Lens aberrations are categorized into first, third, and no second order due to the cylindrical symmetry of lenses. First order aberration is defocus, while third order aberrations include spherical aberration, coma, astigmatism, distortion, and curvature of field. The variation of these aberrations is defined by their dependence on the distance from the lens center, with first order varying as h and third order as h^3. The absence of second, fourth, and sixth order aberrations is explained by this symmetry. Understanding these concepts is crucial for improving lens design and image quality.
