Crop factor and DOF

Factors impacting depth of field (revised)

Depth of field  (DOF) is impacted by the following factors:

Factor Details
Aperture The wider the aperture opening, the narrower is the depth of field.
Focal length The longer the focal length, the narrower the DOF.
Camera to subject distance Sorter distances (or focusing distances) give narrower DOF.
Viewing distance and size Large print (or small print under magnifying glass) will reveal more details and DOF will appear narrower
Circle of confusion Circle of confusion (CoC) is a parameter used in DOF calculations to determine acceptable level of blur. CoC actually does not change DOF, it only tells the formula what is our tolerance for blur and what should be considered in focus and what out of focus. Smaller CoC means that smaller blur is considered out of focus.

Using equivalent focal length lens

Compared to full frame (FF), crop format cameras have smaller sensors and smaller field of view. Therefore, photographers who use such cameras generally use shorter lenses to achieve the same field of view compared to “reference” full frame camera. Equivalent focal length can be calculated by multiplying actual focal length by crop factor. For example, Nikon APS cameras have crop factor 1.5.  50mm lens mounted on Nikon APS will have equivalent field of view of 50 x 1.5 = 75mm lens on FF. And conversely, 50mm lens mounted on FF camera will have equivalent focal length 50/1.5 = 33mm.

Shorter lenses have greater depth of field, so if a photographer uses equivalent focal length lens on a crop camera, achieved depth of field will be deeper than on full frame. Focal length is the key, but not the only factor here. If we compare prints from a FF camera and a crop camera of equal size, the crop camera print, coming from smaller chip, will be enlarged more.  In that Nikon example, we have to enlarge 1.5x compared to FF. More enlarged edges and details will look less sharp and will give perception of shallower depth of field.

The following chart takes the different levels of enlargement into account and depicts hyperfocal distance in meters at different f-stops (1.4 – 22) for 50mm lens on FF and equivalent focal lengths on crop cameras.


Parameters:

Parameter Value
Focal length 50mm for FF

38.5 for 1.3x

33.3 for 1.5x

31.25 for 1.6x

25 for 2x

CoC Variable, based on 13MP, starting at 18µm for FF
Crop factor Variable (1, 1.3, 1.5, 1.6, 2)

The above chart shows that even if we consider the greater enlargement needed for crop factor, using equivalent focal length lens on crop camera will provide more depth of field than FF. That means that FF can achieve shallower depth of field than cameras with smaller sensors. It also means that if FF photographer and crop photographer shoot scene from the same distance and maintain the same subject size in their viewfinder and use the same f-stop, the crop photographer will have greater DOF in his shot.

But does it also mean that with crop factor we can achieve greater depth of field?

Factoring in diffraction limit

If great depth of field is our goal, we stop down the lens. We should not stop it down beyond diffraction limit though.  The following chart shows hyperfocal distance for various crop factors at diffraction limited (largest sensible) f-stop for each format (for all sensors at 13MP). The chart is for 50mm for FF and equivalent lenses for crop factors > 1.

Parameters: same as above.

It appears that if we take 50mm lens of FF camera and stop it down to f/13, or equivalent FL lens on a crop factor and stop it down to their diffraction limit, the achieved maximum depth of field is about the same. Minor differences between crop factor bars in the chart are apparently caused by rounding error.

Using the same lens

If using the same lens, in order to achieve the same subject size, photographer with crop camera must step further away compared to photographer with FF camera. Depth of field increases with distance, so even though the lens and f-stop are the same, the DOF will be larger with crop camera.

The following chart shows depth of field in meters for FF and crop camera. The distance on x axis is for shooter with FF camera, crop shooter is further away to achieve the same field of view.


Parameters:

Parameter Value
F-stop 4
Focal length 50mm
CoC FF 18µm
CoC crop 12µm
Crop factor 1.5
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