We correct errors arising from two incorrect equations in our original manuscript.
© Optical Society of America
In sections 5.2 and 5.4 of our original manuscript , there are missing factors of 2 in the equations for coherent combining efficiency of one-dimensional Gaussian beams with mismatched spot size W or divergence Θ. These equations should read, respectively: η = ηBC[1 – σW 2/(2W 2)], and η = ηBC[1 – σΘ 2/(2Θ 2)]. Hence, Fig. 4 of the original manuscript should be replaced by Fig. 1 . For further clarification, we also remind the reader that these perturbative Gaussian beam results are calculated for one-dimensional variations. If, as is typical for example, the beam size varies symmetrically in both transverse x and y axes, then the losses would add in the perturbative limit, increasing by a factor of two and leading to overall efficiency of η = ηBC(1 – σW 2/W 2). The same consideration also applies to displacement, pointing, and divergence mismatches, so that symmetric mismatches in both x and y axes would lead to twice the losses incurred by mismatch along only one axis.
The remainder of the original manuscript is unaffected by these errors. We thank our colleague Stuart McNaught for bringing these errors to our attention.