MAS.856: SYNTHETIC HOLOGRAPHY

Spring 2001

Course Information

Instructor: Professor Stephen A. Benton

Secretary: Dina Freedman, Office: E15-4l6, Tel.: x3-0632

Office hours: by appointment via Ms. Freedman (usually Tues. & Thurs. afternoons)

Teaching Assistants: To Be Named

Class meets Tues. & Thurs. mornings, 10:30 am to 12:00 noon, in Room E15-335.

The first meeting of the class is on Tuesday, Feb. 6, 2001.

Class Schedule:

Course Outline

1. Introduction: Issues in synthetic holography. Scope of the course.

2. Elements of Fourier Optics: Complex signals, two-dimensional spatial frequencies, holography in 3-space, 3-D ray tracing, the sampling theorem, space-bandwidth products, digital Fourier holograms.

3. Computer-Generated Holograms: Binary representations (cells versus fringes), sampling and quantization effects, fast Fourier transforms, information reduction schemes, recording of CG holograms.

4. Holographic Stereograms: One- and two-step methods, taxonometric analysis, aberration effects in stereograms, perspective distortions. Fundamental limits: diffraction limits, the 1/N law.

5. Practical Holo-Stereography: Image limitations, rendering and recording, mastering and transferring. Issues of color, size, and angle of view.

6. Projection and Transmission of Holographic Images: Directly and indirectly viewed holograms, optical and electronic transmission, sampling and compositing techniques for optical and electronic holograms, display technologies.

 

Conduct of the Course

This subject will explore ideas for the creation and presentation of holographic images derived from digital data. That is, the synthesis of holograms of objects that do not, or cannot, exist. The emphasis is clearly on 3-D imaging, but some of the applications to holographic optical elements and to optical information processing are straightforward and useful, and will occasionally be cited. But in general we will concentrate on the conceptual, theoretical and practical aspects of new forms of computer-based holographic imaging.

This course has been presented only a few times, and is still very much a work in progress. As such, it will be, to a large extent, a workshop in the development of a new course. In fact, no comparable class exists anywhere in the world, and most of the subject matter is the subject of ongoing basic research. Thus the class will be conducted primarily as a seminar course, with attendance limited to ten persons. MAS 450/854 "Holographic Imaging" or equivalent background is a prerequisite, and many concepts from linear systems theory will also be employed. There is no textbook for this course; a series of research and review papers will be read and discussed. Seminar participants are expected to contribute to these discussions, and to the resolution of technical questions as they arise. We hope that there will be occasional laboratory exercises, depending on the availability of experimental and computer resources, and people to get them going.

Participants will be expected to complete a small research project at the end of the semester, which can be either written or experimental (as circumstances permit).

Suggested Background Reading:

books:

W.T. Cathey, Optical Information Processing and Holography.
(John Wiley & Sons, NY, 1974; recently reprinted) esp. Chs. 1 & 2

J.D. Gaskill, Linear Systems, Fourier Transforms, and Optics,
(John Wiley & Sons, NY, 1978) esp. Chs. 2 & 10

J.W. Goodman, Introduction to Fourier Optics,
(McGraw-Hill, San Francisco, 1968; 2nd edn. 1996) ISBN 0-07-024254-2; esp. Ch. 2

L.P. Yaroslavskii & N.S. Merzlyakov, Methods of Digital Holography,
(Consultants Bureau, Plenum Publishing Co., NY, 1980)

articles:

W.J. Dallas, "Computer-Generated Holograms," in
B.R. Frieden, ed., The Computer in Optical Research,
(Springer-Verlag, NY, 1980) Ch. 6, pp. 291-366

G. Tricoles, "Computer Generated Holograms: an historical review,"
Applied Optics
, 26-20, pp. 4351-4360 (15 October 1987)

Plus articles as circulated.

 

FIRST READING ASSIGNMENT: Goodman’s Ch. 2, as handed out, for discussion starting Thursday 2/8/01.