A numerical investigation of laser Doppler acoustic field reconstruction with ultrasonic attenuation

In this paper, we confirm the feasibility of characterizing ultrasonic filed through laser Doppler echo light, which is based on the theoretical modeling of acousto-optic effects and simulations of acoustic field reconstruction. This article derives the fundamental equations of the acousto-optic effect and proves that the variations of the refractive index of the medium are proportional to the ultrasonic filed pressure. Considering the propagation distance and frequency of ultrasound in a homogeneous medium, we quantitatively discuss the attenuation characteristics of ultrasonic waves as they travel through the air medium. We obtain the refractivity distribution models of plane wave sound source, spherical wave sound source and cylindrical wave sound source through theoretical analysis and simulation experiments. The projection of the ultrasonic filed pressure in the direction of beam propagation can be described mathematically by means of the Radon transform, which makes it feasible to reconstruct an ultrasonic filed by the filtered back-projection algorithm. We prove following viewpoints with quantifiable formulas and intuitive numerical simulations: the ultrasonic attenuation coefficient is mainly determined by the transmission distance and ultrasonic frequency, and ultrasonic attenuation cannot be ignored in the ultrasonic propagation; the angle resolution and filter type provide higher contribution to the ultrasonic filed reconstruction. This paper provides an ultrasonic field reconstruction model including the ultrasonic attenuation and verifies the feasibility of accurately inverting the sound field using this model.