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I was talking to some people who complain that their pictures are "soft", and I suggested several tests to try to identify if the problem is the camera, the focusing system, or the lens. It wasn't as simple to explain as I would have liked. Plus, I realized I know how to test my lenses for decentering but I've never actually done so. Which takes me to: blog post, here I go.
First of all: everybody calls it "decentering", but the usual problem is actually tilt. If you want to learn more technical stuff related to this, go here. For my purposes, summary: your lens is composed of several pieces of glass, and if any of them is not in a perfect position, the images won't be as sharp as they could be. And no lens ever has all elements in the perfect position. Not even very expensive brand new lenses. Particularly if it's a zoom (prime lenses have a better chance of being close to perfect, because they are simpler so there's less stuff to go wrong). In any case, it's much more of a problem for old lenses, particularly if you ever dropped them, as I once dropped my very expensive Leica Summilux-R 50mm f/1.4 (it's a 40-years-old lens so I'm sure it wasn't its first time either).
Also: even if your lens is perfectly-aligned, it will probably have some field curvature: it will focus closer in the center than in the edges, or the other way around, or closer in the center, farther in the sides, and closer again in the edges. I sold my Leica Summilux-C 40mm f/2.8, among other ghints, because the field curvature was absolutely crazy. I didn't like that lens at all.
Second: this doesn't make sense for many lenses. If your lens is not able to blur the background, this test won't tell you anything. It only works well with fast lenses (maximum aperture of f/2 or wider, unless it's a super-telephoto, in which case f/2.8 or f/4.0 may be enough).
So, take your camera and the lenses you want to test (in my case, my four 50mm primes plus the zoom in my RX100 IV), take something to work as a target (for me that was a can of cola), and go find a place with a detailed, textured floor. Put the can (or whatever) on the floor, a few meters in front of you (in my case, 4 meters) and use it as focusing target for all the tests. And in all the tests, set your lens to maximum aperture (f/2.8 or f/2.0 or f/1.8 or f/1.4 or whatever).
Before testing for decentering, in case you're using AF, let's test your camera+lens combo for systematic autofocus issues. If your camera has a mirror (DSLR) and your lenses are fast (maximum aperture of f/2 or wider) this is likely to be an issue. On mirrorless cameras, in genral, it's not a problem. But let's test it. So: focus at the floor just one meter in front of you, then focus at the can and take a picture. Focus just in front of you, then focus at the can and take a picture. And so on, eight or ten times, resetting the AF by focusing close to your feet, then testing it with the can and taking a picture.
Then, test for decentering: focus at the can (or whatever target you're using) and take a picture in horizontal position. Then rotate the camera 45º and take another picture in this diagonal position. Then another 45º and take a vertical picture. Then another 45º to get the other diagonal. In total, four pictures, all with the can in the centre, looking like this:
(On my lenses, only the horizontal pics ended up being useful, but maybe on yours the other ones will help understand what's going on)
Then repeat all of this for each one of the lenses you want to test. Then go home.
At the computer, sort out all the lenses, labeling them with whatever lenses or settings they correspond to (if you don't do it now, you never will).
In principle, you can just look at them and see which areas are in focus and which are not, but if you're lazy and/or your asessment is likely to be inconsistent, you can just open Photoshop and apply a filter called stylize > find edges. It will give you a white image with the sharp edges of the original image marked in color. Similar to the ones you'll see below.
These are the autofocus tests with my Sony FE 50mm f/1.8 on the a6000:
In my case, since it's a mirrorless camera with in-sensor phase detection, I can't have systematic backfocus or frontfocus issues, but if you're using a DSLR you may find that it tends to focus slightly in front or behind your target. If that's the case, you better have a camera that allows for autofocus microadjustment. That's a simple software trick that corrects for this bias, and it should be in every camera but manufacturers usually reserve it for high-end models, just because they want you to spend more money: entry-level DSLRs don't usually have it. If you have backfocus or frontfocus issues and your camera doesn't have AFMA, then you can either send back the lens and get a new copy (if you just bought it) or resort to focusing manually whenever focus accuracy is important for the shot. I know it sucks, but that's how it is. In any case, knowing you have this issue is a good thing: you can shoot with a narrower aperture (f/2.8 instead of f/1.8) to minimize the problem, for example.
You can also see that whith this camera+lens combo I'm getting very consistent focus. Other camera+lens combos will get more variance, with some shots ending up slightly frontfocused and some slightly backfocused. As long as it's not very often and not always in the same direction, it's not a big problem. But knowing how often it happens is a good thing: if it's a problem in half of your shots, make sure you take three or four shots whenever you take an important picture.
