Photoelastic Grain Solver v2.0: An updated tool for analysis of force measurements in granular materials

Abrar Naseer; Ben McMillan; Carmen L. Lee; Dong Xie; Karen E. Daniels; Kerstin Nordstrom; Lori McCabe; Ted Brzinski; Tejas Murthy

REVIEW 3 major objections 7 minor 1 cited by

Photoelastic Grain Solver v2.0: An updated tool for analysis of force measurements in granular materials

T0 review · 3 major / 7 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read PeGS v2.0 fixes a boundary error in photoelastic contact-force measurements.

desk verdict A useful, honest software release note whose abstract overpromises: the boundary fix and modular rewrite are real, but resolution and efficiency claims are unbenchmarked. read the letter →

arxiv 2507.01933 v1 pith:LHEVYYDV submitted 2025-07-02 cond-mat.soft

Carmen L. Lee , Lori McCabe , Ben McMillan , Abrar Naseer , Dong Xie , Ted Brzinski , Karen E. Daniels , Tejas Murthy

show 1 more author

Kerstin Nordstrom

This is my paper

classification cond-mat.soft

keywords photoelasticitygranularmaterialscontactforcemeasurementinversemethodparticletrackingpseudo-imagechainsopen-sourcesoftware

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 presents PeGS v2.0, the successor to the open-source Photoelastic Grain Solver that converts polariscope images of birefringent granular disks into measurements of every interparticle contact force. The update's central physics fix is a corrected stress-free boundary term in the pseudo-image calculation, which previously produced nonphysical fringe patterns and could bias solved forces. The paper also adds particle tracking across image sequences, standardizes input and output data structures, makes the regression algorithm and force-balance constraint user-selectable, and restructures the code into modular functions so the community can insert or replace components. This matters because photoelastic imaging is currently the only proven experimental way to measure both the magnitude and direction of contact forces in a granular packing, and the corrected solver directly changes the accuracy of force-chain measurements.

What carries the argument

The central object is the pseudo-image: a synthetic intensity field produced by Eq. (1) from a candidate set of contact forces, assuming each particle is a linearly elastic flat circular plate. diskSolve.m repeatedly computes the principal stress difference $\sigma_1-\sigma_2$ at every pixel, renders the expected polariscope intensity $I=I_0\sin^2(\pi d C(\sigma_1-\sigma_2)/\lambda)$, and iteratively adjusts the forces until the pseudo-image matches the experimental fringe pattern. The load-bearing fix is the corrected stress-free boundary term in the transformation to circular geometry, which removes nonphysical fringes from the pseudo-image. Around this core, v2.0 standardizes modular functions for particle detection, contact detection via the intensity-gradient-squared $G^2$ measure, tracking, and optional adjacency-matrix output.

What would settle it

Take a calibration image of a single disk under a known diametric load, run both v1.0 and v2.0 through the pseudo-image and force-solving pipeline, and compare the recovered force vector and the residual intensity mismatch to the measured fringe pattern; if the corrected pseudo-image does not reduce the boundary fringes and recover the applied load, the central improvement claim is refuted.

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Extended reading notes

Core claim

The authors claim that PeGS v2.0 substantially improves the reliability and usability of photoelastic force imaging. The key correction, taken from an external validation study [17], concerns the stress-free boundary term that arises when the photoelastic stress field is transformed to a circular particle geometry; the earlier formulation left a spurious boundary contribution that created unphysical fringes. With the updated pseudo-image, the solver compares a physically consistent intensity field against the measured polarigraph and iteratively refines contact-force estimates. New to v2.0 is a particle-tracking module that assigns each grain a stable ID across images, enabling studies of flowing granular systems, and the modular architecture is designed so future algorithms can be dropped in without rewriting the pipeline. The paper presents the solver as an open-source community resource, with standardized file and data-structure conventions.

Load-bearing premise

The load-bearing premise is that the boundary-term correction supplied by an external validation study [17] is physically correct and was implemented faithfully in the reorganized code; if that correction is wrong or the implementation diverges, the claimed gains in force accuracy collapse.

Editorial extensions

If this is right

Static packing analyses get contact force vectors with a pseudo-image that no longer carries nonphysical boundary fringes.
The particle-tracking module gives each grain a stable identity across image sequences, opening the same solver to shear and flow experiments.
Standardized module interfaces let users swap particle detection, contact detection, or regression routines, such as an adapted version that solves for tensile forces in cohesive grains.
The user can choose the regression algorithm, tolerances, and whether to enforce force balance on each particle.
The code remains open source with a planned team structure, documentation, and training materials, so the tool can be maintained beyond a single research group.

Reading between the lines

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

The authors do not state this, but if the boundary error biased weak-force contacts in v1.0, published conclusions built on v1.0 force measurements may need rechecking in low-force or edge-dominated packings.
The standardized adjacency-matrix output positions PeGS output for direct use in graph-theoretic and topological studies of contact networks, a connection the paper only hints at.
The unused blue channel could carry fluorescent markers that encode particle orientation or material labels in future versions, extending the tracking idea.
Because the correction is sourced externally, a natural next test is an independent benchmark comparing v2.0 force sums against global measurements such as the weight of the overburden.

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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

Quick take: this is a solid, honest software release note, not a research paper, and the main quantitative claims in the abstract overstate what the text supports. The genuinely new things are the modular re-architecture of PeGS, the particle tracking module, and the correction of the stress-free boundary term in the pseudo-image calculation. The code and test data are public and the workflow is clearly documented; that is real and useful.

What it does well: the structural changes are described with a clear flowchart, standardized data structures, and a visible wrapper. The tracking module is described adequately for users. The boundary-term fix is the most consequential physics change and the authors correctly flag that it fixes nonphysical fringes; they cite McMillan et al. [17] for the derivation. That is a responsible way to handle an inherited correction, though it also means the present paper does not itself validate the fix.

Soft spots: the abstract promises improved resolution and efficiency but the text contains no timing measurements, no force-error comparison between v1.0 and v2.0, and no validation case for the corrected boundary term. The stress-test note is right: from the text alone, the central improvement claims are unfalsifiable. That is a real weakness for a methods paper. It is not fatal for what this is—a conference proceedings update for a community tool—but it should be fixed or explicitly softened. Also, the corrected boundary term is not written out; a reader who wants to check the implementation has to go to the repository and to Ref. [17]. That is acceptable for a release note, but not ideal.

I disagree slightly with the implication that the missing benchmark should block acceptance. For a proceedings software note, the bar is lower; the code is public and the test dataset exists. A referee can reasonably ask the authors to either add a simple benchmark or remove the quantitative language. The core value of the release—modular code, tracking, boundary fix—does not depend on the unproven efficiency claim.

Who is this for: experimental granular physicists who use photoelasticimetry. A reader outside that subfield gets little. It deserves a serious referee, mainly because the tool is community standard and the boundary-term fix has consequences for all existing PeGS-based force measurements. Send it to peer review with a request for a benchmark or a scaled-down abstract.

Referee Report

3 major / 7 minor

Summary. The paper describes version 2.0 of the Photoelastic Grain Solver (PeGS), an open-source MATLAB package for measuring interparticle forces in two-dimensional photoelastic granular experiments. The authors report a substantial architectural rewrite from a scripted to a modular function-based code, standardized input/output data structures, new user-selectable regression options, a new particle tracking module, and an updated pseudo-image formulation that corrects a stress-free boundary term error identified by McMillan et al. [17]. The abstract and Table 1 claim improved resolution and efficiency, and the paper provides a test dataset and links to the repository. The text is primarily a software description with workflow details and a figure showing outputs of the main modules; no quantitative benchmarks or validation experiments are reported.

Significance. If the stated improvements are real, PeGS v2.0 is a valuable resource for the granular-physics community: it is open source, ships with a test dataset, and the modular design lowers the barrier for community extensions. The paper explicitly credits the correction of a documented physics error in the pseudo-image calculation, and the external provenance of that correction in Ref. [17] gives it credibility. However, the paper's central quantitative claims—improved force resolution and efficiency—are not supported by any measurements in the text. The absence of runtime data, force-error comparisons, or validation of the boundary-term correction makes the headline improvements impossible to assess from the manuscript alone. This is a software-description paper in a proceedings context, so the bar for validation can be lighter than for a methods paper, but the specific claims made here require at least one concrete benchmark or a comparison of old versus new output on the provided test dataset.

major comments (3)

