Summary Statistics for Fun Dough Data Acquired at LLNL

Abstract

Using x-ray computerized tomography (CT), we have characterized the x-ray linear attenuation coefficients (LAC) of a Play Dough{trademark}-like product, Fun Dough{trademark}, designated as PD. Table 1 gives the first-order statistics for each of four CT measurements, estimated with a Gaussian kernel density estimator (KDE) analysis. The mean values of the LAC range from a high of about 2100 LMHU{sub D} at 100kVp to a low of about 1100 LMHU{sub D} at 300kVp. The standard deviation of each measurement is around 1% of the mean. The entropy covers the range from 3.9 to 4.6. Ordinarily, we would model the LAC of the material and compare the modeled values to the measured values. In this case, however, we did not have the composition of the material and therefore did not model the LAC. Using a method recently proposed by Lawrence Livermore National Laboratory (LLNL), we estimate the value of the effective atomic number, Z{sub eff}, to be near 8.5. LLNL prepared about 50mL of the Fun Dough{trademark} in a polypropylene vial and firmly compressed it immediately prior to the x-ray measurements. Still, layers can plainly be seen in the reconstructed images, indicating that the bulk density of the material in the containermore » is affected by voids and bubbles. We used the computer program IMGREC to reconstruct the CT images. The values of the key parameters used in the data capture and image reconstruction are given in this report. Additional details may be found in the experimental SOP and a separate document. To characterize the statistical distribution of LAC values in each CT image, we first isolated an 80% central-core segment of volume elements ('voxels') lying completely within the specimen, away from the walls of the polypropylene vial. All of the voxels within this central core, including those comprised of voids and inclusions, are included in the statistics. We then calculated the mean value, standard deviation and entropy for (a) the four image segments and for (b) their digital gradient images. (A digital gradient image of a given image was obtained by taking the absolute value of the difference between the initial image and that same image offset by one voxel horizontally, parallel to the rows of the x-ray detector array.) The statistics of the initial image of LAC values are called 'first order statistics;' those of the gradient image, 'second order statistics.'« less