Scanning a focus through scattering media without using the optical memory effect

Bahareh Mastiani; Ivo M. Vellekoop; Tzu-Lun Ohn

REVIEW 3 major objections 7 minor 23 references

Scanning a focus through scattering media without using the optical memory effect

T0 review · 3 major / 7 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A wavefront-shaping approach called Sparse Field Focusing forms a focus behind a strongly scattering medium and scans it over tens of micrometers by measuring only a subset of the transmission matrix, bypassing both the optical memory…

desk verdict New trick for scanning a focus through scattering media, demonstrated convincingly, but the efficiency gain number is weaker than advertised without a check on target orthogonality. read the letter →

arxiv 1908.08436 v1 pith:OPUU5CEJ submitted 2019-08-22 physics.optics

Bahareh Mastiani , Tzu-Lun Ohn , Ivo M. Vellekoop This is my paper · ORCID

classification physics.optics

keywords wavefrontshapingtransmissionmatrixsparsefieldfocusingopticalmemoryeffectscatteringmediafocusscanningisoplanaticpatchenhancement

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 introduces Sparse Field Focusing (SFF), a wavefront-shaping method that forms and scans an optical focus through a strongly scattering medium without relying on the optical memory effect and without measuring the full transmission matrix. Instead of optimizing a new wavefront for each focus position, SFF optimizes a set of M wavefronts, each of which emerges as a plane wave, then superposes them and scans the focus by applying relative phase shifts. The authors demonstrate a focus scanned over roughly 30 micrometers through a zinc-oxide layer whose isoplanatic patch is below 0.38 micrometers, with about 6.0 ± 0.8 resolvable scan points per measured transmission-matrix row. The measured enhancement matches an analytical model in which the focus intensity follows the diffuse background intensity distribution. This matters because full transmission-matrix measurements are slow and memory-effect range is often tiny in biological tissue.

What carries the argument

The central object is the sparse set of optimized wavefronts, i.e., M rows of the transmission matrix measured instead of the full matrix. Each optimized wavefront is shaped so that, after scattering, it produces a plane wave with constant phase across the image plane; the superposition of M such plane waves creates a focus by constructive interference. Scanning works by applying a linear phase ramp across the target positions in the back focal plane, adding $\phi_m = k_{mx}\Delta x + k_{my}\Delta y$ to each wavefront; because the phase shift is global across the spatial light modulator for each wave, the wave's propagation through the medium is unchanged. The analytical model predicts enhancement $\eta(x,y) = |\gamma|^2 M(N-1)/N_s \, F(x,y) + 1$, where $|\gamma|^2$ is the wavefront-shaping fidelity, $N$ the number of controlled segments, $N_s$ the number of speckles in the background, and $F$ the normalized ensemble-averaged intensity distribution; the model shows enhancement follows the diffuse intensity envelope, defining the scan range. The prefactor $D$ in the derivation normalizes the superposed incident intensity by assuming the M target modes and N segments are orthogonal.

What would settle it

Measure the transmission-matrix rows for pairs of targets separated by less than one speckle diameter (30 µm in this setup) and compute their overlap or the singular-value spectrum of the 500-target subset; if the rows are not approximately orthogonal, the enhancement will deviate from Eq. (2) and the gain of 6.0 ± 0.8 will not be reproducible.

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Extended reading notes

Core claim

The central claim is that scanning a corrected focus through a scattering medium does not require the memory effect or a full transmission matrix; a sparse subset of rows suffices. The authors construct a focus by optimizing M incident wavefronts so each produces an apodized plane wave at the image plane, measuring their relative phases interferometrically, and coherently superposing them. Shifting the relative phases by $\phi_m = k_{mx}\Delta x + k_{my}\Delta y$ moves the constructive-interference peak to $(\Delta x, \Delta y)$, because each shaped wave propagates through the medium in the same way and only its overall phase changes. In the experiment, 500 optimized waves produced a focus 47 times brighter than the unshaped speckle, and the focus could be scanned over 30 µm, while tilting or shifting the incident wavefront (the memory-effect approach) did not move it. The paper claims this yields a gain of 6.0 ± 0.8 scan points per measured matrix row, meaning roughly six times fewer measurements than a full transmission matrix for the same number of focus positions.

Load-bearing premise

The derivation assumes that the M targets used for feedback are spaced far enough apart that their transmission-matrix rows are independent and orthogonal; if two targets lie within the same speckle, the superposition formula and the gain estimate no longer hold.

