Confocal Raman microscopy inside sessile multicomponent droplets

Alexander Erb; Johanna Steinmann; Robert W. Stark; Youngeun Lee

REVIEW 3 major objections 5 minor 1 references

Confocal Raman microscopy inside sessile multicomponent droplets

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The geometric distortion in confocal Raman images of sessile droplets is caused by refraction of the laser cone at the curved liquid-vapor interface and can be predicted with Snell's law from the droplet contour.

desk verdict Useful curved-droplet refraction correction, but the headline horizontal contact-line concentration maps are presented in the region where the model admittedly cannot compute the focus. read the letter →

arxiv 2507.00208 v1 pith:LMJDS3RY submitted 2025-06-30 physics.flu-dyn physics.chem-phphysics.optics

Alexander Erb , Johanna Steinmann , Youngeun Lee , Robert W. Stark This is my paper · ORCID

classification physics.flu-dynphysics.chem-phphysics.optics

keywords confocalRamanmicroscopysessiledropletsrefractionfocusshiftconcentrationgradientsevaporationthree-phasecontactlinemarker-freeimaging

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

Evaporating multicomponent droplets build up concentration gradients that drive the flows governing printing, coating, and cooling, yet measuring those gradients without adding surface-active marker molecules has been difficult. This paper establishes that the geometric distortion seen in confocal Raman images of sessile droplets is caused by refraction of the laser cone at the curved liquid-vapor interface, and that a Snell's-law ray-tracing calculation using the droplet's side-view contour predicts the distorted shape. It introduces a horizontal-laser configuration, created by placing a 45-degree mirror in the beam path, that reaches the region near the three-phase contact line where vertical illumination fails. The method is demonstrated on evaporating glycerol/water droplets, resolving a local water depletion at the contact line as evaporation proceeds. If correct, the work offers a marker-free guide for high-resolution concentration mapping inside evaporating droplets.

What carries the argument

The load-bearing object is a ray-tracing routine that computes the focus shift: for each intended focus position, it finds where the two outer rays of the objective's laser cone intersect the droplet contour, imported and fitted from a side-view image. At each intersection it applies Snell's law using the local surface normal, and it sets the new focus as the intersection of the two refracted rays. A 45-degree mirror placed in the beam path turns the vertical laser into a horizontal one, making the lower part of the droplet accessible. The calculation depends only on the drop shape and the cone aperture angle, set by the numerical aperture, and not on the drop size.

What would settle it

Embed a thin, Raman-active film at a known depth inside a transparent sessile droplet, record vertical Raman scans, and compare the apparent depth of the film with the ray-tracing prediction; systematic disagreement just below the surface, where Gaussian-beam effects are strongest, would show the outer-ray intersection model is wrong.

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Extended reading notes

Core claim

The central claim is that the apparent shape of a sessile droplet in a confocal Raman image is the locus of focal points shifted by refraction, and that this locus can be computed from the droplet contour and Snell's law. For vertical illumination, the shift grows near the three-phase contact line and deep focal points can be refracted into the substrate, limiting measurements to the upper part of the droplet. For horizontal illumination, the lower part of the laser cone can be cut by the substrate, producing a lower-intensity band, but the contact-line region remains measurable for contact angles in the range studied. The paper reports that the simulated drop shape fits the measured shape well for both configurations and uses the horizontal configuration to map water concentration in an evaporating 4.2 µL 10 mol% glycerol/water droplet, finding that the water concentration at the three-phase contact line decreased from 81.3 mol% to 71.9 mol% during evaporation.

Load-bearing premise

The whole correction rests on treating the focused Raman laser as a geometric cone whose new focus is the crossing point of its two outermost refracted rays, an approximation that is not exact for a real focused beam and that cannot be computed at all when part of the cone is blocked by the substrate.

