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Albert Fannjiang¹, Hsiao-Chieh Tseng

¹Department of Mathematics, University of California, Davis, California 95616-8633, USA. fannjiang@math.ucdavis.edu

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Summary

This study introduces a compressed sensing method for near-field imaging, enabling accurate reconstruction of surface profiles from sparse measurements. The technique effectively recovers the angular spectrum, even when traditional assumptions are violated.

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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.