The other day I was pondering the peculiarities of my AF Sigma 10-20mm,
the lens exhibits a significant "curvature of field" effect and despite the
massive potential depth of field offered by the focal length it is possible to
take shots where there is not uniform sharpness across the entire image, at
first I thought this was a lens defect as there were many reports of these
lenses being sold with elements that were de centred but after some testing I
realised that I could take a succession of pictures with the lens wide open and
re composing the focus each time and that each picture would have a different
plane of focus despite common sense telling me everything from a few meters to
infinity should be in focus no matter what.
A typical set of results would include a picture where only the extreme background or foreground is sharp, a picture where edges are soft and a picture where the entire scene is in sharp focus.
Obviously with an ideal lens if you focus on an object that is 3m away in the centre of the frame then any other object 3m away anywhere in the frame should be sharp too but some lenses seem to exhibit a distinct shift towards the edges of the frame either inward or outward.
I have noticed on a few lenses now (mostly wider focal lengths) that if I focus on the centre using the magnification mode of live view and then move the focus point to the edge of the frame that I have to readjust focus to get the picture sharp. It seems some lenses have a flatter field of focus than others and if you just take crops from the edge of a shot that was focused in the middle it will not always accurately display the potential edge sharpness of some lenses.
It is entirely possible to get uniform sharpness for most subjects even if a lens has field curvature but you have to account for this when focusing in order to avoid soft areas. There are 3 basic types of field when dealing with camera lenses, a flat field, a field that curves outwards at the edges and a field that curves inwards at the edges.
Out in the real world this issue is not as obvious or even as relevant because the circumstances in which it arises are not as commonly found but certainly under some conditions it can be noticeable. The kind of shot that most often shows up the problem is when people take "wall shots" or use test charts as part of a lens review to demonstrate both centre and edge sharpness. Some lenses that have a curved field can end up being sold short in terms of edge sharpness because people tend to always use the centre of the image to focus such pictures, now all that needs to happen is for the tester to focus from in front of the subject if a lens has an inward curving field or focus from behind the subject if the lens has an outward curving field and the corners could instantly be rendered soft giving the false impression that a lens has soft edges when it doesn't.
Note: When I say focusing from behind I mean starting off with the lens focused beyond the subject when you begin adjusting the focus ring and likewise when I say in front I mean you start off with the lens focused somewhere in from of the subject before you begin turning the focus ring. The following illustrations will show you that where the focus comes from has an effect on the sharpness across the image when using a lens that suffers from field curvature.
In these examples we are imagining our lens has a plane of focus that curves outwards at the edges away from the photographer. The black bar represents the subject and the violet bar represents the area of focus with an outwards curve.
In this first image the photographer has focused on the edge from in front of the subject, due to the field curvature the centre of the subject falls outside of the area of focus:
If he had instead pulled the focus in from behind the subject then the entire subject would have been inside the area of focus:
So with a lens that has an outward curving field of focus it is best to either focus from in front of the subject if you are using the centre as a focusing point or focus from behind if you are using the edges. Obviously with a lens that has an inward curving field of focus the opposite is true.
It's important to remember that you are working with a narrow margin of error so you have to stop turning the focus ring just as soon as focus is achieved or you will go right through that margin or error and end up back where you started. An easier way to make sure is to take several shots with slight adjustments to the focus made between shots so that one of the shots has captured the entire subject inside that small margin, people call this focus bracketing and it is especially useful for this problem and also for AF lenses that have a tendency to be indecisive about if they are sharply focused or not.
Another way which I recommended is to use live view if you have such a luxury, using live view you can quickly confirm that you have achieved uniform sharpness before snapping away.
Obviously the more pronounced the curve is the harder it is to make sure the entire subject falls into the area of focus but even when using a wide aperture the depth of focus is usually not paper thin, all you need is for the focus depth to be enough to contain the subject even with the curvature going on. Even if a lens cannot focus on the centre and edge of a flat object simultaneously there is usually a good compromise between the two. When it comes to lens tests and reviews it still seems unfair and technically inaccurate to base edge sharpness on an image where the lens is not correctly focused at the edges, perhaps re composing focus between the centre and edge whilst making a note of the field curvature would be a fairer method. Under "real world" conditions we seldom take photos of flat surfaces with the lens wide open so it's less of a problem but it's better to be aware of such issues and how to get around them and it's certainly better to be aware of such issues when you are conducting a lens review!
This is just a brief explanation and doesn't account for the fact that some lenses have a varying field of focus depending on how far away the subject is, some lenses have a flat field with close subjects but a curved one with distant subjects and vice versa. Another variable is with zoom lenses where different focal length settings can have an effect on the field of focus. It is also worth considering that film is to an extent three dimensional and more forgiving where as digital sensors are completely flat and less forgiving but all of this is certainly both beyond the scope of this post and beyond my level of intelligence!