Editorial extensions

If this is right

Imaging through scattering media can be performed with sparse transmission-matrix measurements, reducing acquisition time and memory requirements relative to full-matrix methods.
The scan range is set by the diffuse intensity envelope rather than by the isoplanatic patch, so the method applies to samples such as deep biological tissue where the memory effect is too small to use.
There is a quantifiable trade-off: increasing the number M of optimized wavefronts raises the focus enhancement but lowers the gain A = n/M, so the method can be tuned for either brightness or speed.
The focus resolution approaches the diffraction limit (measured FWHM 0.520 µm versus 0.407 µm theoretical), so sparse sampling does not sacrifice spatial resolution for scan range.
Adapting SFF to embedded guide stars could enable focusing inside scattering media at positions where a guide star is not available, as the paper envisions.

Reading between the lines

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

If the target rows are independent, the same superposition principle should extend to three-dimensional scanning by applying phase ramps along additional axes, so the number of measurements would scale with the number of distinct output speckles rather than the number of scan positions.
A direct test of the orthogonality assumption would be to place feedback targets closer than one speckle diameter and measure the gain; the model predicts the gain should drop, which would give design rules for target spacing.
Because the method controls only relative phases, it might be combined with polarization or wavelength multiplexing to scan multiple foci simultaneously, an extension the paper does not discuss.
The scan range is ultimately bounded by the diffuse intensity envelope, so engineering the illumination or the sample's angular spread could extend the range well beyond the demonstrated 30 µm.

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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

Here's the two-sentence version. The idea is to measure a small set of transmission-matrix rows corresponding to Fourier-plane targets, then superpose those optimized wavefronts with programmable phase offsets to scan the focus independent of the optical memory effect. That is a real and useful contribution, and the experiments show a clean 30-micrometer scan through a strongly scattering zinc-oxide layer, far beyond the ~0.38-micrometer isoplanatic patch.

What earns credit: the method genuinely breaks the memory-effect limit without requiring the full transmission matrix; the measured focus is 47x above speckle and near diffraction-limited; the scan behavior follows the diffuse envelope as expected; and the write-up is honest about many practical details. The Appendix A model is a reasonable Gaussian-TM treatment.

The soft spots are real but not fatal. The derivation's normalization D in Eq. (6) assumes the M target-optimized wavefronts are mutually orthogonal. The paper reports each target is smaller than a speckle but never reports the target separations, so we cannot check independence. If targets overlap in the Fourier plane, the input-space overlap is nonzero, D is too large, and the enhancement formula becomes an upper bound. Since the headline gain of 6.0 +/- 0.8 is obtained by thresholding that enhancement, the central efficiency claim is not fully established. At minimum the authors need to show the Gram matrix or target separations, or soften the claim to a lower bound. Relatedly, the comparison to 'full transmission matrix' is not direct: they never measured a full TM, only asserted similar resolution, and F(x,y) is taken from the measured envelope, making the fit in Fig. 3(d) partly a consistency check. No data or code is provided, which is a minor issue for an experimental techniques paper but worth noting.

Who this is for: wavefront shaping and deep-tissue imaging people. It deserves a serious referee: the concept is new and the experiment is believable, even if the quantitative gain needs to be pinned down. I would send it out, with a request for the orthogonality check and a more measured abstract.

Referee Report

3 major / 7 minor

Summary. The paper introduces Sparse Field Focusing (SFF), a wavefront-shaping method for focusing and scanning light through a strongly scattering medium without relying on the optical memory effect. Instead of measuring the full transmission matrix, the authors optimize a set of M target spots in the back focal plane, measure the relative phases among the resulting optimized wavefronts, and superpose them to form a focus in the image plane. By applying phase ramps to the individual wavefronts, the focus can be scanned over a range of about 30 micrometers through a zinc-oxide sample whose isoplanatic patch is stated to be below 0.38 micrometers. Experimental results show a focus 47 times brighter than the background speckle, and a gain of 6.0 +/- 0.8 scan points per measured matrix row. An analytical model in Appendix A predicts the enhancement as a function of scan position, Eq. (2), and is compared with the measurements in Fig. 3(d).

