Modelling of imaged ellipse intensity profiles using Euclidean geometry

Raf Theunissen

Research output: Contribution to journalArticle (Academic Journal)peer-review

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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 hamper 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 is discussed.
Original languageEnglish
Pages (from-to)321-331
Number of pages11
JournalImaging Science Journal
Issue number6
Early online date4 May 2015
Publication statusPublished - Jun 2015


  • convolution
  • Hermite polynomial
  • diffraction
  • ellipse
  • FFT
  • blur


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