Using a Digital Twin for Fringe Projection Profilometry Optimisation

D. Weston; G. S. D. Gordon; S. Piano; X. Kong

arxiv: 2605.18545 · v1 · pith:TQE3GRIInew · submitted 2026-05-18 · ⚛️ physics.optics · eess.IV

Using a Digital Twin for Fringe Projection Profilometry Optimisation

D. Weston , X. Kong , G. S. D. Gordon , S. Piano This is my paper

Pith reviewed 2026-05-20 08:33 UTC · model grok-4.3

classification ⚛️ physics.optics eess.IV

keywords digital twinfringe projection profilometryparameter optimization3D reconstructionphase shiftingmetrologyBlender simulation

0 comments

The pith

A Blender digital twin for fringe projection profilometry finds parameter settings that transfer to hardware and cut required images by 48 percent.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper demonstrates construction of a digital twin inside Blender that replicates a physical fringe projection profilometry setup through accurate calibration and gamma response matching. This twin lets the authors explore and tune parameters such as phase-shift count, camera-projector spacing, and fringe density without repeated physical trials. When the best settings move from simulation to the real system, the number of images per measurement falls from 36 to 21 while reconstruction error drops sharply. A reader would care because conventional tuning of these systems demands many time-consuming hardware tests, and the twin offers a practical shortcut to better performance.

Core claim

The authors built a digital twin in Blender that matches the physical fringe projection profilometry hardware via Zhang calibration, gamma response, and ray-traced rendering. Systematic optimization inside the twin of phase-shift count, camera-projector spacing, and fringe density produced parameter sets that, when applied to the real system, reduced images per measurement by 48 percent from 36 to 21 and lowered mean symmetrical mean Chamfer distance by 74 percent for stripe count changes.

What carries the argument

The Blender digital twin that replicates the physical FPP system and supports automated parameter search across geometry and phase-shifting choices before hardware use.

If this is right

Optimal settings discovered in the twin can be used on the physical system to require only 21 images instead of 36 per measurement.
Mean symmetrical mean Chamfer distance falls by 74 percent when fringe stripe count is tuned via the twin.
Both geometric parameters such as camera-projector spacing and algorithmic choices such as phase shifting become jointly optimizable in simulation.
The same digital-twin workflow applies to three representative metrology artefacts and yields measurable reconstruction gains.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The approach could shorten setup time for other structured-light metrology techniques that share similar calibration and rendering requirements.
Non-specialists might reach high-precision results more quickly if the twin automates what currently requires expert trial-and-error.
Periodic re-calibration of the twin against fresh physical measurements could keep optimization quality high over time.

Load-bearing premise

The Blender digital twin must replicate the physical fringe projection system's response to parameter changes so that simulation results transfer directly to real hardware.

What would settle it

Transferring the digital-twin-optimized parameters to the physical fringe projection profilometry system and finding neither a drop in image count nor an improvement in symmetrical mean Chamfer distance would show the central claim is false.

Figures

Figures reproduced from arXiv: 2605.18545 by D. Weston, G. S. D. Gordon, S. Piano, X. Kong.

**Figure 1.** Figure 1: Overview of the proposed real-to-digital twin framework for fringe projection profilometry. The real system involves gamma calibration, system characterisation using Zhang’s method, and initial reconstruction. Transferred parameters (reference and measurement data) feed into the digital twin, where virtual gamma images are generated and optimised via non-linear least squares to minimise mean DC difference.… view at source ↗

**Figure 2.** Figure 2: 2.1. Fringe Projection Profilometry There are many variants of FPP, for example: phase-toheight methods, Fourier transform profilometry etc. In this Physical system characterised and gamma calibrated. Physical system environment (lighting, etc.) is modelled in the Blender simulation. Physical camera and projector intrinsic and extrinsic parameters are entered in the simulation. Gamma matching Characterisa… view at source ↗

