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PSMS

Source: vignettes/psms/index.Rmd
index.Rmd

Overview

Benchmarked Validated
Theory Implementation

The prolate-spheroidal modal-series solution (PSMS) calculates scattering from a homogeneous prolate spheroid. It is the geometry-matched reference for smooth elongated canonical targets.

Core idea

Separate the Helmholtz equation in prolate spheroidal coordinates, expand the fields in angular and radial spheroidal wave functions, and solve the retained boundary system (Spence and Granger 1951; Furusawa 1988).

Best for

  • Fixed-rigid, pressure-release, liquid-filled, or gas-filled prolate spheroids
  • Canonical elongated-body benchmarks
  • Reference comparisons for the prolate branch of TMM

Supports

  • ProlateSpheroid shapes carried by FLS or GAS scatterers
  • Broadside and oblique monostatic calculations with explicit roll angle
  • Configurable truncation, integration, adaptive evaluation, and numerical precision

Main assumptions

  • An exact prolate-spheroidal outer boundary
  • One homogeneous interior region
  • Linear time-harmonic acoustics
  • No shell, secondary component, or arbitrary body profile

Validation status

  • Benchmarked against the canonical prolate-spheroid spectra stored in benchmark_ts.
  • Validated against the external Prol_Spheroid and echoSMs implementations on shared prolate cases.

Family pages

  • Implementation: supported branches, numerical controls, output, and benchmarks
  • Theory: spheroidal coordinates, wave functions, and boundary systems

References

Furusawa, Masahiko. 1988. “Prolate Spheroidal Models for Predicting General Trends of Fish Target Strength.” Journal of the Acoustical Society of Japan (E) 9 (1): 13–24. https://doi.org/10.1250/ast.9.13.
Spence, R. D., and Sara Granger. 1951. “The Scattering of Sound from a Prolate Spheroid.” The Journal of the Acoustical Society of America 23 (6): 701–6. https://doi.org/10.1121/1.1906827.