A method for the inspection of contained flowable materials which by their nature will be expected to have a single generally homogeneous composition within containers comprising the steps of: performing a radiation scan of a target item container of contained flowable material in a radiation scanning system to derive a spatially distributed and spectroscopically resolved measured dataset of the intensity of radiation emergent from the target item; considering the spatially distributed and spectroscopically resolved dataset of transmitted radiation intensity to be nominally determined in accordance with a relationship: O ⋅ δ = λ where λ is a system response vector in space and energy comprising the spatially distributed and spectroscopically resolved radiation intensity response produced by a target item, and O is a space and material derived operator, which projects vector δ on to the scanning system response vector λ ; characterised by the steps performed prior to scanning of: determining a pre-determined set of elements for a column vector δ comprising a notional theoretical set of elements related to parameters inherent in a target item that characterise the scanning response of the target item, constructing a representative operator O (space, material) for the configured scanning system for the pre-determined set of elements defined for vector δ ; and wherein the method comprises numerically processing the measured dataset in order to derive a best fit solution of: δ = O − 1 ⋅ λ and using that derived solution to determine the threat status of the target item. performing a radiation scan of a target item container of contained flowable material in a radiation scanning system to derive a spatially distributed and spectroscopically resolved measured dataset of the intensity of radiation emergent from the target item; considering the spatially distributed and spectroscopically resolved dataset of transmitted radiation intensity to be nominally determined in accordance with a relationship: O ⋅ δ = λ where λ is a system response vector in space and energy comprising the spatially distributed and spectroscopically resolved radiation intensity response produced by a target item, and O is a space and material derived operator, which projects vector δ on to the scanning system response vector λ ; characterised by the steps performed prior to scanning of: determining a pre-determined set of elements for a column vector δ comprising a notional theoretical set of elements related to parameters inherent in a target item that characterise the scanning response of the target item, constructing a representative operator O (space, material) for the configured scanning system for the pre-determined set of elements defined for vector δ ; and wherein the method comprises numerically processing the measured dataset in order to derive a best fit solution of: δ = O − 1 ⋅ λ and using that derived solution to determine the threat status of the target item. determining a pre-determined set of elements for a column vector δ comprising a notional theoretical set of elements related to parameters inherent in a target item that characterise the scanning response of the target item, constructing a representative operator O (space, material) for the configured scanning system for the pre-determined set of elements defined for vector δ ; and wherein the method comprises numerically processing the measured dataset in order to derive a best fit solution of: δ = O − 1 ⋅ λ and using that derived solution to determine the threat status of the target item. <EOS>