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Is an Apo overkill for splitting double stars?


Neil English

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Hi Folks,

Some more info for those interested. It has come to my attention that Paul Couteau, a famous double star astronomer formerly based at Nice Observatory also favoured the classical achromat over the perfect achromatism of the mirror. In his 1983 book he states that the restricted wavelengths available to the achromatic refractor (yellow- green) ie focused within the Airy disk, had the added effect of heightening the acuity of the human eye ( which is most sensitive at these wavelengths) allowing greater resolution of tight doubles. This, together with my findings at the beginning of the thread, make a very compelling case indeed for the virtues of achromatic refractors as fine double star instruments.

Regarding folded refractors; I think there is case to be made for such an instruments in apertures >4" and at focal ratios higher than F/20. The late Ernie Pfannenschmidt was a fine optician and his knowledge of practical optics was superb. I learned a trick or two from his work.

Kind regards,

Neil.

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I tried a little experiment tonight - I was using my synta 6" F/8 achro refractor to compare some decent quality eyepieces and one of my "test" objects was Porrima (Gamma Virginis) which is quite a tight double at the moment - around 1.4 seconds of arc I believe. I was getting a suspected split at 130x a clear split at 171x and 240x and a very clear split at a rather silly 330x !.

Despite the thin cloud the seeing was clearly quite good and the scope well cooled so I thought I'd try stopping down the aperture using the 110mm aperture cap built into the lens cap. The result was very interesting - the scope was now a 110mm F/10.9 so the effects of chromatic abberation were reduced. Porrima was still very nicely split at 330x but the image, though a little dimmer, seemed noticably "cleaner" to me - the airy disks of the stars were a little bigger but now sported a classical and neatly defined single faint diffraction ring around each star disk and the thin strip of space between them was also more cleanly defined.

Overall it was a nicer view than the full aperture had managed I think and I'm surprised that the quality of the split held up under the rather unreasonable magnification I was using.

I'll give my F/6.5 Vixen ED refractor a shot at this double at the next opportunity and see how that fares. My experiment tonight has certainly whetted my appetite for a medium aperture, long focal length achromat though :)

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How about a 5" f9.4 refractor??:eek:

Which I've gone and sold of course ....... :(

Actually I have a 6" F/12 in my minds eye at the moment :eek:

I'm sure glad my wife can't read my mind ........ at least I think she can't :)

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the airy disks of the stars were a little bigger but now sported a classical and neatly defined single faint diffraction ring around each star disk and the thin strip of space between them was also more cleanly defined.

Likely the view quality has improved because the outer parts of the lens are less well corrected than the inner - a 6" f/8 really needs aspheric figuring (like parabolizing a mirror) to avoid spherical aberration, also there is a chance that "pinching" of the edges of the objective by the cell may be spoiling its figure.

Stopping an objective down almost always improves the diffraction pattern, but only improves the resolution if the figure of the objective is poor.

You can pretty well eliminate chromatic aberration from any scope by using a narrow bandpass filter - for bright objects, the Baader solar continuum filter is particularly interesting as it has a narrow 10nm passband at 540nm, right in the middle of the eye's most sensitive response and at the "turn" of the usual achromation correction. If you suspect chromatic aberration is limiting the resolution of your scope, filtering is the way to prove it as stopping down will reduce other aberrations as well.

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...a 6" f/8 really needs aspheric figuring (like parabolizing a mirror) to avoid spherical aberration....

Celestron claim aspheric figuring for their Omni refractors whereas Skywatcher, for their equivilent models, do not. Assuming that Celestron's claim is valid, that means that Synta has put the objectives destined for Celestron scopes though a further stage of figuring to acheive this and yet the Ommi scopes are less expensive than their Skywatcher counterparts :) - "go figure" as our US friends are fond of saying (pun intended !).

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I'd like to go over a few points Neil mentioned. Sorry for not picking up the other threads. I'm unused to chat rooms and find it awkward navigating the different topics.

The radius of the Airy disc: The linear radius to the first dark space is 1.22 x the focal ratio x wavelength or 1.22 Lambda N, but when you convert from linear to angular, it transforms to 1.22 Lambda / Aperture radians, and if you then multiply by 206265, to convert radians to arcsecs, @ 550nm (22micro-inches) it becomes 5".45/D"arc where D" is the OG aperture in inches.

If you have either a 2-inch f/10 & a 4-inch f/10, the Airy disc will have the same linear size (because the linear size is proportional to the f/ratio), but the angular size will be in the ratio 2:1.

