Detection limits for single small flaws and groups of flaws when using focussed ultrasonic transducers

The performance of ultrasonic imaging systems, using line-focussed transducers, was evaluated theoretically by employing a simple technique based on convolution. The analysis considered the response of single reflectors, which are mainly voids, and also multiple reflectors located both on a single plane and on multiple planes, which represent a porous layer or bond-line. The limits of detection for each of the above cases, in the presence of different levels of acoustic noise in the object under test were also calculated. The results presented are expressed as a function of a dimensionless flaw size, incorporating the ultrasonic frequency and beam F-number. The results can be used to identify the best match between ultrasonic equipment and a specific imaging problem. They can also serve to guide decisions regarding the most suitable detection method for use with the chosen equipment. If the inspection is properly designed, surprisingly small flaws could be reliably detected — even in objects where significant levels of incoherent acoustic noise are found. The method and results presented in this paper for line-focussed transducers fit qualitatively the case of spherically focussed transducers. The method is highly versatile and it can be extended to cover a range of problems, outside the scope of this paper, including, quantitatively, that of the spherically focussed transducer by employing a formulation which uses more computer time and memory.