The firnification process of dry polar firn is of central interest in the context of refined interpretations of climate proxi parameters in deep polar ice cores. Especially the dating of enclosed air relies on realistic densification models. However, recent models follow mainly an empirical approach and do not account for the observed strong firn stratification which could generate significant errors under different climate conditions. More physically motivated models seem to be needed on the basis of comprehensive descriptions of microstructure. In this study we combine two experimental methods to investigate the microstructure of polar firn: The three dimensional structure of the ice and pore phases has been measured with the means of X-ray micro-computer tomography (µCT). This method offers a large set of parametrizations for the description of layered firn. Our approach includes different definitions of ice and pore clusters, neck radii , intercept lengths, distributions of surface normals, surface density, anisotropy ratios, tortuousity, Euler number and connectivity functions. Surface sections of cut 3D-sample are additionally analysed with the means of the 2D-microstructure mapping method (µSM). The µSM under microscope and in reflected light records grain boundaries and pore structures with high resolution. From µSM the classical grain and pore size distributions, two dimensional derivations of neck radii and shape factors are estimated. All measurements were carried out on shallow firn cores during the field campaign 2005/2006 at the EPICA (European Project of Ice Coring in Antarctica) DML-drill site, Antarctica. We show that the number of bonds per cluster in samples near the surface is highly correlated to their respective density. Accordingly, the neck radii are anticorrelated to the density. Maxima of pore size and anisotropy are observed at 2 to 3 meter depth where the metamorphism is dominated by temperature gradients. To highlight the methodological aspect we present different size parametrizations in detail and discuss the three dimensional CT- approach in relation to the standard two dimensional techniques.