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$Interference and Diffraction$ 02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.

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Two parabolic-hyperbolic oriented partial differential equations for denoising in electronic speckle pattern

Wenjun Xu, Chen Tang, Junjiang Zhang

|July 21, 2015

Summary

New parabolic-hyperbolic oriented partial differential equations (PH-OPDEs) enhance fringe pattern denoising. These models offer improved numerical stability and computational efficiency over existing OPDE methods for ESPI applications.

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Area of Science:

Image processing
Computational mathematics
Optical metrology

Background:

Oriented partial differential equation (OPDE)-based filtering is effective for denoising fringe patterns while preserving fringe details.
Existing OPDE models face challenges in numerical stability and computational efficiency.

Purpose of the Study:

To introduce novel parabolic-hyperbolic oriented partial differential equation (PH-OPDE) filtering models.
To evaluate the performance of PH-OPDEs against existing OPDE models for fringe pattern denoising.

Main Methods:

Development of new PH-OPDE filtering models using variational methods.
Testing PH-OPDEs on simulated and experimental Electronic Speckle Pattern Interferometry (ESPI) fringe patterns of varying quality.

Main Results:

PH-OPDE models demonstrate superior performance in numerical stability.
PH-OPDE models exhibit enhanced computational efficiency compared to previous OPDE models.
Effective denoising and fringe preservation achieved on low-quality ESPI fringe patterns.

Conclusions:

The proposed PH-OPDE models represent a significant advancement in fringe pattern denoising.
PH-OPDEs offer a more robust and efficient solution for ESPI data processing.
These new models improve the reliability and speed of optical measurement techniques.