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136 TECHNOLOGY / LIGHT SOURCES


we know them as the perception of colour is achieved by a complex process that starts with the differential output of these cells in the retina and it will be finalised in the visual cortex and associative areas of the brain. This differential effect may be one reason why having two or more v-CCT light fixtures appear different especially if the LEDs are pulsed as that also adds the fur- ther dimensional complexity of time! It is also important to remember that the peak response of human cone cells varies, even among individuals with ‘normal’ colour vision so what looks acceptable to one per- son may not be for another. Therefore, referring to figure 2, a range of wavelengths of light stimulates each of these receptor types to varying degrees. Yellowish-green light, for example, stimu- lates both L and M cones equally strongly, but only stimulates S-cones weakly. Red light, on the other hand, stimulates L cones much more than M cones, and S cones hardly at all; blue-green light stimulates M cones more than L cones, and S cones a bit more strongly, and is also the peak stimu- lant for rod cells; and blue light stimulates S cones more strongly than red or green light, but L and M cones more weakly. The brain combines the information from each type of receptor to give rise to different percep- tions of different wavelengths of light.


THE LUMINOSITY FUNCTION The luminosity function or luminous effi- ciency function describes the average spec- tral sensitivity of human visual perception of brightness. It should not be considered perfectly accurate in every case, but it is a very good representation of visual sensitiv- ity of the human eye and it is valuable as a baseline for experimental purposes and is used heavily for computing various efficacy and colour metrics in lighting. The CIE luminosity function V(λ) is a standard function established by the Com- mission Internationale de l’Éclairage (CIE) and is used to convert radiant energy into luminous (i.e., visible) energy. It also forms the central colour matching function in the CIE 1931 colour space. In essence there are two main luminosity functions in common use. For everyday light levels, the photopic luminosity func- tion best approximates the response of the human eye. For very low levels of intensity (scotopic vision), the sensitivity of the eye is mediated by rods, not cones, and shifts toward the violet, peaking around 507 nm for young eyes; the sensitivity is equivalent to 1699 lm/W or 1700 lm/W at this peak. Recently, a third luminosity function has been proposed called Mesopic vision which


is a combination of photopic vision and scotopic vision in low but not quite dark lighting situations. Mesopic light levels range from luminances of approximately 0.001 to 3 cd m-2


. Most night-time outdoor


and traffic lighting scenarios are in the mesopic range. The luminous flux (or visible energy) in a light source is defined by the photopic luminosity function. The following equa- tion calculates the total luminous flux in a source of light.


Where:


is the luminous flux in lumens. is the spectral power distribution of the radiation (power per unit wavelength), in watts per metre. (also known as


variable, the CIE defined the standard (colourimetric) observer. Originally this was taken to be the chromatic response of the average human viewing through a 2° angle, due to the belief that the colour-sensitive cones resided within a 2° arc of the fovea. The standard observer is characterised by three colour matching functions as shown in figure 3. The CIE has defined a set of three colour- matching functions, called , , and , which can be thought of as the spec-


tral sensitivity curves of three linear light detectors that yield the CIE XYZ tristimulus values X, Y, and Z. The tristimulus values for a colour with a spectral power distribution are given in terms of the standard observer by:


) is the standard


luminosity function (which is dimen- sionless). is wavelength in metres.


The standard luminosity function is normal- ized to a peak value of unity at 555 nm and the maximum efficacy of 683 lm/W is achieved according to human vision charac- teristics.


CIE 1931 COLOUR SPACE In the study of colour perception, one of the first mathematically defined colour spaces is the CIE 1931 XYZ colour space de- rived from a series of experiments done in the late 1920s. The results were combined into the specification of the CIE RGB colour space, from which the CIE XYZ colour space was derived. The tristimulus values of any particular co- lour can be conceptualised as the amounts of three primary colours in a tri-chromatic additive colour model. Due to the distribution of cones in the eye, the tristimulus values depend on the observer’s field of view. To eliminate this


where


is the wavelength of the equiva-


lent monochromatic light (measured in nanometers).


Since the human eye has three types of colour sensors that respond to different ranges of wavelengths, a full plot of all vis- ible colours is possible however the concept of colour can be divided into two parts: brightness and chromaticity. The CIE XYZ colour space was deliberately designed so that the Y parameter was a measure of the brightness or luminance of a colour. The chromaticity of a colour was then specified by the two derived param- eters x and y, two of the three normalised values which are functions of all three tristimulus values X, Y, and Z:


Figure 3: The CIE standard observer colour matching functions.


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