Lenses and Optics

Field Curvature and Stopping Down

Published September 28, 2014

Ignorance more frequently begets confidence than does knowledge. Charles Darwin

What I know that I don’t know doesn’t cause me much trouble. I don’t know the formulas for 7th order optical aberrations for example. I don’t know enough math to calculate those formulas even if I did memorize them. But I’ve got shelves of books on optics and friends who know way more optical theory than I do. So if I need to find out something about 7th order aberrations (mercifully, to date that hasn’t been necessary) I can go find out about them.

What I don’t know that I don’t know causes me all kinds of trouble. I had yet another learning experience last month relating to field curvature (more accurately, the plane of focus curvature). Like everyone else I knew that when I stopped the aperture down on a lens the image got sharper and the depth of field got larger. I knew that the center might sharpen up more than the corners, at least at first. But I assumed that if the corners were getting sharper, and the center was getting sharper, than everything in between was getting sharper, too. It turns out that isn’t always the case.

I’d also never really thought about what happens to field curvature when you stop down.  If I thought about it at all, I probably assumed it would flatten out. Or maybe stay the same but the increasing depth of field would make it less noticeable. Turns out that isn’t always the case either. So, because I made assumptions and didn’t know what I didn’t know, I wasted a lot of time. Weeks of time.

But that’s a really geeky story I won’t bore most of you with (I’ll put it as an addendum at the bottom for you fellow geeks who can’t wait for the next episode of ‘Roger figures out what he should have already known’). For the rest of you I’ll just make a nice, quick practical demonstration of how field curvature behaves as we stop down, using the lenses I blogged about last week – the wide-aperture 35mm lenses.

What These Graphs Are

Let’s do some quick terminology so we’re all on the same page. Most of us call what I’m going to describe today field curvature, but plane-of-focus may be a better term. Basically if I focus the center of my lens on an object at a certain distance away, that object is (in theory) at the sharpest possible focus the lens can provide.

Let’s say the object I focus on is a perfectly straight barbed wire fence at right angles to my camera. Let’s pretend there’s a row of rocks a few yards in front of the fence and some trees a few yards behind. If the plane-of-focus of the lens is perfectly flat, then the entire fence is in focus from one side of the image to the other, with the rocks and trees just a bit softer.

If the field curves, however, at some distance from the center the rocks (or the trees) may be in better focus than the fence. If the curvature is complex (so-called mustache curvature) the fence is sharpest in the center, but as we move away from the center to the edge of the image the rocks get sharper, then the fence comes back in focus, and finally the trees are the sharpest. Or some similar variation on the theme.

The optical bench lets us look at the plane of best focus for any lens at infinity, and I’ve been showing it for the lenses I’ve recently tested. But I’ve only been showing it at the widest aperture. I think you might find it interesting to see how the field behaves as we stop the aperture down.

Remember, the sagittal and tangential field curvature is different for most lenses; at least most wide-angle lenses. These are representative samples from a single lens; the number of points that goes into these calculations makes averaging multiple copies difficult, so we test several of them and show you one of the ‘average’ ones. Sometimes there’s a very slight tilt to the field (usually the tangential field) that is noticeable on the optical bench, although it wouldn’t be in a photograph.

35mm Wide-Aperture Field Curvatures






I’m not going to go into great detail telling you what you can see for yourself in the graphs. But I do think it’s worth pointing out a couple of things. First, the thick horizontal line across the center of each graph is where the center is focused. If you follow it from one side to the other on the sagittal graphs, you’ll note that for most of these lenses are a bit sharper at the absolute edges (because it’s in better focus) than in the area about 3/4 of the way from the center to the edge. It may be a bit clearer on the graphs that are stopped down a bit than on the wide-open ones.

For some lenses (the Zeiss in particular, but the Sigma does, too), the field curvature near the edge is going in opposite directions on the tangential and sagittal curves. Stopping down to f/5.6 is not going to eliminate astigmatism along the edge in these lenses.

My major point is that when stopping down, the field doesn’t really flatten. If you look very, very closely, in a few instances the curvature actually increases in certain locations as you stop down, but that’s a geeky detail. The takeaway message is that stopping down a lens doesn’t flatten the field. You have to stop down enough that the depth of field becomes greater than the curvature.

