obtaining a reliable measurement.
Data from a SAS 3 observation of Cygnus X-1 have been analyzed, assuming a simple shot-noise model for the time variability. The results confirm the suggestion of Sutherland, Weisskopf, and Kahn that the shot parameters are constant when the source is in its low state. The first significant measurement of the time sense of the shot-noise pulses was performed, with the result that the average pulse shape is time-symmetric, not asymmetric as has been previously assumed.
The Unsteady Pressure-Sensitive Paint (uPSP) is widely used to measure the surface pressure of scaled models in wind tunnel tests. Compared to the conventional pressure transducers, uPSP has the advantage of high spatial resolution. With multiple high-speed Complementary Metal Oxide Superconductor (CMOS) cameras, the uPSP data collected with the camera pixels are mapped to the surface grid of the scaled model and converted to pressure. The shot noise is the dominant component of the noise in the uPSP measurement. The integrated pressure is usually computed on the grid nodes of a user-defined patch. The effect of shot noise is reduced in the integrated pressure on the patch; however, the measurement of the aerodynamic pressure may also be attenuated by the decorrelation of the flow pressure field being measured. This paper discusses the Joint Acceptance Attenuation Factor (JAAF) of the integrated pressure with uPSP measurements. The JAAF, a function of frequency, is defined as the ratio of the Power Spectral Density (PSD) of the integrated aerodynamic pressure on the patch to the average PSD of the aerodynamic pressure on the grid nodes of the patch. In this paper, the JAAF is investigated for the integrated pressure on rectangular patches, whose edges are defined in the direction along the streamline or across the streamline. Based on the assumption that the surface pressure field can be described by the Corcos model, the closed-form formulas to compute the JAAFs of the integrated pressure on the discrete grid nodes of a rectangular patch and over the continuous area of a rectangular patch are derived respectively. It is shown that the JAAF of the integrated pressure over the continuous area of a rectangular patch is the limit of that on discrete nodes of the rectangular patch when the number of nodes in each row or column goes to infinity. The closed-form formulas of the JAAF derived in this paper, with estimated parameters of the model, are verified with the measurements of the uPSP and the conventional pressure transducer collected in the Space Launch System Ascent Unsteady Aerodynamics Test at NASA Ames Research Center in November 2017. The closed-form formulas of the JAAF of the integrated pressure on the rectangular patches, based on the Corcos model, provide an efficient method to estimate the attenuation of integration by the decorrelation of the flow pressure field and set references for the comparison of the spectrum of the integrated uPSP measurements and the conventional pressure transducer measurements. The work described in this paper is a part of NASA’s development of a new state-of-the-art uPSP capability in production wind tunnels. Funding was provided by the NASA Aerosciences Evaluation and Test Capabilities Portfolio Office.