We describe the functional capabilities of the time-resolved photothermal common-pass interferometry method. For two thermo-optical effect-based methods, photothermal common-pass interferometry and time-resolved photothermal common-pass interferometry, the achieved detection limit for absorption measurements in ultrapure quartz glasses (5 × 10−7 cm−1 and 2 × 10−9 cm−1, respectively) is given. The problem of calculating the variation of the refractive index tensor under local heating trigonal-symmetric crystals of class 32 by a focused laser beam is considered. For these crystals, it is shown that the problem of the influence of deformations on the measured signal is reduced to determine a thermo-optical parameter (an analog of dn/dT). The calculation of this parameter does not require a complete solution to the strain problem when the crystals are heated locally by laser radiation. The formulas for calculating the thermo-optical parameter P and its numerical values are presented. They are required to calibrate absorption measurements in crystalline quartz using the time-resolved photothermal common-pass interferometry scheme. For a full understanding, formulas of the theory of equilibrium deformations used in this study are presented. An analysis of the relevance of improving the thermo-optical method sensitivity for concentration measurements of pollutant inclusions in crystals, ultrapure quartz glasses, and ambient air is presented.