Search NASA⌕ Search

SEARCH · Search NASA

Results for “AMPLITUDE MODULATION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 451 records · Page 25

A Compact 600 GHz Electronically Tunable Vector Measurement System for Submillimeter Wave Imaging

The design of a complete vector measurement system being tested over 560-635 GHz is presented. The topics include: 1) Current State-of-the-Art in Vector Measurements; 2) Submillimeter Active Imaging Requirements; 3) 600 GHz Vector Measurement System; 4) 450 MHz IF Signal; 5) 450 MHz IF signal @ 1 kHz Res. BW; 6) 450 MHz IF Signal Mixed with Shifted 450 MHz Reference Signal; 7) Reference Signal Offset Generator; 8) Cavity Bandpass Filter; 9) Miniature Multistage Helical Filter; 10) X36 450 MHz Multiplier; 11) 600 GHz Test Setup; 12) 600 GHz Transmit Module; 13) 600 GHz Receive Module; 14) Performance Tests: Amplitude Stability & Dynamic Range; 15) Performance Tests: Phase Stability; 16) Stability at Imaging Bandwidths; 17) Phase Measurement Verification; and 18) The Next Step: Imaging.

phase measurements↗

A spectroscopic and photometric study of FK Comae in 1989

Results of an observational campaign, coordinated between visual photometry, optical spectroscopy, and UV spectroscopy, to elucidate the characteristics of FK Comae are presented. The photometry showed complicated but systematic behavior. Photospheric absorption lines were distorted by a Doppler-shifted bump caused by dark starspots resulting in small apparent radial velocity variations. No radial velocity variations characteristic of orbital motion were seen to a level of 3 km/s. Broad emission in H-alpha was modulated at the photospheric rotational amplitude, implying an origin no farther from the rotational axis than 1 stellar radius. The strengths of Ca II lines are modulated in phase with H-alpha but do not have velocity-modulated wings like H-alpha.

Huenemoerder, David P.↗

A Probabilistic Model for Global EMIC Wave Activity Using Van Allen Probes Observations

Electromagnetic ion cyclotron (EMIC) waves play a key role in radiation belt dynamics through resonant interactions. However, their low occurrence probability, high variability, and spatial intermittency pose challenges for accurate modeling. In this study, we present a machine learning (ML)-based global EMIC wave model built on the entire data set from the Van Allen Probes mission. To capture the distinct statistical characteristics of wave occurrence and amplitude, the model is separated into two modules: an occurrence model trained using ML techniques, and a wave amplitude model sampled from observed probability distributions. The input parameters are limited to real-time or predictable variables to ensure practical applicability. Our model shows strong performance across the entire test set and demonstrates improved predictive capability over a baseline random occurrence model, particularly during quiet geomagnetic conditions. Evaluation during both quiet and active periods confirms the model's ability to represent the clustered and intermittent nature of EMIC wave activity. Furthermore, the model provides global estimates of wave power, enabling integration with radiation belt electron data and showing signatures consistent with wave-induced scattering. We found a good correlation between the global wave activity from the model and relativistic electron observation by Van Allen Probes, regardless of the availability of in situ wave observations. The modular structure of the model also allows for straightforward expansion for additional wave properties, such as wave frequency, which can be modeled independently. This flexible, event-sensitive approach offers a promising framework for data-driven radiation belt simulations and space weather applications.

