A method is developed which makes it possible to scan and reconstruct an object with cone beam x-rays in a spiral scan path with area detectors much shorter than the length of the object. The method is mathematically exact. If only a region of interest of the object is to be imaged, a top circle scan at the top level of the region of interest and a bottom circle scan at the bottom level of the region of interest are added. The height of the detector is required to cover only the distance between adjacent turns in the spiral projected at the detector. To reconstruct the object, the Radon transform for each plane intersecting the object is computed from the totality of the cone beam data. This is achieved by suitably combining the cone beam data taken at different source positions on the scan path; the angular range of the cone beam data required at each source position can be determined easily with a mask which is the spiral scan path projected on the detector from the current source position. The spiral scan algorithm has been successfully validated with simulated cone beam data.

This paper addresses the long object problem in helical cone-beam computed tomography. We present the PHI-method, a new algorithm for the exact reconstruction of a region-of-interest (ROI) of a long object from axially truncated data extending only slightly beyond the ROI. The PHI-method is an extension of the Radon-method, published by Kudo, Noo, and Defrise in issue 43 of journal Physics in Medicine and Biology. The key novelty of the PHI-method is the introduction of a virtual object fpsi(x) for each value of the azimuthal angle psi in the image space, with each virtual object having the property of being equal to the true object f(x) in some ROI omegam. We show that, for each psi, one can calculate exact Radon data corresponding to the two-dimensional (2-D) parallel-beam projection of fpsi(x) onto the meridian plane of angle psi. Given an angular range of length pi of such parallel-beam projections, the ROI omegam can be exactly reconstructed because f(x) is identical to fpsi(x) in Omegam. Simulation results are given for both the Radon-method and the PHI-method indicating that 1) for the case of short objects, the Radon- and PHI-methods produce comparable image quality, 2) for the case of long objects, the PHI-method delivers the same image quality as in the short object case, while the Radon-method fails, and 3) the image quality produced by the PHI-method is similar for a large range of pitch values.

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The development of a system is described here that, for the first time, utilizes acoustic microscopy techniques to evaluate materials and processes on a scale practical for support of automated manufacture. The properties of acoustic microscopy attractive for this application are the ability to inspect the elastic structure of the surface and the subsurface of materials. In the past, several barriers have prevented its use except for near-surface inspection of a very limited area (a few square millimetres). These barriers include critical alignment requirements, very shallow penetration, and limitations in resolution and the size of the workpiece. Presented here is a unique configuration that differs from high-frequency or conventional acoustic microscopy methods in these ways: ( a ) images are formed directly by displaying amplitude of broadband acoustic pulses (centre frequencies: 10-100 MHz; bandwidths: 80% -120%), rather than by displaying amplitude variations resulting from interference between narrowband pulses (carrier frequencies: 0.5-4.0 GHz; bandwidths: 0.5% -1.0% ); ( b ) the short pulses, having only a 2-4 wavelength duration, are readily time resolved by gating the surface wave and thus eliminating interference from the direct reflection. This technique avoids the complex analytical problem of separating the surface waves from the direct reflection; ( c ) a single-crystal silicon acoustic lens is used instead of the sapphire acoustic lens conventionally used. Incorporating these methods, a large-scale, 10-100 MHz scanning microscopy system has been developed with the following advances over previously reported ultrasonic non-destructive testing systems and acoustic microscopes: ( a ) reliable detection and display of surface-breaking cracks is possible at all orientations for non-destructive evaluation purposes; ( b ) imaging accuracy is independent of small variations in the water gap (the distance between lens and workpiece); in contrast, such variations are a major consideration in determining the imaging quality of conventional acoustic microscopes; ( c ) magnifications of 2-20 times instead of 1000 times allow interrogation of much larger areas and volumes of material; ( d )the compound resolution of large against small features is theoretically explained for the first time by a combined ray tracing-diffraction model; ( e ) a practical method for the inspection of volumes and even interior surfaces results from the use of longer wavelength signals, where previously the use of shorter wavelength signals limited penetration to the first few micrometres of the subsurface; ( f ) shear-wave images of subsurface features, which give the most dependable information on the integrity of bonded interfaces, are available, as well as longitudinalwave images. Practical applications are presented, such as inspection for near-surface inclusions in aircraft engine materials and inspection of heat-sink bonds in semiconductor power devices. The broadband-wave method presented here allows scanning acoustic-microscopy methods, previously available only on a scale useful for the materials scientist, to be used on a scale practical for industrial materials evaluation, with a capability for an interrogated volume 12 orders of magnitude greater than that possible with the higher frequency methods.