Terahertz time-domain spectroscopy (THz-TDS) is a reliable technique used for studying the complex optical properties of materials. Its frequency range makes it suitable for detecting low-energy collective excitations such as phonons, magnons, and plasmons. THz-TDS in transmission geometry has gained much attention over the years. However, despite the need for exploring reflective samples, the advancement of THz-TDS in reflection geometry has faced several obstacles, mainly due to its strict requirement for sub-micron precision in the placement of the sample and reference. Here, we demonstrate a technique for measuring samples in reflection geometry using THz-TDS which involves systematically resolving the alignment issue by first isolating and correcting sources of error in the experimental setup. We then use a novel and robust phase correction method to detect and rectify the remaining misplacement with nanometer precision. This provides us with precise values for the phase of the THz pulse, which in turn allows us to accurately compute the complex optical properties of different types of materials. We use well-known bulk semiconducting samples such as Si and InSb to validate the reliability of our technique. The experimental results of incident angle and polarization-dependent measurements are shown along with the retrieved complex refractive index of these samples. This method immensely simplifies the procedure for obtaining the optical properties of samples in the THz range.

We extend this technique to temperature-dependent measurements and, through a series of additional steps, present a method for studying SrTiO₃, a material with strong temperature-dependent spectral features in the THz range. By combining the phase correction method with a novel self-referencing approach, we successfully extract the optical properties of SrTiO₃ without the requirement of a reference measurement. These techniques collectively provide a robust and accessible approach for spectroscopic studies of materials in the THz range and can be applied without the requirement of expensive, high-precision equipment. We anticipate that these techniques will be used to study a wide variety of materials with collective excitations in the THz range.