[§2.5 and Abstract] The paper's most consequential claim is that PeGS v2.0 provides an 'updated formulation for the pseudo-image, accurately resolving the boundary terms' and that the old error produced 'nonphysical fringe patterns and potentially... erroneous values for the solved forces.' Yet the manuscript gives no equation for the corrected term, no test case, and no error metric; it only cites McMillan et al. [17]. If the correction is wrong or partially implemented, the central improvement claim fails silently. Please include the corrected formulation (or a pointer to the specific code lines) and show a direct comparison of pseudo-image quality and/or force accuracy on a validation case, such as the GitHub test dataset or a known-force calibration.
[Abstract, Introduction, Table 1] The claim that the 'new version improves resolution and efficiency' is not supported by any quantitative evidence in the text: there are no timings, no force-error statistics, no resolution comparison with v1.0, and no analysis of the test dataset beyond a representative image. Since this is a central advertised benefit, please add a benchmark section reporting at least runtime per image and force accuracy on a public test case, ideally comparing v1.0 and v2.0 on the same data.
[§2.6] The new particle tracking module is advertised as a feature that makes PeGS2 'more useful for studying granular systems in flowing states,' but no test of tracking accuracy is provided. The polygon-projection method may fail for large inter-frame displacements or rotations; at minimum, please report the tracking success rate on a sequence of images with known displacements (e.g., from the test dataset) or specify the conditions under which it is expected to work.

minor comments (7)

[Eq. (1)] The sentence introducing Eq. (1) has a grammatical error: 'light is attenuated due to this phase difference is' should be 'light is attenuated due to this phase difference, giving' or similar.
[Fig. 1 caption] The caption says 'photoelastic fringes due to forces'; 'due to' reads awkwardly, and 'fringes' could be 'fringe pattern' for clarity.
[§2.3] The MATLAB function name is misspelled: 'imfindcircle' should be 'imfindcircles'.
[Table 1] 'Customizeability' is misspelled; it should be 'Customizability'.
[§2.5] The module is described as calling 'stress_engine_original.m', which suggests a code artifact; consider renaming to a more descriptive function name or clarifying that this is the original stress engine retained in the modular architecture.
[General] The paper inconsistently writes 'PeGSv2', 'PeGSv2.0', and 'PeGS v.2.0'; please standardize the version notation.
[Data availability] The test dataset is mentioned only in the Fig. 3 caption; please add a dedicated data-availability statement with the repository DOI [10] and instructions for reproducing the workflow shown in Fig. 3.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: PeGS v2.0 is a software-description paper whose core technical correction is grounded in an externally published validation study, not in a self-referential derivation.

full rationale

This manuscript is a software and methods description rather than a derivational or predictive study. The central physics claim is the correction of the stress-free boundary term in the pseudo-image, stated in Section 2.5: 'During inspection of the original PeGS code, we noticed [17] that the stress-free boundary term arising from the transformation to a circular geometry was incorrect... In PeGS v2.0, we provide an updated formulation for the pseudo-image, accurately resolving the boundary terms.' The correction is not derived within this paper; it is attributed to McMillan et al. (Reference [17]), a separate peer-reviewed article in Measurement Science and Technology that validates and corrects the photoelastic technique. Although one of the present authors (B. McMillan) is an author of Reference [17], that citation points to an externally published and validated result rather than to an unpublished assertion, so it functions as independent evidence rather than as a self-citation chain. The other updates (modular architecture, standardized data structures, particle tracking, user-selectable regression) are implementation features, not quantities fitted to data and then relabeled as predictions. The paper makes no claim to derive force measurements from first principles within this article; it describes an inverse method whose inputs are experimental images and whose validation is referenced to the prior literature. No equation in the paper is equivalent by construction to an input datum, and no fitted parameter is renamed as a predicted outcome. The skeptic's concern that the boundary-term fix is not revalidated in this paper is a reproducibility or verification risk, but it is not circularity. Accordingly, no circular steps are identified and the score is 0.

