To investigate the optical properties in non-periodic dielectric systems, we study here the reflection of light from nanostructured porous-silicon-based period doubling heterostructures. The multilayered systems are fabricated in such a way that the optical thickness of each layer is one quarter of 650nm. The results for the optical reflectance are presented and compared with that of Fibonacci, Thue-Morse, and random structures fabricated under the same conditions. Numerical simulation for the reflectance along the lines of the transfer matrix approach is performed. In addition, optical reflection from Gaussian porous silicon multilayers is also briefly discussed. We find that porous silicon Period Doubling dielectric multilayers could demonstrate the optical properties similar to the classical periodic Febry-Perot interference filters with one or multiple resonant peaks, but with an advantage of having total optical thickness much lesser than that of the periodic structures.