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Modulation Transfer Function...What does it mean
Msmoto
Posts: 5,398Moderator
As noted by I believe TTJ, this topic deserves its own thread. So, let the action begin. Any discussion about MTF, its uses, an explanation of what these charts represent, all can be stated here.
Msmoto, mod
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Comments
http://www.luminous-landscape.com/tutorials/understanding-series/understanding-mtf.shtml
One teaser quote:
"The... thing to realize is that resolution is not a quantifiable scientific absolute"
We tend to equate MTF with lens ratings, but every part of the camera in the image processing chain has an effective MTF -- nothing is perfect.
So the sensor also has an MTF. The bayer array has an MTF. The micro-lenses, the IR filter, and the AA filter all have MTFs.
Not only that, even the post-processing chain has an MTF! E.g., the RAW converter you are using, has an effective MTF. It's not surprising if you think about it: with different RAW converter you can get different contrast, sharpness, etc.
Even with a perfect lens, there are enough imperfections on all the other components of the camera that we can never fully resolve all the lines in the sensor.
The total system MTF is essentially a multiplication of all the component MTFs.
We used to use MTF for our products, but too few customers understood it. Now we use a go/no-go resolution test where we take an image of a 1/2 mil (12.5 micron) wire across an 18% gray card, avoiding specular reflection. That is something our users can understand and it quickly tells them and us if we have all our optics and detectors set up properly.
"Discovery consists in seeing what everyone else has seen and thinking what nobody else has thought"--Albert Szent-Gyorgy
Before we go on and try to explain eachother things that the other had already understood 15 years ago, let me try to clear the wording up – also so we all know we're in the same boat. I feel there is a misunderstanding about the wording.
There is a huge difference in something being:
- quantifyable/not quantifyable
- relative/absolute
- dependent/independent on components and/or measurement procedures and equipment, and
- a reproducible measurement or not
These are four completely different categories, and I feel we're using these interchangebly, so let's differenciate:1. Quantifyable or not:
If you can assign a measurement a concrete value (be it whatever), a measurement is quantifiable. If you put your finger up in the wind and say "wow, it's windy today", that's not quantifiable. If you put a measurement tool up in the wind to measure its speed, that's a quantifiable measurement.
So, Is a value of LP/IH a quantifiable measurement? Absolutely! You get a quantified value, a number that you can compare to another number, and, most of all, can be reproduced if you repeat the measurement with the same setup just an instance later. But that's something for point #3
2. Relative or absolute
A relative value is something that is put into relation to something else. Miles per hour. Frames per second. In can contain an absolute statement, like in these cases of speed. Speed is a relative value to time but it expresses something that is a matter of performance and makes an absolute statement: A car that goes 200mph will always go 200mph and this will be a lot faster, always, than the one with 100mph. A camera with a framerate of 10 per second will always be faster than one with 1,5/s.
Then, there are relative values that have no absolute statement, like i.e. the aspect ratio. a 16:9 aspect ratio says nothing about the sensor size, just the ratio.
So why does a relative value deliver an absolute statement in one case and not the other? Easy: Because the first category of relative values (i.e. speed) contains an ABSOLUTE value: in this case TIME. One second is always one second. Whereas 9 (of 16:9) is nothing unless you specify it. I.e. 9 inches.
So, is LP/IH a relative value? Yes, it's line pairs on top, divided by image height. Does it make an absolute statement? Yes, it sure does, IF you specify what the image height is. Which you do when you tell the camera model.
So far, we have a quantifiable, relative value with an absolute statement. What about the last category?
3. Dependency on components of the system and the measurement methods
Of course, all these measurements are dependent on the components. If you get another copy of the lens, if you change the alignment slightly etc. And especially, if you use a different camera. Because the camera is the measurement tool that you measure resolution with. Since the camera itself has a native resolution, it's natural that it will influence the result. So whether you take a D80 or a D800 makes a huge difference. But...
4. Reproducibility
Should a different person with the same setup (tested gear, measurement equipment etc.) get the same results?
Theoretically yes. The results of the measurement should be reproducible. But due to so many factors influencing the whole setup (like the neighbors tearing up concrete floors, as in Roger's example), you may have slight differences. Nevertheless, within these boundaries, MTF results are reproducible.
Should a different person with the same tested gear but different measurement tools get the same results?
No. A different set of tools will lead to different results. This includes the camera used, since it is part of the measurement equipment. And it does include test charts.
In so far, the results are only really strictly comparable to each other within one and the same setup.
