Extended Kalman filter and extended sliding innovation filter in terahertz spectral acquisition

Terahertz spectral acquisition has a fundamental limitation in implementation due to long experimental acquisition time. The long experimental acquisition time in terahertz spectral acquisition is a result of the required high integration time associated with usable dynamic range signals acquired through delay stage interferometry. This work evaluates the effectiveness of a non-linear version of the Kalman Filter, known as the extended Kalman filter (EKF), and the recently developed extended sliding innovation filter (ESIF), for increasing dynamic range in terahertz spectral acquisition. The comparison establishes that the EKF and ESIF can reduce integration time (time constant) of terahertz spectral acquisition, with EKF reducing the integration time by a factor of 23.7 for high noise signals and 1.66 for low noise signals to achieve similar dynamic ranges. The EKF developed in this work is comparable to a nominal application of wavelet denoising, conventionally used in terahertz spectral acquisitions. The implementation of this filter addresses a fundamental limitation of terahertz spectral acquisition by reducing acquisition time for usable dynamic range spectra. Incorporating this real-time post-processing technique in existing terahertz implementations to improve dynamic range will permit the application of terahertz spectral acquisition on a wide array of time sensitive systems, such as terahertz reflection imaging, and terahertz microfluidics. This is the first implementation, to our knowledge, of Kalman filtering methods on terahertz spectral acquisition.