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I have a doubt about the effect of putting a filter (polarizer, UV etc) on the autofocus system.

In theory, a lens which is put in front of the lens will affect the focus (we must set a different focus setting in order to keep in focus the same subject, with respect to the situation without the filter).

My question is: does the autofocus system looks at the subject through the lenses, and so is able to keep the subject in focus even with the filter?

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    There are many types of camera, with many autofocus systems. Which do you have in mind? Focus (including AF) through the imaging lens is kind of the point of SLRs for example, with which filters may commonly be used. On the other hand there have been active systems that rely on measuring distance – Chris H Jan 9 at 14:00
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    pretty sure that some DLSR cameras had a secondary sensor that handled AF, while mirrorless cameras are focusing directly off the main image sensor. In both of these cases the light is coming through the lens. – user5359531 Jan 9 at 14:09
  • Could you elaborate on your statement that a lens(filter?) in front of the lens will affect focus. This would only hold true, if the filter would bend light in any way, which most filters don't. They are just thing glass with coating. An exception would be the Close Up filter. – John Sørensen Jan 9 at 14:32
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This is more of a question of whether the AF system is fully closed loop (eg CDAF systems on mirrorless cameras - will focus until something it finds something being darn well in focus), or an open loop system (AF system measures distance, even if doing that through the lens, then sets the lens up in a way that it ASSUMES is correct for the measured distance), or a mix of both (that uses open loop for coarse focus, and closed loop for fine ... if you confuse such a system during coarse focus, it might misbehave).

See also How can lens cause consistent front or back focus?

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Yes, the AF "looks through the lens". For macro you can add a "close-up" filters (that are just converging lenses) to your lense and your lens and camera AF still work(*). Of course in that case the distance indication on the lens AF ring is wrong...

Another indication is that plain polarizing filters make the AF misbehave. The polarization light that the filters forwards down the lens is dimmed by further reflections that also have a polarizing effect. So you have to use a Circular Polarizing filter (aka CPL) that de-polarizes the light after filtering it.

(*) to some extent, because the sharpness area is fairly small with a strong close-up lens, and some AF systems can be confused by this.

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Most of the polarizers that you can buy today are circular polarizers. A circular polarizer responds to incoming, linearly polarized light (e.g., light from the sky, light reflected from shiny surfaces) in the same way that a simple, linear polarizer responds, but the light coming out the back of it does not have linear polarization.

I don't know the technical details, but some auto-focus systems that do not work well with a linear polarizer have no trouble with a circular polarizer.

https://www.amazon.com/s?k=circular+polarizer&ref=nb_sb_noss_1

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