At 3:36 AM +0100 1/15/05, Listar wrote:
>From: "Jeff Keller" <jrk_om@xxxxxxxxxxx>
>Subject: [OM] Re: f-stops (Was: Solstice web-site news)
>Date: Fri, 14 Jan 2005 09:15:35 -0800
>
>[snip]
>The simple and elegent experiment proposed earlier by Julian of placing a
>point source of light at the focal plane on the lens axis and measuring the
>diameter of the light coming out the front would be a good way to actually
>measure the maximum aperture. If the point source is exactly at the focal
>plane the light coming out the front would neither converge nor diverge. The
>rays would be parallel.
More fundamental than f-stop is "Numerical Aperture" (NA), which can
be computed from the angle of the converging cone of light from a
distant source, as the cone comes out of the back element of the lens
and converges upon an image point. It is not necessary to know where
the actual aperture of the lens is; this is good, because the actual
exit-pupil aperture is often physically inaccessible, or not really
known.
The NA is n sin(a), where "n" is the refractive index of the
image-space medium and "a" is the half-angle of the converging code
of light. For a photographic lens, the medium is air and so
n=1.0000.
The point is that all you need to know is that half-angle. You do
not need to know anything of the internal construction of the lens.
The half-angle "a" can be computed from the f-stop:
Tan(a)=(diameter/2)/(focal length). For our purposes, the NA isn't
needed.
So, measure the diameter of the converging cone of light just after
the last lens, and also the distance from the plane in which that
diameter was measured to the image plane (where that cone ends in a
point), and compute the f-stop from that: fstop= distance/diameter.
It isn't necessary to actually compute the half-angle.
>The f-stop concept works because light spreads out on the camera side of the
>lens with the square of the distance. A lens having the same diameter but
>twice the focal length would have 1/4 the light intensity at the film. By
>keeping the ratio of diameter to distance constant irrespective of focal
>length, the intensity remains constant.
There is a missing step in the above description, being that the area
of the aperture varies as the square of the aperture diameter, so
when one doubles both the aperture diameter and focal length, their
ratio the f/stop is unchanged, and the increase in aperture area
exactly compensates decrease in image brightness due to
inverse-square loss, leaving the image brightness unchanged,
controlled only by the surface brightness of the object being imaged.
Joe Gwinn
http://www.optics.arizona.edu/Palmer/OPTI400/SuppDocs/f_word.pdf
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