Jump to content


Photo

Plato's challenge

  • Please log in to reply
260 replies to this topic

#1 nirvanix

nirvanix

    Surveyor 1

  • -----
  • Posts: 1744
  • Joined: 07 Jun 2007
  • Loc: Saskatoon, SK

Posted 08 January 2014 - 05:24 PM

When do people think is the best time to go after Plato's craterlets? It's first quarter, so tomorrow, the day after? I had some success last year but can't remember how many days past the quarter it was? :question:

Kind regards.

#2 brianb11213

brianb11213

    Cosmos

  • *****
  • Posts: 9047
  • Joined: 25 Feb 2009
  • Loc: 55.215N 6.554W

Posted 08 January 2014 - 07:23 PM

About 2 days after Plato is illuminated. Friday is probably optimum for this lunation. Too low sun gives low illumination levels making it harder to pick up the small craterlets (or at least that's what I find). With sufficient optical power the main craterlets can be seen under full moon illumination as light spots.

#3 edosaurusrex

edosaurusrex

    Messenger

  • *****
  • Posts: 406
  • Joined: 30 Jan 2007
  • Loc: Ft Worth, TX

Posted 08 January 2014 - 11:14 PM

Here are the predicted times for the Sun altitude to be 12 degrees at Plato's center. Rising time plus a few days or setting time minus a few days should put viewing at the conditions stated in the earlier posts.

PLATO PREDICTIONS FOR 2014
MMM DD HHMM UT

JAN 10 2336 RISING
JAN 22 2214 SETTING

FEB 09 1412 RISING
FEB 21 1157 SETTING

MAR 11 0518 RISING
MAR 22 2356 SETTING

APR 09 2015 RISING
APR 21 1028 SETTING

MAY 09 1027 RISING
MAY 20 2013 SETTING

JUN 07 2331 RISING
JUN 19 0559 SETTING

JUL 07 1122 RISING
JUL 18 1629 SETTING

AUG 05 2212 RISING
AUG 17 0416 SETTING

SEP 04 0825 RISING
SEP 15 1733 SETTING

OCT 03 1841 RISING
OCT 15 0813 SETTING

NOV 02 0539 RISING
NOV 13 2345 SETTING

DEC 01 1755 RISING
DEC 13 1525 SETTING
DEC 31 0740 RISING

#4 Sarkikos

Sarkikos

    Hubble

  • *****
  • Posts: 16824
  • Joined: 18 Dec 2007
  • Loc: Per sylvam ad astra

Posted 09 January 2014 - 07:04 AM

With sufficient optical power the main craterlets can be seen under full moon illumination as light spots.


Yes, this is true. But sticklers will say that you're not really "seeing" the craterlets, you're only detecting their albedo spots. Personally, I'm not that persnickity.

:grin:
Mike
  • STE411 likes this

#5 nirvanix

nirvanix

    Surveyor 1

  • -----
  • Posts: 1744
  • Joined: 07 Jun 2007
  • Loc: Saskatoon, SK

Posted 09 January 2014 - 11:06 AM

Hey, thanks for the responses folks :flower:

I'm supposed to get clear skies Friday so I will give it a go. Last year I believe I got 7 recognizable and, as you say Mike, an albedo spot. I'm in your camp with regards to that - everything we see is photonic stimuli so if a set of photons causes an albedo spot to be seen then as with everything we see we have to deduce what is actually there, in this case a craterlet.

I recently got an autocollimator and after looking at the moon Tuesday night I feel that it has improved my dob collimation enough to make a difference, so I'm looking forward to going after Plato. On Tuesday I spent a good deal of time looking at the central peak of Theophilus - the illumination was such that it looked all the world like a snow-capped peak. Just beautiful.

#6 Sarkikos

Sarkikos

    Hubble

  • *****
  • Posts: 16824
  • Joined: 18 Dec 2007
  • Loc: Per sylvam ad astra

Posted 09 January 2014 - 11:13 AM

I have a new old - as they say on "American Pickers" - C5 that I want to try out for lunar/planets/doubles ... if the skies clear up and the snow and ice melt. The number of craterlets seen in Plato would be a good test if I can catch the right night.

Mike

#7 nirvanix

nirvanix

    Surveyor 1

  • -----
  • Posts: 1744
  • Joined: 07 Jun 2007
  • Loc: Saskatoon, SK

Posted 09 January 2014 - 11:31 AM

Well good luck to both of us Mike. I wonder if the American Pickers ever found a great telescope in someone's barn?

#8 Asbytec

Asbytec

    Guy in a furry hat

  • *****
  • Posts: 8251
  • Joined: 08 Aug 2007
  • Loc: La Union, PI

Posted 10 January 2014 - 09:33 AM

Nirv, here's an excellent guide to Plato's craters. (Source unknown)

I've managed the big 5 A through E. A through D one one night long ago and picked up E recently. Add a few others as specks, I think my own total is about 11, if memory serves including the speck count.

Good luck, it's a great challenge. The times above are nice for picking them up, maybe catch the waning moon in that seeing might be a tad better later in the night.

Attached Files


  • OrlandoMatt likes this

#9 nirvanix

nirvanix

    Surveyor 1

  • -----
  • Posts: 1744
  • Joined: 07 Jun 2007
  • Loc: Saskatoon, SK

Posted 10 January 2014 - 01:47 PM

Thanks Norme. I've seen A-E and g,h. Will have to try for i,j. There is no l,n, o ?

#10 David Knisely

David Knisely

    Hubble

  • *****
  • Posts: 15577
  • Joined: 19 Apr 2004
  • Loc: southeastern Nebraska

Posted 10 January 2014 - 02:07 PM

With sufficient optical power the main craterlets can be seen under full moon illumination as light spots.


Yes, this is true. But sticklers will say that you're not really "seeing" the craterlets, you're only detecting their albedo spots. Personally, I'm not that persnickity.

:grin:
Mike


With the "white dot" albedo features, you are at the very least, "detecting" some of the craterlets. However, when the moon is not full, it takes a little more aperture (and good seeing) to resolve the craterlets and show them as the true pits they are than it does the tiny white spots that some of them generate under full moon illumination. Clear skies to you.

#11 Sarkikos

Sarkikos

    Hubble

  • *****
  • Posts: 16824
  • Joined: 18 Dec 2007
  • Loc: Per sylvam ad astra

Posted 10 January 2014 - 02:39 PM

With the "white dot" albedo features, you are at the very least, "detecting" some of the craterlets. However, when the moon is not full, it takes a little more aperture (and good seeing) to resolve the craterlets and show them as the true pits they are than it does the tiny white spots that some of them generate under full moon illumination. Clear skies to you.


Agreed.

Mike

#12 Asbytec

Asbytec

    Guy in a furry hat

  • *****
  • Posts: 8251
  • Joined: 08 Aug 2007
  • Loc: La Union, PI

Posted 10 January 2014 - 10:37 PM

Nirv, well done. That's a great craterlet count. Seems you've set the bar. :grin:

Correct me if I'm wrong, but the challenge with Plato is it's floor albedo is relatively dark making the smallest craterlets normally resolvable in craterform (rim and floor seen) by an aperture a little more difficult.

//Thinking out loud

If the rim is highly illuminated, it should stand out nicely against Plato's dark floor offering up a nice speck. However, the craterlet floor is also pretty dark, so unlike a brighter rim the contrast with Plato's floor is very small making the crater difficult to observe in true crater form. We should be able to see anything on the moon that is bright enough to create a diffraction artifact (disc) that stands out against the bright surface. This can include a crater that is the angular diameter of a point source provided its (rim is) bright enough relative to the background.

If so, then it's rim should create diffraction effect somewhere near FWHM of a point source very near Lamda/D or 113.4/Dmm. At the moon's average distance that should create an Airy disc subtending an apparent diameter of about 0.9 miles for a 6" aperture. So, to be seen then, the crater would have to be slightly larger in order for it's darker floor to be seen outside and separated from the edge of the diffraction disc formed. So, the rim has to be bright enough to form a diffraction artifact brighter than the moons surface and the floor must subtend a diameter larger than Lambda/D limit and closer to the Dawes limit.

If there is a shadow in the craterlet floor and it's diameter is at least the Dawes limit, it's contrast against the moon's brightly lit surface should remain high enough to be seen (as a bright speck and a dark speck.) The Dawes limit seems to account for the illumination of not only the rim but also the brighter moon's surface surrounding the crater floor just as it does with a nearby star.

