Monte Carlo uncertainty estimation for wavelength calibration

TL;DR

This paper compares Monte Carlo and GUM methods for wavelength calibration uncertainty estimation, demonstrating that Monte Carlo conditions are better fulfilled and suggesting a switch to GUM for this specific case.

Contribution

The study analyzes application conditions for uncertainty estimation methods in wavelength calibration, highlighting the suitability of GUM over Monte Carlo in this context.

Findings

Monte Carlo conditions were fully satisfied for the calibration case.

GUM application condition was found unsatisfactory.

Results suggest replacing Monte Carlo with GUM for this calibration.

Abstract

CIPM published the Supplement I for GUM in 2008 as not only an alternative approach to estimate the uncertainty for a given calibration measurement but also as a proper uncertainty estimation one, whenever any of the conditions imposed in GUM which must be satisfied does not hold [1, 2]. Before the introduction of the new approach in the Supplement I, namely Monte Carlo (MC) method, the GUM rules have been always applied even if in cases where the mentioned conditions were not fulfilled. After or even before the official introduction of this MC method, a number of published papers in uncertainty estimation by using MC method had been shown up, giving more insight for the ways the uncertainties estimated and also for the specific calibration measurements under investigation themselves [3 - 16]. However, in most of those published papers, the application conditions required before a method selection should be analyzed, in fact, has been ignored. In our uncertainty study for wavelength calibration by using beat frequency technique, the application conditions have not been ignored but analyzed carefully and it was found that a GUM application condition was unsatisfactory. However, all the MC method conditions for this calibration problem have been well fulfilled. A computer program was then coded [17] following the steps in the Supplement I. The resultant outputs showed difference in statistical nature and suggested to replace the MC method to the GUM one as soon as possible for this case.