OK, I trust you guys know your optics and related math much better than I do. I'm just trying to figure something out here that's not quite making sense to me yet so if you care to indulge following the path I'm on with this, please tell me which step I slipped on.
I'll use round numbers for convenience but referring to the numbers jrista provided on a previous page.
- A digital image sensor (e.g. D800e) with pixels that are 5 microns square = 100 lp/mm physical sensor resolution with no AA filter.
I presume with whatever kind of algorithm is used, it is possible to read alternating rows of pixels, if they are properly stimulated, such that it would be possible to electronically extract the maximum of 100 lp/mm from this sensor. If this were a monochrome rather than Bayer sensor then likely even simpler.
The resulting contrast ratio, if one were to stimulate alternating rows of pixels with high and low (dark) intensities would depend on the spot size of the illumination and how it was modulated during the raster.
Let's cheat a little bit, for fun.
I'm thinking if a visible light laser beam could be focused to about 1 micron, then rastered across the sensor in perfect geometric alignment and modulated such that the beam was ON only while the edge of its spot fringe was entirely located within a given pixel (row) such that no appreciable amount of that light were to enter an adjacent pixel (row), then the resulting contrast ratio would be quite high as there would be no bleed-over to the pixels in the dark row resulting from the fuzzy fringe of the spot.
This would be cheating because it would not be a perfect square wave function but would required a reduced ON time vs the normal 50% ON to 50% OFF of a square wave.
Thus we have applied a pattern of light and dark lines to the sensor synchronized with the sensor's physical pixel layout such that every second pixel is illuminated and alternating ones are dark.
We get 100 lp/mm equivalent signal from the sensor. Still, we may have slightly less than perfect maximum (MTF) contrast ratio between rows but it's likely to be much higher than the typical 50% MTF standard.
If we were to instead modulate the light spot (without cheating) so that it was turned ON and OFF as its center crossed the boundary from one (row) of pixel(s) to the next, then that will have an equivalent contrast ratio you could calculate at about 5:1.
Are there any errors in this hypothetical assumption so far?
- we have some lens that is capable of resolving 150 lp/mm at an MTF of 50% as measured on some optical bench...
This same lens should have a better than 50% MTF result if it were resolving a test target at 100 lp/mm.
Any error in step 2?
- we take the lens in step 2 and use it to focus a 100 lp/mm image onto the sensor in Step 1. (We can use monochrome light if we have to minimize focus errors from CA)
We must now carefully align the focused image to the pixels on the sensor so that the middle of the bright line corresponds to the middle of a pixel (row) with the middle of the dark line aligned to the middle of the next pixel (row). This should yield the maximum readable contrast ratio from the electronic sensor.
IF the alignment is PERFECT then the contrast ratio should still be a reasonably good number. As the alignment shifts away from perfect the resulting contrast ratio will drop to a low of 1:1 (2.5 micron shift) for adjacent pixels which means no discernible contrast at all.
Are there any errors in step 3?
If there were no errors in the 3 steps above then it is possible for a lens and sensor combination to resolve the physical maximum lp/mm of the sensor if the lens has a sufficiently higher resolving power in at least the ideal circumstance described.
Add angular and positional misalignments and mismatches in spatial frequency and you'll get aliasing and all manner of things that throw the above out the window and the math explained in this thread describes the system behavior.
is the conclusion correct within the limitations stipulated?
Your have it somewhat, and some things are slipping through your grasp.
First thing. Yes, it is possible to use a lower contrast ratio than 50%. If you do that, then your results are generally in a different context than lens tests done anywhere else, as testing at MTF 50 is very standard. It's what all the major testers use. It is not invalid to reference a lower contrast level, however there is a diminishing guarantee that any given sensor can actually resolve any differences below a certain contrast level. The human eye is capable of barely detecting contrast at 9%. The human eye has some advantages that sensors do not, however, such as our brains doing real-time superresolution enhancement on everything we observe.
It's "safe" to refer to spatial resolution at MTF 50. It's a well-known context, it's easily comparable with results from other testers, official sites, etc. You can also very easily find LP/MM numbers for primary apertures, and sometimes half or third stops, in tables for MTF 50. You can also usually find the same for MTF 10, although there is no guarantee that a sensor could actually separate detail (real detail, not noise) at that low of a contrast level. (Noise tends to dominate at that low of a contrast level, and things like LPFs may smooth detail out, and conversely the LACK of an LPF may result in even more noise at an even higher contrast level.) MTF30 might be a good contrast level that sensors can still resolve...however there isn't a lot of readily availble information on lens resolving powers at that level. You would have to compute all that yourself (which is certainly possible, but it makes it harder for others to verify your claims.)
Some other things to account for as well.
First, lens aperture. Lens resolving power changes with aperture, as smaller apertures increase the impact of diffraction more. I have found that, based on my own testing as well as tests from official testers like DPR, PZone, etc. that lenses generally top out in resolution somewhere around f/4 to f/5.6. Diffraction-limited spatial resolution at those apertures is somewhere between 123lp/mm and 173lp/mm. There are some few lenses that may resolve more than that at wider apertures...something like the Otus could very well resolve the 247lp/mm diffraction limited resolution of f/2.8...and possibly, in the center of the lens, resolve upwards of 350-400lp/mm at f/2-f/1.4. I haven't actually looked at a real MTF chart to know for sure.
Keep in mind though...those resolutions are ONLY possible at those apertures or WIDER. The moment you stop down more, your maximum diffraction-limited resolution drops. Those are pretty fast apertures. Even f/4 is getting fairly fast. Very few lenses actually exhibit "ideal" behavior at f/4 or faster...optical aberrations generally have some kind of impact, even if it's small. Sometimes the impact of an aberration is simply a loss of contrast...resolving power might be the same, but its now at a lower contrast (i.e. MTF30), which means detail will become increasingly more difficult to differentiate from noise.
Finally, and I make this mistake myself, sensors really don't get their "theoretical maximum" resolution...not unless they are just a bare, monochrome sensor (no filters of an kind). Only a bare mono sensor is really going to be capable of resolving line pairs anywhere close to the size of their pixels. For all other sensors, the use of filters (even just IR/UV filters) will reduce resolution a bit, and the use of a CFA obviously has an impact (although more in color than in luminance, for sure). So, the D800E, with it's 4.9 micron pixels, has a raw mono spatial resolution of about 102lp/mm. It's real-world spatial resolution is going to be diminished, however. I'd say the D800 probably loses some 20-30% or so due to the CFA and filter stack. The D800E has that funky reversed LPF, so it won't lose as much, maybe 15-20%.
Given the existence of the CFA on the D800E, despite the lack of an LPF, there is no way anything could ever actually resolve anywhere remotely close to 36mp, with any lens. It just isn't possible. Hence the reason why DXO's results are so highly suspect. I could believe ~30-31mp, with a very good lens. I have a very hard time believing anything higher than that on average, though...unless it was an absolutely stupendously kick-ass god-quality lens that ACTUALLY resolved some 400lp/mm at f/1.4...and, assuming the results were actually for f/1.4, I think 33mp, maybe 33.5mp, is really the best your going to get...I mean, your WAY up there, really pushing the sensor to its absolute limits.