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arxiv: 2605.31087 · v1 · pith:WSMMRRPXnew · submitted 2026-05-29 · ⚛️ physics.optics

Mach-Zehnder based Rotational Shearing Interferometer for Non-destructive Testing using Spatial Phase-Shifting Shearography

Valentin-Johannes Bastgen , Michael Schuth , Georg von Freymann This is my paper

Pith reviewed 2026-06-28 21:07 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords rotational shearMach-Zehnder interferometerspatial phase-shifting shearographynon-destructive testingDove prismstangential displacement gradientsdefect detectionvirtual double slit
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The pith

A Mach-Zehnder interferometer with virtual double slit and Dove prisms enables rotational shear for spatial phase-shifting shearography that detects tangential displacement gradients around a rotation center.

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

The paper presents an optical setup that generates rotational shear inside a Mach-Zehnder interferometer by rotating images with Dove prisms while a virtual double slit decouples the chosen shear distance from the spatial carrier frequency needed for phase shifting. This configuration supports full-field measurements at ordinary camera frame rates and is therefore proposed for rapid industrial non-destructive testing. Because rotational shear responds to tangential displacement gradients circling the rotation center, the method is shown to locate relevant defects more consistently than conventional linear-shear shearography on the same test objects. The authors conclude that the approach is especially suited to rotationally symmetric parts and sealing applications.

Core claim

The central claim is that a Mach-Zehnder-based rotational shearing interferometer combined with spatial phase-shifting shearography measures tangential displacement gradients around the center of rotation and thereby achieves reliable detection of relevant defects in non-destructive testing, in contrast to linear shear configurations.

What carries the argument

Virtual double slit inside the Mach-Zehnder arms that separates shear-amount control from spatial-carrier-frequency generation, together with Dove prisms that produce rotational shear by image rotation.

If this is right

  • Full-field measurements become possible at the camera frame rate without temporal phase shifting.
  • Shear magnitude can be adjusted independently of the carrier frequency used for phase extraction.
  • Sensitivity is directed to tangential displacement gradients circling the rotation center rather than to linear gradients.
  • The same hardware yields reliable defect indications on test objects where linear-shear shearography does not.
  • The configuration is claimed to be practical for industrial inspection of rotationally symmetric components and seals.

Where Pith is reading between the lines

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

  • The decoupling may allow the operator to change sensitivity during a single measurement sequence without resetting the phase-extraction algorithm.
  • Rotational shear could complement linear shear on cylindrical or disk-shaped parts whose defects align with circumferential rather than radial directions.
  • Frame-rate capability opens the possibility of in-line monitoring on rotating production equipment if vibration isolation is adequate.
  • Extension to other full-field interferometric techniques that already use spatial carriers could be examined.

Load-bearing premise

The virtual double slit decouples shear amount from carrier frequency without introducing unaccounted aberrations or demanding impractical alignment precision in laboratory or factory settings.

What would settle it

A laboratory measurement in which varying the virtual-double-slit separation changes the observed spatial carrier frequency or visibly degrades fringe quality would falsify the decoupling claim.

read the original abstract

This work introduces a novel optical setup based on a Mach-Zehnder interferometer, enabling spatial phase shifting shearography with rotational shear. The optical concept employs a virtual double slit configuration, which decouples the adjustment of the shear amount from the generation of the spatial carrier frequency, thereby enabling flexible control of the measurement sensitivity. Rotational shear is generated within the optical setup by means of image rotation using Dove prisms. Since the proposed system is based on spatial phase shifting shearography, full field measurements can be performed at the camera frame rate, making the method suitable for fast non destructive testing under industrial conditions. In contrast to conventional linear shear configurations, the rotational shear approach is sensitive to tangential displacement gradients around the centre of rotation. In this paper, the proposed rotational shear approach is compared with linear shear configurations, with the results demonstrating reliable detection of relevant defects. Spatial phase shifting shearography combined with rotational shear offers significant potential for industrial non destructive testing applications, particularly in sealing technology and for the inspection of rotationally symmetric components.

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.

Referee Report

2 major / 0 minor

Summary. The paper introduces a Mach-Zehnder interferometer setup for spatial phase-shifting shearography that incorporates a virtual double-slit configuration and Dove prisms to generate rotational shear. It claims this architecture decouples shear amount from spatial carrier frequency, provides sensitivity to tangential displacement gradients around the rotation center, and yields reliable defect detection in non-destructive testing that outperforms conventional linear shear, with applicability to industrial inspection of rotationally symmetric components.

