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photonovore
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Clavius , craterlets and resolution new
      #1197187 - 10/14/06 05:29 AM

Been busy imaging this lunation. Decent seeing and the high moon combined with crystal clear skies makes it a crime somehow not to... Among the images I've taken is this one of Clavius, a crater everyone seems to love. I liked the way it turned out so thought i'd share...



The resolution in the above image is less than what was available visually at 276x using binoviewers (at the time this image was taken this was ~0.3km better), but still this image serves to accurately illustrate what 2.5km resolution looks like.

Clavius is one of the best craters with which to judge the grade of resolution, and thus the state of seeing, you are getting during a session. Inspired by Chuck Wood's "calibrated" image of Mare Serenitatis, I have made several more of various areas of the Moon, using images courtesy of the Consolidated Lunar Atlas, with Clavious being the first of these:



(printable version available here.)

By identifying the size of craterlet you can see *as* a craterlet, you can both get an idea of the resolution floor you are getting as well as the limit to your seeing vis a vis that resolution. Basically, 1"arc resolution on the Moon would mean being able to resolve a craterlet as a pit rather than a spot at a minimum diameter of ~1.9km. A 1.5"arc seeing resolution floor would allow similiar resolution of craterlets ~2.8km. 2"arc seeing would limit resolution to those craterlets 3.7km in diameter and larger. Considering that this represents the best resolution through the best windows of clarity during a given level of seeing, the *median* seeing (or average median of the upper and lower range of the overall amplitude) will be ~0.5" arc more, i.e. 1" arc as described above would be astronomically considered to be 1.5"arc median seeing. Using a calibrated image, such as the above, helps an observer to quantify their seeing conditions in a consistent and repeatable way for records & future reference. (the first image above, with a resolution floor of ~2.5km represents what would be discernable visually at ~1.3"arc "best" seeing and the calibrated CLA image, with a resolution floor of ~2.1km represents detail visible in ~1.1"arc seeing. Median seeing values would be accordingly higher.)

Speaking of resolution, in order to obtain sufficient image scale for the eye to be able to resolve such small features, rather high magnifications must be used. Just to give you an idea of how ikmage scale works, a ~2km diameter craterlet magnified 250x will appear the same angular size as a spot 1/64 of an inch in diameter viewed at a distance of 12" with the naked eye. That is less than 1/2 a millimeter, less than the lead diameter of a fine point mechanical pencil! To obtain this image scale at the Rayleigh limit of resolution per any aperture, a magnification in the vicinity of 55x/inch must be used. As a practical matter, especially when viewing monocularly, magnifications of around 65x/inch are often necessary in order to actually realize the diffraction limited resolution capability of one's scope.

As an example, with my 5inch refractor, I can just differentiate a ~2.1km craterlet from a peak (tell a pit from a peak) using a magnification range of between 276 to 325x--and this during only the best of (my local) seeing conditions of course. As a image scale comparison, related to eyepiece image scale per magnification, the first image has an image scale, when viewed at a distance of one foot and as displayed on a 19" monitor at a screen resolution of 1024x768 (the most commonly used) that is equivalent to that scale as seen in the eyepiece at about 500x. Note how small a 2.6km craterlet appears at even that high of a magnification. The lunar surface is truly a high resolution playground!

So, what size craterlets, identifiable *as* crater forms, are you usually able to discern within Clavius? Knowing the answer to this, you can easily determine just how much (and how often) your scope's resolution is being influenced by your local seeing conditions. This knowledge, in turn, can help you estimate the resolution limitations of your observing site and thus help you answer such (potentially costly) questions such as what the seeing limited aperture actually is for your backyard.

--------------------
Mardi




4" achromat, ETX-70, 8"cat.
Whitepeak Lunar Observatory Website


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kraterkid
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Re: Clavius , craterlets and resolution new [Re: photonovore]
      #1197480 - 10/14/06 11:17 AM

Mardi thank you for these great images/calibration map and your excellent discussion of resolution. I'll be checking my seeing through this straight forward technique. Lately I've been quite impressed with the quality of the views, especially because of the high elevation (it topped out at 84 degrees on the 13th!) and I know there are bound to be several more days this month that will prove useful for such a test. Wonderful discussion!

