Determination of error of calculation of effective energy of a combined X-ray beam

• Published in: Biomedical engineering 2006-05, Vol.40 (3), p.128-129
• Main Authors: Petrushanskii, M G, Kornev, E A, Pishchukhin, A M
• Format: Article
• Language: English
• Subjects: Biomedical research; Comparative studies; Error analysis; Radiation; X-rays
• ISSN: 0006-3398; 1573-8256
• DOI: 10.1007/s10527-006-0060-4

Comparison of different methods of evaluation of the effective energy of a combined X ray beam generated under different conditions enabled us to derive a formula for assessing the error of calculation of the effective energy of the combined X ray beam and its dependence on X ray tube anode voltage Ua and thickness of filter made of a certain material. The following expression for the effective energy Eef was obtained: Eef = hc(3), (1)where h is Plancks constant; is the speed of light in vacuum; is electron charge; Ua is anode voltage; df is thickness of filter made of material with mass photoelectric extinction coefficient m and density; d is thickness of an additional layer of the same material; and n are con stants incorporated in equations for the dependence of the mass photoelectric extinction coefficient m on radia tion energy E in each material [2]:m(E) = (hc)n/En. (2)Equation (2) was approximated from tabular values of mass photoelectric extinction coefficient mi, X ray energy quanta Ei for aluminum ( = 2.700 g/cm3), and reference value reported in [3]. The following values of the coeffi cients were obtained: = 14970 cm2/(gcm3), n = 3.053. The thickness of the additional layer of the attenuating material was chosen to be d = 103 cm, because pre liminary calculations revealed that such a layer caused insignificant changes of the effective energy Eef (less than 102 keV). Therefore, the radiation passed through the fi ter of such thickness is virtually uniform.