Optics 261: Interference and Diffraction

Course Objectives: This course provides an introduction and in-depth examination to wave models of optical propagation. This class considers properties and behavior of light in conditions when the wave nature of light becomes dominant. Topics that will be considered: Simple harmonic motion, complex representation of waves; scalar diffraction theory; Fresnel and Fraunhofer diffraction and application to measurement; diffraction and image formation; optical transfer function; coherent optical systems, optical data processing, and holography.

Prerequisites:
Physics: Introductory Electricity and Magnetism.
Math: Mth164, (Mth281 and Mth282 are desirable. Complex analysis is very helpful.)
Numerical Analysis: Calculation and graphing proficiency with MATLAB, Mathematica, Excel or equivalent.

Instructor:
Jim Fienup, Email: fienup@optics.rochester.edu
Office: Wilmot 410. Phone: 275-8009
Office Hours: Thursday 4:00-5:00 pm. Also, by appointment

Teaching Assistants:
(varies)

Class Periods: Tuesday, Thursday 9:40 - 10:55 am, Wilmot 116

Office Hours: Thursdays 4:00 - 5:00 pm

Recitation Periods: (varies)

Grading Basis:
20% Homework Assignments
30% Mid-term Exam
45% Final Exam
  5% Class Participation

Homework and Test Policy: There will be weekly homework assignments. These will be due one week from the hand-out date, during the class period. Late homework loses 10% of the grade for that homework per 24 hours, beginning immediately following class. The homework will be reviewed at the recitation sections. There will be one midterm exam, one final exam, and possibly one pop quiz (which would count as an additional homework assignment). There will be no make-up exams .

Lab: A 1-Credit Lab Course, OPT 198, will be held in Wilmot 5th floor. Its content is synergistic with OPT 261. It is required for Optics majors taking OPT 261; it is optional but highly recommended for others. There are six experiments.  Labs will be held every two weeks.  Per Adamson and another Professor run the lab.

Required Text:
Optics, 4th ed., E. Hecht, Addison-Wesley, NY, 2001
(this course does not follow Hecht per se, but many readings are from Hecht and problems from the book are assigned)

Recommended Texts:
Introduction to Modern Optics (2nd ed.), G.R. Fowles, Dover, ISBN 0-486-65957-7
Fundamentals of Optics (out of print), F.A. Jenkins & H.E. White
Physical Optics Notebook: Tutorials in Fourier Optics (Available at www.spie.org)
Schaum’s Outline of Theory and Problems of Optics, E. Hecht, McGraw-Hill,
ISBN 0-07-027730-3

Optics 261: Interference and Diffraction: Topics Covered
1. Overview of models of light; Examples of diffraction

2. Simple harmonic motion and addition of waves (Ch. 2)

3. Propagating waves (Ch. 2)
Complex representation of waves:
Plane waves: sign convention, propagation directions
Spherical waves:
Converging waves
Diverging waves
Paraxial approximation

4. Superposition of Waves (Ch. 7)
Addition of propagating waves: Introductory interferometry (Ch. 9.1-9.6)
Two Beam Interference:
Division of Wavefront Interferometers (Young’s Experiment and variants)
Division of Amplitude Interferometers (Michelson Interferometer)
Multiple Beam Interference:
Division of Wavefront Interferometers (Multiple coherent oscillators)
Division of Amplitude Interferometers (Fabry-Perot interferometer)

5. Diffraction theory: (Ch. 10)
Huygen’s principle,
Fresnel Formulation of Huygen’s Principle
Rayleigh-Sommerfeld diffraction
Paraxial Approximation
Fresnel diffraction
Fraunhofer diffraction

6. Diffraction from Apertures
Fraunhofer and Fresnel Diffraction from rectangular apertures,
Fraunhofer diffraction from circular apertures,
Fresnel diffraction from straight edges;

7. Fourier series and integrals: Dirac delta function, Fourier theorems (Ch. 11)

8. Wave model of lenses and imaging

9. Diffraction using a transform lens

10. Coherent Optical Fourier Processor (Ch. 10.2, Hand-out)
Amplitude Impulse Response
Coherent Transfer Function

11. Introduction to Holography (Ch. 13.3)

12. Incoherent Imaging
Intensity Impulse Response
Resolution
Incoherent Transfer Function

13. (Time permitting:) Array Theorem (Ch. 11.3.3), Fresnel zones and zone plates