DoF made simple

Started Apr 17, 2011 | Discussions thread
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Bernard Delley Contributing Member • Posts: 887
DoF made simple

Knowing the DoF can be surprisingly simple when taking the reduction ratio (RR) from the image-object to the sensor as the key variable rather than object distance.

The idea behind DoF is to allow a tad loss in sharpness as compared to the optimal sharpness at the plane which is precisely in focus. Of course, his tad can be disputed without end. I define it at the point where out of focus softness equals the fundamental softness of the sensor. For open apertures, the 'fundamental' softness comes from the AA filter, which must be near 2 x pixel size.This is approximately CoC = 0.01 mm for a DX camera. For smaller apertures than f/8, aperture number kA greater than 8, diffraction is limiting sharpness and CoC becomes proportional to kA. The formal rule for the full DoF is:

DoF = 2 * CoC * kA * RR * RR

where the DoF is split equally between front and back.
A good value to memorize for DX sensors is:

DoF = 64 mm

at aperture f/ 8 , RR = 20 which means a width at the object plane of 20 x 24 mm corresponding to a fairly tight head portrait. As you step closer and zoom out to keep the object framed at RR = 20, nothing happens to the DoF. Almost nothing, as the plot DoF in function of focal length shows:

As you step closer, zooming, the back part of the DoF gets slightly larger
and the front part gets slightly smaller. The yellow part of the diagram
is a reminder that there is no Nikon DX lens shorter than 10 mm.

The use of the memorized 64 mm is:

  • for more open apertures, divide D0F by two for two stops.

  • for smaller apertures double DoF at each stop, while getting

increasingly soft images due to diffraction.

  • the reduction ration RR enters in power 2.

For example with kA = 16, and RR = 30 you get 4x1.5x1.5 times the DoF of portrait example. As you step even closer and zoom out you can reach the magic focal length

fh = CoC * kA * RR

where you hit hyperfocal conditions. In the second example this is at 10 mm focal length.

If the DX image is prepared for WEB presentation at 25%, CoC may be
referred to the pixel size in the final image, which is CoC = 0.02 mm .
This is incidentally the CoC value shown in the exif data for Nikon DX
cameras. If you are working with this Nikon/WEB25% CoC value
the crossover to diffraction limited is when kA is greater than 16.

here is an example with
kA = 16 focal length 10 mm example RR = 30 in focal plane,
some cherry blossoms are closer, 17x reduction
(on front side RR_f = 15 is the 'end' of the DoF )
D90, AF-S 10-24mm at 10mm f/16 1/320s
distance focal plane - sensor plane 0.5 m (MF), image size 25%.

For FX shooters, the portrait example to memorize is:

64 mm at RR = 14, CoC = 0.015 and f/11 , the diffraction limited crossover value.

and the hyperfocal example comes to
RR = 20 kA = 22 fh = 14

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