--------------------
Rich



My CN Gallery




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LivingNDixie
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Re: Clavius , craterlets and resolution new [Re: kraterkid]
      #1197733 - 10/14/06 02:14 PM

Mardi,

I kinda confused... The numbers on the second Clavius are those diameters of the craters?

--------------------
Preston
Meade 10in LX200R GPS UHTC
blog (updated 02/15/2013)




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photonovore
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Re: Clavius , craterlets and resolution new [Re: LivingNDixie]
      #1197787 - 10/14/06 03:02 PM

Preston, yes, the white numbers indicate the diameter in kilometers, that's right.

--------------------
Mardi




4" achromat, ETX-70, 8"cat.
Whitepeak Lunar Observatory Website


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LivingNDixie
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Re: Clavius , craterlets and resolution new [Re: photonovore]
      #1197871 - 10/14/06 03:45 PM

So craterlet J is 1.3 km in diameter? It looks bigger then some of the ones that are in the 3-6km range. Should that be a 13?

--------------------
Preston
Meade 10in LX200R GPS UHTC
blog (updated 02/15/2013)




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photonovore
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Re: Clavius , craterlets and resolution new [Re: LivingNDixie]
      #1198274 - 10/14/06 08:37 PM

Preston, if you look at the full-scale image that i provided a link for, Clavius J is marked 11.3km in diameter. The first "1" didn't come through clearly on the jpeg i made to conform to the forum's image size limitations, that's all. Sorry for the confusion.

--------------------
Mardi




4" achromat, ETX-70, 8"cat.
Whitepeak Lunar Observatory Website


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Pasquale
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Re: Clavius , craterlets and resolution new [Re: photonovore]
      #1198285 - 10/14/06 08:50 PM

Hi Mardi, thanks for the info... I'll try this as soon as the moon comes back and the clouds disappear... Clavius is one of my favorites!

--------------------
Pasquale
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trainsktg
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Re: Clavius , craterlets and resolution new [Re: Pasquale]
      #1198287 - 10/14/06 08:52 PM

As always, excellent thread topic, Mardi.

Keith

--------------------
He was a good little monkey and always very curious.


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LivingNDixie
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Re: Clavius , craterlets and resolution new [Re: trainsktg]
      #1198317 - 10/14/06 09:12 PM

Thanks Mardi, I am going to try this chart out next time on Clavius!

--------------------
Preston
Meade 10in LX200R GPS UHTC
blog (updated 02/15/2013)




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reflector74
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Re: Clavius , craterlets and resolution new [Re: photonovore]
      #1198588 - 10/15/06 02:55 AM

Quote:

As an example, with my 5inch refractor, I can just differentiate a ~2.1km craterlet from a peak (tell a pit from a peak) using a magnification range of between 276 to 325x--and this during only the best of (my local) seeing conditions of course. As a image scale comparison, related to eyepiece image scale per magnification, the first image has an image scale, when viewed at a distance of one foot and as displayed on a 19" monitor at a screen resolution of 1024x768 (the most commonly used) that is equivalent to that scale as seen in the eyepiece at about 500x. Note how small a 2.6km craterlet appears at even that high of a magnification. The lunar surface is truly a high resolution playground!

So, what size craterlets, identifiable *as* crater forms, are you usually able to discern within Clavius? Knowing the answer to this, you can easily determine just how much (and how often) your scope's resolution is being influenced by your local seeing conditions. This knowledge, in turn, can help you estimate the resolution limitations of your observing site and thus help you answer such (potentially costly) questions such as what the seeing limited aperture actually is for your backyard.




Sorry, but your magnification range with only five inches of aperture yield a very, very small exit pupil, which to me is extremely uncomfortable to use. I do not need ~400x even through my 12" to discern what you are talking about. Resolution capability or potential is a function of the diameter of the aperture and the conditions that allow it.

--------------------
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photonovore
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Re: Clavius , craterlets and resolution new [Re: reflector74]
      #1199507 - 10/15/06 06:56 PM

"Resolution capability or potential is a function of the diameter of the aperture and the conditions that allow it."