The moon's point source brightness plays an important role, too. The moon is pretty bright even on point source scales (not sure the exact figure.) So, diffraction artifacts are both a tiny bit larger and also appear to be larger due to the eye response. However, higher magnification upwards of about 50x per inch expands and dims the image of the moon's surface. Since a point source angular diameter remains constantly small, it also dims those diffraction artifacts making them smaller in angular diameter. The surface feature, like a crater rim, is also less brilliant in terms of our eye's response. So, some high magnification is useful. It would seem while you could resolve a crater at 1mm exit pupil (being the average magnification to see an Airy disc), the moon is just too bright. In practice it might require closer to 0.5mm.

That's theory and something to shoot for in diffraction limited seeing. In practice may be more difficult. The best I've done (and very rarely) is something approaching 1 mile in diameter in excellent seeing. That's just approximately Dawes (given some slop with accuracy of measuring the diameter and with error in the moon's distance.) Plato's E crater is about 1.2 miles in diameter. Being the smallest crater form I've noted (again, rarely) within Plato, it suggests they are a bit more difficult than smaller craters against a brighter background.

Thoughts? Sorry for rambling, but the idea of seeing what can be theoretically seen is interesting. It opens up so much for us to see when we can see it.

//End thinking out loud.

#13 azure1961p

azure1961p

    Voyager 1

  • *****
  • Posts: 10386
  • Joined: 17 Jan 2009
  • Loc: USA

Posted 10 January 2014 - 11:59 PM

Ok here's what's vexing me a bit Norme...

The gold standard for finest crater resolution per aperture has a crater half filled with light and shadow. There's a correlate to Dawes that seems to generalize a fair rule of thumb. Hence, 1.5 miles for a 6" aperture.


What happens when the craterlet is far smaller and puts fourth nothing larger than perhaps Osiris did? Say its a bright crater pit in a dark floor - nice contrast - what's the smallest of this type a 6" can resolve at least as a point source?

Think of Osiris or some of the other truly small features eeking in just under half a sec of arc.

Is it too far fetched at least in theory to suggest a 6" can *resolve*, ie; see - a craterlet perhaps .37 miles across as a singular dot?


The moment a craterlet can be seen as a veritable diffraction point through contrast - the smallest crater - 9/D would seem to be ~ a fourth of that?

You see where Im going?

Pete

#14 David Knisely

David Knisely

    Hubble

  • *****
  • Posts: 15577
  • Joined: 19 Apr 2004
  • Loc: southeastern Nebraska

Posted 11 January 2014 - 01:46 AM

Nirv, here's an excellent guide to Plato's craters.

I've managed the big 5 A through E. A through D one one night long ago and picked up E recently. Add a few others as specks, I think my own total is about 11, if memory serves on the speck count.

Good luck, it's a great challenge. The times above are nice for picking them up, maybe catch the waning moon in that seeing might be a tad better later in the night.


And you have used exactly the same crater ID's that I created many years ago when I first put this article up on-line in 2003, 2005, and 2007 on sci.astro.amateur (as well as several other prior times on Cloudynights):

. . . . . . . APPROXIMATE CRATER DIAMETERS . . . . . . .
. . . . . . . . . . (+/- 0.2 miles uncertainty) . . . . . . . . . .

. . . The "BIG FOUR" (+1) . . .
A = 1.6 miles (2.6 km) B = 1.3 miles (2.1 km) C = 1.4 miles (2.3 km)
D = 1.2 miles (2.1 km) W (on west-northwest wall) = 1.9 miles (3.1 km)
NOTES: Although many amateurs rarely seem to see very much on the apparently smooth dark floor of Plato, the above craterlets are the ones most often reported by those lucky enough to get really good seeing. "A" is the easiest of this group due to its fairly prominent ramparts, and has been reported in a 4 to 5 inch aperture, although the unresolved "bump" of craterlet-A's ramparts is visible in only a 3.1 inch. 3 or 4 of these craterlets can sometimes be observed under low sun angle and in good to excellent seeing in apertures 6 inches and *larger*. These four can sometimes be "detected" as very tiny white spots in 3 to 5 inch scopes during the full moon, although to show them all as true pits often requires a 7 or 8 inch aperture. The "East Wall Pit" is a much larger irregular feature (4 miles across) which often hides in the shadow of the eastern wall during the lunar mornings. It may not be an impact crater, but more of a slumping of a segment of Plato's wall. There is also a small but prominent craterlet "W" low on the west-northwest wall north of the west-rim bow-in which is about 2 miles across. It is somewhat more difficult to observe than its size would indicate, mainly due to wall-shadow concerns and the crater's tilt.