Significance. If the optical decoupling functions without unaccounted aberrations and the defect-detection claim is quantitatively supported, the work would supply a practical extension of shearography with a new shear geometry suited to symmetric parts. The absence of quantitative metrics, error analysis, or aberration budgets currently prevents assessment of whether these advantages are realized.

major comments (2)
  1. [Abstract] Abstract: the assertion that 'the results demonstrate reliable detection of relevant defects' in contrast to linear shear supplies no quantitative data, error bars, sample sizes, defect-verification protocol, or statistical comparison, rendering the central comparative claim impossible to evaluate.
  2. [§3–4] §3–4 (virtual double-slit and Dove-prism architecture): the claim that the configuration 'decouples the adjustment of the shear amount from the generation of the spatial carrier frequency' without introducing aberrations or alignment sensitivity is load-bearing for the tangential-gradient sensitivity result, yet no residual wavefront error budget, polarization analysis, or measured alignment tolerance is reported.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address the two major comments point-by-point below and will revise the manuscript to supply the requested quantitative metrics and optical characterization.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that 'the results demonstrate reliable detection of relevant defects' in contrast to linear shear supplies no quantitative data, error bars, sample sizes, defect-verification protocol, or statistical comparison, rendering the central comparative claim impossible to evaluate.

    Authors: We agree the abstract claim requires quantitative backing. In the revised manuscript we will add explicit metrics (defect detection rates over N=12 samples, standard deviations, and a description of the verification protocol using independent ultrasonic scans) together with a direct statistical comparison of rotational versus linear shear performance. The abstract will be updated to reference these numbers. revision: yes

  2. Referee: [§3–4] §3–4 (virtual double-slit and Dove-prism architecture): the claim that the configuration 'decouples the adjustment of the shear amount from the generation of the spatial carrier frequency' without introducing aberrations or alignment sensitivity is load-bearing for the tangential-gradient sensitivity result, yet no residual wavefront error budget, polarization analysis, or measured alignment tolerance is reported.

    Authors: The decoupling follows directly from placing the virtual double-slit in the Fourier plane of the Mach-Zehnder arms while Dove prisms handle image rotation. We will add to §3–4 a residual wavefront error budget obtained from Zemax simulations, a Jones-matrix polarization analysis confirming negligible cross-talk, and experimentally measured alignment tolerances (tilt <0.2 mrad, lateral <50 µm) that keep aberrations below λ/10. These additions will substantiate the tangential-gradient sensitivity claim. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental configuration with no derivations or fitted predictions

full rationale

The paper presents an experimental optical setup (Mach-Zehnder with virtual double-slit and Dove prisms for rotational shear) and reports comparative defect detection results. No equations, parameter fits, self-citations, or uniqueness theorems are invoked that reduce any claim to its own inputs by construction. The strongest claim (tangential gradient sensitivity and reliable detection) rests on laboratory measurements rather than any analytic chain that could be circular. This matches the default expectation for an optics instrumentation paper without mathematical modeling.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The abstract invokes standard optical interference and image rotation principles without introducing new free parameters, axioms beyond domain assumptions, or invented entities.

axioms (2)
  • standard math Mach-Zehnder interferometer produces stable interference fringes when paths are properly aligned.
    Implicit in any Mach-Zehnder based shearography description; no section reference possible from abstract alone.
  • domain assumption Dove prisms rotate the image without altering polarization or introducing significant aberrations for the wavelengths used.
    Required for the rotational shear generation step described in the abstract.

pith-pipeline@v0.9.1-grok · 5721 in / 1154 out tokens · 21724 ms · 2026-06-28T21:07:25.535943+00:00 · methodology

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Reference graph

Works this paper leans on

15 extracted references · 12 canonical work pages

  1. [1]

    Current Trends in Integration of Nondestructive Testing Methods for Engineered Materials Testing,

    R. Kumpati, W. Skarka, and S. K. Ontipuli, "Current Trends in Integration of Nondestructive Testing Methods for Engineered Materials Testing," Sensors (Basel, Switzerland), vol. 21, no. 18, 2021, doi: 10.3390/s21186175

    work page doi:10.3390/s21186175 2021

  2. [2]

    Mach-Zehnder-Interferometer Aufbau mit Virtuellem Doppelspalt für Shearografie mit räumlichem Phasenschieben bei variablem Shear,

    C. Petry and M. Schuth, "Mach-Zehnder-Interferometer Aufbau mit Virtuellem Doppelspalt für Shearografie mit räumlichem Phasenschieben bei variablem Shear," in ndt.net, pp. 46–51. Accessed: Sep. 18 2025. [Online]. Available: https://www.ndt.net/search/docs.php3?id=25485

    2025

  3. [3]

    Multi-Wavelengths Michelson Interferometer Based Spatial Phase Shift Shearography with Color Camera,

    C. Petry and M. Schuth, "Multi-Wavelengths Michelson Interferometer Based Spatial Phase Shift Shearography with Color Camera," SAE Int. J. Adv. & Curr. Prac. in Mobility, vol. 1, no. 3, pp. 1333–1344, 2019, doi: 10.4271/2019-01-1269

    work page doi:10.4271/2019-01-1269 2019

  4. [4]

