Harnessing modal fields retrieved from speckle for multi-dimensional metrology

Although speckle is a powerful tool for high-precision metrology, large datasets and cumbersome training are always required to learn from the encoded speckle patterns, which is unfavorable for rapid deployment and multi-dimensional metrology. To enable high accuracy and fast training, physics-informed machine learning enforces physical laws to address high-dimensional problems. Here, we harness the modal fields in a few-mode fiber, which follow the law of beam propagation, to enable high-accuracy and fast-training parameter estimation. Anti-noise fast mode decomposition is implemented to retrieve the modal fields from the speckles. The accuracy is enhanced since the modal fields enable parameter estimation at random points in the continuous space-time domain. Artificial tactile perception and multi-dimensional metrology are achieved with high accuracy because the modal fields respond diversely to different parameters. Meanwhile, the number of specklegrams for training is reduced by around 5 times. The training time of machine learning is significantly reduced by 800 times, from 9 hours and 45 minutes to 40 seconds. Therefore, harnessing the modal fields paves a new way for the speckle-based metrology to develop efficient, low-cost, multi-dimensional sensors, making it suitable for intelligent wearable devices, industrial robots and healthcare applications.