Understanding the (so-called) Dawes Limit

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Understanding the (so-called) Dawes Limit


Post by mikemarotta »

"Hence it follows that the tests of separating power furnished by close double stars are by no means to be relied on as determining the character of a telescope; and further experience has fully confirmed me in this opinion." -- W. R. Dawes, 1867.
We may be extending the original work of William Rutter Dawes beyond its useful limits.

"Catalogue of Micrometrical Measurements of Double Stars"
Dawes, W. R. [William Rutter]
Monthly Notices of the Royal Astronomical Society, Vol. 27, p.217-238
March 1867

Full text available here
http://articles.adsabs.harvard.edu/pdf/ ... ..27..217D
Full text available here
The full text runs 346 pages from Page 137 to page 502.
Here is the salient point.

7. It is a point of considerable interest to determine the separating power of any given telescopic aperture. Having ascertained about five and thirty years ago, by comparisons of the performance of several telescopes of very different apertures, that the diameters of star-disks varied inversely as the diameter of the aperture, I examined with a great variety of apertures a vast number of double stars, whose distances seemed to be well determined, and not liable to rapid change, in order to ascertain the separating power of those apertures, as expressed in inches of aperture and seconds of distance, I thus determined as a constant, that a i-inch aperture would just separate a double star composed of two stars of the sixth magnitude, if their central distance was 4".56 the atmospheric circumstances being moderately favourable.

It might be not unreasonably imagined that the brightness of the stars would make a great difference in the central distance to which any given aperture could reach. But though it may make some difference, it is in fact far less than would at first sight appear probable. This arises from the much higher powers which the brighter stars will bear ; and as the diameter of the disks does not increase in proportion to the power, the separability of all magnitudes is nearly the same, provided the state of the air is such as to bear well the increase of power.

8. Nor is so great a difference as seems to be generally supposed produced by a moderate degree of uncorrected sphe- rical aberration. I was struck with this fact nearly 40 years ago, when I happened at the same time to be in possession of one of the very best, and also of one of the worst, telescopes I ever had. The good one was made for me by Dollond, and was of the ordinary size called the 2-foot ; the focal length being 19J inches, and the aperture 1*6 inch. It had, as was usual at that time, a triple object-glass, and was in a portable mounting with sliding tubes, and furnished with one of Dr. Kitchiner’s Pancratic eye-pieces, magnifying from 45 to 180 times ; other eye-pieces of the Huyghenian construction being afterwards added. With powers of 60 and upwards the disks of [alpha],Lyrae, Capella, Rigel, &c., were shown with scarcely the slightest trace of a ring ; and the small companions of Polaris and Rigel were readily seen, and not by myself only. The former however was often seen by me with the aperture contracted to 1.4 inch; and on one occasion, under an unusually pure sky, with r3 inch: and this is the smallest aperture with which 1 have ever been able to see it with certainty. As a contrast to this exquisite instrument, I had a 45-inch refractor with aperture 2.75 inches; but so bad was the figure that any aperture exceeding if inch showed considerable spherical aberration and with the whole the error was enormous. With the aperture contracted to 1.6 inch, the appearance o£ Castor was almost precisely the same as with the perfect 2-foot and this first proved to me that the ratio of focal length to aperture does not affect the size of star-disks. But notwithstanding the wretched figure of the larger telescope, any increase of aperture beyond 1.6 inch was found to diminish the disks so decidedly that the perfect little glass had no chance in the comparison. The two double sets, which together constitute [epsilon] Lyrae, were shown with the 2-foot, [e-sub-1] (4) Lyrae just neatly separated; and [e-sub-2](5) Lyrae in close contact, power 120. But with the 45- inch, both sets were widely separated with the same power. Pursuing these observations, I came to the conclusion that with the 2-3/4 inch aperture the disks were of the proper size for that aperture; but that round the brighter stars the false and scattered light.was enormously too great; and it is principally in this particular that the effect of a bad figure is seen. Hence it follows that the tests of separating power furnished by close double stars are by no means to be relied on as determining the character of a telescope; and further experience has fully confirmed me in this opinion. The severest test of figure is the similarity of the image of a bright star when the focus is a little too long, and to an equal extent too short. If the rings in these out-of-focus images are similarly disposed in both cases, the figure is perfect; but a moderate deviation from this perfect equality does not stamp a telescope as bad, or even unfit for delicate work. And it is a fact, which I have proved by experiment, that the difference between an object-glass which bore this most severe test perfectly well, and one which fell obviously short of it, was not to be discovered by any decided superiority of the one over the other, either in separating power upon close double stars, or even in the perception of faint objects close to bright ones; though this latter is more likely than the former. The question is much more important how a telescope shows a difficult object, than whether it can show it at all. It is therefore my confirmed opinion that a list 1 of test objects is of comparatively small importance in the trial of a telescope, especially as so much must depend on the eye and the habit of the observer, and the circumstances under which the scrutiny is performed.


Best Regards and Clear Skies,
Mike M.
Michael E. Marotta
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Re: Understanding the (so-called) Dawes Limit


Post by Makuser »

Hi Mike. An excellent post on the Dawes Limit. Here is a link to a brief description between the Dawes Limit and the more stringent Rayleigh Limit which takes into account the color or wave length of the target(s) and most used by the professionals:
https://www.optics-trade.eu/blog/raylei ... esolution/
Thanks for the article Mike and the best wishes for clear skies back at you.
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Re: Understanding the (so-called) Dawes Limit


Post by helicon »

Very interesting piece Mike. Thanks!
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Re: Understanding the (so-called) Dawes Limit


Post by Don Pensack »

Here is a more calculated approach to Rayleigh, Dawes, and Sparrow limits:
https://www.telescope-optics.net/telesc ... lution.htm

Note also that the resolving ability of a scope depends on shape and contrast.
An array of alternating black and white lines will show a better resolution at all apertures.
For example: a 3" telescope can make out the Cassini Division on Saturn, yet this is <0.5" in width, which is smaller than a 3" telescope can resolve a double star.
Astronomer since 1963
Currently using a 12.5" dob and a 4" apo refractor
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