Modulation Transfer Function curves are helpful indicators of the performance of a lens. Seen for the first time MTF curves are very far from intuitive (not helped by the fact that different manufacturers use different testing methods) but once you understand the concepts behind them they become less daunting.
Do I need to know this?
Probably not. Likelihood is anyone curious about MTF curves will be trawling the internet for lens reviews from test sites and photographers, examining example images and so on in order to gain a sense of how their next lens performs in real-life situations—far more informative than staring at graphs, especially because there are other parameters beyond contrast and resolution that determine how the photographer perceives the final image quality produced by a lens. But, with that said, let’s delve into what these curves are all about…
The first problem we face is that ‘sharpness’ is very much subjective: two people can have differing opinions about whether lens A is sharper than lens B or vice versa. Consequently, optical engineers must try and come up with an objective framework by which to judge a lens, and here the two critical factors that give the end viewer a sense of an image being sharp are resolution and contrast.
Resolution is simply the ability of the lens to resolve detail; the higher, the better. Contrast, on the other hand, can be divided further into global contrast and local contrast (or acutance, if you prefer the more technical term). When we are concerning ourselves with contrast and perceived sharpness then we are talking about acutance. Global contrast refers to the difference in colour or brightness across the entire image. Acutance is contrast only at the edge of two different colours or shades.
Only the image to the left above can really be perceived as sharp, especially noticeable when comparing the details in the leaves. The following diagram should further illustrate the importance of local contrast when we are talking about image sharpness. However, acutance or resolution alone is not enough for an image to be perceived as sharp…
So what about MTFs?
Here is what an MTF curve looks like:
On the y-axis we have the MTF value and on the x-axis gradually increasing line pairs per mm. Line pairs per mm (or “spatial frequency”) is the number of black and white line pairs per millimetre, gradually increasing (so lines getting thinner) as you move along the x-axis. The MTF value is most intuitively defined as the contrast between the black and white lines at a given spatial frequency relative to the contrast at low spatial frequencies. Performing this calculation at each spatial frequency along the x-axis will give you the MTF curve.
In the graph above, we showed the MTF value for a hypothetically perfect lens and a diffraction-limited lens. All lenses are diffraction-limited: you can’t alter the physical properties of light. Accordingly, there becomes a point when even a real-world perfect lens can no longer distinguish between the black and white lines. Now, you may have noticed that the example MTF curves from Canon and Nikon had numbers along the x-axis going from 0 to about 22. These are not line pairs per mm—they are the distance in millimetres from the centre of the frame or sensor.
As you are probably aware, camera lenses do not perform equally well from centre to corner. Typically, we would see the strongest performance at the centre and a degradation in image quality as we move towards the edge of the lens. Measuring this degradation is an important factor in assessing the sharpness of a lens.
With this in mind, and remembering that photographers are most concerned with resolution of detail and good acutance (to give photographers that “pop out” or “punchy” feel), manufacturers choose two fixed spatial frequencies by which to judge lenses—10 lines per mm and 30 lines per mm. The former to judge acutance; the latter to judge resolution. These two spatial frequencies are laid out concentrically and radially to the centre of the frame (or perpendicular or parallel to the line from the centre to the edge of the frame). Meridonial and sagittal are the technical terms used. Better shown in a diagram:
The reason for testing lines perpendicular to each other is that lenses do not give the same MTF reading for each (intuitively you might expect it not to matter but it does). By testing with lines in both directions, we can easily see whether the lens displays any signs of astigmatism, where the lens does not focus equally in the horizontal and vertical direction, or lateral chromatic aberration.
There is an argument that low astigmatism (indicated by the solid and dashed lines being close together) is desirable for bokeh or background blur; however, in reality you cannot tell from an MTF alone whether a lens will have good bokeh—other factors also play an important role (e.g. diaphragm). Because astigmatism and lateral chromatic aberrations would both result in meridonial and sagittal lines being further apart which is to blame is difficult to discern, although lateral chromatic aberrations is the more likely culprit. Lines close together indicate that neither is present, however. In MTF graphs thick, thin, solid, and dashed lines are used to signify spatial frequency and line direction.
With the above in mind, let’s take another look at that MTF graph for the Nikon 50mm lens shown at the beginning of the article (follow the colour coding in the key below the graph—colour section of the table above applies only to Canon lenses).
As pointed out, Nikon perform their MTF test with the lens only wide-open; whereas Canon perform their tests wide-open and at ƒ/8.0. This is why the Canon MTF graph shown above had eight lines versus Nikon’s four. Testing at ƒ/8.0 provides useful information because (1) it provides a point of consistency when testing two lenses with the same focal length but different maximum apertures e.g. 50mm ƒ/1.2 vs 50mm ƒ/1.8, and (2) not all photographs are taken at maximum aperture—a landscape photographer for instance would value the data at ƒ/8.0 vs wide open.
Now that you can read the MTF curves, it’s worth remembering what they cannot tell you. MTF curves tells us nothing about:
- Colour reproduction
- Lens flare
- Longitudinal chromatic aberration
MTF-50 graphs are useful because they can give an excellent indication of a lens’s “sweet spot”—the aperture at which images are sharpest (typically between ƒ/8.0-ƒ/11). They show at each aperture the point in line pairs per mm at which the MTF curve drops to 50%. A 50% level is chosen as this correlates well with our own perception of sharpness (at this level we will still perceive the image to be sharp). The MTF-50 test will typically be performed at the centre of the image.