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Fractional Fourier transformers through reflection.

Kurt Bernardo Wolf1, Guillermo Krötzsch

  • 1Centro de Ciencias Físicas, Universidad Nacional Autónoma de México, Cuernavaca, Morelos. bwolf@fis.unam.mx

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|June 7, 2002
PubMed
Summary

An arbitrary paraxial optical system combined with its reflection in a warped mirror acts as a pure fractional Fourier transformer. This research introduces the geometric action of reflection for optical systems and addresses aberration correction.

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Area of Science:

  • Optics
  • Fourier Optics
  • Optical Systems

Background:

  • Fractional Fourier transform (FrFT) is a generalization of the Fourier transform.
  • Optical systems can perform complex transformations on light.
  • Aberrations limit the performance of optical systems.

Purpose of the Study:

  • To demonstrate that a compounded optical system can function as a pure fractional Fourier transformer.
  • To introduce and develop the geometric action of reflection for paraxial optical systems.
  • To briefly address aberration correction using mirror warping.

Main Methods:

  • Axiomatic introduction of the geometric action of reflection.
  • Development of reflection geometry within the paraxial regime.
  • Analysis of compounded systems including reflection in a warped mirror.

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Main Results:

  • An arbitrary paraxial optical system compounded with its reflection in a warped mirror is shown to be a pure fractional Fourier transformer.
  • The geometric action of reflection is formally defined for paraxial optical systems.
  • Mirror warping is identified as a method for aberration correction.

Conclusions:

  • Compounding optical systems with reflections in warped mirrors offers a novel method for achieving pure fractional Fourier transformation.
  • The presented geometric framework provides a basis for understanding and designing such optical systems.
  • Warped mirrors present a potential solution for correcting aberrations in optical systems performing fractional Fourier transformations.