Rugate thin film optical filters are useful for designing arbitrary-shaped spectra, such as multistep or triangular spectra. A technique for synthesizing the refractive index distribution of rugate filters was used to suppress unwanted ripples on the spectrum. The refractive index of an amorphous hydrogenated silicon oxide (a-SiO_x: H) rugate thin film was minutely controlled with a resolution of 0.001 using radio-frequency (RF) magnetron sputtering. The fabricated rugate filters had multistep bands over a wavelength range of 1260-1670nm or good linearity over 1290-1650nm.