I am quite certain that I have thousands of Nikonians rivited to the edge of their seats reading this resolution stuff . As such, I have one more contribution, and I promise it is the last . But I think the most important in order to try to understand print resolution.
In reply #28 I discussed the seeming discrepency between my results with the resolution line chart and my experiences observing Epsilon Lyra, and double stars in general.
Here is a scale model of what you would see through a telescope while observing E Lyra on a very steady night:
(edit: see reply 31 for an updated model)
If you download this image it should be 500 x 500 pixels at 100 PPI. However, as you will see, if you care to expend the black ink and print it you should change it to 90 ppi.
It would be better to do this test directly from your monitor and if you want to fully simulate the conditions of an astronomical observation you would do this in a dark room after allowing at least 10 minutes for your eyes to adapt to the darkness, and preferably a half hour. Astronomy is not a fast paced hobby and requires some patience .
I included a summary directly on the image, which you may want to erase from your displayed test copy if you find it distracting.
My monitor (Dell 2209WA) has a resolution of 90 PPI. If your monitor is different than you need to adjust the distance math accordingly. The dots are so small (10 pixel diameter) you may have trouble trying to re-size it.
The two dots represent either of the two binary pairs of E Lyra, both having separations within 10% or so of each other. That's within the range of uncertainty I have as to the exact width of the airy disks in my catadioptric scopes, which varies a bit from theory based on refractive lenses.
The outer circles are the first diffraction rings, which are quite obvious in a cat scope and only slightly less so in a refractor. On a very steady night with very dark skies the 2nd (outer) diffraction rings are probably visible but they are not important to the view (in my opinion) so I left them off. It would be somewhat difficult to estimate the correct luminosity without being able to consider it in real time, Lyra being a very early morning object now.
The figure 8 or peanut shape of the diffraction rings is a critical part of the fascination many have with these binary pairs. Thus I had to throw in one set . They won't affect your test; they will mostly disappear at the limits of resolution.
At 100% you get a good idea of what the view looks like at high powers.
For the purposes of the test you will want to zoom out to 50%. On a 90 PPI monitor, at 50%, the two stars are separated by 0.11 inches. At 100% the stars have a diameter of 10 pixels, with 10 pixels separation between the airy disks (the central stellar disk). At 50% they are 5 pixels diameter with 5 pixels separation.
(This is as precisely to scale as I can calculate for my 89mm diffraction limited catadioptric Questar scope. The scale will vary depending on lens aperture according to the well known formulas of diffraction, which is a function of lens clear aperture. As aperture increases the separation remains constant for a given magnification but the size of the airy disk shrinks proportionately, resulting in relatively wider separation verses airy disk diameter. I actually prefer the view of E Lyra through my smaller aperture 89mm scope)
With your monitor at 50%, the equivalent resolution at several critical distances are noted on the image. You want to slowly back up until you bump into a wall, trip backwards over that couch, or, ideally, you can no longer see any indication of black space separating the two airy disks. Your distance number is that furthest distance allowing you to see some clear indication of some black space ("a clean split").
If you run out of distance, cut the zoom to 25% and then cut the indicated distances in half. It is all perfectly linear. The longer the distance the less trouble you may have with close vision problems, as I have. That's why the test should not be scaled down to normal desktop viewing distances.
When I did this test immediately after making the image I got 100" and 102" on two different attempts done an hour apart. That equals 3.75 arc-minutes or 225 arc-seconds of visual resolution/acuity.
My results are exactly equal to the standard COC of 225 arc-seconds and also exactly consistent with what I said earlier (before I built this model) about my estimated acuity when observing E Lyra and double stars in general. I've done this before (in real life) and for 15 years I've known "my number" with fair precision. Simply to say that this model appears to very accurately reflect "real life" behind the eyepiece of a scope on a very steady night.
Earlier I stated that most experienced amateur double star observers need about 100x magnification to cleanly split these pairs. That is equal to exactly 230 arc-seconds for the slightly tighter of the two E Lyra pairs (with separations of 2.3 and 2.6 arc-seconds). My results here are very typical.
In reply #28 I said I could argue the merits of the line chart verses this "dot test" either way. The argument in favor of this test is that typically images do not predominantly include straight parallel lines. The exceptions, of course, could be architecture and the classic picket fence. But in general, images are irregular or chaotic at the pixel level.
This "binary star test" well models what you see when you are viewing any two "visual pixels" on an image as defined by the COC at the distance you view it.
The argument for the line test would mainly be that it is regular geometric shapes that most define our perceptions of sharpness and the relatively few geometric shapes in an image are what defines our impression of the image as a whole. Take your choice. Attachment#1 (jpg file)