Directional edge enhancement in optical tomography of thin phase objects

Area of Science:

• Optics and Image Processing
• Mathematical Imaging

Background:

• Phase objects are crucial in various scientific fields.
• Traditional imaging methods struggle with directional edge detection in phase objects.

Purpose of the Study:

• To propose a novel method for directional edge enhancement of phase objects.
• To introduce the concept of a Hilbert-sinogram for improved image reconstruction.

Main Methods:

• Applying Hilbert-transform to projection data of phase objects.
• Constructing a Hilbert-sinogram from modified projections.
• Utilizing a 4f optical correlator with a phase-shifting spatial filter.
• Implementing a 180° spatial filter turn for directional control.

Main Results:

• The inverse Radon-transform of the Hilbert-sinogram yields the directional Hilbert-transform.
• The reconstructed image demonstrates directional edge enhancement of the slice function.
• Numerical results validate the mathematical model and the effectiveness of the proposed method.

Conclusions:

• The Hilbert-sinogram technique offers precise directional edge enhancement for phase objects.
• This method provides a new tool for analyzing and visualizing phase information in imaging.