A double bandstop rugate filter is an optical filter in which the refractive index profile varies as the sum of two sinusoids with different frequencies. The design and simulation of such double bandstop rugate filters is described. Furthermore, computer-controlled plasma-enhanced chemical vapor deposition is employed to grow such a compositionally varying optical filter using silane, nitrogen, and nitrous oxide as the source gases, The flow rate of the nitrous oxide and the deposition time are computer-controlled to grow layers of silicon oxynitride with a varying refractive index profile. The measured spectral response of a double bandstop rugate filter is in good agreement with that predicted from simulation.