Mode decomposition & fiber-based waveguides

1:03:54G. >> That's that's three different piano keys that are put down, right? How does your ear hear it? Your ear actually hears the three different notes. The way it's doing it is there's hardware inside of our ear that's in the cookia. The cookia is this curled up little thing. That's a hardware part of our ear. And what it does is it's made out of cells of different thickness. Okay? The lower frequency, the bass notes are going to vibrate the cells with the big thickness. And the higher frequency are going to vibrate the thinner, smaller cells. So where in this spiral the cells are getting excited tells you which piano notes are being played. >> Okay? Our ear has hardware that is

1:04:35breaking down the sound that is coming in into its respective modes as you would say into its respective like components. >> Okay. >> We're going to do the same thing with the light that's coming through a telescope. >> Okay. >> Okay. What we have is we've got a wave guide that takes in the light that's coming in from the telescope. >> Yes. >> Okay. And then what it's going to do is make it go through this fiber optic sort of chassis. Okay. >> And all of that multimodal the the sound that's coming from an instrument is going to be broken down into these modes. >> Yes. >> Into each individual fiber optic cable. >> Yes. >> Okay. And so you're decomposing the

1:05:15light field >> into a basis of what are the notes that make up that light field >> which also changes over time. >> Yes. And each of those notes has a certain phase to it. >> Right. >> Mhm. >> Because some of the notes are going to be arriving a little bit later. some of them earlier, some of them going to be louder than the others. And so if you go to the next one, we'll have this is what the light notes look like on the on the on the left hand side over here, we've got >> the actual image. Let's say it's it's a dot with a ring around it or something like that. That can be broken up into a dot in the center. Yes. >> Then there's maybe two loes this way. There's two loes this way. And what we can do is we can say what are the what

1:05:56are the modes which are these individual notes. How do they add up to make the image that I'm seeing? That's what that's what that deconstruction is doing. >> You know what this looks like for any video or film editors that are listening? It looks like the uh color panel on Da Vinci Resolve when you're color correcting your video footage. It gives you the color wheels of all these different permut literally looks just like it. It's actually >> it's it's kind of similar in that sense, right? It's like it's extracting this like low information, right? All the stuff that makes it up. This is only really possible if you look at very simple objects. For example, a single star or like stuff around a single star.

1:06:38If you wanted to, you know, image the Eagle Nebula or something that this wouldn't really work. But the mathematics is simple because the source is simple. And because the source is simple, I only need to worry about the first like 20 notes. >> I got I don't need to worry about cuz you can I mean in theory you can recreate any image using like just a bunch of like notes like this but in practice it's going to get difficult with a simple >> objective which is just we we're looking at a star we want to resolve the stuff in the star and around the star very very nicely that's what we can do and the key principle is the phase information of that input is now converted into a measurable intensity difference between all of these different notes right if the stars position for example it shifts then one

1:07:20of those fiber optic inputs is going to be brighter than the other. If it ships the other way, then another fiber optic input is going to be brighter. Right. >> Yes. >> And the raw data has gone from being a CCD >> to now it's not a picture of the star, but it's 38 different spectra in each of these different modes. >> Okay. So, it's like how how >> how loud was this note at this frequency? >> Yes. >> So to speak, >> so to speak. Right. Right. This is but but that's the best way that I can describe it. >> They're trying to distill it into an analogy that doesn't require us to go through more. >> Yeah. Go through all of the all of the data, but it's like it's like they've basically got 19 different notes and two

1:08:02polarizations because polarization is also important, right? The electric field oscillating this way or this way tells us something about this what the what the thing is that is producing that light. So, it's 19 different nodes all in two different polarizations to get 38 different spectra. The the idea is before we were looking at just like one box and now we have like 19 boxes with two flavors >> uh to analyze the same object we were looking at before that was just one box. >> Yes. Exactly. And the and the one box sure it had the direct information of how bright this thing was. But now we're just sophisticating it right. We're no longer taking let's say just how loud the sound is but what are the thingies

1:08:44on top? The another analogy this makes me think of is like uh for DJs you when you get a track, right, the track is like one audio waveform and it has the drums, it has the vocals, it has everything as one waveform. >> Exactly. >> Now there's all these AI tools that allow you to separate out the drums from the vocals from the synths and now you have it as these indiv and like there is information when you're looking at just the individual instrument that is hard to decipher when you're looking at the single >> waveform. Yeah. Yeah. And this is very similar to that. Yeah. Yeah. Yeah. I think I think I think that's a good analogy, right? It's taking that aggregate light and it's decomposing it into these individual modes, you know.

1:09:24Um, >> and what you can do now, the the the second thing that you can do is this star it's >> it's got two different So, this star specifically, what they're looking at is um a star in Canis Minorus, Beta CMI. It's 162 lighty years away. It's surrounded by a gas of hydrogen. Canis Minoris is one of the two dogs that are the hunting companions of Orion the the hunter. And so this star specifically, it's got a gas of hydrogen around it. And that gas is spinning so fast that we can see a Doppler shift where on one side there's it's blue shifted cuz it's

1:10:05coming at us and on the other side it's red shifted cuz it's going away. Right? So what we want to do is resolve this gas cloud. Okay, there's two ways to do this. There's two steps. The first is to say, okay, all of the light, most of the light is coming from the star, right? >> There's going to be some jitter >> because of the adaptive optics. Remember when we talked about um the episode