Diffraction and Interferometry (3 units). Interference and interferometry; concepts of coherence; diffraction theory; Fresnel and Fraunhofer diffraction; optical transfer function; Gaussian beam propagation; holography; volume diffraction; speckle. Prerequisites: OPTI 501 and 512R

Meeting Times:
Lectures: T & Th 9:30-10:45
Recitation: W 2:00-4:00

Course Outline (75-minute lectures):

1. Introduction to Theory of Interferometry and Diffraction

2. Maxwell's Equations

3. Wave Equation

3.1 Transverse waves
3.2 Plane waves
3.3 Complex representation
3.4 Spherical waves
3.5 Linear superposition
3.6 Polarization

4. Basic Interference

4.1 Two plane waves
4.2 Two spherical waves
4.3 Plane wave ans spherical wave
4.4 Plane wave and cylindrical wave
4.5 Methods of beam division

5. Concepts of Coherence

5.1 Coherence time
5.2 Coherence length
5.3 Theory of partial coherence
5.4 Fringe visibility reduction
5.5 Fringe localization
5.6 Correlation interferometry

6. Classical Two-Beam Interferometers

6.1 Plane parallel plate
6.2 Fizeau
6.3 Michelson
6.4 Twyman-Green
6.5 Mach-Zehnder
6.6 Lateral shear
6.7 Radial shear

7. Multiple Beam Interference

7.1 Airy’s formula
7.2 Absorbing coatings
7.3 Fabry Perot (plane and spherical)
7.4 FECO

8. Multilayer Films

8.1 Theory
8.2 AR film
8.3 High reflectance film

9. Direct Phase Measurement

9.1 Methods of phase shifting
9.2 Algorithms

10. Preliminary Description of Diffraction

11. Mathematical Description of Diffraction

11.1 Helmholtz equation
11.2 Green’s theorem
11.3 Integral theorem of Helmholtz and Kirchhoff
11.4 Kirchhoff formulation of diffraction by a plane screen
11.5 Kirchhoff boundary conditions
11.6 Fresnel-Kirchhoff diffraction formula and Huygens-Fresnel principle
11.7 Rayleigh-Sommerfeld formulation of diffraction by a plane screen
11.8 Plane wave spectrum approach
11.9 Babinet's principle

12. Fresnel and Fraunhofer Diffraction

12.1 Fresnel approximation
12.2 Fraunhofer diffraction

13. Fresnel Diffraction

13.1 Fresnel zones
13.2 Circular aperture
13.3 Zone plate
13.4 Rectangular aperture
13.5 Large aperture - long slit and stright edge
13.6 Talbot images

14. Fraunhofer Diffraction

14.1 Single slit
14.2 Rectangular aperture
14.3 Circular aperture
14.4 Double slit
14.5 Multiple slits. Binary diffraction gratings
14.6 Sinusoidal amplitude and phase gratings

15. Optical Transfer Function

15.1 Coherent imaging
15.2 Incoherent imaging

16. Gaussian Beams

16.1 Basic theory
16.2 Propagation through optical systems

17. Holography

17.1 Physical description
17.2 Mathematical proof of reconstruction process
l7.3 Minimum reference beam angle to separate orders
17.4 Recording and playback geometry
17.5 Light sources and recording materials
17.6 Volume holograms
17.7 Applications

18. Speckle

18.1 Physical origin
18.2 Applications

• homework 20%
• two in-class, closed book exams 40%
• final exam 40%

• Born and Wolf: Principles of Optics (Pergamon Press)
• Goodman: Introduction to Fourier Optics (McGraw-Hill
• Hecht: Optics (Addison-Wesley)