sa = 4 * (x^2 - x^4 - 1/6)
where x varies from 0 -> 1.
If you graph it and play a bit with it, the function goes from -2/3 at x = 0, up to 1/3 at x = sqrt(1/2) and back to -2/3 at x = 1. This gives a dounut shaped abberation across the whole mirror, if you rotate the curve about the x = 0 axis. There is a total difference of 1 between the maximum and the minimum. If you scale x from one to the radius of the mirror by setting x = h/r where r is the radius of the mirror then I get:
sa = WL * 4 * ((h/r)^2 - (h/r)^4 - 1/6)
where WL is 0.000021654, or the wavelength of yellow-green light in inches.
The saggita of the mirror is
h^2/(4*FL)
where FL is the focal length. I just added the abberation to the saggita at each point to find the abberated sag. I used this value and the slope of the curve at each point to find the line that intersects the grating.
Now if anyone's still with me :-), if I trade the above function for a straight
sa = k * (h/r) ^ 4
term for the abberation, where k is scaled to give one wave difference at the edge of the mirror, then the pictures match Suiter's book much more closely. Unless I am way off course here, I believe he is playing a bit of a game with us - the trashing he gives the ronchi diagrams is based on a *different* abberation function than the one he uses with the star test diagrams.
This is why I'd like some independent "audit" of the situation. Does anyone have a picture of a ronchi diagram of a mirror with a known spherical abberation? I can use this to get into the right ballpark, anyway.
Bob
>Bob Bond writes :
>
>>> (hacked Mel's Ronchi program)
>> It looks like it does *something* but I need some way to calibrate the
>> results against a known mirror or program. Does anyone have some code
>> that does this, or have a mirror they can check it against?
>
>> Any ideas?
>
>How 'bout inputing the mirror with _known_ spherical abberation ? Use
>100% parabola, (that of course should come out with straight lines),
>undercorrected mirror with say 1/2 wave spherical abberation (examples
>of that should be in Suiter's book), or just plain spherical mirror !
>
>Bratislav