79 ASTRONOMY AND ASTROPHYSICS↗

L-Band Transmit/Receive Module for Phase-Stable Array Antennas

Interferometric synthetic aperture radar (InSAR) has been shown to provide very sensitive measurements of surface deformation and displacement on the order of 1 cm. Future systematic measurements of surface deformation will require this capability over very large areas (300 km) from space. To achieve these required accuracies, these spaceborne sensors must exhibit low temporal decorrelation and be temporally stable systems. An L-band (24-cmwavelength) InSAR instrument using an electronically steerable radar antenna is suited to meet these needs. In order to achieve the 1-cm displacement accuracy, the phased array antenna requires phase-stable transmit/receive (T/R) modules. The T/R module operates at L-band (1.24 GHz) and has less than 1- deg absolute phase stability and less than 0.1-dB absolute amplitude stability over temperature. The T/R module is also high power (30 W) and power efficient (60-percent overall efficiency). The design is currently implemented using discrete components and surface mount technology. The basic T/R module architecture is augmented with a calibration loop to compensate for temperature variations, component variations, and path loss variations as a function of beam settings. The calibration circuit consists of an amplitude and phase detector, and other control circuitry, to compare the measured gain and phase to a reference signal and uses this signal to control a precision analog phase shifter and analog attenuator. An architecture was developed to allow for the module to be bidirectional, to operate in both transmit and receive mode. The architecture also includes a power detector used to maintain a transmitter power output constant within 0.1 dB. The use of a simple, stable, low-cost, and high-accuracy gain and phase detector made by Analog Devices (AD8302), combined with a very-high efficiency T/R module, is novel. While a self-calibrating T/R module capability has been sought for years, a practical and cost-effective solution has never been demonstrated. By adding the calibration loop to an existing high-efficiency T/R module, there is a demonstrated order-of-magnitude improvement in the amplitude and phase stability.

Andricos, Constantine↗

Tides and Decadal Variability

This paper reviews the mechanisms by which oceanic tides and decadal variability in the oceans are connected. We distinguish between variability caused by tides and variability observed in the tides themselves. Both effects have been detected at some level. The most obvious connection with decadal timescales is through the 18.6-year precession of the moon's orbit plane. This precession gives rise to a small tide of the same period and to 18.6-year modulations in the phase and amplitudes of short-period tides. The 18.6-year "node tide" is very small, no more than 2 cm anywhere, and in sea level data it is dominated by the ocean's natural Variability. Some authors have naively attributed climate variations with periods near 19 years directly to the node tide, but the amplitude of the tide is too small for this mechanism to be operative. The more likely explanation (Loder and Garrett, JGR, 83, 1967-70, 1978) is that the 18.6-y modulations in short-period tides, especially h e principal tide M2, cause variations in ocean mixing, which is then observed in temperature and other climatic indicators. Tidally forced variability has also been proposed by some authors, either in response to occasional (and highly predictable) tidal extremes or as a nonlinear low-frequency oscillation caused by interactions between short-period tides. The former mechanism can produce only short-duration events hardly more significant than normal tidal ranges, but the latter mechanism can in principle induce low-frequency oscillations. The most recent proposal of this type is by Keeling and Whorf, who highlight the 1800-year spectral peak discovered by Bond et al. (1997). But the proposal appears contrived and should be considered, in the words of Munk et al. (2002), "as the most likely among unlikely candidates."

Ray, Richard D.↗

Photochemically induced acousto-optics in gases

Acousto-optics consists of launching acoustic waves in a medium (usually a crystal) in order to modulate its refractive index and create a tunable optical grating. Here, in this article, we present the theoretical basis of an alternative scheme to generate acousto-optics in a gas, where the acoustic waves are initiated by the localized absorption (and thus gas heating) of spatially modulated UV light, as was demonstrated by Michine and Yoneda [Commun. Phys. 3, 24 (2020)]. We identify the chemical reactions initiated by the absorption of UV light via the photodissociation of ozone molecules present in the gas, and calculate the resulting temperature increase in the gas as a function of space and time. Solving the Euler fluid equations shows that the modulated, isochoric heating initiates a mixed acoustic-entropy wave in the gas, whose high-amplitude density (and thus refractive index) modulation can be used to manipulate a high-power laser. We calculate that diffraction efficiencies near 100% can be obtained using only a few millimeters of gas containing a few percent ozone fraction at room temperature, with UV fluences of less than 100 mJ/cm 2 —consistent with the experimental measurements. Our analysis suggests possible ways to optimize the diffraction efficiency by changing the buffer gas composition. Gases have optics damage thresholds 2–3 orders of magnitude beyond those of solids; these optical elements should therefore be able to manipulate kilojoule-class lasers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High-resolution high-throughput spatiotemporal strain imaging reveals loss mechanisms in a surface acoustic wave device

Surface acoustic wave devices are key components for processing radio frequency signals in wireless communication because these devices offer simultaneously high performance, compact size and low cost. The optimization of the device structure requires a quantitative understanding of energy conversion and loss mechanisms. Here we use stroboscopic full-field diffraction x-ray microscopy to reveal an unanticipated acoustic loss in a prototypical one-port resonator device. A non-uniform acoustic excitation in the active area was responsible for the substantial end and side leakages observed at the design frequency. Quantitative analysis of the strain amplitude using a wave decomposition method allowed the determination of several key device parameters. This high-resolution high-throughput spatiotemporal strain imaging technique is more generally applicable to the study of dynamic strain modulation in nanoscale acoustic, electronic, optical and quantum devices. The high sensitivity allows precise measurement of the strain modulation with picometer-scale amplitude.

