A signal processing apparatus includes a differential processing unit to differentiate a reflection signal corresponding to a pulse measurement beam that is periodically scanned in a polarized manner; an arithmetic unit to obtain, with a rising time of a first-order-differential reflection signal as a reference, a barycentric position of the first order differential reflection signal as a detection time of a reflected beam, and to calculate a distance to a measured object based on a time difference between an output time of the measurement beam and the detection time of the reflected beam; and a waveform determining unit to determine whether the reflected beam includes a plurality of overlapping reflected beams from a plurality of measured objects, based on rising and falling characteristics of the first-order-differential reflection signal and based on a rising characteristic of a second-order-differential reflection signal obtained by the second order differential of the reflection signal.