AI-interpreted Optical Scattering for Robust and Focal Depth-Aware Imaging

Corey Hart; Eunji Ko; Patrick Ross; Wolfgang Losert

REVIEW 3 major objections 6 minor 14 references

AI-interpreted Optical Scattering for Robust and Focal Depth-Aware Imaging

T0 review · 3 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper claims that optical scattering, usually treated as an obstacle, can make captured images more robust to occlusion and can encode the focal depth of an object hidden inside the scattering volume.

desk verdict Scattering-as-feature proof-of-concept with a genuinely novel split-latent VAE, but the focal-depth experiment is underspecified enough that the paper's second central claim is not yet established. read the letter →

arxiv 2607.22867 v1 pith:7VEQMTTU submitted 2026-07-24 physics.optics cs.AIcs.LG

Eunji Ko , Patrick Ross , Corey Hart , Wolfgang Losert This is my paper · ORCID

classification physics.opticscs.AIcs.LG

keywords opticalscatteringspeckleimagingvariationalautoencodersplit-latentVAEfocaldepthdiscriminationocclusionrobustnessMNISTinformationdistribution

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

The paper is trying to establish that scattering is not only a lossy corruption but a physical process that reshapes how information is stored in light. By projecting MNIST digits through scattering media of three strengths and decoding the resulting speckle patterns with a variational autoencoder, the authors show that object information spreads across the whole detector plane: scattered images survive circular occlusion far better than unscattered ones, with heavier scattering moving the accuracy-versus-masked-area curve toward the uniform-information limit. They also claim that the same speckle patterns carry a decodable signature of the axial focal depth where the pattern was projected inside the medium, and that a split-latent VAE can separate this depth information from the digit content. These results matter because they suggest a way to build imaging systems that use obstacles and volumetric scattering as part of the sensing mechanism, rather than only as something to undo.

What carries the argument

The load-bearing object is the speckle field generated by multiple scattering—light redistributed into a grainy intensity pattern that carries object information across the full detector rather than in compact central features. The load-bearing architecture is the split-latent VAE, a variational autoencoder whose latent vector is split into two disjoint subspaces: a digit subspace $\mathbf{z}_{\mathrm{digit}}$ used exclusively to decode clean MNIST images, and a focal subspace $\mathbf{z}_{\mathrm{focal}}$ used together with the digit subspace to decode scattered images and, through a jointly trained classifier head, to predict focal depth. This split enforces a functional separation: the digit subspace must carry the object content, while the focal subspace absorbs depth-dependent and scattering-dependent variation. The occlusion analysis fits the scattered-data accuracy curves to a power law whose exponent quantifies how uniformly information is distributed, and the depth analysis measures cluster separation in the focal subspace via silhouette scores and centroid distances.

What would settle it

Repeat the focal-depth experiment while changing only the axial distance of the projected pattern relative to the scattering medium—for instance, translating the medium along the optical axis with the camera, lenses, illumination, and SLM untouched. If the focal classifier drops to chance once magnification and intensity are held constant, the claimed depth encoding is not a property of scattering; if the pattern must be refocused and any refocusing changes image scale or brightness, those confounds need to be controlled and shown not to drive the result.

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Extended reading notes

Core claim

On its own terms, the paper claims two concrete discoveries. First, information in a speckle pattern is spatially distributed: under a centered circular mask whose radius reaches 192 pixels of a 384×384 image, reconstruction of unscattered MNIST collapses to roughly 10% SOPCNN accuracy, while scattered datasets remain substantially decodable, and the fitted power-law exponent $\alpha$ rises from 0.692 (low) to 0.757 (high) scattering—toward 1, the value for perfectly uniform information distribution. Second, scattering imprints axial position into the speckle field: using a split-latent VAE whose digit latent subspace alone reconstructs clean images and whose focal subspace is trained by a classifier head to predict one of three focal depths, the authors obtain focal classification accuracy that rises with scattering strength, reaching about 98% for high scattering, with silhouette scores and inter-cluster distances increasing accordingly. The trade-off is explicit: stronger scattering improves depth discrimination while degrading digit reconstruction accuracy from roughly 96–97% to about 85%.

Load-bearing premise

The focal-depth result assumes that the three datasets differ only in the axial position of the projected pattern inside the scattering medium, with no unintended changes in intensity, magnification, or camera alignment supplying the classification signal.