Zhou, Tao [ESRF - The European Synchrotron, Grenob↗

Three-dimensional organization of otolith-ocular reflexes in rhesus monkeys. I. Linear acceleration responses during off-vertical axis rotation

1. The dynamic properties of otolith-ocular reflexes elicited by sinusoidal linear acceleration along the three cardinal head axes were studied during off-vertical axis rotations in rhesus monkeys. As the head rotates in space at constant velocity about an off-vertical axis, otolith-ocular reflexes are elicited in response to the sinusoidally varying linear acceleration (gravity) components along the interaural, nasooccipital, or vertical head axis. Because the frequency of these sinusoidal stimuli is proportional to the velocity of rotation, rotation at low and moderately fast speeds allows the study of the mid-and low-frequency dynamics of these otolith-ocular reflexes. 2. Animals were rotated in complete darkness in the yaw, pitch, and roll planes at velocities ranging between 7.4 and 184 degrees/s. Accordingly, otolith-ocular reflexes (manifested as sinusoidal modulations in eye position and/or slow-phase eye velocity) were quantitatively studied for stimulus frequencies ranging between 0.02 and 0.51 Hz. During yaw and roll rotation, torsional, vertical, and horizontal slow-phase eye velocity was sinusoidally modulated as a function of head position. The amplitudes of these responses were symmetric for rotations in opposite directions. In contrast, mainly vertical slow-phase eye velocity was modulated during pitch rotation. This modulation was asymmetric for rotations in opposite direction. 3. Each of these response components in a given rotation plane could be associated with an otolith-ocular response vector whose sensitivity, temporal phase, and spatial orientation were estimated on the basis of the amplitude and phase of sinusoidal modulations during both directions of rotation. Based on this analysis, which was performed either for slow-phase eye velocity alone or for total eye excursion (including both slow and fast eye movements), two distinct response patterns were observed: 1) response vectors with pronounced dynamics and spatial/temporal properties that could be characterized as the low-frequency range of "translational" otolith-ocular reflexes; and 2) response vectors associated with an eye position modulation in phase with head position ("tilt" otolith-ocular reflexes). 4. The responses associated with two otolith-ocular vectors with pronounced dynamics consisted of horizontal eye movements evoked as a function of gravity along the interaural axis and vertical eye movements elicited as a function of gravity along the vertical head axis. Both responses were characterized by a slow-phase eye velocity sensitivity that increased three- to five-fold and large phase changes of approximately 100-180 degrees between 0.02 and 0.51 Hz. These dynamic properties could suggest nontraditional temporal processing in utriculoocular and sacculoocular pathways, possibly involving spatiotemporal otolith-ocular interactions. 5. The two otolith-ocular vectors associated with eye position responses in phase with head position (tilt otolith-ocular reflexes) consisted of torsional eye movements in response to gravity along the interaural axis, and vertical eye movements in response to gravity along the nasooccipital head axis. These otolith-ocular responses did not result from an otolithic effect on slow eye movements alone. Particularly at high frequencies (i.e., high speed rotations), saccades were responsible for most of the modulation of torsional and vertical eye position, which was relatively large (on average +/- 8-10 degrees/g) and remained independent of frequency. Such reflex dynamics can be simulated by a direct coupling of primary otolith afferent inputs to the oculomotor plant. (ABSTRACT TRUNCATED).

