Motion detection, the Wigner distribution function, and the optical fractional Fourier transform

Area of Science:

• Optics and Photonics
• Image Processing
• Metrology

Background:

• Speckle photography is a technique used for measuring deformation and motion.
• Estimating both surface tilting and translational motion independently presents a challenge.
• The fractional Fourier transform (FrFT) offers novel ways to analyze optical signals.

Purpose of the Study:

• To independently estimate surface tilting and translational motion using speckle photography.
• To introduce a method utilizing the optical fractional Fourier transform (FrFT).
• To provide a geometric interpretation for the motion estimation technique.

Main Methods:

• Capturing consecutive images in two different fractional Fourier domains.
• Applying the speckle photographic technique.
• Utilizing the Wigner distribution function for geometric interpretation.

Main Results:

• Independent estimation of surface tilting and translational motion was achieved.
• The method is effective even with limited prior information about the motion.
• A geometric interpretation of the FrFT application in motion analysis was established.

Conclusions:

• Speckle photography in fractional Fourier domains enables independent estimation of surface tilting and translational motion.
• The Wigner distribution function provides a valuable framework for understanding this optical technique.
• This method advances the capabilities of motion estimation in scenarios with minimal prior knowledge.