Editorial extensions

If this is right

Imaging systems with scattering in the optical path can tolerate large central occlusions or dead sensor regions, because the information needed to reconstruct the object is spread across the speckle field rather than localized.
A single speckle exposure can be read for two kinds of information at once: the object identity and its axial position inside the scattering volume, without a separate depth-sensing path.
Scattering strength becomes a tunable design parameter: heavier scattering buys better focal-depth separation (up to about 98% classification accuracy) at the price of reconstruction quality (SOPCNN accuracy down to about 85%), so a system can be optimized for one goal or the other.
Because the digit and focal subspaces are trained to be functionally separate, the split-latent VAE provides an interpretable route to disentangling object content from viewing conditions in scattering-based imaging.

Reading between the lines

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

The authors test only three discrete focal depths; a natural extension is continuous axial localization, which would reveal whether the focal latent manifold is ordered by physical depth or merely separates the three trained positions.
The occlusion study uses centered circular masks; testing random pixel dropout or arbitrary geometric occlusions would show whether the robustness is a general consequence of information spreading or specific to the mask shape.
The observed asymmetry between adjacent focal planes under high scattering may encode physical properties of the medium, such as its thickness or particle distribution; measuring those properties could turn the asymmetry into a calibration signal.
If the depth signal is truly carried by speckle statistics rather than by alignment artifacts, the same split-latent approach could be applied to three-dimensional objects instead of MNIST planes projected at three depths, testing whether real-volume depth is similarly separable.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The occlusion-robustness result is solid and the split-latent VAE is a genuinely new architecture, but the focal-depth claim is undermined by an underspecified experimental setup. Fig. 5(a) never says how the three focal depths were produced, so the classifier may be reading intensity, magnification, or alignment differences instead of depth.

The good parts first. The circular-masking experiment is a clean proof-of-concept that scattering spreads digit information across the detector. Fitting no-scattering data with a sigmoid and scattered data with a power law is a reasonable way to compare information distributions, and the visual examples in Fig. 3 are convincing. The split-latent VAE is the real novelty: forcing clean reconstruction from the digit subspace alone is a clever architectural constraint, and jointly training a focal classifier on the other subspace is a sensible way to test depth decodability. Five seeds, held-out test metrics, and silhouette/inter-cluster distance checks are above the usual bar.

The soft spots are in proportion. The biggest is the focal-depth confound. The full text gives one sentence about 'projecting the same MNIST pattern onto each of three focal depths of the scattering medium,' with no mention of whether the medium, camera, SLM phase curvature, or 4f relay was changed. Each of those changes other optical parameters. This is load-bearing: if the three datasets differ in total intensity or magnification, the ~98% classification and high-scattering cluster separation are explained without any physical depth signal. This is fixable with a proper experimental methods paragraph and ideally control measurements, but right now the second central claim does not hold.

Second, the monotonic alpha claim is overstated. Table I shows 0.692 ± 0.030, 0.694 ± 0.022, and 0.757 ± 0.047. Low and moderate are statistically indistinguishable; the trend only clearly appears at high scattering. Saying alpha increases monotonically with scattering density is not supported by the data as presented.

Third, the functional forms were chosen post hoc. The sigmoid for no-scattering and power law for scattering fit the data, but there is no independent reason given for those choices. Minor.

Fourth, the focal classification is trained with a classifier head and focal loss on the same labels, so the separation is partly fitted. The held-out test set and cross-seed consistency reduce this concern, but the architecture only shows that the latent space can encode depth when explicitly pressured to do so, not that depth is intrinsically decodable.

Finally, no code, data, or hyperparameters are provided, which makes reproduction harder than it should be for a methods-focused paper.

Who this is for: people working on speckle imaging, scattering-based sensing, or interpretable latent spaces. It is a proof-of-concept, not a definitive result. I would send it to peer review because the architecture is novel and the occlusion result deserves an audience, but the referee should require the experimental details and a revision of the alpha claim. If this comes back with the focal-depth method specified and the data available, it could be a solid contribution.

Referee Report

3 major / 6 minor

Summary. The paper studies whether optical scattering can play a beneficial role in image reconstruction and depth discrimination. The authors generate MNIST-based speckle images under four conditions (no scattering and low/moderate/high scattering through ZnO-doped PDMS) and train VAEs to reconstruct the original digits. In the first set of experiments, center-occlusion masks of increasing radius are applied to the inputs, and the VAE-based reconstruction is scored by a pre-trained SOPCNN classifier; the authors report that scattering slows the accuracy degradation and fit the accuracy-vs-radius curves with a sigmoid (no scattering) and power laws (scattering), with an exponent alpha that is said to increase with scattering strength. In the second set of experiments, a split-latent VAE divides the latent space into a digit subspace and a focal subspace, with a classifier head on the focal subspace, and is trained on three focal-depth versions of the scattered MNIST patterns. The authors report that focal classification accuracy, silhouette scores, and inter-cluster distances in the focal latent subspace increase with scattering strength, reaching about 98% accuracy under high scattering, while digit reconstruction accuracy drops to about 85%. The central claims are that scattering distributes object information across the detector plane, enhancing robustness against pixel loss, and that scattering can enable focal-depth discrimination.

