Apparent brightness of stars and lasers

Foremost among issues affecting the potential use of astrometric techniques to locate and track laser-carrying spacecraft is the apparent brightness of a laser relative to reference stars. Broadband detectors offer improved sensitivity to stars, but not to lasers. The important and fundamental step of calibrating laser and star brightnesses according to detector spectral sensitivity is performed for four representative kinds of broadband detectors, located above and below the atmosphere. Stars are identified according to parameters traditionally used by astronomers: temperature and apparent brightness at visible wavelengths. These are translated into an energy and photon flux for each kind of broadband detector and are then compared with the corresponding flux from a laser. The comparisons are also given as magnitude correction factors. Astrometrists typically characterize the sensitivity of their instruments in terms of the precision with which they can make a relative measurement of position and the minimum brightness needed to achieve that precision. Given this information and the instruments's spectral sensitivity, the calculations described can be used to infer the detectability of a laser and the precision with which it could be located and tracked. Since the limiting brightness quoted for a particular instrument is typically firm to within 4.0 dB, judging a laser's detectability by its visible brightness alone could lead to serious underestimation of the requirements on its effective radiated power. The laser brightness corrections given solve this problem.