The recently detected polarization of the cosmic microwave background (CMB) holds the potential for revealing the physics of inflation and gravitationally mapping the large-scale structure of the universe, if so called B-mode signals below ${10}^{-7},$ or tenths of a $\mu \mathrm{K},$ can be reliably detected. We provide a language for describing systematic effects which distort the observed CMB temperature and polarization fields and so contaminate the B modes. We identify 7 types of effects, described by 11 distortion fields, and show their association with known instrumental systematics such as common mode and differential gain fluctuations, line cross-coupling, pointing errors, and differential polarized beam effects. Because of aliasing from the small-scale structure in the CMB, even uncorrelated fluctuations in these effects can affect the large-scale B modes relevant to gravitational waves. Many of these problems are greatly reduced by having an instrumental beam that resolves the primary anisotropies (full width at half maximum $\ll {10}^{\prime }).\mathrm{}$ To reach the ultimate goal of an inflationary energy scale of $3\times {10}^{15}\mathrm{GeV},$ polarization distortion fluctuations must be controlled at the ${10}^{-2}–{10}^{-3}$ level and temperature leakage to the ${10}^{-4}–{10}^{-3}$ level depending on the effect. For example, pointing errors must be controlled to ${1.5}^{″}\mathrm{rms}$ for arcminute scale beams or a percent of the Gaussian beam width for larger beams; low spatial frequency differential gain fluctuations or line cross-coupling must be eliminated at the level of ${10}^{-4}\mathrm{rms}.$

• Received 4 October 2002

DOI:https://doi.org/10.1103/PhysRevD.67.043004