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Structured illumination microscopy (SIM) has become a widely used tool for insight into biomedical challenges due to its rapid, long-term, and super-resolution (SR) imaging. However, artifacts that often appear in SIM images have long brought into question its fidelity, and might cause misinterpretation of biological structures. We present HiFi-SIM, a high-fidelity SIM reconstruction algorithm, by engineering the effective point spread function (PSF) into an ideal form. HiFi-SIM can effectively reduce commonly seen artifacts without loss of fine structures and improve the axial sectioning for samples with strong background. In particular, HiFi-SIM is not sensitive to the commonly used PSF and reconstruction parameters; hence, it lowers the requirements for dedicated PSF calibration and complicated parameter adjustment, thus promoting SIM as a daily imaging tool.