In biomedical ultrasound imaging, many studies show the advantages of harmonics to obtain a better quality of image; this is particularly true in echography and diffraction tomography. Recent work confirms that lateral resolution can be improved by the use of the harmonics generated by a nonlinear distortion in the medium. In this study, the enhancement made by the use of the second harmonic in ultrasound reflection tomography is shown. A focused transducer containing both concentric 2.5 and 5 MHz elements composes the experimental device. They are, respectively, the transmitter/receiver of the fundamental field and the receiver of the second harmonic field. The tests are carried out with PVC tubes. The first object is a single tube whereas the second one is an asymmetrical structure made up of two tubes. The image reconstruction is made from the measurements of the fundamental and second harmonics of the reflected fields using the back-projection method. This technique of relying on higher harmonics seems to provide a better resolution of tomographic images.

Abstract-The non-linear propagation of ultrasound in medical imaging has recently been exploited to improve image resolution and remove near field artifacts generated by overlying tissue structures. The images are formed using the second harmonic energy generated by nonlinear propagation. Second harmonic beams have narrower beam width and lower side lobes than the fundamental. The second harmonic draws energy from the fundamental continuously along the propagation path. These characteristics contribute to improve the quality of medical ultrasound images.In this paper, our objective is to show that the choice source aperture has significant consequences on the quality of the field transmitted in term of directivity. We also studied the field generated by three apertures sources, in a nonlinear medium. Theoretical approach, based on the Khokhlov-ZabolotskayaKuznetsov (KZK) parabolic approximation is used in order to consider the diffraction effects related to the use of a focusing real source. The fundamental ultrasonic fields and the second harmonic are compared at three distances from the source. Width and side lobes were used when recording three distributions of the beam form. Keywords -Nonlinear, ultrasound, harmonic, KZK I. INTRODUCTIONIt has been shown since that several physical phenomena related to ultrasound propagation can not be explained by linear theory [1]. Among these phenomena one finds the nolinearity, the diffraction and the absorption. Indeed the local variations of velocity and density can not be neglected. Thus it is necessary to enhance these approximations and then obtain a non linear differential equations system. These variations result in a deformation of the temporal profile of the emitted ultrasonic wave. This distortion manifests itself in frequency domain as the harmonics generation with multiple components of fundamental frequencies which did not exist in the spectrum of the emitted signal. This phenomenon is more significant when the intensity or the frequency of the wave are high [2].Linearity has an effect on all the methods of measurement and characterization of the mediums and ultrasounds equipment. For this reason, it is primordial to consider that in the definition, design and the development of the equipment using the ultrasonic waves. A theoretical study is essential as a preliminary to demonstrate the distortion of the wave along the propagation in order to be able to simulate the experimental study. The general wave equation which is valid for no linearity, diffraction, and absorption in sound beams was derived by Kuznetsov [3] Zabolotskaya and Khokhlov [4]. This model was obtained starting from the physical basic laws by improving the approximations of the second order linear theory. It was validated by several researchers [5,6]. The objective of this work is the theoretical study of diffraction effects in the case of real sources [7,8]. We present, here particularly, the case of a focusing circular source. Three apertures: uniform, cosine and exponential were studied. ...

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