For the 35mm f/1.4 lenses that means at least f/8. As we do field curvatures for other lenses you’ll see that isn’t always the case. There are some general guidelines we’re seeing. For example telephoto lenses (even at 85mm) have less field curvature. Wide-angle lenses tend to have more, or at least more complex curvatures.

For most of you who are stopping down for landscape or architectural work, lenses with flatter fields might be more important than the sharpest lens. If you like the Canon and Nikon lenses (and there’s a lot of reason to like them) you might want to be aware that the absolute edges might actually be slightly sharper than the area just short of the edges. (This may seem unimportant, but I know some people who frame an image expecting to crop the absolute edges, so that they keep the ‘sharpest’ part of the image.)

Finally, I should point out that the frequency of MTF measurement makes a difference in the depth of the field. All of the above graphs are done at 30 lp/mm, which I think is a nice compromise between acutance (contrast) and resolution (fine detail). But to give you an idea, I’ve repeated the f/1.4 graphs for a Canon 35mm f/1.4 lens below, at frequencies from 10 lp/mm to 75 lp/mm.

As you can see from the 10 and 20 lp/mm graphs, the curvature is less dramatic at lower frequencies, while it becomes more pronounced at higher frequencies. Someone taking images of large objects with strong contrast and posting them online isn’t going to care much about the field curvature. Someone who finds fine detail critical and makes large prints, like a landscape photographer, may find it a critical issue.

The Geeky Stuff

This part is of no practical importance, but I know some of you like reading about those frequent occasions when our research shows me something I don’t understand. Or that I don’t believe. Or both.

This all started when I wanted to do stop-down MTF curves for all of the lenses. I started with a Canon 35mm f/1.4 lens and did our usual 4 quadrant MTF curves wide open, and then repeated at f/2.0 and f/2.8, which I’ll graph below.

If you look at the MTF charts above you’ll see as we stop down from f/1.4 to f/2 the sharpness in the center of the lens (from -5mm to +5mm) gets dramatically better, as I expected. The corners get just a little better, as I expected. But look at the high frequency sagittal lines (the green, blue, and orange solid lines) between 10mm and 15mm from the center. They get worse. Much worse. That is absolutely damn not what I expected.

But hey, it was just one lens and weird things happen sometimes. So we tested another 5 copies. They were all the same.

So OK, maybe it was the Canon 35mm f/1.4 lenses. So we tested a batch of Nikon 35mm f/1.4s. They did the same thing, too. Well, that made it obious that something must be wrong with our machine. But when we had everything checked out and recalibrated, it was all fine. So obviously something must be wrong with our technique. So we redid the tests in a blackout room, then using just green light, then just blue light. Then doing sagittal and tangential tests separately. Then we did a full vibration isolation thing, slowing down the testing so that it took four times as long to make each measurement. Nothing mattered. Finally we asked the experts at Trioptics to look over our results and repeat the tests on a different machine in a different location. They got the same results we did.

Finally, at the suggestion of some consultants, we started testing field curvature (more detailed testing than the graphs we’re using for demonstration; actually measuring the distance in microns of best focus for each position across the test axis). What we found was in that area around 13mm where the sagittal MTF curves drop there is focus shift that is different from the overall focus shift. (Just to be clear, the 35mm f/1.4 lenses don’t have bad focus shift, it’s barely noticeable in photography, but it makes a difference in testing.) But if the center focus changed 3 or 4 microns when stopping down, the area around 12-16mm off axis changed about 6 or 7 microns.

That was enough to make the MTF curves softer at high frequencies. The big hint we should have gotten was that the sagittal MTF curves were dropping but not the tangential ones. Looking at the field curvature graphs, it’s the sagittal fields that have the complex curvature with the curve maximizing right at the point we saw the softening.

The bottom line is the MTF is lower because the area is more out of focus — when measuring MTF you determine best center focus and then measure every spot at that focusing distance.

You may already know this. I wish I had. It would have saved, oh, about 100 hours of our time. Just so you know, this doesn’t happen with very many lenses. But it does happen with most of the 35mm f/1.4 lenses and some other wide angles.

Roger Cicala and Aaron Closz


September, 2014

Author: Roger Cicala

I’m Roger and I am the founder of Lensrentals.com. Hailed as one of the optic nerds here, I enjoy shooting collimated light through 30X microscope objectives in my spare time. When I do take real pictures I like using something different: a Medium format, or Pentax K1, or a Sony RX1R.