. . . The "Little Four" . . .
e = 1.1 miles (1.8 km) f = 0.9 miles (1.6 km) g = 0.9 miles (1.3 km) h = 1.4 x 0.9 miles (2.2 x 1.4 km)
NOTES: Craterlet-e has been sighted in a good 8 inch, but craterlet-f may take a bit larger scope to see with any regularity. "e" tends to hide in the long early morning shadows, as "f" does also in the low lunar evening. The Lunar Orbiter shots of Plato show that "h" is a tiny double craterlet with 0.9 and 0.8 mile diameter components, forming an elongated 1.4 x 0.8 mile feature visible in larger apertures, but not fully resolved. Again, very high lunar sun may allow some of these cratelets to be "detected" as tiny white spots near full moon. The "Big Four", and the "Little Four" probably represent most of the craterlets on the floor of Plato which might be visible to amateurs using moderate to large apertures under excellent seeing.

. . . The "Tiny Ten" . . .
i = 0.8 miles (1.3 km) j = 0.8 miles (1.3 km) k = 0.8 miles (1.3 km) l = 0.7 miles (1.2 km)
m = 0.7 miles (1.2 km) n = 0.7 miles (1.2 km) o = 0.8 miles (1.3 km, double craterlet)
p = 1.0 x 0.6 miles (1.6 km x 1.0 km, triple craterlet) q = 0.9 x 0.6 miles (1.4 km x 1.0 km, double overlapping crater)
r = 0.8 miles (1.3 km)

NOTES: These are extremely difficult to observe as anything other than tiny white spots or rimless pits, although i, j, m, and o2 have been imaged by Maurizio Di Scuillo using a CCD camera on a ten inch Newtonian optimized for high resolution planetary work. Craterlet k has a very small pit to its west and will be tough to resolve easily. Craterlet m is a fairly shallow bowl with little in the way of a rim, so it is more difficult than its size would indicate. "n" is a very small rimless pit just to the east of a tiny white spot which is often mistaken for a crater (may be a small mound or ejecta blanket). Craterlet o is a double craterlet, which forms a 1.2 mile x 0.6 mile elongated feature. p is a triple, consisting of 0.7 mile, 0.6 mile, and 0.3 mile craterlets in close proximity, which might be detectable in very large apertures as a single almost rimless 1.4 mile x 0.6 mile feature (not resolved). Craterlet q is two very small overlapping craterlets which form a single 1.2 mile x 0.5 mile feature. r is right on the edge of the north-eastern floor of Plato and is hard to see due to shadowing. Lunar Orbiter images show a large number of smaller pits down to 0.25 miles across on the floor of Plato, but the above three "families" are probably the only ones which have much of a chance of being seen visually from Earth.

Below is the "rectified" Lunar Orbiter image that was used for the initial measurements (courtesy NASA):

Clear skies to you.

Attached Files



#15 Asbytec

Asbytec

    Guy in a furry hat

  • *****
  • Posts: 8251
  • Joined: 08 Aug 2007
  • Loc: La Union, PI

Posted 11 January 2014 - 01:57 AM

Yea, I see where're you going. Osiris is a great example, actually. It's a white speck in much the same way white specks are on the moon and probably for the same reason. So, yes, at less than true resolution of light and about 5% grey space we see specks smaller than the resolution of our aperture when seeing allows it.

Ideally, I would assert, you could see a point source "speck" at 1/4 Raleigh limit and even smaller if it were bright enough (enough contrast at maximum spacial frequency.) You could see something as small and bright as the apparent angular diameter and magnitude of Sirius if such an object existed on the moon. Or maybe if such a small feature existed and was properly illuminated on the dark side of the terminator. It would have more contrast there. I wonder how many of those "city lights" are very small features just over the terminator? Lit crater rims certainly appear brighter, yea?

I may be off my rocker on this being theory, its likely more difficult in practice in average to good seeing. But, I assert, it's always about contrast and not about angular diameter, though some angular diameter near Dawes at a minimum is required for craterfrom resolution. Specks have no such limit and can be seen as small as you like, provided they are bright enough relative to the lunar surface.

