Generalized central slice theorem perspective on Fourier-transform spectral imaging at a sub-Nyquist sampling rate

Area of Science:

• Optics and Photonics
• Spectroscopy
• Image Processing

Background:

• Fourier-transform spectral imaging (FTSI) provides high spectral resolution, broad spectral range, and high photon flux.
• Traditional FTSI requires high sampling rates beyond the Nyquist limit for time delay scanning, leading to low efficiency and stringent motion control demands.
• Aliasing artifacts necessitate oversampling, limiting measurement efficiency in conventional FTSI techniques.

Purpose of the Study:

• To propose a new perspective on Fourier-transform spectral imaging using a generalized central slice theorem.
• To enable high-efficiency hyperspectral imaging and spatiotemporal optical field characterization.
• To overcome the limitations of Nyquist sampling in FTSI for improved measurement efficiency.

Main Methods:

• Utilized a generalized central slice theorem analogous to computerized tomography.
• Employed angularly dispersive optics to decouple spectral envelope and central frequency measurements.
• Reconstructed spectral-spatial intensity envelopes from interferograms acquired at sub-Nyquist time delay sampling rates.

Main Results:

• Demonstrated a novel FTSI approach enabling sub-Nyquist time delay sampling.
• Achieved high-efficiency hyperspectral imaging without loss of spectral or spatial resolution.
• Enabled spatiotemporal optical field characterization of femtosecond laser pulses.

Conclusions:

• The proposed generalized central slice theorem perspective offers a significant advancement in FTSI.
• This method enhances measurement efficiency and relaxes motion control requirements.
• The technique provides a powerful tool for advanced optical field characterization and imaging applications.