More on Factoring In the Crop Factor: Depth of Field
Continuing with our exploration of the effects of sensor size and digital crop factor, it's time to consider depth of field. Normally, DOF changes when focal length does, but since digital doesn't really alter focal length, it might be tempting to think that sensor size won't affect depth of field. In reality though, it does, but by how much, and even whether it decreases or increases, depends on how we compare things.
The formulas for calculating depth of field are a bit complicated, and I won't delve into the math in depth here, but they include something known as the "circle of confusion" (often abbreviated as "CoC"). While this term may sound like a bad photographer joke, it needn't be as confusing as its name implies.
Imagine a point source of light such as a quite distant light bulb, a reflected specular highlight, or even a star in the night sky. Anything that will appear to be a single point rather than a shape. If you focus a camera on it, it should still look like a single point. If you press the shutter release and make a print from the resulting image, it should look like a point here too. If instead, you focus sufficiently in front of or behind it and take a picture, the resulting print won't show a point since the light won't all be focused close enough to the same point and will spread or bloom to be more of a fuzzy circle.
If you start focused on a point light source and take a series of images, slowly defocusing the lens a bit more between each shot, there will come a point where you can't definitively say whether what you see on the final print is a point or a circle. At this point, the diameter of the light source's image on your film or sensor is known as the circle of confusion. Literally, when a viewer looks at the print, they will be confused as to whether what they see is a circle or a point. Hence the term: "circle of confusion." Smaller than this, and they will definitely see it as a point. Bigger, and it will clearly be a circle. Right at this limit, they can't tell.
This value is meaningful since it affects not only point light sources, but everything you photograph. If your focus is off by too much, things will look blurry. If focused more accurately, your print will still appear acceptably sharp, even if you aren't focused exactly on your subject.
Just how big you print it and how close you stand when you make this judgment is a subject of some difference of opinion, but most agree that the print should be somewhere in the 8 x 12 inch range, and you should evaluate it from two to three feet away. Those who are more demanding may use more stringent criteria of course. As a consensus standard, most sources use 0.03 mm for 35mm film or full-frame digital, but some prefer the lower 0.025 mm value instead. Remember now, this is the size on film (or digital) where things get "confusing," not necessarily how big it comes out if unfocused on the final print.
Now that I've devoted this much space to explaining what the circle of confusion is all about and what value is generally used for 35mm film or equivalent sized digital, the obvious question is, how about on cropped digital such as Nikon's DX format?
Since the way the circle of confusion is derived includes the evaluation of a printed image, in order to be consistent, we'd need to use the same size printed image regardless of whether our test image came from film or digital. But since the sensor in almost all digital cameras is smaller than a frame of 35mm film, we'll need to enlarge the resulting digital capture more to achieve that print size than we would from a film capture. Because of this, any potential focus errors will be more visible on the print from digital as they will be enlarged during printing too. To compensate, we'll need to use a lower circle of confusion value. How much lower depends on how much smaller the sensor is than film. Using the same standards of judgment, we'll need to divide 0.03 (the circle of confusion for 35mm film) by the crop factor for the DX digital format we are using to get the CoC value for that format. So, for my Nikon D2x which has a 1.5x crop factor, I'd need to use a circle of confusion value of 0.02 (that is, 0.03 divided by 1.5). Circle of confusion values for other digital cameras can be calculated similarly, or simply looked up on this helpful page.
Because a smaller circle of confusion value means we need to focus more critically with digital, it follows that if we shoot from the same subject distance with the same aperture, the depth of field will be less on DX digital than on film or FX digital.
But the image we record on DX digital will also be more tightly cropped, mimicking the angle of view we'd get with a longer lens on a film body so it is reasonable to ask whether this is a fair comparison. If instead we use a wider angle lens or increase our distance from the subject to get the same framing and subject size with digital we are seeing with the lens we started with from the original location on film, this too will affect the resulting depth of field. Indeed, now we'll actually get more depth of field on the DX digital shot. The increase in depth of field due to either the decrease in focal length or the increased shooting distance will more than offset the decrease due to the lower circle of confusion value.
Reference image from film (not really, but it could have been)
D Digital shot from the same distance gives tighter cropping than film and less DOF
DX Digital shot from further away or with a wider angle lens gives same cropping as film and greater DOF
OK, maybe circle of confusion for digital is a bit confusing after all. The bottom line though is that it depends on how you want to compare things. If you shoot from the same subject distance and with the same lens, changing nothing but the film/sensor size, you will lose depth of field with digital but end up with images that look as if they were shot with a longer lens. If instead you switch to a wider lens or back off with the digital body in order to compare images that look the same in terms of subject size and framing, you will get more depth of field from digital. All due to the various effects of the smaller sized sensor, which is generally measured in terms of crop factor.
Next week well tackle the effects of crop factor on hand holding.
Update 12/28/2007 - I've updated some of the wording throughout now that Nikon has released the full-frame D3 digital SLR. Since its FX-sized sensor has the same dimensions as 35mm film, all effects of sensor/film size will be the same for film as for the D3 and other full-frame digital cameras.