AUTOMATIC DIFFERENTIATION AND ITS APPLICATION IN METROLOGY

This paper describes automatic differentiation techniques and their use in metrology. Many models in metrology are nonlinear and the analysis of data using these models requires the calculation of the derivatives of the functions involved. While the rules for differentiation are straightforward to understand, their implementation by hand is often time consuming and error prone. The complexity of some problems makes the use of hand coded derivatives completely unrealistic. Automatic differentiation (AD) is a term used to describe numerical techniques for computing the derivatives of a function of one or more variables. The use of AD techniques potentially allows a much more efficient and accurate way of obtaining derivatives in an automated manner regardless of the problem complication. In this paper, we describe a number of these techniques and discuss their advantages and disadvantages.