Imaging phase objects with square-root, Foucault, and Hoffman real filters: a comparison.

Area of Science:

• Optics and Photonics
• Image Processing
• Wave Phenomena

Background:

• Phase objects modify light wavefronts without amplitude changes.
• Accurate phase imaging is crucial for metrology and microscopy.
• Traditional phase imaging methods have limitations in sensitivity and interpretation.

Purpose of the Study:

• To investigate and compare the performance of frequency-domain real filters for phase object imaging.
• To evaluate the square-root filter's derivation from fractional-order derivatives.
• To assess the utility of phase-shift measurement techniques using these filters.

Main Methods:

• Inferred the square-root filter using Riemann-Liouville integral definition of fractional-order derivatives.
• Compared square-root, Foucault, and Hoffman filters in a frequency-domain context.
• Simulated filter performance in a 4f imaging system with coherent illumination using VirtualLab 1.0 software.

Main Results:

• The square-root filter's output intensity directly relates to the object phase's first derivative.
• Foucault filter yields output intensities described by Hilbert transforms.
• Hoffman filter's output intensity lacks a simple analytical formula.
• The square-root filter shows potential for quantitative phase-shift measurements.

Conclusions:

• Frequency-domain filters offer distinct approaches to phase object imaging.
• The square-root filter provides a direct link to phase information, beneficial for measurement.
• Filter selection depends on the specific application requirements for phase-shift quantification.