The way you described the Fourier formula was so clear and elegant. The best description I have ever heard. Something so fuzzy became so clear. Fantastic video.
This is how the toy laser pointers that project images work, but in reverse. The swappable 'masks' that you change on the tip of the laser pointer are fourier images on photographic film.
It is as though you have condensed and presented an intriguing novel with the lucid flow of exposition, rising action, climax and denouement. What an incredible amount of effort you invested to elevate the science into beautiful art.
Amazing. I've been familiar to FFT's since college (I'm an acoustic engineer), and used it a lot, but never had seen such a clear explanation before. Never seen an optical FFT before either!
As many others have noted, this is a wonderful video clip ! Optical fourier filtering was done on seismic data a few km from you at the Shell Laboratory in Rijswijk over 50 years ago. Research geophysicists did bandpass, wavenumber and even deconvolution filtering on a set up there. I never saw it in action but saw some of the results. The technique had a low dynamic range, was very fiddly, and was quickly superseded by digital methods, though some optical filtering research continued there into the 70's. They sent optical equipment for a system to their exploration group in Melbourne. I made a brief, unsuccessful attempt to get it to work there without a manual (or experimental talent).
this is so good! I love seeing the setups. thanks for sharing. I remember reading about an old government project that was trying to identify missile silos from aerial images using this technique, before computers
Well that certainly is exotic. I guess they never got it to work because the recognition was not specific enough and they were hitting silos with grain and cattle food instead...
I was about to leave a comment about this too. I couldn't recall if it was cold war era silos or WWII era aircraft identification but the necessity (I assume) of lasers eliminates the later.
This video made things so exceptionally clear to me that by the time I was done watching the video, my ears could calculate FFT's all by themselves... All jokes aside, thanks for the amazing content.
This is a brilliantly clear explanation! My compliments. As a side note you can transform back using an other lens, which means you can select parts of the spatial frequencies to get edge enhancement, or removing unwanted raster lines as was done by Nasa on some of their satellite photos.
I find the comment at 14:15 very fascinating, but not for the obvious reason. I think it is amazing that a medium speed CPU that is doing hundreds of things simultaneously is "only" a few billion times slower than a beam of light doing the same thing. It speaks to just how far modern computers and optimisations have come in the past decades, as before that time doing an equivalent calculation to a physical phenomenon would have been unthinkable.
Really great explanation. As a photo-lithography engineer, I can confirm that your accent adds a level of authority when talking about optics to my ear! Keep up the great content.
Absolutely incredible. I've enjoyed learning quite a bit about many different applications of Fourier transforms, but nothing like this. Thank you for sharing, and say hi to the budgies for us!
Randomly came across one of your videos yesterday and have been watching a few as a result. You have fantastic information and you're able to explain it in a very understandable way. Thank you very much for sharing! I look forward to watching more!
Very cool proof of concept demo at the end! Also I can't express how important Fourier transforms are and their wide ranges of uses even in places where you'd least expect it. Definitely one of the most important and useful things I've learned over the years!
I am excited that your information might be the very one to help me program a "realistic" star filter. I didn't expect your videos to be so easy to follow, even the most difficult topics.
Not only you look like a very nice couple (I like the way you switched voices in the end), your explanation of the Fourier Transform was so unexpectedly clear! Clear as light which, I guess, is appropriate for this channel.
Dankjewel, Jeroen! I now understand much better how the Arago effect plays into everyday optics and recognition. My supermarket bar code scanner is much less a magician today.
Amazing how we have a physical high resolution comb filter in our ear. Great series of experiments into optical processing. A complexly etched surface seems to me could calculate a range of complex functions depending on where input is fed and where output is measured.
Since much of the energy of the Fourier transform is concentrated near the central region, one method to reduce this effect is to offset the object (letters A, B) from the optical axis of your setup. The optical Fourier transform is invariant under translation in the filter plane such that the correlation peak will also be offset. Instead of a photodiode, one can use a camera to observe the correlation spike in the image plane. If you move the object, the correlation spike will also move.
