The rest of what we're about to do for this lesson is just talk a little bit  more about some of the properties of, of image formation and lenses and cameras.  Actually belongs more in a course called Computational Photography.  And my colleague Irfan Essa at Georgia Tech teaches one.  And there are others online.  And it teaches you sort of the math of the, of, of photography.  I'm only going to talk a little bit about it here.  Because next time we'll sort of run back and  revert to a very simplified model of imaging.  And do a much more complicated notion on recovery of computer vision.  So, the first thing about computation photography is well,  we don't actually use pinhole cameras.  Right? We use lenses.  And lenses have this notion of focus.  And in general, lenses are designed so that all the points at  a particular distance away will all be focused to the same point on your film or  on your recording medium.  One of the challenges there is that another point that's at  a different distance away, so here the blue point on the tree,  they're not all going to be focused at that point.  They're going to be sort of spread out a little bit.  And in fact, that spread is referred to sometimes as the circle of confusion.  It's a, if it's a single point there's a circle that it cuts out.  So, the way you change where things focus and  how much is in focus have to do with changing the shape of the lens.  So, talk just a little bit about lenses. 

Sort of our slightly simplified view of lenses as follows.  One is that lenses have an optical axis,  along which light passes straight through unbent.  The other is,  is that light that comes in parallel are all bent to the same point.  And that's referred to as the focal point.  The other thing is in order to reduce the amount of spread of things,  lenses also have an aperture.  But now the aperture, instead of being just a single point,  is restricting the set of rays that are coming in.  It used to be that almost all lenses were cut out of parts of spheres,  because if we understood the mechanics of that and were easy to make, and  you could do the math.  But these days there are many of what are called aspherical elements  because it's all computer modeling.  We'll talk about that just a little bit at the very end.