Construction of limited diffraction beams with Bessel bases

Limited diffraction beams have a large depth of field. They could have applications in medical imaging, tissue characterization, Doppler velocity estimation, nondestructive evaluation (NDE) of materials, as well as other physics related areas such as electromagnetics and optics. In this paper, a method is developed that uses limited diffraction beams discovered previously, such as, Bessel beams and X waves, as basis functions to construct new limited diffraction beams that may have practical usefulness. The method is implemented with linear matrix operations. Results show that the method is powerful and can obtain limited diffraction beams that are not intuitive to get directly from solving the wave equation