Robust Fourier-based slanted-edge method to measure scatter ratio

Background: Patient scatter incident on an x-ray detector reduces radiographic contrast and adds quantum noise, and minimizing scatter is critical in some specialized techniques such as dual-energy and energy-subtraction methods. Existing methods to measure scatter are either labor-intensive (multiple disks) or not appropriate to use in radiography where scatter often exceeds the width of the x-ray beam. Purpose: Develop a method to measure the scatter-to-primary ratio (SPR) that can be used for a wide range of radiographic and mammographic conditions, both with scatter equilibrium (scatter function does not exceed primary-beam width) and without. Methods: Fourier theory is used to show the SPR can be measured from the low-frequency drop (LFD) of the Fourier transform of the derivative of a normalized edge profile. The method was validated both experimentally and by simulation for radiography and mammography under scatter equilibrium and nonequilibrium conditions. Results: The theoretical derivation showed that by normalizing an edge profile with a profile without the edge, scatter equilibrium is not required and the method accommodates a nonuniform primary beam from beam divergence and Heel effect. The method was validated by a simulation study for a range of scatter-LSF widths, primary-beam widths, and image regions of interest used in the analysis. Experimental scatter measurements agreed with a similar edge-method published by Cooper when scatter equilibrium is achieved. Conclusions: A simple and direct method of measuring the SPR obtained with both uniform and nonuniform test phantoms is described. Validated both experimentally and theoretically, it uses the Fourier LFD obtained from a normalized slanted-edge profile and works for a wide range of practical mammographic and radiographic conditions.