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Algorithm for phase extraction from a set of interferograms with arbitrary phase shifts.

J F Mosiño¹, J C Gutiérrez-García, T A Gutiérrez-García

¹1Universidad Tecnológica de León, Blvd. Universidad Tecnológica # 225 San Carlos, León, Gto. 37670, Mexico. jfmosino@gmail.com

|March 30, 2011

Summary

This summary is machine-generated.

Researchers developed a generalized analytical quadrature filter for interferograms with phase shifts. This method uses combinatorial theory and convolution for tunable filters, enhancing signal processing capabilities.

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Area of Science:

Optics and Signal Processing
Mathematical Physics

Background:

Interferometry is crucial for precise measurements, often requiring robust signal processing techniques.
Phase shifts in interferograms can complicate data analysis and filter design.

Purpose of the Study:

To derive a generalized analytical quadrature filter applicable to interferograms with arbitrary phase shifts.
To develop both symmetrical and non-symmetrical algorithms of any order for filter construction.

Main Methods:

The study employs the convolution of two-frame algorithms.
Combinatorial theory is utilized to derive the analytic expression for the filter.
The generalized filter is constructed from a set of interferograms with varying phase shifts.

Main Results:

A generalized analytical quadrature filter has been successfully obtained.
Both symmetrical and non-symmetrical algorithms of arbitrary order are reported.
The derived solution allows for the creation of generalized tunable quadrature filters.

Conclusions:

The developed method provides a flexible framework for designing quadrature filters in interferometry.
The application of combinatorial theory offers a novel approach to analytical filter derivation.
The generalized tunable filters can be applied to various interferometric applications requiring precise phase analysis.