I have found an explanation on this, however I cannot seem to picture what the explanation is saying. From a Toshiba technical article:
Remember that the previous subsection mentioned that the depth of focus is the conjugate of the depth of field. A change in the object-side depth of focus caused by a displacement of the image plane by half the depth of focus is equal to half the depth of field. A slight displacement of an image plane causes the object-side focal point to shift by as much as a change in the image-side depth of focus divided by the longitudinal magnification of the lens. Because the depth of focus is symmetrical around the image plane, the depth of field is also symmetrical around the image plane.
However, if the optical magnification of a lens differs greatly at both ends of the depth of focus, the front and rear depths of field are not equal as described in 3 and 4 above. Equations for the depth of field are presented in the following subsections. In the case of machine vision and other applications requiring relatively close focusing, we recommend using an equation with an optical magnification term. Otherwise, we recommend using an equation with a subject distance term.