Simplified approach for quantitative calculations of optical pumping

We present a simple and pedagogical method for quickly calculating optical pumping processes based on linearised population rate equations. The method can easily be implemented on mathematical software run on modest personal computers, and can be generalised to any number of concrete situations. We also show that the method is still simple with realistic experimental complications taken into account, such as high level degeneracy, impure light polarisation, and an added external magnetic field. The method and the associated mathematical toolbox should be of value in advanced physics teaching, and can also facilitate the preparation of research tasks.