To understand radiometry, we need just a couple of things. And the first is a good set of units and jargon. And without that, you're really in trouble. So let's get those first. We're going to talk about the total amount of optical flux that we get through our system. This is in watts or joules per second. I don't know if this is good jargon or bad, but the symbol that's traditionally used for power, thi, is the same symbol we use for optical power of a lens describing whatever its focal length. And I could've used the different sample here, but thi is the standard in the literature, so I'm giving you with the unit you'll run into. So just have to keep track of the fact that we mean different things by power in different cases here. Also problematic is that everyone, or most everyone, is a bit sloppy on the word intensity. And I've used this already in this class to mean watts per area, power per area. However, formally in the discipline of radiometry, intensity is a different thing. And intensity is of a point source, and it's the total power radiated into a solid angle described in steradians, that's what sr is there. So when we're being careful and doing radiometry we have to be formal with the language. That intensity is a quantity of point sources, power per solid angle, not of areas. The thing which describes the power in an area is irradiance with a symbol E, that's watts per unit area. So formally we should say whenever we talk about how much light is falling on an area we should say irradiance. It's extremely common in optics to be a little sloppy and to instead use the more English or common jargon word of intensity. Throughout this radiometry section, I will be careful and I will use these quantities correctly, and I'll try to always mention the units to remind you. So yeah. Total power watts. Watts per unit solid angle intensity, watts per area irradiance, and probably most important quantity of all is the combination, watts per solid angle per area. And that may not make sense yet, but one of the primary goal of this module is to make you understand the radiance concept and how incredibly fundamental it is. These are sort of a scientific units to describe radiometry as we have coined this power in watts and joules for energy. There's a parallel set of units that describe how things appear to the human eye and the difference there is that our eye has a spectral response curve and it's most sensitive in the green. So a certain number of watts isn't actually way to describe how illuminated the appears to the eye. You have to care about the spectrum. So it's a parallel set of units that are all like these that have that spectral response built in. And they don't add anything, that the physics is fully captured by these more scientific sets and units so I'm just going to use them. However, you should know that this concept of radiance, which is so important in the photometric units, the ones that know about they eyeballs specter response curve, their radiance is called brightness. And again this concept of radiance is so important that another sloppiness you will hear is that people will use the word brightness interchangeably with radiance. We will hear about the constant radiance theorem here fairly quickly. And you will hear it referred to and I have done it myself as the constant brightness theorem. It's not wrong they are both the same quantity fundamentally, one simply has a spectral response built in. But just again jargon, you may hear people use radiance and brightness somewhat interchangeably. And they have roughly the same units, but there's an extra integration in the photometric units to deal with the eyeballs' response. Okay. Language. Now let's start putting some math on things. You may not be used to dealing with solid angles. I'll review that here in a minute. But fundamentally, a solid angle, I'll give you a little cartoon here, is defined as, if you took a portion of a sphere, the area of the cap of that cone divided by the radius of the sphere. And that describes a solid angle, because notice by analogy here, regular angle theta would be the length of an arc over the radius of the arc. So it's just the analogy from one dimensions now to two dimensions. And we're going to be radiating light to the two dimensions a lot. So we're going to need that. So if we had a point source who remember who would be describe by this intensity quantity, we would take the total power in watts. And divide by some cone that were gathering up from that point source. And we describe that cone to its solid angle. So there is the definition of intensity. Conversely, if we were looking at a surface of plane, either light going on to a plane or coming off and there's a formerly, a slightly different jargon there, but, for our purposes it doesn't really matter which direction the lights going. So, for planes we talked about the total optical power, in watts, divided by the area of the plane we're looking at. And then, finally, radiance must be the combination of those. If we're looking at a plane, it turns out that each point in that plane can be thought of as a little point. And therefore it radiates into some solid angle, but then we might also be interested in how much of the plane we're looking at, capital A and so that's where this quantity radiance shows up. Real sources radiate both into angle and have finite area and hopefully that's beginning to immediately ring a bell about the shape of light, and that it's described by two rays. Or in the case of Gaussian beams, well two rays as well. That the combination of area and angle is related and you need both quantities. And this is just the beginnings of how we're going to take these units and start using them. So, for example, if you stop this video right now and find a piece of paper and you tilt the piece of paper to look at how the light that appears to come off that paper changes as you foreshorten the paper. As you see more and more of the unit area on the paper, but in a projection it'll look smaller to you by the cosine theta. And the question is does the paper appear to be brighter and does the paper as you tilt it to be 90 degrees. So now the entire piece of paper is collapsed to an infinitesimally small point. Do you blow the universe up or do you blind yourself because the light is so incredibly bright? I think you will find you don't. But this argument would kind of suggest you do because you're for shortening that paper and seeing all of it in a smaller and smaller area. These are the kinds of questions we are going to figure out in this module.
