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msc
sage
Reged: 08/10/06
Posts: 263
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Ed, this is approaching my limits of optical wizardry..... and i have already put in an 14 hr day.
The method I used, when changing magnification, the f stop changes, which continues to change the diffraction limit. Not being very familar with your method, I am not sure you are incorporating this the same way, but it appears to be reflected in the magnifcation ....
but regardless, what is your conclusion regarding what I was presenting?
I can honestly say, when I test the BV/scope under this scenario, the results relate very well to the formula results. I used the 100 lp/mm projected resolution as equal to 3 lp/mm viewed at 10" as the cross check. 3 lp/mm on a reflected target is sharp when viewed at 10". Although some humans can resolve up to 6 lp/mm (200 lp/mm projected) on a target at 10" viewing distance. I can not, and when the projected rez increased over 100 lp/mm, I really can not discern any improvements as its above my resolution limit....however, when I fall below 100 lp/mm projected on the retinal with the BV, sharpness falls off, just like it does when I veiw 2 lp/mm on print, then 1 lp/mm on print, etc. hence why I feel this formula is very consistent with reflected targets using the unaided eye at 10"... so it seems very validated.
of course with optics, I will never rule out being fooled.... so how do you assess this?
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EdZ
Professor EdZ
Reged: 02/15/02
Posts: 12789
Loc: Cumberland, R I , USA42N71.4W
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This discussion started out as a comparison of binoculars to binoviewers, several aspects, but in this particular instance regarding resolution. And somewhere along the line you stopped talking about the resolution of the scope/BV or binocular and started talking about the resolution of the retina. You are using a formula developed for determining resolution at the film plane to show resolution on the rods and cones of tthe retina. Whereas I have continued to talk in terms of resolution of the instrument.
This difficulty of understanding represents just another potentially widely-varying expression in terms of resolution in how someone can be discussing instruments using terms that don't relate.
Several months ago we went thru a period of discussions that helped clear up some misunderstandings of the terms used for measuring line pair resolution using USAF LP charts. It was interesting then, because it got to the bottom of why people believe, when they read elsewhere in print, that they can see 60 arcseconds resolution. There are few, if any, instances in anything astronomical where people can see to a resolution of 60 arcseconds, which is another discussion altogether and I won't digress to that here. But we have had people quoting resolution values in terms of snellen letters, point sources, line pairs, lines and now retinal resolution. They all represent different things and cannot be used interchangably.
In fact lp/mm retinal resolution is already a conversion and is not even actually lp/mm. It is converted from rod/cone density/mm to a term people recognize, lp/mm. To use this term in discussions in reference to telescopic resolution can be very confusing.
You are using a term commonly used for calculating resolution at the image plane, or in this case the retina of the eye. However you are using those values to talk in terms of resolution of the telescope. I've got to admit, we seldom if ever hear people talk of telescopic resolution in terms of lp/mm at the retina. The difficulty arises here in that the values are not interchangable. Just like snellen, lines/mm and line pairs/mm, there can be found a conversion between the values, but you cannot use the values of one to reperesent the resolution of the other.
You mentioned 100 lp/mm projected on the retina as equal to 3 lp/mm resolved at 10" by the scope. I've been discussing all along the appropriate values for measuring the resolution of the scope. I have not been discussing resolution of the eye. Actually, I been studying and writing about resolution for about 5 years. This is the first time I've ever engaged someone in discussing resolution of a telescope who is using terms of lp/mm at the retina.
Maybe a few things would help here.
We generally do not talk about resolution of a telescope in any terms that are related to resolution measured at the image plane from an object seen at 10". That is not to say you cannot discuss retinal resolution values. They are simply seldom ever heard when discussing telescopic resolution. We do not refer to the values of lp/mm at the retina as the resolution of the telescope.
Typically, when referring to resolution in terms of lp/mm it would be required to state the distance to target, since obviously resolution would change with distance. That is why, when you wish to compare the resolution of scopes or binocuars, measure the angular resolution directly and compare. This incorporates the distance factor.
Although lp/mm can be used to measure resolution of a scope, results are more often stated in angular resolution. This is the far more common term for resolution of telescopes that nearly everyone understands.
edz
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photonovore
Moonatic
Reged: 12/24/04
Posts: 2488
Loc: tacoma wa
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Regarding stereopsis, there can be no advantage, contributing to gains inherent in binocular summation upon acuity, from using a binocular telescope instead of BVers in astronomical viewing (infinity) as there is no additional information (disparity) between the binocular images present than there is in the images a BV produces from a single telescope pupil. The situation is essentially the same regarding any of steropsis' effects upon summation. Even in the settings where summation's acuity gains have been clinically measured in the first place, any effects (pro or con) of image disparity (stereopsis) are eliminated-- as the target used to quantify summation gains (eye chart whatever) is also two dimentional.
So the *sole* factor remaining which has the potential to affect summation acuity gain differences between a binocular telescope and a binocular viewer is difference between the illumination levels within the exit pupils produced by each viewing method. The binocular telescope will deliver more illumination to each exit pupil than the BVer working off a single telescopic pupil (all else constrained at equivalency). But this must be qualified; such increased exit pupil illumination does not begin to positively affect acuity until gains result in illumination rising above ~10 millilamberts. (A single sixth mag star comes in at ~200millilamberts) Obviously the additional illumination of the exit pupil that binocular telescopes provide over BVers is not contributive to increased acuity, such that it negatively affects the positive acuity gains resultant from binocular summation, at any target illuminations other than those considerably dimmer than a sixth magnitude equivalent.
Regarding the reality of the false stereoptic effect present in viewing two dimentional images with binocular vision, this is certainly real enough. For example, in viewing lunar photos of crater fields etc, (even those not particularly sharp at all...) a commonly reported effect is that such images can appear to arbitrarily reverse their "depth" perspective, becoming not a field of negative elevation features but one of positive elevation instead (craters into domes). This depth relationship reversal would not be possible if stereoptic effect could not be simulated by the brain when viewing two-dimentional images. But how this relates to any gain in interpretive value is not clear, especially since (as evidenced by the above scenario) the brain can be fooled into a complete false reversal of perspective reality!
I can also confirm the effect sharpness can have in initiating a depth response in a two dimentional image--the first time I watched a high quality DVD vid on a computer screen I recall vividly noticing the "three dimentional" effect being extant in the images--while that effect was absent in other (lower quality) computer video i had seen previously.
At any rate it is clear that all depth perception as experienced upon any astronoomical object is a "simulateed effect" regardless of the type of optical instrument used. Such effect, when seen, is the result of binocular viewing alone, and not the related to the presence or absence of a separate telescope for each eye.
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Anyway, this tiny bit of depth in a single eye view I believe is created by the ultra sharpness of the optics. With the optics adding contrast to the image and edge sharpness, with a low enough pupil diameter, say 2mm, (which is the perfect balance between the eyes abberations vs. pupil diffraction),
This seems to indicate that you are still misapplying the effects of naked eye pupil diffraction to telescopic diffraction. Pupil diffraction has no effect upon a telescopicly generated image as expressed within the exit pupil. Let me explain what is going on.
The variable aperture pupil) of the unaided eye has two efffects upon image quality (point spread function): that induced by diffraction and that induced by eyelens aberrations. These effects are ilustrated separately ibelow. First the effects of pupil diameter (aperture) upon diffraction:
Notice how reoslution increases with the pupil aperture. This would imply that the sharpest vision (highest resoluution) would be obtained at the largest opupil apertures---but this is most certainly not the case. the next graphic illustrates the effect of eyelens aberrations upon the above diffraction inherencies:
One can see, for the unaided eye, why exactly a 2-3mm pupil size produces the best quality image. It represents the pupil aperture where the smallest psf in combination with a point of acceptable eyelens aberration is found. This is the aperture of the diffraction limited unaided eye.
Now here is the crucial point: When we use a telescope to produce the image the eye examines, we have effectively replaced the pupil aperture with the exit pupil of the telescope, which in turn derives it's informational content--psf from the telescopic pupil (objective lens/mirror) and aberration level from that and the intervening optics. The only diffraction effects in this artificially produced telescopic pupil are derived from the telescope itself and nothing from the eye pupil aperture contributes--regardless of the size relationship between the exit pupil and the eye pupil. In other words, the application of a telescope to the eye replaces the eye pupil's diffraction characteristics (as illustrated in the first image) with the much smaller static diffraction pattern contained within the exit pupil of the telescope. The only effect the eye pupil can have upon the exit pupil is to reduce the telescopic aperutre through reduction of the exit pupil aperture--and this only in the case of the eye pupil being smaller than the exit pupil. But this rarely happens in astronomical telescope useage as observing is done in the dark at wideopen eye pupil apertures that exceed almost any conceivable telescopic exit pupil. Only at very low magnifications (and large exit pupils) can the eye pupil posssibly have any reductive effect upon the telescopic aperture.