To sum it up, we DO have:
- quantifiable values (=> line pairs)
- absolute numbers (mathematically relative, but with an absolute statement: 500 line pairs on an image height, which is 1000 pixels)
- within reason, reproduceable results of the measurements, which are
- dependent on equipment used
Are we all in the same boat?To my understanding, it will. But the values (again: the same lens on the same camera) should approximate somewhat. Because what it measured is, how many line pairs will the lens be able to resolve on one full image height (which is defined by the camera).
This value can't be higher than the resolution of the measuring device, naturally. But if it's substantially lower, it means the measuring device resolves higher than the lens tested.
Ok, so far, so much. Oh dear. So much text. Sorry. :-)
Now, if I see wild splitting of the lines meridional vs. sagittal it suggests issues with bokeh.
And, the old thread from months ago:
http://forum.nikonrumors.com/discussion/468/mtf-chart-interpretation/p1
Apologies for another long post, but please bear with me.
The MTF50 test does not measure the "true" (or "absolute") resolution of a system. It wasn't designed for that.
To explain, lets continue with FlowtographyBerlin's car analogy.
Suppose I just bought a (used) Porsche 911 and I would like to characterize it's performance. What kinds of tests might I design to do so?
1. I could design a test to measure the Porsche's top speed. For example, I could take the car to the Bonneville Salt Flats on a windless day. There I am assured that my Porsche will reach terminal velocity -- the absolute highest speed the car can achieve under her own power.
Let's assume, at Bonneville, my car achieved 200 mph.
2. I can also take the Porsche to my local race track (called Shannonville) during a "track day", and measure its lap times & top speed.
Suppose at Shannonville, my Porsche did 1:51 lap times with a top speed of 136 mph.
My friend Jim's Corvette did 1:57 lap times at 130 mph.
My friend Bob's BMW did 2:04 lap times at 114 mph.
3. Or, I can take the Porsche to a larger race track (called Mosport). Mosport has longer "straights" than Shannonville (but the long straight runs uphill).
At Mosport, my Porsche hit 150 mph.
Jim's Corvette did 140 mph.
Bob's BMW did 126 mph.
What are the differences between these tests?
- The first test (at Bonneville) is an absolute speed test. I would expect the results to correlate directly to the maximum speed the car can actually achieve. I expected my Porsche to hit 200 mph and it did. If it only hit 140 mph, I'd be really worried that I'd purchased a 'lemon'.
- The 2nd and 3rd tests are relative tests. All I care about is beating my buddies' cars for bragging rights. I'm happy that my car hit 136 at Shannonville and 150 at Mosport. I'm even happier that Jim's and Bob's cars were slower than mine. I wasn't even attempting to get to my car's absolute top speed -- that would be physically impossible at these tracks.
The fact that my imaginary car hit 136 at one track and 150 at another track is arbitrary. On another track it might be 110. On a fourth track it might be 162. The numbers are not comparable to each other. Also, a higher number from one track is not "more valid" compared to a lower number from another track. And importantly, the numbers do not at all correlate to the absolute maximum speed my car can achieve.
MTF50 testing as presented by lensrentals, Photozone, etc., are similarly relative tests. They are not measuring absolute max resolution. They are measuring the camera+lens MTF performance at the very specific, non-standardized test conditions with different charts, lighting, RAW conversion, etc.
Just like the track tests, the lensrental and Photozone numbers are not comparable. The Photozone numbers aren't more valid because they're higher than the lensrental numbers. Neither set of numbers have anything to do with the absolute resolution of the camera. And lastly no, the lower lensrental numbers do not in any way imply that the sensor is "out-resolving" the lens.
After all, I've no doctor in physics.
It was a very good point trying to clear up the wording, Flowtography Berlin. But the assumption, somebody did understand things 15 years before is not valid for me. I did understand things but frequently it turns out, I was on the wrong path. Either the thing I understood was explained poorly or is the other way round or I didn't understand but took my conclusion as "that's it!". Occasionally it happens that the Earth has become something else than a flat disc.
Now, your assumption, 1000 pixel = 500 LP is in my eyes wrong. I always see the charts mostly being black and white. To reproduce them with a Bayer pattern, with a Foveon sensor or with a monochromatic sensor will drastically change that parameter. So even if you understood what a pixel is for you it might not be the same for me.
Also, I learnt no lens will be equally sharp over the whole, flat sensor surface at open aperture, so all MTF numbers have a slight problem there. And because the design and construction of the Bayer pattern, the outer zones are already in disadvantage. Especially with an AA filter in front of them.
So, not understanding the MTF curves as I would not be able to explain them properly to my colleague the physics doctor who gets on my nerves explaining a simple thing with clarifying all given influences first, I still take some ideas out of it.
