Reconstruction of local emissivity profile from line integrated data using Abel transform.

Area of Science:

• Plasma physics
• Optical diagnostics
• Image reconstruction

Background:

• Line-integrated measurements are common in plasma diagnostics.
• Reconstructing local emissivity profiles from these measurements is crucial for understanding plasma behavior.
• Existing Abel inversion methods can suffer from numerical errors and singularities.

Purpose of the Study:

• To develop an efficient and stable Abel inversion method.
• To reconstruct local emissivity profiles accurately from line-integrated data.
• To minimize errors and avoid singularities in the reconstruction process.

Main Methods:

• Utilized Zernike polynomials for emissivity profile reconstruction.
• Employed Cormack's method to avoid numerical integration.
• Developed a derivative-free and singularity-free inversion technique.

Main Results:

• Successfully reconstructed emissivity profiles for parabolic, Gaussian, and non-monotonic distributions.
• Achieved a small standard deviation for reconstructed profiles (e.g., 0.0887 for a parabolic profile, n=3).
• Validated the method using Kolmogorov-Smirnov and chi-square tests, yielding low KS statistic (0.002) and reduced chi-square (0.857) values.

Conclusions:

• The developed Abel inversion method is efficient and stable.
• The Zernike polynomial-based approach with Cormack's method provides accurate and reliable emissivity profile reconstruction.
• The method's robustness is confirmed by statistical tests and low reconstruction errors.