You are seriously talking past each other now, and things are mixed up beyond belief.
Disregarding the real-world effects of a TC (increased reflection and absorption losses, decrease in sharpness due to optical imperfections)
from now on through this entire post: Yes, of course a TC magnifies the diffraction circle by exactly the same amount as the rest of the image. But that is also the point; the object referred diffraction is already determined at the front of the optical system, by the entrance pupil (as long as we're within reasonably Gaussian systems, for microscopes and other applications with very high magnification you need to look at angular aperture in stead of numerical aperture)
. A teleconverter will magnify both this object referred diffraction and target detail, a wide-converter will decrease magnification on both diffraction and target detail. It varies the projected image magnification and not the angular object referred diffraction, which is what optically limits your target resolution.
You are misunderstanding what a TC does. A teleconverter is a magnifying glass. It simply enlarges what the original lens projects. It magnifies everything....including diffraction. You cannot add a TC to a lens an not increase the effects of diffraction, despite the facts you just described above.
What YOU forget to mention in your little maths excursion under the qouted text above is that the f/# number also implicates that you have a reproduction scale. This indicates both that you're within Gaussian optics rules (as opposed to in microscopy, where angular aperture is the metric used) and that you have an Airy disc diameter that is constant with f/# on the image plane. A 50mm used on f/11 will give the same Airy disc size on the sensor
as a 100mm f/11 used on teh same sensor.
But the target magnification (reproduction ratio) is twice as high on the 100mm option, so you have:
-same Airy disc size on the sensor
-twice the reproduction ratio!
This means that if you shoot a side view of say "a car" from a distance where 50mm would give you a car length of 500 pixels on the image and a diffraction effect of maybe 3 pixel widths, using the 100mm lens at f/11 would give a car size on the sensor of 1000 pixels, but still a diffraction effect of 3 pixels
- and that means that you've halved the diffraction effect on the car, i.e halved the angular object referred diffraction. Doubled the optically limited usable target resolution - since you doubled the entry pupil size.... (50/11 = 4.5mm pupil, 100/11 = 9mm pupil)
Diffraction and Airy disc size are linearly scaled by the same constant
since the angular diffraction in front of the lens depends on the entry pupil diameter and nothing else (until you hit the Gaussian model limit, see angular aperture). If the airy disc covers, say, a one inch detail on an object far away, the SAME one inch detail will be covered by the exact same relative Airy disc, no matter what magnification/resolution you inspect the projection with in the image plane.
This isn't actually very hard to see in reality (most of us do have a zoom lens available I suppose?
Take one shot at say 100mm and F11
of a distant object. With the same camera, directly after that take another shot aimed at the same target from the same distance, but now with 200mm and F22
. They both have the same entrance pupil diameter (9mm), and they're both into diffraction limited range on most modern sensors.
Which of the two will have the highest target resolution?
Since one has twice the target reproduction ratio or magnification
we need to either downsample the 200mm image or upsample the 100mm image to compare them at equal size presentation. And unless your aperture calibration is seriously off on the lens you use, the 200mm F22 shot will have equal or better target resolution!Don't doubt, try for yourself.
In astro (which is a purely Gaussian limited application with ordinary systems, with infinity focus targets) this is extremely
important, since the angular resolution in front of the lens is
determined by the entrance pupil. NOTHING you do behind that can make things better, in any way. It doesn't matter what focal length you use, the entrance pupil determines how small the (infinity distance) details you can accurately resolve optically
is. Within practical limits of course, but this depends more on lens manufacturing and smallest available pixel size with good performance. You won't find many spectacularly detailed shots of the moon taken with a 24mm lens.
Keeping the entrance pupil constant: If you use a shorter focal length you get a smaller reproduction ratio, and you need smaller pixels to accurately resolve the optical projection image. Use a longer focal lens, and you can use larger pixels. It will not in any way have an effect on the object space angular resolution of the system, you just adapt the sensor resolution to fit the optical resolution.
So: You get the same optical far-field target resolution (again using the elusive "perfect" TC) if you use a 400/4.0 with 2x TC, as if you use an 800/8.0 on the same camera, or indeed as you do if you use a 400/4.0 on a half size (quarter area) sensor with the same amount of pixels. Diffraction limitation of the target does not change, light energy per pixel captured per second does not change.