Have you seen my acutance? A few words about sharpness and MTF charts
Many of you know one of my pet peeves is strident internet arguments between photographers who are splitting hairs or misinformed. One major cause of these arguments is terminology: people use a nonspecific term which means something different to each of them. Others join in because the term means something slightly different to them. Pretty soon all are convinced all the others are idiots who just don’t understand. Its amazing, really, what a poorly defined term can do to take an interesting discussion and turn it into a screaming match. As Justice Stewart once said when describing pornography: “I can’t define it, but I know it when I see it”. Unfortunately, we all see things a little differently. When we can’t define a term, even though “we know it when we see it”, pretty soon we’re comparing apples and oranges.
One of the terms we photographers use that way is sharp. Seems simple enough—we all know a sharp photograph when we see it. Everybody wants a sharp lens. But it really means different things to different people. Lets be very superficial first. I have a friend who says his Canon 28-135 is very sharp. I’ve shot with several copies of that lens and never thought it was more than adequate. But he hardly ever makes prints, he posts his photographs online. And he shoots on a crop frame camera. I make mostly large prints of the shots I like (11 X 14 and up) and shoot on a full frame. So there’s the first misunderstanding. My definition of sharp is “What does it look like shot on a full-frame camera and printed to 11 X 14.” His is “What does it look like downsized and displayed on the web.” But sharp is a term that can lead to a lot more misunderstandings than just that.
Lets get a bit more scientific here. What does “sharp” really mean in photography? This is quite a complex topic if you want to get into it: we could discuss circles of confusion, Airy patterns , even Nyquist-Shannon theory and Rayleigh criterion. We could, but we’d all be bored to tears. Especially me. (And truth be told, I’ve read about that stuff a dozen times and I’m still not sure I understand half of it.)
So lets go for a more practical definition. There are two related, but slightly different things that determine ‘What is sharp?” They are Acutance and Resolution. Once you know what those are you will understand related terms like microcontrast. One more paragraph and you’ll understand that ultimate photography term modulation transfer function (MTF). And with just a little more reading, you’ll understand what those “MTF charts” really tell you about a lens.
What I’m offering you here is a veritable Rosetta Stone of sharpness terminology. After reading this little blurb, my friends, to the amazement of your supporters and chagrin of your adversaries you (YES YOU!) will be able to log on to your favorite photography forum and say things like “As you can clearly see from the MTF chart the lens has excellent acutance and microcontrast in the center but is going to exhibit softness and distortion at the edges and corners that would limit its usefulness for landscapes. Plus it will have harsh out-of-focus highlights wide open”. Is that great, or what?? Oh, yeah, I forgot. You’ll also be able to make better choices about which lenses you want to try without relying on someone else’s opinion quite so much.
Acutance and Resolution
Sharpness, as we discuss it in photography, is made up of two components: Acutance and Resolution. Acutance is about how sharply an edge transitions. Look at the figures below. Figure 1-1 has a high acutance, the transition from white background to black bar is sudden and complete (it represents a very good lens). Figure 1-2 has a bit less acutance and figure 1-3 still less (representing a not very good lens). Now here’s the take home message about acutance: Figure 1-4 is just figure 1-2 with a moderate amount of sharpening applied in Photoshop and figure 1-5 is just figure 1-3 with a high amount of sharpening applied. When we sharpen, either in postprocessing the image or with in-camera sharpening, we have increased the acutance, one of the two components of what we refer to as sharpness.
If we make the bars from figure 1 thinner and closer together eventually we will reach a point where the lens can no longer tell that they are separate black and white lines — they will just look like a gray area. We can measure this point for a given lens (assuming we have a good camera, so its not the camera sensor that is the limiting factor) in ‘lines per millimeter’. (In case you’re curious, the terms ‘line pair’ and ‘line’ are used interchangeably for this purpose.) Resolution therefore is an actual measurement, given in lines per millimeter, of the smallest details a lens can resolve. It, along with acutance, is what we perceive as sharpness. Some people will refer to high resolution (the ability of a lens to show small objects clearly) as ‘good microcontrast’.
One important point about resolution and postprocessing must be made. Figure 2 is similar to the one we used to demonstrate acutance, but this time the lines are much smaller and closer together. Notice that figure 2-3, our symbolic not-so-good lens, is at the limits of its resolution: you can sort of tell the lines are there, but it really looks more like a gray box than black and white lines. Like we did with the first set images, figures 2-4 and 2-5 are the best Photoshop sharpening I could get from figures 2-2 and 2-3. Unlike the acutance example above, however, postprocessing can’t restore resolution very well. Figure 2-4 is better than Figure 2-2 but its still clearly inferior to 2-1. Figure 2-5 is a bit improved over 2-3, but not much and there are obvious artifacts. Unlike acutance, resolution (AKA microcontrast) can’t really be improved in postprocessing. If the image doesn’t have it, you’re not going to add it later, no matter how good you are. (BTW—resolution is very important in large prints, but not so much in online jpgs. For those acutance is much more important.)
