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Appnote --> Para. 4.4
and Related Topics (continued)
4.4 Diffraction Limit
Using lenses of normal quality, you've surely noticed
that definition gets worse if you open the iris diaphragm (increasing lens
speed). This is because the outer zones of the lens elements do not focus
the light as good as the inner ones do.
But with some rare lenses you're going to be surprised: the more you
open the iris, the better the definition gets. These precious lenses are
called "diffraction limited".
You see, the iris aperture acts like a kind of
obstacle to the incoming wave front. With decreasing obstacle size the diffraction
effects increase. And this is true with a n y kind of a lens.
But with normal lenses, the residual correction errors (increasing with
aperture size) are much bigger than diffraction effects. And only with these
precious diffraction limited lenses all residual errors are so small that
they easily hide behind diffraction effects.
In paragraph "4.3 depth of focus" we defined a blur circle with the diameter
DBC. Naturally diffraction limited lenses also produce blur with DBC as a
spot diameter, if they are defocussed. But here in pragraph 4.4 we deal with
the optimum-focused lens. Even though focussed, the lens images a
spot into a circle.
Most of the residual lens errors contribute to the size of this circle.
But with diffraction limited lenses, the size attains its
minimum possible value, and this is the "Airy (Sir George Bidell, 1801
- 1892) disk" diameter ADD.
The ADD depends on the diffraction properties of the aperture stop in
the following way:
ADD = 2.44 * (lambda)
* f / DAP
where (lambda) = wavelength of light used
f = focal distance
DAP = diameter of exit
pupil (or aperture stop diameter)
As stated in paragraph 2.1, equation (7), f / DAP is the
nominal f-number k .
Using this and additionally some approximation for
(lambda) = 550 nm , we get
ADD = 1 Micrometer
You see a very useful, fast, and simple approximation of the Airy disk
... And it shows that with pixel sizes of 5 um (and smaller), we already
approach the limits of a diffraction limited (!) lens with the f-stop of
Now it's time that you are rewarded for reading so patiently.
I'd like to show you a fine image of an Airy disk.
But I didn't produce it myself, and so I must forward you to
(believe it or not).
In their picture you see the central well-illuminated circle, surrounded
by a first minimum and several further maxima and minima. (The diameter of
the first minimum is taken for ADD.)
continue: Image Luminous Incidance and Shading
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Last modified Nov.28th,