Observables

The physical observable of interest in any scattering experiment is [1-3] the differential cross section

$${\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ens... ...ma}}}}}{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{d}{}\, }}\Omega}}}}}}}$$

as a function of direction $\Omega$ . To measure that directly we should operate with zero-width point detectors, with instant measurement and unit incident intensity. Practically the quantity we can actually measure - putting a detector in a position covering a certain solid angle for a certain time with a certain incident intensity - is

$${I_0}\Delta t \Delta\Omega{\ensuremath{\displaystyle{\frac{{\ensu... ...ma}}}}}{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{d}{}\, }}\Omega}}}}}}}$$

If $\Delta t$ , $\Delta\Omega$ are small and known and $I_0$ is separately monitored, we can (have to) normalize the observations by simply dividing them out.

Specifically for the powder diffraction field, historically, this is not usually done because - as it is normally true with anode sources and point detectors and usual procedures - the counting times $\Delta t$ , the solid angle width $\Delta\Omega\propto \Delta {\ensuremath{{2\theta}}}$ and the incident intensity $I_0$ are considered constant and therefore go into some 'global scaling' constant that is usually considered arbitrary.

However, as we have more sophisticated acquisition methods, we may need revert to the original approach and consider the counts divided by time and angular width as the real observable.