Wavefront error question

So how do you measure wavefront error at the EYEPIECE, anyway? Example: If your primary AND your secondary both have the same measurement (say, 1/15 wavefront leaving the surface of the mirror) then do you have a 1/15th wavefront optical system at the eyepiece? Or do you add the measurements together for (1/15th+1/15th=1/7.5th wave) at the eyepiece? A lot of talk is heard about "diffraction limited" optics, but is that at the primary or at the eyepiece? And what is considered an "acceptable" minimum for wavefront error AT THE EYEPIECE? Any help with these questions would be very greatly appreciated, thanks in advance!
Larry Seguin
Taos, New Mexico

The wavefronts are cascaded, which is to say they can add or cancel along the optical axis, across their 2-dimensional apertures point by point, depending on whether the errors lead or lag. Typically there will be some sort of averaging. But no exact predication can be made without interferometry.

No, you get no usable data from adding, subtracting, or conjuring on the wavefront errors of primary and secondary and eyepiece.

It is possible that one is out one way, and another is out another way, and they cancel out (That is why we were able to fix the Hubble--and why Meade and Celestron match corector plates to primaries when they assemble SCT's.). But it is most likely just a mess, with no matching. In which case, they probably multiply--not add. There is just no way to generalize.

Lord Raliegh says that most of the energy of a pinpoint source of light is within the first diffraction ring, and to oversimplify, the Raliegh criterion says that if an optic is within one eighth of a vavelength of correct, you cannot tell the difference between it and perfect because it has that much amoung of light--or nearly that--in the first diffraction ring. At the eyepeice tests generally prove this true, although an experienced observer can in fact sense some difference.

Light, as you know, does not travel in perfectly straight lines, but "diffracts" around edges and in other ways bends. In short--nothing is ever perfect since diffraction will limit you. WHen there is no difference between as good as it gets with diffraction, and what your optics systems do, then you have "diffraction limited" optics.

And usually, when somebody quotes the wave rating of an optic, they are quoting it for the primary optic, not at the eyepiece--although theoretically, there is nothing that says they can't quote it for the eyepiece. (I am not familiar with the test that could render this number for you, though.)

There is a lot more to say on this subject (Such as what type of "Wave rating" ? Peak to Valley, Deviation from mean? What?

Alex

http://www.astromart.com/articles/article.asp?article_id=80
Please read this article about system Strehl by Rick Shaffer and I think you will find your answers.

An objective should focus all light within an Airy disc because this image can be magnified by the eyepiece to any extent. An eyepiece should only focus light within a couple of minutes of arc because this is not magnified further, and the eye cannot resolve smaller detail. Hence, an eyepiece doesn't need to be diffraction limited. Optimally, it should cancel objective's aberrations like coma and field curvature.

Dmitri

Larry Seguin said:

So how do you measure wavefront error at the EYEPIECE, anyway? Example: If your primary AND your secondary both have the same measurement (say, 1/15 wavefront leaving the surface of the mirror) then do you have a 1/15th wavefront optical system at the eyepiece? Or do you add the measurements together for (1/15th+1/15th=1/7.5th wave) at the eyepiece? A lot of talk is heard about "diffraction limited" optics, but is that at the primary or at the eyepiece? And what is considered an "acceptable" minimum for wavefront error AT THE EYEPIECE? Any help with these questions would be very greatly appreciated, thanks in advance!
Larry Seguin
Taos, New Mexico

Ideally, the rating should measure system wavefront error--that is, wavefront error at the eyepiece. You would not ordinarily expect the surface error of the primary and that of the secondary to be related in any way. (Exception: Any situation where the secondary is shaped or selected to match the primary, as in many commercial SCTs.) So giving just the primary's surface error would not be sufficient.

The wavefront errors represented by the primaries and secondaries (and other optical elements) also do not add in the way that you're probably used to. In this connection, we'll use RMS wavefront error; it is not very useful to use P-V errors. If one element contributes 1/40-wave RMS, and another contributes 1/30-wave RMS, the result is not 1/40 + 1/30 = 7/120 (which is about 1/17). Rather, since they're RMS, you add them by first squaring each, then adding the squares, then taking the square root of the result.

In this case, that gives you 1/1600 + 1/900 = 1/576, and then taking the square root yields 1/24. One caveat: This only works well for errors that cover the whole surface of the mirror, and are uncorrelated with one another. For example, in some sense, light has to deal with the surface error of a primary mirror twice, once upon incidence, and a second time upon reflection. If its surface error is 1/40-wave RMS, however, it does not add as 1/1600 + 1/1600 = 1/800, with the square root yielding about 1/28. No--the errors are perfectly correlated (because they're exactly the same), so in this case, they add the way you're used to: as 1/40 + 1/40 = 1/20. In short, a primary mirror's contribution to system wavefront error is double its surface error.

An error in an objective lens's surface is much less damaging. It depends on the index of refraction of the glass: the wavefront error contribution is roughly the surface error times the excess of the index of refraction over one. For instance, if the surface error is 1/30 and the index of refraction is 1.6, then the wavefront error contribution is 1/30 times 0.6, or 1/50. On the other hand, each lens has two surfaces, not one. If both surfaces yield 1/50-wave RMS of wavefront error, then they add as 1/2500 + 1/2500 = 1/1250, square root yielding about 1/35. (Also, with a lens, you must worry some about inhomogeneities, which are much less of a concern with mirrors.)

In spite of all this addition, we do generally concern ourselves more with the optical quality of the primary (whether it's a lens or a mirror) because it's so large, and it's rather more difficult to get a 1/50-wave RMS surface on a 10-inch mirror, say, than it is to get it on a 2-inch diagonal. It's also easier to replace a diagonal with a better one than it is to replace the primary mirror with an equivalently better one. It's the element that represents the telescope to many of us: we might replace the tube, the focuser, even the mount, and still retain some of the telescope's identity, but many of us (myself included) would feel that something vital had changed if we swapped out the primary.

As I understand it, it used to be that some unscrupulous manufacturers would give primary surface errors where system wavefront errors were expected, making their telescopes look better than they were. Fortunately, that practice has essentially vanished.

Brian Tung