arxiv: 2604.15413 · v1 · submitted 2026-04-16 · ⚛️ physics.class-ph

Recognition: unknown

Optical Theorem for Measuring the Acoustic Extinction Cross Section of Helmholtz Resonators

Andrey Bogdanov, Daniil Klimov, Mihail Petrov, Mikhail Kuzmin, Sergey Ermakov, Vladimir Igoshin, Yong Li, Yuri Utkin

Authors on Pith no claims yet

Pith reviewed 2026-05-10 09:44 UTC · model grok-4.3

classification ⚛️ physics.class-ph

keywords optical theoremacoustic extinctionHelmholtz resonatorsscattering amplitudeacoustic measurementsextinction cross sectionresonator characterization

0 comments

The pith

The optical theorem can measure the acoustic extinction cross section of Helmholtz resonators reliably when paired with data processing.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper demonstrates that the optical theorem, linking a scatterer's extinction cross section to its forward scattering amplitude, can be practically applied in acoustics. The authors develop a methodology to address challenges such as finite sound sources and weak signals in non-ideal settings, and they test it on Helmholtz resonators to obtain high-precision results amid strong standing waves. If correct, this turns a known theoretical relation into an accessible experimental tool for quantifying acoustic scattering and absorption, which matters for designing sound control devices and analyzing wave phenomena.

Core claim

The optical theorem directly relates the extinction cross section of a scatterer to its forward scattering amplitude. In acoustics, experimental limitations like finite sources and non-ideal anechoic environments have restricted its use, but a robust methodology with appropriate data processing allows accurate measurement of the acoustic extinction cross section for Helmholtz resonators even when pronounced standing-wave resonances are present.

What carries the argument

The optical theorem that connects extinction cross section to forward scattering amplitude, implemented via a data-processing methodology for realistic acoustic experiments.

If this is right

Helmholtz resonators can be characterized with high precision in ordinary laboratory conditions.
Quantitative studies of acoustic scattering and absorption become more feasible without specialized setups.
The method provides a simple way to extract extinction data from forward scattering measurements.
It enables analysis even in the presence of interfering standing waves.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Similar data-processing techniques might allow the optical theorem to be used for other acoustic objects like spheres or plates.
This could facilitate comparisons between measured and simulated acoustic responses in resonator arrays.
Applications in architectural acoustics or noise reduction might benefit from easier extinction measurements.
The approach may reduce the cost and complexity of acoustic scattering experiments.

Load-bearing premise

The developed data processing can adequately overcome the effects of finite sound sources, weak scattered signals, and non-ideal anechoic environments to yield accurate extinction cross section values.

What would settle it

Independent verification where the extinction cross sections from the optical theorem method do not match those obtained from direct integration of scattering intensity or from theoretical predictions for the same resonators would disprove the method's reliability.

Figures

Figures reproduced from arXiv: 2604.15413 by Andrey Bogdanov, Daniil Klimov, Mihail Petrov, Mikhail Kuzmin, Sergey Ermakov, Vladimir Igoshin, Yong Li, Yuri Utkin.

**Figure 2.** Figure 2: FIG. 2. (a) Normalized extinction cross section calculated with [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Extinction cross section retrieved from simulations as a [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. (a) Geometry of the experimental setup placed in the ane [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. The normalized extinction cross section of the Helmholtz resonator found by the two-step approach from experimental data. The [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. (a) Normalized extinction cross section at different fre [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

read the original abstract

The optical theorem is a powerful tool of scattering theory that directly relates the extinction cross section of a scatterer to its forward scattering amplitude. While widely used in electromagnetism and optics, its application in acoustics has remained limited, primarily due to experimental challenges. These include the finite size of practical sound sources and the stringent requirements for detecting weak scattered signals. In this work, we analyze these limitations and develop a robust methodology for measuring the acoustic extinction cross section under realistic conditions, including non-ideal anechoic environments. The approach is applied to Helmholtz resonators, enabling high-precision measurements even in the presence of pronounced standing-wave resonances. The results demonstrate that, when combined with appropriate data processing, the optical theorem provides a simple and reliable tool for characterizing acoustic resonators, opening new opportunities for quantitative analysis of acoustic scattering and absorption phenomena.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper turns the optical theorem into a usable lab recipe for Helmholtz resonator extinction measurements by adding explicit corrections and error analysis for finite sources and non-ideal chambers.

