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The diffusion orientation distribution function (dODF) is primarily used for white matter fiber tractography. Here the resolving power of the dODF is investigated for a simple diffusion model of two intersecting axonal fiber bundles.The resolving power for the dODF is evaluated using the Sparrow criterion. This is determined for the exact dODF and also for q-space imaging (QSI), q-ball, and kurtosis approximations.Based on theoretical and numerical calculations, the resolving power is found to depend on the eigenvalues of the diffusion model and on the degree of radial weighting for the dODF. The resolving powers of the QSI and q-ball dODFs improve with increased b-value. The kurtosis dODF has a resolving power similar to that of the exact dODF.The dODFs, whether exact or approximate, have finite resolving powers that limit their sensitivity to fiber crossings. The resolving powers for the different dODFs considered here provide convenient benchmarks for assessing and comparing their performance. Magn Reson Med 76:679–688, 2016. © 2015 Wiley Periodicals, Inc.