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A Story About MTF
An introduction to the art of understanding MTF
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Modulation Transfer Function (MTF) is a very popular tool to measure resolution of optical systems. Unfortunately, it is often misunderstood by both engineers and photographers. People tend to rely on mathematics and forget about general physical principles. Of course, MTF charts can explain many interesting things. But they cannot explain everything. This article gives some physical interpretations of MTF without paying a lot of attention to technical details. Its purpose is to teach you how to treat MTF curves and how to derive truly valuable information from them.

What kind of function is MTF? Suppose you drew several black and white lines on a piece of paper and took a picture of them, what would you see? On your photograph, the black lines will become lighter, while the white lines will become darker. In other words, the contrast will decrease. In different parts of the image, the contrast will drop to a different degree. An MTF curve shows to what extent the contrast drops at any particular distance from the image center.

For any given lens we can get a number of different MTF curves, depending on: 1. how we draw lines (we may place them along radiuses pointing away from the image center, or we may place them along circles around the image center); 2. the spatial frequency, i.e. the number of lines on every millimeter; 3. the f-stop.

When the contrast drops below the resolution level, we will not be able to distinguish black and white strokes in the image. Everything will be equally gray. It would take too many words to discuss the resolution level here. Another boring article could be written on this issue. To keep things simple, just believe this level is somewhere between 10 and 50 per cent.

Generally speaking, the decrease in contrast causes the decrease in sharpness. Thus, MTF curves show how sharp are images produced by lenses.

Now let us consider a simplified example. The picture below shows two MTF curves for two different lenses. Let us assume the curves were obtained under the following conditions:

- f-stop = 5.6;
- spatial frequency = 20 line pairs per millimeter;
- the radial pattern of strokes was used.

What can we say about those lenses? 1. The first lens (the red curve) performs perfectly within the central part of the image (70 per cent in linear terms or ca. 50 per cent in area terms). But the picture it produces can be blurry at the edges. 2. The second lens (represented by the blue curve) is not that good in the center. The difference between the two lenses can be up to 15 per cent in the central area. But the image quality does not decrease at the edges. The curve is almost flat with some small irregularities.

Which one is better? There is no simple answer to this question.

Imagine four different photographers with for different approaches.

Photographer A may say: I always place the object in the central area. For the first lens, the contrast drops below 50 per cent only on the 1/5th border. There can hardly be anything significant in that part of the picture. My choice is Lens#1.

Photographer B: The 15 per cent difference in the center is negligibly small. Nobody can see it. However I think that the entire picture should be of the equal quality. I would buy Lens#2.

Photographer C: I am going to install this lens on my new digital SLR camera. Its sensor is smaller than the regular 35mm film frame. Lens#1 is the best performer for my purposes.

Photographer D: Judging by the curves, the lenses are practically equal. I would like to see the pictures they produce before I make a decision.

Of course, the situation is simplified. Besides resolution there are many other important factors, such as distortion, vignetting, flare-control, reliability, etc. But even if we forget all such things, the choice will not be very simple and obvious.

Sometimes, integral values are used to grade lenses. And many people do believe that a lens with 3.9 points is better than a lens with 3.6 points. I believe, such an approach is crazy! MTF curves provide us with a lot of information that cannot be reduced to one value. Let us get back to our example.

Imagine we introduced the following quality criterion: the bigger the area under the MTF curve, the better. In our example the area under the red curve is larger by 6 to 7 per cent. We can give 4.9 points to Lens#1 and 4.6 points to Lens#2. Does this make sense? I do not think so. As I have shown above, we cannot say Lens#1 is undoubtedly better. Of course, the difference in 2 points would tell us something, but only spurious statements can be made based on the 6% difference. Moreover, I could easily redraw the curves, making only minor changes in their shapes and leaving slightly larger area under the blue curve. Will "Photographer A" change his mind in that case? Of course, he will not.

The integral values at the Photodo website absorb considerably larger information, taking readers away from physics to statistics. But calculators are a poor substitution for both the common sense and physical understanding. Market prices for lenses can be much better indicators, I believe.

Thus, MTF curves can be very informative. But it is important to understand that they cannot represent the entire idea of lens quality. They cannot tell us everything even about sharpness.

1. MTF curves for lenses are usually obtained when the lenses are focused at infinity. Will they change much, if we focus at a near object?

2. What will happen if we use a mosaic pattern, like a chess-board, instead of the pattern composed of bands?

3. It may be also important to know why the resolution drops. Does this happen because of chromatic aberration or something else?

4. What if we use color bands instead of black and white bands for our measurements?

I can easily continue asking questions. But the idea is simple. There are no perfect instruments. There are no perfect methods. There will always remain unclear questions.

MTF curves are used not only to describe sharpness of lenses, but of many other devices as well. But their appearance differs from what we saw above. For example, if we analyze films it does not make sense to place distance on the horizontal axis of our charts. Film quality is the same in every part of the frame. In such cases, the decrease in contrast is shown as a function of spatial frequency (to say the truth, this is a more common appearance of MTF curves). As an example, the MTF curve for the AGFACOLOR OPTIMA II 400 film is shown here.

MTF curves are a very useful instrument. The more we understand this, the more reasons we have to learn how to use them correctly.

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Links

1. If you are looking for a mathematically rigorous deduction and more details, please read "Understanding Image Sharpness" by Norman Koren.

2. A lot of real MTF curves for many available lenses can be found at Photodo.

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