Using Legendre polynomials Formulas at Fresnel Integral Diffraction | ||
| Journal of Communication Sciences and Information Technology | ||
| Volume 6, Issue 1, December 2024, Pages 11-18 PDF (502.51 K) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/jcsit.2024.332554.1012 | ||
| Authors | ||
| Reham Abd Elsadek Gomaa* 1; Ahmed Yehia Sayed2; Emil Sobhi Shoukralla3; Alfaisal Abd Elhameed Hasan4; Nermin Abd Elsatar Saber5 | ||
| 1Basic and applied science department, Faculty of Engineering, Arab academy for science, technology and maritime transport, Aswan, Egypt | ||
| 2Physics and Engineering Mathematics Department, Faculty of Engineering at Mataria, Helwan University, Cairo, Egypt. | ||
| 3Faculty of Electronic Engineering, Menofia University, Egypt | ||
| 4Basic and Applied Sciences Department, College of Engineering and Technology, Arab Academy for Science, Technology and Maritime Transport (AASTMT), Aswan, Egypt | ||
| 5Faculty of Energy and Environmental Engineering, British University in Egypt. | ||
| Abstract | ||
| Many advanced scientific phenomena of optics, light, and physics can be represented mathematically in the form of Volterra integral equations. In this paper, we studied the diffraction phenomena of the light beam. Since the most important category of scalar diffraction theories is the Fresnel diffraction integral. These integrals have been used in numerous studies on the propagation effects of structured light beams. These scalar diffraction theories have been widely utilized in studying the propagation of structured light. finally, we applied first-kind shifted Legendre polynomials to find the interpolate solutions of weakly singular Volterra integral equations of the second kind, where the Fresnel integral of diffraction will be involved. Numerical examples have been included in order to show the efficiency of the presented method. The exact solution of the represented example is compared to the approximate solution and the absolute error is calculated to illustrate the efficiency of the proposed method. | ||
| Keywords | ||
| Volterra Integral equations; Fresnel diffraction integral; Diffraction theory; Legendre polynomials | ||
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