Continuation of acoustic near-fields.

Area of Science:

• Acoustics
• Wave Propagation
• Numerical Methods

Background:

• Acoustic pressure fields are often measured on finite surfaces.
• Extending these measurements to a larger region is crucial for applications like source localization and acoustic imaging.
• Analytic continuation is a mathematical technique to extend a function beyond its original domain.

Purpose of the Study:

• To develop and validate an iterative algorithm for the analytic continuation of coherent acoustic pressure fields.
• To extend a measured pressure field from a finite sheet to a larger, tangential region.
• To assess the algorithm's performance with noisy data and its applicability to different surface geometries.

Main Methods:

• Utilizes Green's function (transfer function) to relate acoustic quantities between conformal surfaces.
• Employs regularization theory to handle inverse problems and noisy data.
• An iterative algorithm is developed and tested on numerical and experimental data.

Main Results:

• The algorithm successfully continues the pressure field into a tangential sheet.
• Results demonstrate accuracy near the original boundary, with the field decaying away from it.
• Extrapolation to an area nearly double the original measurement region was achieved for a point-driven rectangular plate.

Conclusions:

• The presented iterative algorithm provides an effective method for analytic continuation of acoustic pressure fields.
• The technique is robust against noise and applicable to both planar and arbitrarily shaped surfaces.
• This work advances the capability to reconstruct or predict acoustic fields beyond measurement boundaries.