# Abbe's Diffraction Theory and Fourier Optics

**URL:** <https://forum.microlist.org/t/abbes-diffraction-theory-and-fourier-optics/2915>\
**Category:** Theory\
**Created:** [December 9, 2024, 12:18pm UTC](https://forum.microlist.org/t/abbes-diffraction-theory-and-fourier-optics/2915 "2024-12-09T12:18:17Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![P\_Tadrous](https://sea2.discourse-cdn.com/flex020/user_avatar/forum.microlist.org/p_tadrous/32/862_2.png) [@P\_Tadrous](https://forum.microlist.org/u/P_Tadrous)\
**Post date:** [December 9, 2024, 12:18pm UTC](https://forum.microlist.org/t/abbes-diffraction-theory-and-fourier-optics/2915/1 "2024-12-09T12:18:18Z")

</div>

My latest video on YouTube covers how a microscope ‘works’ in terms of wave optics with an easy-to-understand explanation of Abbe’s diffraction theory backed up by practical demonstrations on the 3D printed PUMA microscope with 3D printed diffraction apparatus (der Diffraktionsapparat nach PUMA):

[![](https://us1.discourse-cdn.com/flex020/uploads/microlist/original/2X/8/8727f08278ca7df03f9853c0c57549cc9e87d0c3.jpeg "Abbe's Diffraction Theory of Microscopic Perception (and an intro to Fourier Optics)") ](https://www.youtube.com/watch?v=Kj4zk91TVwo)

# CONTENTS

00:00 Limitations of ray theory (why a new theory was needed)  
03:05 Abbe’s diffraction theory for ‘straight up’ illumination (intro)  
05:17 Abbe’s theory continued and intro to Fourier Optics  
13:02 The numerical aperture of illumination (Abbe’s resolution formula)  
15:31 An alternative perspective (Rayleigh’s resolution formula)  
18:28 Der Diffraktionsapparat (nach Abbe and nach PUMA)  
21:15 Interpreting optical diffraction spectra (for beginners)  
23:28 Abbe’s experiments (Fourier optics with a PUMA microscope)  
33:52 The BFP image as a convolution of the condenser’s aperture image with a Fourier PSF.  
40:01 Conclusions

Share the link with your students.

P