That is, as I tried to show, only half the story for visual observation as the eye then becomes a part of the resolution equation as well-- and the eye has it's own resolution limitations, quite separate from those of the telescope.

In the ideal resolution case, that of a double star, the minimum separation required by the human eye has been shown again and again in observation reports to be ~180" apparant separation. To achieve this apparant separation in a 12" telescope, where the Rayleigh theoretical resolution is 0.45" arc, requires 400x magnification. (180/0.45)

A craterlet is not as ideal a resolution situation as a pair of point sources. A topographical positive or negative lunar feature (peak or crater respectively), in order to be resolved as such, requires separate resolution of the shadow and the highlight (set upon a neutral background), the spatial relationships of which to the direction of illumination determines what the feature actually is--peak or pit. This is a more demanding resolution situation upon the eye than that presented by a pair of white points upon a black background. This is why spatially resolving the shadow and highlight of a crater pit or peak requires a generally higher degree of image scale than that which suffices for point source resolution. From my own observations, I have found that for a craterform of 1"arc in diameter, enlargement to ~240"-300"arc apparant diameter is necessary in order to discern the relationship of shadow to highlight on a reliable basis. A quarter dollar coin viewed at a distance of 75feet is an example of this same angular size.

There's no need to take any of this on faith...you can measure and prove to yourself how image scale affects what you see in the eyepiece, in the perfect seeing conditions of your own home, no less!

A Cloudy night resolution experiment

Here's a cloudy night experiment anyone can do to determine how much image scale YOUR EYES need to be able to resolve a craterlet on the Moon!

First, find a lunar photo showing craterlets clearly resolved down to about 1mm in diameter, as measured on the actual photo. For best acuracy be sure and measure from the edge of the black shadow to the edge of the white highlight--the whole should fit between the 1mm tics on a good ruler. A magnifying glass helps pick out the craterlets that are just the right size. ( of For those who have Wood's Personal Moon the Ptolemaeus area picture on page 136 does nicely.)

Next, set the image up under bright room light so you can see it very clearly at distances up to about 10 feet away.

In the image of the Ptolemaeus area from Chuck Wood's book mentioned, Ptolemaeus D happens to measure about 1mm in diameter. Pefect! You can now calculate how much image scale you need to be able to resolve a crater as a craterform and not just a speck by noting the maximum distance from the image where Ptolemaeus D visually transitions from a detectable craterform to just a spot.

Here's the formula:

26.5mm= 1 minute of arc at 300 feet. (1.0472"@100yards).

So, 26.5/300 gives us the mm per arc minute equivalent at 1 foot, which is 0.088mm. Divide this result by 60 to get the mm equivalent in arcseconds at one foot; this is 0.0015mm. Now, divide 1mm by this number to get the apparant size in arc seconds of our 1mm diameter Ptolemaeus D craterlet at a 1 foot viewing distance: 1mm/0.00142mm is 666.6arc" at 1 foot.

Now we can calculate the arc seconds Ptolemaeus D will subtend at different viewing distances as follows:

1ft = 667"arc apparant diameter
2ft = 600"arc
3ft = 533"
4ft = 467"
5ft = 400"
6ft = 333"
7ft = 267"
8ft = 200"
9ft = 133"
10 feet = 66.7"arc

The distance where Ptolemaeus D becomes just a spot is your image scale floor for 1" arc lunar surface resolution of basic landforms. It also indicates the magnification you need to use to access this level of resolution.

For example, say you find that further out than about 7 feet you can't tell Ptolemaeus D is a crater any longer--it begins to appear as just a spot instead. The image scale at 7 feet is 267"arc. So, for you to be able to resolve a craterlet at 1" arc diameter (about 1.9km on the moon) you will need to use at least 267x magnification. Anything less and you won't get resolution. (and remember--our experiment is done under *perfect* seeing conditions! But our real life observations unfortunately never are... )

There are all kinds of interesting experiments you can conduct with images scaled to apparant angular measures like this. For example, do the above experiment with just *one* eye instead of two-- and compare the results. You'll likely find your minimum distance increases because monocular acuity is usually considerably less than binocular acuity. (And here lies the visual resolution advantage of binoviewers.)