I aced my signal analysis class at U.C. Berkeley. I can do Fourier Transform in my sleep, but I never understood the fundamental reasonings. Your explanation is by far the best and easiest to understand. Thank YOU !!
Excellent video and a very interesting subject that I had never heard of before! I hope you will be able to make many more videos like this one in the future. Respect!
I understand the fourier transformation and did calculate it manually a few times, but I just couldn't fully grasp the Fourier optics. Several PhDs tried to describe it to me with no success. Books didnt help ither. Yout did a great Job in a few minutes, you gave me the right understanding for it. Thank you so much.
I went to college for mechanical engineering and we did a lot of work with signal processing and FFT for those signals, and in your short explanation was far more illuminating than my college was able to do in years of instruction.
I can’t believe I understand now the FT space of frequencies. I just couldn’t do it before by reading papers or watching other videos. Thank you for such a wonderful explanation!!
This is best ever video that describes Fourier so clear! Thank you so much! I have not understand Fourier for four years. You only make me understand it in five minutes! Hope you can make more videos. Thanks!
This is one of my favorite videos in UA-cam watched several times, and wish I could 👍 it every time. The idea of light processing is on my mind for a long time and after watching yours videos the ideia is trapped like loop 😀 The logic gates for light. Pattern recognition. I'm pretty sure this will be the future of computers and AI (pre trained "filters"), or ASICs. Opto Electronics will be the next technological breakthrough!
I’m sending this video to friends just to explain Fourier transforms, that cut right through the usual bs everyone else goes through to make themselves feel smart (which usually alienates the audience)..... this just felt like it was accessible to a 10 yr old, and still have a decent understanding
Nice video! I like how you used a DLP projector to simulate filters. To distinguish patterns like A from AB, one can set each filter's threshold value instead of setting one threshold value.
Reminds me of the DSP classes I took in university. A real headscratcher at first. I don't think we ever applied it to image recognition but we did go in to image filters like edge detection. Goed bezig ouwe ;)
I had a good chuckle when you compared the speed of the lens to that of the computer. Years ago in my college physics class, I remarked how complicated and one of our mathematical results seemed to be and how long it took to derive. My professor exclaimed "just think that Mother Nature solves this system of equations instantaneously!"
Takes me back to a class on Fourier optics at university. I remember I couldn't understand what they meant by the Fourier transform in the focal plane. After all Fourier transform is just numbers representing frequencies. How can it exist in a physical plane? The moment we got in the lab and stuck some pinholes in the laser beam, I got it. Needless to say I was the most excited student in the lab that day, It proved to be one of my favorite classes of all time. Thanks for reviving that memory. b.t.w. you explained better than my professor.
Such an intuitive and simple explanation, excellent content! You could even have combined this topic slightly with convolution/cross-correlation without causing too much divergence
Excellent expositions of why what everything is, is the zero-infinity integration of pulse-evolution differentiates here-now-forever, of time-timing, phase-locked sync-duration recirculation-> re-evolution. What You See Is What You Get in this format. This is real-time Quantum Operator Logic Fields Computational Information Technology. Instantaneous coherence-cohesion objectives in temporal superposition identification. A very gratifying for Physicists video who want to learn by doing experience before making up theories about what the origins of dimensionality coordination is in Actuality. Time Duration Timing Conception.., QM-TIME Universe.
Watched a full series of video on how scientist manage to image distant exo-planets without actually getting all the Fourier transform model gibberish. This video illuminated me
Great demonstration & explanation of the fourier transform / mechanism! Some computational perspective: the fft takes O(n^2 log n) to compute for a square n x n image. To read out the signal on a photo-sensor of the same size, it takes O(n^2) time. So the gain in time is miniscule (log n).
Why would the photosensor have to be of a comparable size? Don’t you mostly just need to distinguish between more and less, not so much where on the sensor it hits?
Exceptional channel, immediate subscribe. I would be willing to bet literally any quantity of money that this is the exact technique the National Reconnaissance Office and or CIA was using to analyze the reams of Corona spysat film in the 60s and 70s (for finding and roughly "counting" eg. jet aircraft in a particular set of film images) long before digital computational power was anywhere near sufficient for such tasks. It is effectively an analogue computer for image analysis that operates at, as you note, fantastic speed, and with extremely low energy requirements.
