A sensor for measuring forces and/or moments on an object, including at least one sensor element for the detection of an expansion of the object in at least one spatial direction, from which expansion a force or a moment can be determined, wherein the sensor element including an optical fiber with a sensor region with a fiber Bragg grating is provided, and the fiber Bragg grating is adapted to be irradiated with light, preferably a broadband light, generating a reflected light having a peak wavelength. The optical fiber is formed by a fiber core and at least one sheath of light-guiding material surrounding the fiber core. The fiber Bragg grating is arranged in the fiber core. The material of the sheath is doped with a fluorescent material and the fluorescent material may be irradiated with an excitation radiation to generate a fluorescent radiation having at least one main emission wavelength.