Cross-correlation technique for phase error correction in reflection mode terahertz time-domain spectroscopy

Terahertz time-domain spectroscopy in reflection mode geometry provides valuable surface and subsurface information, making it suitable for a layer analysis, coating, and non-destructive testing applications. The exchanging of the sample and reference’s position introduces a phase error when the position or alignment of the sample is not precisely maintained during measurements. This micrometer order of pitch error (1x) between the reference and the sample could lead to an inherent error in the phase spectrum of the sample. In the present work, a novel approach, to the best of our knowledge, based on the cross-correlation with an envelope technique, has been demonstrated to reduce the uncertainty in the phase and reveal the hidden characteristic features of the given sample in THz TDS spectroscopy. In conjunction with experimental verification, we have employed a finite element analysis in COMSOL Multiphysics to simulate a misplacement error between a lossy dielectric medium (n = 1.2 to 3.0 and k = 0 to 0.9) and a reference. We have investigated the impact of varying properties of the lossy dielectric medium on delay measurements using a cross-correlation with an envelope analysis. We illustrated and demonstrated the advantage of our approach by measuring the optical properties of Teflon, quartz, and RDX by correcting the misalignment of the 15.75, 17.55, and 20.70 µm ranges, respectively.