Field curvature and eyepieces.

[mental4astro]

Hi all,

This weekend finally saw me understand the term "field curvature" and its manifestation in eyepieces.

In a nutshell, it means the ability of an eyepieces to deal with the steepness of the cone of light towards the edge of its FOV. This in turn can become more obvious as the f/ratio gets faster, or the FOV exceeds the EP's design capabilities.

It has nothing to do with coma as such, as you can have a 100deg EP show terrible field curvature in an f/15 scope, yet in a 45 deg EP, the entire field can be pin sharp in an f/4 scope.

Coma correctors may or may not help.

I've been trying to find some reference where I can look up the suitablity of different EPs in a range of different f/ratios. What may work just fine in an f/15 scope can be totally useless in an f/4 scope (I saw this on the weekend). Most eyepieces "lists" I've seen don't mention field curvature capability, and their "design description", plossl, kellner, nagler, etc, can be meaningless.

Is there a reference somewhere to do with field curvature & f/ratio with respects to eyepieces, like a list noting brand vs. properties? A tool like this can be invaluble in determining EP suitability, and not have to go through heart ache to find that your $400 EP isn't much chop in your f/3.3 scope.

Cheers,

Mental.

[casstony]

Field curvature is only related to f/ratio for a particular design of telescope and when the aperture is kept constant. It's more correctly related to the focal lenth and radius of curvature of a newtonian main mirror, such that a very large aperture, fast mirror will have less curvature than a small aperture, slow mirror.(the large mirror having a longer focal length than the small mirror).

Different designs and sizes of telescope have varying degrees of field curvature and eyepieces are designed with different amounts of curvature. How the telescope and eyepiece interact determines whether or not curvature is visible at the eyepiece. If the respective curvatures are of the opposite sign they tend to cancel each other out; I think this is why the Andrews 30mm Ultra Wide performs better in a SCT than a Newt.

[ausastronomer]

This is all 100% correct. The F-Ratio of the Telescope is not even the tip of the iceberg. It comes back as Tony says to the radius of curvature of the primary optical surface and the design of the optical system. It gets even more complicated than that in fact. For example with a SCT the field curvature of the telescope system is dependent on the radius of curvature of the primary optic. Most SCT's have a primary of F2 to F2.5 hence they have a very short radius of curvature and hence exhibit a very curved focal plane. This is why a field flattener is combined with a SCT for astrophotography, notwithstanding the telescope "system" is usually about F10. You then need to consider the interaction of the telescope field curvature with the eyepiece field curvature. In some cases the two can cancel out and exhibit a perfectly flat field. In other cases they compound.

Cheers,
John B

[mental4astro]

John & Tony, many thanks for your insight. It is more complicated, I see. I'm still coming to terms with the influence and relationship of focal length, the f/ratio, and diameter.

My question still remains, where can I find the necessary info about this property of eyepieces? This is such a significant element with such a range of telescope optics, to not have this information is such a let down to us, and a rip-off considering the surge of eyepieces with a FOV over 68 degrees. I now know it is a complicated thing, field curvature, but it's like the eyepiece producers/brands, don't want to admit that their gear has limitations in their suitablility. Hmmm.

Alex.

[casstony]

Unfortunately most manufacturers don't publish this information and it's left to us to find apropriate eyepiece/telescope combinations through trial and error. Pentax is an exception: http://pentaxplus.jp/archives/tech/xo-xw/64.html

If I'm reading the diagram correctly, the solid and dotted lines represent two focal surfaces formed by the eyepiece (tangential & saggital) with the point of best focus lying between the two. The farther this point of best focus lies away from the vertical axis, the greater the field curvature. You can see that the 14, 20, 30 and 40mm XW's have a field curved in the opposite direction to the other focal lengths. When the solid and dotted lines are close together (as in all of these eyepieces) astigmatism is minimised.

[ausastronomer]

Hi Tony,

Yes you are reading this correctly. As can be seen from the diagrams the 3.5mm, 5mm, 7mm and 10mm Pentax XW's all have -ve field curvature. When combined with a fast newtonian which has inherent +ve field curvature the two cancel out and present a lovely flat field view. The 14mm and 20mm XW's have +ve field curvature, which when combined with a newtonian which also has +ve field curvature, compounds and gives a fairly soft view at the edge of field. The 30mm and 40mm XW's have a reduced amount of +ve field curvature and give reasonably good views in a newtonian. A paracorr whilst designed to correct for coma, has inherent -ve field curvature which cancels out a lot of the +ve field curvature of a newtonian, consequently it flattens the field noticeably when used with the longer focal length Pentax XW's (14mm and longer).

Cheers,
John B

[casstony]

Thanks John :thumbsup:. Clear as mud Alex :).