Using the small angle formula, I get Dawes to be closer to 1 mile in diameter than 1.5 miles at the moon's average distance, where angular measure in arc seconds = 206265 * diameter/Distance. So, a crater 1 mile across at 238,855 miles distance would be about 0.86" arc. That's comfortably above Dawes (and even a bit more than Raleigh for a 30% obstructed 150mm aperture calculated using a factor of 1 -co^2 ~ 0.91 * Raleigh limit.) Of course, that is the diffraction limit and seeing must allow it, otherwise it becomes an observation "in practice."

In theory, solving for diameter in the equation above and assuming theta to be 0.77" arc (Dawes for 6" aperture) we should be able to see crater's down the about 0.9 miles in diameter provided contrast remains above 5% due to surface albedo, seeing, aberrations, obstructions, and everything else that reduces contrast on those scales. Actually, Dawes should be somewhat less in an obstructed scope. In theory, nearer to 0.7" arc for a 30% 150mm aperture using the same 1 - co^2 factor as an approximation near maximum spacial frequency. So, that should reduce the theoretical diameter of a lunar crater to about 0.8 miles. Now, in practice with aberrations, seeing, and loss of contrast in a less than perfect obstructed optic that figure is probably closer to 1 mile when it's all said and done...in practice.

That means any craterlet about 1.6km, such as g or h, /might/ be in crater form when conditions are perfect for a 150mm aperture. But, this may be where Plato's darker floor comes into play lowering the contrast against what remains of the shadow's ~5% contrast transfer on the focal plane - makes those two extremely difficult if not impossible and slightly larger craters tough but not impossible. For larger craterlets, seeing disrupts them more often than not.



#16 Asbytec

Asbytec

    Guy in a furry hat

  • *****
  • Posts: 8251
  • Joined: 08 Aug 2007
  • Loc: La Union, PI

Posted 11 January 2014 - 02:23 AM

Dave, I'm sure I got both from you years ago (but cannot find the thread to link the source.) It's a great piece. Mulling over your thoughts. I've read them before, but need a refresher. Thanks.

Initially, if crater diameters are (understandably) off by +/- 0.2 miles, that changes which ones can be resolved a bit. But, I did nail E one in 150mm, nothing smaller on Plato, yet. So, at least that one is doable and above the resolution limit for that aperture as a minimum.

I am not sure what is meant by optimizing for high resolution lunar and planetary imaging. Often that means a smaller CO and better contrast on scales out to the first ring or so. Really what's needed is to push high resolution into that tiny realm where obstructed scopes out perform perfect unobstructed ones on smaller scales near the spurious disc. That normally means a larger CO on the order of 40% to maximize that high frequency range. And it means everything needs to be diffraction limited, including seeing and aberrations...the aperture needs to be the limiting factor. Again, that's in theory and a benchmark to shoot for.

In practice, I think Plato's floor contrast ups the ante on these tiny ones. All we see is a speck in modest apertures because the floor washes out the already very low contrast of the craterlet's pit and the rim or wall should be brightly lit, as well, to see it in speck form. They do need more aperture in practice for crater form resolution and in this special case of Plato. Out on the brighter open plain, the story changes in favor of higher resolution pushing closer to theoretical resolution of a perfect optic as possible. This is where I could push closer to 1 mile resolution, and haven't done so on Plato yet.

That's the essence of this Plato challenge, right? To see where this proverbial contrast wall stops us in various apertures? How small can we go in crater from resolution is a function of how much contrast (seeing, aperture, obstruction, aberration, etc.) is available. Otherwise, we see a speck if anything at all.

#17 David Knisely

David Knisely

    Hubble

  • *****
  • Posts: 15577
  • Joined: 19 Apr 2004
  • Loc: southeastern Nebraska

Posted 11 January 2014 - 05:26 AM

Asbytec wrote:

Initially, if crater diameters are (understandably) off by +/- 0.2 miles, that changes which ones can be resolved a bit. But, I did nail E one in 150mm, nothing smaller on Plato, yet. So, at least that one is doable and above the resolution limit for that aperture as a minimum.


The lunar distance varies by about 5.5 percent from its mean value, so you can expect up to an 11% variation in the resolution. The old "9/D" (D is the aperture in inches) for craterlet diameter (in miles) approximation is just that, so craterlet e might just be possible in a 150mm aperture scope depending on the conditions. I have only managed it in 8 inch and larger apertures, but you never know.

I am not sure what is meant by optimizing for high resolution lunar and planetary imaging.


