Decoder - Field Curvature

Field Curvature,  A Tricky Bastard

The above photo is taken at 28mm at f11 on an ancient Minolta 28-85mm lens, the focus was set to about 2.5 meters and according to the depth of field scales everything should be in focus but it isn’t, in fact there is considerable separation between my patient model and friend Perc Carter and the background, which is easy to see in the crop below, yet the edges seem to be in reasonable focus, how the hell can this happen? That folks is the product of the significant rearward tending field curvature characteristics of this lens, which in plain words means the centre is focused well forward of the edges. 

Yep, there is no way that the background is anything close to being in focus in the centre, despite what the depth of field scales and f11 are promising.

Up front let me say "field curvature” is not that pesky problem where images with straight lines in the frame seem to bow in or out as you move towards of the corners, that would be distortion, which comes in two core flavours, barrel and pincushion, with moustache as a somewhat recalcitrant but rare third option.  There is a relationship between distortion and field curvature, but we won’t be getting into that in this article.

Field curvature can be a right little bastard, causing time dilation, warping gravitational fields, interfering mercilessly with photons and fooling with quantum calculations.....well actually I won't do any of those things but it can indeed be a tricky bastard if you don't know what it is and how it might impact on your pics.

In addition to photos included to help get the ideas across I've drawn up some rough diagrams to help explain the concepts. Actual images, when shown at web resolution, are simply not viable for adequately demonstrating the concept and the effects are hard to understand if you're just looking at a 100% zoomed in view of the corners without respect to the rest of the image.  Also, and this is important, please bear in mind that field curvature is 3 dimensional in nature, but for the purposes of our conversation, we are just visualising it in 2D terms to try and keep things manageable for our minds.

With an entirely corrected lens, the plane of focus would be a flat plane parallel to the camera's sensor. Specifically, you would be able to focus on a flat object parallel with the sensor plane and it would appear sharp from edge to edge, corner to corner. Some lenses can indeed get close to this, generally, these are macro lenses which really have to work in such a way if they are to succeed at their intended purposes, which includes photographing flat artwork and similar flat plane subjects. In most cases, the “plane of focus” with general purpose lenses is anything but "planar". (You may now be able to understand exactly what Zeiss mean when they add the "Planar" moniker to some of their lenses.)

It's very challenging to design and build a true planar lens and most lenses wearing that moniker are only genuinely planar at some focus distances, usually, in the close-up range, the old Nikkor 55mm f3.5 Micro Nikkor is a good example. The f3.5 55mm micro was and still is wonderfully planar close-up but was nothing like planar as you focused out towards infinity and thus did not perform well at all as a normal lens, the later 2.8 version solved that issue and is to this day "planarly" excellent across the whole focal distance range.

This is what flat plane rendering should look like.

With flat field rendering, the plane of sharpness is pretty much a straight line that runs parallel to the sensor of the camera but in fact it's not so much just a line but of course a plane, as we are dealing with a 3 dimensional scene but we can stick with the concept of a straight line for our discussion purposes.

Simply put, field curvature means a lens does not focus planar objects with equal clarity across the width of the subjects area, in other words, the centre may be sharply focused at say 5 metres but at the edges of the frame objects along that parallel line are way out of focus, but objects at parallel distance of 10 meters on the edge of the frame may actually be in sharp focus. Field curvature can work in both directions, of course, you could have the centre in focus at 5 metres and the edges in focus as say 2 metres, it can also significantly vary with focus distance.

Fortunately, most modern lenses do not display dramatic field curvature and the issue is far more likely to crop up with wide angle lenses, the wider you go, the higher the chance of experiencing it, but regardless of the degree, it's an issue that can mess with your image making.

The quick and easy way to see the effects of field curvature is to focus on a flat field object, for example, a brick wall using the wide open aperture, a lens with field curvature will render only where you focused in the centre of the frame sharply.  A confirmation can be easily made whilst you're at it, if the lens has a field curvature issues rather than just being mushy and unable to resolve properly you should be able to place the focus point out towards one of the edges and then get is properly focused on that spot, which will now, of course, render the centre out of focus.

You can also roughly work out which way the curvature is running by the above method, if you have to turn the focus ring to a much closer distance to get the outer edges sharp the curvature is rearward tending in nature, and if you have to go to a longer focus distance than the centre it must be "forward tending". (probably not the correct technical terms but that's what it call it)

Forward Tending Field Curvature

Digital capture is far less accommodating of field curvature than film was, principally because resolution levels are so much higher that any variation in the actual plane of focus now easily stands out in stark contrast to the “in focus” areas. There is also another reason that may be a little hard to understand, film has thickness and the silver halides can be at different depths within the film meaning there is a bit more forgiveness in focus with film, but digital has to be perfectly in focus on the front surface of the sensor plane.  This little aspect also relates to why a lens may exhibit little chromatic aberration when used on a film body yet creates dreadful colour fringing that insults your lookin-peepers on a digital body. 

