Refraction correction in holographic interferometry and tomography of transparent objects.

Area of Science:

• Optics and Photonics
• Computational Imaging
• Tomographic Reconstruction

Background:

• Tomographic reconstruction of refractive-index fields is crucial for various optical applications.
• Significant refraction poses a major challenge in accurately reconstructing these fields.
• Existing algorithms often struggle with the nonlinear nature of the problem.

Purpose of the Study:

• To review and extend state-of-the-art algorithms for 1-D and 2-D refractive-index field reconstruction.
• To compare the performance of a perturbation approach against iterative procedures in holographic interferometry.
• To identify robust methods for mitigating refraction errors.

Main Methods:

• Numerical simulations of holographic interferometry experiments were conducted.
• A perturbation approach was implemented and evaluated.
• Two iterative reconstruction procedures were tested and compared with the perturbation method.

Main Results:

• Iterative algorithms exhibited divergent behavior in the presented examples, making general conclusions difficult.
• The perturbation technique demonstrated significant power in reducing refraction errors.
• The perturbation method proved easier to implement and faster to run compared to iterative methods.

Conclusions:

• The perturbation approach is a powerful and efficient technique for tomographically reconstructing refractive-index fields with significant refraction.
• Iterative methods, while explored, showed limitations due to nonlinearity and divergence in this context.
• The findings highlight the practical advantages of the perturbation method for holographic interferometry.