Rayleigh backscattering is an important physical process in optical fibers, and the Optical Time Domain Reflectometer (OTDR) based on the rayleigh backscattering, is one of the most important and widely-used optical fiber measuring equipments. Rayleigh backscattering progress with arbitrary input optical pulses in the fiber was analyzed theoretically, the impulse response function was derived on the basis of regarding fiber as a linear system, and backscattered output pulse of square pulse and pulse with vibrating was discussed. For the square pulse, the theory of impulse response was demonstrated by commercial OTDR instrument. For the pulse with vibrating, the experimental results show a good agreement with the simulation.