Posts Made By: Vladimir Sacek

Ad in the S&T says they have up to 86 degrees, 3 to 30mm f.l., good eye relief, sharp down to f/3.5, flat-field, perfect achromatism with 4-5 *single* lens elements. Anyone knows something more?

There is always a lot of discussion about the effect of c.obstruction (which, btw, almost always takes more of the blame than it deserves). For some reason, people are much more tolerant to bad effects of chromatism. One of the reason is probably that its characterisation doesn't go beyond "chromatism-free" (for f/D~5D", or slower), or "least acceptable" (for f/D~3D"), for ordinary achromats. This doesn't give much info to compare it with other aberrations, or c.obstruction, does it?

Well, it bugged me enough that, since I couldn't find no "official" source for comparing chromatism to other aberrations (mtf, encircled energy,etc.), I did it on my own. Just an approximation, but seems to be making sense. The results are as follows: taking the chromatism-free level of F=5D" as a unit (Fo), energy lost to the Airy disc (beyond the unavoidable 16%) is 44% at F=0.2Fo, 29% at F=0.3Fo, 18% at F=0.5Fo, 14% at F=0.6Fo and 6% at F=Fo.
For a 4" refractor (Fo=20), that would be for an f/4, f/6,
f/10, f/12 and f/20 systems, respectively.

The amounts of energy lost allows for a rough comparison with the effects of spherical aberration and c.obstruction.
An f/4 4" achro is at the, level of 1/2.3 waves of spherical aberration, or 57% c.obstruction. An f/6 is at the level of 1/3 wave of s.a. or ~43% c.obstruction. An f/10 slightly better than 1/4 wave of s.a. or ~33% c.obstruction. An f/12 is at about 1/4.5 wave of s.a. or
~30% c.obstruction. And an f/20 is at about 1/7 wave of s.a. or ~18% c.obstruction.

In regard to the often quoted rule that an obstructed system of aperture D and obstruction C is about as good for low-contrast planetary details as a (D-C) unobstructed system, it may be close to a real-life situation, but it is not c.obstruction to be blamed for all of it. The rule is deducted very approximately, from a "regular" MTF graph, which is for brightly illuminated objects with high inherent contrast. Obviously, not quite appropriate for the purpose. As others already pointed out on different occasions, Rutten and Venrooij give much more appropriate approximation, with a low contrast graph and minimum contrast required taken into account. According to it, resolving power of obstructed apertures is not nearly as much inferior. In a simple form, the effective aperture reduction factor due to the effect of c.obstruction would be closely enough expressed by c^2/(1-c), with c=c.obstruction/aperture (linearly). For obstructions Bellow ~35% it would be even slightly smaller, with the reduction factor going to zero at ~20% c.o.

The rest of real-life inferiority of obstructed apertures should go on the account of their generally greater sensitivity to optical quality, (mis)collimation, thermal instability, baffling, etc.

That is basically the same thing, because
log(LGP) can be written as 2logA-2logP, and log2.51=0.4 (A=aperture diameter and P=eye pupil diameter at the limiting visual magnitude).
"P" in inches comes to 0.25, for which the log is -0.6.
That gives you LM=6+5logA+3=9+5logA.

Like Ron said, this formula neglects a number of important factors. One of them is also darkening of the sky background at high magnifications, when it gets considerably darker than when looked at with the naked eye. This alone can add up to a couple of magnitudes to this basic formula.

SCTs have quite a bit of field curvature. A common f/10 arrangement with ~f/2 primary and ~5 secondary magnification has secondary-to-primary r.o.c. of ~0.31.
With zero astigmatism, field curvature would follow so called Petzval's surface, given by 1/(2/R2-2/R1). For an
8" it gives field curvature ~180mm, and for an 11" ~250mm.

Actual field curvature is determined by the amount and sign of astigmatism, which is in turn determined by the amount of deviation in the power of the corrector from the design value. A dead-on corrector would result in a minimum amount of astigmatism, worsening field curvature by 10%-15%. Quite small deviations - something to expect in mass production - would result in significant increase of astigmatism (and coma), which would - depending on its sign - either further worsen, or lessen field curvature. It is possible that an 8" SCT has less field curvature than an 11" - everything is individual.

