An optical spectrum analyzer is implemented with a detector combined with a tunable filter mounted on a stage capable of 360-degree rotation at a constant velocity. Because of the constant rate of angular change, different portions of the input spectrum are detected at each increment of time as a function of filter position, which can be easily measured with an encoder for synchronization purposes. The unidirectional motion of the mirror permits operation at very high speeds with great mechanical reliability. The same improvements may be obtained using a diffraction grating or a prism, in which case the detector or an intervening mirror may be rotated instead of the grating or prism.