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

No new physical entities are postulated. The method relies on standard photoelasticity assumptions and user-tunable detection thresholds. The central claim depends on the correctness of the external boundary-term correction [17] and on the linear-elastic stress model.

free parameters (4)

particleDetect sensitivity (MATLAB imfindcircles)
User-set parameter that controls circle detection; affects which particles are found and hence the whole force analysis.
G2 contact detection thresholds
Predefined user thresholds used to decide whether intensity gradients indicate a contact; directly determine the contact network.
Regression algorithm and tolerances for diskSolve
User-selectable solver and tolerance settings for the inverse fringe-fitting; affect the accuracy and convergence of force estimates.
Force balance enforcement flag
Boolean choice to impose force balance on each particle; changes the optimization constraints and results.

assumptions (4)

domain assumption The stress-optic law (Eq. 1) linearly relates birefringence to the principal stress difference.
This is the physical basis for converting intensity patterns to stress; standard in photoelasticity and cited from prior work.
domain assumption Particles behave as linearly elastic, flat, circular plates, so the stress field can be computed from contact forces via the solution described in Ref [4].
The stress_engine_original function assumes this model; if the particles are not well described by it, the pseudo-image generation is invalid.
domain assumption The G2 intensity gradient provides a semi-quantitative proxy for contact stress (Ref [15]).
G2 is used for contact detection; the reliability of this proxy is assumed from the literature.
domain assumption The circular-polariscope imaging setup produces images with uniform contrast and at least 50 px/particle as required for fringe fitting.
The method relies on high-resolution, well-lit images; the paper states this as a rule of thumb but does not test robustness.

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Cite this review

Pith. "Pith review of Photoelastic Grain Solver v2.0: An updated tool for analysis of force measurements in granular materials." pith.science (2026). https://pith.science/paper/LHEVYYDV

@misc{pith2026250701933,
  author       = {Pith},
  title        = {Pith review of: Photoelastic Grain Solver v2.0: An updated tool for analysis of force measurements in granular materials},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LHEVYYDV}},
  note         = {Machine review of arXiv:2507.01933}
}

read the original abstract

Photoelastic force imaging is an experimental technique whereby a birefringent granular material is imaged with a polariscope to characterize the internal stress state of a granular material. Photoelasticimetry is the only proven experimental technique that allows researchers to measure the shear and normal forces at every particle contact in a granular packing. In 2017, Kollmer et al. [Rev. Sci. Instrum. 88, 051808 (2017)] developed an open-source software to perform this analysis. Here, we present the next substantial update to this software package. The new version improves resolution and efficiency and substantially changes the software architecture. The structural changes better facilitate add-ons, modules, and future improvements to the performance, accessibility, and versatility of the tool. Besides updates to the core software, we introduce new infrastructure to support the ongoing development of software, documentation, and training materials. The full development team, software, and supporting resources are available at https://github.com/photoelasticity .

Figures

Figures reproduced from arXiv: 2507.01933 by the authors.

**Figure 1.** A single grain imaged so that green light passes through a polariscope, revealing a photoelastic fringes due to forces at the perimeter of the grain. The top half of the image is overlaid with its pseudo-image (see section 2.5). light is attenuated due to this phase difference is I = I0 sin2 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗

**Figure 2.** Schematic of the workflow and I/O of PeGS v.2.0. Dashed lines indicate optional functions and their input/outputs. contact forces which gave rise to a particular fringe pattern. The established procedure is to (1) identify particles in a polarigraph of the system; (2) identify possible contacts between particles; (3) estimate the magnitude of those contact forces; (4) generate the expected intensity across the part… view at source ↗

**Figure 3.** Images produced from the GitHub test dataset. From the red channel of (a) the raw image, particleDetect.m identifies (b) all circular particles (the number label indicates bulk (0) or edge (non-zero) grains). The contactDetect.m module identifies (c) the contact network (red and green lines) using the particle locations and the green channel of the original image. The contact information is used to generate a (d) P… view at source ↗

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Stress network dynamics influence on large particle segregation
cond-mat.soft 2026-04 unverdicted novelty 5.0 of 10

Larger size ratios produce longer force chains and stress fluctuations that drive large-particle segregation through squeeze expulsion in granular shear flows.

Reference graph

Works this paper leans on

17 extracted references · 16 canonical work pages · cited by 1 Pith paper

[17]

McMillan, S

B. McMillan, S. Dalziel, N. Vriend, Valida- tion and correction of photoelastic techniques for frictional granular systems, Measurement Science and Technology 36, 055212 (2025). 10.1088 /1361- 6501/add48b

work page 2025
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Dijksman, N

J.A. Dijksman, N. Brodu, R.P. Behringer, Refractive index matched scanning and detection of soft parti- cles, 88, 051807 (2017). 10.1063/1.4983047

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S.A. Hall, M. Bornert, J. Desrues, Y . Pannier, N. Lenoir, G. Viggiani, P. Bésuelle, Discrete and continuum analysis of localised deformation in sand using X-ray µCT and volumetric digital image correlation, Géotechnique 60, 315 (2010). 10.1680/geot.2010.60.5.315

