**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)

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