Now, let's look at the decentering and field curvature tests with my Leica 50mm f/1.4. First, the horizontal photo, which is the easiest one to read:
As you'll see, not only does it have some field curvature (focusing closer on the edges than in the centre) but it also is unable to get as sharp on the right side of the image as on the left side: it's slightly tilted. Not much, just a bit, but it's there. It was probably more symmetrical originally, but then I dropped it and something moved just a few microns inside, and the optical result is that now it focuses closer and sharper on the left than on the right. This field tilt means that, whenever I'm about to shoot a portrait with vertical framing (where the face usually ends up away fromt he center of the image), focusing at the center is going to be a bad idea: the clothes will be sharp, but the face not as much. And I'm going to get the same bad result if I put the face in the center, focus there, then reframe and shoot. What I'll have to do whenever I take a vertical portrait is to move the little focusing square off to one side and focus on the face, without reframing after focusing. And the slight tilt means that it's better if I rotate the camera clockwise instead of counterclockwise in order to take a vertical portrait: this way the face will be sharp, and the soft side of the lens will cover the feet. It's going to be awckward, but well, that's how it is.
The diagonal and vertical tests don't show much more info in this case (or with any other of my lenses), but anyway, here they go:
You coud get a lens with a soft corner, or two soft corners, or a soft side, basically any option is possible, that's why all these rotations have to be tested.
As an extreme case, here's my Kodak Anastigmat 50mm f/1.6, an S-mount cine lens from ~1947 that's absolutely amazing -I've only used it once and I'm already in love with this lens- but not because of its sharpness: as you'll see, the center is super sharp, but everything else is, well let's say soft but that's a huge understatement:
If I really cared, I could close down the iris a bit, to f/2.8 perhaps, and test it again, to see if it's tilted or not. But I really don't care. This is a crazy lens and I'll always use it wide open, with the subject in the center. At least I know the sharp bit is in the center, and not actually decentered, off to one side or the other.
My Industar-61 52mm f/2.8 from 1969 is also battle-tested, but surprisingly doesn't show big tilt issues. Maybe the right side focuses a bit closer than the left, but as long as I don't reframe after focusing it's not going to be an issue:
Back to the Sony FE 50mm f/1.8, it has some field curvature but not much, and I don't see a significant tilt in any of the rotations. Maybe the left side focuses a bit closer than the right, but the problem here is not that, but that the field curvature is not so small: enough that I won't be doing AF in the center and then reframing. Instead, I will either move the little AF square to wherever I want the camera to focus, or use the center AF point but not reframe afterwards (instead, crop in post, which means I lose resolution and shallow-depth-of-field capabilities, but at least the images will be properly focused). Clearly, moving the AF point is the better option, and since this camera has face-detect AF (it moves the square automatically to wherever it finds a face), well, that's what I'll use, whenever possible.
Luckily for me, unluckily for you, all the lenses I tested are kind-of-OK, withot great tilt issues, and with relatively boring fields of focus. My Summicron-C 40mm f/2.8 would be showing some crazy butterfly patterns in these tests, but I sold it so, well, go to this article again if you want to see some "interesting" field of focus examples.
Finally, here's my RX100 IV, shot at both 70mm f/2.8 and 24mm f/1.8 (always in FF-equivalent focal lengths). The sensor is so small that it's not easy to get a defocused background, at least not at 4m. On the 70mm test, this miniature won't show much, but the full-resolution version of the image does show a clear difference: the left side is sharper and focuses closer than the right side. It's a zoom, and zooms do this, almost always. The lens is tilted. As with my Leica 50mm, I'll have to take vertical portraits with the left side of the sensor covering the face, which is not what I'm used to.
The 24mm shot has such a deep DoF that it's hard to see anything. Maybe the left side is sharper and focusing closer than the right side, or maybe I just chose a bad place to shoot my test and there's sharper stuff on the left than on the right. Given the 70mm results, though, I'll go with "it's tilted". I don't usually shoot vertical at 24mm, so in this case what I will do is close a bit the iris when I shoot at 24mm with interesting stuff on the right side of the frame (f/2.8 should be enough).
So, that's it. I hope this was useful. The idea is to know your gear, and how best to use it, but remember that you didn't get a camera because you wanted to shoot cola cans, there's much more interesting stuff to do with your camera than spending your life testing it and worrying about sharpness. Happy shooting!