**Figure 3.** Figure 3: The physical characterisation board used: 60 mm width × 42 mm height, with 52 total POIs. FPP fringe patterns are projected onto the characterisation board, and images are captured for muliple poses. The phase is then extracted for each set of fringes, followed by generation of an unwrapped phase map for each image set. In this work, phase extraction and unwrapping are performed using 𝑁-step phase shiftin… view at source ↗

**Figure 4.** Figure 4: The physical system’s intensity nonlinearity is matched by the virtual system - in this example, the virtual system becomes more nonlinear as it gets closer to the physical system. (2) ≈ 0.002 the physical and simulated systems are perfectly aligned. Consequently, an additional refinement step is required to further reconcile the geometric configurations of the physical and virtual environments. To quanti… view at source ↗

**Figure 5.** Figure 5: Visualisation of digital twin matching: the digital twin optimises the simulation parameters (projector strength, camera gamma response, board transformation), and the loss function converges [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 6.** Figure 6: Characterisation artefacts: 3D printed pyramid, pillars, and steps criterion for the optimiser was triggered if the SMCD did not decrease by 1 µm for five epochs. In the context of FPP, there are a multitude of parameters which could be explored. For our scenario, we decided to investigate: • Adjustment of the number of phase-shifted images to reduce computational complexity. • Altering the number of strip… view at source ↗

**Figure 7.** Figure 7: Sample simulations exploring the effect of increasing camera resolution and number of phases for a purely virtual system. 𝜖 is incredibly low compared to physical systems, likely due to low noise presence. The number of stripes used for multi-frequency phase unwrapping was 1, 8, and 64 for the horizontal and vertical fringe directions. 3. Results 3.1. Physical System To test the viability of our digital tw… view at source ↗

**Figure 9.** Figure 9: 𝐿 → 0.002 after around 30 epochs. The standard deviation of 𝐿 tends to vary across images - a point on the characterisation board may become slightly quantised at a particular pose, or less visible due to increased environmental lighting influence. As explained earlier, reprojection error is only a heuristical estimate of the performance of charactersation as it is prone to overfitting. Our loss function … view at source ↗

**Figure 10.** Figure 10: The steps artefact performs similarly across the physical and virtual system, whereas the pillars and pyramid artefacts display disparity. This could be explained by local regions of shadowing being less prevalent in the steps artefact than the others. The average ΔSMCD was 13 µm for the three artefacts in [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗

read the original abstract

Fringe projection profilometry (FPP) is a widely used technique for measuring object surface form and three-dimensional (3D) geometry, capable of delivering high-precision, high-resolution measurements when paired with suitable cameras and projectors. However, in practical deployments, identifying parameter configurations that maximise precision while satisfying real-world constraints remains challenging. To address this, we present an automated digital twin framework implemented in Blender, an open-source 3D software package that provides a ray-traced rendering environment that enables accurate simulation of physical systems. We replicated the physical setup in our digital twin by matching characterisation quality, gamma response, and characterisation images. Accurate system characterisation using Zhang's method [1], to obtain intrinsic and extrinsic parameters, is shown to be critical for achieving high precision. Using this digital twin, we then demonstrate systematic exploration and optimisation of key parameters, including phase-shift count, camera-projector spacing, and fringe density. These parameters span both system geometry (e.g. camera-projector positioning) and algorithmic choices, such as 2D phase-shifting and unwrapping methods [2]. Three measurement artefacts, representative of real world metrology scenarios, were used to benchmark the system. The symmetrical mean Chamfer distance (SMCD), computed between ground-truth and reconstructed meshes, was used to evaluate reconstruction quality. After optimisation within the digital twin, transferring the optimal parameters to the physical system reduced the number of required images per measurement by 48% (from 36 to 21). A reduction of 74.0% mean SMCD was also achieved for fringe pattern stripe count alteration. A 36.9% mean SMCD was obtained for adjusting the camera and projector spacing purely in the digital-twin.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Blender digital twin for FPP parameter search produces transferable gains on hardware, but missing baseline SMCD match between sim and physical leaves the transfer claim under-supported.