NASA Discipline Neuroscience↗

Nonlinear interaction between a pair of oblique modes in a supersonic mixing layer: Long-wave limit

The nonlinear interaction between a pair of symmetric, oblique, and spatial instability modes is studied in the long-wave limit using asymptotic methods. The base flow is taken to be a supersonic mixing layer whose Mach number is such that the corresponding vortex sheet is marginally stable according to Miles' criterion. It is shown that the amplitude of the mode obeys a nonlinear integro-differential equation. Numerical solutions of this equation show that, when the obliqueness angle is less than pi/4, the effect of the nonlinearity is to enhance the growth rate of the instability. The solution terminates in a singularity at a finite streamwise location. This result is reminiscent of that obtained in the vicinity of the neutral point by other authors in several different types of flows. On the other hand, when the obliqueness angle is more than pi/4, the streamwise development of the amplitude is characterized by a series of modulations. This arises from the fact that the nonlinear term in the amplitude equation may be either stabilizing or destabilizing, depending on the value of the streamwise coordinate. However, even in this case the amplitude of the disturbance increases, though not as rapidly as in the case for which the angle is less than pi/4. Quite generally then, the nonlinear interaction between two oblique modes in a supersonic mixing layer enhances the growth of the disturbance.

Balsa, Thomas F.↗

Smooth Phase Interpolated Keying

Smooth phase interpolated keying (SPIK) is an improved method of computing smooth phase-modulation waveforms for radio communication systems that convey digital information. SPIK is applicable to a variety of phase-shift-keying (PSK) modulation schemes, including quaternary PSK (QPSK), octonary PSK (8PSK), and 16PSK. In comparison with a related prior method, SPIK offers advantages of better performance and less complexity of implementation. In a PSK scheme, the underlying information waveform that one seeks to convey consists of discrete rectangular steps, but the spectral width of such a waveform is excessive for practical radio communication. Therefore, the problem is to smooth the step phase waveform in such a manner as to maintain power and bandwidth efficiency without incurring an unacceptably large error rate and without introducing undesired variations in the amplitude of the affected radio signal. Although the ideal constellation of PSK phasor points does not cause amplitude variations, filtering of the modulation waveform (in which, typically, a rectangular pulse is converted to a square-root raised cosine pulse) causes amplitude fluctuations. If a power-efficient nonlinear amplifier is used in the radio communication system, the fluctuating-amplitude signal can undergo significant spectral regrowth, thus compromising the bandwidth efficiency of the system. In the related prior method, one seeks to solve the problem in a procedure that comprises two major steps: phase-value generation and phase interpolation. SPIK follows the two-step approach of the related prior method, but the details of the steps are different. In the phase-value-generation step, the phase values of symbols in the PSK constellation are determined by a phase function that is said to be maximally smooth and that is chosen to minimize the spectral spread of the modulated signal. In this step, the constellation is divided into two groups by assigning, to information symbols, phase values that result in equal numbers of clockwise and counter-clockwise phase rotations for equally likely symbols. The purpose served by assigning phase values in this way is to prevent unnecessary generation of spectral lines and prevent net shifts of the carrier signal. In the phase-interpolation step, the smooth phase values are interpolated over a number, n, of consecutive symbols (including the present symbol) by means of an unconventional spline curve fit.

Borah, Deva K.↗

On the nonlinear stability of a high-speed, axisymmetric boundary layer

The stability of a high-speed, axisymmetric boundary layer is investigated using secondary instability theory and direct numerical simulation. Parametric studies based on the temporal secondary instability theory identify subharmonic secondary instability as a likely path to transition on a cylinder at Mach 4.5. The theoretical predictions are validated by direct numerical simulation at temporally-evolving primary and secondary disturbances in an axisymmetric boundary-layer flow. At small amplitudes of the secondary disturbance, predicted growth rates agree to several significant digits with values obtained from the spectrally-accurate solution of the compressible Navier-Stokes equations. Qualitative agreement persists to large amplitudes of the secondary disturbance. Moderate transverse curvature is shown to significantly affect the growth rate of axisymmetric second mode disturbances, the likely candidates of primary instability. The influence of curvature on secondary instability is largely indirect but most probably significant, through modulation of the primary disturbance amplitude. Subharmonic secondary instability is shown to be predominantly inviscid in nature, and to account for spikes in the Reynolds stress components at or near the critical layer.

