Gradient operators for extracting the derivative of a function described by an interferometric fringe field

David Kerr; Jon N. Petzing; Massimo Facchini

doi:10.1117/12.195913

12 December 1994 Gradient operators for extracting the derivative of a function described by an interferometric fringe field

David Kerr, Jon N. Petzing, Massimo Facchini

Author Affiliations +

Proceedings Volume 2340, Interferometry '94: New Techniques and Analysis in Optical Measurements; (1994) https://doi.org/10.1117/12.195913
Event: International Conference on Interferometry '94, 1994, Warsaw, Poland

Abstract

Many engineering applications of interferometry, such as fracture mechanics and stress analysis, require the extraction of the first derivative of some measured function g(x,y) which is in turn represented by a 2 dimensional, digitized fringe pattern I(x,y). The conventional approach is to obtain an intermediate function (phi) (x,y) which represents the modulo 2(pi) interferometric phase change related to some change in optical path. It is first necessary to `unwrap' this phase information to obtain a smooth and continuous function, which may then be numerically differentiated to obtain the desired quantity of g(x,y). This analysis process, while reasonably straightforward, may be computationally expensive and in any case sensitive to noise, bad data, and quantization error. In this paper, we investigate the use of gradient operators for the direct extraction of the derivative of the interferometric phase function. Our goals are to be able to apply local gradient operators directly to the wrapped phase data, thus removing the `unwrapping' part of the process, and to reduce the susceptibility to noise of such operators.

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David Kerr, Jon N. Petzing, and Massimo Facchini "Gradient operators for extracting the derivative of a function described by an interferometric fringe field", Proc. SPIE 2340, Interferometry '94: New Techniques and Analysis in Optical Measurements, (12 December 1994); https://doi.org/10.1117/12.195913

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