Roger Cicala: Understanding field curvature for fun and profit (part 2)

Hi, Roger here – I’m going to talk about field curvature again. And first, some admin: If you only use primes with flat fields, shoot only at F11 or F16, or like to pretend your zoom lenses have flat fields, then this article will be of no interest to you.

In my last article I discussed how to evaluate your lens for field curvature and why that’s worthwhile information to have sometimes. Today I’m going to show an overview of what to expect from different types of lenses. There are some general tendencies of field curvature, but remember, there are also a lot of exceptions to those tendencies.

I’m going to use just one type of graph, hopefully minimizing the chaos I so often create. Sagittal field curve on the left, tangential on the right, and the graph curving up towards the top means the field is curving back towards the camera.

By F4 or F5.6 you won’t notice a mild field curvature very much. At F2.8 or wider you often will

We all know the depth of field increases when the lens is stopped down and the field curvature graphs show that. When the depth of field increases enough, sagittal and tangential fields overlap, reducing astigmatism and the edges come into focus at the same plane as the center. The field curvature doesn’t change shape, it just get broader.

Here’s an example, stopping down a lens from F1.4 to F2.8 and then F5.6. The field doesn’t change shape, but the increase in depth of field tends to make the curvatures overlap better and puts the edges in focus despite the field curvature. This what field curvature is like on most lenses; by F4 or F5.6 you won’t notice a mild field curvature very much. At F2.8 or wider you often might – if you know what you’re looking for.

Depth of field at F1.4, F2.8, and F5.6. The shape of the curve doesn’t change much, but as the field gets larger the effects are less noticeable along the plane of focus. For this particular lens F5.6 gives you good sharpness along the entire focusing plane, F2.8 does not.

One unexpected thing: When you stop down just a bit, sharpening the field but not making it much broader, the field curvature may become more obvious. In the above example, at F1.4 the tangential field looks fairly flat because it’s just not very sharp. At F2.8 the curvature is obvious.

Several people have made comments like “just stop down until the depth of field is greater than the field curvature”. It works well for mild curvatures like the lens above, but it doesn’t always work. How far would you have to stop down the Voigtlander Nokton 35mm f1.4 lens below, (which is already at F5.6) to conceal the field curvature? F64 maybe?

But if you focus off-axis (the purple line) you could probably get acceptable edge-to-edge sharpness around F11, maybe even at F8. Focusing off-axis is almost as powerful a tool as properly framing the shot when you’re working with a lens with field curvature.

These plots show field curvature of the Voigtlander Nokton 35mm F1.2. Stopping down won’t mask the effects of this curvature if you center focus (black line), but focusing off axis (purple line) can.

That doesn’t turn this into a great architectural lens, but it gives you the option to use the curvature to emphasize various areas by moving them in and out of focus, or shifting your focus point to get the entire full-field sharp. I find that to be a useful tool, but then I love using tools.

Field Curvature Variation

For prime lenses, field curvature doesn’t vary copy-to-copy nearly as much as sharpness and other things do. Below are eight copies of the Zeiss 85mm F1.4 Milvus lens. There is a bit of tangential tilt in some, but the field curvature is basically the same for all. Really bad copies may have different field curvature, but such lenses are so obviously bad that it doesn’t matter.

Field curvature for eight copies of the Zeiss Milvus 85mm F1.4 lens. There’s some sample variation when it comes to tilt, but the curvature shape is identical.

That being said, a given lens may have some changes in field curvature when you’re focusing far away versus close up. It’s most common in lenses that allow close focusing, like macro lenses (most macros have flat fields at macro distances, curving fields at normal distances). For most lenses, the field doesn’t vary much in shape but the curve becomes more pronounced at one focusing extreme and flatter at the other. If you do ‘find edges’ shots at a couple of focusing distances it’s pretty apparent. (As has been mentioned, you can use focus peaking instead of find edges, but it’s often hard to see in a viewfinder or on an LCD.)

This lens curvature is more significant at 10 meters than it is close up.

Different Designs Have Different Curvature

I think most people know this, but I’ve seen things online like “35mm lenses all have wavy field curvature”, so I thought I’d better mention it. Below are five different 85mm F1.4 lenses.

