There is some debate in the filmmaking community – even among professionals – as to whether sensor-size crop factor should be applied to aperture. As you may recall, the size of a camera’s sensor affects the apparent focal length of a lens – so, a 25mm lens on a four-thirds sensor has the same field of view as a 50mm lens on a full frame sensor. Is aperture affected in the same way?
The answer is… sort of. Aperture is the measure of the size of the opening in the lens through which light enters the camera, which affects brightness and depth of field. The size of the sensor does not change the size of a lens’s aperture, so the overall brightness does not change. However, depth of field is directly affected by focal length – long lenses produce a shallower depth of field than short lenses. So the depth of field (the amount of background blur) is affected by by crop factor since, for example, a 25mm lens will always produce less background blur than a 50mm lens at the same aperture. In short, depth of field is affected by sensor size (indirectly), but overall brightness is not.