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

This paper presents a novel Mach-Zehnder-based rotational shearing interferometer utilizing spatial phase shifting and Dove prisms to enable fast, full-field non-destructive testing of rotationally symmetric components by decoupling shear adjustment from carrier frequency generation and detecting tangential displacement gradients.

Original authors: Valentin-Johannes Bastgen, Michael Schuth, Georg von Freymann

Published 2026-06-01

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Valentin-Johannes Bastgen, Michael Schuth, Georg von Freymann

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to find invisible cracks or weak spots inside a delicate, round object, like a rubber seal or a metal ring, without touching it or breaking it. This is the job of Non-Destructive Testing (NDT). The paper you shared describes a new, high-tech "magic eye" that does this job much better than the old methods, especially for round objects.

Here is the breakdown of how it works, using simple analogies:

1. The Problem with the Old "Flashlight"

Think of traditional testing methods like shining a flashlight on a round ball. If you want to see the whole ball, you have to keep moving the flashlight or spinning the ball around and around.

The Limitation: The old way of doing this (called "Linear Shearography") is like using a ruler to measure a circle. You can only measure a straight line at a time. To see the whole circle, you have to take many pictures, stop, rotate the object, and take more pictures. It's slow and clunky.
The Vibration Issue: Some older high-speed methods are like trying to take a photo of a hummingbird while standing on a shaky boat. If the factory floor vibrates even a little, the picture gets blurry.

2. The New Solution: The "Rotating Camera"

The authors built a new machine based on a Mach-Zehnder interferometer. That's a fancy name for a device that splits a laser beam into two paths and then smashes them back together to create a pattern of light and dark lines (interference).

Here is the clever part:

The "Virtual Double Slit": Imagine you are looking through a window with two tiny holes. In the old setup, moving the holes to change the view also changed the pattern of light on the wall, making it hard to control. In this new setup, the authors created a "Virtual Double Slit" (VDS).
The Analogy: Think of the old method as trying to change the zoom on a camera by physically moving the lens, which also accidentally shifts the picture sideways. The new method is like having a camera where you can zoom in and out (adjust sensitivity) without the picture ever shifting sideways. This gives them total control.

3. The Secret Weapon: The "Dove Prism"

To make the system work for round objects, they used special glass blocks called Dove prisms.

The Metaphor: Imagine holding a picture of a clock. If you rotate the picture by 10 degrees, the hands move. But if you use a Dove prism, it acts like a magical mirror that rotates the image inside the machine by double the angle you turn the prism.
The Result: Instead of moving the laser in a straight line (left-to-right), the laser now "shears" (slides) the image in a circle. It's like spinning a record on a turntable instead of sliding a book across a table.

4. Why "Spinning" is Better for Round Things

The paper explains that this new "Rotational Shear" is a game-changer for round objects (like sealing rings).

The Old Way (Linear): If you slide a ruler across a round tire, you only see the part of the tire the ruler touches. You miss the rest.
The New Way (Rotational): Because the laser spins around the center, it sees the entire round object in a single snapshot. It is sensitive to cracks that run from the center out to the edge (radial cracks), which are common in these parts.
Speed: Because it captures the whole image at once (at the speed of a camera taking a photo), it can check parts as fast as a factory conveyor belt moves. No need to stop and spin the part.

5. The Experiment: The "Swiss Cheese" Test

To prove it worked, the team tested a metal block with holes drilled into it (like Swiss cheese) to simulate defects.

They pumped air pressure into the block to make it bulge slightly.
They compared the old "straight line" laser method with their new "spinning" laser method.
The Outcome: Both methods found the holes. However, the new spinning method found them just as reliably but with a unique advantage: it highlighted the direction of the stress perfectly around the center. It proved that the machine can detect tiny flaws in round parts in a single, fast shot.

Summary

The paper introduces a new optical tool that uses a spinning laser effect (rotational shear) instead of a sliding one.

Old Way: Slow, requires moving the object, struggles with round shapes.
New Way: Fast, captures the whole round object in one go, and is immune to factory vibrations.

The authors conclude that this is perfect for checking safety-critical round parts, like the seals used in airplanes, nuclear plants, or oil rigs, ensuring they don't have hidden cracks without taking them apart.

