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We present an exact expression for the $1/f$ contribution to the noise of theCMB temperature and polarization maps for a survey in which the scan pattern isisotropic. The result for polarization applies likewise to surveys with andwithout a rotating half-wave plate. A representative range of survey parametersis explored and implications for the design and optimization of future surveysare discussed. These results are most directly applicable to space-basedsurveys, which afford considerable freedom in the choice of the scan pattern onthe celestial sphere. We discuss the applicability of the methods developedhere to analyzing past experiments and present some conclusions pertinent tothe design of future experiments. The techniques developed here do not requirethat the excess low frequency noise have exactly the $1/f$ shape and readilygeneralize to other functional forms for the detector noise power spectrum. Inthe case of weakly anisotropic scanning patterns the techniques in this papercan be used to find a preconditioner for solving the map making equationefficiently using the conjugate gradient method.

An exact result concerning the $1/f$ noise contribution to the large-angle error in CMB temperature and polarization maps