Ensemble modeling of nanoscale thermal drift in high-precision linear axes for photonic integrated circuit testing

The consistently growing demand for robust automated assembly, testing and packaging of photonic integrated circuits, is increasingly oriented towards high volume and continuously sets new challenges to overcome concerning throughput and cost-efficiency. Among the predominant positioning error sources in high-precision robots used in this market, thermally induced position drift is often a major cause of deviation from operational conditions required to meet this demand. Environmental temperature fluctuations and the excess heat generated by the machine itself, can induce position drifts upwards of 100 nanometer per minute that prevent axis systems from meeting positional precision and repeatability required for optimal functioning, eventually imposing the integration of expensive temperature control systems and hardware changes that minimize the impact of thermally induced errors. In this paper, a data driven approach for modeling the temperature induced position drift and its dependency on the underlying temperature gradients is proposed. We suggest a formulation that allows to identify temperature gradients calculated over time windows of variable, optimal widths, that capture longer and shorter term drift components, introducing the concept of dynamic-range thermal features . By extracting several features from a single sensor, it is possible to reduce the amount of sensors required for an accurate reconstruction, resulting in significant hardware simplification and robustness towards variable field conditions. Additionally, an auto-weighted voting regression algorithm is proposed to separate the modeling of transient states from static and quasi-static states; an auto-regressive model of the position gradients with exogenous temperature gradients and a linear regression model of temperature gradients, are trained independently and combined in a voting ensemble paradigm. Experimental results are presented to quantify the effects of a model-based position compensation schema. Under high ambient temperature fluctuations of ± 1 degree Celsius, position drift is reduced from 23 nanometer per minute to 8.7 nanometer per minute root mean squared error. The proposed approach is validated in the context of photonic die testing with a heated chuck hosting the chip. Correction actions reduce thermal effects from 53 nanometer per minute to 10 nanometer per minute root mean squared error under normal working conditions. Finally, effects on the optical coupling loss and the system settle time are evaluated. Optical losses over 5 min measurement time of components with mode field diameters under 3 micrometer, can be reduced below 0.05 decibel for chuck temperatures up to 50 degree Celsius and a two-sided optical alignment; for chuck temperatures above 50 degree Celsius, the settle time to reach sufficient stability for optical measurements is reduced from 82 min to 32 min.