Piezoelectric flextensional actuators (PFAs) are an efficient alternative to systems that demand nano-positioning of devices, such as in nanotechnology. Optical techniques constitute an excellent choice for contactless measurement of nano-displacements. In particular, optical interferometry constitutes an adequate choice for characterizing PFAs. There are several types of interferometers, as well as optical phase demodulation methods, used in practice. One interesting class of demodulation methods uses the spectrum of the photo-detected signal and its intrinsic properties when there is a harmonically varying time-domain modulating signal. In this work, a low cost homodyne Michelson interferometer, associated with simple electronic circuits for signal conditioning and acquisition, is used. A novel dynamic phase demodulation method, named J(m)&J(m+2), is proposed, which uses only the magnitude spectrum of the photo-detected signal, without the need to know its phase spectrum. The method is passive, direct, self-consistent, without problems of phase ambiguity and immune to fading, and presents a dynamic range from 0.45 to 100 rad displacements (between 22.6 nm and 5 mu m, for lambda = 632.8 nm). When applied to the measurement of half-wave voltage in a proof-of-concept Pockels cell, it presents errors smaller than 0.9% when compared to theory. For the estimation of PFA displacement, it allows the measurement of linearity and frequency response curves, with excellent results.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)