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Currently working with a trial-copy of QuickMTF (Imatest's software kept crashing on me), and I'm trying to get some basic MTF readings for my Canon 85 f/1.8 lens on a 6D. My first set of test shots was at f/2.8 (going to get another set of readings at 1.8 tonight), and I get results around 1300-1500 lines per height in the center. Given the 23.9mm sensor height, that works out to something like 54-63 lines per mm depending on which POI I use.

Taking these numbers, I can easily compare my results with those on many review sites, and more importantly, I can keep them for future checkups so I know when something's wrong with the lens. What I can't figure out is how the LPH or LPmm values compare to the "official" MTF charts Canon provides, which are based on the contrast levels at 10 l/mm and 30 l/mm. The closest I can think of is to try adjusting the MTF level I'm testing for, but I won't know for sure if those are accurate until I get a chance to test again at 1.8.

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Have you seen this related question? How do I interpret an MTF Chart? –  dpollitt Mar 11 '13 at 19:30
    
You are comparing your MTFs to Canon measured MTF charts or computed MTF charts? Cause you know that comparison against computed MTFs is meaningless? –  MarcinWolny Mar 11 '13 at 20:59
    
@dpollitt No, but I know how to read an MTF chart. My problem isn't reading their chart, it's how to compare their values with mine when we're using two different systems to measure with. –  Amazingant Mar 11 '13 at 21:37
    
@MarcinWolny Canon's measured MTF charts off their website. –  Amazingant Mar 11 '13 at 21:39
    
When you say "measured MTF charts"...what web site are those on? To my knowledge, the only MTFs Canon posts for their lenses are computes from the models of the lenses that drive their manufacture. Those MTFs represent, fairly closely as they account for aberrations and diffraction and all of that, the actual LENS' resolution and sharpness. You cannot "measure" a lens without impacting the result with the medium you use to do the measuring. That is "system resolution" as I explained it below, and would never be adequate, and would force extrapolation of the MTF from a model anyway. –  jrista Mar 12 '13 at 1:07
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1 Answer

up vote 3 down vote accepted

Producing and comparing MTF's is not really as easy as it may seem. Different manufacturers use different contexts, sensors are often tested in a different context than lenses, and direct apples to apples comparisons can be difficult.

That said, the way Canon MTF charts work is fairly strait forward. The 10lp/mm MTFs are intended to measure sharpness at a moderate level of contrast. That is supposed to correspond to MTF50. MTF50 is used because it has been demonstrated to closely determine whether an optical system can produce results that the average human viewer will perceive as "sharp, with good contrast". MTF50 is not exactly a resolution test, it aims to measure how IQ will be perceived. These days, as the resolving power of sensors and lenses has increased, 10lp/mm may increasingly become more similar to an MTF80 than MTF50 (based on the separation of airy discs at wider apertures). With a diffraction-limited lens at f/8, 10lp/mm better represents MTF50...but still, it is not entirely the same.

The 30lp/mm MTFs are intended to measure resolving power. That corresponds better to MTF10, however it has the same problem as 10lp/mm and MTF50. Both lenses and sensors resolve much more today than they did a decade ago. MTF10 is really a resolution test at the Rayleigh Criterion. Rayleigh is effectively a systems minimum resolving power according to the following:

The Rayleigh criterion is the generally accepted criterion for the minimum resolvable detail - the imaging process is said to be diffraction-limited when the first diffraction minimum of the image of one source point coincides with the maximum of another.

MTF at Rayleigh is usually performed at a low contrast, ~9% (for vision, 10% in most imaging test cases). A high line pair count is best to determine resolving power and maximum resolution. These days, with such high resolution sensors, the use of a 30lp/mm test chart is probably insufficient to effectively determine what an imaging system is really, truly capable of resolving. Canon's MTF's measure how accurately that 30lp/mm test chard is reproduced, and as sensor and lens resolving power increases, the accuracy at which the test chart is reproduced certainly increases. A resolution of 30lp/mm might correspond better to MTF20, I am not really sure.


Theoretically, ignoring some of the complexities of bayer arrays and pixel interpolation...a modern sensor in luminance-only resolution is capable of resolving much finer detail than 30lp/mm (assuming a perfect lens at a wide enough aperture.) The Canon 1D X is capable of a luminance spatial resolution of ~72lp/mm, the 5D III ~80lp/mm. The Canon 7D is capable of 116lp/mm. The prototype 7D Mark II, currently rumored to have a 24.1mp APS-C sensor, would in theory be capable of resolving as much 135lp/mm. With a near-perfect f/4 lens, these sensors could resolve considerably more than 30lp/mm...AT MTF50!

For a little math, just using a bit of the theory, here is what the 1D X, 5D III, and 7D II could theoretically resolve with the exceptionally good EF 600mm f/4 L IS II lens (which, for all intents and purposes...at least based on Canon's current MTFs, might as well be perfect).

Quick Fact: Total System Resolution is based on the total system blur, which is the Root Mean Square of the resolutions of each independent component. As such, the resolving power of the combined system is always going to be lower than the highest resolution of the best component. Improving the resolving power of the poorest component is the best way to improve resolution as a whole.

To truly derive the system resolution of an imaging system, you would need to account for each factor...individual lens elements, pockets of air between lens elements, the effect of each layer of the filter stack (IR cut, low pass, etc.) on top of the sensor, etc. That is generally impractical for something like this. So, we'll assume that, at a lenses optimal aperture, it is effectively behaving as a purely diffraction-limited lens, and thus capable of the theoretical maximum resolution at that aperture. The EF 600/4 II performs optimally at it's widest aperture, so we'll assume that it is capable of 173lp/mm (which is the theoretical max for MTF50). We'll assume that for the three cameras, they are capable of 68% of the physical spatial resolution (the numbers I mentioned above: 72lp/mm, 80lp/mm, 135lp/mm). I say 68% to account for the differences in spatial resolution between green and red/blue pixels, as well as the sparse sampling rate.

