Numerical processing of speckle photography data by Fourier transform

Area of Science:

• Optical Metrology
• Digital Image Processing

Background:

• Digital speckle pattern interferometry (DSPI) is a non-contact optical method for measuring surface displacements.
• Numerical processing of specklegrams, particularly via discrete Fourier transform (DFT), is essential for extracting displacement data.
• The diffraction halo in specklegrams can influence the accuracy of displacement measurements.

Purpose of the Study:

• To investigate the impact of diffraction halo removal on the accuracy of displacement measurements obtained from double-exposed specklegrams using DFT.
• To quantify the relative errors introduced by neglecting diffraction halo removal.

Main Methods:

• A 1-D analysis of double-exposed specklegrams was performed.
• The discrete Fourier transform (DFT) was employed for numerical processing.
• The influence of diffraction halo removal on displacement data was systematically evaluated.

Main Results:

• Relative errors in displacement measurements were observed when the diffraction halo was not removed.
• These errors increased with decreasing fringe visibility and fringe density.
• Errors were found to be less than 0.5% for fringe densities exceeding six fringes within the diffraction halo.

Conclusions:

• Accurate numerical processing of specklegrams requires proper handling of the diffraction halo.
• Neglecting diffraction halo removal can lead to significant errors in displacement determination, particularly under challenging fringe conditions.
• The study provides quantitative insights into the error margins associated with diffraction halo presence in DSPI data processing.