  We describe the injection locking of two infrared (794 nm) laser diodes which
are each part of a frequency-doubled laser system. An acousto-optic modulator
(AOM) in the injection path gives an offset of 1.6 GHz between the lasers for
driving Raman transitions between states in the hyperfine split (by 3.2 GHz)
ground level of $^{43}$Ca$^+$. The offset can be disabled for use in
$^{40}$Ca$^+$. We measure the relative linewidth of the frequency-doubled beams
to be 42 mHz in an optical heterodyne measurement. The use of both injection
locking and frequency doubling combines spectral purity with high optical
power. Our scheme is applicable for providing Raman beams across other ion
species and neutral atoms where coherent optical manipulation is required.
