To evaluate and quantify neutron images, standard correction procedures have to be performed (Mannes et al. 2009b). The images were corrected by the quantitative neutron imaging correction program (QNI) developed by Hassanein (2006): a) dark current correction caused by the camera background; b) flat field correction; c) median filtering and spot cleaning (filter width: 3 pixels, threshold: 10%); d) referencing to the start image.

The analysis of the corrected images was carried out with the image data processing program Fiji (Schindelin et al. 2012). For every experimental run each of the four specimens was cropped separately with some surrounding area in the acquired images. In each of the cropped stacks, the sample images were aligned with the plugin ‘StackReg’ with the transformation specification ‘Rigid Body’ (Thévenaz et al. 1998). Then, a region of interest (ROI) was selected covering the whole area of the specimen in the most swollen state.

Thereby, the mean attenuation of the ROI could be defined as the sum of the attenuations of the particular radiated materials (Equations 4+5). For the specimen in the maximal swollen state:

$$\begin{array}{c}\text{-ln(}{T}_{wet}\text{)}={\sum}_{I}\cdot {z}_{I}+{\sum}_{Al}\cdot {z}_{AI}+{\sum}_{H.wet}\cdot {z}_{H.wet}\\ +{\sum}_{w}\cdot {z}_{H.wet}\end{array}\text{\hspace{1em}(4)}$$(4)

For the specimen in the dry state [low (or zero) MC]:

$$\text{-}\mathrm{ln}\mathrm{(}{T}_{dry}\mathrm{)}={\Sigma}_{I}\cdot {z}_{I}+{\Sigma}_{Al}\cdot {z}_{Al}+\frac{{A}^{\prime}}{A}{\Sigma}_{H.dry}\cdot {z}_{H.dry}+\frac{{A}^{\prime}}{A}{\Sigma}_{w}\cdot {z}_{w.dry}\text{\hspace{1em}(5)}$$(5)

where *T*_{wet} and *T*_{dry} are the transmissions of the wet and the dry specimens, *A* the whole area of the ROI, *A*′ the area of the dry wood specimen, Σ the attenuation coefficient and *z* the thickness of a material with the indices: *I*=isolation material (here rockwoll), *Al*=aluminium, *H.wet* and *H.dry*=wood in the maximal swollen and in the dry state, respectively, *w*=water and *w.wet*and *w.dry*=water in the wet and dry wood specimen, respectively.

The density of the wood material (without water fraction) differs between the two states due to shrinkage effects and can be described as follows (Equations 6+7):

$${\rho}_{H.wet}=\frac{{m}_{H}}{A\cdot {z}_{H.wet}}\text{\hspace{1em}(6)}$$(6)

$${\rho}_{H.dry}=\frac{{m}_{H}}{{A}^{\prime}\cdot {z}_{H.dry}}\text{\hspace{1em}(7)}$$(7)

where *ρ*_{H.wet} and *ρ*_{H.dry} are the densities of the wood material (ovendry) at the maximal swollen and at the dry state and *m*_{H} is the oven dry mass of the wood specimen.

Due to the fact that the attenuation coefficient of wood corresponds directly with its density (Mannes et al. 2009a), the attenuation coefficients of the two states differ. The attenuation coefficient of the dry state can be derived from the attenuation coefficient of the maximal swollen state as follows (Equation 8):

$${\Sigma}_{H.dry}={\Sigma}_{H.wet}\cdot \frac{{\rho}_{H.dry}}{{\rho}_{H.wet}}={\Sigma}_{H.wet}\cdot \frac{A\cdot {z}_{H.wet}}{{A}^{\prime}\cdot {z}_{H.dry}}\text{\hspace{1em}(8)}$$(8)

Through insertion in Equation 5 and reduction, it results (Equation 9):

$$\text{-}\mathrm{ln}\mathrm{(}{T}_{dry}\mathrm{)}={\Sigma}_{I}\cdot {z}_{I}+{\Sigma}_{Al}\cdot {z}_{Al}+{\Sigma}_{H.wet}\cdot {z}_{H.wet}+\frac{{A}^{\prime}}{A}{\Sigma}_{w}\cdot {z}_{w.dry}\text{\hspace{1em}(9)}$$(9)

