Posts Made By: Vladimir Sacek

A two-mirror system with spherical primary would suffer from exorbitant coma. Required secondary conic to correct for both, coma and spherical aberration would be too high
to even consider making it. The next simplest solution to a "lensless Schmidt" (which in this case would require 80mm effective aperture for 0.025mm s.a. blur) would be Schmidt plate with neutral zone at the center - in effect, a very mild plano-concave lens (it would be onlu ~0.1mm deep at the center in this case). It would have four times the (sphero)chromatism of an optimized Schmidt corrector, but it would still be not more than 0.03mm at 400nm violet.

Actually, this "cassefractor" has similarities to Houghton-Cassegrain, except that the second mirror has to be convex in order to throw the focus out of the tube. Houghton is a full aperture corrector that consisit of air-spaced positive and negative lens (both same common crown glass), correcting for spherical aberration of spherical primary/secondary. It gives as good image as an SCT, or better, but with only ~1/3 its field curvature. Also, by adjusting the air-space, correction can be nearly perfected in an assembled unit. Alas, the c.obstruction can't go much bellow 30%, just like with any other Cassegrain-like system.

An alternative is Lurie-Houghton, in which the secondary is replaced by a diagonal, for a Newtonian-like configuration.
The system is nearly perfectly color corrected at f/4 and the only aberration is astigmatism (yes, field curvature is also negligible), which is less than 1/10 of the coma of an f/4 Newtonian, and less than 1/5 of the coma in a comparable Mak-Newtonian. For some reason that eludes me, neither system is commercialy available (except as a custom order, which is likely to be - ouch! - expensive.

BTW, the "cassefractor" scheme could be somewhat modified to fold long-focus refractor. Primary flat would be tilted downward, reflecting the light cone to the secondary flat bellow the objective lens; secondary flat would reflect it parallel to the axis to the diagonal. A 6" f/18 achromat could be folded down to less than 30% of its original length.

For 1.52" diagonal and 7mm 100% illumination you'd need no more than 160mm diagonal-to-focus separation. For field of full illumination diameter in a Newtonian you can use
(A-s/F)/(1-s/f), with
A=diagonal minor axis, s=diagonal-to-focus separation, F=f# and f=focal length. It has to be a positive number; negative number would indicate too small a diagonal (i.e. stopping down the aperture).

The problem with mirror-focusing scopes is that their effective focal length changes with the location of focus.
For c8, the f/10 (f.l.=2030mm) is likely to be for the focus located at the top of 1.25" diagonal. If it is so, switching to an average 2" diagonal would result in extending the focus location by ~1.5". This would be "produced" by moving the primary ~1mm closer to the secondary, with resulting secondary magnification (and effective focal length) increased by 4-5%. So you could count with more likely f.l. of 2100+mm.

The effective f.l. would also vary with different eyepieces, since their effective field stop location also vary. But it shouldn't exceed a couple of percent.

If you want to find out what is your scope's f.l. you could measure the exit pupil, devide the aperture with it, and multiply the result with the eyepiece's f.l. But for this you need to be sure what is the eyepiece's f.l. and you can't be unless you measure it up yourself. Another method is to take the eyepiece off and, say, have the Sun - **with the sun-filter on** - projected onto semi-transparent paper screen with engraved mm-scale located at the chosen location behind the back opening and measure up the diameter of its focused image.

With Sun's angular disc going between 31.6' in the summer to 32.6' in the winter, it will focus into ~19mm diameter disc, and your f.l. will be given by 57.3S/0.54, where "S" is the diameter of Sun's image on the projection screen. Assuming you can mesure Sun's image to within 1/4mm accuracy, the measured f.l. will have accuracy somewhat less than +- 1/100.

Ed, a two-mirror system with spherical primary needs very strongly aspherized convex secondary (oblate ellipsoid) in a Cassegarin-like arrangement (known as Pressmann-Camichel).
Unless you want to punish yourself, better stay away from it. Besides, it has nearly ten times the coma of a comparable classical Cassegrain.

The only difference with Gregorian arrangement is much easier to make concave secondary. For accessible focus, you'd need secondary magnification of 3.3 (for an f/10 system) or more, and 50%+ c.obstruction. In this case, a f/2+ secondary would be relatively mild hyperbola (-1.2 conic). Please note that I said it's much easier to make than Pressmann-Carmichel's secondary, not that it's easy It could probably be pulled down to -1 conic(parabola) by combined increase in c.obstruction and decrease in sec. magnification, but it still would be a challenge.