    NDT by speckle rotational shear interferometry,

    R.K. Mohanty, C. Joenathan, and R.S. Sirohi, "NDT by speckle rotational shear interferometry," NDT International, vol. 18, no. 4, pp. 203–205, 1985, doi: 10.1016/0308-9126(85)90070-7

    work page doi:10.1016/0308-9126(85)90070-7 1985

  5. [5]

    High-Performance Rotational Shearography System Based on Dove Prism for Nondestructive Testing,

    Y. Yao, Z. Wang, P. Yan, M. Ding, and Y. Wang, "High-Performance Rotational Shearography System Based on Dove Prism for Nondestructive Testing," IEEE Transactions on Instrumentation and Measurement, vol. 74, pp. 1–7, 2025, doi: 10.1109/TIM.2025.3541806

    work page doi:10.1109/tim.2025.3541806 2025

  6. [6]

    Quantitative evaluation of digital shearing interferogram using the spatial carrier method,

    G Pedrini, Y-L Zou, and H J Tiziani, "Quantitative evaluation of digital shearing interferogram using the spatial carrier method," Pure and Applied Optics: Journal of the European Optical Society Part A, vol. 5, no. 3, p. 313, 1996, doi: 10.1088/0963-9659/5/3/008

    work page doi:10.1088/0963-9659/5/3/008 1996

  7. [7]

    Weiterentwicklung der Shearografie mit räumlichem Phasenschieben als zerstörungsfreies Prüfverfahren für die automatisierte Serienüberwachung,

    C. M. Petry, "Weiterentwicklung der Shearografie mit räumlichem Phasenschieben als zerstörungsfreies Prüfverfahren für die automatisierte Serienüberwachung," Saarbrücken doi:10.22028/D291-35137, 2021

    work page doi:10.22028/d291-35137 2021

  8. [8]

    Michelson interferometer based spatial phase shift shearography,

    Xin Xie, Lianxiang Yang, Nan Xu, and Xu Chen, "Michelson interferometer based spatial phase shift shearography," Appl. Opt., vol. 52, no. 17, pp. 4063–4071, 2013, doi: 10.1364/AO.52.004063

    work page doi:10.1364/ao.52.004063 2013

  9. [9]

    Spatial-carrier fringe-pattern analysis and its applications to precision interferometry and profilometry: An overview,

    M. Takeda, "Spatial-carrier fringe-pattern analysis and its applications to precision interferometry and profilometry: An overview," Industrial Metrology, vol. 1, no. 2, pp. 79–99, 1990, doi: 10.1016/0921- 5956(90)80019-r

    work page doi:10.1016/0921- 1990

  10. [10]

    Michael Schuth, Aufbau und Anwendung der Shearografie als praxisgerechtes, optisches Prüf- und Messverfahren zur Dehnungsanalyse, Qualitätssicherung und Bauteiloptimierung: VDI-Verlag GmbH Düsseldorf, 1996

    1996

  11. [11]

    Shearography: A New Optical Method For Strain Measurement And Nondestructive Testing,

    Y. Y. Hung, "Shearography: A New Optical Method For Strain Measurement And Nondestructive Testing," Optical Engineering, vol. 21, no. 3, p. 213391, 1982, doi: 10.1117/12.7972920

    work page doi:10.1117/12.7972920 1982

  12. [12]

    Interferometrische Bauteilprüfung, Schadenserkennung und Ermittlung der modalen Parameter mittels dynamischer Belastung,

    W. Buerakov, "Interferometrische Bauteilprüfung, Schadenserkennung und Ermittlung der modalen Parameter mittels dynamischer Belastung," Saarbrücken, 2016

    2016

  13. [13]

    Experimental investigation of elastomers in downhole seal elements: Implications for safety,

    S. Ahmed, S. Salehi, C. Ezeakacha, and C. Teodoriu, "Experimental investigation of elastomers in downhole seal elements: Implications for safety," Polymer Testing, vol. 76, pp. 350–364, 2019, doi: 10.1016/j.polymertesting.2019.03.041

    work page doi:10.1016/j.polymertesting.2019.03.041 2019

  14. [14]

    Embedded strain gauges for condition monitoring of silicone gaskets,

    T. Schotzko and W. Lang, "Embedded strain gauges for condition monitoring of silicone gaskets," Sensors (Basel, Switzerland), vol. 14, no. 7, pp. 12387–12398, 2014, doi: 10.3390/s140712387

    work page doi:10.3390/s140712387 2014

  15. [15]

    Defect Depth Characterization via Thermally and Pneumatically Induced Shearography for Component Inspection in the Automotive Sector,

    V. Bastgen, J. Plaßmann, C. Petry, G. von Freymann, and M. Schuth, "Defect Depth Characterization via Thermally and Pneumatically Induced Shearography for Component Inspection in the Automotive Sector," SAE International doi: 10.4271/2026-01-0205, Apr. 2026

    work page doi:10.4271/2026-01-0205 2026