No matter who's doing the MTF he/she usually gives an aperture range and within that one can see what would be the best resolving aperture. Great, but usually I need other apertures to get a wider or smaller DOF, now what? Yesterday I tried to get a nice photo of the Ulmus carpinifolia seed I put in PAD. I found a dry one and used the 105 Micro at f/18. As I expected, it was not very sharp on a D7100. With high density sensors you get earlier punished to use small aperture numbers. After doing a focus stack (with a D7000 because the stacking software doesn't support newer bodies) at f/5.6 which needed 10 pictures from most distant to closest point, sharpness was better. That said, for your origin question "which lens is the highest resolving on my D800?" the answer can be "doesn't matter, use the one you have at optimum aperture and stack enough pictures to get your DOF - if possible". The highest resolving lens could as well be the poorest on your tabletop because the necessary aperture is way beyond and already in the wastelands of diffraction.
Without the MTF curves, although I don't understand them fully, I won't have got the idea to do it that way.
@Ade as illustrative as I found your car examples: I need to close my eyes intensively against the variables in it. Different drivers, fuel consumption of the cars so they become lighter in different times and so on. But in general I thought, let the variables be equal and he's right.
The lens tests, though, try to create lab conditions. It would be more comparable to someone testing top speed (Bonneville case one) with the same methodology, but on a different course. The wind may be a bit different, and maybe some other factors, but he's still using a straight road. In the race course example, there are far too many variables in there that cannot be reproduced: the driver's condition, the driver's skill, the track pattern/layout, the surface of the track, the temperature, the wind etc. Now, what variables do you have in a lens test? The test chart content, the camera, the evaluation software, maybe floor shake, but ideally not. All variables that are about the ability of a human individual should not influence the equation, which is the whole idea of a lab-type test.
But as I said, I get the point you're trying to make, it's just that I don't really understand it yet :-) Which is because I still don't understand what Line Pairs mean if not... line pairs. So, what is it? (I'm serious, just in case you consider this a stupid question... ;-) ) I guess you got me wrong, that example didn't take the Bayer array into account. The 'rule' is a physical given, you need two pixel for a line pair (given this is defined as one white, one black, like in this case). You can't go any smaller. So the maximum line pair amount that can be represented on a pixel scale is half its pixel amount. The Bayer array, as I believe I already mentioned earlier, is said to take away about a third of the resolution of the whole pixel array, that's the rule of thumb at least. Say you have 3000 pixel image height, that would leave it at 2000 lines resolution and hence, 1000 line pairs.
Lastly, just to make this clear, this is about as irrelevant for photography as the non-stick pan was to landing on the moon. I'm only here because I want to take the opportunity to learn from your explanations and finally understand this issue a bit better :-)
And it looks like it's only the three of us left in here anyway, so it's a pretty cosy feeling, too.
Present. :!!
And, now that we all know what an MTF chart is.....the four of us that is........they are fun to look at and I like to see what happens with the wide lenses away from the center....
One thing for sure, I will not be driving the Porsche anywhere unless it has been fine tuned for any steering wheel pull.
Forget about the number of lines (or line pairs) on the sensor. The sensor resolution is important but not actually relevant to the discussion (you'll see why in a moment). What's important is the line pairs on the test chart. Let's simplify a test diagram as follows:
test chart (input) --------> camera+lens system --------> picture image (output)
The picture image might be RAW data which can be analyzed.
Imagine for a moment a test chart with various line pairs. E.g., the test chart might have an area with black & white line pairs at (an equivalent of) 10 lines/mm, a second area with finer pairings (at 30 lines/mm), and a third area with very fine pairs at 60 lines/mm. The lines/mm represent "spatial frequency".
Our camera+lens system isn't perfect. At higher frequencies, more contrast is lost.
Let's say, at 10 lines/mm, most of the contrast from the input is well preserved on the output. At 30 lines/mm, visible amount of contrast might be lost. And at 60 lines/mm, it's now very hard to tell between what was black & what was white.
I've drawn an illustration for an example:
Suppose for our camera+lens, at the center of the image we have the following data corresponding to the picture above:
For (a) input = 10 lines/mm, output = 80% contrast preserved (vs. max contrast)
For (b) input = 30 lines/mm, output = 50% contrast preserved
For (c) input = 60 lines/mm, output = 10% contrast preserved
Our camera+lens system was able to resolve the 60 lines/mm input but with only 10% contrast remaining. A better system might be able to resolve the same 60 lines/mm input with 50% contrast remaining.
