Saturday, November 8, 2008

Crop Factor affects the apparent Depth of Field

The topic of crop factor and depth of field comes up once in a while in debates on the net. Specifically on certain forums on, where there are people who consider an extremely limited range of depth of field a virtue ...

Some people do not believe in the NxA Rule, something I picked up on a web site that is sadly no longer visible. However, this rule tends to work out, despite its rudimentary approach to the topic. Basically, N is the *crop factor* from the camera's sensor size to a full frame sensor size. Roughly, this corresponds to the diagonals of the two sensors.

A Fuji F11 (my favourite compact until they release something that is truly better feature for feature) has a 1/1.7" sensor, which has a diagonal of 9.5mm. A Nikon D300 (my favourite dSLR until I win the lottery and grab the D700 and a selection of appropriate lenses) has the Nikon APS-C variant, which has a diagonal of 28.4mm. And a full frame camera (any 35mm film, and the majority of full frame digital SLRs like the aforementioned D700) have sensors with a massive diagonal of 43.3mm.

So the crop factors for the Fuji F11 and D300 are 4.56 and 1.47 respectively. Interestingly, this disagrees with Fuji's reported crop factor (FOV factor if you will) of 105mm effective at 24mm actual. That makes it a 4.38 crop factor. No matter, they are close enough.

What this means is that a D300 shot at f2.8 will have an effective DOF (relative to the FF camera) of 1.47(N)*2.8(A) which comes to f4.1. The F11 shot at f2.8 will have an effective DOF of f12.7.

That's some kind of difference. In fact, it makes it nearly impossible to get pleasing bokeh from the F11. Only in extreme macro situations can the background be smoothed out really nicely. This is why the debates rage in the forums ... compact and bridge cameras are considered by many to be unsuitable for any photographic pursuit where pleasing bokeh is a requirement. But they have their defenders, who staunchly suggest that dSLRs cannot get the same DOF and therefore are actually less appropriate for certain types of photography, the primary example being landscape photography.

One problem, of course, is that most bridge cams and compacts have only a few apertures available at full zoom to keep their lenses reasonable in size. The F11 has a range from f5 to f8, which is 2.33 stops. The S100fs bridge cam goes from f5.3 through f8 in automated modes (a hair over two stops) and adds f11 (ok, does this get confusing with the Fuji's model or what?) in manual modes (a hair over three stops.) I.e. they all start pretty high in the range at full zoom.

So what does this mean in practice? Well, it means that the subject isolation and bokeh you will get on the dSLR shot at anything below about f16 is simply unattainable on the small sensor cameras. Whaaaaaaat, you say? No, it's true. The crop factor predicts something close to this, and a demonstration shows it pretty clearly. It also shows that the maximum DOF is pretty close between the two, although in both cases one is reaching into diffraction-limited territory.

I shot a series of images from a tripod placed less than 2 feet from my subject, a Kirk Enterprises D2 L-Bracket lying around from the days when I owned a D2 series camera (eventually I'll get it together and sell the darned thing.) There are boards stacked against the wall between 12 and 15 feet behind this subject, which make a pretty good test. By the time they come into partial focus, we're well into the teens in aperture. At least, at macro ranges.

A note: At macro ranges it is my experience than you can shoot at minimum aperture (f8 for the F11 and f32 for the lense used on the D300) without significant diffraction impact. I presume that this is caused by the magnification of the subject.

When I shoot the F11 at 105mm to match the lense I had on the D300, I start at f5 and shoot at f5.6 and f8 as well. These should line up somewhere around f15 through f24 on the D300, but my experiment shows it to be more like f16 through f32. This probably because the Fuji could not focus as close, even in macro mode and had to be moved back a few inches. This does not invalidate the test because the relationship between subject distance and background distance is pretty vast and is hardly affected by this slight change.

So ... here is what it looks like. (Click on it to see it at its full size.)

And here is a second test, created when challenged by a user on the Fuji Talk Forum. I was extremely careful to match effective focal lengths and subject distances ... and the result was the same. This is also not a macro shot, with the subject distance to background distance ratio being closer to 1:5 this time.

From this experiment, we can conclude two things:
  • Small sensor cams have great difficulty isolating subjects.
  • Large sensor cams are able to pretty much duplicate the wide DOF of small sensor cams because of their much larger range of useful apertures.
And remember that the difference is maintained as subject distance increases in relation to background distance. So dSLRs have to use lenses with much wider apertures to get any subject isolation from a distance. While they have little trouble getting most everything in focus at long landscape distances without resorting to their maximum diffraction-limited apertures.

There is a slight advantage to small sensors when one wants to shoot something very close to the lense (e.g. a flower) while still retaining the field in good focus. This requires decent apertures to maintain shutter speeds yet requires very wide depth of field from close distances. Since this is usually done at wide angle, the problem is not as severe as with the telephoto macro examples shown here, but it still exists. Raising ISO helps (and there is a lot of headroom there in modern dSLRs) .... but what really does the trick is the tilt-shift lense, which is available for all dSLRs. This lense reorients the plane of focus to match the plane of the sensor, allowing stunningly wide apparent depth of field ...

I have to say that I prefer the wide range of options to the rare convenience offered by the small sensor camera. Of course, the solution is to own both and shoot the small sensor camera when it really does have the advantage. The Canon G10 is likely to follow the G9's success as the backup / travel cam for many dSLR owners because of its dSLR-like control and compact size. But I very much hope that Fuji releases a real competitor once again ... rejuvenating the E-series camera line would be a great thing ...

No comments: