In the manuscript, titled “U and Th zonation in apatite observed by synchrotron X–ray fluorescence tomography and implications for the (U–Th)/He system”, the authors describe a clear and well-documented novel method to investigate (U-Th)/He thermochronology. Great value is found in this manuscript, as the authors do a great job of making clear every step of the process they followed, in a way that allows the reader to reproduce it. Furthermore, the proposed method makes use of non-destructive analytical methods, which pose a great complementarity to the currently existing mainly destructive methods. The obtained results are fairly similar to the results obtained using the previous benchmark methods, and the authors discuss what and how these differences are caused.

All in all, this manuscript is very nice to read, the science within is sound and the story is well-supported by data. There are, however, some parts that could do with some additional elaboration. Please find my comments and suggestions below:

Abstract: in the first sentence, the “(…) in whole apatite crystals at the scale of one µm³.” is found to be misleading. Perhaps it is better to specify that this is the resolution scale, instead of the crystal size scale.

P7, line 168: The authors state the focal spot size of the beam was 1×2µm² (V×H). Can the authors provide a measure of the beam’s divergency, as this will affect the voxel size of the tomographic reconstruction, particularly at the edges of the sample.

P7, line 180: please provide the density of apatite that was used for these calculations.

P10, line 207: “to determine an overall scaling factor between abundance for each element of interest and the full intensity of its fluorescence. These elemental scaling factors are then calibrated to give reasonable total abundances and used to produce sinograms of abundances”: This statement is rather vague and unclear. What do the authors mean by ‘the abundance for each element of interest’? Is this the average abundance within the full apatite crystal, or some locally determined abundance? How did the authors determine either? This should be stated in the manuscript. In a similar way, it is unclear whether the approached method can indeed be followed to generate a sinogram of ‘abundances’, as of course every pixel in a sinogram in fact represents the total yield of a line through the sample (at a specific sample orientation). For instance, reconstructing said sinogram will not result in a virtual cross-section displaying the spatially resolved abundancies/concentrations (at least not without further scaling of said cross-section, using pre-existing data). Given how careful the authors are in describing the used methodologies, it would be opportune to elaborate on this (important) step as well.

Later in the publication mention is made of ppm quantified results. Unless the above quoted sentence entails this, please provide (additional) information on how the quantification procedure was performed. In addition, a method validation (or reference thereof) would be greatly appreciated.

P10, line212: The authors state that XRF-CT attenuation correction is difficult and error prone. Although I agree with the former, and am sceptical about the latter statement, it may be opportune to cite here a few recent manuscripts that pertain this attenuation correcting, for readers who might be inclined to attempt to do so. Additionally, some methods exist that seemingly do not impose much errors in the final reconstruction, are fairly straightforward to use and do not require any chemical information input by making use of a neural network. These methods may be worthwhile to investigate.

P 10, line 220: It could be noteworthy to mention that in principle U and Th signals can also be detected by their K-line excitation (in contrast to the L-line excitation used here), which corresponds to significantly higher energies (>90keV) and thus is virtually non-affected by attenuation effects in these samples. The drawback is of course that one has to obtain measurement time at high energy beamlines that allow microscopic focussing.

P11, line 244: “Because strontium follows calcium and does not have an issue with self-absorption”: It is more prudent to state that Sr has less of an issue with self-absorption, as also Sr characteristic fluorescence photons will be absorbed within the apatite matrix (~43% in 100µm apatite, per your calculations stated at p7, line 181). Additionally, would it not be possible to use Ca in any case, as the outer shell of the Ca should be visible/reconstructed and thus a total volume can be defined (assuming that there are no cavities within the crystal, perhaps this is what the authors fear/expect?).

In any case, an intricate issue with such approaches is always where/how the difference between background and sample is determined. In the images provided in the manuscript, the background is cut away (white). Which threshold value did the authors set? How was this determined?

P12, line265: please explain the acronym SA/V equivalence

P13, line285: In the process, carefully described by the authors, usage is made of mean alpha stopping distances. At a later stage (line 295) these mean distances then essentially have to be rounded to the nearest integer value.

However, one could argue that using the mean alpha stopping distance is already an oversimplification of the physics that occur? Perhaps it would be more accurate to provide a sigma-deviation on this stopping distance, probed by another random number for each of the randomly oriented alpha decay vectors? Did the authors consider this, and is there a grounded reason why it was elected to forego this?

