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As I see it, as light comes through approximately same angular area of the lens, it should have less aberrations, and at the same time, it should still have high θ -> diffraction limit should stay as without this diaphragm.

What am I missing?

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Less spherical aberration, yes, but not less coma, nor less astigmatism.

The diffraction would look like on a telescope with a very important central obstruction. It will not have the usual diffraction pattern, but the diffraction-limited MTF will be bad for low spatial frequencies (rapid decay of contrast) and then flatten out in such a way that the ultimate resolution (extinction of contrast) will be the same as for the full aperture.

Edit: I found this page with nice simulations of the effect of a central obstruction on both the MTF and the images:

http://www.damianpeach.com/simulation.htm

Scroll down to "Part 2. Performance effects of different size central obstructions". As you can see, although the resolution (at MTF = 0) is the same, the image with 50% obstruction looks bad because of the loss of contrast at mid and low frequencies.

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If you want to see what this can look like, have a google for pictures taken with a 'reflex' telephoto lens (constructed using a curved reflector which blocks the center of the pupil.) They are light and have little chromatic aberration but very distinctive 'donut' bokeh effect. –  user2963 Jul 1 '11 at 1:33
    
@zephyr - these are called catadioptric/cassegrain lenses. –  ysap Jul 1 '11 at 16:08
    
Hehe by chance I own Sony 500/8 Reflex ;-) –  BarsMonster Jul 2 '11 at 17:34
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