Telescope Reviews: Re: Mirror Source

Ok, I'll take a *preliminary* stab at this.

For diffraction-limited performance, 1/4 lambda is generally taken as the desired maximum peak-to-valley deformation of the wavefront. But that's for 0.5mm to perhaps 1mm exit pupil diameters, where diffraction effects become visible. Let's be conservative and use 1mm, which applies to sharp-eyed observers.

Because you're using the mirror in the full-aperture configuration, wavefront error (over that large surface) is more critical than when using a mirror in a diagonal. The peak-to-valley error mus apply to an area at least as large as the instrument's aperture * 1.41 (for 45 degree tilt). Beware mirrors which specify quality PER INCH, for example. Across larger dimensions the total deformation my be rather larger!

With the comparatively low magnification (read: large exit pupil) of binoculars, the wavefront error criterion is necessarily more relaxed. By how much? Simply as the ratio of your bino's exit pupil to the diffraction-limited pupil diameter of 1mm.

So here's my off-the-cuff formula:

Max wavefront error = exit pupil / 1mm * 0.25 lambda

Example:
20x80mm bino (effective aperture at 45 degrees = 80 * 1.41 = 91mm)
Exit pupil = 4mm

Max wavefront error = exit pupil / 1mm * 0.25 lambda
= 4mm / 1mm * 0.25 lambda
= 4 * 0.25
= 1 lambda

Now, that's the wavefront error *after* reflection. But a mirror of given *surface* quality doubles the wavefront error. So the mirror's surface *surface* quality must be 1/2 the allowable delivered wavefront error.

Therefore, if surface quality is specified, in this example for a 20x80 bino, a mirror having no more than 1/2 lambda deformation over 91mm is desirable.

I've not considered the impact of mirror tilt, but I do believe it further constrains mirror quality, such that it should be 40% better than the figure derived. (Lambda * root 2)

Again, this is a "back-of-the-envelope" treatment, and I can stand to be corrected.

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Home-made 11X50 right angle bino, 8.1 deg. FOV
Modified 26X100 bino, 3.5 deg. FOV

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