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REVIEW 4 major objections 6 minor 46 references

Spatiotemporal Tracking of Persistent, Localized Speckles in Turbulent Atmospheric Propagation

T0 review · 4 major / 6 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read Turbulence produces individual speckles that persist as localized objects over distances several times their Rayleigh length, and their lifetimes encode turbulence strength.

desk verdict New object-level speckle tracking with a genuinely useful persistence diagnostic, but the headline scalings sit on an unspecified radius threshold and no sensitivity analysis; worth refereeing with a request for robustness checks. read the letter →

arxiv 2511.07688 v2 pith:GAYGHUUW submitted 2025-11-10 physics.optics physics.app-phphysics.data-an

Travis M. Crumpton , Luat T. Vuong This is my paper · ORCID
classification physics.opticsphysics.app-phphysics.data-an
keywords speckletrackingatmosphericturbulenceopticalpropagationpersistencebeamfragmentationscintillationrefractiveindexstructureparameterpartiallocalization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that speckles in turbulent propagation are not just anonymous members of a random intensity field but discrete, trackable objects with well-defined creation and death events. Using simulations of the paraxial wave equation with modified von Kármán turbulence, the authors detect speckles by an intensity threshold and track them plane by plane. They find that speckles are spatially confined and persist over distances significantly longer than their associated Rayleigh length. The persistence statistics shift from a bimodal to a near-exponential distribution as turbulence strengthens, with the speckle count increasing sevenfold and mean lifetime dropping fourfold from weak to strong turbulence. If correct, this means that short-exposure multi-plane measurements of speckle lifetimes could be used to estimate the atmospheric refractive-index structure parameter C_n^2, complementing the usual ensemble intensity statistics.

What carries the argument

The key machinery is an intensity-based speckle detection and tracking algorithm. Each speckle is identified as a local maximum above η=0.01 Imax, with adjacent or collocated peaks removed by a radius threshold. Persistence Δz_j is the propagation distance between creation and disappearance events, normalized by the speckle's diffraction length z_0,j; confinement r̃_j(z) is the average radius of the 1/e^2 intensity contour. A magnitude-squared coherence C(z) between vacuum- and turbulence-propagated fields defines the decorrelation distance at which fragmentation begins. These definitions convert a continuous random field into discrete object-level statistics.

What would settle it

Vary the detection threshold η from, say, 0.001 to 0.05 Imax in the same simulated propagations. If the 7× increase in speckle count and 4× decrease in average lifetime between weak and strong turbulence disappear, or if no speckle survives beyond one diffraction length under strong turbulence, the central claim of turbulence-encoded persistence would be falsified. Alternatively, a field experiment with a high-speed camera at two or more observation planes that finds no persistent localized intensity features under strong turbulence would contradict the result.

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Extended reading notes

Core claim

The central claim is that individual speckles can be tracked as persistent, localized objects, and that their persistence and confinement are not fixed properties but scale with turbulence strength. The authors report that beam fragmentation coincides with complete spatial decorrelation as measured by magnitude-squared coherence, and that larger beams decohere and fragment closer to the source, indicating that smaller beams retain coherence longer. Past the decorrelation distance, the beam behaves as a collection of statistically independent speckles, some of which survive multiple diffraction lengths: under strong turbulence about 10% of detected speckles propagate at least one diffraction

Load-bearing premise

The entire population of tracked speckles is defined by a fixed intensity threshold of 1% of the initial maximum and an unspecified radius threshold that merges nearby peaks; if that definition is changed, the counts, lifetimes, and scaling may not hold.

