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REVIEW 4 major objections 4 minor 17 references

Calibration of Scanning Thermal Microscope using Optimal Estimation of Function Parameters by Iterated Linearization

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read OEFPIL, a deterministic errors-in-variables fitting algorithm, calibrates a scanning thermal microscope and estimates unknown thermal conductivities with uncertainties in a single automated step, giving the same results as the…

desk verdict A useful, honest case study in applying an existing algorithm to SThM calibration, but the robustness claim goes beyond the evidence and needs revision. read the letter →

arxiv 2501.08961 v1 pith:Z4FZXURP submitted 2025-01-15 physics.data-an cond-mat.mtrl-sci

Anna Charvátová Campbell , Petr Klapetek , Radek Šlesinger , Jan Martinek , Václav Hortvík , Viktor Witkovský , Gejza Wimmer This is my paper · ORCID
classification physics.data-ancond-mat.mtrl-sci
keywords scanningthermalmicroscopySThMcalibrationOEFPILerrors-in-variablesregressionconductivitymeasurementuncertaintyevaluationautomatedcurvefitting
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

Scanning thermal microscopy can map heat conduction at the nanoscale, but calibrating the probe is hard because the response is nonlinear and only a few reference materials are available. The paper claims that the OEFPIL algorithm, a deterministic errors-in-variables fitting method, can take the raw reference-subtracted voltage data, fit the calibration curve, and estimate the unknown thermal conductivities of new samples in one step, complete with their uncertainties. If this works, SThM users no longer need Bayesian priors or separate manual calibration and prediction stages, and the whole procedure can be automated for routine laboratory use. The authors demonstrate it on two independent measurement sets with six reference and five unknown samples, and report that the one-step and two-step fitting routes give identical estimates of the curve parameters and the unknown conductivities.

What carries the argument

The machinery is the OEFPIL algorithm for nonlinear errors-in-variables regression, which separates directly measured quantities (the reference conductivities and the voltage-difference measurands $Y$) from indirect measurands (the curve parameters and the unknown conductivities) and iterates a linearized solution until convergence, returning estimates along with a covariance matrix. The model is constrained by equations (3) and (4), which force the calibration and unknown samples to satisfy the same curve $Y = a k/(b+k)+c$. Repeated image measurements are combined into one value and uncertainty per sample, and the fitting step absorbs both reference-sample errors and measurement errors without prior distributions.

What would settle it

Take a set of samples whose thermal conductivities are known independently by a traceable method (for example laser flash), spanning the steep part of the curve from roughly $0.1$ to $10$ W/(m K), apply the OEFPIL calibration, and check whether the reported 68 percent uncertainty intervals contain the independent values; if coverage is systematically below 68 percent, or if the fit p-values remain very low when more and better data are used, the assumed curve or uncertainty model is wrong.

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Extended reading notes

Core claim

The central claim is that the nonlinear calibration model $Y = a k/(b+k)+c$, fitted jointly to the reference samples and the unknown samples by OEFPIL, yields a consistent estimate of both the curve parameters $(a,b,c)$ and the thermal conductivities of the unknown samples together with their covariance matrix, so calibration and uncertainty propagation are solved at once. The paper also claims that in this model the simultaneous fit and the two-step procedure (fit the curve first, predict conductivities later) give identical estimated values and uncertainties, because the estimators of the curve parameters are uncorrelated with the estimators of the unknown-sample $Y$ values. This is supported by Monte Carlo comparison, with agreement to a few percent for values and around ten percent for uncertainties for most samples.

Load-bearing premise

The load-bearing premise is that the three-parameter curve $Y = a k/(b+k)+c$ correctly describes the true relation between the voltage difference and thermal conductivity for every calibration and unknown sample; if that shape is wrong, every estimated conductivity and its uncertainty inherits the error.

Editorial extensions

If this is right

  • SThM calibration can be run as an automated, unsupervised measurement: the same script acquires images, computes the reference-subtracted voltages, and feeds them to OEFPIL.
  • Users get the thermal conductivity of an unknown sample together with a standard uncertainty in a single deterministic computation, with no priors and no MCMC sampling.
  • The one-step/two-step equivalence means a calibration curve can be estimated once and reused later for prediction without losing consistency, as long as the uncertainty matrix of the direct measurements remains block-diagonal.
  • In the demonstrated setup, the useful range of the method is roughly $0.1$ to $10$ W/(m K); above that the curve is too flat to resolve conductivity.
  • Manual post-processing of images affected by contamination or probe jumps reduces the uncertainty of the estimated conductivities by 15 to 60 percent, so automated acquisition still benefits from careful data screening.

