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4. Resolution 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 of lens
             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 * k

You see a very useful, fast, and simple approximation of the Airy disk diameter.

... 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 5,6.

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.)

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Last modified Nov.28th, 2002 18:14