Propagation of the measurement uncertainty for the numerical reconstruction of holograms in Fresnel approximation

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

doi:10.1117/12.2318661

7 September 2018 Propagation of the measurement uncertainty for the numerical reconstruction of holograms in Fresnel approximation

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

Author Affiliations +

Proceedings Volume 10834, Speckle 2018: VII International Conference on Speckle Metrology; 1083408 (2018) https://doi.org/10.1117/12.2318661
Event: SPECKLE 2018: VII International Conference on Speckle Metrology, 2018, Janów Podlaski, Poland

Abstract

This communication presents a set of expressions to evaluate the standard uncertainty and covariance of the real an imaginary parts of the complex-valued field resulting from the reconstruction of digital holograms by using the Fresnel approximation. These expressions are derived by applying the law of propagation of uncertainty as defined in the “Guide to the expression of uncertainty in measurement” to the numerical evaluation of the Fresnel integral, understood as a linear function of the values in the digital hologram. The expressions are eventually applied to holograms produced by the interference of speckle patterns with uniform reference beams, and assuming that the square of the standard uncertainty in the digitized hologram depends linearly with its local values, according to the noise model adopted in the EMVA 1288 camera characterization standard. The resulting uncertainties and covariance of the real and imaginary parts of the reconstructed fields can be subsequently propagated to measurements of the phase change between holograms by following the procedure already presented in our previous work on the propagation of the measurement uncertainty in Fourier-transform digital holographic interferometry.

Citation Download Citation

Ángel F. Doval, Cristina Trillo, José Carlos López-Vázquez, and José L. Fernández "Propagation of the measurement uncertainty for the numerical reconstruction of holograms in Fresnel approximation", Proc. SPIE 10834, Speckle 2018: VII International Conference on Speckle Metrology, 1083408 (7 September 2018); https://doi.org/10.1117/12.2318661

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KEYWORDS

Holograms

Digital holography

Monte Carlo methods

Fourier transforms

Cameras

Holography

Imaging systems

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