A mathematical model relating changes of grey values to changes of thicknesses of a stepwedge

The purpose of this report is to present a mathematical model relating changes in grey values to changes of thicknesses of a stepwedge. Radiographs of a stepwedge were obtained through a limited exposure range on a single Kodak 6100 charge-coupled device detector at 63 kVp and 70 kVp. Grey values from each step were evaluated relative to the corresponding step thickness. All possible regression fits were evaluated based on their coefficient of determination (R2) value and their mean squared errors (MSEs) relative to the original thickness. For all exposure settings, the fifth-degree polynomial was the best possible fit, with the highest R2 value and the lowest MSE.