Structured illumination microscopy (SIM) is a kind of wide-field super resolution imaging technique which achieves the resolution improvement by exploiting the interference patterns to obtain the information out of the observable region in Fourier space. The resolution improvement in SIM is done by analyzing the obtained image and restored the observed sample with software. This process is sensitive to the measured PSF, as the PSF is the main factor to do the image deblurring and parameters estimation. Frequently, the PSF of a SIM system is obtained by fitting the recorded beads image with the Gaussian function. However, the Gaussian fitting cannot retrieve the aberration and noise in the PSF. The blind image deconvolution method is a family of algorithms which can be used to restore the object and corresponding PSF from the degraded images. The novel Tangential Iterative Projections (TIP) algorithm is a kind of blind image deconvolution algorithm proposed by Wilding et al.. This algorithm is simple, fast and robust to the noise condition. It is proved that TIP can be implemented on both the multi-frame deconvolution scenario and single-frame scenario. The aim of this thesis is to verify whether TIP algorithm can retrieve a PSF, which can be used to do the SIM image reconstruction, from the SIM data. For this purpose, a simulated SIM optical system is built in Matlab to generate the SIM images, and both the single-frame TIP and multi-frame TIP frameworks are used to do the PSF retrieval. In addition, a new constraint for the PSF which is generated based on the diffraction limit of the optical system is implemented. In order to reduce the execution time and avoid the overfitting of the algorithm, a stop criterion is introduced. The result shows both the multi-frame TIP and single-frame TIP can be used to retrieve an effective PSF from the SIM data, and the single-frame TIP is more applicable and more accuracy compared with the multi-frame TIP.