Spectroscopic ellipsometry and scanning electron microscopy (SEM) experiments are employed to characterize porous aluminum oxide obtained by anodization of thin aluminum films. Rutherford backscattering spectra and x-ray diffraction experiments provide information on the composition and the structure of the samples. Results on our thin film samples with a well-defined geometry show that anodization of aluminum is reproducible and results in a porous aluminum oxide network with randomly distributed, but perfectly aligned cylindrical pores perpendicular to the substrate. The ellipsometry spectra are analyzed using an anisotropic optical model, partly based on the original work by Bruggeman. The model adequately describes the optical response of the anodized film in terms of three physically relevant parameters: the film thickness, the cylinder fraction, and the nanoporosity of the aluminum oxide matrix. Values of the first two quantities, obtained from fitting the spectra, are in perfect agreement with SEM results, when the nanoporosity of the aluminum oxide matrix is taken into account. The validity of our optical model was verified over a large range of cylinder fractions, by widening of the pores through chemical etching in phosphoric acid. While the cylinder fraction increases significantly with etch time and etchant concentration, the nanoporosity remains almost unchanged. Additionally, based on a simple model considering a linear etch rate, the concentration dependence of the etch rate was determined.