The image sensor format of a digital camera determines the angle of view of a particular lens when used with a particular camera. In particular, image sensors in digital SLR cameras tend to be smaller than the 24 mm x 36 mm image area of full-frame 35 mm cameras, and therefore lead to a narrower angle of view.
Lenses produced for 35 mm film cameras may mount well on the digital bodies, but the larger image circle of the 35 mm system lens allows unwanted light into the camera body, and the smaller size of the image sensor compared to 35 mm format results in cropping of the image compared to the results produced on the film camera. This latter effect is known as field-of-view crop; the format size ratio is known as the field of view crop factor, crop factor for short, or focal-length multiplier.
All other things being equal, a larger sensor captures images with greater dynamic range than a smaller sensor. The larger area provides a larger "well" in which photon-freed electrons can accumulate before overflow (highlight clipping) occurs.
As of December 2007, many DSLRs have sensor areas around 370 mm2, while many compact camera sensors have one-fifteenth the surface area: a standard 1/2.5" sensor has a surface area of 24.7 mm2. Thus, a typical DSLR will have a signal-to-noise ratio that is nearly 4 times higher than a typical compact digital camera:

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