Adjusting Relative Luminosity to Simulate the Visible Spectrum

Relative luminosity is very important in optical design. By defining appropriate weighting per the characteristics of the optical system, we can better model what we would expect to see. This article demonstrates a method of using wavelength weighting to model the relative luminosity of the visible spectrum as perceived by the human eye.
Kayo Sugiyama, translated by Jade Aiona
Sequential Ray Tracing

How Photoreceptor Cells Function

The cells in the human eye have different strengths of sensitivity to different wavelengths of light, which is referred to as the luminosity factor. The photoreceptor cells in the retina are composed of two types of cells, rod cells and cone cells, which function differently in bright and dark environments. Rod cells have high sensitivity in darkness, but they cannot sense color. On the other hand, cone cells can sense color, but they do not function well in dim lighting conditions. Since rod cells work in dark places and cone cells work in bright places, we can recognize objects in less ideal lighting conditions but we cannot see color in dark places.
While there are about 20 times more of the dark-sensitive rod cells than the color-sensitive cone cells, there are fewer rod cells in the macula at the center of the retina. Instead, they are widely distributed annularly around the retina. On the other hand, cone cells are densely packed in the macula, and the number of them decreases as you go further from the center. For this reason, we can clearly recognize the color of objects seen at the center of our field of view, but have a harder time with the objects at the edge of our field of view and we are more sensitive to small amounts of light when the light is coming from the regions just beyond the macula rather than the center of our field of view.
Vision in a well-lit environment is called photopic vision and vision in a dimly-lit environment is called scotopic vision. For photopic vision, the relative luminosity of long wavelengths is high, while for scotopic vision, the relative luminosity of short wavelengths is high. For photopic vision, the color red appears bright and the color blue is relatively darker. However, with scotopic vision, the color red appears relatively dark and the blue color appears relatively bright. This is called the Purkinje phenomenon.

Luminosity Function

The luminosity function quantitatively describes relative luminosity as a function of wavelength. The spectral sensitivity curves are different for photopic vision and scotopic vision. The luminosity function is determined by the International Commission on Illumination (CIE). While the commission generated curves that are intended for use across the human race, there are multiple factors that affect an individual's spectral sensitivity, such as gender and age.

Graph of luminosity function
The graph shows the luminosity function curves for scotopic vision and photopic vision.



When designing optical instruments that deal with the visible spectrum, it is important to adjust the relative weight of each wavelength according to its relative luminosity. Here, as an example of photopic vision and scotopic vision, the relative weight of each wavelength is set to represent the visible spectrum.
It is important to note that these values are just an example of weighting wavelengths according to the visible spectrum. The relative weighting required is different for each optical system so it is important to set more detailed values according to your optical system. For example, for an apparatus using a CCD or a CMOS, the sensitivity to long wavelengths is higher than for the human eye, so it is important to adjust the weighting in favor of longer wavelengths.
The figures below show the relative luminosity values of each of C line, d line, e line, F line and g line and compare this with the relative luminosity graph.
Relative Luminosity in Wavelength Data

Relative luminosity graphs and the Wavelength weighting data

When designing an optical system, by appropriately setting wavelength weighting, we can generate a design that is close to the actual appearance of the system by simulating the relative luminosity.