### Project 1

(Posted on Lecture 14; Presentation on Lecture 18.)

Prepare a 1 hour lecture to present to your classmates on one of the topics listed below. You will prepare the lectures in teams of 3 or 4, and you can use any visual aids you like (blackboard, overheads, Powerpoint, PDF, VHS, DVD, … the classroom is equipped for everything!). The topics are from Goodman’s book (the relevant sections listed next to the topics). You should plan to share the hour-long lecture equally among project mates (i.e. a total of 20 or 15 min each, in either order). The presentations will be held for four hours on Lecture 18 (pizza and drinks will be served). Please prepare to ask George questions during the preceding office hours or by arranged meetings with the teams (no more than 2 meetings per team, please).

#### Topics

- Statistical Properties of spatially-integrated intensity (Section 6.1) Duration: 1 hour.
- Propagation of mutual coherence through a single-lens imaging system (Section 7.1) Duration: 1 hour.
- Calculating image intensity in a partially-coherent imaging system (Section 7.2) Duration: 1 hour.
- Partially coherent image formation and the importance of phase information (Sections 7.3, 7.4) Duration: 1 hour.

### Project 2

(Posted Lecture 19; Presentation on Lecture 26.)

Prepare a 1/2 hour talk describing your team’s results on the topics described below. You will be working in teams of 3 or 4 and again any visual aids for your presentation are acceptable. You should plan to share the presentation equally among project mates and leave sufficient time for questions at the end. One good way to do this is to plan for 8 min of presentation each (for a team of 3) or 6 min each (for a team of 4) and be prepared to answer questions from the rest of the class for 6 min at the end in team mode (i.e. either team member can answer). The presentations will be held on Lecture 26 for two hours (pizza and drinks will be served).

#### Part A

Read the following papers (at least the introductory parts, without getting bogged down by the details).

- Barbastathis, G., and A. Sinha. “Information Content of Volume Holographic Imaging.”
*Trends in Biotechnology*19, no. 10 (2001): 383-392. - O’Sullivan, J. A., R. E. Blahut, and D. L. Snyder. “Information-Theoretic Image Formation.”
*IEEE Transactions on Information Theory*44, no. 6 (1998): 2094-2123. - Neifeld, M. A. “Information, Resolution, and The Space-Bandwidth Product.”
*Optics Letters*23, no. 18 (1998): 1477-1479.

#### Part B

Use the information from the lectures and the papers to follow up with your own results on the following:

#### Topics

- Read the paper “Statistical solution to the two-point resolution problem” by G. Barbastathis,
*Proceedings of the OSA Topical Meeting on Integrated Computational Imaging Systems*(ICIS; Albuquerque, NM, November 2001) pp. 33-35. Discuss the difficulties involved in extending the analysis to more than two point sources, and use the Monte-Carlo method to produce numerical results instead for the dependence of the information on the space-bandwidth product (similar to Neifeld’s paper above). - Read the paper “Axial imaging necessitates loss of lateral shift invariance” by A. Stein, A. Sinha, and G. Barbastathis,
*Proceedings of the OSA Topical Meeting on Integrated Computational Imaging Systems*(ICIS; Albuquerque, NM, November 2001) pp. 26-28. Replace the authors’ calculation of resolution by use of the information theoretic metric (assuming Gaussian noise statistics). Discuss if a general proof is possible to strengthen the authors’ conjecture. - Read Goodman sections 8.1-3 about effects of random screens on image quality and do some simple simulations to evaluate the effect of random screens on information transfer through an imaging system.
- Calculate the information-theoretic content of the Radon transform (Born & Wolf 7th edition sec. 4.11; Bertero & Boccacci sec. 8.2, 11.1-3). Discuss in particular the results of radial sampling on the stability of the inverse problem, e.g. compare radial with rectangular sampling. Is the information content variable over the image?

#### Schedule

Please do all the necessary reading during the first week so we can discuss whatever is unclear in the papers during Lecture #21. This gives you two weeks to digest the reading further, do some calculations (Warning: some will take a long computing time so the earlier you start the better) and prepare your presentations. It’s ok if your presentations are not flashy, as long as there is substance.