 Okay, hello. Welcome back. Let's continue onward. In the last lectures, we covered light, some of the basic physical properties, the propagation of light, and then got into optical systems. I explained various kinds of lenses and what happens to objects at various distances, explained real images and virtual images. And then we explained the eye's ability to form images on the retina using its lens to change the diopter of the eye. And so I gave you several cases of that. And I want to now explain what it looks like when in a head-mounted display, you have a screen placed in front of the eye with a convex lens in between. So this is a very common situation and this is what you have in the lab. So if we take the eye, again I am drawing the same kind of pictures like I did last time. So the retina is in the back here. I have the lens of the eye here. Suppose we have light coming in through parallel rays and then it focuses on the retina. In this particular example, I will let the place called the fovea which is the place of highest visual acuity which is something that we will cover today. As we go along today, I will be explaining human vision, the biology of it, some of the neuroscience, some of the particular components that we have trying to get you to understand how visual perception happens in our brains. So I want you to get an understanding of that because that is a critical part of engineering of VR systems overall. All right. So we have this and then I have a display. Let us say here. So this is a visual display. If you put a display very close to your eyes, can you focus on it? Right? So if it is very, very close, you will not be able to focus because if you remember from last time, if you consider each one of these pixels as a point source of light, the rays are going to be very much diverged, right? So and remember the diopter will tell you if you have parallel rays, how far it will take before they converge back from the parallel case. If they are diverged, it will take a very, very powerful lens to do that. The lens in your eye can compensate for some of that, but not all of it. So if I take a very weak lens, so I just brought a weak convex lens with me today and if I want to go up and try to focus on some particular part on the board, I have to stop the lens about, if I put it very close to my eye and see how close I can get, I have to stop about right here. I tried with some students in the class a little bit before the class started and they could get it up quite a bit closer because they are using this lens to further converge the rays, they are using their eye muscles to further converge. I have lost about 30 percent of my ability to do that, so I have to hold it back and maybe in a year or two, I will have to hold it even further back. So what is going to work for me? A more powerful lens, right? So it is going to do all of the work that this lens used to do when I was younger and more, so that it will work for everyone, at least everyone who is able to focus on light coming in at in parallel rays and focus it on to the retina. You could adjust some lens that you put in between back and forth to cover different cases of near-sightedness and far-sightedness, but what you cannot easily compensate for is astigmatism, which is one of the lens aberrations that we talked about last time and the human eye is subject to astigmatisms, the eye becomes ellipsoidal in shape in some way and then the focusing becomes asymmetric. So if you remember there is a horizontal focal plane and a vertical focal plane for example and they are not the same when there is an astigmatism, but you can at least by adjusting the lens location have some range of diopters, which makes it compatible for a very large range of people. So I put a lens in the middle here and I did not bring a powerful enough lens to really illustrate being able to go very close. You need a powerful, if you if you go out and buy a very powerful magnifying lens it will be it should be exactly right for this and you can do the experiment yourself. So this comes out of the lens, but the point I may be looking at here the pixel that I may be looking at has very divergent rays, if I draw this right here may be very divergent rays, but then they bend through the lens and come out parallel not quite drawing that right, but the lens should be taking these divergent rays and making them come out parallel. If they come out converging then you have a problem right, they may come out converging and then no matter what you do with your lens you will you will see blur because they are converging short of the retina. So you got to be careful with that. If you go the other way if they are still diverging a little bit maybe your eye can compensate right. So that is how depending on your ability to change your lens right. Questions about that? So the retina is this part all the way around the back here. I am going to go into the details of the retina and the neurons that are very close to it and then I will eventually cover the visual pathways that we as the signals go all the way back into the visual cortex which is back here under your skull. So placed along the retina are what are called photoreceptors. The photoreceptors let me write it out photoreceptors I like to think of these as the input pixels right if we think of engineering terminology. So the display has its pixels on it right RGB pixels there are essentially input pixels on the retina whereas the display is producing the output pixels and there is some kind of interface going on here that involves a significant amount of optics right the eyes lens the cornea remember is doing the most amount of light bending and the engineered lens as well. So all of this comes together there are two kinds of photoreceptors you may have seen this before rods and cones regarding rods we have about 120 million per eye. So and for cones we have far fewer only about 6 million and the function of these different types