Modelling of imaged ellipse intensity profiles using Euclidean geometry

Abstract

To model the evolution in intensity of an ellipse image along randomly oriented profiles, this paper starts with the derivation of an analytical solution involving infinite summations of products of Hermite polynomials, which is consequently argued to be impractical. Generation of profiles adopting Fourier analyses hampers the extraction of arbitrarily located intensity distributions as a direct result of equidistant spatial sampling, and an alternative procedure is therefore presented to calculate the sought for intensity at isolated spatial locations. The algorithm introduced is based on the overlap area between the ellipse and concentric circles, which can be performed using basic trigonometric properties. The simplicity of the proposed method allows, contrary to Fourier based analyses, the modelling of intensity profiles with high resolution while demanding minimal computational memory. The proficiency of the method is demonstrated numerically, and its generality and applicability to real images in terms of motion induced image blurring and digitisation are discussed.

Keywords:

• Convolution
• Diffraction
• Ellipse
• FFT
• Hermite polynomial
• Blur