Computed-tomography imaging spectrometer: experimental calibration and reconstruction results

Area of Science:

• Optics and Photonics
• Computed Tomography
• Spectroscopy

Background:

• Traditional imaging spectrometers often involve scanning mechanisms, limiting speed and complexity.
• Computed tomography (CT) offers powerful reconstruction techniques applicable to imaging systems.
• The central-slice theorem is a fundamental concept in CT for image reconstruction.

Purpose of the Study:

• To develop and characterize a temporally and spatially nonscanning imaging spectrometer.
• To apply computed tomography principles, specifically the central-slice theorem, to spectral imaging.
• To reconstruct a three-dimensional (x, y, λ) object cube from limited-view projections.

Main Methods:

• Utilized a sequence of three transmission sinusoidal phase gratings rotated in 60° increments for spectral dispersion.
• Interpreted dispersed images as 2D projections of a 3D object cube.
• Employed the maximum-likelihood, expectation-maximization (MLEM) algorithm with a Poisson likelihood law for object cube reconstruction.
• Experimentally measured the point spread function (PSF) as a function of wavelength and field position.

Main Results:

• Demonstrated a nonscanning approach to spectral imaging using CT concepts.
• Successfully reconstructed the three-dimensional object cube from limited-view-angle data.
• The imaging spectrometer exhibited performance suitable for both broadband and narrow-band emitters.
• Characterized the system's point spread function across different wavelengths and spatial locations.

Conclusions:

• The developed nonscanning imaging spectrometer effectively leverages computed tomography for spectral data acquisition and reconstruction.
• The system provides a viable alternative to scanning spectrometers, particularly for applications involving broadband and narrow-band sources.
• Further advancements in limited-view-angle reconstruction algorithms could enhance performance for complex spectral imaging scenarios.