Uncertainty propagation through polynomial fitting and integration procedures with GUM and Monte Carlo applied to x-ray streak camera yield measurements

Abstract

On the Laser Integration Line (LIL) facility at Commissariat à l'Energie Atomique (CEA) near Bordeaux (France), streak cameras (SCs) are extensively used as x-ray detectors by plasma physicists for the recording of transient phenomena as short as 100 ps. For proper interpretation of the experimental results measurements of the SC yield are carried out before each experimental campaign. The yield is actually an indirect measurement that depends on several other measured quantities. The uncertainty associated with the yield is evaluated using the analytical GUM approach and the Monte Carlo (MC) approach using GUM Supplement 1. It is shown in particular that in the assessment process the standard uncertainty and the probability density function of some input quantities propagate through polynomial fitting functions and integrals. A sensitivity analysis is also performed to identify the critical input quantities. The study shows that after correction of the manufacturer's fact sheet the GUM evaluation converges to MC evaluation when the uncertainties associated with non-linear input quantities become small. When propagating uncertainties through integrals it is observed that the uncertainty of the output quantity is mainly dominated by strong correlation effects with the covariance components adding up to produce large uncertainties. Finally, by comparing the experimental yield with a theoretical model good agreement is found.