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A photometer is a general term for an instrument measuring brightness. The term is commonly used in astronomy for an astronomical instrument specifically designed to measure the brightness of a single star, a usage that predates the advent of CCDs. A typical design incorporates a photomultiplier tube, and can be thought of as a single pixel large enough to capture all the light of an airy disk. The terms photo-electric photometer and photo-electric photometry were common in the early/middle 20th century to distinguish their use from astronomical photography.
In astronomy, the term photometry generally refers to such brightness-measurements of a source's light with each measurement that of its light passing through a selected filter so as to measure its brightness across just a range of wavelengths, multiple measurements with different such filters providing very rough but very useful data on source's spectrum. This may be carried out using a photometer as described above, but the term photometry is used more generally, also applying to brightness measurements carried out through photography or through use of newer sensors such as CCDs. The latter is equivalent to a grid of tiny photometers, the grid laid out so an image can be focused on it: the apparent brightness of a particular star can be found by adding the count of all the photons detected in the Airy disk of the star in question.