So, the math:

TSB = sqrt(LR^2 + SR^2)

Where:

  • TSB = Total System Blur; Size of "blur" in microns
  • LR = Lens Resolution; Diffraction limited "blur" in microns
  • SR = Sensor resolution; Pixel pitch in microns times 0.68...approximate blur for bayer

For the 1D X, system blur is:

TSB = sqrt(2.89µm^2 + 9.174µm^2) 
    = sqrt(8.3521µm + 84.1623µm) 
    = sqrt(92.5143µm) 
    = 9.6184µm

The blur circle size is 9.6 microns. In terms of spatial resolution in units of line pairs per millimeter, that is:

SR = 1l/(TSBµm / 1000um/mm) / 2l/lp

Where:

  • SR = Spatial Resolution, in line pairs per millimeter
  • TSB = Total System Blur, diameter of blur circle in microns
  • Additional conversions to reduce microns to millimeters (as lines per millimeter), and from lines to line pairs

So, system spatial resolution:

SR = 1l/(9.6um / 1000um/mm) / 2l/lp
   = 1l/(0.0096mm) / 2l/lp
   = 104.l7/mm / 2l/lp
   = 52.085p/mm

The maximum resolving power of the 1D X and the EF 600/4 II is 52.085p/mm, assuming the lens is diffraction limited at an MTF of 50%. That is nearly twice the 30lp/mm Canon measures, and five times the 10lp/mm measures. If we run the same numbers for the forthcoming 7D II:

SR = 1/(sqrt(2.89^2 + 4.9^2) / 1000) / 2
   = 1/(sqrt(32.3621) / 1000) / 2
   = 1/(0.0057) / 2
   = 175.4 / 2
   = 87.7lp/mm

If the next 7D is released with a 24.1mp sensor, it'll be capable of resolving approximately 87 line pairs per millimeter, at MTF50. At MTF10, maximum resolving power is FAR higher than at MTF50 (theoretically, while diffraction-limited f/4 resolving power is ~173lp/mm, at MTF10 it is 373lp/mm! So a 30lp/mm test chart is still generally inadequate to measure maximum resolving power of any modern camera with a modern lens.)


Finally, all of the math above assumes a diffraction-limited lens. In your test cases, you are testing with the lenses at very wide apertures. MOST lenses do not perform optimally when wide open like that. For most lenses, the sweet spot is around f/4, maybe slightly wider, often closer to f/5.6. A lens must be diffraction limited in order to have a moderately good idea of how well it is able to perform. At wide apertures, such as f/2.8 and, to a significantly worse degree, f/1.8...lenses become aberration limited. Optical aberrations occur in a variety of corms, each with their own mathematical contributor to the PSF of the lens as a whole. It is far more difficult to know how well a lens is performing when it is aberration limited than when diffraction limited (as when diffraction limited, diffraction is by far the primary contributor to the PSF.)

Resolution in an aberration-limited context can be significantly worse than in a diffraction limited context. Especially at ultra-fast apertures like f/1.8. I did a visual test of the effects of aberrations and diffraction on IQ (it is in a thread somewhere here), and at f/1.4 through f/2.8, IQ was WORSE than at f/22!! So, if you are testing lenses wide open, do not be surprised if resolution (which in your case looks like l/ph, or lines per picture height) is much lower than you would prefer it to be.

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Holy wow. I don't know how you just wrote that up in under an hour. +1 for effort since I have no knowledge to verify any of your notes. –  dpollitt Mar 11 '13 at 20:33
    
I'm sorry, but I'm not getting how this compares the two systems. I understand most of the non-math material you wrote, but what I get out of all this is how to come up with the theoretical maximum resolving power of a lens and camera together. What I'm looking for is to take a resolving power that I already know, either in lp/mm or lp/h, and make at least a general ballpark comparison to the system Canon uses to make their charts. They seem to be opposite systems, where Canon's uses the 30 line pairs to check the contrast level, and MTF50 tells me how many line pairs I get at 50% contrast. –  Amazingant Mar 11 '13 at 22:16
    
The math just demonstrated the inadequacy of Canon's MTFs, theoretically or real-world. Canon uses 30 lp to test system resolution. They use 10 lp to roughly measure IQ. The closest synonyms between the two is 10lp/mm and MTF50...however they are not synonyms. There is no way to directly correlate the two, and even if you could...given that modern sensors can resolve far more than 10lp/mm AT MTF50... I don't really know how else to answer your question. MTF50 gives you the minimum spacing of two points or lines that will still give viewers the perception of sharp, microcontrasty detail, ... –  jrista Mar 11 '13 at 22:39
    
...which could be far smaller than 10lp/mm for any given system. The only way I know how to understand Canon's MTFs is that the closer to 1.0 the MTF plots are, the more accurately the lens is reproducing Canon's test chart. As for correlating those results to an entirely different system...you would have to develop the formulas to translate between Canon and System X on your own, either through a deep mathematical understanding of both...or maybe an empirical derivation of the differences made from a series of your own test results generated by QuickMTF. –  jrista Mar 11 '13 at 22:47
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So, to answer your question...since you want a simple answer: There is no way to compare your QuickMTF LP/H measurements to Canons MTFs. Apples and oranges. Sorry I couldn't be of more help. –  jrista Mar 11 '13 at 23:04
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