Optimized Signal Estimation in Nanomechanical Photothermal Sensing via Thermal Response Modeling and Kalman Filtering

We present an advanced thermal response model for micro- and nanomechanical systems in photothermal sensing, designed to balance speed and precision. Our model considers the two time constants of the nanomechanical element and the supporting chip, triggered by photothermal heating, enabling precise photothermal input signal estimation through Kalman filtering. By integrating heat transfer and noise models, we apply an adaptive Kalman filter (AKF) optimized for field-programmable gate array (FPGA) systems in real time or offline. This method, used for photothermal infrared (IR) spectroscopy with nanomechanical resonators and a quantum cascade laser (QCL) in step-scan mode, enhances response speed beyond standard low-pass filters (LPFs), enabling faster data acquisition and reducing the effects of drift and random walk. Measurements show the significant impact of the thermal expansion coefficients’ ratio on the frequency response. The AKF, informed by the QCL’s input characteristics, accelerates the system’s response, allowing rapid and precise IR spectrum generation. The use of the Levenberg-Marquardt algorithm and power spectral density (PSD) analysis for system identification further refines our approach, promising fast and accurate nanomechanical photothermal sensing.