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