Possible Laminographic and Tomosynthesis Applications for Wolter Microscope Scan Geometries (2004)

The Wolter microscope includes a number of attractive features for x-ray imaging, and possible connections to laminographic and tomosynthesis 3D object recovery algorithms. This type of instrument employs x-ray optics to sift out single energy x-rays from a broader spectral energy source, and direct those x-rays to a ''focus plane'' similar to the operation of a optical microscope (see Figure 1 for schematic of a Wolter instrument). Unlike optical microscopes the 3D object can be thick in the direction of the x-rays and in this case more of the intensity of the image is affected by the out-of-focus planes, since the ray-paths span the entire depth of the object. It is clear that the ''in-focus'' plane of a Wolter contain more 3D information than a simple ''point-projection'' radiograph. However, it is not clear just how the impact of the out-of-focus planes obscures or distorts features of interest for the in-focus planes. Further, it is not clear just how object positioning can be combined with multiple acquisitions to enable recovery of other planes within the object function or the entire object function. Of particular interest here are Wolter microscopes configured for mesoscale objects (mm extent with um features). Laminographic and tomosynthesis scanning methods can be strategic for this type of inspection instrument. First, photon output for inspection purposes can be meager in this type of ''small field of view'' system. With laboratory x-ray sources a single image can require up to 10 minutes to accumulate adequate signal. Techniques that can obtain 3D object information from small numbers of views, rotational or translational, are consequently at a premium. Laminographic and tomosynthesis scanning methods require relatively small numbers of views (2-30). Secondly, the Wolter microscope scan geometry in a single view is a fit with the type of source-detector geometry achieved through source-object-detector re-positioning in laminographic and tomosynthesis systems. Figure 2 contains a picture of the Wolter optics geometry for inspection. Figure 3 contains an illustration of the scan geometry used in single-plane laminography for flat objects, while figure 4 contains a picture of the scan geometry and motion for a class of tomosynthesis algorithms. The Wolter transmission paths depicted in figure 2 are similar to laminographic and tomosynthesis paths and they provide opportunities to exploit either of these algorithms for removing out of plane blur from Wolter optic images. Other algorithms may arise from the sequence of images obtained by translation through the focus of the Wolter microscope. A variety of LLNL programs have developed iterative and semi-iterative schemes for utilizing prior knowledge from drawings, or other physical measurements to improve defect recognition and inspection of objects. One such algorithm would use the laminographic estimate of each plane as the first estimate of the object function, then iterate on the object function until the forward projections match the acquired sequence of projections translated through the focus of the Wolter microscope. Unlike the laminography and tomosynthesis approaches this particular approach requires a forward model of the projection through the object. We employed an LLNL developed Wolter simulation code [Jackson 2004] to evaluate possible scanning options since a working Wolter was not available. Six synthetic objects were formulated: (1) concentric spheres with a cylindrical void, (2) concentric spheres with a cylindrical inclusion, (3) a sphere with a number of successively smaller sphere-voids arranged in the mid-plane of the object, (4) a sphere with a number of successively smaller sphere inclusions arranged in the mid-plane of the object, (5) a slab object with voids at the entrance plane and at the exit plane of the thickness, and (6) a slab object with inclusions at the entrance plane and at the exit plane of the thickness. Of the six synthetic objects only the middle two (the sphere with different size spheres arranged at the mid-plane) were studied extensively. A number of scan regimes were specified for simulation. First, we simulated ''translation through focus'' scanning. For this type of scan regime the object was placed at focus and moved in small increments towards the detector. An illustration of this type of scanning is shown in Figure 7. The second scan mode is rotation of the object. The third scan mode is horizontal and vertical translation of the object. These three motions taken together would enable any of the possible scan trajectories for various algorithms (including CT) to be implemented. Termination of the LDRD SI project allowed only the first scan mode to be implemented and simulations generated.