MTF charts, which are often used by test labs to judge a lens’ performance quite readily indicate the presence and effects of field curvature. But.. I must caution you that using an MTF chart alone as a means of judging lenses' worth is nowhere near as instructive of real-world performance as you might initially think.  Of course, if you intend to use your new lens solely for the purposes of photographing flat field objects, like brick walls and artwork the MTF cart will be spot on for you.  Generally most of the time most of us are shooting 3D items!

As said, field curvature may cause the focus plane to curve away from the camera at the edges or it may come closer to the camera on the sides, and the degree of curvature can in some rare cases be very strong.  Some lenses produce a complicated form of curvature where it may curve outwards as you move away from the centre and then move inwards again at the corners of the image, this is known as "wave type" field curvature and it's an absolute devil of an issue to deal with or use creatively. Frankly with such lenses I either use them stopped right down to mask the curvature or surrender, generally, they are just bloody evil.

Uneven field curvature, this is very difficult if not impossible to use creatively as its effects can be highly unpredictable.

The effect of significant field curvature shouldn't be underestimated, it makes for some very unpredictable results and may lead you to make entirely wrong assumptions about your lenses performance or lack of it. Probably even more frustrating, field curvature makes a complete mockery of depth of field scales as DOF calculations tables are created on the simple assumption that the lens is planar and the depth of field rendering is evenly distributed across that flat plane of focus.

It might be a little hard to conceptualise this next bit but bear with me.  Let's say you have a lens where the plane of focus is curved away from the camera as you moved towards the edges/corners of the frame.

  

Now let's take an example and run some numbers:

You have a 35mm lens mounted on a full frame body, the aperture is set at 5.6 and you have the lens focused at 5m.  Now using my trusty iPhone DOF scale app, I should get a total depth of field that extends from 3 m to about 17 m, or total depth of field of about 14 m  (Don’t take this as gospel there can be a bit of variation between calculations depending on what parameters were used to devise the scale)

So far so good, now let’s say that this particular lens due to curvature actually crisply focuses the central edges of the frame at parallel distance of 10 meters (which is well within the bounds of possibilities by the way).  The depth of field available on the edges would run from 4.2 meters to infinity!

See what I mean, that makes a complete mockery of the idea of a Depth of Field scale and indeed makes it much harder to work out just where you may place the focus for the best overall result for say a landscape image.

If the aperture is closed down enough the increased overall depth of field will mask or may even eliminate the field curvature issue, again let's look at some numbers.

Take the same example as above but merely close the aperture down to f8, the depth of field at 10 meters (on the edges) will extend from 3.4 meters to infinity, which is pretty close to the 3.0 metres near limit in the centre at f5.6, but now the centre has a depth of field that ranges from 2.5 m to 170 m, thus the difference between the centre and the edges will be nowhere near as pronounced at f8 as it was at f5.6.

Let's take that one stop smaller, at f11 the edges will have a near limit of 2.7 m extending to a far limit of infinity (which of course is unchanged from the previous example), while the centre will range from 2.1 metres to infinity.  Put it another way despite the significant field curvature by f11 the rendering across the whole frame will be pretty even.  The downside to all this is you get virtually no separation as everything is effectively in focus and by this aperture, setting diffraction is starting to slightly impact on your image quality. (It would have significant effect if you were shooting on the M4/3 format).

You can imagine that at wide apertures the disparity across the image regarding sharpness will be significantly variable due to field curvature.

But wait, there's more potential problems in store, field curvature for zooms varies with focal length which makes it quite impossible to use the classic "focus long then reframe wide" techniques accurately with par-focal zoom lenses, (which incidentally are quite rare) this is especially the case with many wide angle zoom lenses. 

The zoom lens used for the pics in this article has field curvature that radically changes from seriously rearward tending (moving away from the camera on the edges) at 28mm to flat at 30mm and then forward tending at 32mm, all this within a focal length shift of just 4 mm!

And yet there's more at play....field curvature is not ordinarily consistent at all focused distances, it could well be quite flat at close up distances but become more curved as you move towards infinity, some macro lenses which are optimised for very close focus distances perform precisely in this way, of course, it could work oppositely with regular lenses as well. 

Here we have the Minolta 28-58mm zoom focused close up at f4@28mm, it's obvious the field curvature at this distance is rearward tending, the opposite of how it works at 32mm, tricky indeed.

