The correction of observational data for instrumental band width

Abstract

The readings Φ(x) of an instrument with the apparatus function g(x) are related to the true values f(x)of the observed function by the equationA three-point interpolation operator can be chosen to simulate the spreading action of a class of functions g(x). Under certain conditions the interpolation operator has an exact inverse which, when applied to Φ(x), gives a function which is a better approximation to f(x). The accuracy obtained is discussed, and the effect of the method on the standard errors in the measurement is found.