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MKV
Carpal Tunnel

Reged: 01/20/11

Re: schmidt plate in osloedu [Re: mark1234]

Mark I couldn't find the "approximate equal" sign (two wiggly lines), so I used tilde to to say the vertex radius (Rv) or 1/2A = (approximately) 119,000. The plate is essentially a zero-power lens so, rounding off the vertex radius to the nearest whole number is fine. It's a theoretical value that changes as soon as oyu move off center, so it;s only function is to determine where the neutral zone will be.

Oh, by the way, the 4th order and subsequent deformation coefficients (i.e. BY^4 + CY^6...) have nothing to do with the vertex radius or the neutral zone location but with 3rd and 5th order SA (i.e. 4BY^3 + 6CY^5...). The 4th order coefficient coefficient B is simply = 1/[4*(n-1)R^3)].

For systems f/3 and slower, as Vla already mentioned, the 5th order SA is usually so small that it can be ignored (i.e. it can be refocused), so only the third order SA term is used. The same probably holds true for even faster systems. refocuisnf cuts down the totla 3rd order SA by a factor of 4.

To illustrate the effects of using only the 3rd order vs. the whole series of coeffcients, this is best illustrated by raytrace. I am using a 200 mm f/3 Schmidt camera as the example below.

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wh48gs
Pooh-Bah

Reged: 03/02/07

Re: schmidt plate in osloedu [Re: wh48gs]

Quote:

However, since the amount of secondary spherical at its best focus is 2.6 times smaller than at the paraxial focus - which is the focus of correction for secondary spherical ...

Well, this is what the Schmidt profile relation implies, but it is not necessarily the best practical solution. Just like primary spherical, the secondary spherical can also be corrected by shaping up the profile to compensate for wavefront deviation at best focus location. I.e. instead of slowing the edge portion of aberrated wavefront by thickening the edge, it can be done by advancing the wavefront section around 0.7 zone. If so, then the secondary aberration term is not A2(dr)^6, but A2[d^6(r^6-r^2)]. Unlike the paraxial function, this one has negative values, directly adding to the depth, which requires much less figuring. In addition, as the graph shows, this term also adds less to the depth, by a ratio (r^6-r^2)/r^6, which for the zone of maximum depth r~0.7 in the numerator, and r=1 in the denominator, gives 0.375, i.e. 2.66 times smaller extra depth at the maximum. I don't know which way it is done by those making the plates, but this seems better.

Vla

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wh48gs
Pooh-Bah

Reged: 03/02/07

Re: schmidt plate in osloedu [Re: MKV]
#5658264 - 02/02/13 02:25 PM

Quote:

For systems f/3 and slower, as Vla already mentioned, the 5th order SA is usually so small that it can be ignored

It is easy to check out, so there's no need to guess. The value of secondary aberration coefficient A2 is the P-V wavefront error at paraxial focus magnified by 1/(n-1) factor, so the error is (n-1)A2. Best focus P-V error is smaller by a factor of 2.6, or W=(n-1)A2/2.6, ignoring the sign. Since A2=3d^6/(n-1)8R^5, that comes to the best focus P-V error W=d^6/7R^5 (ratio P-V/RMS is nearly identical as with primary spherical, nearly 3.4).

For a 200mm f/3 Schmidt (d=100, R=-1200), it comes to 1/10 wave P-V.

Vla

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mark1234
member

Reged: 04/15/08

Re: schmidt plate in osloedu [Re: wh48gs]

Vla and Mladen, this is one area where ray tracing indulges with too much perfection on offer, but it is interesting to see how the shift in zone for best OPD chromatic error has been rationalised for example. It is likely to be easier to figure for one thing.
I set the plate up with the spherometer as a dummy run. I realised there is a gap in my comprehension of David Rowe's formulae - attached, hope he doesn't mind because I can't fathom why Poissons ratio is re-introduced "s" when the whole point is to pull the plate into a catenary with a calculated centre displacement and grind a shallow sphere into it - at that stage the plate could be made of anything as long as the original (say flat underside) returns to its previous (say flat) shape with the asphere on the ground side. Maybe not then? His spreadsheet doesn't work with my software - too old or something. It means I can't see what he's put in the calculation boxes either.

Mark

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mark1234
member

Reged: 04/15/08

Re: schmidt plate in osloedu [Re: mark1234]
#5659394 - 02/03/13 06:25 AM

I guess the answer here is that it's the physics of plate deformation at work and that's how the equations have been reduced to get the needed values. I can't argue with Poisson and the variation in the actual value for my sample of glass is not going to make a significant difference to the deflection? s=0.21 seems the best guess based on the most recent information on the web for plate glass.
Thanks for all your help so far.

Mark

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wh48gs
Pooh-Bah

Reged: 03/02/07

Re: schmidt plate in osloedu [Re: mark1234]
#5659397 - 02/03/13 06:31 AM

Mark,

Have you seen

http://www.oamp.fr/people/lemaitre/Active%20optics%20-%20Aspherization%20of%2...

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).

Vla

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mark1234
member

Reged: 04/15/08

Re: schmidt plate in osloedu [Re: wh48gs]
#5659432 - 02/03/13 07:07 AM

Yes I worked through that one, thanks Vla.
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.

Mark

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mark1234
member

Reged: 04/15/08

Re: schmidt plate in osloedu [Re: mark1234]
#5659448 - 02/03/13 07:22 AM

Vla, the variation in refractive index by neutron bombardment technic mentioned in your reference would make an interesting new thread.

Mark

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wh48gs
Pooh-Bah

Reged: 03/02/07

Re: schmidt plate in osloedu [Re: mark1234]
#5659553 - 02/03/13 09:10 AM

I have zero experience with making Schmidt corrector this way (or any other), but with so many hard to specify, or control variables, it seems realistic to expect that some manual final lap-correction to the figure will be needed.

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.

Vla

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Ajohn
sage

Reged: 12/03/07

Re: schmidt plate in osloedu [Re: wh48gs]
#5661559 - 02/04/13 11:17 AM

The spreadsheet mentioned may work if libreoffice is downloaded. It will load microsoft excell from version 5 onwards which is probably as far back as windows for workgroups aka 3.??. This suite should be available for linux,mac and windows. Is the spreadsheet about on the web?

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.

John
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MKV
Carpal Tunnel

Reged: 01/20/11

Re: schmidt plate in osloedu [Re: Ajohn]
#5661780 - 02/04/13 01:27 PM

John, the g coeffcient is used for systems other then Schmidt cameras. The factor equates the corrector's figuring strength (optical correction) to the an optical path difference (OPD) equivalent Schmidt camera. Third order design usually provides all the information needed to figure out what the "g factor" is. But in all cases it is coefficient.

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.

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MKV
Carpal Tunnel

Reged: 01/20/11

Re: schmidt plate in osloedu [Re: Ajohn]
#5661845 - 02/04/13 01:59 PM

Quote:

Is there one available for Baker's Reflector Corrector in ATM III?

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.

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.

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