Digital phase contrast with the fractional Fourier transform

Area of Science:

• Optics and Photonics
• Digital Image Processing
• Wave Phenomena

Background:

• Digital phase contrast microscopy is crucial for visualizing transparent specimens.
• Traditional methods often require specific illumination or complex setups.
• Processing diffraction patterns for quantitative phase retrieval remains a challenge.

Purpose of the Study:

• To introduce a new digital phase contrast method utilizing fractional-order Fourier reconstruction.
• To demonstrate the effectiveness of this method for analyzing pure phase objects.
• To establish a generalizable technique applicable to various optical configurations.

Main Methods:

• Development of a digital phase contrast technique based on fractional-order Fourier transforms.
• Analysis of linear chirp functions within diffraction patterns of phase objects.
• Utilizing optimal fractional orders for longitudinal object localization.
• Reconstructing phase object parameters like diameter and phase shift.

Main Results:

• Demonstrated that diffraction patterns of pure phase objects exhibit linear chirp functions.
• Showcased the ability of fractional Fourier transform to process these patterns effectively.
• Successfully determined the longitudinal location, diameter, and phase shift of phase objects.
• Validated the method through both simulations and experimental results with Gaussian illumination.

Conclusions:

• The proposed fractional-order Fourier reconstruction method offers a robust approach for digital phase contrast imaging.
• This technique provides accurate quantitative phase retrieval from simple diffraction patterns.
• The method's generality, demonstrated with Gaussian illumination, suggests broad applicability in optical metrology.