Also, don't be afraid to try 1 millimeter craterlets found in other images. The image of Rima Ariadaeus on page 200 of Rukl's offers a selection of 1mm diameter craters to test with, too. Lunar Orbiter images also work great for this experiment.

--------------------
Mardi




4" achromat, ETX-70, 8"cat.
Whitepeak Lunar Observatory Website


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reflector74
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Re: Clavius , craterlets and resolution new [Re: photonovore]
      #1201537 - 10/16/06 10:19 PM

To be honest, I don't pick apart matters like these while I enjoy high res visual observing of the lunar surface.

Now if I were to get into astro imaging, I would see the necessity to get mighty technical. I am a visual observer, needing to witness the views in real time. Can't wait for my 16" to "show me the light" on the Moon.

--------------------
Two eyes and a preference to use both


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photonovore
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Re: Clavius , craterlets and resolution new [Re: reflector74]
      #1202732 - 10/17/06 03:00 PM

Well, I too am primarily a visual observer but I also happen to understand imaging as well. And in both, image scale plays a crucial role in resolution obtained.

As far as relative complexity goes, the optical aspects of visual observation are in fact much more complex than those of imaging, which is, in reality, threefold more basic than the former case. In imaging, the optical train ends at the objective's image plane (the most basic optical level), while the visual optical train continues on to the exit pupil and thence through the eye lens before finally focusing upon the retina.

Most imagers I know would agree that most of the complexity (and creativity) of their activity lies in the post-processing rather than in the taking of an image, which latter is actually the most straightforward part of the process.

Knowing the "why" and "how" of a process allows objective determinations of both capabilites and limitations of that process; the alternative is reliance upon baseless subjective opinion for such estimations.

Knowing the why & how is also useful in a practical way; for example a lunar imager will know that the reason the 1km threshold in resolution cannot be broken by an 8" instrument is because of optical limitations, not for lack of trying or skill--so no time need be wasted trying to do what is not in reality even possible. The imager simply knows that to obtain images with better resolution, using a larger aperture is the only course available. In a similiar vein, a visual observer will waste no time seeking out Rima Suess as they know that this feature is not visully detectable in any aperture--nor will they be subject to mistake this undetectable feature for the detectable but discreet mare ridge which happens to run parallel to it.

The "I know what i can see" school of thought is certainly much more populous than the "i know why I know what i can see" school and more's the pity...as the latter invitiably contributes to the process of converting mistaken assumptions into popular myth and then (unfortunately for all) into "fact"--which is further sustained though a continued lack of critical examination.

The particular bit of "conventional wisdom" I have attempted to dispell here is that around 30x/inch is all it should ever take to see all the detail any aperture will offer on a planetary target and that any more magnification is inevitably "empty". In reality it is poor seeing which "empties" higher magnifications, not the optics of a decently made telescope, yet--this is rarely mentioned as the controlling proviso. Also not mentioned is that 30x/inch offers insufficient image scale to even be able to *see* the resoltuion limit of any aperture, regardless of how excellent the seeing may be. Two fatal flaws are thus revealed, exposing the 30x/inch rule as nothing but misinformation.

Escape from the tethers of such errant 'conventional wisdom' is one of the rewards of making an effort to actually understand why & how one sees what one does. Understanding how your telescope works in concert with how your eyes work also helps to put the brakes on what I call 'wishful observing'; that is 'seeing' what cannot possibly be seen, a distressingly umbiquitous problem common to those of the "I know what i see" school. From such understanding we can know that expecting resolution of a 2km craterlet at 180x (or 30x/inch for a 6" scope) is simply wishful thinking, as no human eye has yet evolved that is possessed of such levels of acuity. Likewise we know that a 12" operating at 400x offers no higher level of angular resolution than that represented by the limits of an 8" aperture. We know that to acccess the resolution limits of the larger aperture, a much larger image scale is required and not merely desireable.

We visual observers are all subject to wishful observing to one extent or another--but it's part of the development of an observing skillset to mitigate these errors as much as possible. "Picking apart these matters" can only help increase the accuracy of one's visual observations while decreasing error. This principle applies equally throughout visual astronomy, in the deep sky, upon double stars or when observing the Moon and planets.

