Courses:

Help support MIT OpenCourseWare by shopping at Amazon.com! MIT OpenCourseWare offers direct links to Amazon.com to purchase the books cited in this course. Click on the Amazon logo to the left of any citation and purchase the book from Amazon.com, and MIT OpenCourseWare will receive up to 10% of all purchases you make. Your support will enable MIT to continue offering open access to MIT courses.

Why Inverse Problems?

Description for Spring 2002

This is the first time that this class is offered as follow-up to 2.710 (Introductory Graduate Optics). In its older incarnation, 2.717 itself was introductory. Not any more; as of the academic year '01-'02, 2.717 requires familiarity with at least the basics of Geometrical Optics, and Fourier Optics (aka "Physical Optics").

The focus (no pun intended!) this year is on two topics: Statistical Optics and Inverse Problems (i.e. Theory of Imaging). The two are very closely related, but seldom taught in conjunction. We will attempt to cover them with equal weight, but emphasizing the connections rather than the peculiarities of each. In particular, we will see how some topics in coherence (Statistical Optics) enter in the design of imaging systems and algorithms; inversely (again, no pun!) we will explore how image quality, indeed the very ability to form images, depend on randomness in optical fields. The ultimate objective is to understand imaging systems; at the same time, the very basic concepts of wave optics are turned inside-out leading, hopefully, to fluent, deep understanding of the subject of Optics itself. By its nature, the topic also involves probability and the theory of stochastic processes; these will be reviewed briefly at the beginning of the class, and will be recurring thereafter.

In a nutshell, the topics covered this semester are:

• Review of Fourier Optics, Probability and Stochastic Processes (~4 weeks)
• Light Statistics and Theory of Light Coherence (~2 weeks)
• The van Cittert-Zernicke Theorem and Applications of Statistical Optics (~3 weeks)
• Basic Concepts of Inverse Problems and Examples (~2 weeks)
• Information-theoretic View of Inverse Problems (~2 weeks)
  

Requirements

• 4 Homeworks (one per week during the first four weeks)
• 2 Projects, organized as follows:
• Project 1: Calculation of the Properties of Integrated Intensity (~2 weeks, 1-page report)
• Project 2: Study of Special Topics Relating to Coherence in Imaging Systems (~4 weeks, lecture-style presentation)

Alternative project topics (e.g. of special interest for your research projects) are also possible by prior arrangement. Projects are collaborative (teams of ~3-4). There are no quizes or final exam.

Grading

Textbooks

Goodman, Joseph W. Statistical Optics. Hoboken, NJ: Wiley-Interscience, 2000. ISBN: 9780471399162.

Bertero, Mario, and Patrizia Boccacci. Introduction to Inverse Problems in Imaging. London, NY: Taylor & Francis, 1998. ISBN: 9780750304351.