Now, with the eye's diffraction replaced by the telescope's diffraction, all that remains to affect the image quality (as delivered to the retina) pro or con is the aberrations of the eye lens--which happen to be dependant upon how much of the eye lens is used to form the image. As the second graphic above illustrates, the less of the eyelens used, the less the aberration level and the better the image quality delivered to the retina. Specifically, the least aberrated (best corrected) condition is when only 1mm or less of the eyelens is utilized in image formation. The eyelens, unaffected by it's own diffraction (as that has been replaced by the telescope's remember) delivers a strehl of close to 1.0 when only 1mm or less of it is used, 0.8 strehl when 2-3mm of it is used to form an image and this decreases with increasing levels of aberration to 0.5strehl when 6mm of the eyelens is used to form an image. Since the size of the exit pupil of the telescope controls how much of the eyelens is used in image formation upon the retina, it is apparant how important the exit pupil diameter is vis a vis the level of image quality the eye is able to reinterpret from the telescopic image plane (exit pupil) to the retina.
What this means in practice is that the highest quality retinal image will be formed using exit pupils of 1mm or less and NOT at 2-3mm as is the case when the eye pupil controls diffraction effects (which latter is the case ONLY when the eye form images unaided by external optics--like a telescope or binocular or microscope.)
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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: 12789
Loc: Cumberland, R I , USA42N71.4W
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Quote:
What this means in practice is that the highest quality retinal image will be formed using exit pupils of 1mm or less and NOT at 2-3mm as is the case when the eye pupil controls diffraction effects (which latter is the case ONLY when the eye form images unaided by external optics--like a telescope or binocular or microscope.)
This agrees with what I experience in observations. I find optimum brightness of images at larger exit pupils, but I find maximum resolution of planetary detail at 125x to 150x in my 5" scope and 150x to 200x in my 6" scope. Both instances generate exit pupils of about 1mm to 0.8mm. I find maximum resolution of bright extended objects at exit pupils about 1.25mm to 1.0mm. I find that resolution of faint extended objects seems much more dependant on image brightness and angular size of object.
As far as optimum resolution for point source resolution, I find optimum varies considerably with the amount of light present in the image, but it can be 100x to 125x in an 80mm scope, 175x to 200x in a 5" scope and 200x to 300x in a 6" scope. I have found that optimum resolution generally falss in a range close to 40x per inch however, I have found also that I cannot achieve the resolution limits of my scopes without employing magnification at a rate of approx 50x to 60x and sometimes even 70x per inch.
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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msc
sage
Reged: 08/10/06
Posts: 263
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Ed, I was in the processing of preparing a lengthy response to your post, then Photons post came in, and I basically *Word deleted by the CN gnaughties gnomes*-canned my long response in lieu of his post.... as I feel like he is presenting very critical information that must be hashed out first. I wanted to comprehend the math resolution vs. real world resolution. Thank you Photon, where have you been? We need you! :-)
To achieve the best resolution on the retina, Photon has made a strong case for 1mm exit pupil diameters. (when eye pupil diam. is larger) I have no argument against his excellent contribution...but, I as I see it, we have a set of competing variables here for max. resolution, i.e. diffraction vs. exit pupil.....
To achieve 1mm exit pupils in a scope, the aperture diam and magnification must be equal. exit pupil = apt/magnification. Also expressed as....the same magnification per apt. inch.
At any given magnification/inch, the f stop (f ratio in Scope talk) of the entire optical train (including the eye fl) will always be equal.
Since apt. diffraction is governed by 1500/f stop, the resolution projected will always be identical when f stops are equal.
