Fundamentals of Optical Fiber Sensing Schemes Based on Coherent Optical Time Domain Reflectometry: Signal Under Dynamic Temperature Conditions

We present a theoretical, algorithmic, and experimental study of temperature sensing using $\varphi$-OTDR with coherent detection. A physics-based model is developed to relate the measured Rayleigh backscattered signal to temperature variations along the fiber, showing that the phase evolution encodes the cumulative temperature change between the interrogator and the sensing location, while the amplitude exhibits only local sensitivity. Based on this insight, we propose robust algorithms for temperature-event detection and temperature-profile reconstruction. Experimental results demonstrate reliable recovery of temperature-induced perturbations in standard single-mode fibers using coherently detected $\varphi$-OTDR.