12 April 2000 Development of ultrasound transducer diffractive field theory for nonlinear propagation-based imaging
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In nonlinear ultrasound imaging the images are formed using the second harmonic energy generated due to the nonlinear nature of finite amplitude propagation. This propagation can be modeled using the KZK wave equation. This paper presents further development of nonlinear diffractive field theory based on the KZK equation and its solution by means of the slowly changing profile method for moderate nonlinearity. The analytical expression for amplitudes and phases of sum frequency wave are obtained in addition to the second harmonic wave. Also, the analytical expression for the relative curvature of the wave fronts of fundamental and second harmonic signals are derived. The media with different nonlinear properties and absorption coefficients were investigated to characterize the diffractive field of the transducer at medical frequencies. All expressions demonstrate good agreement with experimental results. The expressions are novel and provide an easy way for prediction of amplitude and phase structure of nonlinearly distorted field of a transducer. The sum frequency signal technique could be implemented as well as second harmonic technique to improve the quality of biomedical images. The results obtained are of importance for medical diagnostic ultrasound equipment design.
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Nikolay A. Kharin, Nikolay A. Kharin, } "Development of ultrasound transducer diffractive field theory for nonlinear propagation-based imaging", Proc. SPIE 3982, Medical Imaging 2000: Ultrasonic Imaging and Signal Processing, (12 April 2000); doi: 10.1117/12.382249; https://doi.org/10.1117/12.382249

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