schmidt plate in osloedu
Posted 03 February 2013 - 06:31 AM
Have you seen
I didn't try to work thru it, but formal description seems complete to me. The only thing, there is no reason to go for 0.866 radius neutral zone, so the Schmidt formula should use (r^2-r^4) for 0.707 zone, instead of (1.5r^2-r^4).
Posted 03 February 2013 - 07:07 AM
I couldn't go on to study optics at college because I have a dyslexic thing with algebra. I usually work all my formulae through MLT mass length time - didn't stop me getting good high school grades but there was a lot of pencil work in the exam paper margins. So in this case, the plate bulges upwards when it is in compression on the top surface. (and sideways/ringwise, creating stresses which aren't incorporated into the equations - they seem to be an approximation but accurate enough). Contrary likewise on the lower surface. And the thickness of the plate doesn't seem to figure in this.. Dave Rowe doesn't say if he did have to do some re-figuring on his primaries or not. I'd rather not touch that sphere after getting a good smooth figure on it, if at all possible. The plate can always be returned to the pan - the centring tolerance is not as bad as it looks at first.
Posted 03 February 2013 - 07:22 AM
Posted 03 February 2013 - 09:10 AM
I'm not sure the article doesn't mention that, but since the equations only cover correction of the primary spherical, it is safer - even desirable - to slightly overshoot (i.e. make the profile slightly deeper at the 0.7 zone, diminishing toward the center or edge). This would minimize, or nearly eliminate secondary spherical (I doubt that the difference between the curves needed for minimizing vs. elimination can be controlled).
That is so elegant, isn't it - forget surface figuring, just figure the refractive index along the plate radius with appropriately profiled neutron bombardment, as desired.
Posted 04 February 2013 - 11:17 AM
Looking though the posts and links I noticed a constant called g which relates to various types of telescope. Is there one available for Baker's Reflector Corrector in ATM III? I'm feeling masochistic - it uses old glass that I have no full data for.
Posted 04 February 2013 - 01:27 PM
Here is an example. Take for instance a Wright telescope whose mirror is a special case oblate spheroid, exactly opposite in correction to the paraboloid. The spherical aberration of such a parabolid is twice the amount of an equivalent sphere.
Say you have an f/4 Wright mirror and would like to know what strength a Schmidt corrector is necessary to correct it. Since we know the amount of spherical aberration is twice that of a spherical mirror, and since the spherical aberration is a cubic function, the proper Schmidt corrector would be the same as that required of a standard Schmidt camera of focal ratio 4/(cube root of 2) = 4/(2^1/3) = f4/1.26 = f/3.17.
On the other hand, a, f/4 prolate elliposoid which has half the amount of spherical aberration of the sphere would require a much weaker corrector than an f/4 Schmidt camera with spherical primary. It would be 4/(cube root of 0.5) = 4/0.7937 = 5.04, so the OPD equivalent Schmidt mirror would be an f/5.04, and the g coefficient here would be 0.7937 instead of 1.26. In general g = f number/(1 + e^2)^1/3, where e^2 is the conic constant, which can be both positive and negative number (negative for conics and positive for oblate figures), and the expression (1+e^2) represents relative amount of spherical aberration present in a signle mirror.
For compound telescopes, such as SMC, things are a little more complicated, as you might surmise. For those solutions look at R. D. Sigler's equations in Applied Optics, Vol 3, No. 8, p.1765 (1974), or S. C. B. Casciogne, Applied Optics, Vol. 12, No 7, p 1419 (1973), or Schwarzschild deformation coefficients.
Posted 04 February 2013 - 01:59 PM
Wow, do you really want to go there? For simple aspheric mirror systems, you can figure out the g coefficeint by finding an OPD-equivalent Schmidt camera mirror ROC, or Req = [y^4/(LAm*sin^2Um)]^1/3.
Is there one available for Baker's Reflector Corrector in ATM III?
For simple mirrors LAm = [(1+e^2)*D^2]/32*f^3, sin Um = y/f, where f = focal length or 1/2R, D = aperture diameter and y = D/2.
Thus for a 6" f/4 Wright, D =6, f = 24, (1+e^2)= 2, LAm = 0.09375, sin Um = 0.125, and Req = 38.0976. Then g = 4/3.80976 = 1.26, or to out it another way you need the same corrector as you would need for a Schmidt camewra of focal ratio f/# = 4/1.26 = 3.17.
For compound catadioptric system such as Baker's, just use raytracing to get the paraxial and marginal parameters and Req, and you'll know what corrector to use.