D.O.F., Sensor Size, Focal Length And Stitching

In any discucussion group, start talking about sensor size, multiplication factors, depth of field and you'd better stand back and hold onto a fire extinguisher because it's opening pandora's box. More mis information couched in scientific terms will be spouted and more harm done than had the subject not been raised in the first place.

Here's a little exercise to warp your mind. We'll take it as given that small sensor cameras have greater depth of field than large sensor cameras given the same f-stop and lenses covering the same angle of view. Anyone who has tried to blur the background with a consumer digicam of normal focal length knows it's nigh on impossible - just too much depth of field, while large format photographers pray that everything in the image is in a single plane of focus such that the lens or back can be tilted to include all, since they know darn well, that no useable f-stop is small enough to get everything from 3 feet to infinity sharp with a 210 mm. lens.

OK, so here's the trick. I decide to shoot an image with one of those 2/3 inch sensor ultrazoom cameras but I'm going to shoot 9 images in a 3 X 3 matrix such that I'm going to end up with a 45 degree angle of view (roughly that of a 50 mm. lens on a 35 mm. camera). I know from experience that the digicam has huge depth of field so I'm going to end up with a stitched image which also has great depth of field, near and far being nice and sharp. That seems to make sense, but then I ask myself, what is the difference between using a single 2/3 inch sensor repeatedly vs. a single sensor 2 inches across (we're ignoring stitching overlap for simplicity). It seems to make sense that there shouldn't really be any difference, except that in one case we use the lens from the digicam to repeatedly move around the image taking multiple shots, and in the other case we need a new lens which will cover the imaginary 2 inch sensor (2/3 inch times 3). We'd need wider coverage for the 2 inch sensor, but we know from our large format days that depth of field doesn't change from a Xenar lens to a Super Symar XL of the same focal length- only the circle of coverage changes, so the fact that our 2 inch sensor needs more coverage is in fact irrelevent.

OK, this is getting complicated. So, if I have discounted the difference in sensor size, how is it that large sensor or film cameras have less depth of field than small sensor cameras? Well, we have to remember that to 'zoom in' to capture 1/9th bites of our image, the small sensor camera has to use a much longer focal length than were it capturing the 45 degrees spread of our subject. In fact, ignoring overlap, we'd need a lens of 15 degrees coverage for each of the 9 images to be stitched, corresponding to a focal length three times that needed to capture the scene in a single shot. We remember of course that on any given sensor size, longer lenses tend to have less depth of field than shorter lenses, distance for distance and shot from the same location. Take a long enough lens (like my 300 mm. on my 1Ds2) and you can run into trouble getting 500 feet and infinity both in focus.

So, when we stitch, depth of field is exactly the same as if we were using a single larger sensor and lens combination - that's to say, less than we thought we were going to get.

Of course, we aren't enlarging those digicam images as much (since it takes 9 of them to make up the image) and we understand that depth of field isn't a done deal and in fact depends on how big a print you make and how close you plan to view it.

Whew.

Hang in there with me just a little longer.

The mathematical formula for depth of field is directly related to the f stop, the maginfication, and the viewing distance, while varying with the inverse of the SQUARE of the focal length - and that's where the single image from a short focal length lens covering 45 degrees on the digicam (say 10 mm.) has a lot more depth of field than a 50 mm. lens on a 35 mm. type camera. 10 squared is 100, 50 squared is 2500. That's what more than makes up for the magnification from sensor size to print size. It's that business of using a 3X longer focal length to make the parts for our stitched image which means that in the end the depth of field is just the same as if we'd used a 3X bigger sensor and lens of equivalent field of view (which just happens to require a lens of 3X the focal length.

Thus it doesn't matter whether you use a 200 mm. lens and small sensor to shoot multiple parts of an image or to shoot the whole thing with a bigger sensor - and that makes sense.

Now wasn't that fun?