The invention is a method and apparatus for identifying and pinpointing the location of unwanted pieces of material or defects in, for example, de-boned poultry pieces. The poultry pieces to be inspected are carried on a conveyor and passed under an impinging collimated X-ray beam. The Rayleigh scattering resulting is detected and measured, as is the Compton back scattering and the data is processed in a processing unit to determine the location and type of foreign matter involved. The ratio of the Rayleigh and Compton scattering is also determined and used to verify the identity of the foreign material. Transmitted X-rays, i.e., radioscopy, are used to normalize the data, and to aid in a pinpointing of the location of the unwanted material.