A new, highly precise, optical fiber outer diameter measuring technique based on near-field resonant backscattered light is described. Relative accuracies of +/-10(-2) microm were achieved in diameter measurements using Fabry-Perot resonances and +/-10(-3) microm in average diameter measurements using dielectric surface-wave resonances for ~100-microm fibers. The shape of a new type of low birefringence spun fiber, made by rapidly spinning a near circular preform in the pulling oven, was measured. We observed a small ellipticity which rotated helically along the fiber. The possibility of making absolute and real-time outer diameter measurements is discussed.