The impact of the different reconstruction parameters in super-resolution structured illumination microscopy (SIM) on image artifacts is carefully analyzed. These parameters comprise the Wiener filter parameter, an apodization function, zero-frequency suppression and modifications of the optical transfer function. A detailed investigation of the reconstructed image spectrum is concluded to be suitable for identifying artifacts. For this purpose, two samples, an artificial test slide and a more realistic biological system, were used to characterize the artifact classes and their correlation with the image spectra as well as the reconstruction parameters. In addition, a guideline for efficient parameter optimization is suggested and the implementation of the parameters in selected up-to-date processing packages (proprietary and open-source) is depicted.