Editorial extensions

If this is right

  • Speckle lifetime distributions can serve as a diagnostic for the effective refractive-index structure parameter C_n^2, using short-exposure multi-plane measurements.
  • Smaller beams retain partial coherence over longer distances than larger beams, which is directly relevant to beam-size selection for free-space optical links.
  • Beyond the decorrelation distance, the beam's dynamics become largely independent of initial beam parameters, simplifying models of deep-turbulence propagation.
  • Persistence and confinement together imply a partial localization of optical energy in substructures of the beam, analogous to localization in disordered dielectrics, which may inform imaging through obscurants.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the persistence statistics are governed by the low-frequency phase structure rather than small-scale intensity fluctuations, then a simpler predictive relation between coherence radius and lifetime distribution may exist; the paper does not test this.
  • The reported 7× count increase and 4× lifetime reduction may be sensitive to the chosen thresholds; a sweep over η and the radius cutoff would show whether the scaling is a property of turbulent transport or of the detector definition.
  • The same tracking framework could be applied to experimental data from a high-speed camera at several observation planes in a real atmospheric path; the paper's simulation-based scalings give concrete predictions to compare against.
  • The connection to localization suggests that speckle persistence might be used to infer not only C_n^2 but also inner scale ℓ_0, since the paper finds ℓ_0 affects the theoretical scintillation index but not the correlation metric.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper presents a numerical study of individual speckle dynamics during Gaussian-beam propagation through atmospheric turbulence. Using split-step propagation with a modified von Kármán spectrum, the authors detect and track speckles via local intensity maxima above ηI_max (η=0.01) and an unspecified radius threshold. They report that beam fragmentation, defined as a rapid increase in speckle number, coincides with the decay of a magnitude-squared coherence metric C(z). They further characterize speckle confinement (width evolution) and persistence (normalized lifetime Δz_j/z0,j) over 500 realizations, concluding that speckles are spatially localized and persist over distances significantly longer than their associated Rayleigh length, with statistics that scale with turbulence strength (e.g., a 7× increase in speckle count and 4× decrease in average lifetime from weak to strong turbulence). The paper suggests these persistence statistics could serve as a diagnostic for the refractive-index structure parameter.

Significance. If the central claim holds, the paper offers a genuinely new object-level perspective on speckle dynamics, complementing the usual ensemble statistics of scintillation and coherence. The methodological strengths are the use of a standard propagation model (split-step with modified von Kármán spectrum), ensemble statistics over 500 runs, and the introduction of four complementary diagnostics (mode field radius, spatial correlation C(z), speckle confinement, and persistence). The finding that speckle lifetimes scale with turbulence strength, if robust, could have practical value for free-space optical sensing and communication. However, the quantitative conclusions are currently conditioned on detection and tracking thresholds that are neither fully specified nor subjected to sensitivity analysis. This is a load-bearing weakness because the headline numbers in the abstract and conclusion—'persistence multiple diffraction lengths,' '7× more speckles,' '4× shorter lifetimes,' '10%/2% survival fractions'—are all computed from a speckle population defined by those thresholds. The paper's significance therefore rests on an as-yet-unverified robustness property.

major comments (4)
  1. [Sec. II.A] The speckle detection algorithm is incomplete: the intensity threshold is given as η=0.01 I_max, but the 'radius threshold' for removing adjacent or collocated speckles is never specified. Every count, confinement, and persistence statistic in Sec. III.C (including the 7× count increase, 4× lifetime decrease, and the 10%/2% survival fractions) is conditional on this unspecified filter. Without stating the radius threshold and providing a sensitivity analysis (e.g., varying η and the radius over reasonable ranges), the reported scalings could be detector artifacts rather than properties of the turbulent field.
  2. [Sec. II.C] The normalized persistence Δz_j/z0,j is defined using z0,j = π w0,j^2/λ, where w0,j is the initial width of the j-th speckle at the time of creation. Both the creation time and the initial width are determined by the intensity and radius thresholds. Consequently, the lifetime histograms in Fig. 4 (insets) are not threshold-invariant observables; changing η shifts the birth/death events and also rescales z0,j. The paper should either demonstrate that the qualitative conclusions are unchanged over a range of thresholds, or define a threshold-independent measure of speckle identity.
  3. [Fig. 1 and Sec. II.A] The tracking between adjacent propagation steps is said to be based on 'nearest neighbor conditions' (Fig. 1 caption), but no matching tolerance is given—e.g., the maximum allowed transverse displacement between steps, or the criterion for distinguishing a reappearing speckle from a new one. Without this, a speckle that moves more than the tolerance between two closely spaced planes would be counted as a death and a later birth, inflating the number of short-lived speckles and biasing the persistence distribution. The matching algorithm must be specified precisely, and the sensitivity of the results to the matching tolerance should be tested.
  4. [Sec. III.C] The paper states that 'strong turbulence across 500 iterations' yields ≈4738 speckles, but it does not specify which C_n^2 value corresponds to 'strong' in this count. From Fig. 3, one infers C_n^2=10^-13 m^{-2/3}, but this should be stated explicitly in the text. More importantly, the 10%/2% survival fractions are quoted without error bars or run-to-run variability; given that only 500 realizations are used, the statistical uncertainty in these tail fractions may be substantial and should be reported.
minor comments (6)
  1. [Sec. III.B] The text says 'Both quantities are plot as functions' — 'plot' should be 'plotted'.
  2. [Sec. III.C] The phrase 'which can be seen in the histograms (Fig. 4, inset)' should be plural: 'insets'.
  3. [Eq. (5)] The integrals for the mode field radius lack explicit integration limits; add 'over the transverse plane' or write ∫∫ over x,y to avoid ambiguity.
  4. [References] Reference [34] is incomplete ('D. G. Voelz, (No Title)'); it should cite the full book: D. G. Voelz, Computational Fourier Optics: A MATLAB Tutorial (SPIE Press, 2011). Reference [46] also lacks publisher location/details.
  5. [Sec. II.B] The quantity C(z) in Eq. (6) is called a 'spatial coherence' metric, but it is actually the overlap between the vacuum-propagated and turbulence-propagated fields, not the mutual coherence function of the field. This terminology could confuse readers; consider calling it the 'field-overlap correlation' or 'vacuum-field fidelity' to distinguish it from standard spatial coherence.
  6. [Fig. 2] The right panels (a1–a4, b1–b4, c1–c4) are described in the caption as 'transverse profiles,' but the axis labels and color scale are not fully explained; it would help to define the color scale (e.g., intensity normalized to I_max) in the caption.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation; threshold dependence is a robustness concern, not a circular reduction.

