The image reconstruction process in super-resolution structured illumination microscopy (SIM) is investigated. The structured pattern is generated by the interference of two Gaussian beams to encode undetectable spectra into detectable region of microscope. After parameters estimation of the structured pattern, the encoded spectra are computationally decoded and recombined in Fourier domain to equivalently increase the cut-off frequency of microscope, resulting in the extension of detectable spectra and a reconstructed image with about two-fold enhanced resolution. Three different methods to estimate the initial phase of structured pattern are compared, verifying the auto-correlation algorithm affords the fast, most precise and robust measurement. The artifacts sources and detailed reconstruction flowchart for both linear and nonlinear SIM are also presented.