Posted in Lenses and Optics
  • william le

    Given that the lens manufacturers, say Canon, would know their own field curvatures, is that taken into account by the camera manufacturer focusing algorithms when using outer AF points? For example if shooting the Canon 35mm 1.4 at f5.6 with an outer AF point, does the camera do an ‘internal AF microadjustment’ to bring the sharpest area of the field curvature into focus point? I imagine you would get the subject in better focus as long as you don’t focus-recompose.

    Thanks in advance if there is a reply to this late question.

  • spaceman

    Hey Roger, can you next time indicate units on the axis. It is good practice to inform what the axis exactly are, even though it may be written in the article somewhere. This article is not very easily consumed 😉

    Interesting findings though. Thumbs up.

  • What about lenses with floating elements for near focus correction, like the Leica 35 and 50/1.4s? The Leica 35/1.4 asph pre-FLE was subject to endless discussion over its focus shifts (and the 35/1.4 Voightlander competitor had undisputed focus shift). So do you have those in the shop to take a look at, and see how they compare? Did the FLE move the problem of focus shift to some other part of the field, or flatten the field as well as shift it?

  • Zak McKracken

    This makes it look as if it was a good idea to quote the MTF figures both for focus in the centre and with best focus at each point.
    Since most people don’t shoot just flat walls while holding the camera exatcly normal to them (especially not with open apertures), it’d make sense to focus wherever the subject is. The “put subject in center, focus, then reframe” approach is a bad idea at large apertures anyway, even with a planar field.

    … wouldn’t it be possible to extract both pieces of information from the optical field data? One is along the x axis, the other is along the line of maximum sharpness. This wouldn’t take the sensor into account but I think that field curvature will be independent of that as long as the sensor is planar, and not having to test every camera/lens combination for this might help justify the effort 🙂

    … having said which: Since sensors will deliver worse images if light is coming in at a larger angle, wouldn’t that mean that stopping down will give you an additional benefit and thus would help more than the optical field measurement suggests?

  • Roger Cicala

    BAB – sagittal is along the line from the center of the lens to the edge, in any direction. Tangential are lines at right angles to that line. Optical lenses render those two types of lines very differently. A great illustration is here: http://toothwalker.org/optics/astigmatism.html

  • BAB

    Roger, can you define tangential and sagittal as it relates to lens testing? I’m a medical professional and my intuitive definitions of those “views” don’t jibe with lenses. Thanks

  • Roger Cicala

    Somebody, it’s at the sensor-pixel level.

  • Somebody

    Please forgive my ignorance, but I don’t understand the concept of lp/mm (line pairs per millimeter). That seems so tiny to have 50 line pairs in a one millimeter space, let alone 10. If you had 50 line pairs, that would be 50 black + 50 white bars, which means 100 segments in a millimeter. Therefore each segment is only 10 micrometers (.01mm) wide? That’s on the scale of the transistor size on the Intel 4004 processor (~1970). This clearly can’t be the resolution of a test chart… Or is this lp/mm as projected from the lens onto the image sensor (so going pixel level)?

  • Roger Cicala

    Somebody, it varies depending on the camera and pixel size. But most modern dSLRs are seeing some diffraction at f/11, and some like the D800 may show at f/8. But it’s not severe at that point.

  • Somebody

    Samuel said: “Also, does the plane of focus bend even more as the lens is stopped down past f/5.6? I photograph mainly landscapes and am often at f/11 and f/16.”

    Roger, but at what point (f-stop) does diffraction start to hinder performance? It seems like that at a certain point you’ll be gaining more DOF (to overcome plane of focus curvature) but loosing sharpness (due to diffraction). Is f/11 when diffraction starts to matter?

  • Anu

    Try rangefinder wide angles with different optical stacks, please. The findings should be interesting.

  • Randy

    Thanks, Roger. A teacher of mine said the one thing a cheap f/2 lens and an expensive f/1.2 lens had in common was they were both pretty good if stopped down enough.

    So, is the point here that field curvature in some wide angles is severe enough that stopping down won’t help…or that an expensive 1.4 lens may actually be worse than a slower lens, because the high speed design introduces more curvature?

