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Factoring in the Digital Crop Factor
Back in the good old days of film, everything seemed so simple. Focal length was focal length and lenses produced the field of view we were accustomed to. But digital changed things. The printed pictures still come out the same size, but there's something sized differently in how they get shot. We call it the "crop factor" or "focal length multiplier," and it's the topic of this week's PhotoTip article.
As you are probably already aware, the root of the issue is the size of the sensor. In most digital cameras, it's smaller than a standard frame of 35mm film. By being smaller, it captures less of the image the lens is projecting on it. Due to their shape, all lenses produce a circular image, but this image is then cropped to the size of whatever medium is used to capture it.
 Forget about the camera for a minute. Just imagine a lens suspended in the middle of open space. An image of whatever is in front of it will get projected behind it, but you probably wouldn't be able to see it due to the amount of ambient light. To create a light-tight environment behind the lens so the image would be visible, imagine instead that the lens is mounted on the front of an empty camera body. With nothing to block it and no other light sources, a round image from the lens would be projected on the back wall inside the camera. If we now place a piece of 35mm film in the proper position, it will get exposed by the projected lens image. The film frame will cast a shadow and only the portion that spills past the sides of the frame will still strike the inside back of the camera. If we replace that film frame with a digital sensor of the same size, the portion of the image that fits doesn't change. But if instead the digital sensor is smaller than a film frame, the image captured by it will be correspondingly cropped. The lens doesn't change and neither does the image projected by it. It's just that now more of it will pass by beyond the sensor's edges instead of striking it.
No matter what we interpose between the lens and the back wall of the camera body, the "image circle" produced by the lens stays the same size. The only thing that changes is how much of that image gets captured by the film or sensor. The lens doesn't even have any way to know how much of its image is being captured and how much isn't. It is unaffected by what happens to the image being projected. Focal length is focal length. Some "digital lenses" are designed to produce a projected image that is sized more appropriately for the smaller digital format, but this only affects the size of their image circle.  So long as this image is at least as big as the sensor, the same image will still be captured.
Fundamentally though, a smaller image capture medium sees less of the image than a larger one. This is as true for digital versus 35mm film as it long has been when comparing 35mm film to medium or large format film. While it doesn't really, it is common to think in terms of the focal length changing in order to understand the difference in captured image size. The decreased coverage resulting from using a smaller sensor will proportionally match what you would get when using a longer lens on a larger sensor. For instance, the sensor size in Nikon digital SLR's is around 16mm x 24mm which is two-thirds the size of a frame of standard 35mm film at 24mm x 36mm. Since the film frame is therefore 1.5 times the size of the sensor (the inverse of two-thirds), we will get the same coverage on our Nikon DX sensor as we would by using a lens with 1.5 times the focal length on 35mm film. The narrower angle of coverage the longer lens will yield mimics the narrower coverage produced by the smaller sensor. Because of this, some people talk of this as being a "focal length multiplier" for digital. Since the effect is produced by the sensor size and the lens focal length doesn't really change, "crop factor" is definitely a more correct term.
Next week, we'll look at what else changes due to sensor size.
Update 03/07/2006 - Careful readers have pointed out that I omitted details such as pixel density and film RMS grain size in the above. Clearly, these become limiting factors on how much detail we can capture using digital and film, respectively. But a smaller surface area will capture a smaller portion of the image. It is entirely possible for a smaller sensor with higher pixel density to capture more detail than a larger sensor with fewer pixels, or for a smaller sensor with sufficient pixels to have better resolution than a larger film frame. For the sake of simplicity though, my focus here is on the sensor size versus image coverage, not on resolution. Glad we got that cleared up.
Update 12/28/2007 - The "FX" full-frame sensor used in the new Nikon D3 has the same dimensions as 35mm film. Since it is not smaller than a film frame, it behaves the same as film with regard to crop factor effects. Nikon DX and other sensor formats that are cropped exhibit what we refer to as the crop factor, but not FX sensors.
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