Deformation of substrate by epitaxial piezoelectric film and implications for interferometry

•A theory is provided for piezoelectricity of a film on a flexible substrate with isotropic lattice mismatch.•Attribution of DBLI signal to thickness change of the thin film only is erroneous.•Contributions of the substrate and the film to piezoelectric response are comparable in magnitude.•Piezoelectric response is calculated for relevant ferroelectrics depending on substrate thickness.