In the illustration above, look at the line pairs of the output. The number of line pairs of the output is limited by the number of line pairs of the input, and the remaining contrast, not by the sensor's physical resolution.
In particular, let's answer these questions for our camera+lens system:
1) What is the resolution (frequency) with at least 50% contrast? 30 lines/mm
2) What is the resolution with at least 10% contrast? 60 lines/mm
3) What is the resolution with at least 5% contrast? unknown
4) What is max resolution of the system? unknown
The last two questions are the interesting ones. We don't know the answers!
You see, we never attempted to find out the absolute max resolution of the system. We only tested to the 10% contrast level.
We also defined resolution as the maximum number of lines/mm where the preserved contrast is above a certain percentage. So resolution is not an absolute measure anymore, but defined relative to a contrast level.
Nikon MTF
Nikon measures the amount of contrast preserved at various areas of the lens (from center outward) at 10 lines/mm and 30 lines/mm. They do it with lines parallel and perpendicular to the diagonal of the lens. The result is a plot of distance (x-axis) vs. contrast (y-axis).
Since they stop at 30 lines/mm, the absolute resolution of the system is not tested.
Imatest MTF50
Imatest plots the preserved contrast at different frequencies, from zero lines/mm to > 200 lines/mm. The reported resolution is the max resolution at 50% contrast. The absolute resolution of the system is not tested.
Further notes
I'm simplifying a lot of the above. For example, on modern charts, there are no "physical" line pairs anymore. Instead, a "slanted edge" is used and the number of equivalent line pairs is calculated.
But I hope everyone gets the point that MTF testing does not attempt to find out the absolute maximum resolution the system can produce. Resolution is defined at a contrast level, and we can arbitrarily define a contrast level where more and more resolution could be detected (at 1%? At 0.1%? At 0.01%?)
Transfer: the recording of the black and white lines by your camera system.
Function: a measure of how well the blacks and whites stay black and white, or how much they degrade to grays, and how that varies with the line spacing.
"Discovery consists in seeing what everyone else has seen and thinking what nobody else has thought"--Albert Szent-Gyorgy
Zeiss lenses have measured MTF curves, not calculated ones. Ade is right, each part of that chain describes it's own curve and they are being multiplied. Truth is a s well: the total result is influenced by each part, but each part is independent from the others. A low res sensor doesn't influence a high res optics, both MTF curves stand for themselves. They are influencing the whole picture, off course.
The paper (in the German version) was from 2008, so the highest resolution sensor ended at 24 MP fullformat and the author mentioned low sensitive black and white film as higher resolving.
I ended up recognizing it's not the LP/mm or LP/IH which counts. A high resolving lens with low contrast is less pleasing than a medium resolving lens with good contrast, therefore they use patterns of different LP/mm modulation (not digital on/off line pairs) to tell the efficiency of the lens at each relevant aperture, at each interesting point on the picture's surface. That said, most important are not the results, most important is the setup therefore one could compare other lenses. It's a huge package of documentation for each lens and it won't become smaller if the candidate in question is a zoom. I found the interpretations highly interesting as their conclusions of what a lens does was not obvious to me just by looking at the curves.
If you go to this Imatest sharpness page, you can see a nice example in the MTF section showing a black & white test chart (at increasing frequency), the resulting signal curve -- squarish at first but becoming a sine curve -- and the measured MTF curve.
Thanks, I think your explanation is understandable for even the geriatric crowd.....LOL.
But the nice visual made clear exactly the issue of measuring contrast and not necessarily the absolute resolution.
Very good explanations, feels like the ETF (explanation transfer function) to my brain is gaining resolution.
As MsMoto said here or on another thread it really just tells you the sharpness from the center outward to the corners.
Personally the only MTFs I pay any attention to are for ultra wide angles and macros where usually the goal is to have the image sharp from corner to corner.
Leica APO-Summicron-M 50 mm f/2 ASPH $8,000
Considered as optical perfection - this is the best MTF measured for a 35mm system if not all systems.
LEICA SUMMILUX-M 50mm f/1.4 ASPH
Considered the best 50mm 1.4 ever produced.
AF-S NIKKOR 50mm f/1.4G
AF-S NIKKOR 85mm f/1.4G
Not this supposedly by DxO is Nikon's sharpest lens
You can see the difference between the MTF superiority of Leica glass (reason for desire & cost) and how the Nikkors are fairly close to each other.
The thing that MTFs I find somewhat useless is that in post, you can add contrast and sharpness to any image and effectively raise the MTFs to match a better designed lens - to a point of course.
http://photographylife.com/how-to-read-mtf-charts