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Design and Analysis of Two-Dimensional Optical Operators for Edge Detection Applications

Mohammadi, Hadi | 2025

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 58292 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Akbari, Mahmoud; Khavasi, Amin
  7. Abstract:
  8. In this PhD thesis, we propose a structure capable of performing two dimensional isotropic differentiation, gradient and divergence computation. This differentiator works based on exciting surface plasmon polaritons at an air-silver interface. In order to excite surface plasmon polaritons, Kretschmann configuration is exploited. For the purpose of implementing the mentioned operator, our proposed two dimentional differentiator is, in fact, a combination of two Kretschmann configurations that are introduced into thetrahedral structure that two of its sides are silver-coated. At the next step, our proposed structure is compared with other differentiators in the literature and it is shown that its performance is excellent. It is worth mentioning that our proposed differentiator is able to compute either the gradient of the field distribution of a polarized light beam or the divergence of the field distribution of an unpolarized light beam. In contrast with its other metasurface-based counterparts that are bulky, complicated and expensive, our proposed differentiator features low-cost, simple and compact structure. In addition, it has high operational gain. we also introduce two ideal cases of spatial differentiators and it is shown that most differentiators in the real world has a transfer function similar to the second case. In this chapter we see that if the resolution of these ideal differentiators is computed by Rayleigh criterion, then the gain and resolution are linearly dependent. At previous works, this linear dependency is used as a figure of merit whereby the resemblance of the transfer function corresponding to a real differentiator and the ideal case are compared quantitatively. In this PhD thesis, it is shown that the Rayleigh criterion is not able to determine the correct value of the resolution for the ideal differentiators. Hence, the figure of merit extracted from the linear dependence between gain and resolution computed by Rayleigh criterion is not correct. Three conditions are proposed that can determine the correct value of resolution. Therefore, these triple conditions can be used as a replacement for Rayleigh criterion. In addition, we observe that if the resolution of these ideal differentiators is computed by the mentiond triple conditions, then the spatial bandwidth and resolution are linearly dependent. In this way, the correct form of figure of merit is obtained and is used to assess the performance of a number of the differentiators in the literature.
  9. Keywords:
  10. Transfer Function ; Two-Dimensional Optical Differentiators ; One-Dimensional Optical Differentiators ; 4f Operators ; Optical Operators ; Optical Metasurfaces ; Figure-of-Merit (FoM) ; Edges Detection

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