full rationale

The paper's load-bearing results are produced by direct numerical simulation of the standard paraxial wave equation (Eq. 1) with split-step propagation and a von Kármán spectrum, then by tracking local intensity maxima above a threshold. The detection thresholds (η=0.01 Imax and an unspecified radius threshold) define the speckle population, and persistence is defined as the distance between threshold-identified creation and disappearance events. This makes the quantitative counts and lifetimes threshold-dependent, and the paper itself acknowledges a related normalization artifact in Sec. III.C: 'A high count in the 0.0 bin indicates numerous short-lived or low-power speckles whose large initial radii artificially inflate their associated diffraction length.' That is a real limitation, but it is not circular: no fitted parameter is renamed as a prediction, no uniqueness theorem or self-citation is load-bearing, and the conclusion that some speckles persist several diffraction lengths is not true by construction—a thresholded object could equally exhibit zero or very short persistence. The central physical inputs (turbulence spectrum, propagation equation, coherence metric) are independent of the reported persistence statistics. The lack of sensitivity analysis and code is a reproducibility/robustness concern, not a circularity in the derivation chain. Therefore no circular step satisfies the evidence bar, and the appropriate score is 0.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The results are simulation-derived. The only inputs are standard propagation equations and turbulence spectra, but the object definitions (threshold η, radius filter, nearest-neighbor matching) are chosen by hand and are not independently validated. There are no fitted constants in the usual sense, but the statistical output is sensitive to these choices.

free parameters (3)
  • Intensity threshold η = 0.01
    Speckles are local peaks above η Imax; η=0.01 is chosen to represent a detector sensitivity. Count, localization, and persistence statistics depend directly on this value; no sensitivity analysis is reported (Sec. II A).
  • Radius threshold for adjacent-speckle removal = not stated
    Adjacent or collocated speckles within an unspecified radius threshold are filtered before analysis, altering the detected population and lifetime statistics (Sec. II A).
  • Outer scale L0 = not stated
    The modified von Kármán spectrum requires k0=2π/L0; no value is given, and the authors note the outer scale may contribute to localization/persistence but is not studied (Eq. 2).
assumptions (4)
  • domain assumption The paraxial wave equation (Eq. 1) and Fresnel split-step propagation are valid for the simulated atmospheric path.
    All results are produced by this model; no comparison with a full-wave solver or experiment is provided.
  • domain assumption Refractive-index fluctuations follow the modified von Kármán spectrum with the stated inner-scale cutoff and unspecified outer scale.
    Eq. 2 defines the turbulence ensemble used in every realization; the missing L0 value makes the spectrum not fully determined for reproduction.
  • ad hoc to paper A local intensity maximum above ηImax and outside a radius threshold corresponds to a single physical speckle.
    This definition creates the tracked objects; persistence and localization statistics are therefore partly determined by the detection rule (Sec. II A).
  • ad hoc to paper Speckle identity is maintained continuously between adjacent propagation steps via nearest-neighbor matching.
    Persistence Δzj is only meaningful if the matching rule is correct; tolerances are not given (Fig. 1 caption, Sec. II A).

