A new reflection approach for field distribution measurement of ultrasonic transducers was investigated. Instead of a point-like reflection target (rigid sphere) or thin wires (line-like targets), a line response func...A new reflection approach for field distribution measurement of ultrasonic transducers was investigated. Instead of a point-like reflection target (rigid sphere) or thin wires (line-like targets), a line response function of experimental knife-edge distribution combined with the inverse Abel transforms was used to estimate the lateral beam distributions of ultrasonic transducers. The measurement steps were as follows:① A knife-edge was scanned perpendicularly to acoustic beam axis of the transducer using an ultrasonic C-scan system to obtain its ultrasonic image line response function, ② the transverse beam distribution was solved by the inverse Abel transforms, and ③ experiments were performed to obtain the lateral beam profiles of two transducers, with and without focus, and the results were compared with those from a hydrophone. The results showed that this method was effective for ultrasonic field measurement and could be as a substitute for hydrophone in most cases.展开更多
By using the first shift operator of the bc2-root system,the elementary spherical functions on the exceptional bounded symmetric domain E6/spin(10)×T are obtained,and the inverse Abel transform for this space is ...By using the first shift operator of the bc2-root system,the elementary spherical functions on the exceptional bounded symmetric domain E6/spin(10)×T are obtained,and the inverse Abel transform for this space is derived.Finally an expression of the heat kernel of this domain is given.展开更多
文摘A new reflection approach for field distribution measurement of ultrasonic transducers was investigated. Instead of a point-like reflection target (rigid sphere) or thin wires (line-like targets), a line response function of experimental knife-edge distribution combined with the inverse Abel transforms was used to estimate the lateral beam distributions of ultrasonic transducers. The measurement steps were as follows:① A knife-edge was scanned perpendicularly to acoustic beam axis of the transducer using an ultrasonic C-scan system to obtain its ultrasonic image line response function, ② the transverse beam distribution was solved by the inverse Abel transforms, and ③ experiments were performed to obtain the lateral beam profiles of two transducers, with and without focus, and the results were compared with those from a hydrophone. The results showed that this method was effective for ultrasonic field measurement and could be as a substitute for hydrophone in most cases.
基金Project partially supported by the National Natural Science Foundation of China.
文摘By using the first shift operator of the bc2-root system,the elementary spherical functions on the exceptional bounded symmetric domain E6/spin(10)×T are obtained,and the inverse Abel transform for this space is derived.Finally an expression of the heat kernel of this domain is given.
