On the analysis of an elliptical Gaussian flux image and its equivalent circular Gaussian flux images

For a continuous elliptical Gaussian flux image over the infiniteX–Y plane, the parameter relationships between the ellipticalGaussian flux image and the equivalent circularGaussian flux images are clearly discussed in bothmathematical and graphicalways in this paper with respect to the radial power distribution around the image centre (peak flux location in image plane). This paper presents six typicalmethods (SIGMA- 2Mean, SIGMA-1Mean, SIGMA-0Mean in Class One, SIGMA-RPeak, SIGMA-RMean, SIGMA-SqrRMean in Class Two) to give the equivalent circularGaussian flux images to the ellipticalGaussian flux image, tries to link these circularGaussian fittingmethods to the relevant solar engineering applications, and makes some assessment comments on the elliptical/circular Gaussian modelling in solar mirror optics. By comparing the approximation performance among these six typical fitting methods, it reveals the reason for the 90%intercept over-estimation phenomenon of Francisco J. Collado’s one-point circular Gaussian fitting practice relative to the experimental flux image. The detailed algorithmfor automatically finding out themajor/minor axes and the image centre of the digital elliptical flux image is also provided in this paper. SIGMA-2Mean and SIGMA-SqrRMean are equivalent for an elliptical flux image, but they are applied in different ways to figure out either the reasonable intercept factor of the experimental flux image on the physical target plane respecting the aperture region of interest, or the power spillage over the limited experimental target plane. At last, this paper introduces the interpolation reconstruction of an elliptical Gaussian flux image over a rectangular domain just based on the boundary pixel values, so it is quite useful for solar engineering, such as fast simulation of a flux image concentrated by a mirror, and also instant approximation of the flux density over the receiver aperture by the linear array of radiometers around the receiver aperture, when the central receiver system is in the normal working state. 2011 Elsevier Ltd. All rights reserved