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Cite this review

Pith. "Pith review of Spatiotemporal Tracking of Persistent, Localized Speckles in Turbulent Atmospheric Propagation." pith.science (2026). https://pith.science/paper/GAYGHUUW

@misc{pith2026251107688,
  author       = {Pith},
  title        = {Pith review of: Spatiotemporal Tracking of Persistent, Localized Speckles in Turbulent Atmospheric Propagation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GAYGHUUW}},
  note         = {Machine review of arXiv:2511.07688}
}
read the original abstract

Light propagation through turbulence produces speckles, whose ensemble behavior is typically characterized by snapshot intensity statistics. Here, we track the spatiotemporal evolution of individual speckles and quantify fragmentation, localization, and persistence under different diffraction and turbulence scales. Beam fragmentation coincides with complete spatial decorrelation defined by the magnitude-squared coherence. Fragmentation occurs closer to the source for larger beams, which indicates that smaller beams are more robust to decoherence. Subsequently, speckles are both spatially localized and persistent over distances significantly longer than their associated Rayleigh length. The combination of localization and persistence impacts the statistics of light relevant to their long-distance signaling and sensing.

Figures

Figures reproduced from arXiv: 2511.07688 by the authors.

Figure 1
Figure 1. FIG. 1. Speckle simulation and tracking. Top row: spatial beam profiles from the source to the receiver plane with representative [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Propagation of Gaussian profiles under (A) weak [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Transition to speckle fragmentation. (A) Spatial coherence [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Evolution of the spot-normalized MFR ˜r [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

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Reference graph

Works this paper leans on

46 extracted references

  1. [1]

    Korotkova and L

    O. Korotkova and L. C. Andrews, inLaser Radar Tech- nology and Applications VII, Vol. 4723 (SPIE, 2002) pp. 73–84

    2002

  2. [2]

    Korotkova, L

    O. Korotkova, L. C. Andrews, and R. L. Phillips, inFree- Space Laser Communication and Laser Imaging II, Vol. 4821 (SPIE, 2002) pp. 98–109

    2002

  3. [3]

    Korotkova, N

    O. Korotkova, N. Farwell, and E. Shchepakina, Waves in Random and Complex Media22, 260 (2012)

    2012

  4. [4]

    Beason, L

    M. Beason, L. Andrews, and S. Gladysz, inEnvironmen- tal Effects on Light Propagation and Adaptive Systems II, Vol. 11153 (SPIE, 2019) pp. 104–120

    2019

  5. [5]

    M. H. Lee, J. F. Holmes, and J. R. Kerr, Journal of the Optical Society of America66, 1164 (1976)

    1976

  6. [6]

    J. W. Goodman,Speckle phenomena in optics: the- ory and applications(Roberts and Company Publishers, 2007)

    2007

  7. [7]

    J. W. Goodman, JOSA66, 1145 (1976)

    1976

  8. [8]

    L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. Al- Habash, Journal of the Optical Society of America A16, 1417 (1999)

    1999

Show all 46 references
  1. [9]

    L. C. Andrews and R. L. Phillips, Laser Beam Propaga- tion Through Random Media: Second Edition (2005)

    2005

  2. [10]

    L. C. Andrews and M. K. Beason,Laser beam propagation in random media: new and advanced topics(2023)

    2023

  3. [11]

    Liguo, G

    W. Liguo, G. Lei, L. Yaqing, Y. Zhiqiang, Y. Lihong, and L. Yao, Heliyon9(2023)

    2023

  4. [12]

    L. I. Goldfischer, Journal of the optical society of america 55, 247 (1965)

    1965

  5. [13]

    O. V. Angelsky, A. P. Maksimyak, P. P. Maksimyak, and S. G. Hanson, Open Optics Journal3, 29 (2009)

    2009

  6. [14]

    Cheng, Y

    X. Cheng, Y. Lockerman, and A. Z. Genack, Optics let- ters39, 3348 (2014)

    2014

  7. [15]

    Migliaccio, L

    M. Migliaccio, L. Huang, and A. Buono, IEEE Transac- tions on Geoscience and Remote Sensing57, 5447 (2019). 7

    2019

  8. [16]

    Migliaccio, F

    M. Migliaccio, F. Abbasi, M. Zahribanhesari, G. Inserra, A. Verlanti, and G. Grieco, inIGARSS 2024-2024 IEEE International Geoscience and Remote Sensing Sympo- sium(IEEE, 2024) pp. 1773–1776

    2024

  9. [17]

    Macintosh, L

    B. Macintosh, L. Poyneer, A. Sivaramakrishnan, and C. Marois, inAstronomical Adaptive Optics Systems and Applications II, Vol. 5903 (SPIE, 2005) pp. 170–177