Of course if the aesthetic experience of observing is one's primary interest, then this level of examination can (and probably should) be ignored.

--------------------
Mardi




4" achromat, ETX-70, 8"cat.
Whitepeak Lunar Observatory Website


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trainsktg
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Re: Clavius , craterlets and resolution new [Re: photonovore]
      #1203278 - 10/17/06 07:56 PM

Quote:

Of course if the aesthetic experience of observing is one's primary interest, then this level of examination can (and probably should) be ignored.




An excellent point. We take from this hobby what we wish, some to test themselves and their equipment, others to receive the pure enjoyment of sitting at the eyepiece. Slightly off topic, but pertinent to the topic (I think)...years ago my dad and a friend tested his 5.5" f11 semi-apo's resolution versus a 3.5" Questar's. They made a series of masks thet reduced the aperture of the refractor to 4", 3.5", 3.25" and 3" in an effort to see what equivalent unobstructed aperture the Questar was operating at. By using the NBS Circular 533 Lens Resolution Charts, they determined that the Questar's resolution was equivalent to that of a 3.25" unobstructed system. This was later confirmed by optical tests at Davro and theoretical calculations found in published material. Most people wouldn't perform these tests, but for those of us who prefer to understand the physics behind the views, performing empirical tests and reading technical literature are essential.

Keith

--------------------
He was a good little monkey and always very curious.


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trainsktg
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Re: Clavius , craterlets and resolution new [Re: trainsktg]
      #1204592 - 10/18/06 02:44 PM

More of a compliment than continuing the thread topic, but...My Dad's been an almost exclusive lunar and planetary observer for 50 years. That said, I'm pretty sure from reviewing Mardi's website over the last six months that she's surpassed his knowledge of fine lunar topography by a wide margin...and that's saying alot. For those who haven't checked it out, its a great site to read.





Keith (This unsolicited opinion is my own and does not necessarily reflect that of CN, its administrators, moderators, affiliates, familes, their pets or neighborhood grocer.)

--------------------
He was a good little monkey and always very curious.


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Matt Looby
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Re: Clavius , craterlets and resolution [Re: trainsktg]
      #1220899 - 10/27/06 07:11 PM

Hello Group,

Just my two cents regarding visual resolution and magnifications.
It all depends on what one considers an object to be resolved.
To me resolution means being able to discern the greatest amount of tonal value within the object that I am observing.
On a the popular gray scale used by artists, etc. that range
is 1 (white) to 10 (black). If all these values are distinguished on the subject being observed, one could proudly say they are observing at the limit of their vision.
But to see these 10 values in a subject, the human eye requires the proper amount of light.
Unfortunately, as the magnification is stepped up the eye's exit pupil decreases. As this occurs the eye's range to distinguish tonal values is severly limited, this is a function of light loss and no increase magnification can somehow compensate to recoup this loss of tonal resolution.
What happens when we pump up the magnifcation to a point where the exit pupil falls below .8mm is that the tonal values now become blurred and the eye now sees the values in terms of blocks of values, large dark swaths and light swaths of value are seen and the view is much less complex, and no longer "resolved" One could keep increasing the magnification and the image will increasingly less resolved. Experienced visual observers, renderers use higher powers to more easily see the more obvious tonal values. This helps to loosely define the image and then it's time to back down the magnification to "home in" on the critical stuff.

I generally use a low power to find the target, and then use high magnifcation to see the subject in larger tonal swaths.
Then I back down to an optimal magnification in order to find all the detail at the limit of my poor vision.

There has been way too much discussion and much written
about the so called 50x-60x/inch rule and virtually no
talk about the most important element- proper and sensible use of exit pupil size.

One very easy way to start thinking about the importance of exit pupil is to walk outside and look at a stand of trees, a row of buildings, etc. Look, now squint your eyes (shut down the light) see how the eye no longer distiguishes as many tonal values? Now really squint, almost with eye lids close shut, see the further loos of value, see the black the white? The eye is always the first limiting factor to resolution....


Thanks,

Matt

--------------------
CN GALLERY


























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