Evaluation of the uncertainty of phase-difference measurements in (quasi-)Fourier transform digital holographic interferometry

Ángel F. Doval; Cristina Trillo; José Carlos López Vázquez; José L. Fernández

doi:10.1117/12.2196205

24 August 2015 Evaluation of the uncertainty of phase-difference measurements in (quasi-)Fourier transform digital holographic interferometry

Ángel F. Doval, Cristina Trillo, José Carlos López Vázquez, José L. Fernández

Author Affiliations +

Proceedings Volume 9660, SPECKLE 2015: VI International Conference on Speckle Metrology; 966007 (2015) https://doi.org/10.1117/12.2196205
Event: SPECKLE 2015: VI International Conference on Speckle Metrology, 2015, Guanajuato, Mexico

Abstract

Estimation of the uncertainty is an essential requisite for high-end measurement systems. In this communication we derive an expression to evaluate the standard uncertainty of the phase-difference measurements resulting from Fourier and quasi-Fourier transform digital holographic interferometry. We apply the law of propagation of uncertainty, as defined in the “Guide to the expression of uncertainty in measurement” (GUM), to the digital reconstruction of two holograms by Fourier transformation and to the subsequent calculation of the phase change between the holographic reconstructions. The resulting expression allows the evaluation of the uncertainty of the phase difference at every pixel in the reconstruction plane in terms of the measured hologram brightness values and their uncertainty at the whole of the pixels of the original digital holograms. This expression is simplified by assuming a linear dependence between the uncertainty and the local value of the original holograms; in that case, the local uncertainty of the phase difference can be evaluated from the local complex values of the reconstructed holograms. 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 found a good correlation between both quantities. This experimental procedure can be also used to calibrate the parameters of the linear function relating the uncertainty with the local value of the digital holograms, for a given set of operational conditions of the acquisition device.

Citation Download Citation

Ángel F. Doval, Cristina Trillo, José Carlos López Vázquez, and José L. Fernández "Evaluation of the uncertainty of phase-difference measurements in (quasi-)Fourier transform digital holographic interferometry", Proc. SPIE 9660, SPECKLE 2015: VI International Conference on Speckle Metrology, 966007 (24 August 2015); https://doi.org/10.1117/12.2196205

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available