Signal and noise in helioseismic holography

Helioseismic holography is an imaging technique used to study heterogeneities and flows in the solar interior from observations of solar oscillations at the surface. Holograms contain noise due to the stochastic nature of solar oscillations. We provide a theoretical framework for modeling signal and noise in Porter-Bojarski helioseismic holography. The wave equation may be recast into a Helmholtz-like equation, so as to connect with the acoustics literature and define the holography Green's function in a meaningful way. Sources of wave excitation are assumed to be stationary, horizontally homogeneous, and spatially uncorrelated. Using the first Born approximation we calculate holograms in the presence of perturbations in sound-speed, density, flows, and source covariance, as well as the noise level as a function of position. This work is a direct extension of the methods used in time-distance helioseismology to model signal and noise. To illustrate the theory, we compute the hologram intensity numerically for a buried sound-speed perturbation at different depths in the solar interior. The reference Green's function is obtained for a spherically-symmetric solar model using a finite-element solver in the frequency domain. Below the pupil area on the surface, we find that the spatial resolution of the hologram intensity is very close to half the local wavelength. For a sound-speed perturbation of size comparable to the local spatial resolution, the signal-to-noise ratio is approximately constant with depth. Averaging the hologram intensity over a number $N$ of frequencies above 3 mHz increases the signal-to-noise ratio by a factor nearly equal to the square root of $N$. This may not be the case at lower frequencies, where large variations in the holographic signal are due to the individual contributions of the long-lived modes of oscillation.Comment: Submitted to Astronomy and Astrophysic

Bayesian Analysis of Femtosecond Pump-Probe Photoelectron-Photoion Coincidence Spectra with Fluctuating Laser Intensities

This paper employs Bayesian probability theory for analyzing data generated in femtosecond pump-probe photoelectron-photoion coincidence (PEPICO) experiments. These experiments allow investigating ultrafast dynamical processes in photoexcited molecules. Bayesian probability theory is consistently applied to data analysis problems occurring in these types of experiments such as background subtraction and false coincidences. We previously demonstrated that the Bayesian formalism has many advantages, amongst which are compensation of false coincidences, no overestimation of pump-only contributions, significantly increased signal-to-noise ratio, and applicability to any experimental situation and noise statistics. Most importantly, by accounting for false coincidences, our approach allows running experiments at higher ionization rates, resulting in an appreciable reduction of data acquisition times. In addition to our previous paper, we include fluctuating laser intensities, of which the straightforward implementation highlights yet another advantage of the Bayesian formalism. Our method is thoroughly scrutinized by challenging mock data, where we find a minor impact of laser fluctuations on false coincidences, yet a noteworthy influence on background subtraction. We apply our algorithm to data obtained in experiments and discuss the impact of laser fluctuations on the data analysis

Signal vs. Noise: Some Comments on Professor Stein\u27s Theory of Evidential Efficiency

In this Essay, I examine Professor Stein\u27s intriguing new theory of evidential efficiency, which posits that judges should admit evidence whenever it has a sufficiently high signal-to-noise ratio. I explore a slightly different definition of the concepts of signal and noise than Stein, based upon likelihood ratio values rather than the underlying probabilities of events, and I explain why these altered concepts may be analytically superior. Additionally, I call into question the strength of the connection between the signal-to-noise ratio of a piece of evidence and the costs of admitting it at trial. Nevertheless, Stein\u27s project is worthy of great praise because it focuses our attention on the fact that evidentiary rules have many costs beyond their direct contributions to outcome accuracy. Failing to consider these costs does great harm to individual litigants, the justice system, and society at large

Noise in coherently radiating periodic structures beam forming networks

Following the noise wave theory, beam forming networks based on Coherently Radiating Periodic Structures (CORPS-BFN) are analysed and proven to be capable of enhancing the Signal to Noise Ratio of the system by analogically multiplexing the signal and noise contributions present at every input port. The geometry of the network determines the maximum enhancement achievable, which is demonstrated to be independent from insertion losses. These findings are supported by a mathematical approach, as well as with experimental data.The authors would like to acknowledge funding from an ESA ITT AO/1-9524/19/NL/AF with Airbus Defence and Space, S.A.U., Spain, to develop the “OverLapped subArray Fed reflector antennas for SAR instrument”, as well as the FPU Program from the Spanish Ministry of Science and Innovation (FPU18/00013)

Signal vs. Noise: Some Comments on Professor Stein\u27s Theory of Evidential Efficiency

In this Essay, I examine Professor Stein\u27s intriguing new theory of evidential efficiency, which posits that judges should admit evidence whenever it has a sufficiently high signal-to-noise ratio. I explore a slightly different definition of the concepts of signal and noise than Stein, based upon likelihood ratio values rather than the underlying probabilities of events, and I explain why these altered concepts may be analytically superior. Additionally, I call into question the strength of the connection between the signal-to-noise ratio of a piece of evidence and the costs of admitting it at trial. Nevertheless, Stein\u27s project is worthy of great praise because it focuses our attention on the fact that evidentiary rules have many costs beyond their direct contributions to outcome accuracy. Failing to consider these costs does great harm to individual litigants, the justice system, and society at large