Semidata-Driven Calibration of Galvanometric Setups Using Gaussian Processes

Abstract

Traditionally, calibration of a galvanometric setup is based upon a mathematical model of an underlying physical reality. These models make a considerable number of assumptions and simplifications. Moreover, they tend to be non-generalizable and lead to non-convex optimization problems encompassing many parameters. Alternatively, several data-driven statistical approaches have been proposed, in which any model of the underlying reality is completely bypassed. The often black-box model is trained purely on the data itself. Although some precautions for overfitting need to be kept in mind, it has been shown that this radically different approach can outperform the traditional mathematical models. On the other hand, some assumptions about the underlying physical truth are both reasonable and simple to implement. We propose to keep the best of both worlds and construct a semi data-driven calibration model with a single built-in assumption: rays exiting the galvanometric setup are straight lines. The data-driven approaches do not exploit this obvious fact. In this work we focus on the intrinsic calibration, i.e. finding the relationship between the input parameters that control the galvanometers and the rays exiting the device. We investigate four different models to predict lines and evaluate them in cross-validation, predicting intersection points on a validation plane and aiming the laser at a specific point in 3D space. We show that our approach outperforms a purely data-driven approach.