In a method of manufacturing a one-dimensionally varying optical filter, a substrate is coated to form a stack of layers of two or more different types. The coating may, for example, employ sputtering, electron-beam evaporation, or thermal evaporation. During the coating, the time-averaged deposition rate is varied along an optical gradient direction by generating reciprocation between a shadow mask and the substrate in a reciprocation direction that is transverse to the optical gradient direction. In some approaches, the shadow mask is periodic with a mask period defined along the direction of reciprocation, and the generated reciprocation has a stroke equal to or greater than the mask period along the direction of reciprocation. The substrate and the shadow mask may also be rotated together as a unit during the coating. Also disclosed are one-dimensionally varying optical filters, such as linear variable filters, made by such methods.