Field curvature may also mess with infinity performance, I have found that sometimes a lens may have to be focused beyond or well in front of infinity at wider apertures to give correct overall infinity focus due to field curvature anomalies.

Many legacy lenses regarded as having terrible edge definition are in reality strongly affected by field curvature, in some cases the lens may have to be focused at just a couple meters or so to bring the extreme edges into focus. Because almost everyone focuses for the centre or reasonably close to it, the assumption is “that dreadful corner resolution” is simply an issue bad lens design.  Strangely enough, if you actually take a lot of these so-called “bad lenses” then focus at a point just a little way in from the corner and have a good look you will find surprising amounts of real edge and corner resolution. 

The image at the top of this article was shot with a lens (an ancient Minolta 28-85 f3.5-4.5 zoom) which has been over the years regarded as a bit of dog having soft mushy corners, but instead it's a lens with very significant rearward tending field curvature at the 28mm setting, once you know this you can work it to your advantage. So it’s not a bad lens at all, just a misunderstood one.

Testing for field curvature is not that difficult, just find a gravel carpark somewhere and get down to a meter of the ground and shoot a series of shots holding the camera at a slightly downward pointing angle with the aperture wide open.  Close examination of your files should give the game away as to what type of curvature you are dealing with, you may find however that stopping down just a bit changes the curvature characteristics so don’t make too many assumptions based on that initial frame.

Here we can see the extreme field curvature of the Minolta 28-85mm zoom in action, the lens is set at 28mm at f3.5 (wide open), it is pretty evident that the plane of focus is curving around the church and coming back towards the camera only in the middle of the frame. In this case, the effect is quite lovely, well to my eyes anyway so sometimes field curvature can be a glorious bastard instead of just a regular bastard.

For zooms, you will, of course, need to take images at the full array of focal lengths as field curvature is almost never consistent across the whole focal length range, but it's highly likely to be far worse at the wider settings.  As a tip, your telephoto zooms are not expected to display much if any field curvature problems.

It’s probable that with your wide angle zoom there will be some wonderful point within the focal length range where the lens is almost flat field, (and may remain that way beyond that point) the focal length will likely correspond very closely to the point where it exhibits no distortion as well,  I have not dwelled on the matter of distortion in this article but as said the two are closely linked.

Rearward tending field curvature

It's possible to actually get a shot with sharp corners from lenses with even strong field curvature, you just have to completely rethink your focusing methods and work outside the optical box.  As far as I am aware no camera makers’ firmware entirely takes field curvature into account when determining how the focus algorithms operate, though I could be totally wrong on that. One thing for sure, even if they did account for the variable curvature, it would only be applied to the native lenses for that system and many other lens issues like decentering could make the whole situation a crapshoot anyway.

Now given all of the above information its easy to conclude that a lens with very little or no field curvature is going to be easier to use for regular photography, you can pretty much set the focus and aperture and be quite confident the bits you expected to be in focus will be and those that should be soft and out of focus are.  It’s for this reason I find it quite satisfying to work with some macro lenses at typical shooting distances despite them lacking the option of wide apertures.  For example I use my ancient 55mm f2.8 micro Nikkor across three different formats  (Full Frame, APS-C and M43) quite regularly, this little lovely has a very flat field rendering even at longer distances and thus gives the appearance of having a shallower depth of field rendering than most of my other lenses “aperture for aperture”. That 55mm micro is also supremely sharp into the bargain which is just icing on the cake for me. 

Unfortunately, you cannot solve the negative results of field curvature in post-capture the way distortion, vignetting and chromatic aberration can be.  You can sharpen the edges and into the corners differentially by using a radial sharpen filter options such as that found in Adobe Lightroom.  There are limits however to sharpening, it's not the same as regaining real resolution, a radial sharpening filter that uses deconvolution sharpening methods rather than the regular unsharp mask methods, however, may be able to get a pretty reasonable result if handled with care.

You might from all the above think that field curvature was just a terrible pest and something to be avoided at all cost, but you'd be totally wrong.  It can be a great creative tool, so great in fact that one manufacturer actually produced a pair of lenses with variable field curvature as part of their design, in fact, they even designated them as VFC (variable field curvature). The company was Minolta and the lenses in question the 24mm f2.8MC VFC and the 35mm Shift CA, the latter is particularly exotic because it offers both shift and VFC in the one lens, which I think makes it pretty much unique in the lens world!  Both of these VFC lenses are typically selling for crazy high prices to those in the VFC know.

http://www.rokkorfiles.com/35mm%20Page%201.htm

here is a link that will give you some insight into the 35mm f2.8 Shift CA

http://www.rokkorfiles.com/24mm%20VFC.htm

And the 24mm VFC Minolta.

