The Tomographic Experiment
What is a Tomographic Image?
A tomographic image or tomogram is a three dimensional array of values representing a continuous distribution of some sample property (such as density).
The tomogram is constructed from a series of X-ray images acquired at fixed angular intervals (the view sampling angle). The interval is arbitrary, but is usually chosen to minimise view sampling artifacts. A typical tomographic dataset might involve image acquisition at 1° intervals around an arc of 180° plus the cone beam angle. For the XuM with detector width of 26.8 mm and SDD of ~259 mm, the cone beam angle will be about 6°. Therefore we need to acquire 186 images.
In medical CT imaging it is normal to rotate the X-ray source and detector around the sample (patient), but in the XuM, we rotate the sample around the centreline of the ROI, while the X-ray source (target) and detector remain fixed. The combination of a point source and 2D detector provides a cone-beam geometry. Effective imaging requires that there exists at least a source in any plane that intersects the sample, i.e., the whole of the sample must be contained within the FOV for all images in the dataset. This condition will dictate maximum allowable magnification.
Each image will consist of a number of frames. To minimise the acquisition time for the whole set of images, the minimum number of frames to achieve required contrast for each image should be determined.
When the full set of images is acquired, a 3-D tomogram reconstruction process converts the 2-D planar cone-beam projections to a volumetric data set. Each image or slice in the data set is made up of an array of pixels. The distance between the centres of any two adjacent pixels represents a real-world (sample) distance known as the inter-pixel distance. In a similar fashion, the distance between consecutive slices represents a real-world (sample) depth, known as the inter-slice distance.
The slices of the data set are stacked according to the inter-pixel and inter-slice distances so that the data, captured as pixel intensities, now accurately represents sample density in the real-world dimensions of the original sample volume.
The tomogram can be sectioned in arbitrary ways to reveal internal structures, or it can be rendered as a full 3-D rotatable model of the sample by applying an opacity transformation function which translates intensity values to opacity. By this means, individual voxels can be made invisible, or partly opaque so that internal structures can be readily differentiated in terms of their density. This is an extremely powerful visualisation tool.
A series of renderings, generated as the volume is incrementally rotated about an arbitrary axis, can be used to create a movie or animated GIF image which provides even greater visual cues to the interpretation of the sample properties.
In the interests of processing speed, images in tomographic data sets are usually constrained to the smallest size which will provide the required resolution, and often to dimensions which are a power of two, such as 256x256, or 512x512 pixels. Some post-processing algorithms will pad or crop to achieve these sizes.
