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Petewp
super member
Reged: 12/04/06
Posts: 185
Loc: Connecticut - central western
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This post is an extension of the "8" resolving power on the moon" post. I thought a lot of things were covered by some pretty knowledgable people. My question is on CONTRAST or linear resoltuion...
This generally seems like "faux" resolving power. You know the kind - when an 80mm refractor shows a line where the ".5 arc sec cassinis is thats just clearly way out of its resolution envelope. Rills down to 1/10'th the angular resolution of a scope can be made out -or so i've read.
Point source resoltution was covered as well as overlapping diffraction patterns, but whats this "contrast" or "linear resolution" thing - and where does it begin? Said another way, whats the aspect ration of a line that makes it apparent just before it goes totally invisible? For example, does a rill or line on the moon need to be say, 10 times its width in length in order for it to appear? Theres got to be some kind of formula here. When is a line - not a line? When is the ratio great enough for it to show unbelievable resolution beyond the Dawes limit?
I ask these questions merely because linear resoltion is this muddled grey world - even mysterious with out the clean cut Rayleigh or Dawes to define it in any manner.
It is resolution, at a bargain basement price - but what outlines its parameters the way dawes and rayleigh outlines, indeed, explains theres?
Thanks guys.
If im being vague here, let me know.
Pete
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SEEKING LUNAR/PLANETARY NEW ENGLAND OBSERVING NIGHT - all welcome. Contact me at tidalid@aol.com
8" F/9 Parks Reflector
70mm TeleVue Ranger
Previous owner of Parks 10"F/5,
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EdZ
Professor EdZ
Reged: 02/15/02
Posts: 12565
Loc: Cumberland, R I , USA42N71.4W
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Well, I'm jumping forums here, but I'll give you part of the answer.
There is a post in the binocular forum called thin line resolution. You may read it for further discusion.
When a series of points are lined up, they overlap to form a long line. That line is not like point sorce resolution because the line crosses over so many mre receptors in the eye that the eye more easily receives the information.
Here's an example. this does not answer the question, it simply illustrates it.
Step back from your computer 20-30 feet and look at the following two lines
first this one
-
then look at this one
__________________
now obviously one is easier than the other to see. That is because th short line is more like a point source. it hits one receptor in the eye. But th long line crosses many receptors an hence you are able to see thin line resolution much finer than you might think IF all you consider is the thickness of the line. How about the length of the line. Is that smaller than point source resolution. No not at all, in fact it is much bigger. Not only that, but there is more to it. The activation of receptors is enhanced by surrounding receptors that are inhibited. But don't fully understand this.
edz
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Teach a kid something today. The feeling you'll get is one of life's greatest rewards.
member#21
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ronharper
Pooh-Bah
Reged: 02/14/06
Posts: 1005
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"I ask these questions merely because linear resoltion is this muddled grey world - even mysterious with out the clean cut Rayleigh or Dawes to define it in any manner.
It is resolution, at a bargain basement price - but what outlines its parameters the way dawes and rayleigh outlines, indeed, explains theres?"
Hi Pete,
You are right, there is more to seeing stuff than being able to resolve two thingies.
If you aren't familiar with it already, you ought to read up on the "contrast transfer function". This is a cool concept, and much more general than "resolution" rules of thumb, which usually are stated for perfect optics and neat, high-contrast point or line objects. It describes how a given optic muddies the image, as a function of spatial frequency and inherent contrast of the object.
Of course, the simplifications of perfect optics and simple objects does buy you something in the way of a common ground for discussion. Different quality optics, and differing objects, is the sticky stuff of the real world. You will be asking yourself what is the contrast transfer function of YOUR telescope, and what is the native spatial frequency and contrast of, say, the Cassini (how about Enke?) division. The popular book "Telescope Optics" by has an nice discussion, but there are plenty of others.
EdZ gives the flavor of the remaining complicated link in the chain, vision. Given the object's native properties, and the telescope transfer function's filtering of them, how will what's left look to the eye?
There ARE answers to these questions, but they require detailed knowledge of object, scope, and eyesight, and a lot of mathematical analysis, and for the amateur astromomer, are practically unattainable.
Lack of hard answers aside, I think you'll find the concept of contrast transfer very useful in this shades of grey kind of problem.