Editorial extensions

If this is right

Vertical Raman scans of sessile droplets must account for the focus shift, or only near-surface measurements are reliable; the measurable region shrinks near the contact line for large contact angles.
For droplets with large contact angles, a horizontal laser configuration extends concentration mapping to the three-phase contact line at a spatial resolution of roughly 14 x 22.5 µm².
Because the simulated Raman droplet outline matches the measured outline across contact angles, the distortion is predictable and can be corrected rather than treated as an artifact.
Marker-free Raman mapping can track preferential evaporation in binary droplets, reproducing the expected local water depletion at the contact line without additives that alter droplet dynamics.

Reading between the lines

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

The same ray-tracing geometry could be inverted to dewarp Raman images into true droplet coordinates, turning the corrected contour into a quantitative mapping tool rather than only an explanation of distortion.
Because the correction depends mainly on local surface slope and cone aperture angle, it should transfer to other curved transparent objects, such as lenses, bubbles, or cells, wherever the outer-ray intersection picture holds.
If concentration gradients become strong enough to change the refractive index, the homogeneous-index assumption would need to be replaced by iterative ray tracing through the measured composition field.
The horizontal configuration's blocked-cone regime could be modeled quantitatively by treating the partial laser cone, which would extend concentration measurements even closer to the substrate.

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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 is my read. The paper does something genuinely useful: it takes Everall's flat-interface refraction correction, applies it to a curved, asymmetric sessile droplet surface by treating the left and right cone rays separately, and adds a horizontal 45-degree-mirror geometry for reaching the contact line. The model is parameter-free with respect to the Raman data—only Snell's law, the stated refractive index, and the measured drop contour go in—and the code is deposited. For the vertical-scan geometry, the simulated drop shapes reproduce the dome-shaped distortion and its contact-angle dependence. That part is solid and worth having.

The soft spot is the horizontal-scan application, and it is not a small one. The paper's own Section 3.3 says the simulation fails to calculate the refracted focus for positions deep in the droplet near the substrate, because the lower beam of the cone is blocked. The authors then assume the remaining cone 'continues to penetrate' so the measurement is simply dimmer. But the measured Raman signal depends on the full overlap of illumination and collection cones; blocking one side can shift the probe volume, not just reduce intensity. No derivation, simulation, or experiment checks that. Yet the headline result—the contact-line water concentration falling from 81.3 to 71.9 mol%—is presented from maps in that very region, with no positional correction. The spatial accuracy of those maps is simply unvalidated. The stress-test note is right.

Other issues are more minor. The 'fits well' between simulated and measured drop shapes is judged visually; there are no quantitative fit metrics, no replicate counts, no error bars on the concentration maps. The concentration calibration comes from the authors' previous PNAS paper rather than being re-established here. And the Discussion concedes Gaussian beam effects near the surface, but does not quantify them. The reference list is broad and the self-citation is reasonable in context.

Who gets value: experimentalists doing Raman on sessile droplets, especially those studying contact-line transport. This deserves a serious referee, not a desk reject, because the vertical-scan refraction model is a legitimate methodological contribution. But the horizontal contact-line concentration claim needs to either be supported by a proper treatment of the partially blocked aperture or be sharply qualified until such treatment exists.

Referee Report

3 major / 5 minor

Summary. The paper develops a geometric-optics ray-tracing model for the focus shift of a confocal Raman microscope when the beam is refracted at the curved liquid-vapor interface of a sessile droplet. The focus is computed as the intersection of the two outer rays of the objective cone after Snell refraction at the measured drop contour. The model is applied to vertical and horizontal laser incidence for droplets of different contact angles, and the simulated droplet shapes in the Raman image are compared with measured CH-integral images. A horizontal-laser setup using a 45-degree mirror is introduced to access the three-phase contact region, and water concentration maps of an evaporating glycerol/water droplet are presented, reporting a decrease in water concentration at the contact line from 81.3 to 71.9 mol%.

