Recent decades have seen continuous advances in ultra-fast lasers with outputs of up to 10 petawatts (PW) [1], [2], [3], benefiting from the development and progress of chirped-pulse amplification (CPA) and optical parametric chirped-pulse amplification (OPCPA) technologies [4], [5], [6]. The focal intensity has achieved 1023W/cm2 under the drive of its widespread application in extreme condition physical experiments such as electron acceleration, laser–matter interaction at ultrahigh intensities, and hard X-ray generation [7], [8], [9]. However, the output capacity of single-channel laser systems has reached a bottleneck owing to the material damage threshold and thermo-optical effects [10]. Coherent beam combination (CBC) is a key technique that can cross these barriers and further improve the outputs of ultra-intense and ultra-short laser systems to 100 PW, even at the exawatt level [10], [11], [12], [13], [14], [15]. By efficiently combining N low-power lasers through a tiled-aperture CBC scheme, the output focal intensity can reach N2 times of a single-channel. Several 100 PW facilities worldwide have put CBC in their project blueprint [11].

The phase error between each sub-beam is the most crucial parameter affecting the efficiency of the CBC system. Therefore, the control of phase jitter is one of the most important issues in CBC research [16]. General phase error measurement methods include the interference fringe method [17], optical autocorrelation [18] and Hansch–Couillaud detectors [19]. However, the methods above are less scalable, and for multi-beam coherent combination systems, the optical structures of these methods are very complicated. A new method with simple structure, high intelligence, and strong scalability is extremely attractive. Deep learning techniques have attracted wide attention in all fields owing to their outstanding recognition ability for images, sounds, and text [20], such as their practical recognizing ability of the complicated features of images. Recently, deep learning has been introduced in the optical measurement field because of its great potential for solving a variety of optical metrology tasks, such as fast correlated-photon imaging enhancement [21], reconstruction ultrashort pulses [22] and medical optical coherence tomography [23]. For the CBC system, the far-field interference pattern is the ultimate evaluation criterion and has been demonstrated to be practical the phase error measurement [13], [24]. Moreover, phase error information is contained in the far-field interference pattern. Thus, phase error information is theoretically possible to recognize using a deep learning technique.

In this study, we demonstrated the feasibility of the far-field interference pattern phase measuring method based on deep learning from both simulation and experiment. The representative deep convolutional neural network (DCNN) algorithm was used because of its capacity to capture critical information from images. To achieve λ/30 Root mean square (RMS) accuracy which is the minimum phase synchronization requirement for CBC at 95% combining efficiency, the result accuracy was improved in the simulation. In the experiments, we built a two-beam tiled-aperture coherent combination setup to investigate the measurement capability of the DCNN further. To the best of our knowledge, this is the first study to use deep learning in tiled-aperture CBC experiments.