where k c is the cut - off frequency of wide - field imaging , and k ex is the spatial frequency of the excitation pattern . With Eq . ( 1 ) , at least in principle , SR - SIM could achieve perfect imaging without sidelobe ( blue lines in Fig . 1a ) . Inspired by the above , we developed a high - fidelity SIM reconstruction algorithm by engineering the equivalent PSF of SR - SIM into an ideal form , called " HiFi - SIM " . The flowchart of HiFi - SIM is shown in Fig . S1 , which contains three main steps . In preprocessing , the raw data was deconvoluted 26 using a theoretical OTF . In reconstruction parameter estimation , an improved normalized crosscorrelation method was used to estimate the pattern wave vectors . In short , a notch filter was applied to the normalized cross - correlation calculation 8,23 , which can effectively suppress contributions from low - frequency signal and local periodic structures to the cross - correlation map , such that the peaks corresponding to the wave vectors protruded enough to be automatically determined from most of raw data , including low SNR data , TIRF - SIM data , and even data with obvious periodic structures ( Fig .   S2 ) . Thus , a pre - set mask or hand - correction was not required as before . Once the reconstruction parameters were correctly determined , the 0 - and ±1 - order spectrum components were separated , shifted , and combined to yield a directly combined spectrumS directlyÀcombined ðkÞ ( Eq . ( 9 ) in Supplementary Note 1 ) , using a method similar to fairSIM . After that , HiFi - SIM performs a two - step spectrum optimization onS directlyÀcombined ðkÞ.