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A photometric system is a set of defined passbands for filters of known sensitivity to various wavelengths of electromagnetic radiation (EMR). The term is generally used regarding EMR in the infrared-to-ultraviolet range. With the specification of passbands, color indices have precise meanings.
The Johnson-Morgan UBV photometric system, which was defined in the 1950s, was widely adopted and is generally still assumed if no particular system is specified or implied. Equipment and scientific needs have prompted the development of new systems, and a major mission or survey sometimes develops its own, e.g., the ugriz photometric system for the Sloan Digital Sky Survey. Among the other systems:
The passbands/filters are generally indicated by letter, some being mnemonic for the color, e.g., B for blue, R for red, but the same letter may have differing specifications under different systems.
Conversion of photometric data from one system to another is non-trivial, given the differences in sensitivity functions, and is inherently imperfect, being an approximation at best. Specifically for stars, which are primarily black-body and follow other general patterns, there are conversion formulae that produce reasonable approximations.
To cite filtered photometric data as magnitudes, a zero-point must be adopted for each passband. The term magnitude system is sometimes used for such a set of zero-points. A long-used convention, termed the Vega system, assigns zero magnitude for each passband to that of the star Vega. A newer alternative, the AB system, simply uses a fixed spectral flux density (3631 janskys) as zero for each passband. The Vega system was traditionally used with the UBV photometric system, but for recent citations, it is worth checking which magnitude system is being used if you are depending upon the value.