Ron
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Petewp
super member
Reged: 12/04/06
Posts: 185
Loc: Connecticut - central western
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It's interesting that this sort of thing oent have a standard rule of thumb like dawes. While Ed covered the linear issue well, and I do appreciate that, his answer is more inline [no pun] with visual acuity reasons than optical. Theres got to be some kind of aspect ratio where linear breaks down, or starts up for that matter. Said another way, how long does something need to be times its width for it to "activate" linear resolving power. Without knowing this Moores claim that rilles on the moon can be seen that are 1/10th the width of the actual angular resolution of a given scope. Without knowing the ratio of length/width, this is an obscure if not meaningless claim.
I think I'm going to have to experiment on this with my binoculars. Land based tests with a tele are just to impractical. Perhaps a human hair cut into shorter and shorter lengths at a given distance 75'? will solve the riddle - atleast for me anyway - lol - and my 8x42's.
Pete
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SEEKING LUNAR/PLANETARY NEW ENGLAND OBSERVING NIGHT - all welcome. Contact me at tidalid@aol.com
8" F/9 Parks Reflector
70mm TeleVue Ranger
Previous owner of Parks 10"F/5,
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photonovore
Moonatic
Reged: 12/24/04
Posts: 2472
Loc: tacoma wa
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Ron mentioned contrast transfer function (optically called modulation transfer function or MTF). This is key to *all* resolution as without sufficient contrast for differentiation there can be by definition no resolution of any kind whatsoever.
Although there have been volumes written about the MTF of telescopes, there seems a lack of information regarding how the eye's contrast transfer function interrelates with the telescopes modulation transfer function (at least regarding photopic vision--R.N. Clark did deal with scotopic vision in his book on visual contrast in the deep sky). Being curious about this i researched it sometime ago and wrote up what i learned here: Resolution, Magnification and Contrast: Their Interrelationships Explained In this referenced article I discuss the various resolution limits used for telescopes and microscopes and then go on to examine the way the eye interprets the contrast delivered at a telescope's focal plane. As a sort of bonus, the scientific basis underlying the 50X/inch magnification limit is explained and a link is provided to a game developed by UCBerkeley, Gabori Attack!, used for testing contrast sensitivity --so you can verify & quantify your own eyes capability to discern varying contrast.
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Mardi
4" achromat, ETX-70.
Whitepeak Lunar Observatory Website
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EdZ
Professor EdZ
Reged: 02/15/02
Posts: 12565
Loc: Cumberland, R I , USA42N71.4W
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That was a very good read Mardi.
edz
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Teach a kid something today. The feeling you'll get is one of life's greatest rewards.
member#21
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Petewp
super member
Reged: 12/04/06
Posts: 185
Loc: Connecticut - central western
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Mardi,
Where o' where did you find that good stuff. I believe in google... or any decent search engine kind of like a miniature version of God in that if you ask hard enough and enough times in the right ways sometimes you get what you want*. Well I tried and tried and really came up against a lot of nothing but darn it if you didnt hit the nail on the head. I think the greatest compliment you can give somebody on a message forum is to let them know it was printed out and added to my astronomy logbook - to say nothing of some good bedtime re-reading. The links on that page too are mint.
Ed again my thanks to you in your help. At the very bottom of this all I want to come up at least with a "formula" describing what ratio is needed to make a given threshold "line" begin to appear or disappear. Of course my simple math skills will make this very difficult "formula" contain a simple _=D/ . Such are the dizzying heights of my mathematical skills.
Pete
* I'm actually a wandering agnostic so my analogy is rather soft if not unrealistic.
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SEEKING LUNAR/PLANETARY NEW ENGLAND OBSERVING NIGHT - all welcome. Contact me at tidalid@aol.com
8" F/9 Parks Reflector
70mm TeleVue Ranger
Previous owner of Parks 10"F/5,
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Petewp
super member
Reged: 12/04/06
Posts: 185
Loc: Connecticut - central western
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I always did find it interesting and some what confusing when double stars would leave this sliver of black space between the airy disks that seemed to defy logic as the sliver was so very much finer than the width of the disk itself. Apparently this goes along the lines of the contrasting/linear thing. It would seem odd after all if the doubles just simply connected or disconnected once they came as close as one airy disk width. I have to give this a good thorough read tonight after work.
P.
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SEEKING LUNAR/PLANETARY NEW ENGLAND OBSERVING NIGHT - all welcome. Contact me at tidalid@aol.com
8" F/9 Parks Reflector
70mm TeleVue Ranger
Previous owner of Parks 10"F/5,
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