But the Encke Division (0.045") is smaller than the angular resolution of my scope!
Actually, no it's not!
The quoted angular resolution given for scopes refers to the scope's ability to resolve two stars - but stars ARE NOT pinpoints of light, but actually disks, the Airy disk, a diffraction pattern in reality - we are not actually seeing the disk of the stars. And the resolution limit is the ability to distinguish between two similarly brilliant stars to be able to make out a pinch between the two Airy disks.
When it comes to extended objects, such as the Moon and planets, the actual resolution capability of a scope can be 10 to 20X finer than the Rayleigh or Dawes limit. When it comes to extended objects, there is no diffraction pattern at play, no Airy disk - the possible diffraction pattern is totally disrupted, and the possible resolution limit is much, much finer.
I have seen the Encke (0.045") division in 7" Maks. I have also not even come close to resolving it in 10" scopes. Photos of Saturn using a 16" scope have also not shown it - could also be that the imager didn't know about the gap and then went about eliminating it!!!
Heck! By strict resolution definition, a 7" Mak SHOULD NOT be able to resolve the Cassini division either!
Firstly, I'd like to see the source (anecdotal or otherwise) for the statement:
" ... the actual resolution capability of a scope can be 10 to 20X finer than the Rayleigh or Dawes limit."
Secondly, the assertion "When it comes to extended objects, there is no diffraction pattern at play, no Airy disk - the possible diffraction pattern is totally disrupted, and the possible resolution limit is much, much finer." I am sorry to say, is incorrect. The level of detail observable on a planetary disc in an unobstructed telescope is directly proportional to the size of the airy disc it produces. Because the visual image of a planet is a mosaic of cheek-by-jowl airy discs.
Larger telescopes (given consistent quality optics) produce smaller airy discs = more detail (given equal contrast elements). Add a central obstruction (one type of contrast element) to any given aperture and more light is pushed from the central dot of the diffraction pattern and into the surrounding diffraction rings -- contrast drops as the size of the central obstruction increases. Add in other poor contrast elements like internal reflections/scatter and dust on the optics and seeing and the image is further degraded.
Keep the central obstruction small (ie less than 20%) and its diffraction effects (in transferring light from the disc to the rings) are quite small to negligible. Once you pass about 25% (rule of thumb) it begins to become noticeable on nights of very good to excellent seeing -- all other things being equal.
This is quite simple and well established physics.
This is fundamentally why, telescopes with large central obstructions show less visual contrast in planetary images compared to those with a small, very small or better no central obstruction -- inch-for-inch of aperture. This is why the instrument of choice for dedicated planetary visual observers, inch-for inch will always be a well made refractor that has no central obstruction and inherently very high contrast features.
This is also why, given excellent seeing and thermal stability, there is no rule, ever; that a good little telescope can beat a good big telescope (assuming equal quality of optics).
The good big telescope will always form smaller airy discs and show more detail visually on planets (given equal contrast elements) than any good small telescope.
Herein lies the whole problem with the understanding of resolution with telescopes. So many of us get caught up with statistics and the orthodoxy, but so few question things or allow themselves to make the connection between what the orthodoxy "says" vs what they are actually seeing - or photographing. We also believe that the gear we have spent hard earned dollars on is the bees knees, & "if I can't see it, then no one else can".
The source of my claims and that of many others in this thread is our own eyes. I very much hear the arguments put by the skeptics, but there it is, the Encke Division in the eyepiece. And at the same time it isn't in other scopes of larger aperture that are immediately beside the scope that is showing it. And not just one pair of eyes, but many.
I also started from the point of wrongly "believing" that the smallest detail I could see through a scope was predicated by the Rayleigh or Dawes limits. But I noticed that I was seeing much finer detail than these limits - the Cassini Division through an 60mm scope as an easy tangible example. And a 60mm scope is quite capable of showing finer detail than the Cassini Division. How many people have actually rationalized this for themselves, that the Cassini Division is finer than the Rayleigh Limit for a 60mm scope?
Then while studying and sketching the Moon I firstly began to be amazed by how fine a detail I could pull, but then followed it up with simple high school trig to work out that what I was seeing was pushing the resolution limit of my scope exactly to 1/10 and finer of the Rayleigh Limit.
Trust your eyes and do the maths.
I can easily resolve details below 500m on the Moon (as always, when conditions allow). But let's just take 500m. On the 10th of May when I did my last sketch of the Moon it was at 2am in the morning at 363776km.
At this distance, that 500m detail is 0.0476" in size. Oh, and guess what, the Encke is 0.045"... Hmmm.
