The optical properties of sea ice such as albedo and transmittance are governed by strong scattering of light in the sea-ice matrix. Due to its crystal structure, most physical properties of sea ice are anisotropic. Nevertheless, the optical properties of sea ice are treated as isotropic in most models although existing measurements give a contradicting picture. Understanding radiative transfer and the light-field geometry under sea ice is crucial for correct conversion of radiance data e.g. in AUV or ROV applications. We present ROV-based measurements of irradiance and radiance under summer sea ice of the central Arctic. They allow for insights into the under-ice light field under ponded sea ice and into micro-optical scattering properties of sea ice. Field measurements are interpreted along with numerical radiative transfer calculations, laboratory experiments and microstructure analysis. Our results show that the ratio of synchronous measurements of transmitted irradiance and radiance shows a clear deviation of the angular radiance distribution from the widely used assumption of an isotropic under-ice light field. We show that the angular radiance distribution under sea ice is more downward-directed than commonly assumed. This implies that assuming isotropic conditions under sea ice leads to significant errors in light-field modeling and the interpretation of radiation measurements. The under-ice light field is directly influenced by the anisotropic scattering coefficient of the bottommost sea ice, and the downward-directed radiance distribution causes a deeper light penetration into the ocean under pond-covered ice.