Lens Field Curvature Visualization

If you to take a look at many of my articles where I measure lens resolution, it becomes obvious that many lenses are poor at their edges. Numbers can be a bit deceiving, however.

The world is, of course, three-dimensional. But all of the lens analysis articles you read present information to you in either one or at most two dimensions. Sure, you’ve probably seen lens resolution plots that are 3-D, but the data shown in them still represents only two-dimensional measurements.

Sometimes, a lens has “hidden” resolution. The extra edge resolution is merely bent from the flat plane where the measurements are taken. This is what we call “field curvature”.

Older lens designs, particularly in lenses with larger apertures, often suffer from excessive field curvature. Sometimes, even very expensive modern optics have this same problem. For instance, the new Kepler space telescope suffers from this issue, but the designers avoid the loss of edge resolution by making the image sensor curved to exactly match the optical field curvature.

For a camera with interchangeable lenses, customizing the shape of the image sensor to match the shape of the lens optimum resolution zone just isn’t practical. The sharpness problem in most cases is minimized by selecting a narrower lens aperture. This solution, however, negates the whole reason for buying your (usually expensive) wide-aperture lens.

Lens Resolution 3-D Plots (Meridional upper and Sagittal lower)

The lens resolution plots look like 3-dimensional information, but they’re actually only 2-dimensional information taken from the flat camera image sensor. The red colors are higher resolution; the blue colors at the frame sides are lower resolution.

Any way you look at it, the edges of the lens results look pretty bad. This (50mm f/1.8) lens may be capable of more resolution on the sides than you think, though.

Lens Field Curvature Ray Trace

Shown above, the zone of sharp focus for a lens with heavy field curvature doesn’t stay in a plane at the image sensor. Instead, the zone follows a curve (a bowl shape in three dimensions). The curvature might even follow a more complex shape, such as the 3-D plot above, for a multi-element camera lens.

How to visualize the shape of the zone of sharp focus

If you want to see if your lens has field curvature (as opposed to some other optical defect) that causes unsharp pictures at the edges, what follows are a couple of techniques to do just that.

Make sure you shoot test shots with the lens wide open, to see the curvature with maximum effect. The more you stop down a lens, the more the curvature will be hidden, due to the increased depth of focus.

Choose a subject that has many, many edges. In my sample shot below, I simply took a picture that is (flat) lawn grass.

Lawn grass, Nikkor 50mm f/1.8

Now that I have a shot with lots of little blades (edges) in it, I need a way to enhance those edges. By enhancing the edges of a subject that stretches across the whole field of view, I will be able to visualize the shape and also the depth of what’s in focus.

Edge enhancement is built into many photo editor programs. One of the most popular editors that possess edge enhancement features is Photoshop. For this article, though, I’m using Corel Paint Shop Pro, which has many of the same capabilities as Photoshop.

Enhanced Edges

To make the picture above, I took a lawn grass shot and then selected Effects | Edge Effects | Find All in the editor. There are similar options, such as “Find Vertical” and “Find Horizontal” instead of “Find All”. Choose whichever option best shows the high-contrast edges.

Note that I ended up with a “U” shaped band of focus. This shows how the lens field curvature causes the zone of sharp focus to move away from the camera image sensor the farther you move toward the edges of the frame.

Instead of just getting out of focus, the focus shifts where it is located. If I were to take a group shot of a bunch of people standing side-by-side, more people would be in focus if they stood along a “U” shape instead of standing in a straight line. For this lens, the people standing on the ends of the line would take a step further away from the camera.

It would of course make a lot more sense to just stop down the lens to make sure a group of people has everyone in focus. If you wanted to artistically throw the background out of focus in your group shot, however, you’d have a problem if everyone was lined up straight.

Visual Field Curvature with Live View “Focus Peaking”

My D850 has Live View focus-peaking. If I turn it on (with “high sensitivity”) and also set my camera to manual focus, I can see the same enhanced edges right on the LCD. I see the characteristic “U” shape when looking at the same lawn grass scene shown above. This would be a realistic technique to determine if everyone in a crowd shot was in focus. That’s preferable to finding out after everybody’s gone home that people at the frame edges are out of focus. Whoops.

Same “U” shape field curvature: focus peaking view in D850

Try shifting the focus farther away from the resolution chart

To see if my “hidden resolution” theory is correct, I need to move farther from the resolution target and re-shoot it. If in fact the field is curved, then this should make the chart center have decreased resolution and the chart edges should have increased resolution, because the edges have been moved into the zone of where the in-focus areas are located. I won’t touch the lens focus ring or refocus; I’ll just move the camera/lens combination farther away from the chart instead.

Target at calibrated focus distance from target: good center, bad edges

Focus unchanged, but camera/lens is shifted farther from target

You can tell in the charts above that the center resolution got worse as the camera was moved further from the target, since the center was now out of focus. Note, however that the edges/corners significantly improved in resolution. The 50mm lens was focused at 2.5 meters in both cases, but physically moved farther away by 3 inches (about 75mm) without refocusing.

Conclusion

If I were to make a lens resolution target that was shaped like a dome (or close to the 3-D plot shape at the top of this article), I could make this lens resolution look much more even from edge-to-edge. This would be the only way to really know how much resolution a lens (with field curvature) possesses at the frame edges using a single shot of the test target. I could alternatively take a series of shots of the flat target at different distances, like “focus stacking” does, and piece together the highest-resolving areas from each shot (entirely too much effort).

The takeaway from this analysis is that lenses with field curvature don’t have the poor edge resolution that most reviewers quote! The resolution/focus has just curved away from a flat plane. It might be wise to shift the camera phase-detect focus calibration to an intermediate position between the frame center and the edge to balance out the resolution over the whole frame.

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