So to achieve the desired 1mm exit pupil, the eye will always project 88 lp/mm to to the retina. 2mm exit pupil = 2x this, or 176 lp/mm. (pretty close to the desired 200 lp/mm, - the max. the retina can resolve)
There is NO way you can deliver a diffraction limited projected resolution (200 lp/mm) to the retina, while still using the eyes sharpest seeing zone of 1mm exit pupil. Therefore, I am suggesting there is two competing variables here. To reiterate, to utilize the eyes best zone of sharpness, at 1mm exit pupil, you force the optics to project diffraction limited views down to 88 lp/mm, which is more than half of what I am proposing the retina can resolve.
So the million dollar question is..... which factor is more significant? Diffraction limiting the projection by optimizing the exit pupil size to allow the eye system to work in its most efficient zone of sharpness at 1mm exit pupil, OR, projecting a ~ 2x larger exit pupil to achieve a diffraction free projection on the retina. Fair question, right?
I went and rechecked my scope today, viewed a close subject.....and...
at 2mm exit pupil the view was 2x sharper than 1x exit pupil (half the EP fl)
The diffraction limited projected resolution is always 88 lp/mm * exit pupil diam. So once again, the 176 lp/mm is delivering what I perceive as 2x sharper view (although its hard to quantify this), which demonstrates with my eye/brain, any gains of using the sweet spot of the eye lens's sweet spot (1mm exit pupil) is trumped by adding more resolution, assuming you have not exceeded the retinas ability to resolve.
From this, I would propose, for terrestrial viewing with no seeing issues, 2 - 2.5 mm exit pupils represent the BEST compromise between the eyes sweet spot of sharpness (as it relates to exit pupil size) and the diffraction limited resolution imposed by using smaller exit pupils. Now, I am curious, if anyone reading this gets their scope out and views something close, please report your findings on this, i.e. 1mm exit pupil vs. 2mm exit pupil, which is sharper?
Ed, I realize you reported the sharpest you seem to experience is at 1mm exit pupils, but your comments were astro based, which IMO is a different animal. Can you run this experiment with viewing something close, the differences I believe will be VERY obvious. I am curious of your findings. I feel I have average eyes, not great as I am getting older, but certainly not poor.
Of course, one explanation if others see a cleaner view at 1mm exit pupil, it could be their eyes have limited ability to resolve, which means, they are benefiting from the eyes sweet spot of 1 mm exit pupil....yet at 2mm exit pupil, they can not resolve the extra resolution and might suffer somewhat from the eyes lenses degrading the view a bit.
I am very curious of any input, we may be narrowing in on something interesting here...but more so for terrestrial again. Here is where I think a gain might be........ the BV will cause larger eye pupil diam vs. binocs, (false exit pupils) as each eye is receiving half the light... these larger pupils allow for easier viewing as the exit pupil is further inside the eye pupil diam, preventing black outs.... just a comfort thing.
But anyway, I am more curious about others who run this test or comment on my methodology here...
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EdZ
Professor EdZ
Reged: 02/15/02
Posts: 12789
Loc: Cumberland, R I , USA42N71.4W
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Using a WO Megrez 80 under the same testing conditions as a dozen different binoculars, I realized gains in resolution up to the limit of testing, 100x. That is a 0.8mm exit pupil.
From the Best Of Links see
Resolution Testing and Res Charts
For these test results see
Resolution Testing w/USAF Charts
This is the posted results found in
Resolution Testing Using 1951 USAF Line Pair Charts
A Williams Optics Megrez 80 SD II scope was used on the same USAF 1951 chart in the same type of daylight conditions. From the binocular results above, normal resolution values were obtained in a range of 97 arcsec apparent, maybe down to 90 or so. The Megrez 80mm scope has a Rayleigh Resolution limit of 1.7 arcsec. It was tested previously and I found I could just barely suspect seeing Lambda Ophiucus (1.69 arcsec) as cleanly split. It took 250x magnification to see stars split at 1.7 arcsec. However the same scope when used to observe e1 e2 Lyra could see e2 Lyra, which is 2.35 arcseconds cleanly split at 67x for an apparent separation of 157 arcseconds, within a few percent of all the best apparent readings I get on stars with any type of instrument, regardless of how big.
Results from the USAF Line Pairs Test
Megrez at
19x80 could see 4.83 arcsec for 92 arcsec apparent, suspected 82.
33x80 could see 3.1 arcsec for 101 arcsec, suspected 90.
40x80 could see 2.43 arcsec for 97 arcsec, but not any less.
