Equivalence does not prove the superiority of full frame (FF) over crop sensor (APS-C, M43) cameras. In fact, equivalence shows that equivalent photos are equivalent in terms of angle of view, depth of field, motion blurring, brightness, etc…including QUALITY. Yes, equivalent photos are equivalent in quality.
Refer to the illustration above where we have a full frame lens (BLUE) on a full frame sensor (GREEN). Some full frame sensors are now capable of shooting in crop mode (APS-C) where only the area in RED is used. When a crop sensor LENS is used on a full frame sensor, only the area in RED is illuminated and the rest of the areas in GREEN are in complete darkness and therefore do not contribute to light gathering. This is also true when the full frame is forced to shoot in crop mode with a full frame lens; the camera automatically crops the image to the area in RED and the rest of the areas in GREEN are thrown away.
As per the illustration above, we can see that the central half of the full frame sensor is really just an APS-C sensor. If indeed, a crop sensor is inferior in terms of light gathering then logic will tell us that every center of a full frame shot will be noisier than the rest of the frame. We know this is not true. The light coming in from the lens spreads evenly throughout the entire frame. Total light is spread over total area. As a matter of fact, the central half is the cleanest because lenses are not perfect and become worse as you move away from the center.
Now suppose we have a full frame 50mm lens in front of a full frame sensor. Notice that the crop mode area (RED) does not capture the entire image that is projected by the 50mm lens. The angle of view is narrower than full frame (GREEN). There are several ways we can capture the entire 50mm view while using crop mode:
- move backward
- use a wider lens (approx 35mm)
Both methods allow the RED area to capture more of the scene. A wider scene means more light is gathered. It means that if we force the RED area (APS-C) to capture exactly the same image as the GREEN area (FF) we will be forced to capture more light! More light means less noise! In equivalent images, APS-C is actually cleaner than full frame!!!
For example, if we go with option #2 using a wider lens, equivalent photos would be something like this:
RED (APS-C): 35mm, 1/125, f/5.6, ISO 100
GREEN (FF): 50mm, 1/125, f/8, ISO 200
This is exactly what the equivalence theory proposes. The difference in f-stop is to ensure that they have the same depth of field given the same distance to subject. The faster f-stop for APS-C (f/5.6) guarantees that TWICE more light is gathered. Notice that the full frame is now forced to shoot at a higher ISO to compensate for the lesser light coming in due to a narrower aperture given by f/8. So if we are to use the same camera for both shots, say, a Nikon D810 to shoot in normal mode with a 50mm lens and in crop mode using a 35mm lens, the crop mode image will be noticeably better. In equivalent photos, crop mode comes out one stop better. In equivalent photos, the smaller sensor results in BETTER quality!!!
The story does not end here though. The full frame shot has twice the area of the crop mode shot. If both images are printed at the same size, the crop mode shot will need to be enlarged more than the full frame shot. Enlargement results in loss of quality and the full frame image will have an advantage over the crop mode image. Whatever the crop mode shot gained by the increase in gathered light is lost by a proportional amount during enlargement. In the end, both full frame and crop mode shots result in exactly THE SAME print quality!!!
Bottomline, full frame will not give you cleaner images than crop sensors, assuming that they are the same sensor technology (e.g. D800, D7000, K5). They will result in equivalent print quality if forced to shoot equivalent images.
Full frame superiority busted!