Astigmatism/field curvature of the eyepiece will determine the final visual astigmatism/field curvature (not to forget astigmatism/accomodation power of the eye).

I know I can see defocus close to 2" barrel in the C9.25, which should have less field curvature than C11 (~300mm Petzval). But how much of it any of us may see is - just like with our telescopes - highly individual.

After it came to me how inefficient focusing can be with with faster telescopes and ordinary focusers, I figured why not to check it out. It appeared to be too bad, and my assumption that the least controlable movement is not much better than 1/100 of a full turn of the knob was just an out-of-head guess.

I cut out an 8" circle, had it attched to the knob of an ordinary 2" R&P, ordinary Crayford and an 1.25" helical.
I was in for a surprise. The smallest move I could repeat a few times measured ~1/4 mm for the R&P and ~1/3 mm for the other two. But it required near-zero backlash/slippage and near perfectly constant finger pressure (even small change in finger pressure would make it up to several times worse). A reasonable smallest controlable move (one that can be achieved most of the time) is probably somewhere around 1/2 mm on the edge of an 8" knob, and that comes down to less than 1/1000 of a full turn - 10 times better than I thought. It can be somewhat better than that but, also, if the focuser is too stiff, or too loose, or mechanically inferior, it can be considerable less precise.

This focusing precision allows approx. 1/6 wave smallest focusing increment at f/5, and four times less at f/10 for the R&P and Cryford. Fine for f/10, but needs better for fine focusing at f/5. Small helical is over half a dozen times more precise, because one full turn makes for les than 3mm travel (as opposed to 20+mm for the R&P and 20-mm Cryford).

These results match fairly well those that I came out for the SCT (it was easy with micrometric focuser), with the smallest controlable knob move also somewhat better than 1/1000 of a full turn. It translates into a less than 1/20 wave smallest focusing increment, which is adequate.

Even with the results as approximative as they are, the likely conclusion is that an R&P or Crayford w/o fine focusing still are not adequate for fast instruments, although not nearly as much as I thought. But they might be still good enough for apertures having ~1/3 wave, or more, of seeing error in 1 arcesec seeing (~12" and larger).

Someone might try to use this test, described in the last S&T issue, to determine spherical aberration present in her/his scope. The method given is supposed to give approximate amount of longitudinal spherical aberration, indicating correction error of the optical set. However, even assuming pure form of spherical aberration, the method described will only give approximate separation between best foci of the aperture area inside and outside the 70% zone. This would make about half of the actual longitudinal aberration.

But even if corrected for this (doubling the measured focal disparity), the figure, as given in the accompanying table, would indicate much greater aberration than there really is.
For instance, a 6" f/8 sphere has longitudinal spherical aberration (given by D/32F) of 0.0234", or nearly 0.6mm. The method described would give ~0.3mm figure. According to the table, that would indicate spherical aberration in excess of 1 wave. The actual aberration here is 1/3.8 wave (from 22.6D/F^3).

There is also a problem with the assumption of pure spherical aberration. It probably exist only in textbooks; real telescopes have it more or less "modified", which changes the geometry of focal zone in a manner that can't be determined without diffraction analysis of the particular "modification". For instance, refractors often have spherical aberration purposely modified so that paraxial and marginal rays have identical focus, while the longitudinal spherical aberration is largest for rays from the 70% zone.
In this case, best focus of the aperture area outside the 70% zone will nearly coincide with the best focus of the area inside the 70% zone, regardless of the size of aberration. In other words, the test will indicate very low spherical aberration, even if it is, in fact, significant.

There is also a test for chromatism, which is not more reliable than that for spherical aberration. According to test results, a 5" f/15 achromat (which has as much chromatism as a 4" f/12) has less chromatism than an AP StarFire. If nothing else, that should have been something to ring the bell. For some reason, it didn't happen...

