Three-dimensional imaging through scattering media based on confocal diffuse tomography

Optical imaging techniques, such as light detection and ranging (LiDAR), are essential tools in remote sensing, robotic vision, and autonomous driving. However, the presence of scattering places fundamental limits on our ability to image through fog, rain, dust, or the atmosphere. Conventional approaches for imaging through scattering media operate at microscopic scales or require a priori knowledge of the target location for 3D imaging. We introduce a technique that co-designs single-photon avalanche diodes, ultra-fast pulsed lasers, and a new inverse method to capture 3D shape through scattering media. We demonstrate acquisition of shape and position for objects hidden behind a thick diffuser (≈6 transport mean free paths) at macroscopic scales. Our technique, confocal diffuse tomography, may be of considerable value to the aforementioned applications.


Reviewer #2 (Remarks to the Author):
The manuscript reports the extension of previous work by the same group on use of f-K migration methods and confocal measurements that allow to greatly simplify inverse retrieval problems that would otherwise be impossible, or close to impossible to solve. These approaches have been applied to non line of sight imaging but are here applied to imaging through scattering materials. The results are very convincing and I believe, demonstrate a significant step forward in this important research area. The paper is very well written and clear. I would therefore recommend publication in nature communications.
I only have one minor comment. The title and text speak of "highly scattering". Although nondescriptive adjectives are always a matter of interpretation, I feel that "highly" might be misused here. The scattering coefficient used here is 0.07 1/cm, less than 10x smaller for example than biological tissue. And the sample is 6 scattering lengths (transport mean free paths). One could argue that with 6 scattering lengths, there is a decent component of ballistic photons -another metric by which one might try to distinguish "scattering" from "highly scattering". I do not want to make too much of a point about this yet, the paper does not lose any interest or impact by simply calling this "scattering" and a large part of the community will recognise themselves as working in the same regime and will therefore be very interested in this technique. I leave this with the authors. Either way, this minor point does not change in any way the quality and impact of the work.
We thank the reviewers for their insightful comments and appreciate their help in improving the manuscript. We have updated the paper to address their comments. In the following, we provide a point-by-point response to the raised concerns.
The paper presents a technique for non-invasive 3D imaging through scattering media at macroscopic scales based on confocal diffuse tomography. We introduce a computational imaging approach that co-designs single-photon avalanche diodes, ultra-fast pulsed lasers, and a new inverse method to facilitate new capabilities of 3D imaging through scattering media.

Referee #1 (Remarks to the Author):
• The Green's function for diffusion in eq 1 is only valid for an infinite medium. The moment light touches the edges, the boundary conditions change and the Green's function is deformed. In particular the tails will decay exponentially. I am not sure how much this will influence the result, but even in the best case scenario the authors should at least mention it.
We agree that the use of the Green's function of the diffusion equation should be clarified. We have adjusted the image formation model section to now state the conditions where the Green's function is valid and clarify that we are using it as an approximation. In general this is a good approximation where the thickness of the scattering media is several times greater than the transport mean free path [39].
• Eq 1 assumes that D is not only constant in time, but also uniform in space. This is understandable for a proof-of-principle experiment, but this limitation (and probably a short discussion on how much more complicate things get when this assumptions is violated) should be clearly discussed in the manuscript.
To make the inverse scattering problem more tractable, we assume that D is constant in time and uniform in space. We now note and discuss this assumption in the Discussion section of the paper. Imaging in dynamic, anisotropic scattering media with non-uniform thickness is a challenging problem that we aim to address in future work.
• The description of the approximation made with the confocal geometry is very long and convoluted, while it can be easily summarized as r_1 ~ r_2. Also, eq 3 would be a lot more striking if somewhere it is shown that eq 2 has a similar form (yes, I know that eq 2 is clearly a chain a convolution products, but not everyone will be super-familiar with it).
This is a good point that the description of the approximation (just before Eq. 3) could be put more succinctly. We have shortened the description and also summarize the approximation as r_1 ~ r_2. We also refer the readers to the Supplementary Methods, where we derive and show the full integral form of Eq. 3, which has a similar form to Eq. 2. We now include a discussion of f-k migration in the supplemental information. We also provide a full implementation of the method (including f-k migration) in the Supplementary Code.

• One of the main mathematical tricks (the f-k migration) is mentioned at the bottom of
• In the discussion section the "stand-off distance" is represented by the letter D. This is a very unfortunate choice, as D was already used as the diffusion coefficient, and there is a serious risk of confusion.
We thank the reviewer for pointing this out, we have adjusted the symbols to avoid confusion. "H" is now used to represent the stand-off distance.

• The resolution of this technique is kept carefully hidden through the whole manuscript. I understand that a complete discussion is probably best left for the Supplementary Information, but the main text must include at least a quick overview and an estimate of this value. In particular, digging in the Supplementary Information one finds that the resolution is approximately 10cm, which puts things in perspective (this is definitively not a high resolution technique).
We agree that the resolution can be better described and quantified in the main text. We have augmented the Discussion section to quantify the axial resolution as approximately 10 cm and the lateral resolution as approximately 15 cm for our hardware prototype. We also include a note to refer to the Supplementary Information for further details, and now provide a table of contents for the Supplementary Information so that the resolution analysis can be located more easily.
• The values of the absorption coefficient and the reduced scattering coefficients are presented without any error bar, but I find difficult to believe that the uncertainty on these quantity is negligible. I would urge the authors to include those error bars.
We now provide a 95% confidence interval on the values of the absorption and scattering coefficients after analyzing the parameter covariance in the non-linear fit to the captured data. We find the absorption coefficient to be u a = 0.069 +/-0.001 cm -1 and the reduced scattering coefficient to be u s ' = 2.41 +/-0.02 cm -1 . The confidence intervals are now provided in the paper, and we provide additional details about the nonlinear fit and confidence bounds in the Methods.
We also demonstrate that the method is relatively robust to errors in the scattering media characterization as shown in Supplementary Figure 9.

Referee #2 (Remarks to the Author):
• I only have one minor comment. The title and text speak of "highly scattering". Although non-descriptive adjectives are always a matter of interpretation, I feel that "highly" might be misused here.
We thank the reviewer for this suggestion. The title has been adjusted to "Three-dimensional imaging through scattering media based on confocal diffuse tomography," and we have adjusted the wording in the abstract and text in a corresponding fashion.