When light falls upon a surface it produces illumination (i.e., illuminance), the usual measure of illuminance being the foot-candle, which is one lumen falling on each square foot of receiving surface.
The area of the image is Am2, in which m, the magnification, is given by Hence, the image illuminance (E) is The image illuminance thus depends only on the luminance of the source and the cone angle of the beam proceeding from the lens to the image.
Then the image illuminance will be The image is very much less bright than the object, a fact that becomes clear to anyone attempting to provide a bright projected image in a large auditorium.
To be sure, a telescope having a large objective lens accepts more light from an object in proportion to the area of the lens aperture, but it magnifies the image area in the same proportion; so the increased light is spread over an increased area of the retina, and the illuminance remains unchanged.
This is a basic and most important relation underlying all calculations of image illuminance.
The problem is to relate the luminance of an object with the illuminance in the image, knowing the transmittance and aperture of the optical system.
The apparent brightness of things seen by the eye follows the same laws as any other imaging system, because the apparent brightness is measured by the illuminance in the image that is projected on the retina.
Apart from this variation, retinal illuminance is directly proportional to object luminance, and objects having the same luminance appear equally bright, no matter at what distance they are observed.
It could, for example, produce blinding glare or dazzle; it might result in high luminance in parts of the visual field, thereby diminishing contrast in other parts of the field; or it could cause adaptation to a higher illuminance level than is appropriate for the remainder of the visual field.
Illuminance was drawn from 15 years of work, and the journey is an epic one.
In addition to the Bortle scale, scientists often use photodiode light sensors to measure and compare base levels of darkness by calculating the illuminance of the night sky as perceived by the human eye.
