Fourier Optics used for Optical Pattern Recognition
HTML-код
- Опубликовано: 31 май 2024
- Optical Fourier transformations were performed using small lithographic patterns of different characters. A DLP projector can be used as a Fourier filter to do simple pattern recognition.
Video contents:
0:00 General introduction
1:44 Fourier explained (simple)
3:45 Digging a bit deeper (sorry, could not resist)
5:55 Fourier on images
9:27 Fourier transforms using optics
12:05 Setup and results
14:15 Fourier filtering
The 2D Fourier transformation images were calculated using freeware developed by Kobe University. You dan download this tool from:
cas.eedept.kobe-u.ac.jp/Welcom...
Conversions of 2D images to 3D were done using Gwyddion. This very advanced piece of software is can be downloaded for free from:
gwyddion.net/download.php
To illustrate 2D Fourier transform on an actual image, a small part of an M.C. Escher drawing was used.
While editing the material for this video I found out that the Applied Science channel made a somewhat similar video on "Optical Fourier" already in 2012: • Intro to Fourier Optic... . Luckily the angle is somewhat different.
This video gives a different (and deeper) perspective on the math behind Fourier transformations;
• Lecture 6A Fourier Opt...
If you want to go all the way, read the wiki page on Fourier. If you dare.
en.wikipedia.org/wiki/Fourier... 
Наука
![Roddy Ricch - Survivors Remorse [Official Music Video]](http://i.ytimg.com/vi/J5IeFzr2GgE/mqdefault.jpg)
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 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.
This might be the most cogent explanation of FT I’ve ever encountered. Thank you!
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!
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.
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.
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).
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.
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!
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.
Sir you have accomplished what today's education and engineering schools have failed to do . Thank you and the youtube algorithm
I'd love to see the inverse FT of those optical patterns to see how well the match up with the original ones!
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.
The most limpid demonstration of FFT that I've ever seen. Amazing, thank you.
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
.... you literally explained the fourier transform better than any of my professors ever could
10/10
Im in the middle of goodman's book, you made so much order in so many things. Amazing work, thank you.
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!
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!
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 !!
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.
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!"
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.
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.
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.
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.
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, also never seen such an intuitive explination for the Fourier Transform
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!!
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
Best description of FT I have ever seen. Didactically unbelievable.
Another amazingly insightful explanation. I can't tell you what a pleasure it is to see your videos and share them.
ive been addicted to your videos lately
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.
University did not make me understand the Fourier transform, but this video did. Thank you!
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!
By far one of the best visual explanations I've seen on Fourier transforms and it's relation to optics. Thank you for posting!
My favourite video on Fourier Optics right now ! This is going to help so much with the class presentation i have to give :)
This is the kind of stuff that makes me wish I did optical engineering instead of comp sci.
Brilliant presentation. The amount of work & preparation you put in is extraordinary, and your explanations, crisp & intuitive. Thank you.
You are every bit as clever as Christiaan Huygens. Inspiring.
So far the best explanation of the Fourier transformation that I have seen. Well done!
This is incredible. Thank you so much for posting it all!
I would like to thank you for the clear explanation
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
Excellent explanation of the Fourier transform. Well done for not going well-trodden ways!
The demos at 12:50 are amazing. The match is so close.
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.
I hope you got a patent and get the reward you deserve for this beautiful idea.
I am amazed by your deep knowledge of the subject. I am humbled and thankful for your contribution. Thank you for sharing!
You explain everything so clearly. Every video you make is a gift to the world.
Fascinating, and deeply thought-provoking!
I'm trying to learn Fourier Optics, and this was an amazing visual way to see the math. Thanks for making this!
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.
thank you for all you do, this is fascinating. your videos have inspired me to build the autocollimator ive always wanted.
@huygens optics
Really enjoyed this, thanks for taking the time to make it!
Good stuff man. I like the clean informative approach too. Increasingly rare these days.
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.
Absolute fascinating topic!
People like you should teach such stuff for big money!
The knowledge you gave my in under 20min would take an average school weeks!
Thank you for sharing this with others!
First class explanation of a very difficult to understand subject, well done and thank you.
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
Whenever I opened a Huygens Optics video I can learn something from it.
Brilliant explenation of the Fourier transform
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!
This is an outstanding video, and a joy to listen to. Thank you very much
This is one of my favorite videos in RUclips 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!
Great video thank you. I remember hearing about an optical lens to detect planes. Now I understand how that was done, thank you.
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 ;)
Thank you for sharing! This was quite inspiring!
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.
This video is so information dense, I love it
wonderfully explained! Thanx!