Five different 85mm wide-aperture lenses: The Canon 85mm F1.2 L; Sony 85mm F1.4 GM; Canon 85mm F1.4 L IS; Sigma 85mm F1.4 Art and Xeen 85mm T1.5.

If you mentally overlay the sagittal and tangential curves, the Canon 85mm F1.2 has a field curving back to the camera with a fair amount of off-axis astigmatism. The Sigma and Sony lenses have less curvature and less astigmatism. The Canon 85mm F1.4 has flatter field, but does have off-axis astigmatism; the sagittal and tangential curves are in almost opposite directions. The Xeen has similar curve to the Canon F1.2, but the tangential field never gets sharp at the edges.

The bottom line is that if we took the same image with all five lenses, they would look slightly different. Often, it’s not a case of “mine is sharper than yours”; rather it’s “mine is sharper in different places and different ways than yours”. I know, I know, that’s not nearly as satisfying in forum wars.

(Some of the above graphs were made at F4 and others at F5.6. I wanted to give some more comparison of how the depth of field changes at different apertures.)

Wide Angle Lenses Tend to Have More Curvature

Wider lenses, in general, have more complex and severe curvatures. Looking at wide-angle field curvatures gives you a little window into how lens designers are trading things off to flatten fields. Or not trading things off to flatten fields.

The Zeiss Milvus 21mm F2.8, for example, has a wicked field curvature, but great sharpness and very little astigmatism. The Sigma 24mm Art has less curvature but still very little astigmatism. The ‘Bat signal’ tangential curve of the Nikkor 24mm F1.4 and the vibrating tangential curve of the Canon 24mm F1.4L almost show the strain of trying to flatten that field.

Wide-angle lenses tend to have more curvature, or more irregular curvature.

Some of the ‘classic’ or older lens designs have the largest field curvature. The Voigtlander Nokton Classic 35mm F1.2 that I showed above is a good example of an old design that’s still somewhat popular. The lens is very sharp (stopped down), the field very curved, and astigmatism is significant in the outer 1/3 of the field. Does this make it better or worse? It depends on what you’re doing with it. It definitely makes it different; you might love the look, or you might hate it. But if you don’t understand its curvature you’re not going to get the most out of it.

Field Curvature Varies in Zoom Lenses

Zooms have a LOT more optical complexity than primes. They change field curvature at different focal lengths, there’s more variation in curvature in different copies of the same lens, and a field tilt is more common. Most copies of a given zoom will have a field tilt at some points in the zoom range and the tilt is usually more significant than that seen in primes. The amount of tilt and where in the zoom range it occurs varies from copy-to-copy. Even the curvature of the field varies a bit in different copies.

Let’s start with a couple of $2,000, wide-angle zooms. For each I put the wide end on top, the long end on the bottom. I didn’t label them because then I’d have to spend days correcting all the ‘my brand is better than this’ comments because, nope, your brand is not. These are actually very good. I’m trying to be gentle as I destroy your expectations.

Wide angle zoom #1, at its widest on top, longest on bottom.
Wide angle zoom #2, at its widest on top, longest on bottom.

The takeaways are pretty straightforward: the wide end is sharper than the long end (that’s generally true of zooms), and the field curvature changes as you zoom in or out. The point of this is just to emphasize that a zoom doesn’t have one field curvature; it has a changing curvature depending on the focal length you are at.

One thing to note on the lenses above, the sagittal field at the short end curves down on the graph (away from the camera). So if you focus at infinity in the center, the edges actually are focused past infinity. That’s all I’m going to say about that because life is short and this article is already long. (There is a good discussion of it in the comments of the previous article).

Telephoto zooms (that start at 70mm and go up) have less field curvature than wide or standard zooms. Below is an ‘as good as it gets’ zoom, the Nikkor 70-200mm F2.8E FL ED VR. The field changes a bit as you zoom out, but not nearly as much as wider zooms. The field is perfectly flat at the 70mm, curves back a bit at 135mm, and just a bit more at 200mm. BTW, this copy is one of the least tilted zooms I’ve ever seen. The chance of getting a zoom with this small of a tilt is similar to the chance of winning Powerball.

Nikon AF-S 70-200mm F.2.8E FL ED VR. As flat a zoom as you will ever see.

Here’s another really good 70-200mm F2.8 zoom, the Canon L IS II (note, the Canon is stopped down more, so the fields are thicker). This is more of a typical tilt you see with zooms. I used the version II so that version III owners can pretend their lens is better than this.

