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Is there a technical approach to calibrating field flatteners?

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#1 donlism

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Posted 14 September 2017 - 03:40 AM

I'm frustrated by the notion that the only way to deal with field flatteners, other than those designed to mate with a specific optical design, is to buy it, mess with various spacings, and see how it does.

 

It seems to me that there ought to be a way to establish the field curvature of the telescope in a reasonably accurate way, and then what I think of as the anti-curve of the field flattener, and figure out where to put the silly thing in the image chain.  This is just based on intuition and what little I know of optics so far.

 

I think I follow the notions of a basic flattener: the goal of a plano-convex at the image plane is to "delay" the wavefront more in the center and less at the edges, to bring the overall wavefront to a plane.  I'm not sure I follow what's going on when the field flattern design is more complex and distant; they seem to be at least two elements, and they want to be placed at some distance from the image plane.  The same sort of thing must be happening, but it's acting at a distance.  Somehow.

 

I have also been exposed to the notion that the field curvature is primarily a function of the strongest element in the optical design, so, for example, you can find a reducer that has been designed with field flattening in it, somehow, and not require a separate flattener.  And that Roland Christen seems to think it's best to design a different flattener for each objective design, though some of them apparently cover more than one telescope.  And that most vendors suggest that their "generic" flattener will cover a range of focal lengths, with a suggested chart for what the spacing should be for each of them.

 

Then there is a gap in my understanding, and we leap to the pragmatic approach of "buy one of them, get some extension tube adjustabiliy in some way, and start tinkering until it works best."

 

My questions are like so:

 

Could I theoretically use a sensor, perhaps with a custom-machined off-axis gizmo that puts the optical axis near one corner of the sensor so that the other corner of the sensor covers a longer radius, combined with automated focusing to try and nail down the best point of focus at the center and out on the radius?

 

Is there a way to measure the radius of the field flattener, to characterize its optical characteristics such that I can compute the right spacing from the objective focus?

 

Or for that matter, what would the typical flattener's design parameters be based on?  Is it simply a matter of focal lengths and curvatures?  Or is the curvature correction going to be a function of focal ratio?  And/or what else would affect how it performs with a particular telescope?

 

There HAS to be at something better than "buy it and try it" -- maybe not a fully derived technical solution, but... something.



#2 Benach

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Posted 14 September 2017 - 05:03 AM

One could always curve the sensor plane. See the image below. But this is not doable for amateur telescopes.

 

 https://upload.wikim...-cutout.svg.png

 

A way to measure the radius of the Petzval curvature: measure the axial distance you have to refocus for the paraxial stars vs. the stars at the edge of the fov and then it is approximately: Rpetzval=(1/2*Sensor diagonal)/(Refocus)^2. But note that the Petzval radius is not always equal for all wavelengths. It is also dependant on the design of the telescope, curvatures of the individual lenses etc.


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#3 MKV

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Posted 14 September 2017 - 05:46 AM

Pretty much what Benach said. The Petzval curvature is the field curvature only in systems free of spherical aberration and astigmatism (anastigmats). Otherwise, a judicial redistribution of astigmatism can flatten the field. This usually leads to flatterfield but not necessarily sharply focused images (as in the Writght telescope, the Petzval portrait lens, the Slevogt Cassegrain, etc).

 

The Petzval surface itself is a sum-total of all curvatures in the configuration. The reasons why there can be "generic" field flatteners is based on the fact that many telescopes consist of the same number of elements with the same or very similar curvatures, but Rland Christen is spot on to suggest that a specific field flattener should be matched to a specific configuration for best results. 

 

As Benach says, you should try to find the focus for axial stars and the most peripherial stars in your field of view. You can construct a focuser with frosted glass, as shown below, and inspect the focus with a mangifier.

 

focuser_a (2).jpg

 

Noting how much axial difference exists between the central and peripheral foci gives you the sagitta or depth of the curve. If you know the sagitta (s), the field radius of curvature is R = (r2 + s2)/2s, where r is the distance from the center (field radius). You're probably best off buying a field flattener rather than trying to make one yourself, uless it's for a Schmidt camera or a Lurie-type anastigmat, where a simple plano-convex lens with a curved side radius of curvature Rf =  R (n-1)/n; of course, R is the measured radius of curvature of the field, and n is the refractive index of the correcting lens. Given that  optical crown glasses have n ≈ 1.5, the formula simplifies to Rf = R/3.

