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DoF and "negligible" decline in sharpness

Doug Kerr

Well-known member
What I call "outlook B" in depth of field planning is this:

We seek to determine the near and far distance limits such that the blurring of objects at those limits (due to their not being in perfect focus) will not cause a "significant" decline in their "sharpness" compared to that of an object in perfect focus.​
"Sharpness" is of course not a good objective term, and I use it at the outset to convey the notion at work here.

Perhaps we can instead speak of the "overall restitution" enjoyed by the various objects. An object at the perfect focus distance enjoys a resolution that is the result of the lens and sensor system performance. An object at a difference distance will enjoy a lesser resolution, as a result of the "piling on" of the blurring caused by imperfect focus.

Now, we might first ask, for a given "perfect focus" resolution, how much blurring "piled on" will result in no decrease of the resolution enjoyed by the object? Answer: none.

So of course this is why we have recourse to the concept of "significant" decline. But if we are going to attempts even a simplistic analytical approach to this matter, we need to articulate some objective concept of how much declined in resolution is "significant".

Suppose we decide to declare a decline in resolution of 30% to be "significant". That is very handy. If we make certain reasonable assumptions about the shape of the blur figure (and as well of the implied bur figure behind the camera's "base" resolution), then if the diameter of the blur figure due to imperfect focus is the same as the diameter of the blur figure implied by the camera's base, the resolution enjoyed by the out-of-focus object will be 0.707 times the camera's base resolution - a decline of about 30%.

A common empirical choice for the COCDL in DoF calculations (the maximum allowable diameter of the blur figure from imperfect focus) is the pixel pitch of the sensor (P), in mm. The base resolution of the camera (in cycles/mm)is typically about 0.375/P.

In that case, the decline in resolution expected from the maximum "allowable" misfocus turns out to be about 20%.

Pretty reasonable for "not significant".

Best regards,

Doug
 
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