Draws the band pattern a mirror of a given diameter, focal length and conic constant should show at the center of curvature, so you can compare it against what you actually see through the tester.
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Five positions spanning this mirror's own zonal spread — from inside the paraxial null out past the edge zone. Click one to jump the slider there.
The band positions are checked against two independent programs — a full 3D ray trace with no paraxial approximation in it, and Mel Bartels' calculator. All three agree on band count in every case tried, f/8 to f/3.5. That check found and fixed a real error: the conic term was off by a factor of two, so the tool had been drawing a mirror of twice the conic constant.
Not covered: both programs assume the same test geometry, so if that is wrong they are wrong together — and the diffraction machinery is checked only against itself. A photograph of a real Ronchigram would settle both, and is worth more than either program.
The zone at height h — where its surface normal crosses the
axis — returns to the axis at
r(h) = R − K·h² / 2R
and with the grating at distance d = R + offset, a mirror point at
radius x crosses the grating plane at
X = 2x · (1 − d / r(h))
Rays alone would say it is dark wherever X lands under a bar. This
draws the wave instead: the grating splits the returning beam into orders
0, ±1, ±3, …, and order m arrives
back on the mirror face shifted sideways by
s = m · λ · d / p
The pattern is what those shifted copies of the wavefront add up to, so the bands carry the soft edges and the fringing you see in the eyepiece. Source and grating ride together on the carriage; the eye sits at the grating.
A point source would fringe far harder than any real tester does. Sliding the source sideways slides the whole pattern across the grating with it, so a slit of finite width is that many patterns averaged together — which is why a slit much narrower than one grating period is worth the trouble.
Switch the model to geometric to drop all of that and draw the hard-edged ray pattern instead. That is what the printed charts you already own were made with, so it is the fair comparison against them — and the difference between the two settings is how much of what you see through the tester is diffraction.
Center-of-curvature testing only, on a solid rotationally symmetric primary. No at-focus or autocollimation mode, no astigmatism, no central obstruction.
The faint circle marks the 70.7% zone, which splits the mirror into equal areas. Your settings live in this page's address — copy the URL to send a mirror to someone else.