Research map / 3D vision / Depth and stereo
Snapshot Lidar: Fourier Embedding of Amplitude and Phase for Single-Image Depth Reconstruction
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Proposes a snapshot AMCW-ToF lidar that captures amplitude and depth in one image by linearly varying the demodulation reference phase across rows (rolling shutter) and recovering a complex ToF hologram via Fourier filtering, inspired by off-axis holography.
Problem
Conventional AMCW-ToF lidars need four sequential quadrature measurements to recover depth and intensity, which lowers frame rate and causes motion artifacts in dynamic scenes.
Approach
Treat the ToF measurement as a complex sinusoid (a "ToF hologram") and spatially vary the exposure phase linearly across rows so the hologram and its twin separate in Fourier space, as in off-axis holography; recover amplitude and phase from one image with Fourier filtering, plus optical prefiltering against aliasing.
Key results
- Snapshot technique reaches SNR 29.86 dB for phase reconstruction vs 28.56 dB for conventional four-bucket quadrature at the same total exposure, with 4x fewer measurements.
- Optimal phase variation rate found around R=4 rows per 2π cycle (k=π/2), with 1D anisotropic prefiltering (sigma=1) in the rolling-shutter direction.
- Fourier reconstruction consistently outperforms the N-bucket approach applied to snapshot images across phase variation rates.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| capture amplitude and phase in one image instead of four quadrature measurements | AMCW-ToF phase reconstruction · Phase reconstruction | SNR: 28.56 dB -> 29.86 dB | Helped |
| capture one image instead of four quadrature measurements | AMCW-ToF capture · Snapshot capture | data bandwidth: 4× less | Helped |
| add optical prefiltering before phase reconstruction (ablation) | Snapshot Lidar · Phase reconstruction | SNR: +3dB | Helped |
| use a 1D blur kernel along the rolling-shutter direction instead of a 2D blur kernel (ablation) | Snapshot Lidar prefiltering · Phase reconstruction | reconstruction quality | Helped |
| set phase variation rate to k = π/2 line−1 (ablation) | Snapshot Lidar · Phase reconstruction | SNR: R = 4 | Helped |
| use Fourier reconstruction instead of the standard N-bucket technique (ablation) | Snapshot Lidar · Snapshot phase reconstruction | reconstruction quality | Helped |
| rotate the phase variation direction to be perpendicular to dominant scene edges (ablation) | Snapshot Lidar · Rectilinear block scene | SNR: 75° | Helped |
Surprising findings
- The snapshot technique performs as well as or marginally better than conventional quadrature despite using one image instead of four.
- Rotating the camera to align phase variation perpendicular to dominant scene edges reduces aliasing and improves SNR.
Limitations
- Requires spatial modulation and optical prefiltering (defocus) to avoid aliasing, which sacrifices spatial resolution.
- Lab prototype uses a Melexis 75027 with galvanometer scanning; the emulated snapshot is built from four quadrature images, and the camera firmware caps frame rate at 100 fps.
Experimental setup
Metrics: SNR (dB) phase reconstruction error
Baselines: conventional quadrature four-bucket CW-ToF N-bucket technique on snapshot images
Builds on: off-axis holography quadrature (four-bucket) CW-ToF reconstruction N-tap technique superheterodyned interferometric ToF
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