Instrumental Response Function for Filtergraph Instruments

Dopplergrams and magnetograms arising from filtergraph instruments such as the Michelson Doppler Imager (MDI), the Helioseismic and Magnetic Imager (HMI), or the Hinode Narrow Band Filter Imager are generally associated with observation heights that are derived from the contribution function of the targeted absorption line, irrespective of the instrument characteristics. Observation heights are important for interpreting the phases of propagating waves, and for the diagnostics of the solar atmosphere. I show in this paper that the formalism presented by Ruiz Cobo and del Toro Iniesta (Astron. Astrophys. 283, 129, 1994) provides a straightforward approach to associate an observation height for each observable given the instrumental algorithm, the transmission profiles and the local stratification at the point of observation. To demonstrate the method, I construct a simple radially symmetric sunspot model and calculate the mean observation height for various MDI observables as a function of horizontal location. It is shown that different ways of measuring the same quantity can result in different observation heights, that the offset velocity caused by the spacecraft motion has to be taken into account, and that observation heights in sunspots vary beyond the pure geometric effect of the Wilson depression.