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Lux meter is a term sometimes used to refer to a light meter. If you mean who invented the light meter, Weston marketed the first photographic selenium meter in 1932, which was not well received. Dr. Bruno Lange is also credited with inventing a much more practical version in 1933 and started a company that year. I believe both of these versions were exposure meters and not designed to simply measure illumination. The meter has gone through various improvements for which patents have been granted for, thus there is more than one inventor of a light meter (Joseph Hostetter applied for a patent for a type of light meter in 1974).

Lux is the metric version of the Imperial measurement called foot candle, which is based on the level of visible light at a point that is one foot away from one candle and spread out over one square foot. Although lux was a known quantity much earlier than the invention of the meter, would not be until the use of modern materials made light measurement possible using electronic means.

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