A conversation with Ian after many scotches at deep sky camp: we were discussing what would happen if you cut a telescope primary mirror in half to make binoculars. Clearly the light intensity would be halved but what about the resolution?
I've now generated the Point Spread Functions for a circular mirror and a semi circular mirror. This shows what a star looks like at very high magnification under very extremely good skies.
(http://homepage.ntlworld.com/the_shelleys/photos/airy_whole_mirror.jpg)(http://homepage.ntlworld.com/the_shelleys/photos/airy_half_mirror.jpg)
The first one on the left is the Airy disc + rings that we all know and love. The second one is what a half mirror would give. Now the size of the central disc governs the resolution of the scope. The half mirror maintains resolution in one direction but in the other direction it is more or less halved.
It would be quite easy to confirm this by experiment - just cover up half the front of the scope.
To make them into binoculars I would suggest rotating one of the mirrors by 90 degrees so one eye has good resolution in the vertical and the other eye in the horizontal.
But why not just use bino-viewers?
Sounds a bit like my contact lenses. A reading lens in the left eye and a sight lens in the right eye.
The brain sorts it out!!
Mark, that's certainly an interesting diffraction pattern for the half-a-mirror. I wonder, as the pattern is more complex than a normal Airy disc, whether you'd lose more definition of a non-point source object than would be accounted for in the loss of resolution at the centre.
However, if it made diffraction spikes even more beautiful, maybe we should try it for that reason alone.
I certainly conclude that the better approach would be to buy a pair of mirrors or some binoviewers...
Yeah, you're probably seeing a superimposition of the effect of the effective aperature being reduced across one axis and the effect of the aperature not being nice and round. Messy...