A sensor for measuring the concentration of an assay substance, such as oxygen in tissue. The sensor comprises an optical fiber (2) which passes through, a gas isolation collar (11) into a cavity (15) defined by a needle tube (13) attached to the gas isolation collar. Both the optical fiber (2) and the needle tube (13) are bonded to the gas isolation collar (11) in gas-tight fashion. The cleaved end (8) of the optical fiber within the cavity is provided with an optically active substance (9) having optical properties, such as fluorescence, dependent on the concentration of the assay substance. The cavity (15) is filled with a polymer (16) which is permeable to the assay substance. Lateral flow passages (18) are provided for the assay substance to pass into the permeable polymer (16) and to the fluorophor (9). Light is supplied to the fluorophor via the optical fiber, and functions of its fluorescence are measured to calculate the concentration of the assay substance.