John, I'm wondering if you're able to confirm something else for me - that the curved field of commercial SCT's is of opposite sign to Newts?
Here's my thinking: the wavefront leaves the primary mirror curved in the same direction as a Newt; the secondary has a shorter radius of curvature and therefore produces stronger curvature than the primary; since the secondary is convex it changes the wavefront to the opposite sign.

[Wavytone]

Casstony,

The field curvature is a function of the telescope design and isn't just a function of the curvature of the secondary mirror.

For example, take several different cassegrain designs having primaries and secondaries of similar radii - the classical cass, Dall-Kirkham, Meade/Celestron SCT, A Gregory maksutov, the RuMak, and the ones that have a corrector at the secondary mirror - all will have quite different field curvatures - some negative, some positive and it is even possible to come up with an aplanatic solution (flat).

There are some optical formulae for analysing two-mirror designs that use conic sections (A.E. Conrady) to determine the curvature to third-order but these don't work for surfaces with complex shapes such as the SCT corrector. The best way is to ray-trace the design to calculate the curvature precisely.

While it is possible to calculate the field curvature for common telescope designs, in some respects it is most unfortunate that eyepiece manufacturers never state what the field curvature of the eyepiece is (or was designed for), consequently finding the best eyepiece to give sharp focus across the whole field (ie to match a specific scope) is frankly trial-and-error - as we all know. The problem mainly affects low and medium power eyepieces - not a big deal for high power ones.

The result is that an eyepiece that works well in an f/5 Newtonian (curved focal plane) may be disappointing in f/7 aplanatic refractor designed for imaging (aplanatic = flat focal plane, to suit a flat sensor).

[ausastronomer]

Hi Tony,

My apologies for the delay in replying. I wanted to check some of my textbooks before I replied. Unfortunately they haven't given me all the answers we are seeking. As Wavytone has pointed out it gets pretty complicated. Also remember I have a Commerce Law degree and run a large Club. I have been an amateur astronomer for many years with an "interest" in optical design. This is really getting out of my league into the league of professional opticians and mathematicians.

Here is a good starting point you can read on telescope field curvature

http://www.telescope-optics.net/curvature.htm

Here is a further section on Schmidt Cassegrains and there own inherent aberrations (off axis)

http://www.telescope-optics.net/SCT_off_axis_aberrations.htm

Essentially, for a each curved surface of the telescope you will have +ve field curvature from a concave reflecting surface and -ve field curvature for a convex reflecting surface

On face value your assumption seems correct looking at the formulas in the links above. As the secondary (convex) in a SCT has a shorter Radius of Curvature (ROC) than the primary (concave), one could reasonably assume the secondary would apply more -ve field curvature than the +ve field curvature induced by the primary, with the net result being -ve field curvature, which is the opposite to a newtonian with it's single concave reflecting surface. I wasn't satisfied with this because my own field testing of the 14mm and 20mm Pentax XW's in several different SCT's indicates that the +ve field curvature of those eyepieces is "compounded" by the telescope or at best, not really improved. In fact it gets further complicated with the field curvature induced by the aplanatic Schmidt corrector. You cannot determine the field curvature of the corrector without knowing the curves used in it's design. I don't know where those numbers lie for the commercial SCT's running around today.

So the short answer is, in theory you might be right. In practice that's not what my eyes tell me and you would need to know the curves of the aplanatic Schmidt corrector and the ROC of both mirrors to work it out.

I am going to give Mark Suchting a call and ask him to have a look at this thread. If anyone on IIS knows the answers, Mark will.

Cheers,
John B

[astropolak]

John essentially said it all.
I can not add much in terms of technical details but have some practical experience...

I used to have Meade 8" SCT, loved it to death but it did suffer from field curvature..., and coma !
My new scope (Meade 200R) suffers from none of those and to my eyes the field is essentially flat.

I think some of our colleagues who do astro-photography with the new R or ACF optics can comment on its field curvature as it should be visible on large format cameras, those have flat focal plane and may show any curvature that exists, eyes are probably not the best tool as they can accommodate some curvature, worst still the amount of such "accommodation" varies on the day.

[casstony]

Thanks for the comments guys. I only interested in the SCT curvature as a matter of curiosity. I must remember to check which way the crayford focuser moves in order to improve the edge of field next time I'm out.

From the links John: "For a pair of mirrors, the curvatures are combined" and " field curvature; of interest are Petzval field curvature (http://www.telescope-optics.net/curvature.htm), which is not affected by the corrector", which supports my earlier assumption. The corrector may not have an impact on curvature because it's curve is so shallow?

Wavytone, for simplicity I'm only looking at the standard Meade/Celestron f/10 SCT's with spherical mirrors, although it is interesting to consider what happens with shallower primaries, larger secondaries, etc.