Significance. If substantiated, the robustness and depth-discrimination results would be a useful step toward exploiting scattering as an information-coding mechanism rather than only as a nuisance. The split-latent VAE approach is a reasonable and interpretable method for attempting to separate content from depth-related information, and the use of five random seeds with reported uncertainties in several tables is a strength. However, the paper's second central claim rests on an unspecified experimental implementation of 'focal depth' and on metrics obtained from a model that was explicitly trained with a focal classifier on the same labels. The first central claim is partially supported by the data, but the claimed monotonic trend of the fitted exponent is not statistically supported. The work is a proof-of-concept with potential impact in scattering-based sensing, but its conclusions require substantially more experimental and statistical detail before they can be accepted.

major comments (3)

[Section III.B (Fig. 5(a))] The manuscript never states how the three 'focal depths' were physically realized. The text says 'we projected the same MNIST pattern onto each of three focal depths of the scattering medium,' but the implementation is not described: whether the medium was moved axially, the SLM pattern curvature was changed, the camera or relay lens was translated, or the 4f system was refocused. Each of these implementations changes magnification, total intensity, illumination spot position, or defocus, any of which provides a legible label for the split-latent classifier. Because the central claim that scattering enables focal-depth discrimination depends on the three datasets differing only in axial position inside the scattering volume, this omission is load-bearing. The authors must specify the focal-depth variation method and provide control analyses (for example, showing that intensity, magnification, and alignment are matched across the three datasets, or that the classifier cannot separate the three conditions without scattering).
[Table I and Section III.A] The claim that the fitted exponent alpha increases monotonically with scattering density (0.692→0.757) is not supported by the data. The low and moderate scattering values, 0.692±0.030 and 0.694±0.022, are statistically indistinguishable; only the high-scattering value (0.757±0.047) is clearly larger. The sentence 'alpha increases monotonically with scattering density (0.692→0.757), approaching the uniform limit alpha=1 at the heaviest scattering condition' should be replaced with a two-level comparison (low/moderate vs high) and the error bars should be propagated into any statement about a trend. In addition, the sigmoid and power-law functional forms are selected post hoc without a derivation or a goodness-of-fit comparison against alternative models; this does not invalidate the qualitative robustness result, but alpha should not be presented as a validated physical parameter without model-selection evidence.
[Section III.B, Tables II and III, Fig. 6(b)] The focal-depth discriminability metrics are computed from a latent subspace that was explicitly trained with a dedicated classifier head and a cross-entropy focal loss on the same three depth labels. Silhouette scores, inter-cluster distances, and classification accuracy on the held-out test set therefore partly reflect the model's success in fitting those labels, rather than an intrinsic property of the speckle patterns. The held-out test set and cross-seed consistency rule out training overfitting, but they do not rule out that the model is using any available cues (including the confounds discussed above) to achieve separation. To support the claim that scattering 'enables' depth discrimination, the authors should either (i) train a VAE without the focal classifier and focal loss and show that the raw encodings or raw speckle patterns still cluster by depth, or (ii) apply an unsupervised clustering method (e.g., k-means) to encodings from a classifier-free VAE and report the resulting adjusted Rand index or similar metric. Without such a control, the conclusions in Tables II and III are circular with respect to the training objective.

minor comments (6)

[Section II.B.1.b] The phrase 'not only the coal depth information' appears to contain a typo; it should read 'not only the focal depth information.'
[Fig. 6] Fig. 6 reports SOPCNN accuracy and focal classification accuracy without error bars or standard deviations, even though the text states that five independent training seeds were used. Please add error bars or report mean±std in the text, as done for Tables I–III.
[Section II.B.2] The sentence 'each experimental condition was run across five independently drawn random seeds' should specify what constitutes a condition (per dataset and per focal-depth set) and whether the SOPCNN pre-trained classifier was retrained for each seed or fixed.
[Fig. 4] The caption states that the fits were performed on average accuracies over five seeds, but the plotted data do not show individual-seed spread or confidence intervals. Including the data points or error bars would help the reader judge the goodness of the sigmoid and power-law fits.
[Section II.A] The description of the 'No Scattering' dataset as a direct SLM-to-camera transmission is ambiguous given that the 4f relay and zero-order blocker are part of the optical path. Please clarify whether the no-scattering case used the same 4f relay and zero-order blocking without the scattering medium, since a zero-order blocker changes the effective image of the phase-only SLM.
[References] Reference [12] is an arXiv preprint; if a peer-reviewed version exists, it should be cited instead. The text also cites [13] for the split-latent architecture but does not specify which aspects of the architecture are borrowed versus newly introduced; a sentence in Section II.B.1.b clarifying this would improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the empirical claims rest on external benchmarks and held-out supervised evaluation, not on fitted inputs or self-citations.

