A method for measuring and mapping displacement fields and strain fields has been developed. It is based on the Fourier analysis of a HRTEM lattice image selecting a strong Bragg reflection and performing an inverse Fourier transform. The phase component of the resulting complex image gives information on local displacements of atomic planes. The two-dimensional (2D) displacement field can then be derived by applying the method to two non-collinear Fourier components. Local strain tensor components epsilon(xx)((r) over bar), epsilon(yy)((r) over bar), epsilon(xy)((r) over bar) and epsilon(yx)((r) over bar) can be obtained by analysing the derivative of the displacement field. Applied to HRTEM images of thin films, this technique gives quantitative information on the variations of the strain relaxations in the different layers. The method is illustrated studying a fully relaxed GaSb/GaAs interface.