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arxiv: 2605.03469 · v1 · submitted 2026-05-05 · ⚛️ physics.optics · math-ph· math.MP

Anisotropy in Fourier space optical memory effect correlations

Niall Byrnes , Matthew R. Foreman This is my paper

Pith reviewed 2026-05-07 15:00 UTC · model grok-4.3

classification ⚛️ physics.optics math-phmath.MP
keywords optical memory effectspeckle correlationsFourier spaceanisotropydisordered mediasingle scatteringwavevector componentsscattered field correlations
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The pith

Optical memory effect correlations depend non-trivially on axial wavevector differences in addition to transverse shifts.

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

The paper investigates anisotropy in Fourier-domain speckle correlations for the optical memory effect in disordered scattering media. While the conventional memory effect is known to constrain transverse wavevector shifts, the work shows that correlation strength also varies with differences in the axial wavevector components. This holds within a single-scattering framework and is confirmed by numerical simulations of a three-dimensional medium. The analysis extends to pseudo-correlations, revealing similar anisotropic behavior in the conjugate memory effect.

Core claim

Within a single scattering framework, the correlation strength associated with the optical memory effect in Fourier space depends not only on transverse wavevector shifts but also non-trivially on differences in axial wavevector components. Numerical simulations of a three-dimensional single scattering medium agree closely with the derived theory, and the same anisotropic dependence appears in pseudo-correlations of the conjugate memory effect.

What carries the argument

The Fourier-space speckle correlation function derived under the single-scattering approximation, which explicitly includes both transverse and axial wavevector differences to capture the anisotropy.

If this is right

  • Models of light transport through scattering media must incorporate axial wavevector effects to accurately predict correlation decay.
  • Imaging and sensing techniques that exploit the memory effect may require calibration for axial variations in addition to transverse ones.
  • The conjugate memory effect inherits the same anisotropy, broadening the range of correlation-based methods affected by axial disorder.
  • Three-dimensional disorder introduces directional dependence in speckle statistics that is absent in simpler two-dimensional treatments.

Where Pith is reading between the lines

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

  • The results suggest that axial sampling strategies in experiments could be optimized to maximize or minimize correlation strength.
  • Analogous anisotropy may appear in other wave systems such as acoustics or microwaves propagating through disordered media.
  • Further work could test whether multiple-scattering regimes preserve or modify the reported axial dependence.

Load-bearing premise

The single scattering approximation holds and axial disorder can be treated without multiple-scattering corrections dominating the observed correlations.

What would settle it

Measurements or simulations in which correlation strength shows no dependence on axial wavevector differences while transverse shifts remain fixed would falsify the central claim.

Figures

Figures reproduced from arXiv: 2605.03469 by Matthew R. Foreman, Niall Byrnes.

Figure 1
Figure 1. Figure 1: FIG. 1 view at source ↗
Figure 2
Figure 2. Figure 2: shows |C P | in the case kiz, kuz > 0 and Eej and Eev calculated in the plane z = z + m, i.e. in transmission. The solid line, computed now from Eq. (6) with signs (si , sj , su, sv) = (1, 1, 1, 1), agrees well with the simulated data. We note that while this choice of signs is identical to that used in view at source ↗
read the original abstract

We investigate anisotropy in Fourier-domain speckle correlations associated with the optical memory effect in disordered scattering media. Within a single scattering framework, we show that while the conventional memory effect constrains transverse wavevector shifts, the correlation strength also depends non-trivially on differences in the axial wavevector components. Our theory is supported by numerical simulations of a three-dimensional, single scattering medium, which show excellent agreement with theory. We extend the analysis to pseudo-correlations, demonstrating that analogous anisotropic behavior arises in the conjugate memory effect. Our results highlight the often neglected role of axial disorder in scattered field correlations.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates anisotropy in Fourier-domain speckle correlations for the optical memory effect in disordered scattering media. Within a single-scattering framework, it derives that while the memory effect constrains transverse wavevector shifts, the correlation strength depends non-trivially on differences in axial wavevector components. The theory is validated by direct numerical simulations of a three-dimensional single-scattering medium showing excellent agreement, and the analysis is extended to pseudo-correlations arising in the conjugate memory effect.

