The goal of this section is to teach you the first techniques you would turn to to reduce the aberrations of an optical system. Designing lenses with minimal aberration is a significantly more sophisticated task, and that's not the purpose of this course. But in this course, we want you to be able to do first-order design, turn those designs into real glass thick optics, put them into a code like optic studio, recognize what aberrations you have through the techniques we just discussed, coma, spherical, et cetera, and now what might you do about a system which probably doesn't perform optimally. The first thing, of course, you're going to do is hit that optimized button, but that's only take you so far. So, this is those first set of techniques you turn to to improve the performance of an optical system. The first thing you do is, repeating the table that ended the previous section, is you identify which aberrations you have and you remember how they scale with aperture stop and field size, your two stops to primary diameters that control system. If, for example, let's say, you have a system which is only working on access, may be you're focusing the laser or you're doing some sort of scanning lithography or scanning imaging, then you can only have spherical, and you remember that spherical scales as the third power of the exponent. It turns out actually, and you'd think from that, that if you reduce the aperture by a factor of two, your spherical aberration would drop by two cubed or a factor eight, and it would. But it's also worth remembering that aperture controls diffraction limited spot size through our zero, the diffraction limited radius. As you decrease the aperture by a factor of two, the diffraction limited radius will go up by about a factor of two. Aberrations are important only relative to the diffraction limited spot size. So, as you decrease the aperture, the diffraction limited spot size goes up and your aberration goes down in between the third power for spherical and first power for astigmatism and petzval. So, for example, in the case of spherical, you're going to find that you win as aperture size to the fourth power, and that's a lot. So, one of the simplest and easiest things you often do is you design a system to work at particular numerical aperture and a particular field, and then you might go, "Well, you know what, I'm willing to give up 20 percent or something of that field because it makes such a dramatic difference on my aberrations." That's a common first step, but you need to understand which aberrations you have and how they scale with aperture and field.