Instruments to measure FAPAR (or in other words PAR above and below canopy so as to calculate FAPAR) can be broadly classified into two types;
In tall canopies such as forests, series of PAR sensors (especially quantum sensors) can be installed to calculate FAPAR at different levels of the canopy. Instruments used to measure Leaf Area Index that employ PAR sensors and are operated such as to take above and below PAR measurements, can also be used to calculate FAPAR. Examples of such instruments: Accupar LP-80, Sunscan Canopy Analysis System.
The errors associated with FAPAR sensors can be very wide depending on the built-up of the sensor, spectral sensitivity, imperfections in hemispherical field of view and orientation of the sensor. Manufacturers report relative uncertainty of about 5%, however this can only be achieved under perfect observation conditions.
Reference:
Mottus, M., Sulev, M., Baret, F. & Lopez-Lozano, R. Photosynthetically Active Radiation: Measurement and Modeling. in Solar Energy 7902–7932 (Springer, 2011). doi:10.1007/SpringerReference_310766