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Introduction to Fourier Optics (SC017)

Length: 5 hours
Course Level: Intermediate
Instructor: Jack D. Gaskill, Univ. of Arizona (United States)
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Course Details

CDV017: The first portion of this course provides a review of a number of mathematical topics, including convolution, Fourier transformation, harmonic analysis, and the analysis of linear shift-invariant systems. Next, the instructor discusses the phenomenon of diffraction, the effects of lenses on diffraction, and the propagation of Gaussian beams. Finally, the concepts of Fourier analysis and linear systems are combined with diffraction theory to describe the image-forming process in terms of a spatial filtering operation, both for coherent light and for incoherent light.

Learning Outcomes

This course will enable you to:

  • understand convolution, Fourier transform, harmonic analysis, the analysis of linear systems, and the general behavior of diffraction in the Fresnel and Fraunhofer regions
  • be able to calculate the Fraunhofer diffraction pattern irradiance associated with various apertures and diffracting objects
  • understand the effects of diffraction on image formation and how diffraction influences image resolution
  • be able to calculate the impulse response, transfer functions and behavior of various image-forming systems, both for coherent and incoherent light
  • understand Gaussian beam propagation and image formation in terms of a linear spatial filtering operation

Part I: Review of Mathematical Background (55 minutes)

  • define several special functions
  • summarize the mathematical operation of convolution
  • summarize the Fourier integral and Fourier series operations
  • describe the properties and theorems of the Fourier transform

Part II: Analysis of Linear Shift-invariant Systems (53 minutes)

  • explain the theory
  • characterize the behavior of such systems by their impulse response functions
  • behavior of such systems in the frequency domain
  • functions of two independent variables

Part III: Diffraction in the Fresnel and Fraunhofer Regions (52 minutes)

  • phenomenon of diffraction and its importance
  • Fresnel conditions and the region of validity
  • Fraunhofer conditions and the region of validity
  • effects of lenses on the diffraction phenomenon

Part IV: Fraunhofer Calculations and Gaussian Beam Propagation (52 minutes)

  • calculate the Fraunhofer diffraction pattern irradiance for several diffracting objects
  • Fraunhofer diffraction patterns
  • explain how the propagation of Gaussian beams is described by the Fresnel diffraction equation
  • surprising behavior of Gaussian beams

Part V: Analysis of Image-forming Systems (52 minutes)

  • effects of diffraction on image-forming process
  • define coherent impulse response and transfer functions for an imaging system
  • demonstrate effects of pupil shape on the nature of coherent images
  • define incoherent point-spread function (PSF) and optical transfer function (OTF)
  • effects of aberrations on performance

Copyright 1999,SPIE

Intended Audience

Scientists and engineers who need to become familiar with or learn more about the
effects of diffraction on the propagation of optical wavefields and on the performance of image-forming


Jack D. Gaskill is Professor Emeritus of Optical Sciences at the University of Arizona where, for more than 30 years, his teaching activities were devoted primarily to the applications of Fourier theory in optics. He has taught more than 40 off-campus short courses in Fourier optics and related subjects. Gaskill is author of the textbook, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978), and is a Past President of SPIE.


Formerly CDV0199.
Recommended Text: Linear Systems, Fourier Transforms, and Optics (Wiley,1978) by Jack D. Gaskill. To order this textbook, contact John Wiley and Sons at (908)469-4400.

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