Roger Cicala: Understanding field curvature for fun and profit

When deciding which 35mm lens to buy, what do you want to know? How sharp it is? How it handles? How much it costs? I want to know what its field curvature looks like. (Spoiler: the plot on the right is from the little guy.)

I’m not a fan of lens testing purely for the purpose of winning pissing contests. I am, however, a great fan of lens testing for learning how to best use a lens. There are a few tests I find particularly useful, and the single most important one is field curvature.

Field Curvature (in metrology speak MTF v Field v Focus) tells me a lot about how to use a lens. It is also the most complete way to test a lens because it’s three-dimensional. Shooting a brick wall or test chart the way most people do is 2-Dimensional. The 2-D chart test below says the lens is sharp in the center and soft at the edges. How nice.

This is a test image of a lens’ MTF, basically what you’d see shooting a test chart except with color representing sharpness. This one is sharp in the center, really soft at the edges, and a tiny bit softer on one side than the other. But what does that tell you about the lens? Not much.

I’ve spent over a decade developing fast, sensitive optical tests. My gold standard is a modified $250,000 optical bench that quickly analyzes field curvature. That test (the graph below) tells me that this lens is actually amazingly sharp at the edges, but that field curvature causes the area of maximum sharpness to be further forward at the edges than at the center. In a 2-D test, the edges look soft because they are out of focus when the center is in focus.

A 3-D (Field curvature) MTF graph. The center focus is along the black horizontal line. The Y axis represents focusing distance, the X axis edge-to-edge sharpness, and the MTF is the color (red is sharpest). So the edges of the lens are very sharp, but not at the same focusing distance as the center.

The 2-D test chart images, like the first graph, are taken right along the black line of best center focus. They show the center is sharp and the edges soft. The 3-D graph shows, the edges are very sharp, but not in the same plane of focus as the center. That’s very, very different than the edges are soft.

Think about that for a second. Photographer #1 gets that lens, knows how to frame with it, and posts about how awesomely sharp the edges are in his photographs, which are 3-D. Photographer #2 buys it, tests it on a 2-D chart and sees the edges suck so he sends it back because it’s supposed to have sharp edges. Again and again.

Inexperienced photographers think a curved field is bad and a flat field good. But a designer may have chosen to let the field curve so the lens has other, wonderful attributes. Not to mention a curved field is a tool that can be useful. Many great portrait lenses are great portrait lenses because of their curved field, for example.

knowing your lens’s field curvature will help you take better pictures

I showed how to check field curvature with just a photo in a previous post. Today I’ll show a slightly different method using a test chart or brick wall. But field curvature isn’t really about better testing; knowing your lens’s field curvature will help you take better pictures.

Take the lens above as an example. I saw a group photo taken with that lens. The photographer positioned everyone in a slight crescent rather than a line because he knew the lens’ field curvature and placed his subjects so they were all in best focus. Someone else (someone without that information) would probably have said the lens was ‘too soft at the edges’ to use in a group shot.

Field Curvature graphs (clockwise from top left) showing overall curvature (this lens doesn’t have much); astigmatism, tangential field, and sagittal field.

A Quick Word About the Graphs

The shape of the field is different for sagittal and tangential rays (the two lower graphs above), which many people don’t realize. Where the fields don’t overlap, there is astigmatism (upper right graph above). The overall curvature (upper left) is what you see at home if you do my not-patented ‘field of grass’ test. Most of the time I’ll just show the sagittal and tangential fields; you can eyeball whether they overlap or not and what the overall curvature would be like.

Testing Field Curvature at Home

If you follow my grass-photo-with-find-edges-filter technique, you get a nice image showing the field curvature. You’ll also know if the field is tilted and if it is, how badly. Here’s the grass test for two copies of the Sigma 24mm f.14 Art, a lens with a bit of field curvature. One copy has tilt problems and it’s pretty easy to see which one.

One copy is good, one is pretty tilted. Can you tell which one is which? I thought that you could. This two-copy test took 60 seconds, was shot hand held, and required no home testing lab.

If you’ve already got a home testing setup and want to put some numbers to your lens, that’s easy, too. First, mount the lens on a tripod and manually focus on your 2-D target of choice: test target, brick wall, treeline, whatever. (If you don’t use a tripod and you don’t manually focus, you should be filled with shame and delete all your test posts because you did NOT test the lens. I never, ever, take a single AF image of a test chart. It’s a waste of time. But you can do the find-edges technique with a hand-held AF shot even if you don’t own a tripod and don’t know how to manually focus.)

Where was I before the rant? Oh, yeah. Take your first image past (distant) to best center focus, then take a series of 6-10 images while manually moving the focus back a bit after each shot until you’ve gone out of focus to the near side.