For a 180mm Mak, Dawe's and Rayleigh limits are 0.64" & 0.77" respectively. This is the smallest aperture that I've seen the Encke Division with. The 9" Mak, Dawe's and Rayleigh limits are 0.51" & 0.61". With both scopes, both the Encke and a 500m lunar feature are less than 1/10 of the Dawe's and Rayleigh limits. 1/17 of the Rayleigh with the 180mm.
There's my proof.
The Rayleigh Limit is a value that has to show a very specific figure 8 shape between two Airy discs. That pinch between the two airy discs is much, much finer than the angular separation between the two airy discs. Rayleigh's Limit is not and never was the finest detail resolvable through a scope.
Last edited by mental4astro; 11-05-2020 at 05:25 PM.
I have been doing some reading on the subject of Diffraction Limited optical systems, and ran across references to Extending Numerical Aperture, which is achieved in Microscopes via side illumination, which can improve resolution by a factor of almost 2x. My source is here, good old Wiki:
If extension of aperture is workable in Microscopes, why not planetary observation, where illumination of the rings comes from, not just direct solar lighting, but reflection from the planetary body, which for Earth based observers, is effectively side illumination?
So moving to a planet albedo, there are two kinds, the directly lit one, and the reflected one, or Geometric and Bond. In the case of Saturn, it's Geometric albedo is nominaly 0.50, and the Bond albedo is 0.34.
Can the existence of this reflected albedo (Bond) improve our ability to resolve the Encke Gap, beyond that available through the diffraction point limit of our telescope?
It appears the argument isn't so much over whether you can see/detect finer detail than the telescope resolves as defined by Dawes and Rayleigh (yes you can) but rather how much finer, exactly. And that it seems is determined by contrast, and observer acuity.
The notches between two partially separated airy disks are an artifact, like the airy disks themselves, they do not exist on the target and so cannot be "resolved" by the telescope in the classical sense.
I can only conclude from this that the dozens of expert professional observers (all astronomers back then were expert professional visual observers before the age of astrophysics and lived or died on their visual acuity), using some of the finest giant refractors mostly much, much larger in aperture than a mass-produced 7-9" Mak, were clearly a bunch of mugs in failing to detect the Encke gap between the 1820s and 1888.
More than that, it's also clear that presently or in the recent past, a large number of highly experienced amateurs who have commented on this and other forums upon similar claims (I'll include myself in that count) with high-quality, considerably larger aperture telescopes that detect the actual gap on a shrinkingly tiny number of occasions -- quite often never, are similarly either using rubbish telescopes, observe in crap conditions or are similarly, mugs.
On my own visual acuity, it's pretty well known I had cataract operations back about a year ago. Before that (back in my 30s and 40s) my vision regularly tested at 6/4 (I had them tested every other year) -- somewhat better than most of the population in detecting fine detail and without glasses. I can see detail at 6m a person with "normal" vision can see at 4m. ie somewhat, if not substantially better than average. I used to enjoy the game with optometrists when he/she said "read the line nearest bottom of the chart you can see", I would read the manufacturer's name at bottom. Two weeks after my operations I tested at the eye-surgeon's rooms at ... 6/4. Three months after that (November 2019) at the optometrist -- ditto.
I'm sorry Alex, I'm not suggesting you are lying, but I would respectfully suggest that what you are claiming to detect here here is the Encke Minima, not the gap. You are misinterpreting what you are seeing in the eyepiece and mistaken. This is no stigmata -- think of all the highly credentialled individuals over the past few hundred years who have made what turned out to be "spurious" observations. There's a truck-load of them.
Some "eye-opening" reading that may help you "resolve" what you are observing and describing.
Again, just for abundant clarity, I'm not suggesting you are lying or falsifying your reports, merely mistaken.
Hi Les, interesting reading, and thanks for clarifying that
Quote:
Originally Posted by ngcles
I'm not suggesting you are lying or falsifying your reports, merely mistaken.
I am sure that, similarly, Alex isn't suggesting
Quote:
Originally Posted by ngcles
that the dozens of expert professional observers (all astronomers back then were expert professional visual observers before the age of astrophysics and lived or died on their visual acuity), using some of the finest giant refractors mostly much, much larger in aperture than a mass-produced 7-9" Mak, were clearly a bunch of mugs in failing to detect the Encke gap between the 1820s and 1888.
I don't necessarily agree with Alex et al. that trying to observe the Encke Gap in a 7-9" optic is a particularly good way to establish whether that optic is good or not, because it might just take a couple of decades for the seeing to eventuate that would permit an observation that is beyond doubt - in any optic. That's certainly the case where I live. I wouldn't want to wait that long, especially if the scope is still under warranty
On the other hand, I would not consider it completely impossible for a skilled visual observer like Alex to detect the drop in surface brightness in the region of said feature, even if it can't be resolved.
