Canon has posted a firmware update (Version 1.1.2) which, "Improves the stability of AF accuracy in AI servo AF when shooting extremely low-contrast subjects."

FROM CANON EUROPE:

Dear photographers,

Wednesday April 30, Canon releases world-wide a firmware update to improve the autofocus performance of EOS-1D Mark III and EOS-1Ds Mark III in some shooting conditions and to add new features in personal functions.
Those improvements have been implemented thanks to the feedback provided by professional photographers.

For more info and to download the firmware, click on the links here after:

http://web.canon.jp/imaging/eosd/eos1dsm3/firmware-e.html

You will need your camera serial number to initiate the download of the firmware. For detailed instructions on how to install the firmware update click here.

— Ken Geiger 

Comments