Fractional derivative Fourier plane filter for phase-change visualization.

Area of Science:

• Image processing
• Fractional calculus
• Optical physics

Background:

• Theoretical discussions of fractional derivatives in 2D images exist.
• Filters for half-order differentiation can be complex or real.
• Phase object visualization is crucial in optical measurements.

Purpose of the Study:

• To demonstrate the utility of fractional calculus for image analysis.
• To show the effectiveness of a semiderivative filter for phase object visualization.
• To establish a direct relationship between output image intensity and input object derivative.

Main Methods:

• Theoretical analysis using fractional calculus.
• Development of a semiderivative filter.
• Computer simulations for one-dimensional semidifferentiation.

Main Results:

• Proved the usefulness of the semiderivative filter for phase change visualization.
• Demonstrated that output image intensity is proportional to the input object's first derivative.
• Presented computer-simulated results of one-dimensional semidifferentiating.

Conclusions:

• Semiderivative filters derived from fractional calculus are effective tools.
• These filters provide a direct method for visualizing phase changes in objects.
• The output intensity directly correlates with the input object's derivative, simplifying analysis.