Diffraction vs Focal Length

Started 4 months ago | Discussions thread
Re: Diffraction vs Focal Length

Sittatunga wrote:

brightcolours wrote:

<snip>

Angels do not come into play with diffraction...

You had me confused there as I didn't think this was a theological discussion...

Actually, the diffraction that limits resolution is all about triangles. If the length of a ray from one side of the aperture is half a wavelength different from the length of a ray from the other side of the aperture the two rays will be out of phase an will cancel each other out. The aperture is the base of the triangle. As the aperture gets smaller the other two sides do so too.

The triangle has its base equal to the linear aperture. The other two sides determine the length to the focal lane. The convergence angle of those two sides are the relative aperture. Telescopes are described by their linear aperture, camera lenses are described by their relative aperture.

The difference in length stays the same so the angle between the out-of-phase rays gets bigger. This is (near enough for calculations) why a perfect circular lens or mirror focussed on a star (point source at infinity) will produce a finitely sized Airey disc surrounded by rings which gradually get dimmer and more widely spaced. As the <inserted: linear> aperture gets bigger the Airey disc gets smaller

Ok, here is where you are making your mental mistake::

as the linear aperture gets larger but the f/ratio stays the same, the Airy (no e) stays the same measurable size.

As the focal length gets longer, the distance on the image plane of objects separated by smaller angles becomes resolved.

So any telescope (or camera lens) operating at F/4 (or pick a favorite F/ratio) will have the same sized Airy disk on the image plane, but the distance between one object and the next will grow with focal length.

At F/4 an Airy disk is about 6.4μ (550nm light) and it does not depend on focal length, 24mm F/4 = 6.4μ, 240mm F/4μ, 2400mm F/4 6.4μ. But on the geometry described by the f/ratio. When one keeps the same f/ratio but makes the linear aperture larger, one resolves more features because each feature is now separated by more Airy disk diameters. Rather than overlapping, they stand out clearly.

And this is one of the reasons I prefer describing optics in linear aperture and focal length than in focal length and relative aperture.

and the rings more closely spaced. If you do the sums you will find that the diameter of the Airey disc is directly proportional to the f number.

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Mitch

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