An accurate linear optical displacement transducer of about 0.2 mm resolution over a range of ∼40 mm
is presented. This device consists of a stack of thin cellulose acetate strips, each strip
longitudinally slid ∼0.5 mm over the precedent one so that one end of the stack becomes a stepped
wedge of constant step. A narrowed light beam from a white LED orthogonally incident crosses the
wedge at a known point, the transmitted intensity being detected with a phototransistor whose
emitter is connected to a diode. We present the interesting analytical proof that the voltage across
the diode is linearly dependent upon the ordinate of the point where the light beam falls on the
wedge, as well as the experimental validation of such a theoretical proof. Applications to nonlinear
oscillations are then presented—including the interesting case of a body moving under dry friction,
and the more advanced case of an oscillator in a quartic energy potential—whose time-varying
positions wer…