HOWEVER, we need to consider the equipment they were using, and not romanticise it.
The gear used were doublet achromats, not reflectors, and uncoated. They were not made using exotic glass types, though of the best glass of their time. Couple this with uncoated eyepieces made of the same glass types as the objectives. Sure these scopes had massive aperture, but they were severely handicapped in terms of resolution, contrast and colour rendition/correction. Yes, those scopes were very well made, but they had severe limitations.
It is not surprising that it took until the 36" Lick refractor to show the Encke. It was finally the 36" Lick refractor that was of sufficient optical quality to show the Encke, and not before. Aperture actually has little to do with it.
And this is where too any of us get hung up on aperture, aperture, APERTURE to see the Encke. And this is why a well made 8" MODERN scope, with MODERN coatings and MODERN eyepieces can outperform say a 24" 1880's professional refractor for resolution, colour rendition/correction and contrast.
We can see this just examining sketches of from the 1880's and older that used scopes other than the 36" Lick refractor, with high quality contemporary sketches. The ability of the respective artists is a constant, but what each could and can see through their respective telescopes at high magnification has changed, be this Saturnian or lunar or other planetary works. Improved manufacturing and materials has improved contrast, resolving capabilities and colour rendition in modern scopes that today can still be seen in those old scopes as being lacking using their original eyepieces.
Mirko and others have hit on the fundamental reason why the Encke can be seen in say a 7" or 9" scope, and a big aperture dob can fail - contrast.
It comes down to the signal to noise ratio - signal theory. How easy it is for a finitely thin line to be seen against a bright monochromatic background. If the background is too intense, that black line will be overwhelmed for our eyes to be able to see it. How our eyes work is also an important factor here.
High magnification is also an important element in this. It improves the signal to noise ratio to allow for finer detail to be seen. Much like increasing magnification improves contrast with DSO's. However, for a big dob, 360X, 400X, even 500X may not be enough magnification to improve the signal to noise ratio for the Encke. You may need to push things to 600X or more.
If you have a big dob, try using a filter to help attenuate the brilliance.
If you would like me to stump up the relevant maths to support the above, just say the word,
Alex.
PS: a well made 36" dob will kick the teeth in of the 36" Lick refractor.
Last edited by mental4astro; 13-05-2020 at 12:12 PM.
I'm not sure the date when the Encke division was discovered, but Will Hay alluded to it in his book of 1933.
Will Hay was a British comedian that did a lot of movies in the 1930's, but he was also a pilot (he trained Amy Johnson to fly) and a passionate astronomer. He had a 12 inch reflector and including the mount weighed 1.2 Tons.
He made headlines around the world for being the first person to see a large white spot (storm) on Saturn.
In his book (photo attached) he says that there is a division in the outer ring that can be seen occasionally.
At the risk of making this an endless battle of opinions (I wasn't going to add further posts to this thread), I'd offer just one other solid fact that bears closely upon whether it is truly possible to observe/detect/see the Encke Division itself as opposed to the minima.
That portion of the "A" ring that lies outside the Encke Division at best measures 0.5 arc-seconds in angular diameter -- somewhat less (about 25% less) than the angular width of the Cassini Division that separates the "A" and "B" rings.
If the angular resolution capability of the telescope employed is higher than 0.5 arc-seconds (for the record 7" is 0.64") the simple effects of diffraction will blend the division into the darkness at the outer edge of the "A" ring, resulting only in a diffuse dimming of the ring edge, rather than the visibility of a narrow division. It matters not how good the observer's eyes are, if the 'scope has insufficient aperture, the wave nature of light will prevent the detail from being viewed.
I'm sorry, but I remain firmly unconvinced that the Encke Division is actually observable/detectable/see-able in apertures less than 25cm (more likely 28-30cm): Even with a perfect (unobstructed) optic set (these don't exist), in perfect seeing and assuming the observer has high visual acuity. Don't blame me, blame physics.
As Foghorn Leghorn said to the the young chicken hawk: "Son, I say son (listen to me when I'm talkin' to yer), you can argue with me, but you can't argue with figures".
Les, why do you insist on the angular resolution capacity of a scope as being the Rayleigh or Dawes limits?
It never has been. Ever. Rayleigh own work says so. HIS figures say so. No where does his work day that the Limit is the final limit of resolution of a telescope. No where.
If this is what you are saying? Because if it is, then we shouldn't see stars as they have zero angular width.
It is an honest question as I otherwise do not follow your last post.
Let's talk rather than continue this here
Last edited by mental4astro; 14-05-2020 at 07:19 PM.