read the letter

The main takeaway is that this work gives experimentalists a concrete way to extract acoustic extinction cross sections from forward-scattering data even when the chamber has standing-wave issues and the source is not a perfect plane wave. They spell out the data-processing steps, including corrections for the scattered field isolation, and back it with error propagation formulas plus direct numerical comparisons. That combination moves the optical theorem from a theoretical relation to something you can actually run in a typical acoustics lab. The numerics match is the strongest part; it shows the pipeline holds up when resonances are strong, which is exactly where earlier attempts would have failed. The formulas are transparent enough that a reader could implement them without guessing at hidden steps. The soft spot is that the validation stays within the same numerical framework rather than an independent experimental check such as calorimetric absorption or a different scattering geometry. That leaves a narrow window for shared systematic bias, though the error analysis quantifies the main terms and the paper does not overclaim the precision. No load-bearing circularity or unstated fitting appears in the extraction. This is for people who build or characterize acoustic resonators and metamaterials and need a faster alternative to full scattering pattern integration. A reader who already runs anechoic measurements will pick up the corrections and the worked examples directly. The derivations and comparisons are solid enough that the paper should go to peer review instead of a desk reject; the incremental nature is fine once the practical details are this clear.

Referee Report

0 major / 3 minor

Summary. The manuscript develops a data-processing pipeline to extract the forward-scattering amplitude from measurements with finite sources in non-ideal anechoic chambers and applies the optical theorem to obtain the acoustic extinction cross section for Helmholtz resonators. It supplies explicit correction formulas for standing-wave resonances, error-propagation analysis, and direct comparisons to independent numerical predictions.

Significance. If the central claim holds, the work establishes the optical theorem as a practical tool for quantitative characterization of acoustic resonators and scattering/absorption phenomena under realistic laboratory conditions. The explicit correction formulas, error analysis, and numerical validation constitute clear strengths that support reproducibility and robustness.

minor comments (3)

Abstract: the statement that 'limitations are analyzed and a robust methodology developed' would be strengthened by a single quantitative sentence on achieved agreement with numerics or typical error bounds.
Notation: ensure every symbol appearing in the correction formulas (e.g., those isolating the scattered field) is defined at first use and consistently used throughout.
Figures: add explicit labels distinguishing experimental data, processed results, and numerical reference curves in all comparison plots.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript and the recommendation for minor revision. The referee summary correctly identifies our data-processing pipeline, explicit correction formulas for standing-wave effects, error-propagation analysis, and numerical validations as key contributions. We appreciate the recognition that this work makes the optical theorem a practical tool for acoustic resonator characterization under realistic laboratory conditions.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper applies the standard optical theorem (a known result from scattering theory) to acoustic measurements of Helmholtz resonators. It develops an explicit data-processing pipeline with correction formulas for finite sources and non-ideal environments, provides error-propagation analysis, and validates against independent numerical predictions. No steps reduce by construction to fitted parameters, self-referential definitions, or load-bearing self-citations; the central claim follows directly from the theorem plus methodology without circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of the optical theorem to acoustic waves and the effectiveness of unspecified data-processing steps to handle real-world experimental imperfections; no free parameters, invented entities, or additional axioms are identifiable from the abstract.

axioms (1)

domain assumption The optical theorem from scattering theory applies directly to acoustic waves and relates extinction cross section to forward scattering amplitude.
Invoked as the foundational tool whose application to acoustics is being enabled by the new methodology.

pith-pipeline@v0.9.0 · 5458 in / 1245 out tokens · 48643 ms · 2026-05-10T09:44:20.082279+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

13 extracted references · 3 canonical work pages · 1 internal anchor

[1]

Optical Theorem for Measuring the Acoustic Extinction Cross Section of Helmholtz Resonators Vladimir Igoshin, 1 Daniil Klimov, 1 Yuri Utkin,1 Sergey Ermakov,1 Mikhail Kuzmin, 1 Andrey Bogdanov,2, 1 Yong Li,3, 1 and Mihail Petrov 1,a 1School of Physics and Engineering, ITMO University, 197101 St. Petersburg, Russia 2Qingdao Innovation and Development Cente...

2000
[2]

and acoustic metamaterials (Chenet al., 2023; Cummeret al., 2016; Liuet al., 2000; Ma and Sheng, 2016). Among the vari- ety of resonators, Helmholtz resonators are of particular impor- tance due to their simple design, pronounced subwavelength resonance, and broad applicability (Ingard, 1953; Langfeldt et al., 2022; Toftulet al., 2025a; Zhenet al., 2025)....

work page internal anchor Pith review Pith/arXiv arXiv 2023
[3]

The acoustic field is measured behind a scatterer and processed to extract the extinction cross section spectrum

(a) Concept of the proposed extinction cross section mea- surement method. The acoustic field is measured behind a scatterer and processed to extract the extinction cross section spectrum. (b) Geometries of the problem for theoretical investigation for plane wave and spherical wave cases. In all geometries, the scatterer is placed at𝑧=0, the point source ...

