We propose a new type of photonic analog-to-digital converter (ADC), designed for high-resolution (>7 bit) and high sampling rates (scalable to tens of GS/s). It is based on encoding the input analog voltage signal onto the phase of an optical pulse stream originating from a modelocked laser, and uses spatial oversampling as a means to improve the conversion resolution. This paper describes the concept of spatial oversampling and draws its similarities to the commonly used temporal oversampling. The design and fabrication of a LiNbO3/silica hybrid photonic integrated circuit for implementing the spatial oversampling is shown, and its abilities are demonstrated experimentally by digitizing gigahertz signals (frequencies up to 18GHz) at an undersampled rate of 2.56GS/s with a conversion resolution of up to 7.6 effective bits. Oversampling factors of 1-4 are demonstrated.