Doug Kerr
Well-known member
Often the "bogey" for the accuracy of a camera autofocus system is stated by the manufacturer in terms of a fraction of the depth of focus. Just what does that mean, and how can we relate it to the familiar concept of front- or back-focusing?
Depth of focus is the distance by which the plane at which the image is brought to perfect focus may vary from the sensor plane while the resulting circle of confusion remains within a diameter criterion we adopt, the circle of confusion diameter limit (COCDL). This is the same criterion of "acceptable blurring" used in the definition of depth of field (a closely related concept).
The amount of AF error, and a "bogey" for the error, is stated in those terms since the actual optical phenomenon occurs in image space (that is, in the vicinity of the sensor).
If the manufacturer says that the bogey for AF accuracy in a certain situation (certain camera, certain type of AF point, certain lens maximum aperture) is "the depth of focus", that means that the location of the image plane of perfect focus will be such that, on the sensor, the diameter of the circle of confusion will be not over the COCDL criterion that has been adopted by the manufacturer.
Incidentally, the two limits of that range are very nearly symmetrical about the sensor plane - the allowed offset of the plane of perfect focus forward of the sensor plane is almost identical to the allowed offset behind the sensor plane.
Now, how does this relate to our usual interest in amount of front- or back-focusing? Well, it turns out that for a focus error that places the plane of perfect image focus forward of the sensor by the allowable amount ("the depth of focus"), then the object plane that will be perfectly focused on the sensor is just at the near limit of the depth of field (for the object distance, lens parameters and COCDL involved) (front-focusing).
Similarly, for a focus error that places the plane of perfect image focus behind the sensor by the allowable amount ("the depth of focus"), then the object plane that will be perfectly focused on the sensor is just at the far limit of the depth of field (back-focusing).
So, in summary, the range of objects that might be in focus over the "allowable" range of focusing error (where that is specified as "the depth of focus") corresponds directly to the depth of field (for the lens parameters and COCDL involved).
Now often, for certain situations, the manufacturer will state the bogey for AF accuracy to be "1/3 the depth of focus". The concept is the same. Here, the acceptable error places the plane at which the image is perfectly focused within a distance from the sensor that is 1/3 the depth of focus distance (a smaller error).
However, when we relate this to front- or back-focusing, that does not mean that the object plane that will be perfectly focused on the sensor will be offset from the focus target by not over 1/3 the near or far depth of field limits. This is a result of the "nonlinearity" of the optical equations involved. (It will be "something like that".) We can use a depth of field calculator in a special way to get the exact result.
Those who are interested in further technical detail on this matter may wish to read my technical article, "Autofocus Accuracy Specifications in Canon EOS Digital SLR Cameras", available here:
http://dougkerr.net/Pumpkin/index.htm#AutofocusAccuracy
Best regards,
Doug
Depth of focus is the distance by which the plane at which the image is brought to perfect focus may vary from the sensor plane while the resulting circle of confusion remains within a diameter criterion we adopt, the circle of confusion diameter limit (COCDL). This is the same criterion of "acceptable blurring" used in the definition of depth of field (a closely related concept).
The amount of AF error, and a "bogey" for the error, is stated in those terms since the actual optical phenomenon occurs in image space (that is, in the vicinity of the sensor).
If the manufacturer says that the bogey for AF accuracy in a certain situation (certain camera, certain type of AF point, certain lens maximum aperture) is "the depth of focus", that means that the location of the image plane of perfect focus will be such that, on the sensor, the diameter of the circle of confusion will be not over the COCDL criterion that has been adopted by the manufacturer.
The choice of a COCDL by the manufacture for use in discussing depth of field, as well as in connection with this matter, is a complicated one, which I will not belabor here. Suffice it to say that it is an arbitrary choice - the value cannot be determined by any kind of optical theory.
Incidentally, the two limits of that range are very nearly symmetrical about the sensor plane - the allowed offset of the plane of perfect focus forward of the sensor plane is almost identical to the allowed offset behind the sensor plane.
Now, how does this relate to our usual interest in amount of front- or back-focusing? Well, it turns out that for a focus error that places the plane of perfect image focus forward of the sensor by the allowable amount ("the depth of focus"), then the object plane that will be perfectly focused on the sensor is just at the near limit of the depth of field (for the object distance, lens parameters and COCDL involved) (front-focusing).
Similarly, for a focus error that places the plane of perfect image focus behind the sensor by the allowable amount ("the depth of focus"), then the object plane that will be perfectly focused on the sensor is just at the far limit of the depth of field (back-focusing).
So, in summary, the range of objects that might be in focus over the "allowable" range of focusing error (where that is specified as "the depth of focus") corresponds directly to the depth of field (for the lens parameters and COCDL involved).
Now often, for certain situations, the manufacturer will state the bogey for AF accuracy to be "1/3 the depth of focus". The concept is the same. Here, the acceptable error places the plane at which the image is perfectly focused within a distance from the sensor that is 1/3 the depth of focus distance (a smaller error).
However, when we relate this to front- or back-focusing, that does not mean that the object plane that will be perfectly focused on the sensor will be offset from the focus target by not over 1/3 the near or far depth of field limits. This is a result of the "nonlinearity" of the optical equations involved. (It will be "something like that".) We can use a depth of field calculator in a special way to get the exact result.
Those who are interested in further technical detail on this matter may wish to read my technical article, "Autofocus Accuracy Specifications in Canon EOS Digital SLR Cameras", available here:
http://dougkerr.net/Pumpkin/index.htm#AutofocusAccuracy
Best regards,
Doug