  • intrnst

    (OK… somebody ate my links, let’s try again)

    Trecento, if the subject Sagittal/Tangential is still blurry* go http://wordpress.lensrentals.com/2009/06/have-you-seen-my-acutance and find the text “so we get a chart like the one below”. You’ll get a unequivocal figure of what is what.

    Then, if you are willing to persevere, a very nice and graphic analysis of S/T focus problem: http://wordpress.lensrentals.com/2010/10/the-seven-deadly-aberrations and find the “Astigmatism” section (Figure 11 is a killer).

    * pun intended

  • intrnst

    Trecento, if the subject Sagittal/Tangential is still blurry* go and find the text “so we get a chart like the one below”. You’ll get a unequivocal figure of what is what.

    Then, if you are willing to persevere, a very nice and graphic analysis of S/T focus problem: and find the “Astigmatism” section (Figure 11 is a killer).

    * pun intended

  • Roger Cicala

    Samuel, we did and the fields didn’t bend further, by f/11 depth of field had started overtaking field curvature.

  • Samuel

    Thanks Roger, I will be eagerly waiting for the 24-70 articles.

    Did you test if stopping down these 35mm lenses past f5.6 causes the field curvature to bend even further?

  • Roger Cicala

    Samuel, I’ll have some 24-70 articles up soon. The Canon II is very flat at 70mm, but I don’t have data for the other focal lengths yet.

  • Samuel

    Hi Roger, thank you very much for this intriguing article. It’s the first time I have ever seen solid evidence of the bending of the plane of focus. I think my Canon 24-70 f/2.8 II behaves much the same way at the wide end of the lens. Are you able to confirm this?

    Also, does the plane of focus bend even more as the lens is stopped down past f/5.6? I photograph mainly landscapes and am often at f/11 and f/16.

  • Roger Cicala


    If you shoot the subject in the center you have maximum subject sharpness. If the subject is off center given this field curvature you’d do well to use the off-center focus point (assuming it’s as accurate on your camera). Focus recomposing with this field curvature, though, is probably a bad idea.

    As to the noticeable in real world – I’m afraid my answers are things like “sometimes” and “possibly”. It might also be that it’s noticeable for catching fine detail but has poorer contrast, etc.

  • FarmerJohn

    Real-world usage question – how does this translate to using the slightly off-center focus points wide open? Say, for portraits…

    Looking at the first 1.4 MTF graph under the “Geeky Stuff” heading, the green Sag30 line goes from ~0.5 at center to ~.63 in the first spike at 7-8 distance from center. Is that ‘typically noticeable’ in real world usage?

    If my subject (face/etc) is off-center for composition purposes, roughly corresponding to that 1/3 radius away from the center, and I use a focus point corresponding that spot, does that mean I get better sharpness because my subject is slightly off center? Is it going to be noticeably sharper than putting my subject in the center, then cropping for composition?

  • Roger Cicala


    Draw a circle. Draw a line from the center to any point on the circle: that’s a Sagittal line. Draw a line at right angles to that line. That’s a tangential line. The circle is the front element of your lens.

    Optical physics makes a lens render sagittal and tangtial lines differently. That may not seem intuitive but look at the curved front element of some wide angle lens. If you draw a sagittal line on it with magic marker (in your mind, don’t really do that) notice how it curves in relation to the flat sensor behind the lens? Do the same with a tangential line, and it curves differently in relation to the sensor. It’s more complicated than my little analogy, but that should give you an idea that mulitple pieces of glass bending those sagittal and tangential lines are going to have slightly different aberrations and effects.

    You can also see sort of the same thing if you look at our OLAF articles. In that case we’re showing the image of a single point of light. It ‘smears’ slightly differently in the tangential and sagittal directions from the same effect.

  • Trecento

    I feel foolish for asking, but I can’t picture what Saggital and Tangental refer to. I’ve googled around a bit, and I get plenty of written descriptions, or descriptions for other fields of study, but nothing that makes intuitive sense. Can you help? I just can’t picture in which direction you are slicing the field of focus.

  • Great analysis, Roger.

    I wonder how would 35mm f/1.8 or f/2 lenses compare to these f/1.4 in field curvature. Specifically for Nikon mount, where Sigma 35/1.4 A and Nikon 35/1.8G ED are choice dilemma for many.

