An increasing number of photonics applications make use of nanoscale optical antennas that exhibit a strong, resonant interaction with photons of a specific frequency. The resonant properties of such antennas are conventionally characterized by far-field light-scattering techniques. However, many applications require quantitative knowledge of the near-field behaviour, and existing local field measurement techniques provide only relative, rather than absolute, data. Here, we demonstrate a photodetector platform that uses a silicon-on-insulator substrate to spectrally and spatially map the absolute values of enhanced fields near any type of optical antenna by transducing local electric fields into photocurrent. We are able to quantify the resonant optical and materials properties of nanoscale (similar to 50 nm) and wavelength-scale (similar to 1 mu m) metallic antennas as well as high-refractive-index semiconductor antennas. The data agree well with light-scattering measurements, full-field simulations and intuitive resonator models.