A method of realizing a compact Fourier transform spectrometer is proposed in this work, which is based on the polarization interference in a single layer of birefringent liquid crystal (BLC). The continuous interference between the ordinary light and the extraordinary light is driven by a continuously adjusted electric field. Benefiting from the single-layer configuration with no moving parts, the spectrometer is easily miniaturized. The method to realize the spectrometer is theoretically analyzed and experimentally demonstrated by a layer of nematic BLC with a 100-mu m thickness. (c) The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.