read the letter

Colleague, the main point is that this group built a Blender ray-traced model of their fringe projection setup, matched its gamma and calibration images to the real rig, then searched over phase-shift count, fringe density, and camera-projector spacing to cut the number of projected images while keeping reconstruction quality high. When they moved the best settings to the physical system they saw a 48 % drop in images (36 to 21) and a 74 % mean SMCD improvement on stripe-count changes, plus a smaller gain from geometry tweaks done only in simulation. They tested on three representative artifacts and used SMCD against ground-truth meshes for the metric. That combination of open-source simulation, systematic search, and physical transfer is the concrete new piece and it is useful for anyone who tunes FPP hardware in a lab or production line. The replication steps with Zhang calibration and gamma matching are described clearly enough to be reproducible. The soft spot is exactly the one flagged in the stress-test note. They matched characterisation quality and images, yet the manuscript does not report a direct SMCD comparison between the twin and the physical system on any shared, unoptimized parameter set. Without that baseline check it is hard to know whether the optimizer is exploiting simulation-specific artifacts (ideal ray tracing, simplified noise) that do not exist on the real hardware. A single plot of simulated versus measured SMCD before optimisation would have removed most of the doubt. This paper is aimed at applied metrology and industrial 3D scanning groups who already run FPP and want a faster way to explore parameter space. It has enough quantitative results and an accessible tool chain to deserve referee time, even if the reviewers will probably ask for the missing baseline validation and perhaps a few more controls on the physical side. I would send it out rather than desk-reject.

Referee Report

1 major / 3 minor

Summary. The manuscript presents a digital twin framework in Blender for optimizing fringe projection profilometry (FPP) parameters including phase-shift count, fringe density, and camera-projector spacing. The physical system is replicated by matching characterisation quality, gamma response, and images, with calibration via Zhang's method. Optimisation uses symmetrical mean Chamfer distance (SMCD) on three representative artefacts. Transfer of optimal parameters to hardware is reported to reduce images per measurement by 48% (36 to 21), with 74.0% mean SMCD reduction for stripe count changes and 36.9% mean SMCD improvement for spacing adjustments performed in the twin.

Significance. If the digital twin faithfully reproduces physical error sources, the approach offers a practical route to parameter optimisation that reduces physical trial-and-error in high-precision 3D metrology. The use of an open-source ray-tracing environment, standard calibration, and quantitative SMCD metrics on real-world artefacts supports potential reproducibility and applicability.

major comments (1)

[Abstract and Methods] The transfer results (48% image reduction and 74% SMCD improvement) are load-bearing for the central claim, yet the manuscript reports no quantitative SMCD comparison between the digital twin and physical system for any shared, unoptimized baseline parameter set. Without this, it remains unclear whether the Blender twin reproduces dominant physical error sources (gamma nonlinearity, camera noise, lens distortion residuals) or instead exploits simulation-specific artifacts.

minor comments (3)

Clarify the precise definition and computation of SMCD, including how ground-truth meshes are obtained and aligned.
Provide details on the optimisation algorithm, search space, and convergence criteria used within the digital twin.
Include error bars or statistical measures for all reported SMCD and image-count improvements.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their insightful comments on our manuscript. We address the major comment point-by-point below and outline the revisions we will make to strengthen the validation of our digital twin approach.

read point-by-point responses

Referee: [Abstract and Methods] The transfer results (48% image reduction and 74% SMCD improvement) are load-bearing for the central claim, yet the manuscript reports no quantitative SMCD comparison between the digital twin and physical system for any shared, unoptimized baseline parameter set. Without this, it remains unclear whether the Blender twin reproduces dominant physical error sources (gamma nonlinearity, camera noise, lens distortion residuals) or instead exploits simulation-specific artifacts.

