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

Take an exposure reading with an incident meter or a reflected meter pointed at an 18% gray subject (gray card). (Meters built into cameras are reflected meters. If the lens is a variable aperture zoom, be sure it is zoomed to where the aperture reading is correct. Turn off special intelligent or evaluative metering modes.) Then use one of the following formulas, where E is illuminance.

E_in_foot_candles = 25 N^2 / (ISO * exposure_time_in_seconds) E_in_lux = 269 N^2 / (ISO * exposure_time_in_seconds)

See the technical notes.

Technical notes:

The object distance, So, as used in the formulas is measured from the object to the lens's front principal point. More commonly one hears of the front nodal point. These two points are equivalent if the front medium and rear medium are the same, e.g. air. They are the effective position of the lens for measurements to the front. In a simple lens the front nodal/principal point is very near the center of the lens. If you know the focal length of the lens, you can easily find the front nodal point by taking the lens off the camera and forming an image of a distant object with the light going through the lens backwards. Find the point of sharp focus, then measure one focal length back (i.e. toward the distant object). That is the position of the front nodal point.

On most cameras the focusing scale is calibrated to read the distance from the object to the film plane. There is no easy way to precisely convert between the focusing scale distance and So.

The formulas presented here all assume that the aperture looks the same size front and rear. If it does not, use the front diameter and note that the formulas for bellows correction and depth of field will not be correct at macro distances. Formulas for this situation are given in the lens tutorial, posted separately.

The formula for angle of coverage applies to rectilinear lenses. An alternative form, 2*arctan(X/(2*Si)), applies to both rectilinear lenses and pinholes. (Rectilinear lenses give the same projection as a pinhole.) These formulas do not usually apply to fisheye lenses, and can't possibly apply to a fisheye lens that covers 180 degrees or more.

The conditions under which the formula for the minimum distance at which the effect of focusing and re-composing will be covered by depth of field are:

1. w is no more than the focal length of the lens. At the edge w=18mm for 35mm, so this will very seldom be a problem. 2. The lens's two nodal points are not very widely separated. But if the front nodal point is in front of the rear nodal point, which I think is the more common case, the formula is too conservative, so this is not a problem either. 3. The camera is rotated about the front nodal point. Almost always the camera will be rotated about an axis behind the front nodal point which again makes the formula too conservative. The guide number given assumes c=.03mm.

The SQF is the weighted average of the MTF over the range .5 to 2 lines per mm referred to a designated print size or magnification. The weighting function is 1/spf, where spf is the spatial frequency. It turns out that this is equivalent to just a simple "visual" average when the MTF is plotted against the log of the spatial frequency. A further mean is taken between the the saggital (optics-speak for radial) and tangential components. It appears to this author that an additional, probably weighted, averaging must be done over regions of the image (center, edges, corners). When I find out the specifics of this weighting I will add it to the lens FAQ.

Note that the section on teleconverters in several places assumed that the aperture diameter was left unchanged. On lenses with mechanical aperture setting levers or rings this will happen naturally if the aperture setting is not changed. However, beware that fancy electronic cameras may compensate for the presence of the teleconverter.

Most camera systems have focusing scales that read from some reference mark on the body, usually at the film plane. With a teleconverer attached, they read from a point the thickness of the teleconverter in front of this reference mark.

The optimum aperture for a pinhole camera depends on what criteria is used. The formula given maximizes the spatial frequency at which the MTF for 555nm light will be 20%.

There is no universal agreement on the constant in the relation between exposure, film speed, and illumination. This document tentatively shows 25 for the foot-candles case, which I reverse engineered from a Gossen Lunasix meter, but one can find values from 18 to 30 in the literature or by reverse engineering other meters. The constant for lux is 10.7639 (the number of square feet in a square meter) times the value for foot-candles.

Continue to: