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Asbytec
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Re: Plato's challenge new [Re: Sarkikos]
      #6309849 - 01/13/14 09:36 AM Attachment (24 downloads)

Pete, yes, I think exactly that. The object contrast is a bit higher allowing us to resolve down to Dawes with 5% remaining. I suspect lunar contrast is not 100% meaning after contrast transfer we loose the 5% "required" by Dawes.

However, at Raleigh, the final contrast is much higher at 28% on doubles which appears black. For lunar, since beginning object contrast is not 100% like the black of space, it is also lower after being transferred by the optic. So, at Raleigh I suspect the crater floor "image" should be closer to grey as the crater floor "object" is probably not entirely black. And grey can be seen in the final image. Now, how about if Plato's floor lowers that object and image contrast even more...you need a bigger crater.

Curiously, Raleigh in a 6" subtends a crater about 1.1 miles in diameter at the lunar mean distance. Yet, I reported seeing one at 1 mile. How can that be? Perigee, maybe? Error in measurement? Surely some error. But, it turns out, due to the shrinking Airy disc problem, that is what an obstructed 150mm aperture should see as a limiting observation - right at 1 mile in diameter - at Raleigh.

Yes, they are complex extended objects. Mike, that lunar and planetary is more difficult is the realization that just dawned on me, so you heard it again. But, that's compared to equally bright close pairs, only, of course say at Raleigh or Dawes.

But, yea, it does seem a small crater to be seen needs seeing that makes 52 Ori look like a nice, clean pair of headlights. I think that's because they don't have that much contrast to loose before they become blurred beyond resolution. A bright equal double star's perfect object contrast can afford a little more loss in seeing and such before it is no longer resolved. That's my guess.

Playing around, and if you trust Aberrator. (I do, pretty much.) Notice how the floor of the 1" crater (slightly larger than Raleigh for a 6") is still grey? It gets darker with aperture and improved contrast transfer. Also, the 10" scope is just barely resolving the 0.5" crater. Maybe on a lighter background that dark speck would show better. Also, these images are processed with a slight bit of seeing and about 1/6th SA. They're approximation, surely, but that 1" arc crater looks a lot like "e" to my eye. (It needs to be smaller, though.)

Edited by Asbytec (01/13/14 09:56 AM)


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Sarkikos
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Re: Plato's challenge new [Re: Asbytec]
      #6309879 - 01/13/14 09:57 AM

I think the crux of the matter is that stars are pointicular objects, craterlets are extended objects, different animals entirely. There can only be limited extrapolation of experience and theory from doubles to craterlets. When we observe craterlets, we are not observing just two diffraction patterns as with double stars, but a complex continuum of many.

Mike


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Asbytec
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Re: Plato's challenge new [Re: Sarkikos]
      #6310036 - 01/13/14 11:14 AM

Sorry if I wasn't clear, but oh yes, totally agreed. You don't even see diffraction discs unless the object is very small and very bright. Even then, it may itself be an extended object and simply look like an Airy pattern.

But, yea, the whole image is a composite of unseen and infinite numbers of diffraction patterns the brighter of which might be Raleigh's angular separation with dimmer ones between. You might be able to segregate those 'pairs' of infinite discs. (LOL) Or rather treat the image as a finite number of small spots no larger than 1/4th the Airy disc diameter, as an approximation. Yes, it's complex.

What would be your take on a resolution criteria and how might that apply to Plato? The best I've done is 1.2 miles (+/-) on "e." That makes sense to me in terms of Raleigh and object contrast and might even be a limiting observation.

Just grabbed a look at Plato under pretty thick thin clouds, if that makes any sense. The moon was in good seeing, but it was very grey. The sky, too. Quickly, just got 4 specks (the big 4.) That's it. Oh, and "W."


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Sarkikos
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Re: Plato's challenge new [Re: Asbytec]
      #6310366 - 01/13/14 02:04 PM

Quote:

You don't even see diffraction discs unless the object is very small and very bright. Even then, it may itself be an extended object and simply look like an Airy pattern.




The diffraction disk at high power is an extended object in the sense that it is "extended." But it is still only one diffraction pattern, not a continuum of them, as is the case with planet and lunar surfaces. This is a distinction with a difference and must have some optical consequences.

Mike


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Sarkikos
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Re: Plato's challenge new [Re: Asbytec]
      #6310384 - 01/13/14 02:12 PM

Quote:

What would be your take on a resolution criteria and how might that apply to Plato? The best I've done is 1.2 miles (+/-) on "e." That makes sense to me in terms of Raleigh and object contrast and might even be a limiting observation.




I've never counted craterlets in Plato, at least not in any systematic way. When I try for challenging lunar features, I usually go after domes or rilles.

The Plato Challenge is something I still need to do under good seeing and a favorable sun angle. The 10" Dob would be my best weapon for that battle. But the 6" SCT or Mak would be much more convenient ... if I can wait for them to cool-down. In my area they are better for summer work.

Mike


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Asbytec
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Re: Plato's challenge new [Re: Sarkikos]
      #6311091 - 01/13/14 08:45 PM

Mike, sure, at some very high magnification the Airy disc does behave like an expanded object since it is not infinitely small in and of itself.

Yea, I hope you can do the Plato challenge. It was a challenge.

As they say, it gets worse before it gets better. I hope that applies to our weather. It's been not so goo and seems worse today. Maybe that disturbance will finally pass in a day or two. I may make nightly speck counts on Plato.


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nirvanix
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Re: Plato's challenge new [Re: Asbytec]
      #6311207 - 01/13/14 09:46 PM

I missed it for this month , had a few days of clouds.

But I hear the moon a callin' I'll be back agin afore ye knows it


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David Knisely
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Re: Plato's challenge new [Re: azure1961p]
      #6312475 - 01/14/14 02:56 PM

Quote:

Dawes for an aberrant 6" obstructed aperture would be 113.4/150mm * (1 co^2) ~ 0.69" arc.


Norme,

I thought .76 arc sec was Dawes for a 150mm.


Pete




I'm afraid Dawes Limit is not defined for any particular telescope (obstructed or unobstructed). It is merely an empirical (and approximate) limit for the separation of equal double stars based on the observations of English astronomer William R. Dawes (1799-1868). It is not based on any optical physics so you can't just modify it in some way to account for a central obstruction the way that might be done with something like the Rayleigh criterion. Dawes Limit is just:

r = 4.56/D, where "r" is the double's separation in arc seconds and "D" is the aperture of the telescope in inches. For a 150mm (5.9 inch) aperture, Dawes limit would be 0.77 arc seconds. You can read the entire paper where Dawes first described his limit here:

http://articles.adsabs.harvard.edu/full/seri/MNRAS/0027//0000237.000.html

Dawes mentions his limit on page 237. Again, Dawes limit is not strictly applicable to extended objects like the moon and planets. Clear skies to you.


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David Knisely
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Re: Plato's challenge new [Re: Asbytec]
      #6312609 - 01/14/14 03:46 PM Attachment (16 downloads)

Asbytec wrote:

Quote:

Playing around, and if you trust Aberrator. (I do, pretty much.) Notice how the floor of the 1" crater (slightly larger than Raleigh for a 6") is still grey? It gets darker with aperture and improved contrast transfer. Also, the 10" scope is just barely resolving the 0.5" crater. Maybe on a lighter background that dark speck would show better. Also, these images are processed with a slight bit of seeing and about 1/6th SA. They're approximation, surely, but that 1" arc crater looks a lot like "e" to my eye. (It needs to be smaller, though.)




You can't use Aberrator quite that way and expect to get results that truly depict what is achieved with the eye observing in an actual telescope. It just isn't highly accurate except for roughly demonstrating what aberrations do to an image. In fact, the creators of the software specifically say:

" The realitive effects from aperture and aberrations on such image will be realistic, but its not what you would encounter at the eyepiece."

Quote:

Curiously, Raleigh in a 6" subtends a crater about 1.1 miles in diameter at the lunar mean distance. Yet, I reported seeing one at 1 mile. How can that be? Perigee, maybe? Error in measurement? Surely some error. But, it turns out, due to the shrinking Airy disc problem, that is what an obstructed 150mm aperture should see as a limiting observation - right at 1 mile in diameter - at Raleigh.





Again point source resolution limits cannot be strictly applied to extended detail on the Moon and planets, so it isn't something to get terribly hung-up on. Just view the moon and record what you see as best you can (and be as certain as you can of exactly *what* you saw).

As for the central obstruction "shrinking" things, that isn't quite the whole story. One frequent statement by some authors is that a larger secondary can help increase the apparent resolving power of a telescope. This is somewhat of an exaggeration. While the diffraction caused by the secondary obstruction does cause a reduction in the diameter of the Airy disk of a star, the actual amount of reduction for common central obstruction sizes is slight, and would not help with detail in extended objects. It may slightly improve the ability of the telescope to resolve some close double stars but only when the obstruction reaches a somewhat large size. Indeed, the diffraction disk of a telescope with a 20 percent central obstruction is only about four percent smaller than that of an unobstructed instrument. Even a 33 percent central obstruction would only yield a 10 percent reduction in the Airy disk size, so for common central obstruction sizes, the "improvement" in effective resolution is minimal. The amount of energy put into the first ring by the obstruction would negate any alleged resolution increase on extended objects, reducing the contrast on high power planetary images and rendering small shallow craterlets near the resolution limit of the telescope more difficult to see. It is still better to keep the secondary obstruction under 25 percent if possible.

I went to the Lunar Reconnaissance Orbiter Camera site and used their PDS Archived Image Interface:

http://wms.lroc.asu.edu/lroc/

I used the scale they supplied at as high a resolution as I could get the craterlets to appear entirely within the frame, and got new somewhat more accurate data for all the craterlets I labeled on my original image:

LUNAR ORBITER RECONNAISSANCE CAMERA
CRATER DIAMETERS FOR SELECTED CRATER PITS
INSIDE THE LUNAR CRATER PLATO

(diameters +/- 0.02 km, measured from rim crest to rim crest)

Craterlet A: 2.51 km (1.56 miles), Craterlet B: 2.00 km (1.24 miles)
Craterlet C: 2.21 km (1.37 miles), Craterlet D: 1.95 km (1.21 miles)
Craterlet W (west wall): 3.14 km (1.95 miles),

Craterlet e: 1.73 km (1.07 miles), Craterlet f: 1.46 km (0.91 miles)
Craterlet g: 1.40 km (0.87 miles),
Craterlet h (triple crater feature 2.24 km x 1.19 km (1.39 miles x 0.74 miles))
components "h-1": 1.19 km, "h-2": 1.08 km, "h-3": 0.79 km

Craterlet i: 1.27 km (0.79 miles), Craterlet j: 1.09 km (0.68 miles)
Craterlet k: 0.95 km (0.59 miles), Craterlet l: 0.94 km (0.58 miles)
Craterlet m: 0.91 km (0.57 miles), Craterlet n: 0.87 km (0.54 miles)
Craterlet o: 1.10 km (0.68 miles)
Craterlet p (triple crater feature approx. 1.8 km x 1.5 km (1.1 mi. x 0.9 mi.))
(components: p1: 1.27 km, p2: 1.04 km, p3: 0.57 km)

Craterlet q (doublet): 0.78 km (0.48 miles)
Craterlet r: 1.19 km (0.70 miles)

Some of the craterlets may be more detectable at lower sun angles due to their more prominent ramparts which extend probably at least 15% to as much as 30% of the crater diameter beyond the actual rim point. This could make them appear larger than their physical rim-to-rim diameters would indicate. For example, the central "A" craterlet is 2.51 km from rim to rim, but from rampart base to rampart base, it is closer to 3.3 km. Indeed, I have seen the "bump" of Craterlet A in Plato with only an 80mm aperture, although clear evidence of the "pit" was not seen. The shadow from one of the rims/ramparts at a very low low sun angle can also make the craterlet appear somewhat larger than when the sun is higher above the lunar horizon. You might see a black dot of the shadow along with a hint of the lighter area up-sun from the up-sun rampart which again, might let you see what appears to be a craterlet fully-resolved. At high sun, of course, you could probably see the lighter albedo of the craterlet and its ejecta blanket at apertures less than that needed to fully resolve the craterlet under low sun angle. Clear skies to you.


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Asbytec
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Re: Plato's challenge new [Re: David Knisely]
      #6313266 - 01/14/14 09:43 PM Attachment (15 downloads)

David, thank you for the discussion. Yes, Dawes is an empirical and approximate limit applicable to stars of a given magnitude. This is why I was referring to Lambda/D as an approximation to Dawes and FWHM. It's reasonably close for a given range of moderate magnitude point sources.

While you cannot modify Dawes, per se, since it is such an empirical limit, the Airy disc dimensions are altered somewhat by the presence of the central obstruction both in terms of peak central intensity due to obscuration and diffraction radii (including the Airy disc radius) due to added diffraction not present in an unobstructed aperture. So, while you really cannot modify Dawes as you say, you can modify Lambda/D as an approximation for Dawes. The amount of modification is unclear, it changes for coherent light and incoherent light.

Quote:

The amount of energy put into the first ring by the obstruction would negate any alleged resolution increase on extended objects, reducing the contrast on high power planetary images and rendering small shallow craterlets near the resolution limit of the telescope more difficult to see.



Yes, I think you are exactly right. Crater floors will be grayed out when they are near the limiting resolution of an aperture. Whether sufficient contrast remains at a given angular diameter is the entire issue. At some point, there is just not enough contrast remaining to resolve the crater floor from any rim brightening or even the general albedo in the area. But is the first ring the culprit or the are brighter central discs finally coming into contact at very small angular diameters. I think you can see 'through' the brightness of the rings (relative to the brightness of the rim) provided the floor has enough contrast and a sufficient angular diameter approaching the Raleigh limit. Maybe even close enough to Raleigh to call that limit in general. Plato is a great place to check this out. My hypothesis is it requires a larger crater diameter, maybe even only by 1/10th or 1/5th of a mile.

I can only assert that there is likely some effect noted viewing doubles near the Dawes limit and slightly below. In diffraction limited seeing, I feel strongly there is room to shave a few hundredths of an arc second from those tight pairs leaving a lesser dark space between them (and given the errors in their recorded separation.) That accords with theory and, again, is highly dependent of the degree of coherence of light observed (which is neither totally coherent nor incoherent.) And it depends on the seeing, too, it cannot add any significant induced aberration to the final image.

An obstruction does have an effect, it's just hard to say exactly how much of an effect. This is the phenomenon that gives the MTF a boost at the highest spacial frequencies over that of a perfect obstructed aperture. So, you can apply the presence of an obstruction to resolution thereby besting the Dawes limit from ~0.91 (approximately Dawes) spacial frequency out to as much as 1.1 spacial frequency (in theory) beyond the spacial frequency normalized 1.

The thing that bugs me is having seen "e" at 1.07 miles. It's angular diameter of course changes with lunar distance, but it's still near 6.3/D. I would be curious to know if it can be resolved in an unobstructed 150mm aperture being that close to Raleigh against a darker floor.

Anyway, David, I do appreciate the discussion. It's a fascinating topic and challenge to explore in theory and in practice.

Edit: Below is an excerpt from a spread sheet (attached) for a 150mm scope using the small angle formula, it shows a difference of about 1/10th of a mile difference between obstructed and unobstructed in theory at Raleigh.

Mean 238855 Miles Theta =0.92" arc d=1.07 Miles Resolved unobstructed d=0.97 Miles Resolved obstructed.

A 6" obstructed can see "e", I have seen it. In theory an unobstructed scope could too just barely in excellent, diffraction limited seeing at 8/10 Pickering or better.



Edited by Asbytec (01/14/14 10:25 PM)


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Asbytec
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Re: Plato's challenge new [Re: Asbytec]
      #6313287 - 01/14/14 09:51 PM

Quote:

" The realitive effects from aperture and aberrations on such image will be realistic, but its not what you would encounter at the eyepiece."



Its not clear what they mean by this, do they mean we will not see the diffraction effects as shown? Or do they mean don't expect to see the pattern so clearly due to seeing? I will admit I've had a hard time getting Aberrator to put up patterns that are exactly what I see at the eyepiece, so the latter may be true.

But, as an approximation, it does pretty well with a scaled very good image of Ganymede when applied to an aberrant and obstructed 150mm aperture. Maybe not perfect, but pretty darn close, actually. So, I trust it as far as I can throw it. The image above might not be perfect, but it has characteristics that make it look pretty darn close including the grey floor of a 1" arc craterlet when applied to a 150mm aperture. That is consistent both with my experience and from what I can gather from theory.


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David Knisely
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Re: Plato's challenge new [Re: Asbytec]
      #6313416 - 01/14/14 11:26 PM

Asbytec posted:

Quote:

Its not clear what they mean by this




Yes, it is quite clear. The relative effects of central obstruction or aberrations on an image are fairly accurate, but the view will not match that of a given aperture on an actual planetary object. You put in an image of the given object and *not* the actual view of the object itself in that given aperture. In other words, it demonstrates the effect of the degradation caused by obstructions or aberrations on a given image, but does not precisely duplicate what is seen with the actual view with the *real* object. That would require an accurate lower-contrast image that matches what could be obtained with perfect optics and the human eye. This isn't what the program uses (and the limit of 10 pixels per arc second really kills the ability to simulate smaller features).

Quote:

But, as an approximation, it does pretty well with a scaled very good image of Ganymede when applied to an aberrant and obstructed 150mm aperture.




Huh?? Are you saying you have actually seen detail on Ganymede in a 150mm MCT?? Ganymede in a 150mm aperture is basically a featureless disk less than 1.84 arc seconds across. This is *especially* true of a 150mm scope with more than a 30% obstruction (Ganymede's angular diameter is only roughly the diameter of the diffraction disk of a star in a 150mm aperture and not much larger than a bright star's spurious disk). Even in my 9.25 inch SCT near opposition, I can only get the vaguest hint of a bit of darkening in one small area on Ganymede at over 400x. My 10 inch (21% central obstruction, 1/19th wave p-v wavefront primary) does slightly better on showing a vague darker area on that moon, but that feature is of *very* low contrast. Otherwise, there is very little obvious detail on Ganymede in that aperture. In my 14 inch Newtonian (22.5% central obstruction) I can see a little more, but the shadings (when they are visible) are still quite subtle. They have far lower contrast than the heavily stacked and processed CCD images of that moon taken by Damian Peach in his 14 inch telescope. Aberrator is a useful piece of software, but not for simulating what the views of real objects or small scale lunar features will look like precisely when viewed by the eye through the telescope. Clear skies to you.


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Asbytec
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Re: Plato's challenge new [Re: David Knisely]
      #6313710 - 01/15/14 05:47 AM Attachment (14 downloads)

Quote:

Huh?? Are you saying you have actually seen detail on Ganymede in a 150mm MCT??



One of the reasons I am a believer in theory is having seen it working as advertised. But, absolutely a 150mm can resolve features on Ganymede.

I guess it depends on what you mean by resolved, though, and what features are observed. Nothing is perfectly clear and distinct like an image, but you can see Osiris and Phrygia Suclus as brighter specks dancing near the limb easily enough. Any darker features are just that, maybe a bit if very indistinct darkening approaching the limb and nothing more. No riles, no patches, nothing other than a darker hemisphere than the other. I will say, however, that the dark feature Perrine Regio was totally not seen even though it looks possible. As you say, it apparently has not enough contrast. So, outside of a darker hemisphere, I doubt 'real' dark feature resolution can be done easily.

So, dark features maybe, but bright craters are definitely seen on Ganymede.

You're description of seeing with 9 and 10" aperture sounds reasonable and more like a bit higher resolution of those apertures. I can only credit this to excellent tropical seeing conditions, but the brighter craters are there to be seen and maybe, just maybe, a slight hint of darkening. Eddgie can see darker features more clearly in his C14, to me its just a very weak darkening to some point on the disc. I doubt it's as good as your 9 and 10" scope show it, but it is detectable.

http://www.cloudynights.com/ubbthreads/showflat.php/Cat/0/Number/6297950/page...

Io has some distinctness about it, too, but nothing "resolved." Those are two Jovian moons a 6" can show as something other than a disc.

Yes, apparently you can resolve detail on an object the diameter of the Airy disc provided, as you say, contrast is large enough (or maybe expansive enough, too.) More to the point, though, the same resolution behavior should exhibit itself on the moon, even though we're not dealing with a single Airy disc (Ganymede might be more than one Airy disc, too, but it's at least an expanded PSF with peaks of varying brightness 4x larger than an optical point source.)

Yea, please don't misunderstand. I agree with you Aberrator is probably not perfect working with extended objects. But it's amazingly close. Here's one of Ganymede with an aberrant 6" applied. Not bad, even though the dark Regio Galileo is better resolved in this image than in the real world, Osiris is plainly visible.

I'd expect similar results with craterlets on Plato's floor. In fact, I am hoping folks report such findings.


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David Knisely
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Re: Plato's challenge new [Re: Asbytec]
      #6314366 - 01/15/14 01:07 PM Attachment (13 downloads)

Asbytec wrote:

Quote:

One of the reasons I am a believer in theory is having seen it working as advertised. But, absolutely a 150mm can resolve features on Ganymede.




I am sorry, but a 150mm aperture cannot resolve *any* features on Ganymede. It is utterly impossible, as the diffraction effects in a 150mm aperture will totally obscure *any* detail on that moon (especially with a whopping 31% central obstruction making things even worse). The diffraction disk of a star in a 150mm aperture and the disk of Ganymede are just too similar in size to allow anything to be even remotely detected on that moon's tiny disk (see diagram below). The telescope simply isn't large enough to pick out any real detail on Ganymede. In fact, at only a 150mm aperture, the aperture is just barely large enough to make the disk of Ganymede itself become resolvable rather than just blurring into a spurious disk in the diffraction pattern of a star-like object. Any detail you might seem to see on Ganymede in a 150mm aperture is totally illusionary, possibly caused by the "noise" of the eye/brain system (or perhaps some seeing effects). It isn't real detail.

I'm afraid that if you believe you see detail on Ganymede with such a limited aperture, this might make me wonder just a little bit about your alleged sightings of the e craterlet in Plato. Clear skies to you.


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azure1961p
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Re: Plato's challenge new [Re: David Knisely]
      #6314833 - 01/15/14 04:14 PM

Not true actually Dave. SKY & TELESCOPE some years back had an article about Gary Nowak seeing a polar brightening with a 6" Apo . I duplicated that observation with my 8". The illustration is accurate you portray but the airy disc size comparative isnt representing contrast resolution that can be seen smaller than its radi or diameter. A stellar diffraction pattern is a different matter altogether.

I think you are misunderstanding resolution Dave.

Pete


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Re: Plato's challenge new [Re: azure1961p]
      #6314963 - 01/15/14 05:29 PM

There appears to be a deficiency in David's diagram: in practice there is a significant brightness gradient in the inner region of the Airy disc, and consequently it doesn't seem unreasonable to be able to resolve high contrast features which are around half the diameter of the Airy disc. I prefer to think of the extended object resolution threshold of an instrument as about the Rayleigh limit (5.45 arc sec divided by the objective diameter in inches). The presence of a central obstruction of the size typical of reflecting or compound instruments of the type likely to be used for lunar/planetary observation really doesn't make much difference, the contraction of the Airy disc with increasing CO being offset by contrast loss.

Anyhow the highest contrast "feature" there is to see on any of the Galilean satellites of Jupiter is the contrast between lit and unlit portions during the beginning or end of an eclipse. At mid eclipse the satellite should show a perfect half phase. Experience is that this is seldom if ever seen with 6" of aperture ...


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David Knisely
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Re: Plato's challenge new [Re: azure1961p]
      #6315161 - 01/15/14 07:02 PM Attachment (17 downloads)

Quote:

Not true actually Dave. SKY & TELESCOPE some years back had an article about Gary Nowak seeing a polar brightening with a 6" Apo . I duplicated that observation with my 8". The illustration is accurate you portray but the airy disc size comparative isnt representing contrast resolution that can be seen smaller than its radi or diameter. A stellar diffraction pattern is a different matter altogether.

I think you are misunderstanding resolution Dave.

Pete




No, I am not misunderstanding anything. We are talking about "detection" of detail. People claim to see all sorts of things right at the limits of visual observation (even in Sky and Telescope), but in this case, the physics of the situation kind of trumps the observation. I do fully understand resolution (I have a B.S. in Physics/astronomy). Detection of very low contrast non-linear detail that is significantly smaller than the stellar diffraction disk diameter for a given telescope is just not possible because the diffraction effects that create the pattern tend to obscure that detail. Reliable claims of observations of detail on Ganymede were first done with apertures larger than six inches (example: observations by H. Camichel, N. Lyot, and M. Gentil, using a 15.2 inch (38 cm) refractor on Pic-du-Midi in 1941). Claims of observations of detail on Ganymede in a 5.9 inch Mak-Cassegrain with a whopping 31% central obstruction are very highly questionable to say the least. It also isn't a question of pure resolution either. The magnification needed to get a 1.8 arc second object up to something even half the apparent size of the full moon would be 500x, which would yield a very dim image of that object in only a 5.9 inch telescope. That aperture would have to approach 50% larger (say, something larger than eight inches) for such an observational claim to be even slightly credible.

As for my diagram, for demonstration purposes, it is reasonably close to being fully correct. The central bright disk seen with stars at high power is *not* the "diffraction disk" (and some authors don't even call it the "Airy" disk either). The diameter of the diffraction disk is defined as the diameter of the central diffraction pattern *at the first minimum* of the pattern (the first minimum is the very center of the first dark ring out from the bright central "spurious" disk). For an unobstructed 150mm aperture in visible light, this is 1.845 arc seconds (twice the Rayleigh Criterion figure of just under 0.923 arc seconds). For a 31% obstruction, the first minimum's diameter is slightly smaller at about 1.677 arc seconds, but as can be seen by closely examining the diagram I created pixel by pixel, the 1.8 arc second drawn disk of Ganymede (72 pixels wide) is still just slightly larger than the first minimum of the adjacent star diffraction pattern (67 pixels wide). The largest Ganymede ever gets is around 1.8 arc seconds and right now near the current opposition, it is 1.72 arc seconds across. This is so close to the size of the diffraction disk (and not all that much larger than the bright central "spurious" disk of a star's diffraction pattern) that the effects of the way light is forming that pattern will obscure detail significantly smaller than that diffraction disk's size. Sorry, I just don't buy claims of detail being visible on Ganymede in modest apertures like a mere 150mm. Clear skies to you.


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Asbytec
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Re: Plato's challenge new [Re: David Knisely]
      #6315283 - 01/15/14 08:02 PM

I would think the spurious disc (not the Airy disc) would be the smallest resolvable feature possible, yet we can see objects 4x smaller than the Airy disc.

To begin with, the spurious disc is already about half the diameter, so you're halfway there, already. In point source resolution without a black space, there is plenty of empirical evidence suggesting very tight double stars can be 'resolved' down to 0.5 times the Raleigh limit - 1/4th the Airy disc diameter. (My personal best is 0.62 times Raleigh limit no doubt influenced by the presence of an obstruction, as is the case with 7 Tau easily split with sufficient dark space to indicate something smaller than Dawes is possible.)

At this spacial frequency, there is not sufficient contrast between to brightly lit spurious discs to show a dark space for hard resolution. And we're well beyond Dawes at this point, anyway. This is a different animal than an extended object, but the example shows the Airy disc is not the limiting feature we think it is.

As an extended object begins to exceed 1/4th the Airy disc diameter (the working definition of an optical point source), it's PSF begins to expand noticeably. When the disc radius is equal to Lambda/F it's FWHM (which is an approximation of what we see near Dawes) is much larger than the PSF of the point source Airy disc at FWHM by a factor of two. In other words, Ganymede is twice the diameter of the spurious disc leaving plenty of room for a high (enough) contrast feature to offer an Airy disc of it's own superimposed on the twice as large FWHM of Ganymede.

It's in the form of a gradient, as Brian says. The high contrast bright feature can peak above the surface intensity of Ganymede, as I understand it. And if the peak is high enough (contrast), such a bright object can be seen on the expanded PSF on an object of Airy disc diameter (whose PSF is twice FWHM of a point source Airy disc.) A dark object, too, if it's of sufficient contrast. Otherwise it might appear as an intensity fall off on one hemisphere if the feature is large enough. Galileo Regio is pretty large and seen as a less bright hemisphere (or limb shading), Perrine Regio is not large and was not seen.

If you have ever seen the diffraction rings around Jovian moons, you will note Io and Europa are more star-like in appearance. Ganymede's rings are more washed out indicating it is, indeed, not a point source and therefore does not offer a point source PSF. Io and Europa are at a diameter that is roughly 1" arc, or about half the Airy disc diameter, and their PSF is barely enlarged beyond that of a point source.

One might even resolve a very high contrast feature on either Io or Europa if one existed on their surface. The resolution would be very difficult and very similar to a very tight equally bright double with a separation near half the Raleigh limit. Io does appear elongated and this may be the cause. Resolution on Io? Surely I jest () I dunno, maybe. Depends on the definition of resolution. Maybe from the behavior of its PSF we can say we resolved it's brighter equator from its darker poles even though we cannot see what's actually going on. Nothing is actually 'split', it's simply elongated.

That's theory and accords with my experience with two bright crater 'specks' seen on Ganymede's surface when seeing is at least diffraction limited. Any induced aberration makes detection that much more difficult.

This is high resolution applicable to lunar observing where contrasts are very high. You are correct, the obstruction makes a tiny difference of about 10% in the realm of the very tiny (near the Airy disc and inside the first ring.) That is a difference between resolving a crater that subtends 1" arc and one that subtends 0.9" arc (which turns out to be a the difference between crater about 1.1 mile in diameter and one that is 1 mile in diameter at the lunar mean distance.) It minor, but doable when your scope is operating in near lab like conditions in the real world. I have seen both "e" on Plato, and IIRC, one closer to 1 mile elsewhere, and surface high (enough) contrast features on Ganymede.

Edit: I was upwards of 400x on Ganymede. Of course, there is no further resolution to be had, only image scale and brightness as you say. But, the relative contrast should remain unchanged and the dimming does have (unknown to me) physiological effects. Being up that high didn't seem to hurt anything, it was just easier to look at. I'd assert the presence of an obstruction was helpful, if minor. It was minor enough.

