Deep-learning-based robust M² factor estimation for multimode fibers from uncalibrated beam patterns

The beam quality factor, or M² factor, characterizes the propagation and focusing performance of laser beams. Its rapid assessment is important for online monitoring and feedback control, yet conventional measurement methods require multi-plane scans or variable-focus configurations. Deep learning enables inference from a single beam pattern, but existing approaches typically rely on standardized imaging conditions. Here, we propose a multi-scale cross-layer feature fusion network with a convolutional block attention module (MSCF-CBAM) for robust single-frame M² factor estimation from uncalibrated multimode-fiber beam patterns. In simulations involving variations in beam scale and position, MSCF-CBAM achieves a mean absolute error of 0.0785, corresponding to reductions of 41.8% and 39.7% relative to VGG-16 and simple-CNN, respectively. Experimental validation further shows a mean relative prediction error of 2.27% for six randomly selected beam patterns subjected to random cropping, compared with 17.52% for VGG-16 and 9.19% for simple-CNN. This model can advance the practical application of deep-learning-based beam-quality estimation and provide an important means of feedback for various real-time control strategies in fiber lasers.