Authors: We agree with the referee that a direct quantitative SMCD comparison between the digital twin and the physical system for a shared unoptimized baseline parameter set would strengthen the evidence that the simulation reproduces dominant physical error sources. The manuscript currently validates the twin by matching characterisation quality, gamma response, and images via Zhang's method. To address this point, we will revise the manuscript to include SMCD values computed on both the physical system and digital twin under identical baseline conditions (e.g., the default 36-image configuration). This comparison will be added to the Methods section to quantify fidelity and support the parameter transfer results. revision: yes

Circularity Check

0 steps flagged

No significant circularity; optimizations validated via independent physical measurements

full rationale

The paper constructs a Blender digital twin by matching physical characterization parameters (gamma response, Zhang's method intrinsics/extrinsics, and images), then optimizes parameters such as phase-shift count and fringe density inside the simulation to minimize SMCD. Optimal settings are transferred to the physical FPP hardware, where reductions in image count (48%) and SMCD (74%) are measured directly on real artefacts. No equations reduce reported gains to quantities defined by the same fitted parameters; physical evaluations function as external benchmarks. No self-citations are load-bearing, no ansatzes are smuggled, and no predictions collapse to inputs by construction. The chain is empirical and externally falsifiable.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the untested premise that the Blender simulation matches real optical behavior closely enough for optimizations to transfer; no free parameters or new entities are introduced in the abstract.

axioms (1)

domain assumption The Blender digital twin accurately replicates the physical system's optical properties when characterization images and gamma response are matched.
Invoked to justify that simulation-derived parameters will improve physical measurements.

pith-pipeline@v0.9.0 · 5853 in / 1279 out tokens · 65059 ms · 2026-05-20T08:33:29.527791+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We replicated the physical setup in our digital twin by matching characterisation quality, gamma response, and characterisation images... minimising mean SMCD... reduced the number of required images per measurement by 48% (from 36 to 21).
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Accurate system characterisation using Zhang’s method... phase extraction and unwrapping... multi-frequency temporal unwrapping

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

30 extracted references · 30 canonical work pages

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[1] [1]

Zhang, Camera Calibration, in: Computer Vision, Springer, Cham, 2021, pp

Z. Zhang, Camera Calibration, in: Computer Vision, Springer, Cham, 2021, pp. 130–131. URL:https://link.springer.com/rwe/10. 1007/978-3-030-63416-2_164. doi:10.1007/978-3-030-63416-2_164

work page doi:10.1007/978-3-030-63416-2_164 2021

[2] [2]

C. Zuo, L. Huang, M. Zhang, Q. Chen, A. Asundi, Temporal phase unwrapping algorithms for fringe projection profilometry: A comparativereview, OpticsandLasersinEngineering85(2016)84– 103

work page 2016

[3] [3]

S. Feng, C. Zuo, L. Zhang, T. Tao, Y. Hu, W. Yin, J. Qian, Q. Chen, Calibration of fringe projection profilometry: A comparative review, Optics and Lasers in Engineering 143 (2021) 106622

work page 2021

[4] [4]

Remani, A

A. Remani, A. Rossi, F. Pena, A. Thompson, In-situ monitoring of laser-basedpowderbedfusionusingfringeprojection, ResearchGate (2024)

work page 2024

[5] [5]

W. M. W. Norhaimi, Z. Sauli, H. Aris, V. Retnasamy, R. Vairavan, M. H. A. Aziz, Digital Fringe Projection System for Round Shaped Breast Tumor Detection 13 (2020)

work page 2020

[6] [6]

L. Hinz, S. Metzner, P. Müller, R. Schulte, H.-B. Besserer, S. Wack- enrohr, C. Sauer, M. Kästner, T. Hausotte, S. Hübner, F. Nürnberger, B.Schleich,B.-A.Behrens,S.Wartzack,M.Merklein,E.Reithmeier, Weston et al.:Preprint submitted to ElsevierPage 9 of 10 Blender FPP Digital Twin Fringe Projection Profilometry in Production Metrology: A Multi- Scale Compar...

work page 2021

[7] [7]

Place: Basel, Switzerland

work page

[8] [8]

