Dependence of the Brillouin gain spectrum on linear strain distribution for optical time-domain reflectometer-type strain sensors

We theoretically derive the shape of the Brillouin gain spectrum, that is, the Briilouin backscattered-light power spectrum produced in an optical fiber under conditions of a strain distribution that changes linearly with a constant slope. The modeled measurement system is an optical time-domain reflectometer-type strain sensor system. The linear strain distribution is one of the fundamental distributions and is produced in, for example, a beam to which a concentrated load is applied. By analyzing a function that expresses the shape of the derived Brillouin gain spectrum, we show that the strain calculated from the frequency at which the spectrum has a peek value coincide. with that at the center of the effective pulsed light. In addition, the peak value and the full width at half maximum of the Brillouin gain spectrum are both influenced by the strain difference between the two ends of the effective pulse. We investigate this influence in detail and obtain the relationship between strain difference and strain measurement error.