Precise measurements of electrostatic fields in harsh environments are required in fields ranging from particle accelerators to industrial installations. Many techniques disrupt the field distribution due to the presence of conductors. We present a fully dielectric sensor for very harsh environmental conditions, that exploits the Pockels effect manifested by electro-optic crystals. This system is designed to allow DC measurements to be performed in the frequency domain. The paper discusses an analytical model and simulations of the system, validated with experimental results. The working principle of the measurement technique is explained in detail along the known limitations and possible solutions to further increase the performance.