Generalized shot noise model for time-reversal in multiple-scattering media allowing for arbitrary inputs and windowing

Abstract

A theoretical shot noise model to describe the output of a time-reversal experiment in a multiple-scattering medium is developed. This ͑non-wave equation based͒ model describes the following process. An arbitrary waveform is transmitted through a high-order multiple-scattering environment and recorded. The recorded signal is arbitrarily windowed and then time-reversed. The processed signal is retransmitted into the environment and the resulting signal recorded. The temporal and spatial signal and noise of this process is predicted statistically. It is found that the time when the noise is largest depends on the arbitrary windowing and this noise peak can occur at times outside the main lobe. To determine further trends, a common set of parameters is applied to the general result. It is seen that as the duration of the input function increases, the signal-to-noise ratio ͑SNR͒ decreases ͑independent of signal bandwidth͒. It is also seen that longer persisting impulse responses result in increased main lobe amplitudes and SNR. Assumptions underpinning the generalized shot noise model are compared to an experimental realization of a multiple-scattering medium ͑a time-reversal chaotic cavity͒. Results from the model are compared to random number numerical simulation.

Time reversal focusing in the audible range using a tunable sonic crystal

“…Even when the impulse responses of x 1 and x 2 are completely uncorrelated, the introduction of the decay time leads to more energy in the beginning of the impulse and raises the expectation value of the cross correlation at the time of reversal. This observation is consistent with Haworth et al (2009), who derived a statistical approximation for the expectation value of the TR focused signal in the case of the shot noise model with a temporal decay showing an increase along with the time constant of the decay.…”

“…The shot noise model is obtained as a superposition of pulses that follows a Poisson point process in time. This model can describe the ideal impulse response of a highorder disordered scattering medium where each pulse corresponds to a different multiple-scattering path (Haworth et al, 2009). We also incorporate three additional features that extend this model so that it applies to our particular system without losing its intrinsic random nature.…”

Tunable time-reversal cavity for high-pressure ultrasonic pulses generation: A tradeoff between transmission and time compression

“…The tunable TRC leads to an amplification of Â15 compared to the solid cavity used in 1-bit TR. To justify this result, the shot noise model proposed by Derode et al 8,9 was used. The random signals can be described with a variance r(t), representing the envelope of the signal s(t).…”

A comparison of impulse response modification techniques for time reversal with application to crack detection

“…22,23 Studies have examined the reliance of focal amplitude on the length of the initial pulse (i.e., the bandwidth). [24][25][26] Physical system adjustments have sought to increase SNR through other means such as the introduction of a chaotic cavity [27][28][29][30] or the use of an acoustic metamaterial-based filter. 31 Recently, Willardson et al published experimental research manipulating TR processing in order to maximize the focal amplitude of audible sound in a reverberation chamber.…”