Measuring time with a picosecond resolution is a complicated process, especially when employing non-specialized hardware. This thesis focuses on the development of a system with a time resolution of roughly 18 ps, with optimizations to reduce its non-linearities and increase the system scalability. A firmware-based time-to-digital converter array is designed and fully implemented in an Artix 7 FPGA from Xilinx. This array is coupled to a single-photon imaging sensor with 23 pixels, enabling photon arrival time measurements with picosecond resolution. A novel approach is taken in the firmware design by enabling a sliding scale measurement principle, drastically reducing the non-linearities. The timestamps are read out through a USB3 connection to be processed in real-time in a C++ software interface.