Chromotomography for a rotating-prism instrument using backprojection, then filtering.

Area of Science:

• Optics and Photonics
• Image Reconstruction
• Computational Imaging

Background:

• Reconstructing 3D spatial-chromatic data from 2D images is crucial for various imaging applications.
• Existing methods for chromatic dispersion correction can be computationally intensive.
• Instrument-specific algorithms are needed for efficient 3D image cube reconstruction.

Purpose of the Study:

• To develop a simple closed-form solution for reconstructing 3D spatial-chromatic image cubes.
• To tailor an algorithm for an instrument utilizing mechanically rotated direct vision prisms for chromatic dispersion.
• To improve computational efficiency in the 3D image reconstruction process.

Main Methods:

• Derivation of a Tikhonov-regularized pseudoinverse operator using linear operator formalism.
• Application of the adjoint operator followed by 1D filtering with respect to the chromatic variable.
• Utilizing the fast Fourier transform for efficient 1D filtering.

Main Results:

• A simple closed-form solution for 3D spatial-chromatic image reconstruction was successfully derived.
• The algorithm reverses the order of filtering and backprojection steps compared to existing methods.
• Computational efficiency is achieved through the use of the fast Fourier transform.

Conclusions:

• The developed algorithm provides an efficient and accurate method for reconstructing 3D spatial-chromatic image cubes.
• The reversed order of operations and FFT-based filtering enhance computational performance.
• This method is particularly suitable for instruments with specific optical dispersion elements.