This system would be corrected for spherical aberration, but would have ~16 times stronger coma than classical arrangement (w/parabolic primary). It would perform at a level of an f/4 parabola coma-wise, but with stronger field curvature. Astigmatism would be also 3-4 times stronger, but of no consequence considering the size of coma.

It would probably be easier to get one of those short-tube 6" catadioptric Newtonians from Celestron and (I think) Skywatcher. They should have ~f/3 spherical primary and a corrector lens in front of diagonal that corrects spherical aberration of the primary and also, being a negative lens, doubles the focal length. This lens would work with any f/3 sphere, assuming it is placed at nearly identical distance in front of the focal plane. These ota's go pretty cheaply, and if you sell other parts, you could get this corrector lens for next to nothing.

If you go this route, just make sure the primary is ~f/3.

Jose, the simplest case of such a field flattener is a thin plano-concave lens placed close to the focal plane. The closer it is, the more negligible aberrations it induces.
Assuming low astigmatism, as it should be in an SCT, needed radius of curvature of the lens surface can be approximated as 1/3 of the SCT's Petzval curvature. Assuming an f/2 primary and secondary magnification 5, Petzval curvature would be 254mm, giving the lens surface radius as ~85mm.

Since SCT's astigmatism is not zero, there would be some very mild field curvature remaining. In order to get zero curvature, you'd need to know optical parameters of your system, determining its astigmatism and field curvature.

The "micron story" should be related to spherochromatism.
I don't think they talk about spot size of actual instruments, because level of correction/optical quality varies. So these spot sizes are design-related. A near-perfect MCT has very low spherochromatism, so that its spot size in all colors is within the Airy disc diameter (theoretical diameter 13.4 microns for green/yellow light at f/10). An SCT has, due to higher spherochromatism, nearly twice larger spot in red light, and somewhat larger than that in violet. This is still at a level of an apo, so that real consequences in regard to image quality are much less than what the bare numbers imply.

Also, claim of 13 or so microns spot doesn't agree with the usual Strehl # that comes with MCTs. A 95%-96% Strehl indicates 1/30 wave RMS wavefront, which for very smooth optics comes down to ~1/6 wave pv wavefront. This level of correction would still have ~8% of the energy lost from the Airy disc, and a faint blur at the best focus about twice the Airy disc diameter. In order to have a 13 microns or less spot size, an f/10 instrument would have to be ~1/12 wave pv wavefront, and 98%-99% Strehl. I don't think they are that good.

The difference in performance between the two comes mainly from the production quality. What makes an SCT harder to manufacture at the same level of quality is the two aspheric surfaces - corrector and secondary. Still, with the SCT production quality improved so that it nearly matches MCT's price-wise, I don't think there would be so much of difference to talk about.

Good aproximation for the Strehl ratio is

S~1-39.5w^2

with "w" being the RMS wavefront error.
This comes in a ratio form; to get it in the more usual
percentage form, you need to multiply by 100.

Destructive interference is part of it, but it is much simpler to look at it as a reflectance "game".
Reflectance at a boundary between two different mediums of refractive indici n0 and n1 is given by
[(n1-n0)/(n1+n0)]^2. So if we have reflectve coating with n=1.35, the amount of light reflected from its front surface will be 1.5%. The amount of light reflected from the coating/glass (n=1.5) surface is only 0.3%, of which 1.5% would be reflected back from the coating/air (n=1) boundary, and so on, and so on.

If the coating layer thickness T=lambda/4n (with "n" being the refractive index of the layer) the 0.3% secondary reflection will destructively interfere with the 1.5% primary reflection, resulting in a total reflection of 1.2%.
Total transsmission is, therefore, 98.2% vs. 96% w/o coating.

This is very simplified picture, but it's also much easier to grasp than going into propagation of electromagnetic waves.

Interesting, and about as it is. Tony Flanders made a good point, that dark skies can be more important than aperture size for certain object types (i.e. galaxies in general). A 4" at 21 mag/arcsec sky would likely show about as much as a 16" at 18mag/arcsec sky. Another thing is that large apertures use in general lower relative magnification, which makes sky background brighter, so that their actual advantage is less than what the nominal light-gathering figure implies.

But for some other object types aperture size is more important factor. Large apertures have also resolution advantage, but only on those objects that can take higher magnifications (this also requires good seeing).

Thanks for interesting and informative reading.