Reading between the lines

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

  • Beyond the paper: if the block-diagonal separability that makes the one-step and two-step estimates identical holds for this whole class of errors-in-variables models, OEFPIL could replace multi-stage or sampling-based calibration in other nonlinear measurement problems with independent direct measurements.
  • Beyond the paper: a targeted test would be to run the same protocol on samples with independently certified conductivities spanning the steep part of the curve and check whether the reported uncertainty intervals actually cover the certified values.
  • Beyond the paper: the very low p-values reported for all fits indicate that either the assumed calibration-curve shape is incomplete or the quoted uncertainties are too small; identifying that missing uncertainty source is the natural next step before the method's coverage claims are taken as settled.
  • Beyond the paper: the visible differences between the two datasets hint that a between-dataset uncertainty component is needed; a multi-day repetition campaign would show whether the within-dataset uncertainties are stable.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper applies the OEFPIL errors-in-variables fitting algorithm to the calibration of a scanning thermal microscope. The authors define an intermediate measurand Y as the voltage difference with respect to an SiO2 reference, model the calibration curve as Y = a k/(b+k) + c, and fit the curve parameters and the unknown thermal conductivities of five samples simultaneously. They demonstrate the procedure on two independent measurement campaigns, a manually corrected version of dataset 1, and a Mandel-Paule pooled dataset, and they compare the OEFPIL results with Monte Carlo simulations. The central claim is that OEFPIL provides robust and single-step evaluation of local thermal conductivities and their uncertainties without Bayesian priors.

Significance. If the central claim were fully supported, the paper would make a useful methodological contribution to SThM calibration by replacing iterative or Bayesian procedures with a deterministic errors-in-variables fit and by automating the extraction of calibration data from images. The manuscript has several genuine strengths: the automated measurement protocol, the explicit treatment of Y and k as uncertain quantities, the use of the Mandel-Paule estimator for between-location variability, and the candid discussion of convergence failures and the limited useful range of the calibration curve. However, as it stands, the evidence does not establish the robustness claim: all fits show very low p-values, the Monte Carlo comparison is internally inconsistent in several entries, and for some samples no meaningful conductivity could be derived. These issues are load-bearing because the calibration curve is the only link between the measured voltage difference and the thermal conductivity.

major comments (4)
  1. [Section 3, paragraph after Table 1] The authors report that 'in all cases, the fit exhibit very low p-values' and attribute this to 'either a problem with the assumed calibration curve expression or significantly underestimated uncertainties.' Since Eq. (2) is the sole functional link between Y and the thermal conductivity, a misspecified curve or an underestimated uncertainty propagates into every reported k* and its uncertainty. The paper does not resolve this ambiguity, so the central claim of robust single-step uncertainty evaluation is not established. Please provide quantitative goodness-of-fit statistics, residual diagnostics, or an independent validation of Eq. (2), and either remove or qualify the robustness claim accordingly.
  2. [Section 3, Table 2 and Conclusion] The Monte Carlo comparison does not support the Conclusion's statement that agreement is 'a few percent for values and around ten percent for uncertainties.' For dataset 1, kC is 9.05 ± 4.39 from OEFPIL versus 27.3 ± 1134.5 from Monte Carlo; for dataset 2, kE is 0.2174 ± 0.0060 versus 0.236 ± 0.327 and b is 0.0327 ± 0.0109 versus −0.0056 ± 0.4182. The text also notes that the algorithm did not converge for all generated datasets, especially dataset 2. Moreover, because the Monte Carlo runs sample from the same model and the same data as the OEFPIL fit, the comparison tests internal numerical consistency rather than model validity. The validation claim should be restricted to the cases where agreement is actually demonstrated and should be described as a consistency check, not as an independent validation.
  3. [Section 3, Tables 1 and 2] The claimed scope of the method is broader than what the data demonstrate. For sample C, no meaningful value could be deduced in datasets 2 and 4; for sample D, no meaningful value could be deduced in datasets 1 and 2; and one sample had to be removed from dataset 2 because results were inconsistent with the assumed model. The text further states that the method 'will not give useful results for thermal conductivities above approx. 10 W m−1 K−1.' The abstract and title promise single-step evaluation of local thermal conductivities without this restriction. Please state the valid conductivity range as part of the central claim and report the success/failure rate for all five unknowns, not only the well-behaved ones.
  4. [Section 3 and Table 1 caption] The provenance of dataset 3 is contradictory. The text says 'manual postprocessing performed on dataset 1 resulting in dataset 3,' while the Table 1 caption states '3 is a manual correction of 2.' Since dataset 3 is used in Table 2 and Figure 5, this inconsistency must be corrected and the affected results re-examined.
minor comments (4)
  1. [Throughout] There are typographical errors that should be corrected, including 'aquired' in Section 2.2, 'conducitivites' in Section 3, and 'Reserch' in Reference [14].
  2. [Section 3, before Table 2] The sentence 'The results are given in Table 2 typical probability distributions...' is grammatically incomplete and should be rewritten.
  3. [Data availability] No raw data or processing code are provided. Depositing the data and the OEFPIL/Monte Carlo scripts would allow independent verification of the p-values, the Mandel-Paule estimates, and the Monte Carlo convergence behavior.
  4. [Section 3, p-value discussion] The phrase 'very low p-values' is vague; actual p-values or equivalent goodness-of-fit statistics should be reported so that the reader can judge the magnitude of the model-data discrepancy.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the OEFPIL calibration results are obtained by fitting an assumed external model to independent reference data, not by construction from the target conductivities.