P14, Figure6: It would be interesting to provide the reader an estimate of the calculation time (e.g. s/CPU) required to perform these calculations. Additionally, the time required to complete these calculations will depend severely on the size of the investigated grains. Can the authors provide some insights on this size-dependency? Is this calculation time a bottleneck in the described method?

P14, line310: How do the authors explain that the outer dimensions of the (alpha decay) 3D array is >30µm bigger than the crystal in all dimensions, while the mean alpha stopping distance is (depending on the isotope) at most 22.25µm? Since the authors do not appear to use a probabilistic deviation on this stopping distance, one could imagine that the alpha decay volume can maximally extend 22/23 (depending on rounding perhaps) µm beyond the outermost apatite grain voxels?

P18, Figure8: is there a reason why the intensity scale maximum for the Sr image has been set to a relatively low threshold, thus rendering the entire image (at least apart from the Zr inclusion) yellow? A more appropriate scale may be selected, providing a more convincing (I expect noisy or heavily fluctuating in intensity?) image, that would still support the same conclusion i.e. that a Zr inclusion is present. Alternatively, a square root or log scale could be applied to the intensities for the Sr image, thus providing a more general overview of the collected data.

General:

• The authors specify quite regularly throughout the manuscript that a 1µm³ resolution/voxel size was attained. This clearly results in a good spatial resolution, but as seen from figure 2B also a 2µm² resolution provides quite clear spatially resolved information. This makes one wonder how the spatial resolution impacts the final results in terms of F_T Would a 5µm resolution scan provide similar results, with the added advantage of a significantly higher sample throughput? A short paragraph discussing this would be of great value to the manuscript.

“U and Th zonation in apatite observed by synchrotron X–ray fluorescence tomography and implications for the (U–Th)/He system” by Sousa et al. is an interesting and well-written manuscript that details a method to non-destructively visualize, in 3D, patterns of zonation in parent nuclides and zircon inclusions in apatite. The manuscript includes clear, step-by-step instructions with sufficient detail such that this study could be replicated. I believe this manuscript should be published in Geochronology and is valuable to the community. Below I outline some general comments followed by technical corrections and suggestions:

General comments: 

The limited access to synchrotron facilities and beamtime seem to be an issue, as explained in Sect. 3.6. It would be helpful to have more details about how you got beamtime, how much it cost, and how long the actual analyses took. 

Could this method be modified or expanded upon for labs interested in acquiring data for multiple grains? For example, you have a grain imaged at a resolution of 2µm² (Fig. 2 caption), does this significantly decrease the analytical time? Is it possible to mount several grains for analysis at the same time? I know you did not do this in this study, but it would be helpful to know if higher throughput is possible. 

I would like a little more justification for the samples you chose to analyze. Why analyze such small grains that have no demonstrated issues with unexplained overdispersion (that could have been attributed to zonation)? Did you attempt to analyze grains that have complex zonation? 

Are there (or could there be) issues with helium loss attributed to heating during analysis? 

A table with sample names, (U-Th)/He ages and references, crystal dimensions, F_T values, and the number of / a brief description of tomographic slices acquired and the resolution would be useful.

L97: Could you include photomicrographs of the analyzed grains? You state that you picked grains with no visible inclusions but in the video supplement for MGB5-2 there appear to be large near-surface inclusions. 

L175: Does the dot of epoxy covering the bottom termination of the apatite in the mount influence the signal? 

L214-L220: You explain in Section 2.5 how concentrations were acquired and the uncertainties on them, but it is distracting that there is no ppm value attached to the color scale in Figure 2. I suggest referring the reader to the discussion in Sect 2.5 in the figure caption. 

L214-L220: Are there relevant citations for, or could you expand upon, how you arrived at the uncertainties on the concentrations? Are these grains degassed/dissolved yet? It would be nice to see if the “reasonable” abundances are actually in line with the actual abundances measured by ICP-MS.  

L240: In Table 1, for the definition of a labelmap, how are voxels that delineate the exterior of the grain classified? 

L245: I would like to see a brief discussion of what other elements (major? minor? trace?) can be visualized with this method. Subsequently, why did you choose to map Sr (and Y?) as a proxy for crystal volume rather than P? 

L297: You emphasize the value of the stopping distance several times throughout the manuscript but then round them. I understand why you have to do this. Do you expect that this has any appreciable impact on the calculated F_T values? Do you expect the resolution of the mapped zonation (e.g., 1µm² vs. 2µm² vs. 10µm²) to have an impact on the calculated F_T value?