 

Mladen

 

 



#4 BGRE

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Posted 14 September 2017 - 06:06 AM

To achieve a flat focal surface The pet

 

Pretty much what Benach said. The Petzval curvature is the field curvature only in systems free of spherical aberration and astigmatism (anastigmats). Otherwise, a judicial redistribution of astigmatism can flatten the field. This usually leads to flatterfield but not necessarily sharply focused images (as in the Writght telescope, the Petzval portrait lens, the Slevogt Cassegrain, etc).

 

The Petzval surface itself is a sum-total of all curvatures in the configuration. The reasons why there can be "generic" field flatteners is based on the fact that many telescopes consist of the same number of elements with the same or very similar curvatures, but Rland Christen is spot on to suggest that a specific field flattener should be matched to a specific configuration for best results. 

 

As Benach says, you should try to find the focus for axial stars and the most peripherial stars in your field of view. You can construct a focuser with frosted glass, as shown below, and inspect the focus with a mangifier.

 

attachicon.giffocuser_a (2).jpg

 

Noting how much axial difference exists between the central and peripheral foci gives you the sagitta or depth of the curve. If you know the sagitta (s), the field radius of curvature is R = (r2 + s2)/2s, where r is the distance from the center (field radius). You're probably best off buying a field flattener rather than trying to make one yourself, uless it's for a Schmidt camera or a Lurie-type anastigmat, where a simple plano-convex lens with a curved side radius of curvature Rf =  R (n-1)/n; of course, R is the measured radius of curvature of the field, and n is the refractive index of the correcting lens. Given that  optical crown glasses have n ≈ 1.5, the formula simplifies to Rf = R/3.

 

Mladen

Not quite the Petzval sum isnt exactly the sum of the curvatures:

https://wp.optics.ar...-Distortion.pdf

However its independent of lens (or mirror) position. Adjusting the relative position of one or more elements doesnt affect the Petzval curvature but will affect other Seidel aberrations such as astigmatism. To correct field curvature over a wide bandwidth as well as correcting astigmatism the field flattener should be customised to the objective/optical system for which a flat field is desired.  

There is no universal field flattener.


Edited by BGRE, 14 September 2017 - 06:37 AM.


#5 donlism

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Posted 14 September 2017 - 08:01 AM

Thanks, all.

 

So now I think I understand that when people are tinkering with the spacing, it's not about the curvature, but attempting to minimize other abberations, and astigmatism seems to be the most interesting.  Yes?

 

And I'm vaguely forming the idea that in a particular optical design, the quality of the image "comes together" at the focal plane, and that if we intercept it upstream somewhere and drop in some additional optics, we're dealing with, in a sense, characteristics that are "not finished yet."  I don't know how to describe what I'm thinking, especially coming as a general, intuitive thinker into a domain where most of the conversation has to be specifically detailed.  But I'm trying to sorta grasp why you can't make a telescope that's well corrected, a flattener that's well corrected, and put them together as a system that's still well corrected.

 

For example, suppose I have a very nicely color-corrected objective, and want to extend the focal length.  Can't I have someone design for me, a nice barlow that itself is nicely color-corrected, and then put the two together and still have a nicely color-corrected system?  (I'm asking about the general principle of combining systems, not the specifics of making a good barlow.)

 

Then my question would be...  why not design the telescope to have the astigmatism well controlled, and a flattener with astigmatism that's well controlled, and stick 'em together to make a nice, flat system?

 

(A fair answer is "Because you don't know enough about optics yet."  :)

 

You see the real-world problem, yes?  The bottom line is I'm unlikely to be able to buy or make a flattener specifically designed for such-and-such telescope, nor do I know the design of said telescope.  Here it sits, on my workbench.  I have to buy a flattener, hopefully with SOME kind of clues about getting the most appropriate one, and then tinker with it until I can make it work as best possible.  And in my inner being, it seems like there ought to be a better way than buy-it-and-try-it.  I'm hearing "Well, no, not really", and it makes me sad!  But let's say I don't need Christen perfection; just something that's going to be significantly better than without a flattener, and ideally, something that's significantly better with "this" flattener than would be possible with "that" flattener.  Anything?

 

(Mladen -- I like the ground glass focuser.  I've been much more successful with large format photography, including many hours of focusing on a ground glass with a loupe, than I have been at flattening an astronomical field here or there!)



