Leonard J. Bond
U. W. Lee
Dept. of Mech. Eng., Univ. of Colorado, Boulder, CO 80309-0427
The transfer functions for focused and defocused, coherent and confocal imaging systems developed in optics are applied to the equivalent ultrasonic imaging systems. Assuming that both of the two systems are free of attenuation and aberrations except defocus, the ideal complex amplitude line-scan signals across a step edge, with various degrees of defocus, are generated. The scalar magnitude of ideal complex image profiles are differentiated to get the unique theoretical IRF's and Fourier transformed to obtain the corresponding TF's. The acoustic system has been operated with a 50-MHz lens-rod design focused transducer. The experimental single frequency and broadband image profiles of a step edge, with varying degree of defocus, are differentiated and Fourier transformed. The experimental IRF's and TF's are compared with the corresponding theoretical data. As the initial theoretical analysis is for the wave propagating in an ideal fluid, the effects of attenuation and aberrations are investigated to enable the experimental data to be compared with the theoretical data. The relation between broadband and single frequency acoustic images is described. A practical model for the detection limits for 2-D cracks using the response for a pair of step edges is proposed. The numerical calculations are compared with experimental data. Usually the strong contrast seen in the imaging of cracks is associated with the excitation of Rayleigh waves in surface. In this study, a similar sensitivity to detect cracks is achieved by the defocus effect of pure longitudinal waves, which can be clearly explained by theory.