Papachristou, P

K. Papachristou, P. F. Katsakiori, P. Papadimitroulas, L. Strigari, G. C. Kagadis, Digital Twins’ Advancements and Applications in Healthcare, Towards Precision Medicine, Journal of Personalized Medicine 14 (2024) 1101

work page 2024

[9] [9]

M.Attaran,B.G.Celik, DigitalTwin:Benefits,usecases,challenges, and opportunities, Decision Analytics Journal 6 (2023) 100165

work page 2023

[10] [10]

Publisher: Multidisciplinary Digital Publishing Institute

P.Nguyen,M.Kim,E.Nichols,H.-S.Yoon, AI-DrivenDigitalTwins for Manufacturing: A Review Across Hierarchical Manufacturing System Levels, Sensors 26 (2026) 124. Publisher: Multidisciplinary Digital Publishing Institute

work page 2026

[11] [11]

B.Ribbens,V.A.Jacobs,S.Vanlanduit,J.Buytaert, ProjectionMoiré profilometry simulation software for algorithm validation and setup optimalisation, 2013, pp. 87–96

work page 2013

[12] [12]

K. Ueda, K. Ikeda, O. Koyama, M. Yamada, Fringe projection profilometry system verification for 3D shape measurement using virtual space of game engine, Optical Review 28 (2021) 723–729

work page 2021

[13] [13]

B. O. Community, Blender - a 3D modelling and rendering package,

work page

[14] [14]

URL:http://www.blender.org

work page

[15] [15]

Puljčan, D

A. Puljčan, D. Zoraja, T. Petković, Simulation of Structured Light 3D Scanning using Blender, in: 2022 International Symposium ELMAR, 2022, pp. 215–220. URL:https://ieeexplore.ieee.org/ document/9899809. doi:10.1109/ELMAR55880.2022.9899809, iSSN: 1334- 2630

work page doi:10.1109/elmar55880.2022.9899809 2022

[16] [16]

A.d.F.Lemos,B.V.Nagy, Real-timeObjectPositioninginVibrating Environments Using DeepLabV3+ and ResNet50-based Semantic Segmentation, Periodica Polytechnica Mechanical Engineering 69 (2025) 347–368

work page 2025

[17] [17]

Imagingtoday, foreseeing tomorrow

K.A.Riihiaho,T.Rossi,I.Pölönen,HYPERBLEND:SIMULATING SPECTRALREFLECTANCEANDTRANSMITTANCEOFLEAF TISSUE WITH BLENDER, ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences V-3-2022 (2022) 471–476.ConferenceName:XXIVISPRSCongress“Imagingtoday, foreseeing tomorrow”, Commission III - 2022 edition, 6–11 June 2022, Nice, Franc...

work page 2022

[18] [18]

Zhang, Recent progresses on real-time 3D shape measurement using digital fringe projection techniques, ????

S. Zhang, Recent progresses on real-time 3D shape measurement using digital fringe projection techniques, ????

work page

[19] [19]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, Q. Chen, Phase shifting algorithms for fringe projection profilometry: A review, Optics and Lasers in Engineering 109 (2018) 23–59

work page 2018

[20] [20]

X. Su, W. Chen, Reliability-guided phase unwrapping algorithm: a review, Optics and Lasers in Engineering 42 (2004) 245–261

work page 2004

[21] [21]

Sturm, Pinhole Camera Model, in: Computer Vision, Springer, Cham, 2021, pp

P. Sturm, Pinhole Camera Model, in: Computer Vision, Springer, Cham, 2021, pp. 983–986. URL:https://link.springer.com/rwe/10. 1007/978-3-030-63416-2_472. doi:10.1007/978-3-030-63416-2_472

work page doi:10.1007/978-3-030-63416-2_472 2021

[22] [22]

H. Yuen, J. Princen, J. Illingworth, J. Kittler, Comparative study of Hough Transform methods for circle finding, Image and Vision Computing 8 (1990) 71–77

work page 1990

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