You are only thinking pixel size, which I guess is one way to look at it.
Yes, that is the subject we are discussing - is there a point to smaller pixels given the lenses we have available, to which the answer is obviously "yes", as can be shown by simple math and by examples from TCs which show you what the center of the image would look like with smaller pixels.
No, the topic we were discussing is whether adding a TC is exactly the same and just as good as using a sensor with a higher pixel density by the same factor as the TC added. Its a bit more complex than simply stating "well we are just talking about pixel size".
If you are referring to optical system resolution, rather than spatial resolution, then I agree. However you keep applying the units "lp/mm" to system resolution, which feels like a major conflation to me. Assuming the optical spatial resolution of the entire lens setup (original lens + TC) remains the same (which is generally impossible when adding a TC, as it reduces your REALTIVE aperture, which implicitly means your optical spatial resolution of THE ENTIRE LENS SETUP is reduced), the final system spatial resolution will be lower than that of the lens or the sensor, as it is the root mean square of the blur each individual component.
I can't even believe you just said that. So, adding a TC reduces optical spacial resolution? Better throw them all out then.
A TC doesn't change optical resolution.
YES, adding a TC reduces optical spatial resolution, because it reduces the RELATIVE APERTURE. Diffraction is dependent on aperture. For a small table, so we all (you, me, and other readers) have the same reference information:
| Diffraction-Limited Aperture | MTF 50 (lp/mm) |
| f/1 | 691 |
| f/1.4 | 494 |
| f/2 | 346 |
| f/2.8 | 247 |
| f/4 | 173 |
| f/5.6 | 123 |
| f/8 | 86 |
| f/11 | 63 |
| f/16 | 43 |
| f/22 | 31 |
If you start out with an f/4 lens, without a TC your lens could achieve up to 173lp/mm, if it was diffraction limited. A non-diffraction limited lens, one which is aberration limited, would have LESS spatial resolution due to the blurring caused by aberrations. If you add a 2x TC to that f/4 lens, regardless of what the focal length ends up being, the aperture is now f/8. That explicitly limits you to 86lp/mm optical spatial resolution on the upper bound, assuming you are, again, diffraction limited, and not aberration limited.
So YES, adding a TC has the effect of REDUCING MAXIMUM POTENTIAL SPATIAL RESOLUTION. Its physics. There is no way around that fact.
What you are referring to is magnification. Adding a TC enlarges the subject, so the portion of the subject that is projected through the lens and onto your sensor is LARGER. It would be similar to moving 1.4x or 2x closer to your subject without the TC...except that if you move closer rather than adding a TC, your relative aperture remains larger, which means the upper bound on spatial resolution remains higher.
I don't know how else to explain it, but magnification and spatial resolution are disjoint. You can technically increase subject magnification without changing your spatial resolution. You could also increase your spatial resolution without magnifying your subject. The two are independently variable. Examples of achieving each optically:
1. Double magnification while maintaining spatial resolution:
- Swap a 400mm f/4 lens for an 600mm f/4 lens.
- Same relative aperture, 2.25x larger subject.
- Subject size in-frame is relative to the square of the ratio of the focal lengths: (600/400)^2 = 1.5^2 = 2.25
2. Double spatial resolution while maintaining magnification:
- Swap a 400mm f/8 lens for a 400mm f/4 lens
- Same subject size, double the relative aperture
- Diffraction-limited spatial resolution increases from 86 lp/mm to 173 lp/mm
3. Quadruple magnification while halving spatial resolution:
- Add a 2x TC to a 400mm f/4 lens
- Half the relative aperture, 4x larger subject
- Diffraction-limited spatial resolution drops from 173lp/mm to 86lp/mm
- Subject size in-frame is relative to square of the ratio of the focal lengths: (800/400)^2 = 2^2 = 4
As you can see, despite losing spatial resolution with a TC, adding a 2x TC QUADRUPLED the size of your subject relative to the same sensor frame. You doubled the amount of resolved detail, despite the loss in spatial resolution...thanks to magnification.
The notion that a camera can usefully resolve anything at MTF 9% (Reighley) is also pretty ridiculous.
Except that we do so all the time, in astro stuff.
You need to back that up with some actual examples...
Better ask Damian (one of the best amateur planetary imagers in the world) why he shoots 5.6 micron pixels at f/30 instead of his scope's native f/11:
http://www.damianpeach.com/best.htm
Look, the facts are simple. If you want to see how a particular lens would perform on a camera with four times as many pixels as your current camera, simply add a good quality 2x TC and see for yourself how the center of that hypothetical sensor would look with the bare lens. Period.
Sure...but you've just invoked cropping. Who buys a 500mp sensor to crop out the middle 18mp? Let's stop equivocating here. There is a huge difference between quadrupling pixel density in a FF sensor, and adding a TC. With the TC, you only get the center 25% crop. With a FF sensor with quadruple the density,
you get the whole subject. Equivocating by saying something along the lines of "My 400mm lens with a 2x TC is the same as having a 369mp sensor" is a fallacy. The 369mp sensor is capable of resolving a 4x more area of your subject with the same amount of detail as the 2x TC. That is a HUGE difference. That is a full two orders of magnitude difference.
The terminology you use in your approach to explain what a TC is doing for you is misleading. You are not increasing spatial resolution, which is what it sounds like you are doing when you equate the effect of magnification offered by a TC to using a higher density sensor of the same physical dimensions. You are
magnifying your subject at a
lower spatial resolution. The math here isn't all that complex. Apertures, diffraction, spatial resolution, magnification. It's all pretty basic, and no amount of wordmincing and dancing around the heart of the debate will get you past the facts.
* TC's magnify.
* Higher density sensors resolve more.
Two very different things.
