Laser Glass Deposition is an additive manufacturing method to produce individualized structural components out of glass. A CO2 laser is utilized as a heat source to melt fused silica filaments and transform them into a formable viscous state. The fiber filament is fed laterally under a defined angle into the process zone. The viscous filament is deposited layer-by-layer using a 3-axis linear system with an integrated rotational axis. To investigate the surface and volume quality of the additively manufactured fused silica components, fully dense test specimens are analyzed in this paper. Quality characteristics such as surface roughness, formation of boundary layers and optical transparency constitute the focus of the investigations. Consequently, fully dense glass components with homogeneous volume structures without pores and boundary layers and a surface roughness of less than 30 nm were printed successfully.