I never, ever, take a single image of a test chart – it’s a waste of time

Next, you take that set of six or 10 through-focused images, find the one with best center sharpness, the one with best right edge sharpness, and the one with best left edge sharpness. If they are all the same image (it happens sometimes), congratulations – you have a very good lens with a flat field. Most of the time, though, you will get one of three other possibilities:

  • Both edges are sharpest in the same image, and the center is sharpest in another. Which means: The field is curved but not tilted.
  • The edges are sharpest in different images: The field is tilted.
  • One edge never gets as sharp as the other: The lens is optically abnormal.

For example, let’s say you take six images. Images #1 and #6 from the sequence shown below were way out of focus, so I’m only showing you images #2-5. The center is sharpest in image #3, the right edge sharpest in #4, and the left in #5.

What this tells me is that I’ve got a lens with a field that is both curved towards the camera and tilted to the left.

Taking a series of images from far focus (2) through near focus (5) lets you evaluate field curvature and tilt.

Let’s all take just a moment to think about all those threads that started with someone posting just image #3 and asking “do you think this lens is OK??” You’ll see 57 or so responses with no definitive conclusion because the OP didn’t give enough information from which to draw a proper conclusion. If they had done a through-focus test, they probably wouldn’t need to ask the question; the answer would be obvious.

Why Should I Bother?

If the field is badly tilted (scroll back up to the first grass images) you’ll know to exchange it for another copy, or if a little tilted you’ll have that information for framing your shots. I had a favorite landscape lens which had a field that was slightly curved and slightly tilted. It gave me great images, usually with a subject of interest closer and on the left side in sharp focus. It was a great lens for me because I knew how to frame my shots with it and I liked the different look that gave.

If the field is markedly curved, you can use that knowledge to better frame your shots. Or perhaps you’ll decide that this lens isn’t for you. Personally, I often prefer a curved field because it’s a tool I can use, but some people want flat fields all the time. I might choose one lens over another for certain shots because of the field curvature. That lens I showed at the beginning is going to focus the edges closer than the center, for example. It might be great for isolating the subject for center-framed portraits. Or to frame shots so the center point of interest is further away than the edge points of interest. I would prefer a different lens with a flatter field for an architectural shot. You might prefer flat fields for all of your shots, for that matter. I find field curvature a fun tool, but some people are flat lensers.

As an alternative, if the field is really curved, focusing slightly away from center gives an overall sharper image. Here’s an example. The Zeiss 50mm T/1.5 has big-time curvature with the edges towards the camera as shown in the top-half of the image below.

Field curvature of the Zeiss 50mm T1.5 showing that if you place the focus point to the left or right of center you get maximum edge-to-edge sharpness. The calculations show the best off-axis point is 9mm from center (about halfway to the edge) but you could eyeball this pretty accurately.

I love a curved field for just this reason. Center focus can isolate my subject but off-axis focus brings good edge-to-edge sharpness. I get to choose. I love getting to choose.

I have some cool software (bottom half of the image) that tells me exactly where to focus to get the best edge-to-edge sharpness (the black line across the field curvature graph) but you can eyeball your homemade field curvature graph and know where it should go – about halfway to the edge in this case. This can serve as an alternative to stopping down for edge-to-edge sharpness, or let you get edge-to-edge sharpness when stopping down isn’t enough.

The big takeaway is you can often get excellent get excellent edge sharpness in lenses with field curvatures if you know how to use them. Many lenses with flatter fields sacrifice edge sharpness to get flat fields, and you can’t find edge sharpness that just isn’t there.

Do you know the focal length at which your zoom lens has the flattest field, or at which focal length the field curvature changes? That’s useful information, and I want to know this kind of thing for every zoom I carry (pro tip, the flattest field is rarely at the center of the zoom range; it’s often 1/3 of the way from one extreme). Some zooms have massive curve at an extreme, but if you zoom just a few mm away from the extreme the field is much flatter. That’s another useful thing to know.

Very often your 24-70mm is curved one way at 70, while your 70-200mm is curved the another (ditto at 24mm, etc.). Knowing that helps choose which lens best frames the shot. (I should also mention that one zoom is always sharper than the other at 70mm. Of course, I probably should also mention neither one is really 70mm. Most 24-70mm lenses are actually 26-67mm; most 70-200s are about 73mm to 190mm.)

Sagittal field of Canon 70-200mm f/2.8 L III and24-70mm f/4 L IS, both set at 70mm.

The 70-200mm has a very slight curve back towards the camera and is pretty sharp (red) even at the edges at 70mm. The 24-70mm has a more significant curve and is not as sharp at the edges. Depending on what you are shooting, those differences could be important.

At least a few of you, I hope, have read this far and are now interested in field curvature. This article is already long enough, so I’ll stop here for today. For the next article though, I’ll show example field curvatures from various kinds of lenses. To be clear, I’m not going to put out 6,342 field curvature graphs for all the lenses at all the focal lengths. I’m showing you how to fish, not hosting a fish fry.

Since everyone tells me I should click-bait tease the next article, here you go: Next time I’ll show how field curvature explains ‘3-D pop’ and ‘microcontrast’. (Spoiler: No, no I won’t. Field curvature explains a lot of things and is a useful tool, but it’s not magic.)

Until Next Time…