Full Sized vs. Cropped Sensors

By Charles Sidney Johnson, Jr.
Questions like this and misleading answers fill the photographic forums. One “expert” says that lenses are not equivalent to anything else, and another claims that a big sensor is necessary to get a small depth-of-field. These are at best half-truths. So what is correct?
It is easier to understand the important points by considering what is necessary to obtain an “equivalent” or identical image with different camera/sensor sizes. In order to obtain an equivalent imageallof the following properties must be the same:

Angle of view (field of view).
Perspective
Depth-of-field (DoF)
Diffraction broadening
Shutter speed/exposure

According to this definition, two equivalent images will appear to be the same in all aspects; and the observer will not be able to detect any evidence of the size camera/sensor that was used. This still leaves “noise,” pixel count, and lens quality to be considered later. The starting point is to recognize that typical cameras have ...