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Reconstruction of multidirectional interferometric data using an isoparametric finite-element method.

Y Zhang, G A Ruff

|November 10, 2010

Summary

This study introduces a new tomographic reconstruction method using finite-element concepts. It achieves higher spatial resolution and improved accuracy by allowing flexible element shapes and sizes, outperforming traditional methods.

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Area of Science:

Scientific imaging
Computational physics
Applied mathematics

Background:

Spatial resolution is crucial for tomographic reconstructions with diverse feature scales.
Traditional methods requiring more data for higher resolution are often impractical.
Existing series-expansion methods on uniform grids have limitations.

Purpose of the Study:

To develop a novel series-expansion reconstruction procedure for enhanced spatial resolution.
To enable arbitrary specification of reconstruction element shape and size.
To improve the accuracy of tomographic reconstructions, especially for complex fields.

Main Methods:

Developed a new series-expansion reconstruction procedure utilizing isoparametric finite-element concepts.
Allowed for arbitrary specification of element shape and size within the reconstruction domain.
Compared the new method against traditional series-expansion techniques using an analytic function.

Main Results:

The new method significantly improves the absolute error of reconstruction compared to traditional methods.
Demonstrated superior performance with identical input data and reconstruction grids.
Showcased the advantages of using a nonuniform grid for complex field reconstruction.

Conclusions:

The proposed finite-element-based reconstruction method offers superior spatial resolution and accuracy.
Flexible element specification overcomes limitations of uniform grid approaches.
This technique is advantageous for reconstructing complex objects with multi-scale features.