  We show that the use of Random Optical Grating using UV Exposure (ROGUE) can
significantly reduce the noise floor of an optical frequency domain
reflectometry (OFDR) measurement of Faraday rotation in the polarization. We
compare it with unexposed spun fiber which shows a S/P minimum ratio (signal
noise floor) 20 dB higher than when using our ROGUE. High sensitivity magnetic
field measurements are achieved by spatially filtering (setting a gage length)
the derivative of the S/P ratio's evolution. Example of a calibrated
electromagnet spatially resolved B-field measurement is demonstrated, which can
measure fields down to 10 mT with 10 cm spatial resolution. The potential for
current sensing using such ROGUE apparatus is discussed and simulation shows a
noise floor of around 1 A with 40 probing loops spatial resolution.