MTF (modulation transfer function) is simply a way to measure how much resolution and acutance a lens has. The formula is simple: (maximum-minimum/maximum+minimum). To make it simpler lets say white = 1 and black = 0. For any line pair in Figure 1 and for Figure 2-1 the maximum for each pair is 1 (the white line of the pair is completely white, at least in its center) and the minimum is 0 (the black line is completely black). Therefore the MTF of a well resolved line pair is (1-0/1+0) = 1. When I check figure 2-2, however, the maximum reading in the lightest area is 0.67 and the minimum reading in the darkest area is 0.33 (the lens can no longer completely separate black and white bars, they’re both shades of gray). The MTF therefore is (0.67-0.33/0.67+0.33) = .34. Figure 2-3 has an MTF of .08.
So MTF gives me a number that tells me how well a lens can resolve black and white lines: 1 means it completely resolves them into pure black and pure white. Lower than 1 means they’re blurred enough that the white isn’t completely white and the black not completely black, but at an MTF of 0.5 for example, the dark part is twice as dark as the light part. I could still tell them apart.
If I tested the lens with two different size lines, say one set at 10 lines/mm and another at 30 lines/mm (remember the terms line or line pair both mean one black and one white line) I find two different types of information. The ability to resolve large lines clearly shows the lens has good acutance (AKA good contrast). The ability to resolve small line pairs (30 l/mm) shows the lens has good resolution (AKA good microcontrast). The two MTF numbers give us an idea of how well the lens resolves large and small objects.
The MTF number we discussed above tells us about one point on the lens. Lets assume the MTF test we just did was at the lens center and found the MTF for 10 lines/mm is .95 and for 30 l/mm is 0.7. That’s something I can compare to other lenses measured at their center. But as we know, lenses give their best resolution in the center — the edges and corners may not be as sharp. If I test the lens for MTF at various distance from the center I can graph the results and get a nice chart that shows me how good the MTF is from the center all the way to the corners, at both 10 l/mm and 30 l/mm. By convention, MTF graphs use thick and thin lines, like Figure 3 below, to represent the MTF of thicker (10 l/mm) and thinner (30 l/mm) lines. (Not every manufacturer does it, but it would probably be a good idea to also test the lens at its widest aperture and its best aperture, say f/8 for most lenses. MTF charts that do this will use one color for f/8 and another for the widest aperture the lens has. I chose black lines for f/8 and blue for wide open for this illustration).
So what does this partial MTF chart tell us about our theoretical lens? It resolves thick line pairs better than thin, like every lens. At f/8 (black lines) its very sharp 3/4s of the way out from the center. After 15mm, though, performance, particularly at 30 l/mm, falls off. I’d expect the reviewers would say “A little soft in the corners, even stopped down”. The blue lines show us that wide open the lens still performs pretty well right in the center, but sharpness falls off steadily as we move away from the center. What does this mean in the real world? A landscape photographer who shoots at f/8 might tell me his copy of the lens is very sharp. So might a portrait photographer whose subject is generally in the center of the lens even if they use it at f/2.8. A wedding photographer who shoots tables of people during the reception at f/2.8 may well say the lens “is so soft its unusable” because the subjects at the edge of the picture are soft compared to those in the center. And all of them would be correct.
Actual MTF charts look a bit more complicated than the sample above because they contain one important piece of data I’ve left out so far. Real lenses have slightly different resolution depending upon which way the line pairs are oriented. If the line pairs are parallel to the radius of the lens (the radius is any line from the center to the edge) they are called sagittal lines (sometimes referred to as radial lines to help keep it confusing); if they are at right angles to the radius they are meridian lines (sometimes referred to as tangential lines). The figure below on the left probably explains it better than words. MTF charts will usually show the sagittal MTF as solid lines and the meridial MTF as dotted lines, so we get a chart like the one below.
It looks a bit confusing at first, but actually its not. Thick lines are MTFs at 10 llines/mm (how good the lens’s contrast is) so we’ll start there. An MTF over 0.8 is excellent, one over 0.6 is good and below 0.4 is generally not OK. So we can see from the thick lines in the chart that the lens has excellent contrast at f/8 almost to the corner (black lines) and good contrast to between halfway and three-fourths of the way to the corner at f/2.8 (thick blue lines). The thin lines (showing the lens’s resolving ability) are good, but not excellent, at f/8 (thin black lines) and really not very good at f/2.8 (thin blue lines).