Canon 70-200mm f2.8L IS II at F4 field curvatures.

This is where some folks will comment “I’ve had 3 of those lenses and none of them were tilted”. What you meant to say is “I never noticed the tilt”. Most people don’t, especially if they test with 2-D charts. Draw a line from one side to the other at the ‘0’ focus mark, which is what you’d see on a chart or brick wall test. Shooting a test chart carefully, you’d probably notice the tilt at 200mm, but not at 70mm or 135mm. Of course, if you did a through-focus test chart set of images you’d see it at all 3 focal lengths, but nobody but me does that.

This lens is a good example of typical zoom tilt. What you see at 70mm and 135mm is normal for a zoom. At 200mm it’s a bit worse than average, but not horrible. You might get a better copy at 200mm if you exchanged it. But it might be worse at 70mm or 135mm. If you mostly shot sports, portraits, or other things with center focus at 200mm, you’d have no reason to ever suspect the field is tilted.

Just one more example of typical zoom tilt, a Sony 24-105mm F4G OSS. This one has the same tilt throughout the zoom range. Note also that the field curvature changes a lot between 24mm and 70mm, but not much after that.

Sony 24-15mm f/4G OSS at 24mm, 70mm, and 105mm.

Smaller Sensors Mean Less Curvature

If you shoot m4/3 or APS-C type sensors, field curvature is far less evident. It doesn’t matter if the lens is designed for the sensor or not, it’s simply about distance from the center on the image. Look at any of the above field curvature graphs for full-frame lenses but instead of going out to the edge of the graph, mentally cut it off just under halfway (m4/3) or just over halfway (APS-C). Only a couple of the lenses I showed above would have noticeable curvature.

So How Is This Really Useful?

For those of you who test lenses, checking field curvature answers two age-old-forum questions: 1) are the edges of my lens really soft? 2) Is the field of my lens tilted? Answering those questions by yourself could reduce forum traffic by 20%, saving zillions of electrons.

I’m not going to ever post a 7,000 graph look-up-your-field-curvature article. First, because time. Second, because it’s easy as cake to check for yourself. You don’t need me to do this. Don’t have the lens? Go download some full-size photos made with it that have good 3-D subjects; landscapes or whatever. You can run a find edges filter on those. (If you’re looking at 800-pixel wide forum jpgs to decide if a lens is good, well, you’ve got some learning ahead of you.)

Field curvature of a Sony 24-105mm F4G OSS from widest at the top to longest focal length at the bottom.

I know what you are thinking: Why don’t all those lens reviewers mention field curvature when they are reviewing and evaluating lenses? I propose to you a Holy Quest: the next time some reviewer says something about soft edges, ask them, “are they really soft, or is it field curvature”? Eventually that might shame them into checking it. Which for most of them will involve learning how to check it.

Why don’t the manufacturers publish the field curvature with the MTF ratings? (A couple do, actually, but it’s hard to find). For that matter, why haven’t I? Well, because as I hinted with the meme at the start of the article, nobody cares. If these articles generate interest, then maybe I’ll start. For primes at least.

Knowing field curvature helps me frame shots and choose which lens I want to use and how best to use it

Until then, I’ll happily continue being the Lone Ranger of Field Curvature. Knowing field curvature lets me know, sometimes, that the lens that Imatest says has soft corners actually has sharper corners than the higher-rated lenses; they’re just not in focus unless you compensate for the curve. It explains why a lens might have very sharp edges in pictures but not on test charts.

Knowing field curvature helps me frame shots and choose which lens I want to use and how best to use it. I actually prefer a lens with curvature most of the time; I can take advantage of the curve for some shots, move my focus point off-axis to maximize edge-to-edge sharpness for others. Most people, I realize, prefer a lens with a flatter field. But if they tried using a curved field to their advantage, some of them might come around to my way of thinking. OK, maybe two or three of them might.

For the rest of you, well, that’s all I have to say about field curvature, so maybe you’ll find the next article more interesting!

Roger


Roger Cicala is the founder of Lensrentals.com. He started by writing about the history of photography a decade ago, but now mostly writes about the testing, construction and repair of lenses and cameras. He follows Josh Billings’ philosophy: “It’s better to know nothing than to know what ain’t so.”