# 09. Illumination - Image Illumination

## Description

This article is from the
Photographic Lenses Tutorial, by David Jacobson with
contributions by others.

# 09. Illumination - Image Illumination

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

References:

G.E. Miniature Lamp Catalog

Gilway Technical Lamp Catalog

"Lenses in Photography" Rudolph Kingslake Rev.Ed.c1963 A.S.Barnes

"Applied Optics & Optical Engr." Ed. by Kingslake c1965 Academic Press

"The Lighting Primer" Bernard Boylan c1987 Iowa State Univ.

"University Physics" Sears & Zemansky c1955 Addison-Wesley

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