Non-linear propagation of limited diffraction beams

Recently, harmonic imaging has been shown to increase image quality in medical imaging. This is believed to be caused by decreased sidelobes. It is also due to a decreased sensitivity to near-field aberrations owing to the lower transmission frequency, and the lower relative amplitude of the second harmonic in the near-field. One of the problems of limited diffraction beams has been the sidelobe level. We performed a simulation of non-linear propagation for Bessel beams and X waves to see what performance gains that could be achieved. We used the angular spectrum method of Christopher and Parker which includes a non-linear substep to predict higher harmonic generation. Simulations of continuous wave Bessel beam excitation on a 15 mm transducer at 2.275 MHz showed about 9 dB decrease in sidelobe level for the second harmonic. The beamwidth was approximately the same as for the first harmonic. Near the end of the depth of field, the sidelobes increased and gave a poorer beamprofile. For pulsed X wave excitation on the same transducer, high sidelobes were present throughout the depth of field. A large 50 mm Bessel transducer at 1.65 MHz gave a second harmonic with half the beamwidth and the same sidelobe level as the first harmonic. By deleting the central lobe of the J0 Bessel beam for the 15 mm transducer, improved second harmonic properties were achieved. The second harmonic beam was characterized by low amplitude in the near-field, a narrow beam and reduced sidelobe level even for large depths. However, the modified Bessel beam loses some of its limited diffraction properties. Comparable results were achieved for the modified X wave, where the second harmonic also showed less energy in the X branches. The modified Bessel beam was compared to a spherically focused beam and showed about the same second harmonic beamwidth at the focal point, and 6 dB sidelobe reduction compared to the first harmonic of a conventional Bessel beam. Outside the focal area, the width of the spherically focused beam increased, while the modified Bessel beam remained narrow for a large depth of field.