Fig. 1. Experimental setup for implementing the DL-based phase control method for CBC. (SL: seed laser; PA: pre-amplifier; FS: fiber splitter; FPM: fiber phase modulator; FA: fiber amplifier; HRM: highly reflective mirror; FL: focus lens; BS: beam splitter.)

Fig. 2. Illustration of the CNN for estimating the phase error in CBC systems.

Fig. 3. Intensity profiles of the beam arrays consisting of (a) 7 elements and (b) 19 elements.

Fig. 4. Average MSE of the CNN as a function of the number of training epochs.

Fig. 5. Performances of the trained CNN for phase control. Far-field intensity profiles (a1)–(a5) without phase error compensation, and with phase error compensation using CNNs trained at (b1)–(b5) the focal plane and (c1)–(c5) the non-focal-plane.

Fig. 6. Far-field intensity profiles of the (a) incoherently combined beam, (b) DL-based coherently combined beam and (c) ideal coherently combined beam, for the case of the 7-element hexagonal array. (d) Far-field intensity profiles along the $x$ axis for the ideal coherently combined beam (red), DL-based coherently combined beam (green) and incoherently combined beam (blue). (e) Power in the bucket (PIB) at the focal plane as a function of the bucket radius for the ideal coherently combined beam (red), DL-based coherently combined beam (green) and incoherently combined beam (blue).

Fig. 7. Far-field intensity profiles of the (a) incoherently combined beam, (b) DL-based coherently combined beam and (c) ideal coherently combined beam, for the case of the 19-element hexagonal array. (d) Far-field intensity profiles along the $x$ axis for the ideal coherently combined beam (red), DL-based coherently combined beam (green) and incoherently combined beam (blue). (e) Power in the bucket (PIB) at the focal plane as a function of the bucket radius for the ideal coherently combined beam (red), DL-based coherently combined beam (green) and incoherently combined beam (blue).