Of resolution and P-mpix

The Issue

A interesting discussion about resolution capability of APS-C and FF was sparked this thread:

http://forums.dpreview.com/forums/thread/3393039?page=8#forum-post-50993057

The crux of the debate is that in one camp, some believe that larger sensor with low MP count (5D1) can provide more resolution than smaller sensor with higher MP count (7D). while the other camp believes it never happens.

The theoretical basis is that although with the perfect lens, higher MP count should result in more resolution, the reality is that most lenses are imperfect. If the lens is imperfect, it will not give the resolution of the sensor to its maximum potential.

Two factors may affect resolution of a sensor mounted with a imperfect lens. The first factor is the MP count, the higher MP count, the more it will resolve. For example, when mounted the same lens, 7D (18mp apsc) will resolve more than 50D (15mp apsc), which in turn resolves more than 400D (10mp apsc). But none will resolve at 100% of their MP count, in fact, the higher the mp count, the further away it gets from 100%.

The second factor is sensor size. Larger sensors uses more area of the lens and thus can resolve more. when mounted the same lens, 5D would resolve considerably more than a 450D even though their 12mp count is close.

So what happens when high MP aps-c meet low mp FF sensor? the answer is not straight forward.

Once understood everything we discussed so far, it does not take a genius to work out there must be a point of lens quality where below it,  low MP count larger sensor should provide better resolution; and above it, a high mp smaller sensor should provide better resolution. in other words it would be stubborn (and not very smart) to insist it will always be one and never the other.

The Proof

The quickest proof we may find on the Internet is DXOmarks. DXO has made this excellent little metric called p-mpix, or Perceptual Megapixel. rather than paraphrasing I think it is best if we just reproduce exactly what DXO say about it:

"P-Mpix is the unit of a sharpness measurement. The number of P-Mpix of a camera/lens combination is equal to the pixel count of a sensor that would give the same sharpness if tested with a perfect theoretical optics, as the camera/lens combination under test"

As for its advantage over traditional MTF, DXO says this:

"

• Describes resolution with a single number,
• Correlates with the way the human vision perceives resolution
• Uses a unit that is well-known to photographers — the megapixel."

Note even though to some people, "sharpness" and "resolution" should have two different meanings, DXO uses them interchangeably.

The idea behind the development of this metric is exactly the same as the idea of this thread. DXO says:

"45% of megapixels are lost due to lens or sensor defects

The Perceptual MPix measure provides photographers with a value that is more strongly associated with the true resolution of their camera sensor when coupled with a lens, or vice versa. For example, a photographer who shoots with a 20-megapixel sensor might produce images that are realistically only 15 megapixels in resolution. A number of factors can cause this loss in megapixels and resolution, including such lens defects as optical aberrations, light diffraction, or an ineffective anti-aliasing filter. The difference in number between a sensor’s megapixels and Perceptual MPix quantifies this loss."

In their explanatory article DXO gives some examples, including the two cameras that were the centre of our discussion:

"[Samyang 35mm f1.4 AS UMC]. On the Canon EOS 5D it scores pretty well at just under 10 P-MPix .... When you mount the Samyang lens on the newer Canon EOS 5D Mark II however, the score is 11.5 P-MPix, a loss of 45% of the camera’s resolution. Effectively the results from the Samyang will be only marginally better from the Canon EOS 5D Mark II than from the Canon EOS 5D....What this is actually showing is the inability of the cheaper lens to resolve detail well at the scale of the pixels in the 5D Mark II,......To further emphasize this, if you mount the Samyang 35mm lens on the Canon EOS 7D which is an APS-C camera and in which the pixels are about half the size of those in the older 5D, the P-MPix score drops to 8.9. This is less than half of the EOS 7D’s actual sensor resolution, a camera with 50% more pixels but a Perceived MPix score lower than the 5D and that, using only the centre of the lens."

They even included a graph to illustrate the point

More examples from DXO

Thanks to DXO's well designed site, it takes less than two minutes to check out some other lens + sensor combinations. Look at 100 F2.8 IS, a very sharp lens, but not the sharpest. with it:

400D resolves 7mp

500D resolves 9mp

7D resolves 11mp

5D1 resolves 12mp

Few lenses can claim to be sharper than the mighty 100L, yet even here the 7D is out-resolved by its older uncle.

Now look at the sharpest lens known to men, 300 F2.8 II, the sex symbol of camera lenses.

400D - 8mp

500D - 11mp

7D - 14mp

5D - 13mp

It is only with this near perfect lens 7D can out resolve 5D1, because 5D1 reached the maximum resolution it can deliver while 7D did not.

A Caveat

One thing worth pointing out is that DXO's p-mpix figure is not derived from a given lens's sharpest aperture, rather, it is that lens's best performing aperture. DXO's "best performing" aperture is one that gives the best IQ under DXO's set condition:

"The DxOMark Score is measured for defined exposure conditions corresponding to low-light scene with 150 lux illumination and an exposure time of 1/60s."

So for example 100L's p-mpix was measured at F2.8 because under that lighting F2.8 give better IQ than F4, even though if lighting was plenty F4 is slightly sharper than F2.8.

This is does not mean p-mpix is not good enough for our purpose, it still is. 100L is still very sharp at F2.8. At F4, its sharpest, it is only 10% sharper than F2.8, at F5.6 it is 5% better than F2.8 and by F8 it is back to the same sharpness as F2.8. Few lens can achieve 100L's sharpness at F2.8. For example one of canon's sharpest zoom - 70-200 F4 IS, at F4 has about the same resolution as 100L at F2.8.

Conclusion

DXO's p-mpix indeed is the right tool for finding out sensor + lens combo resolution. Using this tool we can gather data that clearly proves the hypothesis that low mp larger sensors can have more resolution than high mp smaller sensors if there is enough imperfection in the lens, and beyond this point higher mp will result in higher resolution.

If you only use the sharpest lenses, then you 7D may have similar resolution as 5D1 most of the time, even beats it from time to time. But if you use mid ranged lens, especially if wide open most of the time, then 5D1 would provide more resolution pretty much all the time.

Final Note

First, this essay does not take into account the question of reach, or colour depth, or high iso noise, or dynamic range, please keep these issues out of this discussion.

Second, this essay is meant for a technical discussion, please do not drag personal egos into this, do not play the "I have used a 7D so I know" or "you have not used a 5D1 so what do you know" card. such posts can only be seen as trolling and flame bating. Mod please keep these posters in check.