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X-ray Imaging and Reconstruction Techniques for Linear Absorption Coefficient Calculation

Explore X-ray absorption coefficient calculation methods through linear projection, imaging reconstruction, and back-projection methods. Understand how X-ray intensity and path length play a role in determining absorption.

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X-ray Imaging and Reconstruction Techniques for Linear Absorption Coefficient Calculation

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  1. X 線透過率 t = (I – Id) / (I0 - Id) = exp(- μ×S) I, I0, Id：X 線強度（光子数） S：X 線透過光路長 μ：X 線線吸収係数 Linear Absorption Coefficient

  2. X 線投影 p = - ln(t) = μ×S or p(r, θ, z) = ∫ μ(x, y, z) ds

  3. 画像再構成 p(r, θ) = ∫ μ(x, y) ds → g(r) = ∫ |u| exp(2 π i u r) du q(r, θ) = ∫ p(v, θ) g(r – v) dv μ(x, y) = ∫0～πq(r, θ) dθ Convolution Back-Projection 法

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