Wave Motion 33 (2001) 309–320 Pupil function splitting method in calculating acoustic microscopic signals for elastic discontinuities M. Ohno, C. Miyasaka, B.R. Tittmann ∗ Department of Engineering Science and Mechanics, The Pennsylvania State University, 227 Hammond Building, University Park, PA 16802-1484, USA Received 28 July 1999; received in revised form 25 January 2000; accepted 19 May 2000 Abstract This paper deals with the output signals of scanning acoustic microscopes observing the elastic discontinuities on sample surface, and presents a new method of calculation. The formulation is based on the angular-spectrum method together with a ray-optical approximation. The key treatment is splitting of the pupil function into two parts. This method clarifies the image-forming factors in acoustic microscopy including large and fine fringes parallel to discontinuities. Calculation for an edge and a metal/ceramic joint showed good agreements with the experimental results. © 2001 Published by Elsevier Science B.V. 1. Introduction Scanning acoustic microscopy has been applied to various scientific investigations and technological examinations since its invention in the 1970s [1], and seems to have established its utility. The main field of its application is sub-surface imaging of optically opaque materials. Internal defects such as cracks, bubbles and delaminations can be visualized with high contrast. The second feature of acoustic microscopy is its validity for material characterization. It has been widely recog- nized that the contrast in acoustic microscopy is significantly affected by the surface acoustic waves that are excited on the sample surface. Thus the elastic properties of the samples have been quantitatively investigated with relation to their surface acoustic wave velocities. The third characteristic of acoustic microscopy is its nature of enhanced imaging of the surface structures. It has been frequently reported that the discontinuities on the sample surface, such as surface-breaking cracks or grain boundaries of polycrystalline materials, can be observed with high contrast, even if their lateral dimensions are much smaller than the acoustic wavelength. In addition, it has been recognized that the images of surface discontinuities are accompanied with fringes that are parallel to them, which enable one to detect them more easily. Yamanaka et al. [2] reported parallel fringes for deep cracks, and attributed them to the interference between the Rayleigh wave travelling towards the crack and its reflection. Ilett et al. [3] also reported the fringe patterns for surface discontinuities, and explained them as the interference of Rayleigh waves as well as bulk waves. Cox et al. [4] calculated the output signal (V(z)) for these surface discontinuities using a ray-optical approach and discussed the relation of V(z)s with the depth of cracks. The fully wave-optical analysis for the image-forming for discontinuities ∗ Corresponding author. Fax: +1-814-863-7967. 0165-2125/01/$ – see front matter © 2001 Published by Elsevier Science B.V. PII:S0165-2125(00)00049-4