Natural Science Forum / Physics / Optics / February 2005

I don't remember exactly why it was derived so. But you must know that
diffraction formula and depth of focus are related.
I mean the formula for diffraction limited resolution.

Certainly we know that when we stop down the aperture in a lens the
depth of focus increases. Stop 8 - 11 gives large depth and stop 2.8
gives small depth.

So:

big aperture --> high resolution (when diffraction limited) and low
depth of focus

small aperture --> lower resolution but larger depth of focus.

It is also logical from a ray-tracing point of view, that when rays
comes to the image plane from a larger cone angle the focus will be
well defined over a shorter distance only.

Look in Born & Wolf or Jenkins & White to put some optics bibles
loosely.

best regards

John

sine squared of half angle = NA squared, which is how you usually see it
written. Depth of field is obviously a somewhat arbitrary quantity and you
see different variations on the formula for it depending on the preferences
of the person who came up with it. These equations are used for high NA
microscope objectives. For low NA microscope objectives and for photography
the depth of field is normally defined using geometrical optics, based on
the circle of confusion.

Johannes

It came from a derivation by Conrady in Applied Optics Vol. 1.

It was available from Dover. There is a Vol II edited by his
son-in-law, Dr Kingslake.

The equation is also in Optical Engineering by Waren Smith.

It represents the amount of defocus before two point sources can no
longer be resolved as individual sources and begin to look like one
source, in the absence of aberrations other than defocus. This is
based upon the assumption of diffraction blur due to circular
apertures.

Sincerely,

Jim Klein
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