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

Problem Statement
Current industrial non-destructive testing (NDT) using shearography (electronic speckle pattern shearing interferometry) relies heavily on linear shear configurations (x, y, or xy-directions). While spatial phase-shifting (SPS) shearography has enabled rapid, full-field measurements at camera frame rates, linear shear presents significant limitations for rotationally symmetric components, such as thin-walled sealing rings. Specifically, linear shear adjustments severely restrict the usable measurement area on such geometries, necessitating multiple measurements and the rotational repositioning of either the object or the sensor to inspect the entire surface. Furthermore, existing setups utilizing rotational shear have historically suffered from low measurement light efficiency or required temporal phase shifting (TPS), which is highly sensitive to vibrations and unsuitable for industrial in-line inspection.

Methodology
The authors propose a novel optical setup based on a Mach-Zehnder interferometer that integrates rotational shear with spatial phase-shifting shearography. The core innovation lies in the implementation of a Virtual Double Slit (VDS) configuration. In this setup, slit apertures are placed in each interferometer arm close to the camera-side beam splitter (BS2), with one slit laterally displaced from the optical axis.

Key methodological features include:

Decoupling Mechanism: The VDS arrangement generates a spatial carrier frequency through the off-axis displacement of the slits. This decouples the formation of the spatial carrier frequency from the adjustment of the shear amount, allowing for flexible sensitivity tuning independent of the carrier frequency.
Rotational Shear Generation: Rotational shear is achieved using Dove prisms as image rotators. Rotating a Dove prism by an angle $\psi$ results in an image rotation of $2\psi$ .
Signal Processing: The system employs the Takeda method for signal processing. Theoretical analysis demonstrates that unlike conventional setups where the spatial carrier spectrum rotates with the image, the VDS configuration maintains a constant spatial carrier-frequency spectrum regardless of the prism rotation angle.
Measurement Principle: The system is sensitive to tangential (azimuthal) displacement gradients around the center of rotation. The local shear amount is position-dependent, increasing linearly with the distance from the image center ( $r$ ), whereas linear shear provides a constant shear amount across the field.

Experimental Validation and Results
The proposed system was experimentally validated using a calibration specimen consisting of an aluminum body with eight circular artificial defects (flat-bottom holes) of varying diameters and residual wall thicknesses. The specimen was subjected to pneumatic overpressure excitation ( $\Delta p = 3$ bar).

Defect Detection: The system successfully detected all defects, regardless of their diameter or residual wall thickness.
Comparison: The results were compared against conventional linear shear configurations (x, y, and xy-directions). Both linear and rotational shear configurations reliably identified the defects, which appeared as characteristic "butterfly" patterns.
Sensitivity Characteristics: The rotational shear configuration demonstrated a distinct sensitivity to deformation gradients in the tangential direction. Consequently, the system showed increased sensitivity to defects propagating radially (from the center toward the outer diameter).

Key Contributions

Novel Optical Architecture: Introduction of a Mach-Zehnder interferometer with a Virtual Double Slit (VDS) that enables rotational shear while maintaining the benefits of spatial phase-shifting.
Decoupled Control: Achievement of independent control over shear amount and spatial carrier frequency, enabling unrestricted sensitivity adjustment without compromising measurement speed or stability.
Industrial Viability: Demonstration that rotational shear can be performed at camera frame rates, overcoming the vibration sensitivity issues associated with temporal phase shifting in previous rotational shear setups.
Full-Field Efficiency: The method allows for full-field evaluation of rotationally symmetric components in a single acquisition ("one-shot"), eliminating the need for multiple measurements and repositioning required by linear shear methods.

Significance and Claims
The paper claims that this approach offers significant potential for industrial NDT, particularly for the inspection of rotationally symmetric components and safety-critical sealing technology (e.g., in aerospace, nuclear, and oil/gas sectors). The authors highlight that the method addresses the limitation of limited measurement areas on thin-walled parts, significantly reducing inspection time.

However, the authors modestly note specific limitations and areas for future work:

Orientation Sensitivity: The rotational shear approach exhibits reduced sensitivity to defects oriented in the circumferential (tangential) direction, as these align with the shear direction.
Future Directions: The authors state that future work will focus on adapting the setup for harsh industrial environments, investigating additional application scenarios, and extending the method from defect detection to defect depth characterization. They also suggest that a combination of rotational and radial shear configurations warrants further study to address the sensitivity limitations regarding circumferential cracks.