 So, there is a very interesting question that arises and and this is this is fundamental to design a virtual reality headsets. If I put a display in front of the eye like this, how much resolution is enough right? How much resolution should this display be given that I know the photoreceptor density in from this plot and from these pictures I have made, we should be able to do some simple calculations and just try to estimate. So, why do I do that just to give an idea because you see this around people in industry are talking about how much is enough I think it is quite difficult to say without doing the experiments. So, somebody has to manufacture high resolution displays um higher than 1080p I mean something like 2k by 2k per eye and then maybe 4k by 4k per eye and maybe 16k by 16k per eye and so forth and see where the limits are right that is the kind of things that should be done. So, how much resolution let us say a display is enough for VR like I will leave my picture right here that I made. Let us suppose I guess I am all the way off at 50 degrees from the picture I have remaining, but even if this were at the fovea let us say and we will return to the other picture then if I had very low resolution in this optical system here, then the pixels think about one individual pixel there like a kind of a square let us say they do not really look like that, but let us suppose they are perfect squares and they get imaged on the retina somewhere. So, if that is the case if the resolution is low there will be this pixel that gets projected onto the retina and then there are a lot of photoreceptors to detect it right and as we increase the density of the photoreceptors here for close to the if we are at the fovea let us say we may have a lot of photoreceptors. So, you perceive there is a square there right you are seeing what is called the pixel structure. Now, it is not exactly a square because and you can do this after class if you like you can use the same magnifying lens walk up to this screen over here and take a look at the sub pixels if you have never done that before. The RG and B components are interlaced in some kind of way. So, they do not make it is not there is not exactly one RGB rectangle right. So, you have to go in and look at the even lower or even higher resolution which is even smaller contributing components to the images that we see. Well, here is one thing I could do I could I could make a rough estimate and say we have 126 million photoreceptors right total because I said we had a what did I say 100 million no 120 million which one cones or rods 120 million cones and about 6 million rods or is the other way around 120 million rods and about 6 million cones good ok because the cones are all concentrated as you can see from the picture the cones are all concentrated around the fovea, but then the rods is quite a lot of them and distribute over a much larger area. So, it makes sense that there are significantly more rods well I could just take the square root of this and that is roughly equal to 11,225 and if I imagine now why did I take the square root well I just imagine that the retina if I were to unwrap it it is really a spherical cap I am just imagining unrolling it and flattening it out. So, if I were to do that ok it does not have a square shape but I am just trying to make a very rough estimate here. So, if I were to do that trying to imagine what a rectangular screen should look like then perhaps it should be 11,000 by 11,000 roughly if I wanted to have the the total number of pixels that I present to an eye match the total number of photoreceptors is that even a good idea I am not sure right. So, we could adjust further and say well why do I just take the area of highest visual acuity which is around here and because I am going to have the fovea let us say aimed at the place where I am looking most of the time. So, why do I say ok that is going to be the place where I am going to be looking for pixels. So, maybe I should use that right. So, I could make a more careful calculation I could say the density at the fovea and I will even round up a bit I will say it is about 200,000 per millimeter squared. So, if I look at it that way turns out that the area of the retina is I looked this up before class this is 1094 millimeter squared of course, there must be some variations among humans, but 1000. So, roughly 1000 square millimeters. So, if I imagine that the retina had maximum density in all places well that is kind of a strange assumption why would I do that I will say why in a minute, but if you imagine that this is the limiting case then if I take the square root of the 200 million that I get because if I had maximum density and I had it spread across let us say roughly 1000 square millimeter square millimeters then this would be about 200 million photoreceptors and if I take the square root of that this is about 14,000. So, a little bit bigger and what is interesting about that the reason why I tried to look at the case of imagining as if the fovea were propagated across the entire retina. In other words imagining at the fovea were so large it has that top density the highest density of photoreceptors everywhere is because this I can rotate right. So, you can rotate the I and look at the top and bottom of the screen as you rotate. So, it effectively becomes like that right if you are trying to ask how high the resolution of the screen should be. So, this is reasonable. So, maybe a reasonable upper bound maybe a 16 let us say 16 K by 16 K display per I should be sufficient should be sufficient for not perceiving pixels. Now, at this point you might ask why do not I just track which way the I is looking and then only present that you know highly dense information exactly in the right place where it needs to be and do not worry about the rest of the image right and that would save a lot of effort in computer graphics a lot of effort in trying to put out so many pixels across this entire display all these pixels have been will be rendered here on the off chance that your I is looking at them, but it does not know where your I is looking. So, it just has to render all of them. So, a great idea it is called foveated rendering foveated rendering is to track the I and then only draw high resolution images in the place where we know that the I is looking where the fovea can perceive these areas of greatest concentration right. So, and that is all fine it is more expensive due to the I tracking and it introduces latency into the pipeline. So, there is tracking latency and then you have to do customized rendering for that maybe a few years down the road that will be feasible in the consumer space consumer space of products and things, but for right now it is not effective enough at low cost and may not even be effective enough at a very high cost, but it is it is right on the kind of thresholds let us say. Questions about this? Now, sometimes I look I look at this and I feel motivated to go even higher and say well maybe it should be 32 K by 32 K because I looked at the number of photoreceptors but I did not take into account the fact that there is RG and B photoreceptors right. So, maybe I should imagine well I need to have enough to which way should I go in that case let us see I have I have I do not have this density of RG and B photoreceptors I actually have a lower if I just pick one of them of just reds I have a lower density of them right and also when I look at my display it has some kind of pattern of RG and B components as well. So, I have not taken into account the patterns of RG and B here and the patterns of RG and B here right along the retina. So, I have not even taken that into account. If I take that into account with this estimate increase or decrease? . Perhaps it would decrease yeah it may decrease this may be sufficient let us say overkill and an interesting question is if I were to make a 4 K by 4 K display would that be enough would you ever be able to perceive anything would there be any need right would you ever see pixels at 4 K by 4 K and the honest answer right now is I do not know I have never experienced it before and I cannot say I am feel fairly certain that at 16 K by 16 K per I would not perceive pixels but you know the brain and the human vision system is often full of surprises. So, who knows but it seems that this should be sufficient questions about that yes yes there is some asymmetry I believe it corresponds to which eye this is and I am afraid to be quoted on this but I believe you go further in this direction which I would guess for evolutionary reasons is that something may be coming from this side to eat you and it is better to see as far as possible whereas your nose tends to block the side anyway and then it is asymmetric you know it is the mirror image for the other eye. So, that is why I believe it is asymmetric like that anyone else I wondered it myself a few months ago and I looked it up I believe that is the answer but could be wrong all right. Let me say a little bit more about photoreceptors and then I want to start to get into the visual pathways let us say that lead from photoreceptors up to your visual cortex I want to say a little bit more about photoreceptors as we go along here.