Two physically separated laser diode arrays were simultaneously injection-locked to the same master laser. The modulus of their mutual coherence function was measured, and the resulting value 0.96 +/- 0.06 was close to the maximum allowed value of 1. The spatial phase of the two injection-locked outputs did not vary from each other by more than 0.05 wave (lambda/20), apart from a phase difference that grew linearly with position, due to the tilt between the two interfering beams. Requirements for the coherent combination of injection-locked laser diode arrays are discussed.