Significance. If the central result holds, the work usefully highlights the often-neglected contribution of axial disorder to scattered-field correlations in Fourier space. The parameter-free single-scattering derivation combined with direct numerical confirmation in a 3D medium constitutes a clear strength, providing a concrete, falsifiable prediction for the axial dependence. This could inform more accurate modeling of memory-effect-based imaging and sensing through turbid media.

major comments (2)
  1. [Theory and abstract] The single-scattering derivation of the axial-wavevector dependence (abstract and theory section) is internally consistent, but the manuscript should explicitly state the range of validity (e.g., optical depth or scattering strength) beyond which multiple-scattering corrections would dominate the reported anisotropy; without this, the central claim risks over-extrapolation.
  2. [Numerical simulations] Simulations are stated to show 'excellent agreement' with theory, yet no quantitative metrics (e.g., mean-squared residual, correlation coefficient, or parameter values for the 3D medium) are referenced; this weakens the validation of the non-trivial axial dependence.
minor comments (2)
  1. [Introduction] Notation for transverse and axial wavevector components should be introduced with a clear diagram or table early in the manuscript to aid readability.
  2. [Pseudo-correlations section] The extension to pseudo-correlations would benefit from a brief comparison table contrasting the conventional and conjugate memory-effect anisotropies.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment, constructive comments, and recommendation for minor revision. We address each major comment point by point below and will incorporate the suggested improvements.

read point-by-point responses

  1. Referee: [Theory and abstract] The single-scattering derivation of the axial-wavevector dependence (abstract and theory section) is internally consistent, but the manuscript should explicitly state the range of validity (e.g., optical depth or scattering strength) beyond which multiple-scattering corrections would dominate the reported anisotropy; without this, the central claim risks over-extrapolation.

    Authors: We agree that an explicit statement on the validity range is necessary to avoid over-extrapolation. In the revised manuscript, we will add a dedicated paragraph in the theory section (and a brief note in the abstract) specifying that the single-scattering framework and resulting anisotropy apply to optically thin media with optical depth τ ≪ 1, where multiple-scattering contributions remain negligible. This is consistent with the assumptions underlying our derivation and simulations. revision: yes

  2. Referee: [Numerical simulations] Simulations are stated to show 'excellent agreement' with theory, yet no quantitative metrics (e.g., mean-squared residual, correlation coefficient, or parameter values for the 3D medium) are referenced; this weakens the validation of the non-trivial axial dependence.

    Authors: We acknowledge that quantitative metrics would strengthen the validation. In the revision, we will add the correlation coefficient and mean-squared residual between theory and simulation data, together with the explicit parameters of the 3D single-scattering medium (scatterer density, radius, and simulation volume). These additions will be placed in the numerical simulations section and referenced in the figure captions. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained within single-scattering wave optics

full rationale

The paper derives the non-trivial axial wavevector dependence of Fourier-space speckle correlations directly from the single-scattering framework and validates it via independent numerical simulation of a 3D disordered medium. No load-bearing step reduces to a fitted parameter, self-definition, or self-citation chain; the central result follows from standard wave optics applied to the scattering integral and is externally falsifiable by the reported simulations. Minor self-citations, if present, are not required for the scoped claim.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on abstract; single-scattering assumption is the main domain premise invoked for the derivation. No free parameters or invented entities are mentioned.

axioms (1)
  • domain assumption single scattering framework
    Invoked to derive the anisotropic correlation dependence on axial wavevector differences.

pith-pipeline@v0.9.0 · 5388 in / 1019 out tokens · 79008 ms · 2026-05-07T15:00:38.170154+00:00 · methodology

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Reference graph

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