considerably different rods are for low light low light intensity and the cones are for color sensitivity. This separation of different types of photoreceptors has a profound impact on the way that we perceive brightness levels color all sorts of things as we process visual information and we get to the perception of vision this fundamental separation. So you may have noticed that if you're outside at night you're getting you're in a low light setting you cannot distinguish colors very well right so it's one of the fundamental outcomes of this. Let me show you a picture of how these rods and cones are distributed around the retina right and notice that you know when the light comes in from say the bottom here it hits this part of the retina right up at the top when the light comes in from the top it hits the bottom part of the retina. So in some sense the image is upside down right why don't I look upside down to you right now right the image on your retina is upside down yeah so I mean you've been your brain has learned to accept that right during your entire lifetime so it's considered normal there's no such transformation that has to be applied to it there's not like a some neurons that go and flip the image don't think so it's just what you've learned you may have heard of experiments where people put on prism glasses that invert the images and then after some number of days or weeks they don't see the inversion anymore everything looks fine again. So your brain can learn the orientation as being correct and it doesn't matter that this is upside down or right side up so it's not like there's a special piece of hardware that you have that's devoted to inverting it and and and correcting it because it in some sense it's it's consistent with what you've had your entire life. All right let's see oh yeah let me show the picture that's what I was going to do. So this shows the the number of receptors per square millimeter and zero is right at the phobia and that's the place where you have the greatest concentration of cones and then as you get a degree or two off from that the cones start to get replaced by rods and then the rod density increases and until you get about 15 degrees away or so to either side except for the strange anomaly over here between 10 and 20 degrees which is the blind spot on the retina and the reason why the blind spot is there is because of the connection to the optic nerve which I'll show the geometry of in just a little bit. So for these different types of photoreceptors that we have the the rods are responsive to light across these wavelengths shown in the dashed line here so centered at let's say 498 and of course they'll respond to an area around that but with let's say lower and lower probability for an equivalent intensity of stimulus and then there are for the cones three different kinds this this amazes me it's a RGB just like the way we design our monitors so and displays so we have a we have red cones green cones and blue cones distributed around in some kind of irregular way along the retina. So let me just draw a little bit here of a picture as well so in the in the fovea at 0 degrees it's all cones and they're very densely packed I'm not drawing them as different colors but there's also some kind of irregular arrangement of of colors. So these are quite small their their diameter is between 1 to 4 micrometers in diameter what I think is interesting about that is that if we think about wavelengths of visible light so let me put that squeeze that up here wavelengths of visible light what did I say it's between a 400 and 700 nanometers last time but let's convert it to micrometers so it's 0.4 micrometers to 0.7 micrometers so using 10 to the minus 6 units instead of 10 to the minus 9th units and if we do that then we see that at the very center of the fovea these things these these cones pack in to the size of 1 micrometer which is not very much larger than the wavelength of visible light which I find really incredible. So if you tried to make these any smaller you would start to get very difficult kinds of interferences right with the waves I mean they would be much smaller than the actual wavelengths and would not operate so well so this seems to be about as small as you can make this and still have it function well which I think is quite amazing that you know the density of these again are down to roughly the size of the wavelengths of visible light so quite small. So these are as I said it's 0 it's all cones already when you get over to 2 degrees off 2 degrees off then you're leaving the fovea what happens there is the cones already are getting bigger and rods start appearing among them. So the cones are in the 4 micrometer to 10 micrometer range whereas the rods are down to 1 micrometer. So they're small like the cones were and the cones are now getting larger and loosely interspersed with a lot of tightly packed rods and then by the time we get all the way over to 50 degrees it's almost entirely rods a few straw couple of cones in there. So that suggests that when we're looking we look forward when the fovea is fixated we have a very high visual acuity in color and then as we look off to the side without rotating the eye right we look off to the side so that the images over to the side of the retina towards the top or bottom from my horizontal picture as I look to the side right. So if we if we're looking over to the side without rotating the eye it's over here then we start losing spatial resolution in terms of color eventually the whole thing tapers off as I showed in this picture here eventually when we get 60 or 70 degrees away you can see that the density is going down significantly. So you end up losing eventually everything right but certainly your ability to distinguish colors out here it's very weak. If you believe you can see colors there it's because your brain is filling in information that's not there right trying to speculate let's say. Questions about this?