Significance. The refraction model is a useful practical tool: it is parameter-free with respect to the Raman data, uses only Snell's law, the stated refractive index, and the measured drop contour, and it qualitatively reproduces the dome-shaped distortion observed for vertical scans and the V-shaped cutout for horizontal scans. The code is publicly available. The horizontal configuration is a reasonable approach for accessing the contact-line region. However, the quantitative validation of the model is presently only visual, and the contact-line concentration map is obtained in a region where the model cannot compute the focus; both points affect the strength of the headline claim. If these issues are resolved, the paper would provide a valuable guide for Raman measurements of sessile droplets.

major comments (3)

[Section 3.3, Figs. 10 and 12] The concentration maps in Fig. 12 are interpreted in the region where the refraction model does not compute a focus. In Section 3.3 you state that for horizontal scans close to the substrate the simulation breaks off at approximately x* = 0.7 because the lower cone beam is interrupted by the substrate, and that 'the simulation fails to calculate the refracted focus.' You then assert that measurements remain possible with reduced intensity, but this asserts that the focus position is unchanged by the partial blockage. If the focus is displaced horizontally or vertically when part of the cone is blocked, the nominal positions in Fig. 12 do not correspond to the probed locations, and the reported decrease from 81.3 to 71.9 mol% at the contact line could be spatially mislocated. Please provide experimental verification (e.g., a scan across a sharp interface or a comparison with a configuration where the focus is computable) that intensity loss is the only consequence, or restrict the quantitative interpretation to the region where the focus is computed.
[Section 3.2, Figs. 1, 7, 8; abstract] The claim that the simulated drop shape 'fits well' with the measured shape is not supported quantitatively. In Figs. 1, 7, and 8 the comparison is visual only; no metric such as the RMS deviation between the simulated and measured contours is reported. Since the validity of the central claim rests on this fit, please provide a quantitative comparison of the contours for the four contact angles studied.
[Section 3.3, Fig. 12 and SI Sec. 2] The water concentration values and maps are presented without error bars, replicate droplet measurements, or uncertainty estimates. The calibration procedure is only referenced to Ref. [16], and the concentration difference between the start and end of evaporation is a key quantitative result. Without an assessment of measurement noise and systematic errors (including the position error discussed in the first comment), the significance of the observed 81.3 to 71.9 mol% decrease cannot be evaluated.

minor comments (5)

[Abstract] The phrase 'the Raman laser has to undergo a phase transition' should be replaced with a reference to the liquid-vapor interface or phase boundary.
[Section 3.3, Fig. 8 caption] The caption contains a duplicated phrase: 'contact line contact line'.
[Section 3.4] The Gaussian beam limitation is acknowledged, but please state explicitly that this limitation may also affect the contact-line maps of Fig. 12, where many measurement points are near the substrate or surface.
[Conclusion] The resolution '14 × 22.5 µm²' is called 'unprecedented'; please provide a comparison with previously reported spatial resolutions in Raman studies of droplets to support this claim.
[General] The manuscript contains several typographical and spacing errors (e.g., 'varie ty of everyday situations' in the abstract); a careful proofreading pass is needed.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity; the refraction model is parameter-free and validated against an external side-view contour, while minor self-citations to the authors' prior PNAS paper are not load-bearing.

full rationale

The central claim—that refraction of the confocal laser cone at the curved liquid–vapor interface explains the geometric distortion in Raman images of sessile droplets—is derived from Snell's law, the stated refractive index (n = 1.33), the objective numerical aperture (NA = 0.25), and the drop contour extracted from side-view photographs (Section 3.1, Figs. 3–4). No parameter is fitted to the Raman images, and the predicted measurable region (where the shifted focus remains inside the droplet) is compared with measured CH intensity maps in Figs. 7 and 11; this is an external, independent comparison. The concentration maps in Fig. 12 use a classical least-squares calibration described in the authors' prior PNAS paper [16] and reproduced in SI Fig. S2; this is a standard external calibration and not a fitted input to the refraction model, so the concentration result is not rendered circular. The paper also explicitly discloses limitations: in Section 3.3 the simulation 'fails to calculate the refracted focus for positions deep in the droplet' near the substrate because the lower cone beam is interrupted, and in Section 3.4 the geometric-optics focus may deviate from the Gaussian beam waist. These passages affect spatial accuracy but are not reductions by construction; no equation-level circularity is present. The remaining self-citations to [16] are method citations (side-image non-interference and concentration-calculation procedure) that are not load-bearing for the validation of the refraction model. Score 2 reflects only this minor self-referential provenance of the concentration quantification, not any genuine circularity in the derivation chain.

