Calibration method for spatially resolved tomographic spectroscopy based on a time-domain interferometer

Low-coherence time-domain based spatially resolved tomographic spectroscopy was developed to simultaneously achieve complex electric field and the tomography of the transparent multilayer samples. More importantly, we constructed a novel calibration method that overcomes the shortcomings of the cross-correlation output of traditional spatially resolved spectroscopy using the Wiener–Khinchin theorem. With the proposed method, we obtained a more accurate complex electric field spectrum for each sample interface, which is fundamental for precisely determining various physical parameters, including power reflectance, refractive index, and geometric length, as long as the turbidity of sample was sufficient for the light signal travel and return to the detector. The proposed theory was experimentally validated with both a single interface mirror (single layer) and double interfaces micrometer-thickness cover glass (three-layers) sample, which was measured by an infrared light source (1.4 μm–1.7 μm). We successfully resolved the precise refractive index of the second layer (1.45) obtained from the power reflectivities of the sample interfaces (3.36% and 3.55%) and obtained the sample depth of 52 μm. The tomography was detected by a high-speed photodetector and recorded by a digital multi-meter (50,000 samples per second). The validity of the spectral calibration was confirmed by comparing the measured spectra with theoretical spectra obtained via numerical simulations.