X-ray intensity and spectrum : theoretical deduction and experimental measurements

• Main Author: Tan, Dagang
• Published: University of Aberdeen 1993
• Subjects: 610.28; X-rays for medical diagnosis
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.335048

Formulas for predicting the absolute X-ray intensity spectra from both Bremsstrahlung and K characteristic X-rays have been developed. These formulas cover a wide range of target materials and target geometry conditions (incident and emission angle) and tube voltage range from 20 to 200kV. For the Bremsstrahlung Intensity Spectrum:vskip 3.5cm Where U tube voltage(kV); J tube current(mA); n&61 1.6; <i>P</i> &61 1.08x10^-6(<i>A/Z</i>^2.5;<i>k_{s}</i> &61 0.32; <i>k</i> &61 <i>K_{m}Z</i>²/<i>A; K</i> = <i>k</i>3/511. The theoretical value of <i>K_{m}</i> is 4.73x10¹⁴<i>keV/mAs.sr.keV</i>. For a Fluency with a Total Filtration of <i>d_{Al} g/cm</i>² Al: <i>F(E)dE = I(E)E^{-1}e^{-μAldAl}dEphotons/keV.mAs.sr</i>. This formula can be used at various incident angles (θi) andemission anglesfor different target material (A, Z, μ) for <i>U</i> from 20-200kV. The angular distribution <i>f</i>(θ) (defined = 1 when θ = 90^o and varies with <i>U</i>) requires definition by experimental measurements. According to this formula the Photon Fluency spectra at different tube voltages, different target angles and different emission directions are calculated and illustrated as spectral curves. There is a good agreement between the formula results and spectra measured by other authors. For K-Characteristic X-ray fluency:vskip 1.5cm Where n&61 1.61; <i>P</i> &61 1.08x10^-6(<i>A/Z</i>)^2.5; k is a factor of 1.0-2.5, which represents the effective depth of K photo production and increases with Z; θ<i>_{i}</i> and θ<i>_{r}</i> the electron incident and X-ray emission angles; Ψ(θ<i>_{i}</i>) &61 <i>cos</i>(7.89x10^-4θ2.6_i) an empirical angle function; <i>N(E_{i}</i>) the fluency of <i>E_{i}</i> characteristic X rays per mAs per solid angle; <i>E_{k}</i> the binding energy of the K sell; <i>F</i>_k the efficiency constant depends on Z; <i>f(E_{i}</i> the fractional emission of the <i>E_{i}</i> characteristic X rays; <i>J</i> the tube current; <i>U</i> the tube voltage. The recommended value of <i>F</i>_Kα, based on measured data, is 3.8-4.7x10^11<i>photon/mAs.sr</i> for values of Z from 25 to 50. The relationship between the target attentuation factor and different target materials, angles and voltages are discussed. This formula can be used at much wider situations and has good agreement with the measured data.