In Maurizio's case, it means a 10 inch f/8 Newtonian with a very very smooth and well-figured set of optics and a small secondary mirror. With a lot of image processing, some of his shots showed more than 20 cratelets on the floor of Plato, which is more than I usually see in my own 10 inch. With my 14 inch, I could see a lot more (I have gone down to around a kilometer or so), but seeing has to be unbelievably good. Clear skies to you.

#18 Asbytec

Asbytec

    Guy in a furry hat

  • *****
  • Posts: 8251
  • Joined: 08 Aug 2007
  • Loc: La Union, PI

Posted 11 January 2014 - 08:27 AM

David, yes, the lunar distance is critical to determining the actual diameters using an aperture's resolution as a guide. Apparent diameters change with distance, for sure, and there is always room for error.

Image processing enhances contrast not readily available to the eye-brain visual image, so that an image captures more is not surprising. But, what can the eye-brain do is the interesting question. I think it starts with Dawes, which is an empirical visual observation made with a real aberrant aperture and in real seeing conditions, then work backwards a bit to find a limit for a given aperture.

Plato will require a little more from us, but how much? That's what makes the challenge interesting. We get to push man and machine to the limits and begin to define those limits. It's a fascinating topic.

I forgot about W, that makes 6 in crater form (attached.)

-------------------Optional and possibly confusing reading below :lol:

Dawes, or actually Lambda/D as an approximation of Dawes, is about 113.4/Dmm. It changes a little with the magnitude of the point source, but we can assume the moon to be mostly bright (crater rims) and any diffraction affects having relatively stable and modest magnitude. Dawes also applies to 100% object contrast between two points in black space and ends with 5% image contrast. The moon is very high contrast, but I doubt its 100%. The lit rims are pretty bright, but the pits may not be completely black and devoid of light so the range between the two is likely a bit less than 100%. So, already it looks like reaching Dawes is very difficult visually.

Dawes for an aberrant 6" obstructed aperture would be 113.4/150mm * (1 – co^2) ~ 0.69" arc. At the moon's mean distance and approximating with the small angle formula we arrive at ~0.8 miles in diameter - at that mean distance. In my experience not having resolved to Dawes (as expected), but getting down to about 1 mile (not in Plato) equates to about 0.86" arc resolution. So, I am sure that level of resolution is possible in diffraction limited seeing. That turns out to be slightly better than 0.92" arc for Raleigh limit (calculated normally with 138.4/Dmm, but observed with an obstructed aperture with a modified Raleigh limit of 0.83” arc.) It's not quite as good as modified Raleigh (caused by to obstruction diffraction effects), however. So, an unobstructed and unobstructed, aberrant aperture should resolve craters at least to about 1.04 * Raleigh limit. (The extreme precision is exaggerated to show how close to modified Raleigh 0.86” arc actually is.)

However, that may not be the best than can be done visually; it's only my own best. That's about 1R for all reasonably good apertures in diffraction limited seeing, IME and IMO. And that makes some sense being that Dawes leaves 5% contrast on the focal plane and Raleigh about 28% (which appears as a black space.) The moon might not be quite 100% starting contrast, so in theory it should not provide 5% on the focal plane at Dawes. But, it should not begin with nor loose, through contrast transfer, so much that Raleigh separation falls from 28% to less than 5% on the focal plane, either. So, it makes sense to me, and seems consistent, any resolution limits should be reached at less than Raleigh (138.4/Dmm) but larger than Dawes for obstructed apertures and right at Raleigh for unobstructed apertures. This is, after all, the domain where obstructed scopes rule.

That "E" being approximately 1.2 miles in diameter set on a darker floor was seen in crater from with a 150mm aperture (assuming mean distance and a diameter close to shown) suggests the same approximation for resolution to lie slightly larger than the Raleigh limit at 1.03” arc, as expected. That 1.2 miles (approx) is closer to 7/D. However, the modified Raleigh limit is closer to 0.83” arc, so the loss is somewhat more significant. This is about 1.2 * the modified Raleigh limit for an obstructed aperture. Applying the same figure to a clear 150mm aperture we might arrive at a resolution of 138.4 * 1.2 = 166/Dmm for Plato craterlets, at least or about 1.3 miles in diameter. Maybe better, but that’s about 8/D.

Such is the effect Plato’s contrast has on resolution; we lose the Raleigh limit by a factor of about 1.2, it seems.

