Antenna arrays can be either reciprocity calibrated (R-calibrated), which facilitates reciprocity-based beamforming, or fully calibrated (F-calibrated), which additionally facilitates transmission and reception in specific physical directions. We first expose, to provide context, the fundamental principles of over-the-air R- and F-calibration of distributed arrays. We then describe a new method for calibration of two arrays that are individually F-calibrated, such that the combined array becomes jointly F-calibrated.