Program Information
A Method for the Rapid Calculation of the Nth Value Thickness of a Bremsstrahlung Spectrum
Bhaskaran K Pillai1*, (1) Amrita Institute of Medical Sciences & Res. Center, Kochi, Kerala, India
Presentations
SU-H1-GePD-I-1 (Sunday, July 30, 2017) 3:00 PM - 3:30 PM Room: Imaging ePoster Lounge
Purpose: In radiation attenuation problems, a frequently calculated quantity is the Nth value thickness of an x-ray spectrum in an absorbing material. N = 2, refers to the half-value-thickness; N = 10, the 1/10 value thickness, etc. The method routinely employed is to compute the intensity at a series of absorber thicknesses chosen in convenient intervals until it reaches a level below a fraction, 1/N of the initial intensity. The Nth value thickness is then determined either graphically from a plot of the transmitted intensity against absorber thickness or by direct interpolation. This method is tedious, especially when large attenuation values are involved. An alternative, rapid method employing an iterative procedure has been developed. This method is especially suited for computer calculations of the complete attenuation curve of the bremsstrahlung spectrum.
Methods: The Nth value thickness tN , is the solution of the transcendental equation relating the exponentially attenuated intensity I(tN ) and the initial intensity I. This solution can be obtained by application of the Newton-Raphson method for transcendental equations which states that if x0 is an approximate solution for F(x)=0 then an improved solution is given by x = x0 + ∆x, where, ∆x is the negative ratio of F(x) and its first derivative.Substituting the improved value of x in the transcendental attenuation equation, the procedure is repeated until Δx is a negligible fraction of the root. The value of x converges in a few iterations.
Results: A Method for the Rapid Calculation of the Nth Value Thickness of an X-ray Spectrum has been developed.
Conclusion: By slightly changing the input parameters, the Nth value thickness and the attenuation curve of a bremsstrahlung spectrum, energy fluence spectrum or the exposure spectrum can easily be calculated. An excel program written for the purpose facilitates rapid iteration.
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