🔬 applied physics

Event-Based Spatial-Carrier Interferometry for Surface-Normal Vibration-Waveform Reconstruction

This paper presents event-based spatial-carrier interferometry, a non-contact technique that utilizes event cameras to reconstruct full-field surface-normal vibration waveforms by demodulating moving interference fringes, thereby overcoming the trade-offs between frame rate, field of view, and spatial resolution inherent in traditional camera-based interferometry.

Original authors: Ryogo Niwa, Tatsuki Fushimi, Yoichi Ochiai

Published 2026-08-05

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CC BY 4.0

Original authors: Ryogo Niwa, Tatsuki Fushimi, Yoichi Ochiai

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 trying to take a video of a hummingbird's wings. If you use a standard camera, you have a tricky choice: you can take a picture very fast to catch the blur, but then you can only see a tiny speck of the bird. Or, you can zoom out to see the whole bird, but then the pictures come too slowly, and the wings turn into a blurry mess. This is the "frame-rate trap" that scientists face when they try to measure tiny, fast vibrations on surfaces, like the wings of a drone or the skin of a bridge. Usually, to see the vibration clearly, they have to scan the surface point-by-point, which is slow and misses the big picture.

To solve this, scientists use a special kind of camera called an "event camera." Think of a normal camera as a flip-book that takes a full page of pictures every second, whether anything is moving or not. An event camera is more like a swarm of hyper-alert fireflies. Each firefly (or pixel) only blinks when it sees a change in brightness. If the scene is still, they stay quiet. If something moves, they flash instantly with a timestamp. This lets them see incredibly fast motion without needing to take full pictures, but until now, they couldn't easily measure the exact shape of a vibration wave, especially when the surface moves back and forth so fast that it's hard to tell which way it's going at the very moment it stops and reverses.

This paper introduces a clever new trick called "event-based spatial-carrier interferometry" to fix that problem. The researchers set up a laser interferometer, which is a device that splits a laser beam to create a pattern of light and dark stripes (like a barcode) on a surface. When the surface vibrates, these stripes wiggle. By using an event camera to watch these stripes dance, the team can reconstruct the exact vibration waveform. The magic happens because they don't just count the flashes; they look at the direction of the light changes. When the vibration stops and turns around (like a pendulum at the top of its swing), the direction of the stripe movement flips, which usually confuses the math. The authors solved this by squaring the signal mathematically, which acts like a "direction-neutralizer," allowing them to see the full wave clearly even at those tricky turning points.

They tested this by vibrating a small mirror and comparing their new method against a gold-standard tool called a Laser Doppler Vibrometer (LDV). The results were impressive: the event camera method matched the LDV perfectly across a wide range of speeds and sizes, as long as the stripes didn't move so fast that the camera's "fireflies" got overwhelmed. They found that to get a good reading, the camera needs to see at least two full stripes across the width of the area it's looking at, and one stripe along the height. If the area is too small, the math gets confused. This work shows that event cameras can be a powerful, non-contact way to map vibrations across entire surfaces instantly, opening the door to seeing the "heartbeat" of mechanical structures in high definition without the slow, point-by-point scanning of the past.

Technical Summary: Event-Based Spatial-Carrier Interferometry for Surface-Normal Vibration-Waveform Reconstruction

Problem Statement
Non-contact measurement of small, out-of-plane (surface-normal) vibrations is critical for evaluating mechanical structures. While Laser Doppler Vibrometry (LDV) offers high sensitivity for single-point measurements, it requires scanning to map spatial distributions, preventing simultaneous full-field observation. Conversely, camera-based interferometry enables full-field measurement but faces a fundamental trade-off: increasing the frame rate to capture high-frequency vibrations typically reduces the field of view and spatial resolution. Furthermore, existing event-camera-based vibration methods relying on apparent motion struggle to reconstruct waveforms when the vibration amplitude is too small to generate sufficient apparent motion.

Methodology
The authors propose Event-Based Spatial-Carrier Interferometry, a technique that leverages the asynchronous nature of event cameras to overcome the frame-rate–resolution trade-off. The system utilizes a Michelson interferometer with a tilted reference mirror to generate spatial-carrier fringes. When the target mirror vibrates along the optical axis, the resulting change in optical path length causes the interference fringes to shift laterally.

The core methodology involves the following steps:

Event Stream Acquisition: An event camera records asynchronous events triggered by logarithmic intensity changes. Each event includes position, timestamp, and polarity (indicating intensity increase or decrease).
Signed Event-Density Mapping: The continuous event stream is converted into discrete "signed event-density maps." Each map is formed by accumulating a fixed number ( $N$ ) of consecutive events. This approach adapts the temporal span of each map to the motion speed (shorter duration for rapid motion, longer for turning points), balancing temporal resolution with demodulation stability.
Spatial-Carrier Demodulation: The signed maps are demodulated using the estimated spatial-carrier wave vector ( $k_c$ ). By multiplying the map by the complex conjugate of the carrier and applying low-pass filtering, the system extracts a complex signal containing the interferometric phase.
Phase Recovery and Ambiguity Resolution: A key challenge is the sign ambiguity at vibration turning points, where the fringe motion direction reverses, causing an apparent $\pi$ jump in the phase argument. To resolve this, the authors square the complex demodulated signal ( $D^2$ ). This operation renders the velocity factor non-negative, allowing for continuous phase unwrapping and the recovery of the temporal interferometric phase $\psi(t)$ .
Displacement Reconstruction: The recovered phase is converted to surface-normal displacement $z(t)$ using the relation $\psi(t) = \frac{4\pi}{\lambda}z(t)$ .

Key Results
The method was validated against a scanning LDV reference using a sinusoidally driven mirror. The evaluation covered a broad range of drive frequencies and displacement amplitudes.

Accuracy: Reconstructed waveforms showed strong agreement with LDV measurements in terms of frequency, amplitude, and phase across a wide operating envelope.
Operating Limits: The performance envelope is primarily bounded by two physical constraints:
1. Dead-Time Limit: When the phase advances by $\pi$ within the sensor's pixel dead time ( $\tau_{dead} \approx 11 \mu s$ ), per-pixel recording becomes unreliable, leading to severe degradation.
2. Bandwidth/Event Loss: At high total event rates, the sensor's readout bandwidth can be exceeded, causing event loss and row-wise spatiotemporal skew, which degrades amplitude recovery.
Spatial Resolution: Local Region of Interest (ROI) tests determined the minimum aperture required for successful reconstruction. The results indicate that a minimum aperture of approximately two fringe periods along the carrier direction and one period along the fringes is necessary to maintain high pass rates ( $P_{pass} \ge 0.94$ ). This suggests that spatial resolution scales with fringe pitch rather than pixel count.

Significance and Claims
The paper claims to provide an empirical basis for full-field, spatially resolved interferometric vibrometry using event cameras. By combining interferometric sensitivity with the high temporal resolution of event cameras, the method successfully reconstructs vibration waveforms from moving interference fringes without the frame-rate limitations of traditional cameras. The authors emphasize that this approach resolves the motion-direction ambiguity at turning points and maps the practical operating envelope defined by sensor performance (dead time and bandwidth) and the required spatial support (fringe periods). The work demonstrates that event cameras can serve as a viable non-contact measurement technique for capturing surface-normal vibration distributions where high-speed, high-resolution sensing is required.

Technical Summary: Event-Based Spatial-Carrier Interferometry for Surface-Normal Vibration-Waveform Reconstruction

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