Optics

Properties of light

Wave particle duality:

Light is a wave

$E=h\nu were E is energy, h is planks constant and \nu is frequancy$

Absorption and Emission

Beer's law

Refraction

Ray tracing

Resolution

Resolution: The ability to separate two objects

A definition of Numerical Aperture

Look at a simple optical system:

Mathematical prediction of the Point Spread Function (PSF)

on the left we have the mathematical point source know as a delta function.

were

the intensity at the Fourier plain can be found by taking the Fourier transform of this function.

this has the same intensity at all points inside the aperture and zero outside. The second lens is now taking a Fourier transform on a box function the width of the aperture.

Substituting in the definition for NA

Now we go back to Resolution. How close together we can position two points and still distinguish them

Notes from:

http://web.mit.edu/2.710/Fall06/2.710-wk12-b-sl.pdf

https://links.uwaterloo.ca/amath353docs/set11.pdf

https://www.thefouriertransform.com/pairs/box.php

http://www.phys.unm.edu/msbahae/Optics%20Lab/Fourier%20Optics.pdf