Full composition range AlGaN refers to AlGaN with an Al composition of 0-1. In this paper, the composition is introduced into the complex refractive index of AlGaN, and a complex refractive index formula for full composition AlGaN is established in the spectral range of 200-800 nm. The optical parameters of sapphire are obtained by ellipsometry and verified by the transmission spectrum. The complex refractive index formula and the multilayer optical film filter model are used to study the transmission spectra of the multilayer AlGaN samples on sapphire substrates. The effect of each film on the transmission spectra of samples and the possible shift of an actual structure caused by the process are analyzed, and a fast analysis method is thus proposed for the transmission spectra of multilayer films.