Pruett, C. David↗

On the nonlinear stability of a high-speed, axisymmetric boundary layer

The stability of a high-speed, axisymmetric boundary layer is investigated using secondary instability theory and direct numerical simulation. Parametric studies based on the temporal secondary instability theory identify subharmonic secondary instability as a likely path to transition on a cylinder at Mach 4.5. The theoretical predictions are validated by direct numerical simulation at temporally-evolving primary and secondary disturbances in an axisymmetric boundary-layer flow. At small amplitudes of the secondary disturbance, predicted growth rates agree to several significant digits with values obtained from the spectrally-accurate solution of the compressible Navier-Stokes equations. Qualitative agreement persists to large amplitudes of the secondary disturbance. Moderate transverse curvature is shown to significantly affect the growth rate of axisymmetric second mode disturbances, the likely candidates of primary instability. The influence of curvature on secondary instability is largely indirect but most probably significant, through modulation of the primary disturbance amplitude. Subharamonic secondary instability is shown to be predominantly inviscid in nature, and to account for spikes in the Reynolds stress components at or near the critical layer.

Pruett, C. D.↗

Laser wavelength dependence of laser imprint

In laser direct-drive inertial confinement fusion, laser imprint is one of the major causes of degradation in target performance through its seeding of hydrodynamic instabilities. Early experiments and simulations have shown that laser imprint could be mitigated with a longer laser wavelength because of its lower critical density and longer conduction zone. Building upon this work, we explore a scenario where the laser wavelength during the picket pulse differs from that of the main pulse in order to gain the benefit of reduced imprint, while avoiding losses in drive coupling efficiency or an increase in laser-plasma instabilities. A series of 2D radiation-hydrodynamic simulations, which test three different laser wavelengths for the picket pulse, has been performed, where the intensity of the picket pulse is adjusted in order to maintain the same implosion adiabat. A detailed analysis of the growth of the mass density modulations at the ablation front over a large range of mode numbers confirms that the laser imprint can be mitigated with a picket pulse operating at a longer wavelength than the main pulse because of the longer conduction zone and enhanced thermal smoothing. The amplitude of the ablation front modulations is found to be lower for all mode numbers, which reduces the seeding of the Rayleigh–Taylor instability without affecting the mode growth rates.

Fourier analysis↗

Laser Metrology for an Optical-Path-Length Modulator

Laser gauges have been developed to satisfy requirements specific to monitoring the amplitude of the motion of an optical-path-length modulator that is part of an astronomical interferometer. The modulator includes a corner-cube retroreflector driven by an electromagnetic actuator. During operation of the astronomical interferometer, the electromagnet is excited to produce linear reciprocating motion of the corner-cube retroreflector at an amplitude of 2 to 4 mm at a frequency of 250, 750, or 1,250 Hz. Attached to the corner-cube retroreflector is a small pick-off mirror. To suppress vibrations, a counterweight having a mass equal to that of the corner-cube retroreflector and pick-off mirror is mounted on another electromagnetic actuator that is excited in opposite phase. Each gauge is required to measure the amplitude of the motion of the pick-off mirror, assuming that the motions of the pick-off mirror and the corner-cube retroreflector are identical, so as to measure the amplitude of motion of the corner- cube retroreflector to within an error of the order of picometers at each excitation frequency. Each gauge is a polarization-insensitive heterodyne interferometer that includes matched collimators, beam separators, and photodiodes (see figure). The light needed for operation of the gauge comprises two pairs of laser beams, the beams in each pair being separated by a beat frequency of 80 kHz. The laser beams are generated by an apparatus, denoted the heterodyne plate, that includes stabilized helium-neon lasers, acousto-optical modulators, and associated optical and electronic subsystems. The laser beams are coupled from the heterodyne plate to the collimators via optical fibers.

Gursel, Yekta↗

Direction-Finding Measurements of Heliospheric 2-3 kHz Radio Emissions

Using data from the Voyager 1 plasma wave instrument, a series of direction-finding measurements is presented for the intense 1992-93 heliospheric 2- to 3-kHz radio emission event, and several weaker events extending into 1994. Direction-finding measurements can only be obtained during roll maneuvers, which are performed about once every three months. Two parameters can be determined from the roll-induced intensity modulation, the azimuthal direction of arrival (measured around the roll axis), and the modulation index (the peak-to-peak amplitude divided by the peak amplitude). Measurements were made at two frequencies, 1.78 and 3.11 kHz. No roll modulation was observed at 1.78 kHz, which is consistent with an isotropic source at this frequency. In most cases an easily measurable roll modulation was detectable at 3.11 kHz. Although the azimuth angles have considerable scatter, the directions of arrival at 3.11 kHz can be organized into three groups, each of which appears to be associated with a separate upward drifting feature in the radio emission spectrum. The first group, which is associated with the main 1992-93 event, is consistent with a source located near the nose of the heliosphere. The remaining two groups, which occur after the main 1992-93 event, have azimuth angles well away from the nose of the heliosphere. The modulation indexes vary over a large range, from 0.06 to 0.61, with no obvious trend. Although the variations in the directions of arrival and modulation indicies appear to reflect changes in the position and angular size of the source, it is also possible that they could be caused by refraction or scattering due to density structures in the solar wind.

