Mapping potential fields on the surfaces of rapidly rotating stars

We present a technique that combines Zeeman Doppler imaging (ZDI) principle s with a potential field mapping prescription in order to gain more informa tion about the surface field topology of rapid rotators. This technique is an improvement on standard ZDI, which can sometimes suffer from the suppres sion of one vector component because of the effects of stellar inclination, poor phase coverage or lack of flux from dark areas on the surface. Defini ng a relationship between the different vector components allows informatio n from one component to compensate for reduced information in another. We p resent simulations demonstrating the capability of this technique and discu ss its prospects.