Bessel-Based Modeling of Acoustic Field Distribution and Its Impact on Measurement Uncertainty in Ultrasound and Photoacoustic Systems

This study presents a measurement-oriented analysis of Bessel functions for modeling acoustic field distributions in ultrasound and photoacoustic systems. It combines the mathematical foundations of Bessel functions with explicit numerical calculations, beam-profile analysis, and uncertainty evaluation. The paper proposes a framework linking Bessel-based field behavior to measurement uncertainty in medical metrology, demonstrating that accurate calibration requires physically realistic field models rather than idealized plane-wave assumptions. The work bridges applied mathematics, acoustics, ultrasound engineering, and measurement science.