Again, applying the small angle formula using the moon's mean distance we arrive at 1" arc resolution for one Plato craterlet (“E” at 1.2miles approximately) on that night, at least. This is slightly above the Raleigh limit for a 150mm aperture and is expected because beginning object contrast on Plato is reduced. So, since contrast and spacial frequency are inextricably bound, we'd expect the diameter to be a bit larger to leave sufficient object contrast transferred to the focal plane.

Thus, the diameter of crater's that can be seen is not so much a function of diameter, but of object contrast. And on Plato, they have to be a bit larger than normal or require slightly larger aperture.

The math above is an approximation based on my own experience with craterlets against the moons brighter surface and on Plato. It does not define anything, it just gives a range - between conventional Dawes and Raleigh for unobstructed apertures - I think one can expect to observe when the air is diffraction limited. Actually, 9/D is a good approximation for average conditions, but I think it might be a bit pessimistic for excellent conditions which can push toward 7/D. And that's fine, they are only approximations given so many variables exist such as actual distance, diameters, and conditions. On most nights I cannot see "E", and often enough even A through D can be tough. But when seeing is diffraction limited, all 6 can be seen when the lighting is right.

Attached Files



#19 azure1961p

azure1961p

    Voyager 1

  • *****
  • Posts: 10386
  • Joined: 17 Jan 2009
  • Loc: USA

Posted 11 January 2014 - 08:57 AM

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

#20 Asbytec

Asbytec

    Guy in a furry hat

  • *****
  • Posts: 8251
  • Joined: 08 Aug 2007
  • Loc: La Union, PI

Posted 11 January 2014 - 09:13 AM

It is, but added diffraction due to an obstruction changes that by a factor of 1-co^2 approximately and for coherent light. So, it is somewhat less than 116/Dmm (or 113/Dmm for Lambda/D criteria for resolution approximating Dawes) depending on the size of the obstruction an with somewhat incoherent light. It might be about 105/Dmm ~ 0.7" arc for a perfect 150mm aperture and somewhat more for a real one. Remember, at this very high spacial frequency is where obstructed apertures /can/ rule and /can/ exceed perfect unobstructed performance given a reasonably good Strehl. This extended spacial frequency can improve high resolution provided the atmosphere is not working against it. So, yes, officially Dawes is 0.76" arc for a 150mm, but it should be a bit less when that aperture is obstructed.

#21 nirvanix

nirvanix

    Surveyor 1

  • -----
  • Posts: 1744
  • Joined: 07 Jun 2007
  • Loc: Saskatoon, SK

Posted 11 January 2014 - 11:16 AM

Norme in your last photo there is a crater near the rim of Plato at the two o'clock position. That is one that I'm certain I detected last winter and wonder why it's not labeled? I remember that one as being resolved along with 6 others, and crater h was the albedo feature I noted.

A star is a point source of light. If my optic catches enough light from that point source it will form an image my eye can see. Any spot of the lunar surface, like the rim of a craterlet, can act as a point source of light that my optic/eye can detect even though my optic isn't capable of resolving that feature. If I used a photosensitive device and digital image processing, I might be able to discern several point sources of light in a curved line that would indicate the structure, even though my eye couldn't. Those multiple points would have to be separable by my optic of course otherwise they'd appear as one spot.

There is the theory and practice of telescopes on earth being separated by distances so that the total resolution becomes something of the order of the separation distance. I wonder if there are any amateurs engaged in that? Or is it really only practical for radio devices :question:

#22 Asbytec

Asbytec

    Guy in a furry hat

  • *****
  • Posts: 8251
  • Joined: 08 Aug 2007
  • Loc: La Union, PI

Posted 11 January 2014 - 11:52 AM

That looks like "f" as labeled in David's graphic at about a mile in diameter. That's a great catch. In your 10" scope? Do you remember what your seeing conditions were or the moon's distance that night?

So, h was a albedo "speck?" That one would be curious to know how it resolves out - as one elongated object (crater or speck) or two distinct features. I cannot remember which specks I saw, would have to dig way back into the CN archives. I don't remember seeing a double speck, anywhere.

Any spot of the lunar surface, like the rim of a craterlet, can act as a point source of light that my optic/eye can detect even though my optic isn't capable of resolving that feature.

Absolutely. I guess that's why we see specks, instead. Normally the smallest craters do not form specks in my scope, they have to be something larger than a point source (being defined as 1/4 Airy disc diameter, or about 0.4" arc. That's pretty small, less than 0.4 miles.) Otherwise Plato should be covered with specks and maybe all of the labeled one in David's graphic, at least.

