# Optics

## Properties of light

### Wave particle duality:

Light is a wave

![](https://latex.codecogs.com/svg.image?E=h%5Cnu&space;were&space;E&space;is&space;energy,&space;h&space;is&space;planks&space;constant&space;and&space;%5Cnu&space;is&space;frequancy "E=h\nu were E is energy, h is planks constant and \nu is frequancy")

[![image-1630006591207.png](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-08/scaled-1680-/image-1630006591207.png)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-08/image-1630006591207.png)

### Absorption and Emission

Beer's law

Refraction

## Ray tracing

## Resolution

### **Resolution:** The ability to separate two objects

[![image-1633036148165.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-09/scaled-1680-/image-1633036148165.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-09/image-1633036148165.jpg)

### **A definition of Numerical Aperture**

[![image-1633036910068.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-09/scaled-1680-/image-1633036910068.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-09/image-1633036910068.jpg)

#### Fourier transform:

Transform from real space to frequency space

[![image-1636115576367.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/scaled-1680-/image-1636115576367.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/image-1636115576367.jpg)

Now we look at a real square wave and frequency space

[![image-1636115856897.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/scaled-1680-/image-1636115856897.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/image-1636115856897.jpg)

### **Look at a simple optical system:**

[![image-1633036975307.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-09/scaled-1680-/image-1633036975307.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-09/image-1633036975307.jpg)

#### Mathematical prediction of the Point Spread Function (PSF)

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

[![image-1633098662004.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/scaled-1680-/image-1633098662004.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633098662004.jpg)

were

[![image-1633098725511.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/scaled-1680-/image-1633098725511.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633098725511.jpg)

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

[![image-1633098872812.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/scaled-1680-/image-1633098872812.jpg) or ](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633098872812.jpg)

[![image-1633100310895.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/scaled-1680-/image-1633100310895.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633100310895.jpg)

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.

[![image-1633099073037.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/scaled-1680-/image-1633099073037.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633099073037.jpg)

or

[![image-1633100364032.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/scaled-1680-/image-1633100364032.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633100364032.jpg)

Substituting in the definition for NA

[![image-1633101363801.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/scaled-1680-/image-1633101363801.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633101363801.jpg)

[![image-1633101383326.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/scaled-1680-/image-1633101383326.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633101383326.jpg)

[![image-1633102388922.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/scaled-1680-/image-1633102388922.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633102388922.jpg)

[![image-1633102956154.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/scaled-1680-/image-1633102956154.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633102956154.jpg)

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

[![image-1633114549481.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/scaled-1680-/image-1633114549481.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633114549481.jpg)

[![image-1633114570726.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/scaled-1680-/image-1633114570726.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633114570726.jpg)

[![image-1633114634257.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/scaled-1680-/image-1633114634257.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633114634257.jpg)

[![image-1633114702326.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/scaled-1680-/image-1633114702326.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633114702326.jpg)

[![image-1633114780018.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/scaled-1680-/image-1633114780018.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633114780018.jpg)

[![image-1633114748922.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/scaled-1680-/image-1633114748922.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633114748922.jpg)

[![image-1633115867409.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/scaled-1680-/image-1633115867409.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633115867409.jpg)

[![image-1633115434455.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/scaled-1680-/image-1633115434455.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633115434455.jpg)

[![image-1633697496290.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/scaled-1680-/image-1633697496290.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633697496290.jpg)

More intuitive approach

[![image-1633697667324.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/scaled-1680-/image-1633697667324.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633697667324.jpg)

Notes from:

[http://web.mit.edu/2.710/Fall06/2.710-wk12-b-sl.pdf](http://web.mit.edu/2.710/Fall06/2.710-wk12-b-sl.pdf)

[https://links.uwaterloo.ca/amath353docs/set11.pdf](https://links.uwaterloo.ca/amath353docs/set11.pdf)

[https://www.thefouriertransform.com/pairs/box.php](https://www.thefouriertransform.com/pairs/box.php)

[http://www.phys.unm.edu/msbahae/Optics%20Lab/Fourier%20Optics.pdf](http://www.phys.unm.edu/msbahae/Optics%20Lab/Fourier%20Optics.pdf)

How to Chose the Optimal Objective Dr. Sebastian Gliem

## Super Resolution Techniques