#6 Benach

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Posted 14 September 2017 - 08:12 AM

Your idea doesn't work because all the aberrations are not linearly independant of eachother and the OSC (Offense against Sine Condition) is unique for every optical design. For a relatively indepth discussion:

http://www.loft.opti...on_paper_v7.pdf

 

Optical design is like a real life version of hammer frog. Once you eliminate one aberration, another pops up. You are making things worse by the desire to create a universal solution. That would be the equivalent of hammer frog with each frog working for one hammer only (reality) and desiring that the hammer becomes a universal hammer for all frogs (your desire).


Edited by Benach, 14 September 2017 - 09:10 AM.


#7 MKV

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Posted 14 September 2017 - 12:44 PM

(Mladen -- I like the ground glass focuser.  I've been much more successful with large format photography, including many hours of focusing on a ground glass with a loupe, than I have been at flattening an astronomical field here or there!)

Thanks, Don. The ground glass (or opal glass -- it's finer) focusing screen shown is for a 35 mm film format (made years ago). You can see the milled outline of the 35x24 mm frame. There's also a central circle inscribed on the screen for centering. At the time the picture was taken I was making a Houghton telescope with reduced astigmatism (the corrector was spaced further form the primary) and wanted to use a simple curved film holder to compensate for the residual field curvature. 

 

Mladen



#8 BGRE

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Posted 14 September 2017 - 02:34 PM

For a thin lens the Petzval radius is equal to the focal length multiplied by its refractive index, for a mirror the Petzval radius is equal to the focal length. However it should be noted that a concave mirror and a positive lens have opposite signs for their Petzval curvatures. The elements do not have to be aplanatic or anastigmatic for this to be correct. However the ROC of the best focal surface in the presence of astigmatism is not equal to the Petzval radius.

In a system comprising more than one element the Petzval curvatures (reciprocals of the Petzval radii) add. 



#9 MKV

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Posted 14 September 2017 - 03:04 PM

For a thin lens the Petzval radius is equal to the focal length multiplied by its refractive index, for a mirror the Petzval radius is equal to the focal length. However it should be noted that a concave mirror and a positive lens have opposite signs for their Petzval curvatures. The elements do not have to be aplanatic or anastigmatic for this to be correct. However the ROC of the best focal surface in the presence of astigmatism is not equal to the Petzval radius.

In a system comprising more than one element the Petzval curvatures (reciprocals of the Petzval radii) add. 

Thank you, Bruce. I stand corrected. It's the sum of powers, or ϕ (be definition the reciprocal focal length, 1/f), not curvatures.



#10 BGRE

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Posted 14 September 2017 - 03:49 PM

 

For a thin lens the Petzval radius is equal to the focal length multiplied by its refractive index, for a mirror the Petzval radius is equal to the focal length. However it should be noted that a concave mirror and a positive lens have opposite signs for their Petzval curvatures. The elements do not have to be aplanatic or anastigmatic for this to be correct. However the ROC of the best focal surface in the presence of astigmatism is not equal to the Petzval radius.

In a system comprising more than one element the Petzval curvatures (reciprocals of the Petzval radii) add. 

Thank you, Bruce. I stand corrected. It's the sum of powers, or ϕ (be definition the reciprocal focal length, 1/f), not curvatures.

 

No, the Petzval curvature is the sum of ϕ/n for a set of thin lenses. Where ϕ  (1/f) is the power of each lens and n its refractive index. 



#11 MKV

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Posted 14 September 2017 - 04:04 PM

 

 

For a thin lens the Petzval radius is equal to the focal length multiplied by its refractive index, for a mirror the Petzval radius is equal to the focal length. However it should be noted that a concave mirror and a positive lens have opposite signs for their Petzval curvatures. The elements do not have to be aplanatic or anastigmatic for this to be correct. However the ROC of the best focal surface in the presence of astigmatism is not equal to the Petzval radius.

In a system comprising more than one element the Petzval curvatures (reciprocals of the Petzval radii) add. 

Thank you, Bruce. I stand corrected. It's the sum of powers, or ϕ (be definition the reciprocal focal length, 1/f), not curvatures.

No, the Petzval curvature is the sum of ϕ/n for a set of thin lenses. Where ϕ  (1/f) is the power of each lens and n its refractive index. 

Yes, but I was specifically giving an example for a mirror/Schmidt camera, where n = 1. 