So, it seems we have crater form to some level of resolution (I'm curious about), bright specks below that (kind of curious about that, too), then we see nothing further down the resolution chain. But, we would if they were bright enough. Most are not. But you know...specks might be a bit easier (and crater from more difficult) on Plato because it is a tad dark.

Anyway, I hope you guys can report sightings, if seeing ever allows good look at Plato I'll join in. Resolution is an interesting topic and Plato is an interesting place to try to understand it and the limits of our equipment and conditions. It gives us a feel for what we can expect to see. Maybe we see more specks per capita on Plato than elsewhere?

It would be very interesting to note the affects of seeing in larger apertures, too. They might be hard pressed to reach the diffraction limit, but they are still supposed to resolve quite nicely since their diffraction limit is much smaller, anyway. So, even if they are not at diffraction limited, they are returning smaller discs (short exposure FWHM) even in less than perfect seeing. That's the theory, does it hold? I'd think so.

#23 Asbytec

Asbytec

    Guy in a furry hat

  • *****
  • Posts: 8251
  • Joined: 08 Aug 2007
  • Loc: La Union, PI

Posted 11 January 2014 - 12:44 PM

Those multiple points would have to be separable by my optic of course otherwise they'd appear as one spot.


This whole idea and the mechanics behind our ability to probe the world beyond fascinates me to no end. I like to really push it for everything it's worth in the real world and try to understand it in theory. Often the two are not far apart. It's just a step we take to delving into our hobby, not unlike a surfer waxing his board and reading the waves for the best break.

I had to come back to your idea of the expanding point source. At some point larger than about 1/2 Raleigh, the visible disc expands noticeably to the eye. This may well be the curve of a crater rim as much as it would be a Jovian moon. So, at some intermediate point between point source and full blown expanded object, we see an expansion of the spurious disc. I wonder how many specks we observe on Plato are actually expanded in this way at least somewhat. Are they indeed expanded perpendicular to the sun's angle? Is the floor visible at this point, or is this the range of angular dimension that defines a speck without a visible floor? Not a perfectly round speck like a spurious disc, but an elongated one defining a crater rim as a speck to our eye?

That needs a closer look. If so, then a speck might well be resolution of a crater rim even if the floor is too dim to see. Or it could be the two are not mutually exclusive, once you see the rim you see the floor and a speck is still a speck.

#24 David Knisely

David Knisely

    Hubble

  • *****
  • Posts: 15577
  • Joined: 19 Apr 2004
  • Loc: southeastern Nebraska

Posted 11 January 2014 - 02:06 PM

Asbytec wrote:

Dawes, or actually Lambda/D as an approximation of Dawes, is about 113.4/Dmm. It changes a little with the magnitude of the point source, but we can assume the moon to be mostly bright (crater rims) and any diffraction affects having relatively stable and modest magnitude.


Dawes limit is *only* applicable as an approximate limit for a pair of equal point sources, not for an object that contains extended detail. A craterlet on the moon is an extended object, and point-source limits cannot apply to them. For that, you have to use a limit that is somewhat larger than Dawes. The British observer Wilkins in 1959 did a detailed set of measurements in various apertures and came up with the approximate relationship that a craterlet half-filled with shadow would be visible on average if it had a diameter (in miles) equal to 9/D, where D is the aperture of the telescope in inches. It is again an approximation, but it is somewhat useful, as in a 150mm aperture (5.9 inch), it predicts a minimum size of about 1.5 miles for t he smallest craterlet visible. I have done some work with high-resolution charts and found this guideline to be fairly accurate. Its predictions are much more realistic than a figure derived from Dawes limit. Smaller linear features such as rilles or tiny mounds can be detected in a given aperture at notably smaller sizes than craterlets due to their simpler diffraction structure, but seeing craterlets as the true pits they are requires a somewhat larger telescope. Clear skies to you.

#25 nirvanix

nirvanix

    Surveyor 1

  • -----
  • Posts: 1744
  • Joined: 07 Jun 2007
  • Loc: Saskatoon, SK

Posted 11 January 2014 - 06:24 PM

You're going deep Norme. Are you angling for a job at JPL :question:






Cloudy Nights LLC
Cloudy Nights Sponsor: Astronomics