Fourier 1 - Perspective and Equations

Here I describe the background and intuition behind Fourier analysis and I also introduce you to the DFT equations together with a recap of complex arithmetic for those who may be a bit rusty from school days.
The FT is essential to a modern understanding of optics, including how a microscope works. You may need to view this video again after seeing later episodes in this series to get the most out of it.
CONTENTS
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00:40 Intuition of the Fourier transform (FT)
05:18 Why bother? (Fourier optics and the convolution theorem)
10:42 Inputs to the FT (Review of complex arithmetic)
21:36 Anatomy of the Discrete FT (DFT) equations
30:21 Conclusions
SUPPORT PUMA
============
PUMA is an open source microscopy project. You can help support the project by:
1. Become a Patron: / pumamicroscope
2. Donate via PayPal: www.paypal.com/donate/?hosted...
3. Simply subscribing to this RUclips channel, like, comment and share these videos.
4. Spread the word - post the news about PUMA and link to this RUclips channel on your social media sites and any other outreach method (tell your friends, colleagues, students or teachers and lecturers about PUMA, for example).
5. Consider purchasing your optics and related supplies from our affiliated online optics store, OptArc.co.uk ( www.optarc.co.uk/ )
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LINKS TO REFERENCED VIDEOS
==========================
Convolution:
• Convolution - A new vi...
OTHER LINKS
===========
If this video seems a bit 'tough' and you need some background knowledge then see my series on 'Photology':
Photology 1
• Introduction to light ...
Photology 2
• Photology 2: Individua...
Photology 3
• Photology 3: Represent...
Photology 4
• Photology 4: Coherence
Photology 5
• Photology 5: Seeing El...
You may also benefit from seeing my series on 'C Programming for Image Analysis' (CPIA), first video in the series is here:
• 00. Introduction to C ...
FOR FURTHER INFORMATION
=======================
1. Open access write-up about PUMA on the FreeCAD blog:
blog.freecad.org/2023/02/13/a...
2. The official PUMA GitHub page where you can download the specs and source files to build or customise your own PUMA system:
github.com/TadPath/PUMA
3. The scientific peer reviewed publication on PUMA that was published in 2021 in the Journal of Microscopy (a journal of the Royal Microscopical Society) available here:
pubmed.ncbi.nlm.nih.gov/34151...
onlinelibrary.wiley.com/doi/1...
Thanks for your interest in the PUMA microscope system.
PJT 18/06/24

[@TheNadOby]

The beginning of the video is one of the best visualization demonstrations of the Fourier transformation.
You can edit it to a standalone video and frame it.

[@jerzmacow]

Wow, I finally understand how ffts actually work!

[@xMisterXHDx]

Greetings from Germany, thank you for this Video. 🙂 👍

[@AliMoeeny]

OMG, it actually works. I have known and even used FFT for many years but this demonstration at 4:00 is so striking. Thank you

[@Andr_27]

Thanks for making these videos, looking forward to the next one!!!