Unique detection of electromagnetic fields and identification of field type and strength as a function of position were used to determine the nature of self-generated fields in a novel experiment with laser-generated plasma bubbles on two sides of a plastic foil. Field-induced deflections of monoenergetic 15-MeV probe protons passing through the two bubbles, measured quantitatively with proton radiography, were combined with Lorentz mapping to provide separate measurements of magnetic and electric fields. The result was absolute identification and measurement of a toroidal magnetic field around each bubble and determination that any electric field component parallel to the foil was below measurement uncertainties.