The recent advent of ultra high frame rate cameras gives rise to the possibility of constructing swept source full-field OCT systems with achievable volume rates approaching 10Hz and net A-scan rates approaching 10MHz. Unfortunately, when illuminated with partially coherent light, full-field OCT in turbid media suffers resolution and SNR degradation from coherent multiple scattering, a phenomenon commonly referred to as crosstalk. As a result, most FFOCT systems employ thermal sources, which provide spatially incoherent illumination to achieve crosstalk rejection. However, these thermal sources preclude the use of swept source lasers. In this work, we demonstrate the use of a carefully configured FFOCT system employing multimode fiber in the illumination arm to reduce the spatial coherence of a partially coherent source. By reducing the coherence area below the system resolution, the illumination becomes effectively spatially incoherent and crosstalk is largely rejected. We compare FFOCT images of a USAF test chart positioned beneath both transparent and turbid phantoms using both illumination schemes.