Optimized Signal Estimation in Nanomechanical Photothermal Sensing via Thermal Response Modelling and Kalman Filtering
Abstract: 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 optimized for 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, reducing the effects of drift and random walk. Analytical calculations show the significant impact of the thermal expansion coefficients' ratio on the frequency response. The adaptive Kalman filter, 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 PSD analysis for system identification further refines our approach, promising fast and accurate nanomechanical photothermal sensing.
- A. Blaikie, D. Miller, and B. J. Alemán, A fast and sensitive room-temperature graphene nanomechanical bolometer, Nature Communications 10, 10.1038/s41467-019-12562-2 (2019).
- L. Vicarelli, A. Tredicucci, and A. Pitanti, Micromechanical bolometers for subterahertz detection at room temperature, ACS Photonics 9, 360 (2022).
- C. Li, Y. Zhang, and K. Hirakawa, Terahertz detectors using microelectromechanical system resonators, Sensors 23, 10.3390/s23135938 (2023).
- K. Kanellopulos, R. G. West, and S. Schmid, Nanomechanical photothermal near infrared spectromicroscopy of individual nanorods, ACS photonics 10, 3730 (2023).
- A. Demir, Understanding fundamental trade-offs in nanomechanical resonant sensors, Journal of Applied Physics 129, 044503 (2021a).
- S. Schmid, L. G. Villanueva, and M. L. Roukes, Fundamentals of Nanomechanical Resonators, 2nd ed. (Springer Cham, 2023).
- R. Burns, Advanced control engineering (Elsevier, 2001).
- R. E. Kalman, A new approach to linear filtering and prediction problems, Journal of basic Engineering 82, 35 (1960).
- R. G. Brown, Introduction to random signal analysis and Kalman filtering (Wiley New York, 1983).
- A. Gelb, Applied optimal estimation (MIT press, 1974).
- B. D. Anderson and J. B. Moore, Optimal filtering (Prentice-Hall Englewood Cliffs, NJ, 1979).
- E. Rubiola, Phase noise and frequency stability in oscillators (Cambridge University Press, 2008).
- A. Demir, Adaptive time-resolved mass spectrometry with nanomechanical resonant sensors, IEEE Sensors Journal 21, 27582 (2021b).
- M. Verhaegen and V. Verdult, Filtering and system identification: a least squares approach (Cambridge university press, 2007).
- J. Wolberg, Data analysis using the method of least squares: extracting the most information from experiments (Springer Science & Business Media, 2006).
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