Most antireflection coatings in use today are derived from concepts based on the use of quarter-wave (Q) and half-wave (H) optical thickness layers. We show an alternative and more general way of viewing the concepts and how special cases reduce to the commonly used forms. The monotonically graded inhomogeneous index layer from the substrate to the medium has been extensively reported by Jacobsson and Martensson(1), Dobrowolski and Ho(2), and others. Various oscillating index profiles between the substrate and the medium show promise in producing superior broadband AR coatings. These concepts have evolved from observation of broadband designs using multiple homogeneous quarter- and half-wave optical thickness layers as described by DeBell(3). The viewpoint leads to some further understanding of the possibilities and limitations of AR coatings in general.