*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