  In many applications, such as the detection of ultra-high energy cosmic rays
using the air fluorescence method, the number of photons incident on the
detector must be known. This requires a precise knowledge of the absolute
efficiency of the photodetectors used. We present an experimental setup for
measuring the single photoelectron gain and efficiency of multi-anode
photomultipliers with a total uncertainty on the order of a few percent. This
precision is obtained by using a comparison to a NIST calibrated photodiode,
and the presented method can be applied to both vacuum photomultiplier tubes
and other photodetectors. This work is motivated by the need to calibrate the
focal surface of the EUSO-Balloon instrument, which is a technical pathfinder
for the future JEM-EUSO mission. A complete discussion of photomultiplier
calibration is presented and the efficiency measurement technique is discussed
in detail. Example results are given to illustrate the key points of the
method.