These results were very similar to all the binoculars tested.
Below these values, I began to approach the Rayleigh Limit, and as expected it takes higher magnification to see the resolution. In all cases of resolution testing, as you approach the difraction limit, you will find it requires higher magnification to see the resolution than normal acuity might indicate for objects with wider separations. So, I was expecting magnifications higher than 97 arcsec apparent separations. That is what the results did show.
With the Megrez 80,
at 67x80, I could see 1.91 arcsec for apparent separation of 127 arcsec.
at 83x80, I could see 1.71 arcsec for an apparent 142 arcsec.
at 100x80, I could see 1.52 arcsec barely split for an apparent separation of 152 arcseconds.
edz
FWIW, I'm also a double star observer, and have tested a number of scopes and binoculars and found that in all cases, the double star resolution and the line pairs resolution correlates. I pointed that out in one of my posts up above. I have tested other scopes using both doubles and these charts and have found the same results. No need duplicting information, the trend is the same.
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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msc
sage
Reged: 08/10/06
Posts: 263
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Ed, very extensive testing, quite a big line up....
I think I clearly understand how we are missing each other....
There is a big difference between resolving a small target by adding magnfication vs. seeing diffraction effects.
I think we are comparing different goals here. In your case, you are trying to resolve targets.... i.e. can you see it? Can you see what it is? Can you resolve it? Etc. When trying to resolve something too small to see, adding magnfication will help you acheive this goal, even when diffraction is degrading the view, I certainly will not dispute this, its the foundation of astro viewing.
The magnication is providing more benefits vs. the continual added apt. diffraction being introduced - as magnification increases. I fully agree with this when the only goal is to resolve something too small to see. Of course this is often the case in astro, but not terrestrial.
When comparing terrestial views, and you are not trying to resolve something 20 miles away ( in which case, there will be more seeing issues to mute this discussion), or relatively close, but very tiny (an ant at 75 ft?)... then going back to my close focus examples, I think this is where we differ.
For example, as I mentioned in my previous post...when I view at the projected 200 lp/mm through the BV, I am not neccessarily trying to resolve a tiny target.... i am simply looking at the view, such as wildlife or birding. Now, if the bird is far enough away, I may need the extra magnfication to see it, and just live with the diffraction being introduced....
One of the points of this BV / Binoc comparison was demonstrating larger apt. diam, allows for greater magnfication of a viewing system, before the view becomes diffraction limited. I still stand by this and I have not read anything to dispute this finding. Of course with astro or long distance terrestial seeing issues, all this can be negated.
So i think all along, we were comparing different objectives here. When you describe using more magnification as your scope apt increases, you are essential supporting my cause... and in your case, the seeing issues are so great, diffraction may not be as noticeable till you really dig deeper into the diffraction zone... (by continually increasing the magnification).
Does this make sense ? I have tested this with 4 people now, and everyone clearly sees the diffraction effects as the levels I described so many times above.
To clearly see this, if you focus on anything, such as a brick wall at 50 ft., 5.5x/inch mangification. With good optics, this will represent a diffraction free view.
Now move to 100 ft at 11x/inch magnification. The view should be identical, still diffraction free. this demonstrates you can add magnfication with no degredation of the view following the formula and methodology I presented.
Now move to 200ft and use 22x / inch magnification. Now these two views should be identical if there was NO apt. diffraction degrading the view, but I propose you will see a much poorer view, 2x worse, less contrast, edge sharpness, etc.
If you really want to watch the image degrade, move to 400 ft with 44x / inch and notice 2x more degredation.
using a good digital camera, you can record this well....
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EdZ
Professor EdZ
Reged: 02/15/02
Posts: 12789
Loc: Cumberland, R I , USA42N71.4W
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Quote:
There is a big difference between resolving a small target by adding magnfication vs. seeing diffraction effects.
I think I clearly understand how we are missing each other.
FWIW, resolving a small target IS how we measure diffraction effects. But if you are convinced you understand how we are missing each other, well then, suit yourself. I (and others) have provided you with all the information at our disposal. Use it or don't. It's yours for the taking.
thanks for the discussion
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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msc
sage
Reged: 08/10/06
Posts: 263
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ED, thanks for the kind response.
