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Propagation of the measurement uncertainty in Fourier transform digital holographic interferometry

Fernández Doval, Ángel ManuelAutor UVIGO; Trillo Yáñez, María CristinaAutor UVIGO; López Vázquez, José CarlosAutor UVIGO; Fernández Fernández, José LuisAutor UVIGO
DATE: 2016-06-30
UNIVERSAL IDENTIFIER: http://hdl.handle.net/11093/493
UNESCO SUBJECT: 3311.11 Instrumentos Opticos ; 2209.07 Holografía ; 2214.02 Metrología
DOCUMENT TYPE: article

ABSTRACT

The derivation of expressions to evaluate the local standard uncertainty of the complex amplitude of the numerically reconstructed field as well as of the phase-change measurements resulting from Fourier- and quasi-Fourier transform digital holographic interferometry is presented. Applying the law of propagation of uncertainty, as defined in the “Guide to the expression of uncertainty in measurement,” to the digital reconstruction of holograms by Fourier transformation and to the subsequent calculation of the phase change between two such reconstructions results in a set of expressions, which allow the evaluation of the uncertainties of the complex amplitude and of the phase change at every pixel of the reconstruction in terms of the measured values and their standard uncertainty in the pixels of the original digital holograms. These expressions are increasingly simplified by first assuming a linear dependence between the squared uncertainty and the local value of the original holograms, and then considering that the object beam is a speckle pattern. We assess the behavior of the method by comparing the predicted standard uncertainty with the sample variance obtained from experiments conducted under repeatability conditions, and find a good agreement between both quantities.
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