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Biomedical Imaging by Sebastian Aeffner, Timo Aspelmeier, Tim Salditt

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Combining these three equations, the index of refraction in the oscillator model is given by

n2=1+1ε0PE=1e2ρeε0me1ω2ωr2+iωΓ,(3.68)

and expressing the numerical constants by r0 and using ω = ck = 2πc/λ yields

n2=1r0λ2ρeπω2ω2ωr2+iωΓ.(3.69)

For typical x-raywavelengths (λ ≈ 1 Å) and electron densities of soft matter (ρe (H2O) = 0.334 Å−3) as well as ωωr, the second term is much smaller than unity. Using the Taylor expansion 1x1x2(x1)yields the x-ray index of refraction

n1r0λ2ερe2πω2ω2ωr2+iωΓfs=1r0λ2ρe2π[ 1+fs+ifs ].(3.70)

Note that by the above derivation, the index of refraction as a macroscopic quantity has been linked to the atomic phenomenon of scattering. The inherent ...

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