I have been testing lenses for 20 years now... and yes, aperture diffraction is "ONE" factor in a lenses ability to resolve a target, thank you for clarifying such. Typically, most lenses have up to 5 different forms of diffraction that can degrade the image, aperture diffraction being ONE of them...and often the one with the most predictable outcome, but not always.
In Astro, quite often the goal is what you preach...., magnify, magnify, magnify...... evaluating when diffraction effects can no longer allow gains of magnfication - this is often the benchmark of astro optical systems.......
I should have mentioned, my discussion revolved around terrestrial viewing at close distances.... Oh, I just went back and checked, I did mention it 9x, sorry.... anyway.....
When using a viewing instrument for birding or wildlife, the user is often less concerned about resolving a target vs. the quality of the overall view. This falls between what you preach....i.e. absolute max. resolving capable before further magnification gains are nullified by diffraction effects, AND, the amount of aperture diffraction acceptable to the viewer for an enjoyable view. Birders are not interested in resolving test targets with their viewing instruments. However, based on the tone of your response, this doesn't fit your concept or understanding of resolution, so it's probably not valid. I will alter my mindset accordingly.
Optics is a mixed bag.... I work with optical engineers on a regular basis and often see them get tripped up over many issues - the field is that complex, and the final chapters have not been written on many optical concepts as well as the human eye. Many succesful lens designs I have contributed on, were almost always a result of much callaboration, as optics is so complex, it's rare one person holds all the cards...... hence why I always remain open minded in optics discusions, and I can see you too remain open minded, right?
Anyway, hopefully some of this information will assist you in understanding the broad range of applications of optical issues. But, that is for you to decide.....
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EdZ
Professor EdZ
Reged: 02/15/02
Posts: 12789
Loc: Cumberland, R I , USA42N71.4W
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Quote:
I went and rechecked my scope today, viewed a close subject.....and...
at 2mm exit pupil the view was 2x sharper than 1x exit pupil (half the EP fl)
The diffraction limited projected resolution is always 88 lp/mm * exit pupil diam. So once again, the 176 lp/mm is delivering what I perceive as 2x sharper view (although its hard to quantify this), which demonstrates with my eye/brain, any gains of using the sweet spot of the eye lens's sweet spot (1mm exit pupil) is trumped by adding more resolution, assuming you have not exceeded the retinas ability to resolve.
From this, I would propose, for terrestrial viewing with no seeing issues, 2 - 2.5 mm exit pupils represent the BEST compromise between the eyes sweet spot of sharpness (as it relates to exit pupil size) and the diffraction limited resolution imposed by using smaller exit pupils. Now, I am curious, if anyone reading this gets their scope out and views something close, please report your findings on this, i.e. 1mm exit pupil vs. 2mm exit pupil, which is sharper?
Ed, I realize you reported the sharpest you seem to experience is at 1mm exit pupils, but your comments were astro based, which IMO is a different animal. Can you run this experiment with viewing something close, the differences I believe will be VERY obvious. I am curious of your findings.
I did just exactly that. Since I already had a number of readings on the Megrez 80, I filled in all the gaps with additional readings.
First let me clarify a few things:
These tests represent daylight observations. I have shown a considerable amount of information regarding resolution testing in daylight. These results are an extension of that work.
These observations were all obtained using a verified USAF 1951 Line Pairs resolution chart at a distance of 125 feet. This is a widely accepted means of measuring resolution of optical instruments.
Prior to observing, I tested my pupils in a fully lit mirror. Pupil diameter is 4mm under 200 watts of indirect light. Therefore, it is assumed eye pupil is always equal to or larger than exit pupil in these tests.
You will see three values plotted for each eyepiece (each exit pupil). The "barely" value represents what I would refer to as the limit of clean resolution for that exit pupil. The "easy" value is just that, a reading that was easy and noticed quickly. It is the best reading that could be easily noticed, in all cases approx 20% to 30% larger than the finest resolved (the "barely" reading) at that exit pupil. I have some other values recorded such as "suspected" or "horz only", none of those are included here.
The "easy" reading is one I would consider representative of extended object terrestrial viewing. All readings larger than that were seen very large and very sharp and were too large to use as a baseline reading. IMO, selecting any arbitrarily chosen larger values would produce convoluted results, since it would be near impossible to maintain any consistancy.
