Special Section on Speckle-Based Metrology

Propagation of the measurement uncertainty in Fourier transform digital holographic interferometry

[+] Author Affiliations
Ángel F. Doval, Cristina Trillo, J. Carlos López-Vázquez, José L. Fernández

Universidad de Vigo, Departamento de Física Aplicada, Escuela de Ingeniería Industrial, Campus Universitario, Vigo 36310, Spain

Opt. Eng. 55(12), 121709 (Jun 30, 2016). doi:10.1117/1.OE.55.12.121709
History: Received April 26, 2016; Accepted June 8, 2016
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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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© 2016 Society of Photo-Optical Instrumentation Engineers

Citation

Ángel F. Doval ; Cristina Trillo ; J. Carlos López-Vázquez and José L. Fernández
"Propagation of the measurement uncertainty in Fourier transform digital holographic interferometry", Opt. Eng. 55(12), 121709 (Jun 30, 2016). ; http://dx.doi.org/10.1117/1.OE.55.12.121709


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