An optical fiber distributed acoustic sensor system makes use of a specially designed optical fiber to improve overall sensitivity of the system by a factor in excess of 10. This is achieved by inserting into the fiber weak broadband reflectors periodically along the fiber. The reflectors reflect a small proportion of the light from the DAS incident thereon back along the fiber, typically in the region of 0.001% to 0.1%. To allow for temperate compensation to ensure that the same reflectivity is obtained if the temperature changes, the reflection bandwidth is relatively broadband. The reflectors are formed from a series of fiber Bragg gratings, each with a different center reflecting frequency, the reflecting frequencies and bandwidths of the gratings being selected to provide the broadband reflection. The reflectors are spaced at the desired spatial resolution of the optical fiber DAS.