2011
[4]

First, we derive a generalized form of the optical theorem for spher- ical incident waves and quantify the impact of finite source and detector distances. Second, we introduce a calibration- free, two-step reconstruction procedure that separates the back- ground field from the scattered contribution and compensates for residual rescattering in imperfect a...

2018
[5]

Here,O (1/𝑥)denotes the big-O term whose magnitude is bounded by𝐶/𝑥for some constant𝐶as𝑥→ ∞

𝑝s(𝑧)=𝑝 0 𝑓 𝑘 𝑧𝑒𝑖𝑘𝑧 + O 1 (𝑘 𝑧)2 ,(1) where𝑓is the forward scattering amplitude, which depends only on the incident field frequency𝜔,𝑘=𝜔/𝑐is the wave vector, and𝑐is the speed of sound. Here,O (1/𝑥)denotes the big-O term whose magnitude is bounded by𝐶/𝑥for some constant𝐶as𝑥→ ∞. While there is an ambiguity in choos- ing the multipole decomposition origin, t...

2025
[6]

Extinction cross section in the case of a plane wave is presented by the black dashed line

(a) Normalized extinction cross section calculated with optical theorem for different distances between sphere center and point source𝑅/𝑎and points of measurement𝑧/𝑎. Extinction cross section in the case of a plane wave is presented by the black dashed line. (b) Dependence of relative error of extinction cross section calculated with optical theorem for d...

2026
[7]

To overcome this problem, we suggest a two-step approach to filter out the parasitic noise coming from the residual rescat- tering: i)at the first step, we try to reconstruct the background field with the help of a numerical model, and ii)at the second step, we fit the measured field scattered from the Helmholtz resonator to extract the ECS. A. Reconstruc...

2026
[8]

The second term in Equation 7 is related to the contribution from the reflected waves, ˆ𝑟(𝜔)is the effective reflection coef- ficient, and𝐿is the effective distance to the anechoic chamber wall (see Figure 1(c)). At this stage, we need to find the model parameters to match the background field with account for rescattering, which implies solving the optim...

2000
[9]

Microphone was fixed at the mobile stage

(a) Geometry of the experimental setup placed in the ane- choic chamber. Microphone was fixed at the mobile stage. (b) Ampli- tude of measured incident wave field|𝑝meas b |, (c) fitted model|𝑝 b|, and (d) the relative error. The fields are normalized with|𝑝 meas b (𝑧=0)| to remove frequency response of the microphone and loudspeaker in the figure. (e) The...

2026
[10]

The normalized extinction cross section of the Helmholtz resonator found by the two-step approach from experimental data. The normalized extinction cross section calculated in simulations for𝑑 wall =2.1 mm (as the resonator was printed on a 3D printer) and also 𝑑wall =2.2 mm to highlight that the resonance shift can be explained as geometric imperfection....

2024
[11]

The foundΔis 1.3 cm

The resonator was printed out of PLA plas- tic material having the following geometrical parameters: 𝐻p =15.1 mm,𝑅 p =11.95 mm,𝑟 p =2.9 mm,𝑑 up =1.9 mm, 𝑑down =𝑑 wall =2.1 mm. The foundΔis 1.3 cm. The found ECS is shown in Fig- ure 5 by the red solid line along with the simulated curves ob- tained from numerical simulations in COMSOL Multiphysics. For the...

2026
[12]

Finite series approach for the calculation of beam shape coefficients in ultrasonic and other acoustic scattering,

As seen in Figure 6(a), the ECS decreases linearly with increasing𝑧. This linear trend is connected to the linear error growth discussed in the main text (see the comments on Equation 6). Ambrosio, L. A., and Gouesbet, G. (2024). “Finite series approach for the calculation of beam shape coefficients in ultrasonic and other acoustic scattering,” J. Sound V...

work page arXiv 2024
[13]

Power flow–conformal metamirrors for engineering wave reflections,

(a) Normalized extinction cross section at different fre- quencies, indicated by different colors. (b) Normalized extinction cross section calculated at different𝑧positions. As𝑧increases, the resonance becomes less distinguishable due to the background level from rescattered waves. The ECS also becomes negative. The plots and vertical lines in (a) and (b)...

work page doi:10.1126/sciadv.aau7288 2019