In our last lecture, I said there were two rays that we're going to use to understand an optical system, like the two rays we used in the Gaussian beam system. The first was the marginal array, which is launched from the object intersection with the axes, and you increase the angle until you hit the first stop in the system, and you call that the aperture stop. The chief ray or second ray that we're going to use is then found by going to the aperture stop. You have to find marginal first because you don't know where the aperture stop is until you've gone through that process with the marginal ray. But once you know where the aperture stop is, you then launch the chief ray, or second, from the aperture stop itself, again, on the axes. And we're going to go through the same process of tilting that chief ray up, shooting up both backwards and forwards until it hits some stop in the system. It could be the edge of a lens if a lens is on a diameter, or it could be an intentional iris somewhere in the system. Note that the chief ray can never hit the aperture stop because it's launched from the aperture stop itself. So whatever we hit is going to be some other stop, and we're going to call that other stop, the field stop. And the reason we call it that is this stop is what's going to limit our field of view, how big an object we can see. So if I take this chief ray, which has just hit the edge of my field stop here, and I come back out here to my object space, this is my field of view. Here's the radius of the field of view. So if I take the chief ray, which has just hit the edge of my field stop here, and I come back out here into object space, this is my field of view. Here's the radius of the field of view at the object plane. And the reason this is the field of view is imagine that I took and launched a ray or had some object out here outside of the chief ray at a larger position here. If I trace that through the system, it's going to hit the field stop. I'm not going to get this light through. So the chief ray determines how big is your field, just like the marginal ray determined what is the angles that you get off the object. And you see again there, this very common theme we're having through this whole system is that there are two things interesting about a bundle of light. One is the range of angles, and the other is how big it is. The marginal ray determines the aperture of the system, and we measure the angular content of the light through the numerical aperture. The chief ray determines the field, and the case of sitting here at the object, we see here a field of view, and that's now how big the object can be. Any object that's bigger than that don't fit,and the edges of it are chopped off. It's convenient sometimes to talk about the diameter of the field of view in object space or image space, of course, differing by the magnification of the system. It's also sometimes handy, particularly when the object distance is very, very large, let's say, you're looking at the moon. It's more convenient to talk about the field of view as an angle. That's just the angle of the chief ray, let's say, in object space. But don't get confused. The chief ray fundamentally talks about the size of the beam of light at the object. It's just sometimes the object is very far away, and instead of talking about the size of the object, we talk about the angle it subtends when seen from the imaging system. So trace the chief ray. I'm going to draw all the chief rays to the system in red, all the marginal rays are in blue because it's very important you keep them separate. Now the question would be is, what does the field stop look like from object space and image space exactly analogous to what we did with the marginal ray? So we call the images of the field stop in object space and image space, windows. They're analogous to the pupils, the image of the aperture stop. Windows aren't actually as important as pupils, but the analogy is good, and it's nice to sort of have all these pieces. The point is the pupils are what appear to limit the angular extent of the beam in object and image space. And the windows limit the physical, the transverse distance extent of the object and the image seen from those two spaces. And so we use exactly the same idea as we imagine sitting here at our image, let's say. Let's start there, in this case, because it's easier. Looking back into the system and asking what appears to limit my field of view, what seems to chop off the shield to the chief ray? In this particular case, since the field stop is in image space, being an image space simply means there's nothing between view and the image because everything after this lens is in image space. In this case, the field stop is in image space, so this is also the exit window. If I come over here to the object space, and I now look at the field stop, I find that they don't see the field stop directly because the optical system is in the way. So, once again, I have to do some retracing to find where is the image of the field stop in object space. We're using a lot of jargon now, but I'm trying to use it quite carefully. So if it doesn't make sense, stop and listen to it again. Well, how do I find an image of this field stop over here? I shoot two or more rays and find out where they intersect. I already have one ray. It's the chief ray. I can shoot the ray right through the center of the lens. That's everyone's favorite because it's easy. In this case, just for the fun of it, I've done one more. I'll shoot a ray parallel to the axes. It, of course, goes through this focal plane, and they all come together out here. So this is my entrance window. This is what the field stop appears to look like from object space. Note that there's something kind of funny here is that my object is here and my window isn't on the object. And that's because I've made the not very optimal Choice of putting the field stop not on the image plane or something conjugate to the image plane. And that would mean that when I put an object here, and I ask how big can that object be, something kind of funny will happen. And let's just imagine extending my middle object arrow down here. When my object arrow is right on my chief ray, then I can tell that the rays off of this object will just pass through the edge of the window. But, actually, it will only be some of the rays, about half of the rays off of the object will get through the window. Rays going at higher angles will actually get blocked, and you'll see this in a minute. It's called vignetting. In other words, what's going to happen is near the center of my object, all light gets through, but as they get out here towards the edge, because my window, the thing is limiting my field isn't at my object. I'm actually going to have the windows of focus as a way of saying it. And I'm going to have sort of a gradual darkening of my object and its ability to get through this imaging system at the edges. So if I put film here in a nice uniform object, I have uniform illumination of the film, and then it would slowly get darker, as I went towards the edge of my field as defined by this chief ray. And that's typically a bad thing. You don't want that. In some photography cases, it's considered kind of arty, and we'll see some examples of that. But that's what happens when your entrance window isn't on your object, and your exit window isn't on your image, is that your light you get through the system is actually blurry, and that's because these windows are out of focus at the plane of the image, and that's not always a good thing.
