Properties of in-order self-similarity function in the Frensel region for the Sierpinski carpet grating

Mario Marcelo Lehman; D. Patrignani; L. De Pasquale; J. L. Pombo

doi:10.1117/12.284206

24 October 1997 Properties of in-order self-similarity function in the Frensel region for the Sierpinski carpet grating

Mario Marcelo Lehman, D. Patrignani, L. De Pasquale, J. L. Pombo

Proceedings Volume 3159, Algorithms, Devices, and Systems for Optical Information Processing; (1997) https://doi.org/10.1117/12.284206
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

Some regular fractals, as Cantor bars and Sierpinski carpet, can be obtained as multiplicative superposition of periodical functions. Adding an exponent to each of this functions we can obtain a system to apply in optics for image processing, because different combinations can be achieved. A parameter to characterize the fractal structures in the Fresnel and Fraunhofer regions is introduced. It is called the in-order self-similarity function, which permit us to determine the periodical components filtered from the initial structure. The application is developed mainly for 2D fractals as the Sierpinski carpet.

Citation Download Citation

Mario Marcelo Lehman, D. Patrignani, L. De Pasquale, and J. L. Pombo "Properties of in-order self-similarity function in the Frensel region for the Sierpinski carpet grating", Proc. SPIE 3159, Algorithms, Devices, and Systems for Optical Information Processing, (24 October 1997); https://doi.org/10.1117/12.284206

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