Optics
Properties of light
Wave particle duality:
Light is a wave
Absorption and Emission
Beer's law
Refraction
Ray tracing
Resolution
Resolution: The ability to separate two objects
A definition of Numerical Aperture
Fourier transform:
Transform from real space to frequency space
Now we look at a real square wave and frequency space
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.
or
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.
or
Substituting in the definition for NA
Now we go back to Resolution. How close together we can position two points and still distinguish them
More intuitive approach
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
How to Chose the Optimal Objective Dr. Sebastian Gliem
Super Resolution Techniques