International School

MSPAS 2010

**(XVI-th Edition)**

"MULTIDIMENSIONAL SIGNAL PROCESSING AND ANALYSIS SCHOOL: METHODS, ALGORITHMS, TECHNOLOGIES, APPLICATIONS"

- dr. George NEMES

**Title: Optical systems and laser beam characterization by matrix methods
- connection to multidimensional signal theory**

(2 lectures of 90 minutes each = 180 min.)

*Introduction: Link between multidimensional signals,
geometrical optics, and laser beam characterization* . 10 min.

**Lecture #1. Matrix treatment of optical systems**
(geometrical optics, paraxial, 2x2 case) . 2 x 40 min.

Outline:

- Preliminaries and assumptions.

- Basic concepts: rays and optical systems represented by matrices.

- Elementary optical systems: free-space and thin lens.

- Cascading (combining) optical systems.

- Examples.

- General ABCD-type optical systems.

Level and intended audience: Students with little knowledge on optics. Good for beginners who are interested in matrix optics. Give the very basics of 2x2 matrix treatment of linear (no aberration) optical systems. Preparatory for understanding beam propagation in optical systems. Mode of presentation: Real-time writing at black/white board (old classical stile).

**Lecture #2. Beams . matrix treatment, Part 1: The idealized
gaussian beam (IGB) and the real beams** (paraxial, 2x2 case) - 2 x 45 min.

Outline:

Part 1 . Ideal gaussian beam (IGB).

- Beam definition.

- The ideal gaussian beam (IGB).

- Physical parameters for IGB.

- Average description of IGB (moments up to second-order) . the beam matrix P.

- Beam propagation through optical systems . matrix method.

- Examples.

Part 2 . Real beams.

- Differences between a real beam and the IGB.

- Definition of spatial parameters for real beams. The M2 parameter.

- Measuring real beams.

- Usefulness and limitations of the beam propagation ratio M2.

- Examples.

Level, intended audience, mode of presentation: Same as for Lecture #1.