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# Depth of Focus

Author: the photonics expert

Definition: the half width of the range of longitudinal positions in which a reasonable focus for a film or image sensor is achieved

An imaging instrument usually contains some objective and an image sensor (e.g. in the case of a digital photo camera) or a photographic film. For focusing to a certain object distance, one obtains an image plane somewhere behind the objective, where the image sensor or film should be placed. If the position deviates from the image plane, the image will be blurred to some extent. The width of the range in which a reasonably sharp image is obtained is called the depth of focus.

The size of the depth of focus depends on the chosen sharpness criterion, as discussed in the article on depth of field. Frequently, one defines a certain maximum diameter <$C$> of the circle of confusion and calculates the depth of focus based on purely geometrical optics. That calculation is simple and leads to the result that the depth of focus is <$C / 2$> divided by the tangent of the half opening angle. The latter approximately equals the numerical aperture for small enough angles.

These considerations were done for a fixed object distance. When the instrument is focused to other distances, the position of the image plane changes, and the depth of focus may also be changed.

The depth of focus is also relevant for the question what amount of tilt of the image sensor is tolerable because that effectively changes the distance of various image points to the plane of the lens. Further, it is relevant if there is some field curvature, i.e., if the sharp image points lie on a curved surface.

## Depth of Focus of a Laser Beam

The term depth of focus is sometimes also used in the context of laser beams. It is essentially the same meaning, but for a quantitative measure it is then more appropriate to use the Rayleigh length (for Gaussian beam) as a well defined parameter. In the case of beams with imperfect beam quality, an effective Rayleigh length can be defined, which is increased by the beam quality factor M2.

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