# Sampling ## How does digital sampling affect resolution ##### Look at imaging these object with a digital camera ##### How close together do pixels need to be? [![image-1637163325668.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/scaled-1680-/image-1637163325668.jpg)](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 [![image-1637163343425.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/scaled-1680-/image-1637163343425.jpg)](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 [![image-1637166398425.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/scaled-1680-/image-1637166398425.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/image-1637166398425.jpg) #### Nyquist sampling [![image-1637166436296.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/scaled-1680-/image-1637166436296.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/image-1637166436296.jpg) #### Under sampling causes aliasing [![image-1637166449555.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/scaled-1680-/image-1637166449555.jpg)](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/image-1637166449555.jpg) ### Optical Transfer Function MTF [![image-1637271420704.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/scaled-1680-/image-1637271420704.jpg)](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)[![image-1637272536733.png](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/scaled-1680-/image-1637272536733.png)](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 [ ![image-1637330338226.jpg](https://www-app.igb.illinois.edu/core-docs/uploads/images/gallery/2021-11/scaled-1680-/image-1637330338226.jpg)](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