So what about the difference between the dotted lines and the solid lines for each pair, the difference in resolving meridian and sagittal lines? If the dotted and solid lines are close together, the out-of-focus areas of the lens will be smooth and pleasing (good ‘bokeh’), while if they are far apart the out-of-focus areas tend to be distorted and less pleasing (bad ‘bokeh’). There are some other significances that we won’t get into today like tendency to flare and smear, and certain types of distortion. The bottom line, though, is if the dotted lines and solid lines are close together that’s a good thing.
Some MTF comparisons
Its important to realize that MTF charts, while very useful, are also very limited. An MTF chart can show you the limitations of a lens, a bad MTF chart usually means a bad lens. On the other hand, a great MTF chart doesn’t always mean a great lens for every purpose. Lens coatings, focusing abnormalities, some forms of aberration, and a host of other things aren’t going to show up in the MTF chart.
It’s also important to not compare apples to oranges. In the old days lensmakers proudly displayed the MTF charts of their creations as measured in the lab. Not many manufacturers do that today (Zeiss and Leica are the only ones I believe). The other manufacturers present their data differently and use different methods to obtain it, so it can be misleading to compare MTF data from two different manufacturers. The MTF chart may be computer generated from a theoretical model, or may only show part of the data we discussed above. Canon publishes very complete charts with separate wide and telephoto charts for zoom lenses, but even they seem to have ‘lost’ the charts for certain lenses (the infamous 17-85 EF-S lens, for example, has no MTF charts to be found). Nikon and Sigma present the wide aperture MTF of their lenses, but not the f/8 data. Tamron and Tokina tend to not publish their MTF charts at all.
Even given all of these limitations, the data from MTF charts can still be quite useful. Lets look at a couple of real world examples from Nikon.
The two charts above compare two 400mm telephoto lenses. On the left is the 80-400 VR at 400mm. On the right is the 400mm f/2.8 VR. The 400 f/2.8 VR may be the best telephoto lens made and the MTF chart shows it: from center to edge the MTF approaches theoretical perfection. The 80-400 is actually no slouch: the 10 lines/mm pair (red lines) remains above 0.8 far to the edge, although the 30 lines/mm pair separate quite a bit and the meridian line drops below 0.6 fairly early on. From the MTF chart I’d realize the 80-400 can get good shots, especially if I stay centered in the lens. The separation of dotted and solid lines also tells me the out-of-focus highlights will be a bit more harsh on this lens, especially toward the edges, while the 400 f/2.8 will be very smooth. This is indeed what we see in the real world.
The next charts compare a pair of wide angle zooms at their widest. Wide angle zooms are more difficult to design and the MTF charts reflect it to some extent. On the right is what is widely considered an excellent wide-angle zoom, the Nikon 17-35 f/2.8 IS. Notice it keeps the MTF of the 10 lines/mm above 0.8 all the way to 15mm from the center. It doesn’t fare nearly as well with the 30 lines/mm MTF obviously. On the left is what is widely regarded as the finest wide angle zoom made: the Nikon 14-24 f/2.8 AF-S. It clearly does a better job with the 10 lines/mm MTF all the way out to 20mm from center, and is also markedly better at 30 lines/mm. While we recommend not comparing MTF charts between manufacturers (they don’t all derive their numbers the same way) if you look at some other good wide angle zooms like the Canon 16-35 f/2.8 or the Sigma 12-24 you’ll find their MTF charts are much more like the Nikon 17-35 f/2.8, showing just how great the 14-24 really is.
When you get a chance, take a look at the MTF charts of some lenses you already know and see how they compare with your experience using them. Canon and Sigma have the MTF charts of each lens on that lenses page on their website. Nikon USA doesn’t publish MTF data online, but the main Nikon site in Japan does (and its in English).
Oh, and one last thing: about my friend’s Canon 28-135, here’s the MTF chart from Canon’s website at both 28mm and 135mm. (In this chart blue lines are at f/8, black are wide open.)
Notice the thick lines are really excellent out to 15mm from the center (which is all that matters on my friend’s 40D), both at 28 and 135mm? The 30 lines/mm pairs really aren’t so great, especially at the 28mm end. There you have it: my friend’s online images, with their emphasis on contrast and acutance look good and that’s his definition of sharp. My big prints from a 5D, with an emphasis on resolution and microcontrast, don’t look as good, and that’s my definition of sharp. We’re both right. But don’t tell him that—he’s busy having an argument about it in one of the forums and wouldn’t want any facts spoiling the debate.