The dynamic normalization is expressed as (11) T ( t i ) T ref ≅ 1 n ∑ k = 1 k = n I meas ( t i , c k ) I OB ( t i , c k ) 1 n ( b − a + 1 ) ∑ i = a i = b ∑ k = 1 k = n I meas ( t i , c k ) I OB ( t i , c k ) ≅ ( b − a + 1 ) ∑ k = 1 k = n I meas ( t i , c k ) ∑ i = a i = b ∑ k = 1 k = n I meas ( t i , c k ) ≅ ( b − a + 1 ) I meas ( t i ) ∑ i = a i = b I meas ( t i ) This formulation does not explicitly treat the effects of incoherent scattering from the sample, which may be significant because of the short sample-to-detector distance used in this study (~5 cm for the CT scans, ~10 cm for the high-speed imaging).
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