This article is from the Photographic Lenses Tutorial, by David Jacobson with contributions by others.
If you know the object luminance (photometric brightness), the f-number of the lens, and the image magnification, you can calculate the image illumination. The image magnification is the quotient of any linear dimension in the image divided by the corresponding linear dimension on the object. It is, in the usual photographic case, a number less than one. The f-number is the f-number for the lens when focussed at infinity - this is what's written on the lens. The formula that relates these quantities is given below:
Eimage = (t pi B)/[4 N^2 (1+m)^2] or: Eimage = (t Bfl)/[4 N^2 (1+m)^2]
where: Eimage is in foot-candles (divide by .0929 to get lux)
t is the transmittance of the lens (usually .9 to .95 but lower for more surfaces in the lens or lack of anti-reflection coatings) B is the object luminance in candles/square foot Bfl is the object luminance in foot-Lamberts N is the f-number of the lens m is the image magnification
G.E. Miniature Lamp Catalog
Gilway Technical Lamp Catalog
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