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Appl Opt. 2006 Oct 1;45(28):7392-400.

Performance evaluation of partial differential equation models in electronic speckle pattern interferometry and the delta-mollification phase map method.

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  • 1Department of Applied Physics, University of Tianjin, China.


The ordinary differential equation (ODE) and partial differential equation (PDE) image- processing methods have been applied to reduce noise and enhance the contrast of electronic speckle pattern interferometry fringe patterns. We evaluate the performance of a few representative PDE denoising models quantitatively with two parameters called image fidelity and speckle index, and then we choose a good denoising model. Combining this denoising model with the ODE enhancement method, we make it possible to perform contrast enhancement and denoising simultaneously. Second, we introduce the delta-mollification method to smooth the unwrapped phase map. Finally, based on PDE image processing, delta mollification and some traditional techniques, an approach of phase extraction from a single fringe pattern is tested for computer-simulated and experimentally obtained fringe patterns. The method works well under a high noise level and limited visibility and can extract accurate phase values.

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