I'm actually speechless... I've been trying to understand how to implement FFT in a computer for so long, every explanation i've found has eluded my comprehension. And you just made me get exactly how to program it with some green and red shading on a graph. I love this channel, thanks so much for this video!
It is indeed a really easy to understand explanation for how the Fourier transform works, but the *fast* Fourier transform algorithm is significantly harder to do. So sadly you didn't learn how to implement FFT, you only learned how to implement a naive slow FT.
@@inv41id ah yeah i understand, it just so happens that the naive method is precisely what I needed because I don't care about phase for my applications.
@@tiggerbiggo Oh I wasn't really talking about phase, I was more so saying that the naive method is much slower, which is pretty significant considering FFT has the word "fast" in the name
@@inv41id yeah that too, at least my understanding is a bit better than it was before, and this naive method seems like it would still be useful in smaller applications where speed is not a big factor. Definitely not suitable for use in audio effects because of the speed and lack of phase information which would be critical for doing the inverse calculation accurately
such a fantastic video, now I understand why and how there was (is?) an optical co-processor you could buy that performed Fourier transforms using optics rather than traditional FFT computation. for certain applications the speed boost could be immense, I wonder if there's a FFT-on-a-chip and if some day we can manage to make an optical FT-on-a-chip. it would need to include spacial light modulation, focusing, and a sensor array.
Before 1978, Fourier Optics was the standard method for reconstructing real images from the data recorded by the Synthetic Aperture Radar (SAR) systems. The received radio signals were recorded on photographic film, and then the film was developed and passed through an optical Fourier transform machine to convert the information into the image of the landscape. SAR technology is still used today in earth observation satellites to obtain high resolution images at night and through the clouds, but all the processing is now done electronically.
The way you described the Fourier formula was so clear and elegant. The best description I have ever heard. Something so fuzzy became so clear. Fantastic video.
Seconded! Amazingly great explanation.
This might be the most cogent explanation of FT I’ve ever encountered. Thank you!
This is how the toy laser pointers that project images work, but in reverse. The swappable 'masks' that you change on the tip of the laser pointer are fourier images on photographic film.
It is as though you have condensed and presented an intriguing novel with the lucid flow of exposition, rising action, climax and denouement. What an incredible amount of effort you invested to elevate the science into beautiful art.
Amazing. I've been familiar to FFT's since college (I'm an acoustic engineer), and used it a lot, but never had seen such a clear explanation before. Never seen an optical FFT before either!
As many others have noted, this is a wonderful video clip !
Optical fourier filtering was done on seismic data a few km from you at the Shell Laboratory in Rijswijk over 50 years ago. Research geophysicists did bandpass, wavenumber and even deconvolution filtering on a set up there. I never saw it in action but saw some of the results. The technique had a low dynamic range, was very fiddly, and was quickly superseded by digital methods, though some optical filtering research continued there into the 70's.
They sent optical equipment for a system to their exploration group in Melbourne. I made a brief, unsuccessful attempt to get it to work there without a manual (or experimental talent).
this is so good! I love seeing the setups. thanks for sharing. I remember reading about an old government project that was trying to identify missile silos from aerial images using this technique, before computers
Well that certainly is exotic. I guess they never got it to work because the recognition was not specific enough and they were hitting silos with grain and cattle food instead...
I was about to leave a comment about this too. I couldn't recall if it was cold war era silos or WWII era aircraft identification but the necessity (I assume) of lasers eliminates the later.
@@HuygensOptics Can you use this for ift?
They used this kind of setup to reconstruct image from synthetic aperturae radar.
Just when I thought Saturdays couldn't get any better! Your channel is amazing : )
Absolutely, unequivocally true!
Sir you have accomplished what today's education and engineering schools have failed to do . Thank you and the youtube algorithm
This video made things so exceptionally clear to me that by the time I was done watching the video, my ears could calculate FFT's all by themselves... All jokes aside, thanks for the amazing content.
I'd love to see the inverse FT of those optical patterns to see how well the match up with the original ones!
This is a brilliantly clear explanation! My compliments. As a side note you can transform back using an other lens, which means you can select parts of the spatial frequencies to get edge enhancement, or removing unwanted raster lines as was done by Nasa on some of their satellite photos.
That's why all of NASA's fotos are fake CGI.
The most limpid demonstration of FFT that I've ever seen. Amazing, thank you.
I find the comment at 14:15 very fascinating, but not for the obvious reason. I think it is amazing that a medium speed CPU that is doing hundreds of things simultaneously is "only" a few billion times slower than a beam of light doing the same thing. It speaks to just how far modern computers and optimisations have come in the past decades, as before that time doing an equivalent calculation to a physical phenomenon would have been unthinkable.
Really great explanation. As a photo-lithography engineer, I can confirm that your accent adds a level of authority when talking about optics to my ear! Keep up the great content.
Incredible explanation of the Fourier Transform!
Absolutely incredible. I've enjoyed learning quite a bit about many different applications of Fourier transforms, but nothing like this. Thank you for sharing, and say hi to the budgies for us!
Im in the middle of goodman's book, you made so much order in so many things. Amazing work, thank you.
.... you literally explained the fourier transform better than any of my professors ever could
10/10
Randomly came across one of your videos yesterday and have been watching a few as a result. You have fantastic information and you're able to explain it in a very understandable way. Thank you very much for sharing! I look forward to watching more!
Another amazingly insightful explanation. I can't tell you what a pleasure it is to see your videos and share them.
Very cool proof of concept demo at the end! Also I can't express how important Fourier transforms are and their wide ranges of uses even in places where you'd least expect it. Definitely one of the most important and useful things I've learned over the years!
By far one of the best visual explanations I've seen on Fourier transforms and it's relation to optics. Thank you for posting!
This is incredible. Thank you so much for posting it all!
So far the best explanation of the Fourier transformation that I have seen. Well done!
You explain everything so clearly. Every video you make is a gift to the world.
Excellent explanation of the Fourier transform. Well done for not going well-trodden ways!
Amazing, also never seen such an intuitive explination for the Fourier Transform
Good stuff man. I like the clean informative approach too. Increasingly rare these days.
I am excited that your information might be the very one to help me program a "realistic" star filter. I didn't expect your videos to be so easy to follow, even the most difficult topics.
Really enjoyed this, thanks for taking the time to make it!
I'm trying to learn Fourier Optics, and this was an amazing visual way to see the math. Thanks for making this!
Not only you look like a very nice couple (I like the way you switched voices in the end), your explanation of the Fourier Transform was so unexpectedly clear! Clear as light which, I guess, is appropriate for this channel.
Best description of FT I have ever seen. Didactically unbelievable.
I am amazed by your deep knowledge of the subject. I am humbled and thankful for your contribution. Thank you for sharing!
Dankjewel, Jeroen! I now understand much better how the Arago effect plays into everyday optics and recognition. My supermarket bar code scanner is much less a magician today.
Brilliant presentation. The amount of work & preparation you put in is extraordinary, and your explanations, crisp & intuitive. Thank you.
Amazing how we have a physical high resolution comb filter in our ear. Great series of experiments into optical processing. A complexly etched surface seems to me could calculate a range of complex functions depending on where input is fed and where output is measured.
Since much of the energy of the Fourier transform is concentrated near the central region, one method to reduce this effect is to offset the object (letters A, B) from the optical axis of your setup. The optical Fourier transform is invariant under translation in the filter plane such that the correlation peak will also be offset. Instead of a photodiode, one can use a camera to observe the correlation spike in the image plane. If you move the object, the correlation spike will also move.
I aced my signal analysis class at U.C. Berkeley. I can do Fourier Transform in my sleep, but I never understood the fundamental reasonings. Your explanation is by far the best and easiest to understand. Thank YOU !!
Excellent video and a very interesting subject that I had never heard of before! I hope you will be able to make many more videos like this one in the future. Respect!
