By applying linear perturbation theory to the radiation transport equation, the inverse problem of optical diffusion tomography can be reduced to a set of linear equations, Wµ = R, where W is the weight function, µ is the cross section perturbations to be imaged, and R is the detector readings perturbations. The quality of reconstructed images depends on the accuracy of W and R, and was studied by corrupting one or both with systematic error and/or random noise. Monte Carlo simulations (MCS) performed on a cylindrical phantom of 20 mean free paths (mfp) diameter, with and without a black absorber located off axis, were used to compute R and W (i.e., matched W). Additional MCS computed Ws for cylinders of 10 mfp, 40 mfp, and 100 mfp diameters (i.e., unmatched W). R and/or W also were corrupted with additive white noise. A constrained CGD method we developed was used to reconstruct images from the simulated R and Ws. The results show that images containing few artifacts and the rod accurately located can be obtained when the matched W is used. Comparable image quality was obtained for the unmatched Ws, but the location of the rod becomes more inaccurate as the mismatch increases. The noise study shows that W is much more sensitive than R to noise. The rod can be reasonably located with 100% noise added to R, while addition of 5% to W totally destroys the image. The impact of noise increases with the number of iterations.