Rayleigh limit and why resolution is hard

51:24>> What they've done is demonstrate subdefraction limited astronomical measurement. Okay. And that key thing is what got me subraction limited. So what does that mean? Okay. There is a limit when it comes to the resolution that you can have with light. Okay. It's dependent on the wavelength and it's dependent on the size of your aperture. Okay. >> It's called the rally limit. If you've got two points of light that are really close together as they are on the right hand side, >> Yes. >> then they're going to look like one point of light and I won't be able to resolve them differently. >> Mhm. >> On the other hand, if I have two points that are a little bit farther apart, then I can resolve them because they're gausian peaks. This sort of like envelope of stuff. It's not technically

52:04gausian. It's like this other function called the airy function. But in any case, they don't overlap enough. I can resolve the two as separate things. Separate things, >> right? >> Yes. >> How far apart they need to be in angle. It's not actually distance, right? Because if something's closer, then they need to be closer away. If they're farther away, then they could be really far. It's the angle that matters. It's like the angle between them, right? And how far away they can be in terms of angle is determined by something called the rally criterion, which is what we just saw. >> It's it's a ratio between the wavelength >> and the diameter. Okay? wavelength divided by diameter times some constant which has to do with the the shape of your aperture. Usually it's 1.22 because your apertures are usually round. Um

52:47>> so the bigger the wavelength, the larger this angle has to be. And that makes sense, right? Because if the wavelength is really large, then you know you we've we've looked at >> large waves that try to go across a rock, they get unbothered because the large waves will just go through. The smaller waves are the ones that'll bend and that bending is what actually gives us any type of information. Um also the larger the diameter of your lens >> the smaller you can resolve. Yes. Right. That makes sense. That's why we have big telescope big big mirrors and lenses. >> Yeah. Yeah. Yeah. One of the reasons is light gathering. But the other reason is so that we can have uh a giant sort of

53:30defraction thingy that like lets us resolve. Yes. >> Okay. And the the one that they're doing here, they're using the 8.2 m Subaru telescope in Hawaii, >> that thing >> um you know, if we take if we take the wavelength of light to be around 656 nanome, the defraction limit there with the 8.2 m Subaru telescope is 20 mill arcsec. >> Okay. >> Okay. And to think about arcsec it's like you got degrees from degrees then you get minutes from minutes you get seconds and then from seconds is divided into 1,000 arcsec. So it goes 60 60 then 1,000. Okay. It's extremely small. Means if we were to look at Pluto right now from from Earth.

54:11>> Yes. >> Um Pluto would be a fifth the size of that angle. So Subaru telescope could actually tell Pluto and Karen apart. >> Oh yeah. >> The two the Pluto and its moon apart. Right. That that's that's >> because because its resolution is is smaller than Pluto's. >> That's that's >> right. Pluto's about 100 arcseconds and this thing's resolution is 20 millc2 times 100, right? Yep. It's a fifth of that. >> Yep. Okay. >> Okay. >> There's a bunch of problems, right? The other problem that gets to us is not just rally rally thing, which is just physics, right? Like even the Hubble has this problem. James Web has this problem. The other thing is we're under the Earth's atmosphere and the Earth's atmosphere causes the twinkling of

54:51stars. It also causes the twinkling of distant lights if you're on top of a mountain, right? Because all the Earth's atmosphere has this turbulent packets of warm air and then cold air and highly dense and then lower dense. So the light is going to is going to start moving around before it gets to your detector >> interacting with the atmosphere on its way to the whatever you're capturing it with. >> Yeah. Exactly. And so and so the resulting disc of your point source, let's say if you're trying to look at a