Target distance was kept constant. However, for comparing any observations, halving the diameter of exit pupil ( which doubles magnification) gives the same result as observing the same target at same magnification and doubling distance to target. But that is not really a factor here.
About the results:
The results show a fairly consistent slope of increasing resolution from a 4mm exit pupil down to about a 1.5mm to 1.25mm exit pupil. As expected, as the resolution nears the diffraction limit, the slope showing the rate of change in resolution begins to flatten. Resolution increases continue, but at a slower rate of change.
There are a couple blips in the data. In the overall scheme of things, they do not skew the data.
Several readings provide exactly, or near exactly one half the diameter exit pupil. There are significant findings with respect to halving the exit pupil.
There was no point where any exit pupil half the size of a larger would show twice as poor a resolution.
Down to exit pupils of 1mm, there is never more than about a 25%-30% drop in resolution as compared to an exit pupil double the size. Meaning this, if a 3mm exit pupil can provide a resolution of 4 arcseconds, then the findings show that a 1.5mm exit pupil can show 4arcsec/2 x (1.25 or 1.3) = 2.5 to 2.6 arcseconds. (If resolution exactly doubled in step with halved exit pupil, then expected resolution for the 1.5mm exit pupil would have been 2 arcseconds).
Below exit pupils of 1mm the drop in resolution for a halved exit pupil was measured at about 40%.
However there was also no point at which any exit pupil half the size of a larger would show double the resolution. The best was a comparison of a 1.6mm exit pupil to a 3.2mm exit pupil. The 1.6mm exit pupil showed 88% of double the resolution or a drop of only 12%.
Resolution Profile of a Megrez 80 SD II
Smaller exit pupils by far show improved resolution. There is no need to limit resolution due to unexpected drops in sharpness. That condition is nevered realized.
This is good news for all you Binocular Telescope observers wanting to use higher powered eyepieces, whether for astronomical or terrestrial use. You can balance off your choice of eyepieces with your needs for bright image or higher power with virtually little loss of resolution down to 1mm exit pupils. As long as you can pass the test of merging, then only brightness and not resolution would be your limiting choice.
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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photonovore
Moonatic
Reged: 12/24/04
Posts: 2488
Loc: tacoma wa
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Very interesting test, Ed. 
Couple of observations begging questions... one, i notice the graph (if reading them correctly) show increases in raw resolution obtained up to and including 0.75mm exit pupil. In fact this is where the diffraction limit (Rayleigh) seems to begin to be reliably accessed. I wonder if finer resolution would continue into the "Dawes regions" upon higher magnifications (even smaller exit pupils) down to .5mm and perhaps below?
Two, I notice in the apparant resolution graphic that the apparant resolution takes a first jump (in degree of slope) at 2.5mm exit pupils and really takes off at ~1.5mm ep. I wonder what accounts for these two changes of slope in the apparant resolution vs. the smoothly rising slope in actual resolution/exitpupil? One idea...the lower the ratio of raw resolution to apparant resolution the more aesthetic the image quality, i.e. the "sharper" appearing-- though not the most resolved (two different parameters i think).
Third, again on the apparant resolution chart, i notice a drop in the last data points. This would imply that eye acuity increased here, reauiring less apparant separation to access still increasing raw reesolution. I wonder if this line would continue this drop at even smaller ep to 0.50mm or less) and where it would begin to rise once again? The point of "re-rise" could be construed as the point where "empty magnification" sets in, that magnification where raw resolution plateaus and increases in magnification beyond that point begin to swell the ratio between raw resolution and apparant resolution once again. (which may still be useful for doubles perhaps but certainly less so for detailed expended objects.)
Anyway, i real curios about the drop up there and if it would continue trending down or not.
comments?
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Mardi
4" achromat, ETX-70.
Whitepeak Lunar Observatory Website
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EdZ
Professor EdZ
Reged: 02/15/02
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Loc: Cumberland, R I , USA42N71.4W
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I think what you are seeing in each case, or at least some of those positions, are minor skewing of the data. For instance, the two readings that stradle the 1.5mm exit pupil. Both eyepieces have exactly the same resolution readings in my data table. That will cause a jump or dip (or both) in the apparent resolution plot. It could be due to target size not being sufficiently stepped to provide the difference between these two eyepieces. That same thing seemed to occur several times in the smaller exit pupil readings. Notice the raw resolution belowed 1.6mm ep is stepped.