full rationale

The paper's derivation chain contains no step in which a predicted quantity is, by the paper's own equations or definitions, identical to a fitted input or to a self-cited conclusion. The robustness claim is benchmarked externally: SOPCNN was trained on original MNIST and then tested on VAE reconstructions, so the comparison of masked-input reconstruction accuracy across scattering conditions is an independent empirical measurement rather than a restatement of the training objective. The focal-depth claim uses a split-latent VAE with a supervised classifier head on z_focal; although the classification loss shapes z_focal, the reported focal classification accuracy is computed on held-out test samples, so it is a supervised generalization test, not a fitted input renamed as a prediction. The silhouette and inter-cluster distances also describe the trained representation; they are not used to define the physical claim, and the cross-scattering comparison could in principle have gone the other way. No load-bearing self-citation occurs: the depth-in-speckle prior work cited [11,12] is external, and the DIVA architecture [13] is an independent methodological source. The main risk to the focal-depth conclusion is experimental: the paper never states how the three focal depths were physically realized, so intensity, magnification, or alignment changes could be the actual discriminant. That is a potential confound and correctness risk, not a circularity, because the paper does not define focal depth in terms of the observed classification outcome. Accordingly, the circularity score is 0.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central claims rest mainly on the experimental datasets and the chosen model architecture. The power-law exponents and sigmoid parameters are fitted to the data; the VAE weights beta and lambda are hand-chosen but unreported. The depth-from-speckle claim assumes the three focal-depth conditions differ only axially, which is not described.

free parameters (7)

alpha_low = 0.692 ± 0.030
Fitted power-law exponent for Low Scattering accuracy curve in Table I; used to claim information becomes more uniform with scattering.
alpha_moderate = 0.694 ± 0.022
Fitted power-law exponent for Moderate Scattering accuracy curve in Table I.
alpha_high = 0.757 ± 0.047
Fitted power-law exponent for High Scattering accuracy curve in Table I.
sigmoid_k = 6.69
Steepness parameter fitted to No Scattering accuracy curve in Section III.A; no error bar reported.
sigmoid_r0 = 141.3 px
Midpoint radius fitted to No Scattering accuracy curve in Section III.A; interpreted as the digit stroke boundary.
beta (KL weight) = not reported
Hand-chosen hyperparameter weighting KL loss in the VAE; value not given in the paper.
lambda (focal classification weight) = not reported
Hand-chosen hyperparameter weighting focal classification loss; value not given in the paper.

assumptions (5)

domain assumption The scattering medium is static and the speckle pattern is deterministic for a given input during data collection.
The analysis treats each speckle image as a fixed transformation of the input; no temporal averaging or fluctuation analysis is described in Section II.A.
domain assumption The three focal-depth datasets differ only in the axial position of the projected pattern within the scattering medium.
Section III.B and Fig. 5(a) do not describe how focal depth was changed; if intensity, magnification, or alignment also changed, the depth classifier could exploit those confounds.
standard math The variational autoencoder objective (ELBO with reparameterization) correctly optimizes the generative model.
The paper relies on the standard VAE formulation in Section II.B.1.a without proving convergence or optimality.
domain assumption A classifier (SOPCNN) trained on original MNIST digits generalizes to the VAE-reconstructed images.
Reconstruction fidelity is measured by SOPCNN accuracy in Section II.B.2; this assumes the classifier's decision boundaries transfer to slightly blurred or modified digits.
ad hoc to paper The sigmoid (No Scattering) and power-law (Scattering) functional forms are the correct models for the accuracy-vs-radius curves.
These forms were chosen because they 'can describe each dataset's behavior' (Section III.A), rather than derived from a physical model; different forms make the Scattering vs No-Scattering comparison less direct.