Resolution of equally bright pairs is adequately defined by Dawes' rule, 4".56/D"arc. The resolution of unequally bright pairs is a far more complex matter. There is a paper on my website <file:///Volumes/MyMac/Free/Website%20Backup/WEBSITE/BrayObsWebSite/BOOKS/TELESCOPIC%20RESOLUTION.pdf> which deals with this, and there is also a nomogram to assist in the calculations.

There are two dominant factors influencing the splitting of close pairs, especially unequal pairs, seeing and Strehl Ratio. There are a few articles on my forum page about this topic. There are also a couple of articles about focal ratio and long focal lengths and seeing, including magnification and seeing.

Depth-of-focus is proportional to the square of the effective focal ratio of the telescope (either prime of Barlowed &c), but seeing induced focus shift is constant, regardless of focal ratio. I have recently posted a proof of this on my forum page <file:///Volumes/MyMac/Free/Website%20Backup/WEBSITE/BrayObsWebSite/HOMEPAGE/forum/THE%20LONG%20%26%20the%20SHORT%20of%20IT.pdf>. It is counterintuitive I know, but the wavefront retardation is preserved after it passes through the objective (or is reflected off it). A 1/4 wave wavefront retardation produces a 1/4 wave focus shift in any telescope, whatever its focal length or aperture.

Returning to refractor objectives (OG) and Strehl ratio (SR). (For those unfamiliar with this term see <http://www.telescope-optics.net/Strehl.htm>). For historic reasons I won't go into, commercial close air-spaced and cemented achromatic doublets are polished to a surface accuracy of 1/2 wave P-V. This means a standard, commercially mass produced achromatic doublet, is only accurate to 1 wave, and has a disappointing SR = 0.6. Individually crafted OG's are figured better than this commercial base standard, some to 1/4 wave, some better. The minimum SR for what is termed a Rayleigh criterion OG is 0.8. What you need to bear in mind is that this figure applies only at the corrected wavelength, typically 546nm (Mercury e-line), and falls off rapidly in the blue (Fraunhofer F-line - H-Beta) & red (Fraunhofer C-line - H-alpha). This is not quite so bad as it seems, because the eye is very insensitive to deep blue F-line sensitivity @486.1nm 17.5%, and not very sensitive to deep red C-line @ 656.3nm 7%. In the near ultra-violet, 400nm only 0.04%, compared to 550nm. The SR across the visual spectrum is referred to as Polychromatic, as opposed to Monochromatic. For a crown-flint doublet, SR falls off significantly from the correction wavelength. This has an influence on the size of blue and red light Airy discs, and because of the eye's relative insensitivity to red and blue light compared to yellow-green, splitting bluish-white stars does not carry the additional resolving power implied by Airy's formula. The eye also has a lower resolving power in blue than green.

Apochromatic OG's possess superior surface figures generally, and far higher Strehl ratios. It is not uncommon for an ED triplet to be figured to 1/16 wave P-V, corresponding to a monochromatic SR=0.99, and a Poly Strehl 0.93. What this means is that despite their lower f/ratio, and shallower depth-of-focus, (by a factor of 4 say), their tighter P-V wavefront tolerance affords correspondingly wider defocus accommodation within the standard Conrady defined depth-of-focus. (All this is dealt with in my Forum #28 article).

There is one other significant factor, seeing & magnification. Although eyepieces are made in a wider range of focal lengths than used to be the case a generation ago (up to the early 1980's), observers tend to use particular focal lengths for high power use, regardless of the focal length of the telescope (within reason). High power focal length eyepieces are typically 2mm to 8mm focal length. The highest useful magnification for small to medium and thru' large aperture refractors was modelled a century ago by the double star observer T. Lewis to be M'~140√D". If you take this upper power rule in conjunction with the exit pupil formula delta-p = eyepiece focal length / focal ratio, you are left with a relationship between OG focal ratio, highest useful focal length & aperture.

Finally there is a rule-of-thumb used as a minimum focal ratio descriptor for achromatic doublets (see Amateur Astronomer's Handbook - Sidgwick - 1971 3rd Ed. p92). N = 3.D" (e.g. a 4-inch needs to be at least f/12). Combine this descriptor (for a Rayleigh criterion achromatic doublet), and you have the essential reason why a good quality high f/ratio OG requires a lower relative upper power limit, than a low f/ratio OG of the same quality. What mitigates against this relationship is the surface figure, or Strehl ratio. Commercial achromatics struggle to reach SR ~ 0.8, whereas high quality apo's attain SR=0.9 or better, and some have mono Strehls close to 1.

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