Gurnett, Donald A.↗

SENSEI: A Search for Diurnal Modulation in Sub-GeV Dark Matter Scattering

Dark matter particles with sufficiently large interactions with ordinary matter can scatter in the Earth’s atmosphere and crust before reaching an underground detector. This Earth-shielding effect can induce a directional dependence in the dark matter flux, leading to a sidereal daily modulation in the signal rate. We perform a search for such a modulation using data from the SENSEI experiment, targeting MeV-scale dark matter. We achieve nearly an order-of-magnitude improvement in sensitivity over previous direct-detection bounds for dark-matter masses below ∼ 1 MeV , assuming the standard halo model with a Maxwell-Boltzmann velocity distribution, and restrict the amplitude of a general daily modulation signal to be below 6.8 e / g / d .

Bloch, Itay M. [UC, Berkeley; LBL, Berkeley]↗

Modeling the Observed Solar Cycle Variations of the Quasi-biennial Oscillation (QBO): Amplification by Wave Forcing

In several papers, the solar cycle (SC) effect in the lower atmosphere has been linked observationally to the Quasi-biennial Oscillation (QBO) of the zonal circulation, which is generated primarily by small-scale gravity waves (GW). Salby and Callaghan (2000) in particular analyzed the QBO, covering more than 40 years, and discovered that it contains a large SC signature at 20 km. With our Numerical Spectral Model (NSM), we conducted a 3D study to describe the QBO under the influence of the SC, and some results have been published (Mayr et al., GRL, 2005,2006). For a SC period of 10 years, the relative amplitude of radiative forcing is taken to vary exponentially with height, i.e., 0.2% at the surface, 2% at 50 km, 20% at 100 km and above. Applying spectral analysis to filter out and identify the SC signature, the model generates a relatively large modulation of the QBO, which reproduces the observations qualitatively. Our numerical results demonstrate that the modulation of the QBO, with constant phase relative to the SC, persist at least for 60 years. The same model run generates in the seasonal variations a hemispherically symmetric Equatorial Annual Oscillation (EAO, with 12-month period), which is confined to low latitudes like the QBO and is also modulated by the SC. Although the amplitude of the EAO is relatively small, its SC modulation is large, and it is in phase with that of the QBO. The SC modulated EAO is evidently the pathway and pacemaker for the solar influence on the QBO. To shed light on the dynamical processes involved, we present model results that show how the seasonal cycle induces the SC modulations of the EAO and QBO. Our analysis further demonstrates that the SC modulations of the QBO and EAO are amplified by the GW interaction with the flow. The GW momentum source clearly shows a SC modulation that is in phase with the corresponding modulations of the QBO and EAO. By tapping the momentum from the upward propagating GWs, the QBO and EAO apparently serve as conduits to amplify and transfer to lower altitudes the larger SC variations in the UV absorbed in the mesosphere. Our model also produces in the temperature variations of the QBO and EAO measurable SC modulations at polar latitudes near the tropopause, and such signatures have been reported in the literature. Contrary to conventional interpretation, however, we suggest that the effects are generated at least in part by the meridional circulation, and planetary waves presumably, which redistribute the energy from the equatorial region where wave forcing is very efficient and thereby amplifies the SC influence.

Mayr, Hans G.↗

Optical Quantum Receiver For Binary Signals

In quantum optical receiver, both amplitude and phase of received optical signal measured to extract as much information as possible, thereby reducing error probability. Phase-modulated received signal mixed with equal amplitude replica of optical carrier generated in phase locked loop. Two signals interfere with each other at photomultiplier cathode. Probability of error with this scheme close to theoretical minimum and implemented with current technology.

Vilnrotter, V. A.↗