Significance. If the method holds up, it is a practically useful alternative to full transmission-matrix measurement in regimes where the optical memory effect is too small to exploit, and it may be adaptable to guide-star-based imaging. The paper's strengths are a clear experimental demonstration, a quantitative model, and a well-defined efficiency metric (gain). The central experimental fact, that a focus can be scanned well beyond the isoplanatic patch by superposing a subset of optimized wavefronts, is convincingly shown. However, the theoretical model rests on an orthogonality assumption for the optimized wavefronts that is not verified in the manuscript, and the agreement with Eq. (2) is partly a consistency check because the diffuse intensity envelope and the fidelity are extracted from the same sample. These issues affect the strength of the quantitative efficiency claim but not the basic feasibility of the method.

major comments (3)

[Appendix A, Eq. (6)] The derivation of the enhancement formula assumes that the M target-optimized input fields are mutually orthogonal, which sets the normalization D = (N M sum_b <|t_ba|^2>)^(-1/2). The manuscript states only that each target is smaller than the 30-micrometer speckle in the back focal plane; it does not report the separations between the 500 targets or the Gram matrix of the optimized wavefronts. If many target separations are smaller than the speckle correlation length, the overlaps <u_m|u_l> are not delta_ml, the normalization is incorrect, and Eq. (2) becomes an upper bound rather than a prediction. This is load-bearing for the model-experiment agreement in Fig. 3(d) and for the interpretation of the gain A as a reduction in measurement effort relative to full TM measurement. Please report the target positions and separations and either compute the Gram matrix of the optimized fields from the measured rows or provide another direct test of the orthogonality assumption.
[Section 'In our experiment' (p. 4)] The claim that 'we obtained the full transmission matrix by performing 6 times less measurement than measuring the full transmission matrix' is not precisely defined. The gain A = n/M is a measured ratio, but its interpretation as a factor of reduction in measurement effort depends on what is meant by measuring the full transmission matrix: the number of input modes, output modes, and phase-stepping steps all matter. It also depends on the M measured rows being independent, which connects to the orthogonality issue above. Please specify the reference full-TM measurement cost and clarify how the number of individual scan points, n = 2984 +/- 390, is obtained from the two-dimensional scan.
[Section 'Next, we tried to test...' and Fig. 3(d)] The experimental protocol for the two-dimensional scan is underdocumented. The text describes a vertical scan and Fig. 3(d) shows enhancement along one axis, but the two-dimensional scan that yields 2984 +/- 390 individual scanning points is not described. It is unclear how the scan grid is chosen, how the enhancement threshold of 10 is applied, and how the 30-micrometer scan range is defined given that the enhancement decreases with displacement. Please provide the 2D enhancement map or a precise description of the scanning and thresholding procedure, including how the uncertainty in n is estimated.

minor comments (7)

[Fig. 3(d)] The plot would benefit from error bars and a statement of how many measurements each point represents; without them, the agreement between experiment and the model cannot be fully assessed.
[Section 'Next, we tried to test...'] The definition of the 30-micrometer scan range should be stated explicitly; it is not clear whether this is the full range over which an enhancement above a threshold is maintained, or the range over which the focus can be visually tracked.
[Section 'We present an analytical model...' and Eq. (7)] The value |gamma|^2 = 0.54 is said to be the average fidelity, but the text does not report how the SNR was measured for the 500 targets or how the average was taken; please add this detail.
[Appendix A, Eq. (6)] The model treats the optimized incident field as a complex field with a normalization factor D, but the experiment uses a phase-only SLM; the text should clarify how the phase-only constraint is represented in the complex-field model, particularly when the M wavefronts are superposed by displaying only the phase of the sum.
[Summary and body] The statement that the isoplanatic patch is less than 0.38 micrometers is not derived or measured in the body; please indicate whether this is an estimate from the sample parameters or a measured quantity, and if measured, how.
[Fig. 2 inset] The inset showing the 500 target locations would be more informative with a scale bar or axis labels so that the separations between targets can be evaluated by the reader.
[General] The reference to 'Visualization 1' should be accompanied by a description in the text, since the video file is not part of the manuscript and the reader cannot otherwise assess the scanning behavior.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the SFF enhancement model is derived from explicit TM statistics and compared with measured data, not fitted to it.

full rationale

The central derivation in Appendix A is a conventional transmission-matrix calculation. It starts from a circular-Gaussian TM model, writes the optimized incident field for M back-focal-plane targets in Eq. (6), normalizes with the explicitly stated orthogonality assumption in the definition of D, and averages over disorder to obtain Eqs. (9)-(11) and hence Eq. (2). This is not a prediction that is equivalent to its input by construction: Eq. (2) contains independently specifiable quantities (M, N, N_s, |gamma|^2, and the diffuse envelope F), and the experimental comparison in Fig. 3(d) is a test of that functional form. The fidelity |gamma|^2 is reported as measured (0.54), not chosen to match the enhancement curve, and the count of scan points (2984 +/- 390) used for the gain A = n/M is obtained directly from the measured enhancement data, independent of Eq. (2). The claim that the enhancement follows F is a substantive model prediction (the optimized intensity scales with F^2 while the background contributes the +1 term), not a restatement of the enhancement definition. The unverified orthogonality of the M target-optimized wavefronts in Eq. (6) is a genuine correctness risk that could bias the predicted enhancement if target spacings are below the speckle correlation length, but it is an explicitly stated modeling assumption rather than a circular step. The self-citations to Vellekoop and Mosk are background references for standard wavefront shaping and fidelity definitions; they are not used as the load-bearing justification for the SFF result. The method is experimentally demonstrated against an external benchmark (formation and scanning of a real focus), so any residual model caveat does not make the central result circular.