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

The refraction simulation itself has no fitted constants: n = 1.33 and the NA values are stated inputs, and the droplet contour is measured. The main assumptions are geometric-optics ray intersection, homogeneity of the refractive index, and an ad hoc allowance that a partially blocked cone still yields interpretable signals in the near-substrate region. No new physical entities are postulated.

assumptions (5)

standard math Snell's law governs refraction at the liquid-vapor interface.
Used in Section 3.1 to compute refracted angles alpha_i2 from incident angles for the left and right laser cone rays.
domain assumption The confocal focus coincides with the intersection of the outer rays of the laser cone.
Sections 3.1 and 3.4; the paper acknowledges that Gaussian beam optics makes the beam waist finite, so this ray-intersection point is approximate, especially near the surface.
domain assumption The droplet has a homogeneous refractive index (n = 1.33).
Section 3.4 states that concentration gradients inside droplets could produce refractive index gradients but they are assumed small; this keeps the Snell calculation tractable.
domain assumption The side-view photograph provides an accurate droplet contour for ray tracing.
Section 3.1 imports and fits the drop contour from side images; any optical distortion or 3D asymmetry in that image would bias the simulated focus shifts.
ad hoc to paper A partially blocked laser cone still produces a usable confocal measurement.
Section 3.3, where the simulation fails near the substrate but the paper asserts that the remaining part of the cone continues to penetrate the droplet and permits intensity-reduced measurements; this underpins the contact-line concentration maps.

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Cite this review

Pith. "Pith review of Confocal Raman microscopy inside sessile multicomponent droplets." pith.science (2026). https://pith.science/paper/LMJDS3RY

@misc{pith2026250700208,
  author       = {Pith},
  title        = {Pith review of: Confocal Raman microscopy inside sessile multicomponent droplets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LMJDS3RY}},
  note         = {Machine review of arXiv:2507.00208}
}

abstract

Evaporating multicomponent droplets are ubiquitous and appear in a variety of everyday situations and technological applications, including coating, 3D printing, and energy conversion processes. During evaporation, concentration gradients are typically induced, resulting in flows within the droplets. Many of the mechanisms underlying multicomponent droplet evaporation are not fully understood. However, most methods utilize markers that can be surface active and thus affect droplet dynamics. Thus, high-resolution marker-free measurements of concentration gradients in evaporating multicomponent droplets are needed. Raman microscopy can provide such a method. However, as the Raman laser has to undergo a phase transition, it is refracted, leading to a distorted drop contour. In this study, we model refraction in the droplet to better understand the shift in focus leading to geometric distortion. The horizontal and vertical shifts in focus are analyzed, and a modified configuration that enables Raman measurements with a horizontal laser is introduced. For both configurations, the simulated drop shape in the Raman image fits well with the measured shape. While Raman measurements with a vertically incident laser allow the study of the upper part of the droplet, for droplets with large contact angles, horizontal Raman measurements allow for the analysis of the region around the 3-phase contact line. As an example, a concentration map of an evaporating 4.2 $\mu$L glycerol/water droplet is presented. The results of this study can be used as a guide for Raman microscopy measurements of droplets. These findings contribute to understanding droplet dynamics during evaporation and provide a basis for developing novel printing, cleaning, and energy conversion technology applications.

Figures

Figures reproduced from arXiv: 2507.00208 by the authors.

