Magneticfieldspervadetheinterstellarmedium ( ISM ) , butaredifficulttodetectandcharacterize.Thenewgenerationoflow-frequencyradiotelescopes , suchastheLowFrequencyArray ( LOFAR : aSquareKilometreArray-lowpathfinder ) , providesadvancementsinourcapabilityofprobingGalacticmagnetismthroughlow-frequencypolarimetry.MapsofdiffusepolarizedradioemissionandtheassociatedFaradayrotationcanbeusedtoinferpropertiesof , andtracestructurein , themagneticfieldsintheISM.However , todateverylittleoftheskyhasbeenprobedathighangularandFaradaydepthresolution.Weobserveda5 ^ { \circ } by5 ^ { \circ } regioncentredonthenearbygalaxyIC342 ( \ell = 138.2 ^ { \circ } , b = +10.6 ^ { \circ } ) usingtheLOFARHighBandAntennasinthefrequencyrange115–178MHz.Weimagedthisregionat 4 \aas@@fstack { \prime } 5 \times 3 \aas@@fstack { \prime } 8 resolutionandperformedFaradaytomographytodetectforegroundGalacticpolarizedsynchrotronemissionseparatedbyFaradaydepth ( differentamountsofFaradayrotation ) .OurFaradaydepthcube*showsrichpolarizedstructure , withupto30Kofpolarizedemissionat150MHz.WeclearlydetecttwopolarizedfeaturesthatextendovermostofthefieldbutareclearlyseparatedinFaradaydepth.SimulationsofthebehaviourofthedepolarizationofFaraday-thickstructuresatsuchlowfrequenciesshowthatsuchstructureswouldbetoostronglydepolarizedtoexplaintheobservations.Thesestructuresarethereforerejectedasthesourceoftheobservedpolarizedfeatures.OnlyFaradaythinstructureswillnotbestronglydepolarizedatlowfrequencies ; producingsuchstructuresrequireslocalizedvariationsintheratioofsynchrotronemissivitytoFaradaydepthperunitdistance.Suchvariationscanarisefromseveralphysicalphenomena , suchasatransitionbetweenregionsofionizedand ( mostly ) neutralgas.WeconcludethattheobservedpolarizedemissionisFaradaythin , andproposethattheemissionoriginatesfromtwomostlyneutralcloudsinthelocalISM.UsingmapsofthelocalISMtoestimatedistancestotheseclouds , wehavemodelledtheFaradayrotationforthislineofsightandestimatedthatthestrengthofthelineofsightcomponentofmagneticfieldofthelocalISMforthisdirectionvariesbetween -0.86 and+0.12 \upmu G ( wherepositiveistowardstheEarth ) .WeproposethatthismaybeausefulmethodformappingmagneticfieldswithinthelocalISMinalldirectionstowardsnearbyneutralclouds .