Rapid Parameter Determination Of Discrete Damped Sinusoidal Oscillations

We present different computational approaches for the rapid extraction of the signal parameters of discretely sampled damped sinusoidal signals. We compare time- and frequency-domain-based computational approaches in terms of their accuracy and precision and computational time required in estimating the frequencies of such signals, and observe a general trade-off between precision and speed. Our motivation is precise and rapid analysis of damped sinusoidal signals as these become relevant in view of the recent experimental developments in cavity-enhanced polarimetry and ellipsometry, where the relevant time scales and frequencies are typically within the similar to 1 - 10 mu s and similar to 1 - 100 MHz ranges, respectively. In such experimental efforts, single-shot analysis with high accuracy and precision becomes important when developing experiments that study dynamical effects and/or when developing portable instrumentations. Our results suggest that online, running-fashion, microsecond-resolved analysis of polarimetric/ellipsometric measurements with fractional uncertainties at the 10(-6) levels, is possible, and using a proof-of-principle experimental demonstration we show that using a frequency-based analysis approach we can monitor and analyze signals at kHz rates and accurately detect signal changes at microsecond time-scales. Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License.