OPTI512R  Linear Systems and Fourier Optics University of Arizona

 Science

This class is a firstyear course in Linear Systems and Fourier Optics as part of the graduate program in Optical Science and Engineering at the University of Arizona. The course covers linear systems theory, Fourier transforms, diffraction, and Fourier optics all from the perspective of propagating electromagnetic fields. The courses uses two textbooks, "Linear Systems, Fourier Transforms, and Optics," by Jack D. Gaskill (Chapters 1  9), and "Fourier Optics, 1st Edition," by J. W. Goodman (chapters 4  6).
For uptodate class announcements, you can follow Prof. Tyo on Twitter @OPTIProfTyo or search on the class hashtag: #OPTI512R. You can also check out the public facebook page for the class: UA Opti512r
Students interested in taking this class for credit should contact the College of Optical Sciences Distance Learning Program through the website at http://www.optics.arizona.edu/academics/default.htm


Lecture 1 Notes: Complex Numbers Review and Mathematical Representation of Physical Quantities
For many applications we find that it is much easier to represent our physical quantities in terms of complex numbers rather than just using real numbers alone. The concept of complex numbers comes from the continuation of functions such as squareroot and logarithm that only apply to positive numbers in their traditional definitions. Figure 1 shows the function √ x. Other functions like ln x, sinx, etc., also have limits on their arguments, and complex numbers allow us to define these functions over the full range of real numbers.


Lecture 2 Notes: Special Functions and The Impulse Function
We will be working not just with functions, but with scaled and shifted versions of functions.

 video
Lecture 3: Harmonic Analysis and the Fourier Series

Lecture 3 Notes: Harmonic Analysis and the Fourier Series
Throughout this course (and in many areas of mathematical physics) it is extremely convenient to write one function of interest as a weighted superposition of another set of functions whose behavior we are familiar with. If our system is linear, we can then analyze the behavior of the system on our function of interest by breaking it up into its components parts and adding up the results. This is the basis of functional analysis which is closely related to linear algebra. For that reason, many geometrical concepts can be leveraged in functional analysis to help understand what’s going on.
Customer Reviews
GREAT Lectures!!!
My first Optics class was at the graduate level as a basis for future remote sensing endeavors. Needless to say, I wasn't prepared. While I used a textbook by Pedrotti for my Geometric optics, this lecture gave me a great understanding of wave optics. I would highly recommend this to anyone interested in Optics whose already taken a Fourier class. This professor's teaching methods and associated course notes are amazing.
Make it a course please
This collection is great for optics students, but please make it a iTunes U Course~