Edited by MKV, 14 September 2017 - 09:08 PM.


#12 BGRE

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Posted 14 September 2017 - 04:13 PM

 

 

 

For a thin lens the Petzval radius is equal to the focal length multiplied by its refractive index, for a mirror the Petzval radius is equal to the focal length. However it should be noted that a concave mirror and a positive lens have opposite signs for their Petzval curvatures. The elements do not have to be aplanatic or anastigmatic for this to be correct. However the ROC of the best focal surface in the presence of astigmatism is not equal to the Petzval radius.

In a system comprising more than one element the Petzval curvatures (reciprocals of the Petzval radii) add. 

Thank you, Bruce. I stand corrected. It's the sum of powers, or ϕ (be definition the reciprocal focal length, 1/f), not curvatures.

 

No, the Petzval curvature is the sum of ϕ/n for a set of thin lenses. Where ϕ  (1/f) is the power of each lens and n its refractive index. 

Yes, but I was specifically giving an example for a mirror/Schmidt camera, where n = 1.

 

Wrong again, n1 = 1, n2 = -1 for a mirror gives the correct result, whereas merely using n =1 gives a Petzval curvature of zero!!!

 

Relevant formula for the Pezval curvature contribution of a single surface is

 

(n2-n1)/(n1*n2*R)

 

where

n1 is the refractive index of the medium before the surface

n2 is the refractive index of the medium after the surface

R is the ROC of the surface.


Edited by BGRE, 14 September 2017 - 04:20 PM.


#13 MKV

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Posted 14 September 2017 - 09:16 PM

For a mirror,  the Petzval radius of curvature = R/2, where R is the radius of curvature of the mirror. It also has the same sign as R. And R/2 = f.

Afocal, zero power (ϕ = 0) correctors do not contribute to the Petzval sum, even though their individual components (i) may have power (i.e. ϕi<>0). Examples are Schmidt correctors, Lurie anastigmat correctors, etc.



#14 donlism

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Posted 15 September 2017 - 06:47 AM

Thanks again to all of you.  I think I grasp some of what y'all are saying.   sigh2.gif 

 

I'll get back in my box, and proceed with studying all this further!



#15 MKV

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Posted 15 September 2017 - 12:39 PM

Thanks again to all of you.  I think I grasp some of what y'all are saying.  

 

I'll get back in my box, and proceed with studying all this further!

I think Bruce summed it up for you the best with the answer "there is no universal field flattener". The rest of the discussion only elaborates why and how different systems require different approach.. 

 

Some systems (i.e. catadioptric anastigmats with zero power correctors) are the easiest to figure out, as I tried to explain; with others (aplanatic systems that include the Wright telescope, some catadioptric Cassegrains, refractors, apos, etc.) things get a lot more complicated because of residual astigmatism.

 

Any surface that has a focus (f) also has converging power (ϕ or 1/f)), and therefore curvature (c or 1/rad. of curv.) will result in an interplay with power and refractive indices involved, and each surface contribution adds up (to give the Petzval sum, or total image surface curvature.

 

As I already said, this is further complicated by any presence of astigmatism. In that case the field can be flattened even if the Petzval sum ≠ 0 by a judicial redistribution of astigmatism (so that the tangential and sagittal surfaces are curved by the same amount but in opposite directions) resulting in a focal surface of best image definition that is flat.

 

Such solutions, however, do not necessarily give pinpoint star images to the edge of the field. To get the stars to look like dots in such systems all the wave across the FOV, multi-element correctors are required, and for that you need to do more than just a Petzval sum! The resulting field flattener will by necessity be uniquely specific to a particular system rather then "universal".

 

The phenomenon of "generic" field flatteners is based on the fact that some systems are similar in design and substrates used, and will work to some extent, more or less, on different models of the same configuration, but don't bet on it too much! :o)

 

Your best approach, imo, is to get an optical design program, such as OSLO.EDU and study their owner's manual. Programs of that type can actually do the calculating for you, even optimization, to the point where you never have to revisit the equations (last time I dealt with what is a Peztval sum was more than two decades ago...it's no accident that I said curvature instead of focal length because they are related but not the same).

 

These programs spoil you as they can create a system from scratch while you'e having coffee. But, like everything else, in order to use such a tool you need to know optics to at least some extent. It's like a calculator: useless without some knowledge of math.

 

Mladen




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