Analytical description of the high and low contrast behavior of a scan-rotate geometry for equalization mammography

Many solutions have been proposed to overcome the problem of imaging the radiographically dense breast with high contrast mammographic film of limited dynamic range. In previous works, we have proposed utilizing a modulated fan-beam in a scan-rotate geometry RSER (Rotary Scanning Equalization Radiography), as an efficient method for producing exposure equalized mammograms. The image quality of RSER is similar to that attained with the inefficient single beam, raster scanning SER (Scanning Equalization Radiography) geometry. RSER has the potential to be a practical, efficient method for improving the detection of cancer in the dense breast. In this work, we present a theoretical analysis of the imaging properties of the RSER geometry in two regimes defined by the variation of x-ray transmission within the object. For low contrast objects, the imaging geometry was analyzed as a linear system, whereas the high contrast regime was studied by determining the contrast limit at which RSER requires nonphysical (negative) exposure modulation for a breast-like object. The low contrast transfer function of the RSER system is shown to be very similar to that of the SER geometry. We show that RSER enables the use of wide scanning beam of approximately 4 cm and thereby significantly reduces x-ray tube heat loading. Analysis of the high contrast behavior shows that a wide range of object contrasts and sizes can be equalized. For example, RSER can equalize a region of 100% glandular tissue within a 4.0 cm thick compressed breast composed of 100% adipose tissue. Thus, the RSER geometry produces images very similar to the more inefficient SER geometry, and is able to produce entrance exposure distributions appropriate for equalization of the range of contrast typically encountered in mammography.