Spectral Unmixing [http://zeiss-campus.magnet.fsu.edu/articles/spectralimaging/introduction.html](http://zeiss-campus.magnet.fsu.edu/articles/spectralimaging/introduction.html)
Multiphoton Microscopy [http://zeiss-campus.magnet.fsu.edu/referencelibrary/multiphoton.html ](http://zeiss-campus.magnet.fsu.edu/articles/spectralimaging/introduction.html)
Fluorescence Lifetime Imaging Microscopy (FLIM) http://www.iss.com/microscopy/components/FastFLIM.html
# Objectives # Optics ## Properties of light ### Wave particle duality: Light is a wave  [](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 [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-09/image-1633036148165.jpg) ### **A definition of Numerical Aperture** [](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 [](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 [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/image-1636115856897.jpg) ### **Look at a simple optical system:** [](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. [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633098662004.jpg) were [](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. [ or ](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633098872812.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. [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633099073037.jpg) or [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633100364032.jpg) Substituting in the definition for NA [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633101363801.jpg) [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633101383326.jpg) [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633102388922.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 [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633114549481.jpg) [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633114570726.jpg) [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633114634257.jpg) [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633114702326.jpg) [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633114780018.jpg) [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633114748922.jpg) [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633115867409.jpg) [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633115434455.jpg) [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-10/image-1633697496290.jpg) More intuitive approach [](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 # Sampling ## How does digital sampling affect resolution ##### Look at imaging these object with a digital camera ##### How close together do pixels need to be? [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/image-1637163325668.jpg) ##### Sampling over time: ##### How often do you need to image a moving sample [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/image-1637163343425.jpg) ### Nyquist theory states that you should sample more than 2 X the frequency that you expect. #### Over sampling [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/image-1637166398425.jpg) #### Nyquist sampling [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/image-1637166436296.jpg) #### Under sampling causes aliasing [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/image-1637166449555.jpg) ### Optical Transfer Function MTF [](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/image-1637271420704.jpg)[ ](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/image-1637272498227.jpg)[](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/image-1637272536733.png) ### When objects get close together the contrast decreases. ##### MTF = Image Modulation/Object Modulation ##### MTF = 2(φ - cosφsinφ)/π and ##### φ = cos-1(λν/2NA) ##### ##### The Optical Transfer function is the Modulation transfer function times a phase component. ##### OTF = MTF × eiφ(f) ### Camera bit depth 0 or 1 00 or 01 or 10 or 11 000 or 001 or 010 or 011 or 100 or 101 or 110 or 111 and so on [ ](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/image-1637330338226.jpg) Jpg is 8 bit Tiff can be 16 bit references [https://imb.uq.edu.au/research/facilities/microscopy/training-manuals/microscopy-online-resources/image-capture/nyquist-conditions](https://imb.uq.edu.au/research/facilities/microscopy/training-manuals/microscopy-online-resources/image-capture/nyquist-conditions) [https://microscopy.berkeley.edu/courses/dib/sections/02images/sampling.html](https://microscopy.berkeley.edu/courses/dib/sections/02images/sampling.html) https://ocw.mit.edu/courses/mechanical-engineering/2-71-optics-spring-2009/video-lectures/lecture-22-coherent-and-incoherent-imaging/MIT2\_71S09\_lec22.pdf # Working in the IGB Core #### Expect to walk into a room with a fully functional instrument #### Let a core staff person know if you see a problem #### Clean up when you leave #### Acknowledge the IGB Core as: #### “Core Facilities at the Carl R. Woese Institute for Genomic Biology" #### Let us know when you publish #### Collaborations with the core facilities staff can be beneficial in the development of unique methods or capabilities.