MOLYBDENUM, RHODIUM, AND TUNGSTEN ANODE SPECTRAL MODELS USING INTERPOLATING POLYNOMIALS WITH APPLICATION TO MAMMOGRAPHY

Computer simulation is a convenient and frequently used tool in the st udy of x-ray mammography, for the design of novel detector systems, th e evaluation of dose deposition, x-ray technique optimization, and oth er applications. An important component in the simulation process is t he accurate computer-generation of x-ray spectra. A computer model for the generation of x-ray spectra in the mammographic energy range from 18 kV to 40 kV has been developed. The proposed model requires no ass umptions concerning the physics of x-ray production in an x-ray tube, but rather makes use of x-ray spectra recently measured experimentally in the laboratories of the Center for Devices and Radiological Health . Using x-ray spectra measured for molybdenum, rhodium, and tungsten a node x-ray tubes at 13 different kV's (18, 20, 22,...,42 kV), a spectr al model using interpolating polynomials was developed. At each energy in the spectrum, the x-ray photon fluence was fit using 2, 3, or 4 te rm (depending on the energy) polynomials as a function of the applied tube voltage (kV). Using the polynomial fit coefficients determined at each 0.5 keV interval in the x-ray spectrum, accurate x-ray spectra c an be generated for any arbitrary kV between 18 and 40 kV. Each anode material (Mo, Rh, W) uses a different set of polynomial coefficients. The molybdenum anode spectral model using interpolating polynomials is given the acronym MASMIP, and the rhodium and tungsten spectral model s are called RASMIP and TASMIP, respectively. It is shown that the mea n differences in photon fluence calculated over the energy channels an d over the kV range from 20 to 40 kV were -0.073% (sigma= 1.58%) for M ASMIP, -0.145% (sigma= 1.263%) for RASMIP, and 0.611% (sigma= 2.07%) f or TASMIP. The polynomial coefficients for all three models are given in an Appendix. A short C subroutine which uses the polynomial coeffic ients and generates x-ray spectra based on the proposed model is avail able on the World Wide Web at http://www.aip.org/epaps/epaps.html. (C) 1997 American Association of Physicists in Medicine.