This is incredible, very good presentation and information, thank you for sharing - subscribed!
Fantastic video!! Thank you!
Also explains a bit how Fourier transform is used for hashing in cryptography :)
This is the coolest thing I have ever seen in my life
I did some undergraduate physics and loved this experiment. Still amazed it's possible, compared to a digital computation.
After watching this video, it is clear that such advanced audio processing could not have come
into existence by random chance as the theory of evolution states.
It is clearly advanced bio-mechanical-electrical engineering.
God's bio-technology is so amazing...
One would assume the cochlea works in a similar way to a mass spectrometer except it,s sound waves hitting the surface vs atoms.
Nice video. For anyone want to do this on a low budget then read on...
You need a laser pointer pen, a convergent lens, a caliber and a microscope crossed grid slide available from Amazon. Due to the poor beam quality of laser pen it serves as a good parallel beam for illuminating the crossed grid target. Place the crossed grid at the focus of the lens to observe the diffraction pattern formed with the laser. At a viewing screen some distance away from the lens observe the image of the crossed grid. Place the jaw of the caliber at the location of the diffraction pattern to observe the effect of spatial filtering. Rotate the caliber and you would be able to observe the vertical and horizontal grids appear and disappear due to spatial filtering of the high frequency components.
Great presentation, thank you.
What an amazing video!! Thank you !
Thanks for this introduction!
what a cool way of showing how video compression works :P
That Fourier Plane makes sense after seeing this video. Quite interesting..
Fourier keeps surprising me with the great number of applications of his work.
Can you imagine that he had this all in his mind, in an era without electronics.. Leibniz, Euler, Fourier, Gauss (and the rest!) too. What would they have come up with when they had access to computers?
oh wao!!! .... Amazing! Thank you so much for this gift.
totally illuminating
Thank you both !
Oh wow....Fourier transforms....the same kind of concept (multiplying by the frequency your're looking for) is the same sort of principle behind netmasks....cool
Brilliant explanation on this topic. Before this video, I always thought the FFT is about the optical frequency instead of the spatial frequency. But even though it seems fascinating, I still doubt if it can be a practical way of image recognition. Since it's mainly based on diffraction, it will require a coherent light source and a very special mask. I'm very curious how this can be applied to ordinary pictures.
Great explanation.
I really, really love your videos.
Just wow... Got in love with the topic, will do it soon in uni :D
boy did i enjoy this
An excellent video, thank you! I would only ask about practical times of performing the electro-optical matching process, as it must be limited by sensor self noise. I mean, there must be effectively an exposure time that is likely to be much longer than the propagation time.
Very good, i’m from brazil and love your videos. Congratulations
if shor's algorithm uses fourier transform, could we do prime factorization with optics?
Bump
We need answers.
I don’t think so, as, the quantum Fourier transform applies to like, the state of a collection of qubits, where the amplitudes of different possible states are playing the role of the different numbers in a usual Fourier transform,
And like, there are 2^n of these numbers.
I don’t yet understand well enough to say “definitely no that wouldn’t work”, but I do think I understand well enough to say that I really don’t think it would?
Though..
[what follows is a confused attempt to identify more precisely what wouldn’t work by trying to think of how it would work if it did work]
Ok, suppose that we split (in how we consider it, not physically split) some interval of space for the beam into 2^n equal parts, where the intensity through each part is the number. Uh, the discrete Fourier transform then, would, uhh,
how does that compare to the usual one which this computes?
Ok uh, so I think you would need to, change the phase of the light in a way corresponding to, exponents of a given integer modulo the number you want to factor, where the power the number is raised to corresponds to the position in the beam???
How could that be done?
If the exponentiation was done by repeated squaring,
Hm.
Ok, I don’t know enough about optics to really say, but that doesn’t seem feasible to me?
Idk
@@drdca8263 I myself am not an expert, but I don't think your reasoning is correct. Firstly, your argument should also apply to electronic quantum computers, which we know do likely work.
Fundamentally though, there is no "2^n distinct states" nor a need (or possibility) to split them in space. Rather, the wave of a single photon has a probability density function across these states (and phase is important too). I don't see any reason that optics cannot propagate these wavefunctions just as electronic quantum gates do.
Please do correct me if my reasoning is wrong, I too want to learn from this!
@@nicktohzyu oh, sorry, yeah if you are using n entangled photons, or whatever, uh, well, Shor’s algorithm can be done with the qubits implemented as photons.
What I was talking about was, trying to implement it without using any quantum mechanical properties of a beam of light, and just using wave properties.
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.
the end was great! I almost pissed myself I laughed so hard!