Therefore it follows that the attenuation based on the wood material of the wood specimen is equal to that of Equation 4 and is therefore independent of the state (wet or dry). Thus, through subtraction of Equation 9 from Equation 4, it remains only the attenuation of the water fraction (Equation 10):

$$\text{-}\mathrm{ln}\mathrm{(}\frac{{T}_{wet}}{{T}_{dry}}\mathrm{)}={\Sigma}_{w}\cdot {z}_{w.wet}+\frac{{A}^{\prime}}{A}{\Sigma}_{w}\cdot {z}_{w.dry}={\Sigma}_{w}\cdot \mathrm{(}{z}_{w.wet}\text{-}\frac{{A}^{\prime}}{A}\cdot {z}_{w.dry}\mathrm{)}\text{\hspace{1em}(10)}$$(10)

The water concentration (*c*) in the wood is based on the volumetric content and can be defined as the ratio of the water to the wood thickness at a given state (Equation 11):

$$c=\frac{{z}_{w}}{{z}_{H}}\text{\hspace{1em}(11)}$$(11)

$$MC=\frac{{m}_{wet}\text{-}{m}_{0}}{{m}_{0}}\text{\hspace{1em}(12)}$$(12)

$$MC=\frac{{\rho}_{w}}{{\rho}_{H}}\cdot c\text{\hspace{1em}(13)}$$(13)

Due to swelling and shrinkage of wood in connection with water uptake and release, commonly the *MC* is used as unit in the field of wood science instead of the water concentration. The *MC* is based on the wood mass at oven-dry conditions, which remains constant in contrast to the volume and is defined as follows (DIN 52183) (Equation 12), where *m*_{wet} is the mass of the wood at wet conditions (this means the wood mass including the water fraction) and *m*_{0} the oven-dried mass of the wood. The water concentration can be converted into *MC* at a given state as follows (Equation 13), where *ρ*_{w} and *ρ*_{H} are the densities of water and of wood, respectively. Thus, the *MC* of the two states can be calculated as follows (Equations 14+15) considering Equations 6 and 7:

$$M{C}_{wet}=\frac{{\rho}_{w}}{{\rho}_{H.wet}}\cdot \frac{{z}_{w.wet}}{{z}_{H.wet}}=\frac{{\rho}_{w}\cdot {z}_{w.wet}\cdot A}{{m}_{H}}\text{\hspace{1em}(14)}$$(14)

$$M{C}_{dry}=\frac{{\rho}_{w}}{{\rho}_{H.dry}}\cdot \frac{{z}_{w.dry}}{{z}_{H.dry}}=\frac{{\rho}_{w}\cdot {z}_{w.dry}\cdot {A}^{\prime}}{{m}_{H}}\text{\hspace{1em}(15)}$$(15)

Therefore, *z*_{w.wet} and *z*_{w.dry} can be defined as follows (Equations 16+17):

$${z}_{w.wet}=\frac{M{C}_{wet}\cdot {m}_{H}}{{\rho}_{w}\cdot A}\text{\hspace{1em}(16)}$$(16)

$${z}_{w.dry}=\frac{M{C}_{dry}\cdot {m}_{H}}{{\rho}_{w}\cdot {A}^{\prime}}\text{\hspace{1em}(17)}$$(17)

Insertion of Equations 16 and 17 in Equation 10 results in (Equation 18):

$$\begin{array}{c}\text{-}\mathrm{ln}\mathrm{(}\frac{{T}_{wet}}{{T}_{dry}}\mathrm{)}={\Sigma}_{w}\cdot \mathrm{(}{z}_{w.wet}\text{-}\frac{{A}^{\prime}}{A}{z}_{w.dry}\mathrm{)}={\Sigma}_{w}\cdot \mathrm{(}\frac{M{C}_{wet}\cdot {m}_{H}}{{\rho}_{w}\cdot A}\text{-}\frac{{A}^{\prime}}{A}\cdot \frac{M{C}_{dry}\cdot {m}_{H}}{{\rho}_{w}\cdot {A}^{\prime}}\mathrm{)}\\ ={\Sigma}_{w}\cdot \mathrm{(}M{C}_{wet}\text{-}M{C}_{dry}\mathrm{)}\cdot \frac{{m}_{H}}{{\rho}_{w}\cdot A}\end{array}\text{\hspace{1em}(18)}$$(18)

Through conversion, the MC differences between two images can be calculated as follows (Equation 19):

$$M{C}_{wet}\text{-}M{C}_{dry}=\text{-ln}\mathrm{(}\frac{{T}_{wet}}{{T}_{dry}}\mathrm{)}\cdot \frac{{\rho}_{w}\cdot A}{{\Sigma}_{w}\cdot {m}_{H}}\text{\hspace{1em}(19)}$$(19)

For the tests, an experimentally determined attenuation coefficient Σ_{w}=2.2 cm^{-1} was used.

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