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Theories About Light Part2: Photometry and Luminous flux

Photometry

Photometry is the light measurement, which is defined as electromagnetic radiation detectable by the human eye (daylight). It is thus restricted to the wavelength range from about 380 to 780 nanometers (1000 nm = 1 μm). Photometry is just like radiometry except that everything is weighted by the spectral response of the eye. Visual photometry uses the eye as a comparison detector, while physical photometry uses either optical radiation detectors constructed to mimic the spectral response of the eye, or spectroradiometry coupled with appropriate calculations to do the eye response weighting. Typical photometric units include lumens, lux, and candelas.

In order to have also a well defined photometer, an “artificial eye” has been constructed to simulate the light sensitivity (Light Intensity Measurement)  of the human eye. The relative response of the normal human eye to monochromatic light at the different spectral frequencies was determined experimentally by the CIE and standardized in 1924. This is known as the photopic luminous efficiency function. The symbol of this function is V(λ) and it is usually expressed as a function of the wavelength of light (in air).

The following procedure was conducted to determine the photopic luminous efficiency function: First, light of constant intensity was emitted and its frequency was varied until the lightness perceived by the observer was found to be maximal. This occurred at a frequency of about 540 THz, corresponding to wavelength λm = 555 nm. The wavelength was then set to another λ and the power was readjusted until the lightness was judged to be the same as at λm. V(λ) could thus be computed as the ratio of the radiated power at λm and λ, respectively.
Of course, this experiment has been conducted by many observers and the resulting average was used to define the so called CIE standard eye which is an optical sensor with sensitivity corresponding to the function V(λ).

The photopic luminous efficiency function serves as a link between the subjective response of the human eye and normal physical measurement techniques. It thus provides the basis for a group of photometric units (see Fig. 1).

Fig. 1: Radiometric and luminous quantities

photometry

Luminous Flux

The lumen is a derived unit for luminous flux. Its abbreviation is lm and its symbol is Φv. The lumen is derived from the candela and is the luminous flux emitted into unit solid angle (1 sr) by an isotropic point source having a luminous intensity of 1 candela. The lumen is the product of luminous intensity and solid angle, cd-sr. It is analogous to the unit of radiant flux (Watt), differing only in the eye response weighting. If a light source is isotropic, the relationship between lumens and candelas is 1 cd = 4π lm. In other words, an isotropic source having a luminous intensity of 1 candela emits 4π lumens into space, which just happens to be 4π steradians. We can also state that 1 cd = 1 lm/sr, analogous to the equivalent radiometric definition.
If a source is not isotropic, the relationship between candelas and lumens is empirical. A fundamental method used to determine the total flux (lumens) is to measure the luminous intensity (candelas) in many directions using a goniophotometer, and then numerically integrate over the entire sphere. Thereafter, we can use this “calibrated” lamp as a reference in an integrating sphere for routine measurements of luminous flux.

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