Transverse cusp diffraction catastrophes produced by the reflection of ultrasonic tone bursts from a curved surface in water: Observations

An experiment was performed to image the acoustical diffraction pattern decorating the transverse cusp caustic. In the vicinity of the cusp point, the wave field is described by the Pearcey function P(w2,w1). The wave field was formed by reflecting sound from a curved surface with the generic local shape h(x,y)=h1x2+h1xy2+h3y2. Images of the reflected wave field were formed by relating the pressure amplitude of points in the observation plane to the gray levels of pixels on a computer screen building a gray-scale picture of the wave field in the observation plane. When the source was replaced by a light source, the optical intensity was recorded for the same geometry. The optical experiment produced images of the caustic curve of the form d(u−uc)3=(v−vc)2 that were used to locate the cusp point in comparisons of imaged acoustical diffraction patterns to calculated patterns. In the region near the cusp point, the imaged and calculated patterns compare very well. There were no adjustable parameters used in the comparison; the calculated patterns were completely determined by the experimental setup. The general agreement between the imaged and calculated patterns supports the use of the paraxial approximation used to calculate the caustic and diffraction pattern.