**Figure 2.** Raman spectra of all the materials and fluids used in this study. Spectra were recorded at 17.6 mW with an integration time of 0.5 s on a 10x/0.25 objective. The average of 10 spectra smoothed with a moving average filter of size 10 is shown. The reason for this geometric distortion is the refraction of the laser beam at the droplet surface. Because this effect depends on the local curvature of the droplet, the shif… view at source ↗

**Figure 3.** Schematic representation of the refraction of the confocal laser cone on a curved droplet surface. The drop with the drop contour Cnf and contact angle β is shaded in gray. The contour can be extracted from side images, which, as it has been shown, do not interfere with the Raman measurement [16]. Because of the refraction, the original focal point F is shifted by the distances ∆x and ∆y to the point F ′ . The lase… view at source ↗

**Figure 5.** Shift in focus at various positions within [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

Figures from the paper (7 more)

**Figure 6.** Figure 6: Horizontal ∆x ∗ and vertical ∆y ∗ shifts in focus when the drop is scanned vertically as a function of the vertical position y ∗ . The positions closer to the 3-phase contact line are shown in light blue. Focal positions that are refracted to positions inside the drop…

**Figure 8.** Figure 8: C–H Raman image of the lower left side of the droplet measured in the horizontal configuration. A 4 µL glycerol droplet was analyzed using a 10x/0.25 objective at 17.5 mW, with a 0.5 s integration time and a resolution of 9.7×20 µm2 . The mirror used to deflect the l…

**Figure 7.** Figure 7: Calculated drop shapes in the Raman image for drops with different contact angles, as indicated in the top right corner. The focal points whose focus did not shift into the substrate are marked in blue. The dome shape with a convex center shown in [PITH_FULL_IMAGE:fig…

**Figure 9.** Figure 9: Shift in focus within the drop during the measurement with a horizontal laser. The focal points marked in green are analyzed in more detail in [PITH_FULL_IMAGE:figures/full_fig_p007_9.png]

**Figure 11.** Figure 11: Calculated drop shapes in the Raman image during a horizontal measurement. Focal points whose laser cones do not intersect the substrate are marked in green. The expected drop shape was evaluated for drops of different contact angles as shown in the top right corner.…

**Figure 10.** Figure 10: Horizontal and vertical shifts in focus during horizontal measurement for a sessile drop at different heights. The positions marked in green in [PITH_FULL_IMAGE:figures/full_fig_p007_10.png]

**Figure 12.** Figure 12: Water concentration maps of the droplet region near the 3-phase contact line. The mapped area relative to the droplet is shown as a black dashed rectangle in the lower right corner. Concentration maps of a 4.2 µL 10 mol% glycerol/water droplet evaporating at 23◦C and…

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Works this paper leans on

1 extracted references · 1 canonical work pages

[1]

Visualization and quantiﬁcation of local concentrati on gradients in evap- orating water/glycerol droplets with micrometer resolution

[1] Alexander Erb et al. “Visualization and quantiﬁcation of local concentrati on gradients in evap- orating water/glycerol droplets with micrometer resolution”. en. In: Proceedings of the National Academy of Sciences 122.20 (May 2025), e2423660122. issn: 0027-8424, 1091-6490. doi: 10 . 1073/pnas.2423660122. url: https://pnas.org/doi/10.1073/pnas.24236601...

work page doi:10.1073/pnas.2423660122 2025

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Visualization and quantiﬁcation of local concentrati on gradients in evap- orating water/glycerol droplets with micrometer resolution

[1] Alexander Erb et al. “Visualization and quantiﬁcation of local concentrati on gradients in evap- orating water/glycerol droplets with micrometer resolution”. en. In: Proceedings of the National Academy of Sciences 122.20 (May 2025), e2423660122. issn: 0027-8424, 1091-6490. doi: 10 . 1073/pnas.2423660122. url: https://pnas.org/doi/10.1073/pnas.24236601...

work page doi:10.1073/pnas.2423660122 2025