L374: For illustrative purposes you calculate an F_T value for a 50 Ma uncorrected age—this sample has a published mean helium date of 5.90 ± 0.42 Ma. Why the discrepancy? Additionally, the small size of the grain is going to have a large impact on the calculated F_T. Would it be possible to recalculate these data for a more typically sized grain?

L374: In Table 2, can the “Qt_Ft” method be additionally labeled as “traditional” or “geometric”? Does the Qt_Ft method use the Ketcham et al., 2011 equations for calculating F_T?

Technical corrections/suggestions: 

• Add a line to the abstract that briefly describes the samples. 
• Where there are multiple citations prefaced by ‘e.g.,’ or other words, there are extra parentheses (for example, L27, L29, L36, L50, etc.)
• L35: the listed stopping distances for apatite in Ketcham et al. (2011) are 5.93-22.25µm but you have 13-34µm listed?
• Adding a discrete color scale next to figure 2F would be helpful rather than explaining the color scale at the end of the figure caption. 
• L222, L224: Gürsoy should have an umlaut.
• L372: FT should be F_T.
• Consider citing Zeigler et al., 2023 (https://gchron.copernicus.org/articles/5/197/2023/) where discussing updates to F_T calculations. 

“U and Th zonation in apatite observed by synchrotron X–ray fluorescence tomography and implications for the (U–Th)/He system” by Sousa et al. 

I will preface this review by making it clear that my expertise lies not in geochronology but in experimental physics, in particular synchrotron-based data acquisition and analysis, with significant experience in XRF mapping. I therefore limit my review to the synchrotron methods and analysis.

This paper aims to increase the accuracy of (U-Th)/He thermochronology by accurately mapping U and Th zonation in apatite crystals using X-ray fluorescence tomography. The improvement in accuracy hinges on accurately measuring the U and Th concentrations throughout the apatite crystals. Table 2 suggests that this method increases accuracy over traditional methods by ca. 10%, and by ca. 7% over assuming homogenous elemental distributions. However, I find a major flaw with this method:

“Importantly, this analysis does not account for attenuation of the X–ray fluorescence by the sample itself. This attenuation varies systematically with the energy of the main fluorescence line. Because the X–ray path through the sample to the detector varies for each x and w value, trying to account for this effect accurately would be difficult and error prone.”

The attenuation of the X–ray fluorescence by the sample itself, known as self-absorption, is significant. For example, for U fluorescence (16.366keV) the attenuation length (where 1/e of the initial intensity remains) is ca. 260 um, while for Th fluorescence (12.252keV) the attenuation length is ca. 130 um (https://henke.lbl.gov/optical_constants/atten2.html). For sample MGB5–2 (diameter < 100um) this may not be an issue, however, for 03PH307A- 2 and AP-1 with diameters more than 200um this will be significant and cannot be ignored. The error introduced from not accounting for self-absorption would be significant, and likely exceed the claimed benefits. Indeed, correcting for this is difficult, but solutions to this problem exist, for example:

1. Zichao Wendy Di, Si Chen, Young Pyo Hong, Chris Jacobsen, Sven Leyffer, and Stefan M. Wild, "Joint reconstruction of x-ray fluorescence and transmission tomography," Opt. Express25, 13107-13124 (2017)
2. Yang, Q., Deng, B., Du, G., Xie, H., Zhou, G., Xiao, T. and Xu, H., Q. Yanget al.. X-Ray Spectrom., 43: 278-285 (2014)
3. Gao, J. Aelterman, B. Laforce, L. Van Hoorebeke, L. Vincze and M. Boone, "Self-Absorption Correction in X-Ray Fluorescence- Computed Tomography With Deep Convolutional Neural Network," inIEEE Transactions on Nuclear Science, vol. 68, no. 6, pp. 1194-1206, (2021). 

Additional comments.

1. How long does each tomography slice take to acquire? How many could you collect in 1 day of beamtime?
2. Is there an application to a lab source? What would need to happen to be able to apply this to a lab?
3. Using self-absorption corrections, what is the viable upper limit of sample size?
4. Can the homogenous approximation be estimated with a simple 2D fluorescence scan? In this case the is there an upper size limit to the measurement? This seems like a possible way to achieve a measurable improvement with significantly fewer experimental complexities.