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Cite this review

Pith. "Pith review of AI-interpreted Optical Scattering for Robust and Focal Depth-Aware Imaging." pith.science (2026). https://pith.science/paper/7VEQMTTU

@misc{pith2026260722867,
  author       = {Pith},
  title        = {Pith review of: AI-interpreted Optical Scattering for Robust and Focal Depth-Aware Imaging},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7VEQMTTU}},
  note         = {Machine review of arXiv:2607.22867}
}

read the original abstract

Optical scattering has conventionally been regarded as an impediment in imaging research due to the degradation of image quality during reconstruction. Nevertheless, this study explores two cases in which optical scattering may serve a beneficial role in image reconstruction tasks. We compared the No Scattering MNIST dataset with three Scattering MNIST datasets, each generated under distinct scattering conditions. To assess the information content of the resulting speckle patterns, we employed a Variational Autoencoder (VAE) approach which achieves accuracy comparable to state-of-the-art deep learning approaches, but has an interpretable latent space. We find that scattering can enhance data robustness against spatial pixel loss by effectively distributing information. We also demonstrate that scattering can enable distinctions of focal depth information. We anticipate that these findings will contribute to more efficient imaging techniques, particularly in the presence of obstacles and three-dimensional signals.

Figures

Figures reproduced from arXiv: 2607.22867 by the authors.

**Figure 1.** Optical scattering imaging setup. A linearly polarized, telescope-expanded laser beam illuminates an SLM, and the modulated output is imaged through a scattering medium onto a CMOS camera via a 4f relay with zero-order blocking at the Fourier plane between lens 3 and lens 4 A. Experimental setup Speckle patterns were generated by passing spatially modulated images, formed using a phase-only SLM (Holoeye LCR-2500, 10… view at source ↗

**Figure 3.** Visual examples of VAE reconstruction results with (a) the No-Scattering MNIST dataset and (b) the Moderate Scattering dataset. The first column shows the input, the second column displays the output, and the last column presents the ground truth (target). Each row represents the cases where a different radius of mask applied to the input images [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** The reconstruction outcomes of center-occluded MNIST images using VAE, assessed by the accuracy of SOPCNN image classification, over increasing radius. No Scattering data was fitted with Sigmoid function, while Low/Moderate/High Scattering datasets were fitted with a power law function. All the data was fitted on average accuracies over N = 5 independent training seeds Table I. Fitted power law parameter 𝛼 for Scatt… view at source ↗

Figures from the paper (2 more)

**Figure 5.** Figure 5: (a) The illustration of generating three different focal depth datasets (b) the schematic of the splitlatent VAE we developed for the focal depth discrimination task [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: The outcomes of the split-latent VAE (a) SOPCNN accuracy for reconstructed clean MNIST images under different scattering conditions, and (b) focal classification accuracy on 𝐳focal ∈ ℝA across different scattering scenarios. Each datapoints is from five different indep…

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Works this paper leans on

14 extracted references · 12 canonical work pages

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

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M., & Mosk, A

Vellekoop, I. M., & Mosk, A. P. (2007). Focusing coherent light through opaque strongly scattering media. Optics letters, 32(16), 2309-2311

work page 2007

[2] [2]

M., Lerosey, G., Carminati, R., Fink, M., Boccara, A

Popoff, S. M., Lerosey, G., Carminati, R., Fink, M., Boccara, A. C., & Gigan, S. (2010). Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media. Physical review letters, 104(10), 100601

work page 2010

[3] [3]

Li, Y., Xue, Y., & Tian, L. (2018). Deep speckle correlation: a deep learning approach toward scalable imaging through scattering media. Optica, 5(10), 1181-1190

work page 2018

[4] [4]

Zhu, S., Guo, E., Gu, J., Bai, L., & Han, J. (2021). Imaging through unknown scattering media based on physics-informed learning. Photonics Research, 9(5), B210-B219

work page 2021

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C., Mi, S

Chen, Y. C., Mi, S. X., Tian, Y. P., Hu, X. B., Yuan, Q. Y., Chew, K. H., & Chen, R. P. (2025). Adaptive vectorial restoration from dynamic speckle patterns through biological scattering media based on deep learning. Sensors, 25(6),

work page 2025

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Xia, W., Li, X., He, G., Luo, Z., Wu, X., & Huang, B. (2025). Imaging through highly scattering media via global transformer mapping. Journal of Optics, 27(4), 045603

work page 2025

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P., & Welling, M

Kingma, D. P., & Welling, M. (2013). Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114

arXiv 2013

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J., Mohamed, S., & Wierstra, D

Rezende, D. J., Mohamed, S., & Wierstra, D. (2014, June). Stochastic backpropagation and approximate inference in deep generative models. In International conference on machine learning (pp. 1278-1286). PMLR

work page 2014