Convolutional Neural Network for self mixing interferometry

Self mixing inteferometry is a well established measurement scheme in which interference between the beam reflected by a target and the reference beam takes place inside the laser resonator (here a semiconductor laser) which emits said beam. This scheme can be used in many contexts (see the review [1] and the roadmap [2] ) including displacement measurements. In this case, when the target gets closer or further away from the laser, constructive and destructive interference lead to minima and maxima of intensity inside the laser resonator which translate into a varying voltage across the laser. When the working parameters of the experiment are carefully chosen, the interferometric signal is sawtooth-shaped and the orientation of the peaks depends on the direction of the displacement. Thus, the displacement can in principle be easily retrieved from the voltage measurement. In practice however, this analysis is often much more complicated than expected due to variation of the target effective reflectivity (in the case of diffusive targets for instance), noisy signal, complicated signal shapes, very broad spectral distribution of the signal etc. In the end, processing this kind of data often requires many heuristics which must be manually tuned to the exact experiment at hand. Here we build and train a convolutional neural network which can efficiently and reliably process very complex experimental data, without any parameter tuning. Specifically, we train the network on a set of periodic displacements consisting of discrete frequencies and amplitudes of motion of a target, with measurements of the interferometric signal in a few different alignment conditions. After this training, we show ( Fig. 1 ) that the network is able to predict complex displacements (with continuous spectrum) in alignment configurations which are not part of the training set. We also quantify the reconstruction error as a function of the measurement noise and show that the network is remarkably robust (not shown).