Search

Some special functions of the Mathematical Physics are a very helpful resource in problems involving the propagation of coherent light beams, which will suffer dispersion in a turbulent media such as the Earth's ionosphere waveguide. Unfortunately, these tools are difficult to use because it involves very complex mathematical developments. For this reason it is interesting to find a friendly method to make the implementation of these special functions possible. Using Maple I will be able to overcome the mathematical difficulty of solving these equations and get to the understanding of these phenomena. Specifically I will consider the excitation of the Earth's ionosphere as a cavity or a waveguide by satellite borne current sources in the form of satellite-based antennas when the medium inside the waveguide is turbulent. As a result, three kinds of coherent light beams will be derived: Bessel beams, for relatively low turbulence, Whittaker beams, for moderate turbulence, and Heun beams, for strong or fully developed turbulence. These beams are represented by the corresponding electric fields but the associated magnetic fields can be derived as well. It is verified that Maple is a very powerful tool in the study of the propagation of an input field through axially symmetric systems using the methods of the Mathematical Physics. It is expected that Maple will have important applications for more general models concerning propagation trough turbulent environments. more...

The purpose of this study is to investigate how well model observer can correlate with human observer in the lesion detection and localization task when the location of lesion is uncertain in CT imaging. A 35 × 26 cm oblong-shaped water phantom was scanned with and without two cylindrical rods (3 mm and 5 mm diameters) to simulate lesions with - 15HU contrast. Scans were repeated 100 times with the rods and 100 times without for each of 4 dose levels. Signal and background images were generated by selecting ROIs with 128x128 pixels, with the location of signal in each ROI randomly distributed. Human observer studies were conducted as three medical physicists identified the presence or absence of lesion, indicated the lesion location in each image and scored confidence level with a 6-point scale. ROC curves were fitted and area under curve (AUC) was calculated. The same data set was also analyzed using a Channelized Hottelling model observer with Gabor channels. Internal noise was added to the test variables for model observer study. AUC of ROC and LROC curves were calculated using non-parametric approach. The performance of human observer and model observer was compared. The Peason's product-moment correlation coefficients were 0.994 and 0.998 for 3mm and 5mm diameter lesions in ROC analysis and 0.987 and 0.999 in LROC analysis, indicating that model observer performance was highly correlated with the human observer performance for different size of lesions and different dose levels when signal location is uncertain. These results provide the potential of using model observer that correlates with human observer to assess CT image quality, optimize scanning protocol and reduce radiation dose. more...