Refiguring the secondary can take care of spherical correction, but will do little for the coma. Any two mirror system with spherical primary inevitably suffer from very strong coma. Paracor also wouldn't help much. It works by generating coma of its own, which is of opposite sign to that of a mirror and cancels it. The amount of coma it generates is determined by f-ratio. For instance, at f/5 it generates enough of opposite coma to cancel most of that inherent to an f/5 parabola; at f/10 it generates much less less coma, enough to cancel that of an f/10 parabola. The problem is that a two mirror system with spherical secondary at f/10 would likely have coma wavefront error at the level of f/4 parabola, and nearly double the physical blur size (which would make it even more noticeable at low-power wide-field observing).

The simplest solution would be some sort of near-focus coma corrector (which also could correct for spherical aberration, if necessary). It would induce some lateral color, but it would be much less of a problem.

Vlad

Gregorian coma is exactly the same as that of
a Cassegrain, which is exactly the same as that
of paraboloidal mirror. No need to worry.

Vlad

Victor,

The central hole on the primary will be determined by the width of the baffling tube, which in turn is determined by the optimum location of the baffle tube front opening. You can have those parameters calculated or, you can make a scaled down drawing
and figure it out that way.

Vlad

Played with WinSpot - a great little tilted systems
program (does axial systems too) - in order to make sure
how much of wavefront error is induced by various shapes
of deformed Newtonian diagonals, when the surface error is smoothly distributed over the entire surface. In my previous post on the subject I came up with some results, but was drawing analogies for some shapes, instead of calculating (plain lazy), so there will be also some corrections.

The results are for an 8" f/5 Newtonian, with 0.25f diagonal to focus distance. In general, for given surface error, there is no appreciable change in the size of induced astigmatism with the change in aperture or focal ratio, nor relative size of the diagonal. Important assumption is that the diagonal is just as wide (minor axis) as the converging cone hitting it. If the diagonal is larger (as it usually is) the error diminishes with the square of relative cone width at the diagonal (that is, if the cone is 0.8 of the diagonal width, both surface p-v error and that induced to the wavefront are smaller by a factor of 0.64).

Since p-v errors for different aberrations have different effect contrast-wise, I'll have the errors for coma and astigmatism standardized to a comparable error of spherical aberration. So, "x" waves of, say, coma, will be effectivelly same as "x" waves of spherical aberration.

According to the WinSpot, the diagonal deformation inducing the least amount of error is one where the edges are flat, and the inside surface (either convex or concave) smoothly curved. This is a toroidal form in which the radii of minor vs. major axis relate as 1:2. Here, any given surface
p-v error "x" results in x/16 waves of coma, combined with some residual astigmatism. Obviously, tolerances for this form of deviation are much greater than what usual ideas are. It would take nearly 4 waves p-v surface error to cause 1/4 wave of coma. Moreover, this is an exception in that the error diminishes with smaller relative diagonal size.

Now, by flattening either of the axes in the above shape, so that ends of one axis are twice as high or deep as ends on the other one, we come to the next surafce deformation shape, in which radius of curvature are identical for both,
minor and major axis. At this point, astigmatism induced to the wavefront has become much larger and entirely dominant over coma. Any given surface p-v error "x" induces about x/2 waves of astigmatism to the wavefront (this agrees pretty well with my calculation - nice).

Further flattening of either of the two axes, until it has zero curvature (symmetrial cylindrical surface), results in doubling of the induced astigmatism, while coma further diminishes. Any surface p-v error "x" here results in "x" wavefront error of astigmatism.

Finally, bending either of the two axes so that their depth is identical, but the radii are of opposite sign, results in
"saddle shape" inducing "x" wave of nearly pure astigmatism
for every "x" p-v surface error. Apparently, size of induced error chages little going from the cylindrical towards various saddle shapes.

Conclusion is pretty much the same: error induced to the wavefront by a diagonal suffering from p-v deformation evenly distributed over the surface varies, depending on the shape of surface deformation, from ~1/16 of to equal to the surface error. However, local surface smoothness is even more important in the case of a diagonal than the primary, because any local surface deformation causes 2.8 times greater local wavefront deformation.


Vlad (in need of a break ')