Is it possible to judge the quality of the lens on his OTF (OTF), is also widely known under the English-language name of the modulation transfer functions (MTF).
The answer is simple: MTF curves speak volumes, but not everything. This article – an attempt to explain the physical meaning of these curves without a detailed discussion of the details and subtleties.
So, what is the curve MTF? Take pictures of alternating black and white strokes of equal width, placed in a location shot. If we consider the result, we find that the contrast of the bars on the film will be compared with the contrast of the original. Black bars will be a little lighter, and white – is darker. Moreover, it is easy to notice that the fall of contrast will depend on where we put our strokes. MTF curve is just shows how decreases the contrast of the middle frame to its edge.
For the same lens can be constructed several curves depending on a number of parameters:
1. Strokes can be placed both on the radii emanating from the center of the frame (radial) and perpendicular to this radius (tangential).
2. At one millimeter can accommodate different number of pairs of lines, ie, the strokes may follow a different spatial frequency.
3. Measure the drop in contrast can be at different apertures.
Clearly, the greater the fall contrast, the harder it will be to distinguish dark from light strokes. If the given initial conditions, the contrast drops below a certain level, it no longer touches the eye vary, and you can say that this spatial frequency at a given frame the lens does not allow it. Here we will not discuss the value of this threshold. This is a separate big topic. Suffice it to say that according to various estimates it is in the range from 50% to 10%.
In other words, the MTF curves tell us detailed information about the resolution. They show how the contrast (and with it, and clarity) on the area of the frame and how it depends on the lens aperture and other factors.
Consider a simplified example. Below the figure shows two curves of MTF for two different lenses. The curves were obtained with the same initial conditions. For example, these:
- Aperture = 5.6
- Spatial frequency = 20 pairs of lines per millimeter
- Strokes are located radially.
What can we say about these lenses?
The first lens (red line) has excellent resolution in the central part of the frame (70% in linear dimensions and about 50% by area). But the edges of the image quality quite falls. At fotozhargone in such cases we say that the lens “soaps” on the edges.
The second lens (blue line) gives the first in the center. The difference in the contrast of up to 15%. But the quality of image formed by this lens, the same across the square frame. MTF curve in this case is somewhat uneven, but the unevenness is small.
Which lens is better? Single answer does not exist.
Photographer Alexander may reason as follows: One way or another, an important part of the plot frame is always in the center. In contrast to the first lens falls below 50% only in the last 20% of the frame. It does not matter, because at the edges of interest is not enough. My choice – lens № 1.
Photo B: The difference of 15% is ludicrous. No it is not visually notice. But the same quality throughout the frame to have a very wanted. My choice – lens № 2.
Photographer Q: I need a lens for my digital SLRs. Matrix it is not full size, so will be used only the central part of the traditional frame. Of course, I like the lens № 1.
Photographer T: On the resolution of these devices are almost identical. It would be nice to look at the real images, which give these lenses.
The situation is somewhat exaggerated. In addition to the resolution there are many other important parameters, such as distortion, vignetting, enlightenment, mechanical strength, etc. But even if for a moment forget about all these details, and even then, looking at the curve of MTF, it is difficult to make an unambiguous choice.
Sometimes, the set of curves “squeeze” to a single number. It happens that on the basis of these numbers are building even ratings lenses. Nothing more absurd can not even imagine! The whole point of MTF curves is in the detailed information. Returning for a moment to our example. We introduce the integral quality criterion: the resolution of the lens the better the larger the area under the curve of MTF. The area under the curve number 1, all the same at 6-7% larger than the area under the curve number 2. Therefore, the lens number 1 can be awarded 4.9 points, and the lens number 2 – 4,6 points. What do these points? Yes, anything! No, of course, if the lenses are distinguished by scores of 40-50% per cent, then that any conclusions could be made. Until then, until the lenses are distinguished by scores of 10-20%, to draw conclusions about the difference in their capacity as impossible. Moreover, in our example could easily be depicted as such in fact two curves, but with more 10% area under the curve number 2. This would affect the choice of “A photographer”? Obviously not!
Quoted on the website Photodo integral estimates lenses absorb more factors, leading the reader from the world of physics in the world of statistics. However, in such cases, calculators are a poor substitute for the physical and common sense. Using as an integral evaluation of the price of the lens, perhaps, would have even greater meaning.
Thus, the MTF curves certainly have a lot of useful information. But much work behind the scenes. Even about the sharpness they say not all.
1. When measuring lenses usually focus on infinity, and yet it would be useful to look at the curves for the case of focusing on close objects.
2. It would, for example, be interesting to analyze the fall of the contrast is not to bar the picture, and for point-to-mosaic (something like a chessboard). The result might have become somewhat different.
3. One could inquire, through which falls permission. The deterioration of sharpness due to chromatic aberration can visually look different than the deterioration of sharpness due to other causes.
4. It would be interesting as an experiment is not black and white, but with colored strokes.
But does it matter what other questions could be asked! In other words, what would have been perfect method and apparatus of measurement, will always be questions that have not yet received a reply. This is absolutely normal. And we should not oversimplify reality to a single assessment, how wonderful would not have been the method of its receipt.
MTF curves can be obtained not only for the lenses, but for a film scanner, digital camera, printing machines, etc. Look like they might be slightly different.
For example, for the film does not make sense to postpone the horizontal axis distance. The film has the same properties throughout its area. In such cases, the MTF curves show how the contrast will depend on the spatial frequency. Strictly speaking, it is even more common and typical form of graphs MTF. The name “OTF” implies that one axis represents the contrast in the percentage of the original, but on the other – the spatial frequency in line pairs per millimeter. As an example, the figure shows the MTF curve for the film AGFACOLOR OPTIMA II 400.
Curves MTF – a useful tool, which finds application in all areas related to the imagery: in optics, printing, scanning, etc. in It is important to correctly use this tool.