Posts Made By: Vladimir Sacek

Going faster with parabolic mirror results in:

- coma limited linear field diameter decreased in proportion to the cube of f#
- coma limited angular field decreased in proportion to the square of f#
- eyepiece astigmatism increased in proportion to the
f-ratio
-eyepiece spherical aberration increased in proportion to the cube of f-ratio

An f/4 parabola has 1/4 wave of coma at 0.55mm off-axis
(from F^3/116). However, an 18" mirror will have field of best definition roughly twice larger, as it seldom will operate at better than ~1/2 wave, due to accumulated errors
(seeing, miscolimation, c.obstruction, etc.). Good definition in the center of the field takes an eyepiece
well corrected for spherical aberration; a Kellner would likely have 5 to 6 arc minutes central blur, and even best corrected eyepieces wouldn't satisfy a ~1' or smaller central spot criterion. How much it really matters depends on one's individual eye acuity - most people won't notice difference bellow 2-3' (besides, an average "good seeing blur" with an 18" is likely to be larger than 1', even at lowest magnifications) .

You need to know Barlow lens' focal length, which is given by f=i/(1-1/M), where "i" is the lens-to-original focus distance when Barlow is in position in which refocuses magnified image to its top opening (where the ep field stop is supposed to be). The inside focus distance "i" is approx. given by L/M ("L" being lens-to-top of a Barlow separation, and "M" its designated magnification).

Once you know "f", magnification of a Barlow for any lens-to-ep-field stop separation "s" is given with a simple (thanks to Mike Hosea) formula M=1+s/f.

For instance, a "shorty" 2x barlow about 60mm long would have the lens inside-focus distance i~60/2=30mm. This would give f~30/(1-1/2)~60mm. With 1.25" diagonal extending the lens-field stop separation by about 60mm, for a total separation of about 120mm, new magnification needed to have image refocused to the ep field stop is M~1+120/60~3.

Note that this is applicable only to reguler Barlows, with a single lens, or lens group.

I'd agree with Kevin that it isn't important. Visible diffraction disc does consist of all the diffraction discs formed by wavelengths from 400nm to 700nm of the visible spectrum mixed together.

Difraction disc formed by, say, 486nm wavelength (blue
F-line) makes only about 0.1% of the total light energy of a white-light source. All the light from the 400nm violet to the 490nm blue-green make only for about 5% of the total
light that can be seen with eyes adapted to bright light conditions. All the light from the red/orange 630nm to 700nm makes for another 7-8%. But whether it will be a "loss" or not depends on the object observed. For instance, a white 6th magnitude star in a 6" aperture will have visible diffraction disc of less than 1/2 of the Airy disc diameter. In other words, wavelengths to which the eye is ~50% or less sensitive will be lost to the eye anyway, chromatism or not. Average eye sensitivity to red/blue light is only about 10% of the max at ~550nm green. In order just to start scrathing the blue F-line visually with a 6" aperture, we have to go one magnitude up, and to get most of this line we need a 3rd magnitude star. But this is assuming that we have a compact, text-book Airy disc for this wavelength (at the green focus), which we don't. Even apos have up to twice larger blue/red blur (sometimes more than that) due to spherochromatism, and achromats have it up to several times larger than that, due to both secondary spectrum and spherochromatism. This makes it even more hard for the eye to detect it. That's why we start seeing these colors (in medium to fast achromats, anyway) only on very bright objects, like zero magnitude stars, bright planets, or Moon. Strictly talking, that light isn't lost from images of bright extended objects: it's still in, only smeared over them, softening their contrast, and beeing most obvious around the outer edge, against darker background.

On the other hand, it isn't lost in any way from the images of fainter objects, because its low intensity would escape eye's attention regardless of the degree of chromatism. And for those very bright objects where a small nominal loss exists, it mostly doesn't matter since there is plenty of light to begin with.

Main problem of faster achromats is that chromatic defocus moves into spectral areas of greater eye sensitivity which, helped by greater correction error and spherochromatism, causes more serious blurring of the diffraction disc and lower image quality. More off-green colors visible around bright objects is merely the most immediate manifestation of the magnitude of secondary spectrum.

Vladimir

When compared to a classical Cassegrain, the only serious disadvantage of the RC is its price. Given systems F# and secondary magnification, there is no considerable differences between the two in their sensitivity to miscollimation (they are both considerably more sensitive to the primary-secondary spacing than systems with less strongly aspherised secondary).

Field-wise, the RC gets ahead with the increase in aperture
and/or lower secondary magnification. For instance, at 200mm f/14 and secondary magnification ~4 they both have aberrated blurs (coma length in the CC and astigmatic blur in the RC) nearly equal to the Airy disc diameter at ~0.4 degrees off-axis. From there, quality angular field diminishes in proportion to 1/D with a classical Cassegrain, and in proportion to 1/sq.rootD with the RC.

Photographic (linear) field is constant in the CC (0.025mm field given by F^2/7.5 in mm), while in the RC increases in proportion to D/sq.rootD, given secondary magnification
(0.025mm field is approx. f*sq.root(1/20Dm) in mm), "f" being the system's f.l. and "m" the secondary magnification.

Fact that the RC gets ahead quality field wise (both visual and photographic) with the increase in aperture is the main reason why the RC was a design of choice for large telescopes. At small apertures, it is not so much of a factor.


Note that even when the blurs are of similar size, the RC still have advantage due to astigmatic blur being, unlike comatic blur, symmetrical.

It should be significantly better mechanically w/2.7" focuser and Takahashi-like (well, almost) tube. Optically,
it is just a Fraunhofer doublet, with 1/6 wave correction guaranteed and all the chromatism that has to go with it. It should also have very smooth optical surfaces, with claimed 1/30 wave RMS, leading to the 96% Strehl (note that the Strehl figure for this fast achromat is not a realistic performance indicator, because it doesn't take into effect chromatism, as it is not a wavefront aberration). If you want the best of this kind of instrument, I'd say it's worth the money.

Not that it's not a exceptional performer, but I wouldn't call it "perfect" just yet. On the first place, it does have residual coma, which is in proportion to the primary diameter vs. mirror from which it's been cut out. In this case, the smallest possible is ~11" f/3.8. A 45% of the coma of this mirror is at the level of an f/5.6. Not really bothersome, just enough not to be mentioning "perfection".

Another thing is that 99% Strehl. It requires an RMS wavefront error of ~1/60 wave at the focus, or somewhat better. With the PV wavefront error at the focus of 1/6 wave, it gives a PV-to-RMS error ratio of 10:1, almost twice higher than "smoothest" traditional (axial) mirrors. Is an off-axis segment cut out of a well made larger mirror so much smoother than "axial" mirrors of the same size? Sort of intriguing.

Rob, if you suspect TDE, try to test with a 90% aperture, or so, mask. If the pattern remains unchanged (it is going to reduce spherical aberration by ~25%) at least you know what it isn't.

There would be a minor vignetting (nearly 1", or 1 degree fully illuminated field, with illumination 1" off axis better ~90%), and you'll probably have more vignetting at the diagonal anyway. I would be more concerned with possible thermal problems due to the tube walls being soclose to the incoming light bundle.

Design-wise, there is a good description of it in Rutten/Venrooij's "Telescope Optics" (p88) with necessary formulae in the "Designing a Schmidt-Cassegrain" section (p272).

Telescope Warehouse have it for $20, and Astro Physics for ~$40.