I understand the fourier transformation and did calculate it manually a few times, but I just couldn't fully grasp the Fourier optics. Several PhDs tried to describe it to me with no success. Books didnt help ither.
Yout did a great Job in a few minutes, you gave me the right understanding for it.
Thank you so much.
I went to college for mechanical engineering and we did a lot of work with signal processing and FFT for those signals, and in your short explanation was far more illuminating than my college was able to do in years of instruction.
I can’t believe I understand now the FT space of frequencies. I just couldn’t do it before by reading papers or watching other videos. Thank you for such a wonderful explanation!!
University did not make me understand the Fourier transform, but this video did. Thank you!
Fascinating, and deeply thought-provoking!
This is best ever video that describes Fourier so clear! Thank you so much! I have not understand Fourier for four years. You only make me understand it in five minutes! Hope you can make more videos. Thanks!
This is one of my favorite videos in UA-cam watched several times, and wish I could 👍 it every time.
The idea of light processing is on my mind for a long time and after watching yours videos the ideia is trapped like loop 😀 The logic gates for light. Pattern recognition. I'm pretty sure this will be the future of computers and AI (pre trained "filters"), or ASICs. Opto Electronics will be the next technological breakthrough!
My favourite video on Fourier Optics right now ! This is going to help so much with the class presentation i have to give :)
ive been addicted to your videos lately
I’m sending this video to friends just to explain Fourier transforms, that cut right through the usual bs everyone else goes through to make themselves feel smart (which usually alienates the audience)..... this just felt like it was accessible to a 10 yr old, and still have a decent understanding
Nice video! I like how you used a DLP projector to simulate filters. To distinguish patterns like A from AB, one can set each filter's threshold value instead of setting one threshold value.
Reminds me of the DSP classes I took in university. A real headscratcher at first. I don't think we ever applied it to image recognition but we did go in to image filters like edge detection. Goed bezig ouwe ;)
First class explanation of a very difficult to understand subject, well done and thank you.
This is an outstanding video, and a joy to listen to. Thank you very much
I had a good chuckle when you compared the speed of the lens to that of the computer. Years ago in my college physics class, I remarked how complicated and one of our mathematical results seemed to be and how long it took to derive. My professor exclaimed "just think that Mother Nature solves this system of equations instantaneously!"
This is incredible, very good presentation and information, thank you for sharing - subscribed!
Takes me back to a class on Fourier optics at university. I remember I couldn't understand what they meant by the Fourier transform in the focal plane. After all Fourier transform is just numbers representing frequencies. How can it exist in a physical plane? The moment we got in the lab and stuck some pinholes in the laser beam, I got it. Needless to say I was the most excited student in the lab that day, It proved to be one of my favorite classes of all time. Thanks for reviving that memory.
b.t.w. you explained better than my professor.
thank you for all you do, this is fascinating. your videos have inspired me to build the autocollimator ive always wanted.
@huygens optics
This is the coolest thing I have ever seen in my life
I would like to thank you for the clear explanation
Such an intuitive and simple explanation, excellent content! You could even have combined this topic slightly with convolution/cross-correlation without causing too much divergence
You are every bit as clever as Christiaan Huygens. Inspiring.
This video is so information dense, I love it
The demos at 12:50 are amazing. The match is so close.
Excellent expositions of why what everything is, is the zero-infinity integration of pulse-evolution differentiates here-now-forever, of time-timing, phase-locked sync-duration recirculation-> re-evolution. What You See Is What You Get in this format.
This is real-time Quantum Operator Logic Fields Computational Information Technology. Instantaneous coherence-cohesion objectives in temporal superposition identification.
A very gratifying for Physicists video who want to learn by doing experience before making up theories about what the origins of dimensionality coordination is in Actuality. Time Duration Timing Conception.., QM-TIME Universe.
Watched a full series of video on how scientist manage to image distant exo-planets without actually getting all the Fourier transform model gibberish. This video illuminated me
Great video thank you. I remember hearing about an optical lens to detect planes. Now I understand how that was done, thank you.
