To further prove the applicability of the IRT algorithm, we used our developed DMD-projection-based LED-illumination SIM system23,24 to carry out the following experiment. The scheme of the SIM system is shown in Fig. 4. A four-wavelength high-power LEDs assembly (LED4D251, Thorlabs Inc.) with switchable wavelengths of 405, 470, 565, and 625 nm is employed as the illumination source for multiwavelength excitation. The LED light enters the TIR-Prism and is reflected to the DMD chip (DLP7000UV, Texas Instruments Inc.), where the fringe pattern is loaded. The light modulated by the DMD passes through a demagnifying optical system, consisting of a collimating lens, and a objective (Apo TIRF, NA1.49, Nikon Inc., Japan), to produce a sinusoidal fringe illumination projected onto the specimen. A quad-band filter set (including a 390/482/563/640 nm quad-band bandpass excitation filter, a 446/523/600/677 nm quad-band bandpass emission filter, and a R405/488/561/635 nm quad-edge dichroic beamsplitter, Semrock Inc.) are used to separate the excitation lights and the emission fluorescence signals. A sCMOS camera with a maximum full-frame rate of 100 fps (Orca Flash4.0, , 16 bits gray depth, Hamamatsu Inc., Japan) is used to capture the two-dimensional image. The phase shifts of the fringe are controlled by the DMD chip without mechanical movement. If the fringe period is designed to occupy pixels on the DMD chip, the minimum value of the phase shift will be . Thus, to achieve a phase shift, just setting four pixels per period on the DMD chip, the illumination fringe phases corresponding to , , and , will be obtained, respectively. In order to achieve a high imaging speed and a simplified pattern design, we apply only two perpendicular illumination fringe orientations in the experiment. Nevertheless, it is possible to generate multiorientation illuminations with specifically designed illumination patterns.