Abstract: The method comprises the following stages: first the attenuation function of at least three reference materials are determined across a wide x-ray spectrum and projection functions (F.sub.p1, F.sub.p2, F.sub.p3, F.sub.p4) forming a base are derived therefrom, then the attenuation function in said x-ray spectrum of at least one target material is determined and the attenuation function of each target material is projected onto said base; further, for each point of the object (1), the attenuation function of the object (1) is determined in said x-ray spectrum and projected onto said base, and the projections so obtained are compared with the projection from each target material and from this comparison an inference is made whether at least one target material enters the constitution of the object (1) at the point of inspection.Application: luggage inspection and control.

Abstract: The object's transmission function is expressed as a finite power expansion of a reference-material reference thickness, each expansion power being equal to a ratio of a reference-material thickness to the reference thickness; the expansion coefficients are determined from the measurements of the intensities transmitted by the selected various thicknesses, including zero thickness, of the reference material exposed to a test beam evincing consecutively several energy spectra and from the measurements of the intensity transmitted by the object exposed to this same variable-spectrum test beam; the attenuation function is derived from the determination of the transmission function.