A simplified approach for the generation of projection data for cone beam geometry

To test a developed reconstruction algorithm for cone beam geometry, whether it is transmission or emission tomography, one needs projection data. Generally, mathematical phantoms are generated in three dimensions and the projection for all rotation angles is calculated. For non-symmetric objects, the process is cumbersome and computation intensive. This paper describes a simple methodology for the generation of projection data for cone beam geometry for both transmission and emission tomographies by knowing the object’s attenuation and/or source spatial distribution details as input. The object details such as internal geometrical distribution are nowhere involved in the projection data calculation. This simple approach uses the pixilated object matrix values in terms of the matrix indices and spatial geometrical coordinates. The projection data of some typical phantoms (generated using this approach) are reconstructed using standard FDK algorithm and Novikov’s inversion formula. Correlation between the original and reconstructed images has been calculated to compare the image quality.     

Optical characteristics of transparent samarium oxide thin films deposited by the radio-frequency sputtering technique

Transparent metal oxide thin films of samarium oxide (Sm₂O₃) were prepared on pre-cleaned fused optically flat quartz substrates by radio-frequency (RF) sputtering technique. The as-deposited thin films were annealed at different temperatures (873, 973 and 1073 K) for 4 h in air under normal atmospheric pressure. The topological morphology of the film surface was characterized by using atomic force microscopy (AFM). The optical properties of the as-prepared and annealed thin films were studied using their reflectance and transmittance spectra at nearly normal incident light. The estimated direct optical band gap energy (\(E_{\mathrm {g}}^{\mathrm {d}}\)) values were found to increase by increasing the annealing temperatures. The dispersion curves of the refractive index of Sm₂O₃ thin films were found to obey the single oscillator model.     

The Leray-Schauder condition for 1-set weakly-contractive and (ws)-compact operators

The main purpose of this article is to prove a collection of new fixed point theorems for (ws)-compact and so-called 1-set weakly contractive operators under Leray-Schauder boundary condition. We also introduce the concept of semi-closed operator at the origin and obtain a series of new fixed point theorems for such class of operators. As consequences, we get new fixed point existence for (ws)-compact (in particular nonexpansive) self mappings unbounded closed convex subset of Banach spaces. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness. Later on, we give an application to generalized Hammerstein type integral equations.