Compressive imaging of subwavelength structures: periodic rough surfaces

Area of Science:

• Electromagnetics and Optics
• Signal Processing
• Computational Imaging

Background:

• Near-field imaging is crucial for characterizing surface structures.
• Traditional methods struggle with sparse data and complex scattering phenomena.
• The Rayleigh hypothesis is a common but often limiting assumption in wave scattering.

Purpose of the Study:

• To propose a novel compressed sensing scheme for near-field imaging.
• To recover the angular spectrum of scattered fields from sparse measurements.
• To reconstruct surface profiles of corrugated structures with high accuracy.

Main Methods:

• Utilizing a compressed sensing framework with random sparse measurements of the near field.
• Leveraging the compressibility of the angular spectrum under the Rayleigh hypothesis.
• Developing iterative nonlinear least squares algorithms in the Fourier basis for reconstruction.

Main Results:

• Demonstrated heuristic and numerical evidence for the compressibility of the angular spectrum.
• Successfully recovered the angular spectrum of the scattered field.
• Achieved accurate surface profile reconstructions, even when the Rayleigh hypothesis is invalid.

Conclusions:

• The proposed compressed sensing scheme is effective for near-field imaging of sparse Fourier components.
• The method provides robust surface profile reconstruction beyond the limitations of the Rayleigh hypothesis.
• This approach offers a powerful tool for analyzing complex scattering scenarios.