Random anti-reflecting surface structures (rARSS) are fabricated on fused silica substrates, for broadband and omnidirectional applications. These structures are fabricated using dry reactive ion etching. Etching parameters, such as RF power, flow ratio of etching gases, and etching time, determine the surface morphology of the random structures. The surface roughness of the random structures induces a gradient index transition over the boundary, yielding transmission enhancement compared to plain polished fused silica. We present variable angle-of-incidence (AOI) and polarization transmission measurements, through rARSS on fused silica at 633nm, and compare the results with conventional AR coating simulations. We tested a number of different samples, all with optimized transmission near 633nm, but different surface characteristics, and found that rARSS have structural characteristics which affect transmission at non-normal angles of incidence. We show that rARSS on fused silica substrates outperform conventional BBAR and SLAR thin film coatings in transmission enhancement, for incident light with AOI from 0° to 55°. We measured rARSS with zero degree of polarization in transmission, for AOI ranging from 0° to 60° in certain cases. A figure of merit that includes both the transmission degree of polarization and transmission enhancement is formulated in order to quantify rARSS performance for both effects. We found that rARSS measured performance is better than SLAR and BBAR, for transmission with AOI greater than 30° and up to 70°, especially for p-polarized incident light, which is the stricter criterion. Applications requiring polarization insensitivity and AR performance can be positively impacted by these surface structures.