The College of Optical Sciences (OSC) at the University of Arizona has long offered a course called "OPTI512R: Fourier Transforms, Linear Systems, and Optics" in its graduate program. The course was initiated and designed by Prof. Jack Gaskill, and was taught largely out of a textbook by the same name that was published in 1978. When Prof. Tyo joined OSC in 2006, he was asked to take over the course, as Prof. Gaskill had retired some years earlier.
I came to the class with an electrical engineer’s classic understanding of linear systems in time and frequency. I quickly came to realize that, at that time, Prof. Gaskill's textbook was the only one written from the perspective of an optical engineer, who needs to take 2D spatial Fourier transforms instead of 1D temporal ones. This difference gives rise to several subtle but important stylistic requirements that Prof. Gaskill captured well in his text. As with most instructors, I began to add my own take on the material over the years. Andrey Alenin joined my group in 2010; he showed a strong interest in both the pedagogy and the presentation of the course material, and the two of us have worked together to refine the presentation over the years. As of the writing of this Field Guide, Prof. Gaskill’s text is still the primary reference in the class. However, when John Greivenkamp discussed with us the possibility of writing a Field Guide on this topic, it gave us the opportunity to go through the notes and reorganize them into a sequence more suited for this handbook format.
The process is, of course, circular. During the current semester of teaching OPTI512R, while we were completing this Field Guide, we have realized that the entire structure of the course will need to be revised going forward. The efforts undertaken to write this book have provided a new perspective on the classic course content.
J. Scott Tyo
College of Optical Sciences
University of Arizona