Field Curvature

How to analyze and work with this ubiquitous lens problem

By Lloyd Chambers Back to

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Field curvature can make a sharp lens look soft when the wrong assumptions are made. Understanding how sharpness varies throughout the frame will help you get the most out of some excellent lenses that might not test well on flat (planar) test targets.

In previous articles, I’ve explored how diffraction and focus shift can lead to images with degraded contrast and resolution. As if that wasn’t enough to think about, another confounding factor is present: field curvature. In the ideal world, a flat (planar) surface would be imaged onto a flat sensor, and a crisp image would result (a “flat field” lens).

The real world doesn’t work that way for many lenses. In the real world, a desired plane of focus is imaged as a varying curve that can focus sharply in front of or behind the sensor, or both, depending on where we look in the frame. Field curvature can also reverse, swinging alternately in front of or behind the nominal plane of focus, depending on distance from the optical center.

Field curvature is an inconvenient problem, because it calls into question the applicability of lab tests and MTF charts that measure lens performance using a flat (planar) test target. Measurements are typically presented as hard facts describing imaging performance. And so they are—for photographing flat targets at the test distance. But unless your work involves photographing perfectly flat subjects at the same distance, the sharpness of a perfectly flat surface has only a rough correlation with real-world results with three-dimensional subject matter. Some outstanding lenses test poorly due to field curvature; others test extremely well but perform poorly for infinity focus.

Field curvature can be exploited to increase the apparent depth of field when it maps nicely onto the subject matter. For example, a lens that focuses more distant edge or corner areas at the same time as it focuses closer central areas can be used to simultaneously capture a sharper, closer element and sharper, but much more distant, edges, even when wide open.

Field curvature varies with distance

Field curvature varies with distance. A lens might exhibit a f lat f ield at close range, yet show strong field curvature near infinity. The Canon EF 14/2.8L II is one such lens, and even ƒ/11 won’t overcome the field curvature at infinity focus (Figure 3). Yet another lens might exhibit a mostly flat field at infinity, but show substantial field curvature at close range—the Zeiss ZF 25/2.8 Distagon is one such lens.

Such variation usually leads to erroneous conclusions about the merits of any given lens, especially in lab settings and “quick tests.”

In the good old days of film, field curvature was somewhat less of an issue than today, because film has significant thickness; a small amount of field curvature still might fall within the film thickness. But with digital sensors having essentially no thickness for the photosites, even a slight error is recorded as blur. Film forgives (a little); digital forgives not at all.

The photos in Figure 2a–d show modest field curvature using the Nikon 20mm ƒ/3.5 AI-S. Optimizing focus for a crisp center yields blurred corners, and optimizing focus for the corners yields a blurred center. Field curvature is generally associated with astigmatism, which causes sagittal (radial) and tangential rays to focus at different distances; this is not obvious in these examples, but is readily apparent at intermediate focusing points that are non-optimal for centers or corners.

The images in Figure 3 are with the Canon EF 14mm ƒ/2.8L II at ƒ/4 on the 21MP full-frame Canon EOS 1Ds Mark III. Focus was near the center. Examination of the image shows strong blur away from the central third of the image, yet very crisp detail on the leaves at upper right, which are a good 30 feet (10 meters) or so in front of the focus point.

This strong field curvature cannot be overcome by stopping down, even to ƒ/11. While the Canon EF 14/2.8L II exhibits a flat field at close range with outstanding performance, focusing near infinity exhibits strong field curvature and very strong blur away from the center. Focusing to infinity at center is like focusing at the bottom of a bowl, with the sharpness following the rising edges of the bowl as they get closer. This could be handy for interior shots, but makes the 14/2.8L unsuitable for many types of outdoor photography with near- infinity focus.

Optical design determines field curvature

There is no choice or workaround with field curvature— the optical design of a lens is fixed. All the photographer can do is to understand the behavior and (ideally) exploit it to advantage while avoiding compositions that are in conf lict with the shape of the curvature. The variation in distance can make the puzzle all the more confusing, but once one learns to look for the clues, the way a lens behaves can be understood.

When reading MTF charts,* the dips and humps seen with some designs, particularly those from Zeiss and Leica, are typically due to f ield curvature—see Figure 4. In fact, some Leica designs for wide angles have very wavy MTF curves showing both strong astigmatism and field curvature; the Leica Super-Elmarit-R

15 mm ƒ/2.8 ASPH is one example. The best focus overall for across-the-frame sharpness is a compromise: adjusting focus for a neutral middle ground, then stopping down, can yield the best results (keep this in mind next time you read simplistic rules about depth of field).

The graphs in Figure 4 (courtesy of Carl Zeiss Inc., from How to Read MTF Curves, by Dr. H. H. Nasse) are the MTF (contrast) charts for the same lens. Figure 4b shows a large dip in MTF with the lens focused a mere 0.05mm (50 microns) differently. According to Nasse, this difference is “about the same order as conventional mechanical camera tolerances such as adjusting the AF and the focusing screen.”

Without knowing that these two graphs are from the same lens, one might conclude that Figure 4a represents an excellent lens for f ine detail, and that Figure 4b represents a marginal one, albeit one with superb central sharpness and contrast. Note that f ield curvature is not a simple curve, but has reversals. In particular, the f ield curves in mid zones reverse as the edges are approached, and again as the corners are approached (frame edges are at an offset of 18mm, corners at 21mm).

