We present the study of the correlation between refractive index profiles and the optical response of rugate filters and multilayer mirrors. The conventionally used method in multilayer mirrors for ripple suppression in the passband will be compared with a similar simple method to remove the rugate filter sidelobes without apodization. The resulting layers are compared in performance with a typical quintic matching layer. An example based on silicon oxynitride alloys with refractive indices ranging between 1.47 and 1.83 was designed and deposited.