Here I show how Ernst Abbe explained image formation in the light microscope using wave optics and diffraction theory. This is also the seed that started the field of Fourier Optics which I also give an introduction to. The video is illustrated not only with animations but also a series of 'live' experiments using a customised PUMA microscope and 'der diffraktionsapparat nach PUMA' (the diffraction apparatus according to PUMA) - 3D printed apparatus designed to show some of Abbe's classical experiments. 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 SUPPORT PUMA ============ PUMA is an open source microscopy project. You can help support the project by: 1. Become a Patron: 2. Donate via PayPal: 3. Simply subscribing to this YouTube channel, like, comment and share these videos. 4. Spread the word - post the news about PUMA and link to this YouTube 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, ( ) --- PARTS AND TOOLS =============== Der Diffraktionsapparat nach PUMA will be made available on the PUMA GitHub page ( ) after I make a separate video describing how to print and use them. LINKS TO REFERENCED VIDEOS ========================== Diffraction: Convolution: For the other PUMA videos mentioned please see my YouTube channel pages. Understanding the Light Microscope by Peter Evennett (BioDIP - Biopolis Dresden Imaging Platform) OTHER LINKS =========== PARD Capture software (free and open source, for Linux): FOR FURTHER INFORMATION ======================= 1. Open access write-up about PUMA on the FreeCAD blog: 2. The official PUMA GitHub page where you can download the specs and source files to build or customise your own PUMA system: 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: Thanks for your interest in the PUMA microscope system. PJT 26/11/24