Efficient phase shift migration for ultrasonic full-matrix imaging of multilayer composite structures

•Double-square-root wavenumber is introduced in wavefield extrapolation directly.•Imaging condition is directly applied in the frequency-wavenumber space.•The method outperforms existing methods in computational complexity and efficiency.•The method has great potential in online detection for large multilayer structures.•The proposed method is well adaptable to the continuous-layered media.