    I know Sigma is widely acclaimed, but I see that it is worse in DX corner here than Nikon:

    Stopped down to f/2.8 the Sigma is worse in one axis only (DX corner) while other axis is sharp so this could be astigmatism where other axis is focused to different distance.

    While Sigma is clearly sharper in FX corners, but the FX corners are quite uninteresting for me if DX corners are bad. I have created this diagram that shows how DX corner is most important part of FX picture:

    Interestingly enough, I bought Nikon 18-35G over Nikon 16-35/4vr, because all the reports of field curvature in 16-35 even quite stopped down: http://www.dpreview.com/forums/thread/3700634
    while nobody complained about the 18-35G.

  • Lars Jansen

    You know, the geeky part is the most interesting part.
    I’m not totally surprised, if you look at the complex optical designs they use these days. Do you see a difference between lens designs, esp. if they use internal focussing aka focussing by changing focal length?

    I think it would be very interesting to do these tests for different vintages of optical design. Starting with the single element all the way through optical history to these ultra-complex zoom lenses they create these days. That might get some myths busted or confirmed.

    Anyway, interesting stuff, and you keep having one of the coolest jobs!


  • Roger Cicala

    CarVac, I’m told they can be either reflections or secondary focusing areas that occur partly because I set the focusing distances overly long (according to the manufacturer). But I started with them set at the maximum 400 micron distance so I’ve kept it just so they’ll all be the same. It tends to only appear with widest aperture settings.

    The color scale is set automatically for each lens: the sharpest area of all the graphs is red, etc. So it’s a good measure of relative sharpness within that lens, but you have to check the MTF scales: red on one lens isn’t always the same as red on the other, etc. A lens’ aberrations and other factors can affect how wide that area looks. That part is automatic and I can’t adjust it in the machine generated graphs, but eventually I may start downloading all the numbers and plotting them myself in a different way. Or maybe not, it will be a huge task.

    For now I think the field curvatures are best taken as a gestalt – just get a feel for what their shape is, which can be useful to know, but ignore the minutia.

  • Edward Jenner

    I have to say, that this does not surprise me one bit. Even stopped down to f8 – f11 I suspect this can be an issue when you are trying to get both maximal sharpness and DOF across the frame, especially when focusing at 2-3ft with an UWA.

    It might not be what I see trying to get sharpest images possible, but I’ve long suspected it is part of it and I think one reason HFD focusing doesn’t do it for me.

    Also another good reason to not focus – recompose if you can help it.

  • CarVac

    What are the little “islands” of sharpness that occasionally pop up? For example in the top center of the Sigma tangential graph, and the corners in several of the lenses.

    Are these real, or are they spurious resolution (where the point spread functions overlap to create virtual contrast) or something else?

    Secondly, it looks like the Sigma and Zeiss have less depth-of-field (not subject isolation, which is often conflated with DOF) than the other lenses, at least in the saggital orientation. Is that perceptable in photographs? Is it just because they’re sharper in an absolute sense? Are the color scales all the same between those graphs?

  • Roger Cicala

    Lee, that’s why I think these field graphs are so important. They can tell us a lot about whether the MTF is showing simply a soft area or an area where field curvature takes it out of focus. The field curvature graphs are actually 420 MTF readings – 21 across the field of the lens each taken at 20 different focus points. They’re exceptionally time consuming to do, but worth it, and I can’t understand why no one ever published these before.

    Truth is, the simpler MTF reading in the graphs (color coded for sharpness) probably is more real world than the actual MTF or MTF50 readings.

  • Lee Saxon

    The thing I find most interesting/frustrating about this is the “how do you evaluate [anything but center] performance” question.

    In a way, center-focused MTF charts are indirect Field Curvature charts. Compare them for two lenses and they might be telling you not which has weaker corners but which has more Field Curvature.

    Since not all (arguably not most) subjects are framed in the center, “how good would this lens be if I focused [anywhere but center]” is not an irrelevant question. But you can’t refocus a lens 573 times during testing to get the best possible MTF at every single point a measurement is taken (and that would be spectacularly misleading even if you did it).

    So where does that leave you? Three MTF charts – one for center focus and one for each “rule of thirds” point? Do you do four more for the extreme edges? Or should it be the extreme corners? I need a nap.

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