The electrically induced thickness variations of homeotropically oriented free standing films of a smectic (C* and A*) ferroelectric liquid crystalline elastomer (FLCE) have been examined. For this purpose an interferometric setup has been built with a resolution of 3 pm at 133 Hz AC excitation frequency. The laser beam has been focussed by means of two “long distance” microscope objective lenses in order to study small homogeneous areas in the film. The changes in optical pathlength through the sample were measured at the first (ω), second (2ω) and fourth (4ω) harmonic of the AC-electric excitation voltage (ω=133 Hz). The measured thickness (optical pathlength) modulation at the 2nd harmonic is in the range of some % and thus stronger than expected from FTIR-measurements on the electroclinic effect in CaF2 cells filled with this sample. Nevertheless, the strength of this quadratic effect and also of the linear effect is greatly increased at the phase transition Sm-C*-Sm-A*, which indicates a correlation of the thickness variation with the electroclinic effect.