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Hurley, S.A

R.C. Hurley, S.A. Hall, J.E. Andrade, J. Wright, Quantifying Interparticle Forces and Heterogene- ity in 3D Granular Materials, Physical Re- view Letters 117, 098005 (2016). 10.1103 /Phys- RevLett.117.098005

work page 2016
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Daniels, J.E

K.E. Daniels, J.E. Kollmer, J.G. Puckett, Photoelas- tic force measurements in granular materials, Re- view of Scientific Instruments 88, 051808 (2017). 10.1063/1.4983049

work page doi:10.1063/1.4983049 2017
[5]

Abed Zadeh, J

A. Abed Zadeh, J. Bares, T.A. Brzinski, K.E. Daniels, J. Dijksman, N. Docquier, H.O. Everitt, J.E. Kollmer, O. Lantsoght, D. Wang et al., Enlight- ening force chains: a review of photoelasticimetry in granular matter, Granular Matter 21, 83 (2019). 10.1007/s10035-019-0942-2

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arXiv 2024

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Majmudar, R.P

T.S. Majmudar, R.P. Behringer, Contact force mea- surements and stress-induced anisotropy in granu- lar materials, Nature 435, 1079 (2005). 10.1038 /na- ture03805

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A. Naseer, K.E. Daniels, T.G. Murthy, Extracting contact forces in cohesive granular ensembles, (Pow- ders and Grains, accepted) (2025)

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Naseer, PeGS_for_cohesion (2025), https:// github.com/nsrabrar/PeGS_for_Cohesion

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C.L. Lee, E. Azéma, K.E. Daniels, The stress-force- fabric relation across shear bands, (Powders and Grains, accepted) (2025)

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2024 doi arXiv

Pith tools

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

[1] [17]

McMillan, S

B. McMillan, S. Dalziel, N. Vriend, Valida- tion and correction of photoelastic techniques for frictional granular systems, Measurement Science and Technology 36, 055212 (2025). 10.1088 /1361- 6501/add48b

work page 2025

[2] [1]

Dijksman, N

J.A. Dijksman, N. Brodu, R.P. Behringer, Refractive index matched scanning and detection of soft parti- cles, 88, 051807 (2017). 10.1063/1.4983047

work page doi:10.1063/1.4983047 2017

[3] [2]

S.A. Hall, M. Bornert, J. Desrues, Y . Pannier, N. Lenoir, G. Viggiani, P. Bésuelle, Discrete and continuum analysis of localised deformation in sand using X-ray µCT and volumetric digital image correlation, Géotechnique 60, 315 (2010). 10.1680/geot.2010.60.5.315

work page doi:10.1680/geot.2010.60.5.315 2010

[4] [3]

Hurley, S.A

R.C. Hurley, S.A. Hall, J.E. Andrade, J. Wright, Quantifying Interparticle Forces and Heterogene- ity in 3D Granular Materials, Physical Re- view Letters 117, 098005 (2016). 10.1103 /Phys- RevLett.117.098005

work page 2016

[5] [4]

Daniels, J.E

K.E. Daniels, J.E. Kollmer, J.G. Puckett, Photoelas- tic force measurements in granular materials, Re- view of Scientific Instruments 88, 051808 (2017). 10.1063/1.4983049

work page doi:10.1063/1.4983049 2017

[6] [5]

Abed Zadeh, J

A. Abed Zadeh, J. Bares, T.A. Brzinski, K.E. Daniels, J. Dijksman, N. Docquier, H.O. Everitt, J.E. Kollmer, O. Lantsoght, D. Wang et al., Enlight- ening force chains: a review of photoelasticimetry in granular matter, Granular Matter 21, 83 (2019). 10.1007/s10035-019-0942-2

work page doi:10.1007/s10035-019-0942-2 2019

[7] [6]

Ramesh, Developments in Photoelasticity: A re- naissance (IOP Publishing, 2021)

K. Ramesh, Developments in Photoelasticity: A re- naissance (IOP Publishing, 2021)

work page 2021

[8] [7]

S. Joseph Antony, Power of photo-stress analysis in unravelling the mechanics of granular materials and its applications in interdisciplinary research, Op- tics and Lasers in Engineering 183, 108512 (2024). 10.1016/j.optlaseng.2024.108512

arXiv 2024