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

The model uses measured experimental parameters rather than introducing new physical entities. The spatial envelope F(x,y) is measured from the same sample, making the enhancement prediction partly self-referential. No new particles, forces, or conserved quantities are introduced.

free parameters (3)

wavefront shaping fidelity |gamma|^2 = 0.54
Measured from the SNR of the stepwise sequential wavefront shaping feedback using Eq. (7), and used in Eq. (2) to predict the focus enhancement.
diffuse intensity envelope F(x,y) = not tabulated
Obtained from the measured image plane intensity distribution and used in Eq. (2) as the spatial envelope that limits the scan enhancement.
number of speckles N_s = derived from measured intensity
Computed as N_s = sum_b I_b / max I_b from the measured speckle intensity, and used in Eq. (2) to set the enhancement scale.

assumptions (3)

domain assumption Transmission matrix elements t_ba are independent, zero-mean circular Gaussian random variables.
Standard model of multiple scattering, invoked in Appendix A, Eq. (4) and used to derive Eq. (9).
domain assumption The optimized incident fields for different targets are orthogonal, allowing the normalization prefactor D in Eq. (6) to be a single scalar.
Assumes the M targets sample independent speckles; the paper only verifies target size, not inter-target spacing.
domain assumption The phase of each optimized wave equals the phase of the original speckle pattern at the target, so relative phases can be measured by phase-step holography.
Stated in the text: 'The optimized waves have the same phase as the original speckle pattern [1]'.

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Cite this review

Pith. "Pith review of Scanning a focus through scattering media without using the optical memory effect." pith.science (2026). https://pith.science/paper/OPUU5CEJ

@misc{pith2026190808436,
  author       = {Pith},
  title        = {Pith review of: Scanning a focus through scattering media without using the optical memory effect},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OPUU5CEJ}},
  note         = {Machine review of arXiv:1908.08436}
}

read the original abstract

Wavefront shaping makes it possible to form a focus through opaque scattering materials. In some cases, this focus may be scanned over a small distance using the optical memory effect. However, in many cases of interest, the optical memory effect has a limited range or is even too small to be measured. In such cases, one often resorts to measuring the full transmission matrix (TM) of the sample to completely control the light transmission. However, this process is time-consuming and may not always be possible. We introduce a new method for focusing and scanning the focus at any arbitrary position behind the medium by measuring only a subset of the transmission matrix, called Sparse Field Focusing (SFF). With SFF, the scan range is not limited to the memory effect and there is no need to measure the full transmission matrix. Our experimental results agree well with our theoretical model. We expect this method will find applications in imaging through scattering media, especially when the optical memory effect range is small.

Figures

Figures reproduced from arXiv: 1908.08436 by the authors.

**Figure 2.** Schematic of the experimental setup. HWP, half [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** (a) Intensity at the image plane with a non-shaped [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

I. M. Vellekoop and A. P. Mosk, Optics Letters32, 2309 (2007)

work page 2007

[2] [2]

Kubby, S

J. Kubby, S. Gigan, and M. Cui, Wavefront Shaping for Biomedical Imaging , Advances in Microscopy and Microanalysis (Cambridge University Press, 2019)

work page 2019

[3] [3]

Freund, M

I. Freund, M. Rosenbluh, and S. Feng, Physical Review Letters 61, 2328 (1988)

work page 1988

[4] [4]

Judkewitz, R

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, Nature Physics 11, 684 (2015)

work page 2015

[5] [5]

Schott, J

S. Schott, J. Bertolotti, J.-F. Léger, L. Bourdieu, and S. Gigan, Opt. Express23, 13505 (2015)

work page 2015

[6] [6]

Osnabrugge, R

G. Osnabrugge, R. Horstmeyer, I. N. Papadopoulos, B. Judkewitz, and I. M. Vellekoop, Optica 4, 886 (2017)

work page 2017

[7] [7]

I. M. Vellekoop and C. M. Aegerter, Optics Letters35, 1245 (2010)

work page 2010

[8] [8]

J.-H. Park, W. Sun, and M. Cui, Proceedings of the National Academy of Sciences112, 9236 (2015)

work page 2015