MSN 510 Notes

2. Fundamental Concepts in Image Formation and Processing

Outline• Summary: Huygens-Fresnel Principle• The Fourier Transform• Diffraction from a single aperture• Convolution• Coherence of a lightwave: White light vs laser• What is a Lens?• Fourier Transforming property of a lens• Optical Filtering• The Eye• Magnifying Glass• A Simple Microscope

Huygens-Fresnel Principle• Each Point acts as a point source

• Complex wave amplitude is calculated by adding up all contributions from source points

Radiation pattern

• A polar plot of the intensity of from a source (measured far away from the source)

The Fourier Transform

• We write a 1D or 2D function as the sum of sinusoids.

Convolution and fourier transforms

Convolution

• Formal Definition

Diffraction from a single aperture

• Slit

Diffraction and FT

Coherence• A measure of how sinusoidal the light is

– Or the length over which it interferes with itself

What is a lens?

Ray transfer matrices

Free Space Thin lens

Interesting Example