I hope you got a patent and get the reward you deserve for this beautiful idea.
the end was great! I almost pissed myself I laughed so hard!
Thank you for sharing! This was quite inspiring!
Another worthy video to watch ads for. Really really good. I relish very video of yours
Great demonstration & explanation of the fourier transform / mechanism! Some computational perspective: the fft takes O(n^2 log n) to compute for a square n x n image. To read out the signal on a photo-sensor of the same size, it takes O(n^2) time. So the gain in time is miniscule (log n).
Why would the photosensor have to be of a comparable size? Don’t you mostly just need to distinguish between more and less, not so much where on the sensor it hits?
@@drdca8263 if youre using radio then youre right, the satelites use laser afaik, it is more efficient & possible in the vacuum of space.
Brilliant explenation of the Fourier transform
I did some undergraduate physics and loved this experiment. Still amazed it's possible, compared to a digital computation.
Just wow... Got in love with the topic, will do it soon in uni :D
wonderfully explained! Thanx!
What an amazing video!! Thank you !
Fantastic video!! Thank you!
One would assume the cochlea works in a similar way to a mass spectrometer except it,s sound waves hitting the surface vs atoms.
what a cool way of showing how video compression works :P
Great presentation, thank you.
boy did i enjoy this
totally illuminating
Thank you both !
I really, really love your videos.
This is the kind of stuff that makes me wish I did optical engineering instead of comp sci.
Very cool stuff. I would love to see something like this used in practice or commercially
Back in the day these setups were used to develop SAR images.
Whenever I opened a Huygens Optics video I can learn something from it.
Very good, i’m from brazil and love your videos. Congratulations
oh wao!!! .... Amazing! Thank you so much for this gift.
Thanks for this introduction!
Exceptional channel, immediate subscribe.
I would be willing to bet literally any quantity of money that this is the exact technique the National Reconnaissance Office and or CIA was using to analyze the reams of Corona spysat film in the 60s and 70s (for finding and roughly "counting" eg. jet aircraft in a particular set of film images) long before digital computational power was anywhere near sufficient for such tasks. It is effectively an analogue computer for image analysis that operates at, as you note, fantastic speed, and with extremely low energy requirements.
Also explains a bit how Fourier transform is used for hashing in cryptography :)
I'm actually speechless...
I've been trying to understand how to implement FFT in a computer for so long, every explanation i've found has eluded my comprehension. And you just made me get exactly how to program it with some green and red shading on a graph.
I love this channel, thanks so much for this video!
It is indeed a really easy to understand explanation for how the Fourier transform works, but the *fast* Fourier transform algorithm is significantly harder to do.
So sadly you didn't learn how to implement FFT, you only learned how to implement a naive slow FT.
@@inv41id ah yeah i understand, it just so happens that the naive method is precisely what I needed because I don't care about phase for my applications.
@@tiggerbiggo Oh I wasn't really talking about phase, I was more so saying that the naive method is much slower, which is pretty significant considering FFT has the word "fast" in the name
@@inv41id yeah that too, at least my understanding is a bit better than it was before, and this naive method seems like it would still be useful in smaller applications where speed is not a big factor. Definitely not suitable for use in audio effects because of the speed and lack of phase information which would be critical for doing the inverse calculation accurately
This is amazing :)
Amazing work !
such a fantastic video, now I understand why and how there was (is?) an optical co-processor you could buy that performed Fourier transforms using optics rather than traditional FFT computation. for certain applications the speed boost could be immense, I wonder if there's a FFT-on-a-chip and if some day we can manage to make an optical FT-on-a-chip. it would need to include spacial light modulation, focusing, and a sensor array.
Great explanation.
Отличная работа!
Before 1978, Fourier Optics was the standard method for reconstructing real images from the data recorded by the Synthetic Aperture Radar (SAR) systems. The received radio signals were recorded on photographic film, and then the film was developed and passed through an optical Fourier transform machine to convert the information into the image of the landscape. SAR technology is still used today in earth observation satellites to obtain high resolution images at night and through the clouds, but all the processing is now done electronically.