full rationale

No circular step is present. The reported conductivities are obtained by solving the errors-in-variables constraints (3)-(4) for the parameters a, b, c and k*_A..k*_E, with input data consisting of measured voltage differences Y computed per Eq. (1) and independent LNE reference conductivities for the six calibration samples. The calibration curve Y = a k/(b+k) + c is taken as an assumed model from Fleurence et al. [11]; it is not defined in terms of the unknown conductivities, so the inversion is not circular. The claimed equivalence between one-step and two-step fitting is a stated mathematical property of the block-diagonal covariance structure, not a result that presupposes the estimated conductivities. The Monte Carlo comparison uses the same model and the same data, but it is used only as a numerical cross-check of the OEFPIL covariance estimates; it is not the source of the reported values, and the paper explicitly reports disagreements for kC and kE. The paper's own admissions of very low p-values and non-convergence in Section 3 are validity limitations, not circularity. Self-citations [15-17] describe the OEFPIL algorithm, but the current application is demonstrated by the paper's own equations and results, so those citations are not load-bearing in a circular sense. The definition of Y relative to SiO2 is a differential measurement; the SiO2 value is a data point obtained from separate images, not a definitional identity forcing the calibration curve through (k_SiO2, 0).

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claim rests on three fitted curve parameters with no physical meaning, a model assumption contradicted by low p-values, traceability of LNE reference values, probe stability, and normality or uncorrelatedness assumptions in the Monte Carlo check. No invented entities. The SiO2-relative definition of Y fixes one calibration point at (k_SiO2, 0) by construction.

free parameters (4)
  • a (calibration curve parameter) = 0.8245 +/- 0.0568 (dataset 3)
    Fitted by OEFPIL to calibration data in Eq. (2); authors state parameters have no direct physical meaning.
  • b (calibration curve parameter) = 0.1892 +/- 0.0244 (dataset 3)
    Fitted by OEFPIL to calibration data in Eq. (2).
  • c (calibration curve parameter) = -0.7128 +/- 0.0601 (dataset 3)
    Fitted by OEFPIL to calibration data in Eq. (2); offset depends on reference SiO2 definition.
  • between-dataset variance (Mandel-Paule) = not reported explicitly
    Estimated when combining datasets 1 and 2 into dataset 4; authors note an estimate based on two datasets is not very reliable.
assumptions (4)
  • domain assumption The calibration curve Y = a*k/(b+k) + c correctly describes the voltage-conductivity relation for all samples.
    Adopted from Fleurence et al. [11], Eq. (2); low p-values in all fits suggest possible model misspecification.
  • domain assumption The LNE reference thermal conductivity values and uncertainties for the six calibration samples are accurate and traceable.
    Used as inputs; if wrong, the calibration curve and unknown conductivities are biased.
  • domain assumption The probe apex, electronics settings, and other influence factors do not change significantly during the measurement campaign.
    Stated in the Introduction; observed voltage jumps attributed to tip changes indicate this assumption can fail.
  • domain assumption Measurement errors are normally distributed and uncorrelated in the Monte Carlo comparison.
    Section 3 states normal distributions and no assumed correlation; this is not validated against the actual residuals.

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Cite this review

Pith. "Pith review of Calibration of Scanning Thermal Microscope using Optimal Estimation of Function Parameters by Iterated Linearization." pith.science (2026). https://pith.science/paper/Z4FZXURP

@misc{pith2026250108961,
  author       = {Pith},
  title        = {Pith review of: Calibration of Scanning Thermal Microscope using Optimal Estimation of Function Parameters by Iterated Linearization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Z4FZXURP}},
  note         = {Machine review of arXiv:2501.08961}
}
read the original abstract

Scanning thermal microscopy is a unique tool for the study of thermal properties at the nanoscale. However, calibration of the method is a crucial problem. When analyzing local thermal conductivity, direct calibration is not possible and reference samples are used instead. As the calibration dependence is non-linear and there are only a few calibration points, this represents a metrological challenge that needs complex data processing. In this contribution we present use of the OEFPIL algorithm for robust and single-step evaluation of local thermal conductivities and their uncertainties, simplifying this procedure. Furthermore, we test the suitability of SThM calibration for automated measurement.

Figures

Figures reproduced from arXiv: 2501.08961 by the authors.

Figure 1
Figure 1. Examples of problematic SThM images of topography (top) and volt [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Left: Example of the voltage signal aquired within dataset 3. Un [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Calibration curve for dataset 3. The uncertainties shown in the image [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: The values of the calibration samples shown in the top part, cover, in [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: Distributions of the calibration curve parameter [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]

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