In my further readings on this subject, particularly the idea that resolution and detection are not the same thing, I found this article from Baader-Planetarium website by Wolfgang Paech: https://www.baader-planetarium.com/e...y-17-aperture/
Notice this in the article:
"At Saturn's distance in July 2018, these 300 kilometres corresponded to only 0.05 arc seconds. However, the resolution of a 17" telescope at the deep red wavelength of 685 nanometres of the IR pass filter is theoretically only 0.33 arc seconds.*So how is it possible that the Encke Gap is visible on our image?
Well, we have to distinguish between "resolved" and "detected", i.e. imaged. The resolution is defined as the separation of two point light sources. In principle, however, objects below the resolution limit can also be detected if the contrast to the environment is high enough and linear structures can also be detected more easily."
Again we come back to contrast differences, and linear objects, which have been discussed before, like in Alex's post #17, and my post on contrast enhancement.
For me rather than debate maths, equations and optical limits I would much rather spend my time just getting out there on a very clear stable dark night and actually try to " see" what the limits of my scope and eyes are.
I may be very wrong but for years I thought Dawes and Raleigh limits are related to the ability of optics to resolve 2 similar "light point sources" and this serves as a good guide as to a telescopes ability to separate close double stars.
A telescopes ability to resolve a dark line on light background requires other considerations such as Edge Spread Function (ESF) as noted on web site below.
.... As mentioned, this limit applies to near-equally bright, contrasty point-object images at the optimum intensity level. Resolution limit for star pairs of unequal brightness, or those significantly above or below the optimum intensity level is lower. For other image forms, resolution limit also can and does deviate significantly, both, above and below the conventional limit. One example is a dark line on light background, whose diffraction image is defined with the images of the two bright edges enclosing it. These images are defined with the Edge Spread Function (ESF), whose configuration differs significantly from the PSF (FIG. 14). With its intensity drop within the main sequence being, on the other hand, quite similar to that of the PSF, resolution of this kind of detail is more likely to be limited by detector sensitivity, than by diffraction (in the sense that the intensity differential for the mid point between Gaussian images of the edges vs. intensity peaks, forms a non-zero contrast differential for any finite edge separation).
FIGURE 14: Limit to diffraction resolution vary significantly with the object/detail form. Image of a dark line on bright background is a conjunction of diffraction images of the two bright edges, described by Edge Spread Function (ESF). As the illustration shows, the gap between two intensity profiles at λ/D separation is much larger for the ESF than PSF (which is nearly identical to the Line Spread Function, determining the limiting MTF resolution). It implicates limiting resolution considerably better than λ/D, which agrees with practical observations (Cassini division, Moon rilles, etc.). Gradual intensity falloff at the top of the intensity curve around the edges can produce very subtle low-contrast features, even if the separation itself remains invisible.
I think this thread has arrived at a stalemate. We need to all go out there and spend time with the scopes....
I am not into the mathematics of θ = 1.22 * λ / d but I have been viewing Saturn for many years using some very high quality optics, including 210, 250 and 300mm Mewlons, TEC MC200 and 18" Newtonians from sites all around western and northern NSW including Coolah, Dubbo, Cookamidgera, Tamworth, Coonabarabran......
I have only seen it twice, both times with 18" scopes....
I've done some more reading to clarify what the difference is between the Encke Minima vs the Encke Division. The picture below shows the two.
With this thread, make no mistake I am talking entirely about the Encke Division (or Gap). Not the minima.
What no one has been able to say who doubts mine and others observations is if we didn't see the Division, what was it that we saw? Likewise the night where multiple people viewed Saturn through different scopes where a 9" clearly showed it, but 11" & 12" scopes didn't, again if it wasn't the Division then what was it? Nor why I am able to see the Cassini Division with 53mm aperture, little lone all of you who see it with 60mm...
If you are still adamant that it takes BIG aperture to see it because it was first seen in a 36" scope, read post No. 48.
Ultimately only time under the stars will tell.
I have never shied away from putting up my scope. You know where it is
I am going to put my hand up as someone who has seen some dark feature outside the Cassini division on just a few occasions. Most recently was a year or two ago (time gets away), when we had a run of exceptional seeing, with a C-11 at 280x (czj 10mm ortho) and 311x (UO 9mm ortho). I don't keep notes (naughty boy) but I also recall seeing it years ago in a 10" f8.2 newt (20% obstruction) at 275 (Celestron 7.5mm plossl).
I am not saying what I saw. My question is: how could I tell? When the Encke Division is visible is the Encke Minima also visible? Or is the minima perhaps too subtle a feature? I don't think anyone has quite addressed this point. And how sharp does the division appear? I expect it appears much more diffuse than in the images.
I'm just happy to see the cassini division in my telescopes, the mind boggles when you look at pics like the one attached, try seeing all this with your earth bound scope.
Because if it is, then we shouldn't see stars as they have zero angular width. 
