Figure 7. High-density areas in reconstructed 3D model of bacteria. (A) Red regions indicate .6.5s above the average intensity. The high-density red regions are clearly located at both ends of the bacterium, which likely suggests the presence of a nucleoid. The complex structure was detected in the central area of the bacterium. (B), (C) High-density regions in the other two bacteria. Both structures indicated that high-density regions exist at the extremities of the bacteria. doi:10.1371/journal.pone.0021516.g007 detector just under EB point. To recover the true tilt images, the horizontal width of the detected images are reduced by the factor cos(hx). Furthermore, to generate the 3D model, each X-ray signal must be transformed into X-ray absorbance (An), which is done using Eq. (1): An~log10(In0=In): 1 ð Þ In Eq. (1), In is the X-ray intensity of each X-ray element n and In0 is the base intensity without the sample. After correction, the X-ray images were filtered by a 2D Gaussian filter (GF, size = 565 pixels, s = 1) via Matlab R2007b. The images were normalized to 8-bit contrast. For 3D reconstruction from the X-ray images, the 12806960 pixel images were reduced to 3206240 pixels. Observation of Atmospheric Samples by 3D-SGXM 3D reconstruction algorithm To generate a 3D model from seven XPD images, we developed a highly accurate reconstruction method that uses an SA algorithm (Figures 3 and 4) that was implemented by a Matlab script. First, a 3D mask was calculated for each 2D mask from the X-ray images (Figure S3). This approach contributes to the short calculation time because it reduces the 3D space involved. The 3D voxel values and all projections were initially set to 0. Starting from the initial value of 0, a position in the 3D mask is randomly selected, and the voxel values in the kernel area at the selected position are randomly shifted. Initially, the kernel area is set to a 3D normal distribution with SD = 15s, and the randomly changed value in the kernel is SD = 0.2s, which is gradually reduced at each calculation cycle. The new 3D volume is reprojected onto the seven directions corresponding to the seven angles of the XPD elements, and the error between each reprojection and its corresponding X-ray image is calculated by the residual sum of the squares. This calculated error is used by the SA algorithm to determine whether to accept the modified volume [29]. If the new error value is less than the previous error value, the modified volume is accepted unconditionally. If the error has increased, the Boltzmann probability factor of P(DE) is calculated using Eq. (2) and is used to determine whether to accept the modified voxel value. P(DE)~exp ({DE=T ): 2 ð Þ In Eq. (2), DE is the change in the error and T is the current temperature. A random number (R) uniformly distributed in the interval 0 to 1 is generated and the volume change is accepted if R,P(DE). If R.P(DE), the volume is returned to its previous state. Next, a new position is selected at random, its volume is randomly shifted and the SA algorithm is applied again. This procedure is iterated 100,000 times. When finished, the temperature, the kernel size and its value-shifting SD decrease exponentially. Furthermore, this entire cycle is repeated 200 times. The temperature, the kernel size and its shifting value are initially set to 10, 15s and 0.2s, respectively. After the algorithm is executed, these values are reduced to 0.1, 2s and 0.1s, respectively. Supporting Information Figure S1 Energy of X-rays emitted by the interaction of EB with CuZn-coated Si3N4 film. (A) Overview of the apparatus to measure the X-ray photon energy, which uses an energy dispersive X-ray spectrometer (EDS) model EX-2100 including SEM model JSM-5601 (JEOL, Japan). EB irradiates the centre of the CuZn-coated Si3N4 film on the Al stage. The EDS detector is positioned 80 mm from the EB-irradiated spot and at a 30u angle with respect to EB; its detection area is 10 mm2. SEM is operated at 5–7 kV for the EB acceleration, 4006 magnification and an EB aperture of 40. The X-ray-acquisition time is 100 s. (B) EDS spectrum for 5-kV EB acceleration. The large peak at 1 keV is due to both Cu and Zn X-ray lines. The weak peak at 1.8 keV is the Si X-ray line, and its presence suggests that a small number of electrons are transmitted to the Si3N4 film through the CuZn layer. However, under these conditions, the 1.5-keV Al peak is not detected (from the Al stage), which suggests that the impinging electrons do not cross the CuZn-coated Si3N4 film. (C) EDS spectrum for 7-kV EB acceleration. Under these conditions, a weak Al peak is detected from the Al stage that is positioned under the CuZn-coated Si3N4 film. Therefore, in this case, the 7-kV impinging electrons penetrate the CuZn-coated Si3N4 film. (TIF) PLoS ONE | www.plosone.org 8 June 2011 | Volume 6 | Issue 6 | e21516