    2005

  10. [18]

    N. R. Van Zandt and M. F. Spencer, Applied Optics59, 1071 (2020)

    2020

  11. [19]

    Gladysz and J

    S. Gladysz and J. C. Christou, The Astrophysical Journal 684, 1486 (2008)

    2008

  12. [20]

    Guyot, M.-C

    S. Guyot, M.-C. P´ eron, and E. Del´ echelle, Physical Re- view E—Statistical, Nonlinear, and Soft Matter Physics 70, 046618 (2004)

    2004

  13. [21]

    Zhang, B

    S. Zhang, B. Hu, P. Sebbah, and A. Z. Genack, Physical review letters99, 063902 (2007)

    2007

  14. [22]

    Garnier and K

    J. Garnier and K. Sølna, Inverse Problems34, 094003 (2018)

    2018

  15. [23]

    Garcia-Caurel, A

    E. Garcia-Caurel, A. Plyer, E. Colin, X. Orlik, and R. Os- sikovski, Journal of the Optical Society of America A42, 1531 (2025)

    2025

  16. [24]

    J. P. Bos, G. Archer, and M. C. Roggemann, inLaser Communication and Propagation through the Atmosphere and Oceans II, Vol. 8874 (SPIE, 2013) pp. 162–170

    2013

  17. [25]

    R. Liu, B. Qing, S. Zhao, P. Zhang, H. Gao, S. Chen, and F. Li, Physical review letters127, 180601 (2021)

    2021

  18. [26]

    Lagendijk, B

    A. Lagendijk, B. v. Tiggelen, and D. S. Wiersma, Physics today62, 24 (2009)

    2009

  19. [27]

    P. A. Lee and D. S. Fisher, Physical Review Letters47, 882 (1981)

    1981

  20. [28]

    Gade, Nuclear Physics B398, 499 (1993)

    R. Gade, Nuclear Physics B398, 499 (1993)

    1993

  21. [29]

    Segev, Y

    M. Segev, Y. Silberberg, and D. N. Christodoulides, Na- ture Photonics7, 197 (2013)

    2013

  22. [30]

    De Raedt, A

    H. De Raedt, A. Lagendijk, and P. de Vries, Physical review letters62, 47 (1989)

    1989

  23. [31]

    Chabanov, M

    A. Chabanov, M. Stoytchev, and A. Genack, Nature404, 850 (2000)

    2000

  24. [32]

    P. W. Anderson, Physical Review109, 1492 (1958)

    1958

  25. [33]

    Kolokolov, V

    I. Kolokolov, V. Lebedev, and P. M. Lushnikov, Physical Review E101, 042137 (2020)

    2020

  26. [34]

    D. G. Voelz, (No Title) , 51 (2011)

    2011

  27. [35]

    R. L. Phillips and L. C. Andrews, Journal of the Optical Society of America71, 1440 (1981)

    1981

  28. [36]

    Garnier and K

    J. Garnier and K. Sølna, Journal of the Optical Society of America A39, 1309 (2022)

    2022

  29. [37]

    Garnier, A

    J. Garnier, A. Picozzi, and T. Torres, Physical Review Letters134, 223803 (2025)

    2025

  30. [38]

    Voelz, E

    D. Voelz, E. Wijerathna, A. Muschinski, and X. Xiao, Optical Engineering57, 104102 (2018)

    2018

  31. [39]

    Malekpour, J

    S. Malekpour, J. A. Gubner, and W. A. Sethares, Journal of the Franklin Institute355, 2932 (2018)

    2018

  32. [40]

    Carter, C

    G. Carter, C. Knapp, and A. Nuttall, IEEE transactions on audio and electroacoustics21, 337 (2003)

    2003

  33. [41]

    D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righ- ini, Nature390, 671 (1997)

    1997

  34. [42]

    Schwartz, G

    T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Na- ture446, 52 (2007)

    2007

  35. [43]

    L. B. Stotts and L. C. Andrews, Optical Engineering63, 041207 (2024)

    2024

  36. [44]

    A. Nair, Q. Li, and S. N. Stechmann, Optics Letters48, 3865 (2023)

    2023

  37. [45]

    Bal and A

    G. Bal and A. Nair, Waves in Random and Complex Media , 1 (2025)

    2025

  38. [46]

    B. E. Saleh and M. C. Teich,Fundamentals of photonics, 2 volume set(john Wiley & sons, 2019)

    2019

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