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Spherical aberration, focus, and autofocus

Doug Kerr

Well-known member
A thin lens with spherical surfaces exhibits the aberration of spherical aberration. We can see what that means in this figure:

opticaljargon7.png

In such a lens, the "hollow cones" of rays passing through different "zones" of the lens (different distances form the axis) do not come to a focus at the same distance from the lens.

As a result, no matter where we place the film or sensor, a point on the object will not produce a "point" on the image, but rather a finite-size blur figure.

We might think that, in the face of this, the "best focus" situation would be where the "narrowest" cross-section of the overall beam would fall on the focal plane. But that does not turn out to be so.

At another location of the focal plane, the overall "diameter" of the spot is greater, but owing to the distribution of luminance across the blur figure, the overall "sharpness" of the image will seem greater to the viewer. This is often called the "best focus" location (duh!).

If we decrease the aperture, the impact of spherical distortion diminishes, and for a very small aperture essentially disappears. Then for all practical purposes all the rays through the lens (from an object point) come to a focus at a point at a certain distance from the lens. This is said to be the "paraxial focus" because it is the one that (for an on-axis object point) results from only rays that are essentially along the optical axis (the prefix par, often para when there is not already a vowel to follow it, means "close to").

As we again increase the aperture, the degree of spherical distortion increases, and the point of best focus moves farther from the "ideal" paraxial focus.

The impact of spherical distortion varies with the aperture setting, and with it, the location of the plane of best focus with respect to the paraxial focus. Dealing with this in various ways is often described as the matter of "best focus". But it is not of great consequence with most modern lenses, which are generally-well-compensated for spherical aberration.

This phenomenon does however figure into the subtleties of phase-detection autofocus systems. The phase-detection system usually measures the focus error on a basis that is affected by spherical aberration. And the phase detection optical chain (to a bunch of "little cameras") typically includes, besides the main lens, various auxiliary lenses, some individual to the individual AF detector, which may have substantial residual spherical aberration.

Thus an error may occur in the AF system's determination of the current "focus error".

To overcome this, for example, in the classical Canon autofocus system, each time a focus error determination is to be made, the lens sends to the camera body information as to an amount by which the "report" of the focus detector should be adjusted to compensate for the expected error due to spherical aberration in the focus detection process.

Because this is somewhat parallel to the actual issue of "best focus", this value is called the best focus correction value (BFCV).

As is so often the case, the name wasn't at all apt for the purpose. The AF detectors weren't "focused". And the system didn't attempt to set the lens to the best focus position for the shot! But this dealt with the same phenomenon as in "best focus".​
On the typical Canon EF lens, there is a table that holds the BFCV for each of many combinations of focus distance, zoom setting (where applicable), and the specific type of AF detector (since often there are several types in the overall array).

Because the precise values may vary with the individual lens (not just the model), these values are particularized during manufacture and the table in the lens populated accordingly.

It is in fact errors in this table (perhaps as a resultant of shifts in lens behavior) that is a major cause of a particular lens giving incorrect autofocus results on a "properly-calibrated" body.

In fact, when one has a Canon lens "recalibrated" at a service center, this primarily consists of updating this table. And Canon bodies that have "AF microadjust" essentially keep, for each lens it knows, a table of adjustments to the table in the lens.

Fun stuff.

Best regards,

Doug
 
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