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Human Vision
Light enters the pupil of the human eye and is focused onto the retina. The retina has two different types of light-sensitive cells: cones and rods. There are three sub-classes of cones that are sensitive to different colors. The cones only function in bright light. The rods are far more sensitive. When darkness falls, the pupil opens to a larger diameter, and the rods create an image of the low-light scene. There is only one color-response curve for rods, which is why you can't see different colors in darkness. Cone-dominated vision is called photopic vision, and rod-dominated vision is called scotopic vision.
Lumens
When it came time for lighting engineers and scientists to create a measurement unit that could be used to set standards for illumination, they assumed that illumination must create bright-light conditions. Logically, then, they used the photopic response to define the unit of interest. That is, if a source needs to light a surface for work, the light needs to trigger the rods in the eye, so that's what should be measured. There is one more complexity to the eye's response: the cones work in bright light, and the rods work in darkness, but they don't just switch at one brightness level. There is a gradual mixing, so that for a middle range of brightness, both the rods and the cones will be active. This implies that the true measure of illumination should be a mix of photopic and scotopic response.
Specifying Lighting
Right now, all lighting standards use lumens or lumen-derived units for their specifications. That is, they use photopic response as the standard. Reputable lighting suppliers use those standards to measure and advertise their products. In response to the concern that this doesn't adequately represent the performance of lighting products in a given application, many lighting suppliers now quote a scotopic to photopic ratio for their different products. The S/P ratio, as it's commonly abbreviated, is a measure of how much of the light has wavelengths that excite rods compared to wavelengths that excite cones. The rods are more sensitive to blue light than cones are, while the cones are more sensitive to red. That's what the S/P ratio measures.
The Meaning of S/P
In different applications, with different lighting levels, the eye response will be a different mix of photopic and scotopic vision. For example, in an office environment, the illumination may be more effective with some blue light --- light that doesn't count much in lumens because it's in the scotopic region. So a lighting engineer will look at the application, the quoted lumens, and the S/P ratio. The engineer will decide on the relative importance of the rods to the cones for the application, and select a factor for (S/P)^n; where n = 1 for pure scotopic vision and 0 for pure photopic vision. The effective illumination will be the quoted output of the light source in lumens, times the (S/P)^n factor.
The Value of S/P
Defining a correction factor for the illumination of every different light source is a lot of trouble to go to, without some strong motivation, but there is a pretty strong motivation: saving energy and money. Right now, some of the newer light sources, such as many LED lights, put a fair amount of their light out at the blue end of the spectrum. The blue end is not weighted heavily in lumens, so to get out the right amount of lumens means more lights need to be used. But if the lighting situation uses rods as well as cones, then those extra lights are wasted, because there already is enough light put out by the LEDs --- it's just not being counted. The S/P ratio is an attempt to make that extra light count.