Detecting field curvature

The quickest way to see field curvature without even taking a picture is to use the Live View feature of most cameras (at maximum aperture). A test chart or newspaper taped to a wall can work well.

Using Live View, focus at center, then move towards the edges, observing image sharpness. Refocus off-center and determine if the image becomes sharper—if so, you’re seeing field curvature (assuming you’ve aligned the camera squarely to the target).

To test for focus shift with images:

1. Choose a scene that offers similar subject matter in the same desired plane of focus. See Figure 6, Pond Scene, for an example.

2. On a tripod, focus near the center, and take a picture at maximum aperture. Then focus at the edge or corner and take another picture. Be sure to use mirror lockup and a release so you don’t blur the image when using slow shutter speeds. Shoot the aperture series from wide open through ƒ/8; the effect may be more obvious at intermediate apertures.

3. Process all images identically, then layer them in Photoshop or a similar program for easy click-on/click-off for comparisons. If there is field curvature, you’ll see unexpected areas of sharpness or blur, depending on placement and distance. Field curvature can be obscured by declining optical performance away from the center, so choice of subject matter is important.

The optical designs of most 50mm lenses are very similar, and nearly all show field curvature that is easily misinterpreted as a lens being “soft.” I tested eight different 50mm lenses from Nikon, Canon, Zeiss, Olympus, and Sigma, and found that all had field curvature that became obvious with the appropriate subject matter.

I did so because in my testing of the Zeiss ZE 50mm ƒ/1.4 Planar, I detected strange variations in image sharpness across the frame, even at ƒ/5.6. At first I thought this was a bad lens, but subsequent testing of the eight 50mm lenses showed this to be common.

The photograph in Figure 5 is what prompted me to do this investigation (logos have been blurred away in this example image to avoid nasty corporate lawyers). We are interested in the horizontal stripes on the semitrailer truck (distance 30 meters or so), which are sharp at center and increasingly blurred at the edges. This is at ƒ/5.6 with a Zeiss ZE 50/1.4 Planar on a Canon 5D Mark II. Focus was apparently too far forward, showing just how misfocus can produce puzzling results; the center is sharp from the truck to the building, but away from the center things go blurry: this is field curvature at work; the zone of sharp focus moves forward away from the center. See Figure 5 for just how strong the blur is.

At first I thought there was something wrong with the Zeiss ZE 50/1.4 Planar, which led me to compare it to the other 50mm lenses. The results showed that they all had similar field curvature, with the Zeiss just making it most obvious due to its otherwise outstanding image contrast.

Pond Scene

The pond scene in Figure 6 looks very strange when the whole image is viewed. A ring of sharpness extends out into the pond showing just where the field curvature occurs—sharpness peaks at about two-thirds of the way from center to corner. Even at ƒ/5.6 the effect is visible and would look quite strange in a medium-sized print: pond scum near the center is blurred, and pond scum approximately two- thirds from center is quite sharp and contrasty.

I discovered this scene by serendipity, and testing of the eight 50mm lenses showed the same interesting field curvature with all them, as well as with other focal lengths in the 40–58mm range.

Working around field curvature

The good news is that with most lenses and subject matter you can safely ignore field curvature. But don’t be surprised to find odd variations in sharpness at the same desired plane of focus.

Macro lenses typically are corrected to offer flat-field performance, at least over most of the frame. Some, like the Zeiss ZF 100mm ƒ/2 Makro-Planar offer a flat field from close up to inf inity, not a small consideration for applications such as stitching images together for high resolution or panoramas.

Especially when comparing different lenses, field curvature is hugely important, because very small changes in focus can shift the sharpness/contrast drastically. In fact, comparing the same lens to itself can “prove” that it is both better and worse than itself, depending on very subtle shifts in focus—one reason that making real images is the only reliable way to assess lens performance and a compelling reason to be skeptical of casual lens tests you might find on the Web.

Mitigating focus shift

Here are useful working tips for detecting and mitigating focus shift

Study the MTF curve. An MTF curve that is flat or slopes off gradually usually indicates little or no field curvature. Astigmatism is also a strong clue. However, an MTF curve might be measured at a distance at which the lens has a relatively flat field, and neither Nikon nor Canon is clear on their measurements, so MTF is not always a reliable indicator. With Zeiss and Leica, MTF is a very good indicator of field curvature, and they indicate the test distance with the supplied MTF graphs.

Know your lens. The only good way to understand your particular lens is to shoot a variety of subjects and watch what happens. Take advantage of Live View when a good subject presents itself, such as the pond in Figure 6.

Exploit it. A lens whose focus shifts rearward toward the edges and corners can be focused more closely near center; this can yield surprising sharpness wide open for the distant elements. A lens whose focus shifts forward toward edges and corners can be used to advantage in building interiors where the walls approach at the edges.

Stop down. Usually, aperture ƒ/5.6 or ƒ/8 is suff icient to pull things in provided that focus is accurate to begin with.

Conclusions

Field curvature can be quite confusing until it’s understood. In an ideal world, it would be something we could always ignore, but with perfectly flat and depth-less ultra-high- resolution digital sensors, it becomes an issue with many lenses, even well stopped down. Enjoying all those megapixels in big prints means paying attention to the quirks of each lens.


About the Author

Lloyd Chambers
LChambers
Lloyd L. Chambers enjoys all-digital photography after shooting film for years in 35mm, 4 X5, 6 X7 and 617 formats. His web site diglloyd.com offers a wealth of material on advanced photographic techniques, and his Making Sharp Images is a reference work on sharpness and blur of all kinds.