Once a data stack has been collected, the projected views are used to reconstruct the object. An absolute requirement is that all the projections within the data stack are well aligned (optimally to within sub-pixel resolution) in order to generate a meaningful reconstruction. This can be achieved either by using fiducial markers (gold beads) or by cross correlation methods, "beadless alignment". We have given users the option of either method. However, since our data from the microscope is already well aligned and all relative x,y,z translation, rotation information etc. are available in the header, and as it eases sample preparation, we generally prefer beadless alignment.
Following alignment, the data is mass normalized. The mass normalization process uses the histogram of each projection to determine a background values which then are fit to an exponential absorption model where a scale value is determined for the projections. Then each pixel is multiplied by its respective scale value to normalize the images (if an absorption model is used the log of each pixel is also taken).
We then use two algorithms for the reconstruction of the aligned mass normalized data: Elliptical Weighted Back Projection (EWBP), and Tomographic Alternating Projection Iterative Reconstruction (TAPIR). Typically we run the EWBP in order to obtain the back projection. This is done in real space with a weighted filter applied in Fouier space. Then, in order to generate a better reconstruction we run TAPIR, using the result of EWBP as a starting guess. This iterative technique imposes positivity and Z-boundedness on the reconstruction during each cycle of refinement. The goal is to minimize the difference between the projected reconstruction and the observed tilted projections. For each cycle of refinement the iterative method computes the differences between projections of the reconstruction and the measured projections. It then updates the reconstruction with the backprojected differences and sets any negative values in the reconstruction to zero. Convergence is monitored by an R-factor which measures the percent difference between the reprojected reconstruction and the observed data.
A simple tutorial is available to walk you through the reconstruction process. That tutorial requires Priism 4.2.3 or later. An older version of the tutorial is also available. It uses a different mechanism to perform the calculation at different resolution levels.