Depth of focus

Determining factors

In small-format cameras, the smaller circle of confusion limit yields a proportionately smaller depth of focus. In motion-picture cameras, different lens mount and camera gate combinations have exact flange focal distance measurements to which lenses are calibrated.

The choice to place gels or other filters behind the lens becomes a much more critical decision when dealing with smaller formats. Placement of items behind the lens will alter the optics pathway, shifting the focal plane. Therefore, often this insertion must be done in concert with stopping down the lens in order to compensate enough to make any shift negligible given a greater depth of focus. It is often advised in 35 mm motion-picture filmmaking not to use filters behind the lens if the lens is wider than 25 mm.

Calculation

If the depth of focus relates to a single plane in object space, it can be calculated from

${\displaystyle t=2Nc\frac{v}{f},}$

where t is the total depth of focus, N is the lens f-number, c is the circle of confusion, v is the image distance, and f is the lens focal length. In most cases, the image distance (not to be confused with subject distance) is not easily determined; the depth of focus can also be given in terms of magnification m:

${\displaystyle t=2Nc(1+m).}$

The magnification depends on the focal length and the subject distance, and sometimes it can be difficult to estimate. When the magnification is small, the formula simplifies to

${\displaystyle t\approx 2Nc.}$

The simple formula is often used as a guideline, as it is much easier to calculate, and in many cases, the difference from the exact formula is insignificant. Moreover, the simple formula will always err on the conservative side (i.e., depth of focus will always be greater than calculated).

Following historical convention, the circle of confusion is sometimes taken as the lens focal length divided by 1000 (with the result in same units as the focal length); this formula makes most sense in the case of normal lens (as opposed to wide-angle or telephoto), where the focal length is a representation of the format size. This practice is now deprecated; it is more common to base the circle of confusion on the format size (for example, the diagonal divided by 1000 or 1500).

In astronomy, the depth of focus ${\displaystyle \mathrm{\Delta }f}$ is the amount of defocus that introduces a ${\displaystyle \pm \lambda /4}$ wavefront error. It can be calculated as

${\displaystyle \mathrm{\Delta }f=\pm 2\lambda N^2}$.