Also, 1.6mm was a transition point from eyepieces with glasses to eyepieces without glasses. I noticed a difference using a 10mm radian (1.6mm) with and without glasses. Without glasses, my astigmatism made raw resolution more difficult. I just could not use the 9mm UO (1.44mm ep) with glasses. Could it perhaps have been slightly improved if I did view thru the 9mm with glasses?
Also in reference to the above,
it is possible some slight differences in eyepieces would cause slight variation off the normal line.
and
It is very possible the net magnification of some eyepieces is not precisely as stated.
For instance, one example jumps out at me. The next to last data point has what may be too high an apparent resolution. This is the only eyepiece that was used in a barlow, an 11mm TV plossl in a 2x TV barlow. If that barlow is not 2.0x but is closer to 1.9x, then it is not the last data point that is skewed downward, but it may be the next to last which is skewed up. Resolution is what it is, but apparent resolution is dependant on the magnification value. If magnification varies from stated it would simply move a point on the res graph along the x axis, but on the apparent res graph it would also move along the y axis. If it is possible that data point magnification is not exactly as stated, the apparent res curve for high magnification may fit nicely.
If curve fitting (curvilinear regression) were applied to the actual readings, those dips and spikes would dissapear and the curve would show a much less abrupt change.
Quote:
One idea...the lower the ratio of raw resolution to apparant resolution the more aesthetic the image quality, i.e. the "sharper" appearing-- though not the most resolved
I tend to think this way also. However, if curve fitting were applied, I think the point of slope change would be found to occur somewhere between 1.6mm and 1.2mm.
I did not test at higher than 100x, or a 0.8mm exit pupil. I completely covered the range I needed for this purpose. May be interesting to expand for future use.
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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photonovore
Moonatic
Reged: 12/24/04
Posts: 2488
Loc: tacoma wa
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Thanks for the response Ed, your points are well taken.
I think that exploring the resolution (on the line pair charts you use since the baselines are so well established with them from prior testing) below 1mm exit pupils would be very interesting, as there is almost no data (in the literature that I can find anyway) on this realm of exit pupil performance.
Worth knowing:
1) what the relationships look like between raw resolution and apparant resolution at exit pupils below 1mm.
And 2) what effects does increasing aperture have upon apparant resolution magnification constrained. IOW, what effects does increased target illumination (in the exit pupil) have upon apparant resolution between apertures? Ex. if the apparant resolution found in an 80mm trhrough a range of exit pupils (5mm to .5mm) were compared with the apparant resolution found in a 5" scope using the same magnifications (image scales) as the 80mm--i think the results would be interesting to see. Would the larger aperture, even when constrained to the image scales of the smaller aperture, still offer greater effective acuity in accessing image detail (as expressed by apparant resolution) and if so how much?
Thanks for your experimental efforts, Ed. I always find the results fascinating.
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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: 12789
Loc: Cumberland, R I , USA42N71.4W
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Mardi,
also, in answer to this
Quote:
I notice in the apparant resolution graphic that the apparant resolution ..... really takes off at ~1.5mm ep. I wonder what accounts for these ... changes of slope in the apparant resolution vs. the smoothly rising slope in actual resolution/exitpupil?
One major factor that would show up, even if all the curve lines were smooth is related to magnification being plotted across a constant measure X-axis based on exit pupil.
from exit pupil 4.0 to 3.5 magnification increases from 20x to 23x, only 13%
from exit pupil 2.0 to 1.5, it increases from 40x to 54x, or 34%
from exit pupil 1.0 to 0.5 , it increases from 80x to 160x or 100%
The slope showing rate of change of magnification increases rapidily for smaller exit pupils. This will influence the curves of the apparent resolution graphs, even if the rate of change in raw resolution is constant, (a straight line). In fact, if the rate of change of resolution is constant, then the differential between magnification and apparent resolution would be constant. In essence, the differential would plot to a flat line. However, that is not the case, but not by very much difference.
I've modified the apparent resolution graph to show magnification.
Revised graph
edz
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Teach a kid something today. The feeling you'll get is one of life's greatest rewards.
member#21
Edited by EdZ (08/22/06 09:24 AM)
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