Equations for solar tracking

Direct sunlight absorption by trace gases can be used to quantify them and investigate atmospheric chemistry. In such experiments, the main optical apparatus is often a grating or a Fourier transform spectrometer. A solar tracker based on motorized rotating mirrors is commonly used to direct the light along the spectrometer axis, correcting for the apparent rotation of the Sun. Calculating the Sun azimuth and altitude for a given time and location can be achieved with high accuracy but different sources of angular offsets appear in practice when positioning the mirrors. A feedback on the motors, using a light position sensor close to the spectrometer, is almost always needed. This paper aims to gather the main geometrical formulas necessary for the use of a widely used kind of solar tracker, based on two 45° mirrors in altazimuthal set-up with a light sensor on the spectrometer, and to illustrate them with a tracker developed by our group for atmospheric research.