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Geometric Unsharpness Calculations

When performing an X-ray inspection, the geometric unsharpness of the inspection setup needs to be taken into consideration, especially when using geometric magnafication. The size of the X-ray tube focal-spot and the magnification factors, namely the source-to-specimen and specimen-to-detector distances, are used to calculate the geometric unsharpness of the inspection setup.   The allowable amount of unsharpness is controlled by specification being followed. In general, the allowable amount is 1/100 of the material thickness up to a maximum of 1mm (0.040 inch).


Geometric unsharpness or the size of the penumbra (Ug) shown in the image above can be calculated using the following equation:

                Ug = f * b/a

                 Where:  f = X-ray generator focal-spot size.
                              a = distance from x-ray source to front surface of material/object
                              b = distance from the material/object to the detector

When magnafication is not needed, the test specimen is usually placed as close as possible to the detector and the source is placed some distance from the sample to minimize the penumbra. A greater distance between the source and the object will reduce geometric unsharpness. However, the intensity of the source decreases as the distance increases. Therefore, the source should be placed only as far away as necessary to control the penumbra. If the test object is placed in direct contact with the detector (like is often done in film radiograph) the following formula can be used that takes into account the material thickness instead of the object-to-detector distance. This formula is:

                  Ug = f * t/d

                  Where:  f = X-ray generator focal spot size
                                 t = the thickness of the material
                                d = distance from x-ray source to front surface of material/object

Example Calculation
Calculate the geometric unsharpness when using an X-ray generator with a 3mm spot size and the test component is 100 cm from the x-ray tube and 50 cm from the detector.

First convert all lengths to like units.  Then plug the known information into the equation and solving for Ug.

                  Ug = f * b/a

                  Ug = 0.3cm * 50cm/100cm

                  Ug = 0.15cm