Course Description: The first portion of this course provides a review of a number of mathematical topics, including convolution, Fourier ransformation, 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.

Course Objectives: After completing this course, you will: 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.

Course Outline by Topical Areas:

Part I: Review of Mathematical Background

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

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

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

calculate the Fraunhofer diffraction pattern irradiance for s 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

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

Course Requirements:

Homework: 3-4 homework assignments

Examinations: Take-home final

Notes:

This course may not be included in an NTU Master's Degree Program.

Degree Applicability:

CE[NA]	CH[NA]	CS[NA]	EE[NA]	EM[NA]	ESM[NA]	MAT[NA]
MBA[NA]	ME[NA]	MES[NA]	MSE[NA]	SE[NA]	SY[NA]

Click here for further information on degree applicability.

NTU Semester Credit Hours: 1
Number of Lecture Hours: NA
Days Class Meets on Campus: NA

Contributing Scholar:
Dr. Jack D. Gaskill
Optical Sciences Ctr
University of Arizona
Tucson, AZ   85721


jgaskill@arizona.edu

Note: Contributing Scholars are responsible for the design, organization, content, and presentation of NTU courses. Online classroom management, student management, and other matters related to academic administration of courses are the responsibility of support "Faculty". Either person is often called "Instructor". To identify and differentiate between these roles, we use the terms "Contributing Scholar" and "Faculty".

Academic/Administrative Contact:  
Ms. Pam Shack
Phone: 520-626-4573
Fax: 520-626-1102
pshack@email.arizona.edu


Textbooks: (Order Materials)

1.	Linear Systems, Fourier Transforms and Optics, Jack D. Gaskill, John Wiley and Sons, 1978, ISBN 0471292885.