We can see in these pics where the clarity is sitting quickly enough, I put some dirty great red arrows there for you just in case you can't, if you look at the images and the arrows you will soon get your head around the fact the plane of focus is quite curved going rearward on the edges, in both these cases it gives a depth of field which well and truly exceeds what you would expect for images being shot at just f3.5 on a full frame camera! It also manages to pull off a rather neat trick, keeping the fence line in focus as it moves away from the lens, yet somehow separating it from the background behind, in fact, in this case, it is almost as if I had used a tilt adjustment!

Here again, it's pretty apparent that the field characteristics are not flat plane, but interestingly it provides for a unique rendering ability. Red arrows again show where the focus sits in the full res image.

Here are a couple of quick examples of how you could make field curvature work for you, rather than against you.

Let's say we take my ancient Minolta 28-85 mm zoom and set it to 33mm.  At this setting, it has strong rearward tending field curvature, but let’s say I want to shoot a building interior and I am standing in one of the corners.  Bearing in mind that the walls a running away from me if I set the focus carefully I can probably get the full depth of the room in focus even when using a quite wide aperture, in fact I know from much experience with this lens I could probably shoot this scene at about f5 and let the odd field curvature do the rest!

Now we will take an opposite approach, say I want to place an object towards the edge of the frame, let's make that a flower on the edge of an open field and I am going to put it on the right-hand side of the frame.  If I focus on the edge of the frame I am bringing the outer focus point fairly close to the camera, but that means the central focus area is now much closer to the camera and most likely out of the range of what the camera is actually seeing and the area in the centre of the frame that it can actually see is now a long way out of focus, much further in fact than you might typically expect.  In this example the very left-hand side of the frame will also be in focus along the same plane as the flower, but then if you cropped the frame so as to exclude that left side you would end up with just the flower rendered crisply all over with everything else in the frame out of focus, such a trick is impossible with a flat field lens and I can still use an aperture small enough to give a full detail rendering of the flower.

The thing is, field curvature can be a great creative tool, but you have to change the way you compose and focus, once you twig to this, those troublesome bastard lenses can be gems.

Here again using the Minolta 28-85 in the near macro realm we can see how the plane of focus curves, Of course, I am only showing it as it moves across the frame horizontally, but it works in all directions; hence it makes this rather lovely rendering possible even at f3.5!  Don't underestimate the creative possibilities of field curvature, it's the prime reason I have kept this particular lens in regular use.  To me, the Minolta 28-85 zoom is almost a VFC Zoom lens without the crazy expense of buying one of those tasty but pricey old school Minolta VLC lenses. 

Unfortunately many DSLRs often don’t make it easy to work with these naughty lenses unless used in live view as the focus systems may not have the ability to place the autofocus in the location that you really need to focus on and you cannot use the old focus in the centre and recompose technique as that method works on the assumption the lens is flat field.

If you're shooting in magnified live view the DSLR is fine, you can usually focus anywhere in the image, the downside, of course, is that it's hard to see the screen and the contrast detection focusing on many DSLRs is as slow as a geriatric tortoise on valium.  Manual focus is of course excellent.

These days mirrorless cameras with good quality EVFs can help enormously and if you have the time when shooting say landscapes you can zoom in on several parts of the image with the cameras “focus magnification option”. Next check the focus and then scroll around the image to find out if everything is sharp where you need it to be and readjust the focusing point accordingly to compensate if desired.  To make life easier many of the mirrorless cameras now feature tap to focus on the LCD which is both accurate and fast, the current model GM Panasonic models being great examples of the breed.

The takeaway from all the info is that using single central point focus is probably not going to be hugely successful with a field curving time dilating bastard, but it’s also likely any version of autofocus is perhaps not going to give optimal results for many images if the lens has significant field curvature and you are shooting at the wider apertures. 

Yes sir, field curvature is a strange beast indeed and it’s probably responsible for a good number of otherwise decent lenses being dis'd as useless simply because the photographer had no real understanding of what was going on and how they might have worked around it.

At least now you have some idea and you can go do some experiments with your own lenses, who knows what creative gems you may uncover, and if nothing else you will learn quite a bit about your lenses and focusing in general.

For further reading you can like to look at these articles:

https://photographylife.com/what-is-field-curvature

A basic article on the subject.

http://tashley1.zenfolio.com/blog/2013/5/field-curvature---a-practical-guide

This article is primarily related to the foibles of field curvature and Leica lens/body combinations, it includes some terrific tech info from Roger Cicala of Lens Rentals for those who want more.

http://toothwalker.org/optics/astigmatism.html

An older technical article on the subject, the diagrams are easy to understand, the explanation a little technical perhaps, it shows the link between field curvature and astigmatism.