Anyway, it's a great discussion and I think it applies directly to the high resolution needed for small Plato craterlets.


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Asbytec
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Re: Plato's challenge new [Re: Asbytec]
      #6315341 - 01/15/14 08:31 PM

Quote:

...and consequently it doesn't seem unreasonable to be able to resolve high contrast features which are around half the diameter of the Airy disc.



Brian, I agree Raleigh is in the ball park for resolution of features with sufficient contrast. Certainly 100% contrast with about 28% remaining contrast transferred. It is likely more difficult on the moon itself and Plato in particular cine object contrast is lower. This threatens Raleigh limit as a limit for extended objects, but if two points leave 28% contrast and it appears black then lunar features of that angular separation can leave something less than 28% final transferred contrast and appear grey.

Yes, the first bright ring (mostly) does seem to make any high contrast features, such as a crater floor, much more grey than black provided it is of a dimension that is lies under those rings in a very complex way. As long as that grey is a different level than it's surroundings, maybe by about 5% in accord with Dawes, then that crater floor should be seen if it is large enough to separate the brighter (and infinite number of) spurious discs in the vicinity.

On your quote above, actually I'd think you could see anything smaller than 1/2 the Airy disc diameter for bright sources all the way down to a geometrical point provided it is bright enough. It will form it's own spurious disc that will be about half the diameter of the Airy disc. Imagine being able to 'resolve' geometrical points on the lunar surface or Jupiter, for that matter. Now that's some resolution when you can 'resolve' points on an extended object.

But we should see them in the same way we see stars - as spurious discs at about FWHM when the extended object disc is at least FWHM or larger - if transferred contrast is sufficient, as you say. On the moon, this could affect the detection of crater specks. We might not know how small they are, we'd only know how bright or how much contrast they offer. One might imagine they'd have to be of some diameter and albedo to reflect enough light putting up enough final contrast.

Fascinating discussion...the proof lay on Plato's floor.

Edited by Asbytec (01/15/14 08:41 PM)


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azure1961p
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Re: Plato's challenge new [Re: David Knisely]
      #6315537 - 01/15/14 10:19 PM Attachment (20 downloads)

I would still disagree (funny because Im not the one making the observation with 150mm but I haven't tried either) .

Buddy, seeing a half a Ganymede , or rather a crescent of Ganymede via an eipse by another Galilean moon was actually had with a 4" apo as reported on thes boards by Buddy Barby. It goes back a couple years but I recall his reporting that quite clearly. And mind you, he wasn't seeking it out as a threshold achievement infact he didn't expect to see such a thing but alas, he reports he had.

David, The trouble that's muddying thes waters is that a stellar diffraction pattern is created by a virtual point source. Ther can be no such contrasts - even if there were to be had from such a minuscule point - hence the pokerface diffraction pattern. By contrast (literally) the surface area of a galillean moon is a different dynamic altogether. Its not a virtual point source at all and the area subtended (granted beyond the angular res if the aperture) is producing a sizable surface area light at any point .

Take Io for example. Before there was a CN with an imaging forum packed with egg shaped Io images, Pickering saw it as ovular with a 5" aperture - not even a 150mm. By using the eclipsed Ganymede as an example though Brian you could say that Pickering couldn't possibly detect the polar darkening evidenced by the ovular Io he observed. Of course he didnt realize it was albedo effect at the poles he assumed it was egg shaped in fact. The truth of course is Pickering with the 5" refractor was RESOLVING the lesser albedo of the poles (however crudely) - and on a disc virtually 1" across. A far greater feat than seeing a half a Ganymede in semi-eclipse.

The trouble here is the moons aren't stars and while diffraction effects certainly serve to mask contrasts it doesn't obliterate them to the degree of absolute erasure. Pickerings Io observation is strong evidence of that this is the case . The fact that Io's poles are hardly black like that of an semi eclipsed Ganymede and it underscores the point. Merely darker material was enough to change the apparent shape of the object. When you factor in the understanding the brighter equator of Io is only about 0.3 to 0.5 arc second this should have been completely missed in such a hole aperture.

I'm bypassing Norme here and going for Pickerings example as its from a time when no high res images were available of course and so that observer couldnt be fooled by prior suggestion.

I respect both of you but Ive got to disagree .


Pete

Edited by azure1961p (01/15/14 10:21 PM)


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