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We measured the reflectivities of various single-walled carbon nanotubes (SWCNTs) by using integrated spheres in the spectral range between 0.5 eV and 6.0 eV. The SWCNTs were made using an arc-discharge method with yttrium as a catalyst and were purified using a standard procedure. The SWCNTs were doped either by atomic hydrogen or fluorine gas for unctionalization. We directly fitted the reflectivity spectra to the Drude-Lorentz equation without using Kramers-Kronig transformation. Combining the reflectivity and the resonance Raman data, we assigned chiral indices (n, m) to the optical structures in the reflectivity spectra. We discuss the modifications of the various optical structures found in the SWNTs after postgrowth treatments of hydrogen and fluorine functionalization. This optical study shows that a reflectivity measurement can resolve the chiral indices and the diameters of SWNTs with the assistance of Raman spectroscopy. We observed an increase in the -plasmon energy of F-doped and H-doped SWCNTs compared to that of the purified ones. We observed a weakening of van Hove singularity transitions in fluorinated SWCNTs and a large enhancement of the intensities of the S11 peaks in hydrogenated ones. For hydrogenated SWCNTs, we also measured and discuss the infrared absorption spectra, which show the incorporation of hydrogen to SWNTs.