Fig. 1. Basic principle of dual-modulation difference stimulated emission depletion (dmdSTED) microscopy. (a)–(c) Time- and frequency-domain forms of the fluorescence signal and the corresponding spectrum under different modulation methods: no applied modulation, only the modulation frequency $f_{m1}$ is applied to the excitation beam, modulation frequencies of $f_{m1}$ and $f_{m2}$ are simultaneously applied to the excitation and depletion beams. (d) Spatial and frequency domain characteristics of different fluorescent signal components. (e) Frequency characteristics of the finally detected fluorescence signal, where $\xi (f_1)$ contains the fluorescence in the center and outer ring areas, and $\xi (f_2)$ corresponds to the fluorescence in the outer ring area.

Fig. 2. Imaging analysis of fluorescence signals at different frequencies and the influence of $C{M}_2$. (a) Fluorescence signals corresponding to four frequency components. Scale bar: 400 nm. (b) Variation of $\xi (f_1)$ images and $\xi (f_2)$ images against $C{M}_2,$ with values of 0.15, 0.3, and 0.4. Scale bar: 500 nm. The analysis is characterized by 40-nm fluorescent nanoparticles.

Fig. 3. 40-nm particle experimental results. (a)–(c) Imaging results of confocal, STED, and dmdSTED, respectively. Scale bar: $1.5\mu \mathrm{m}$. (d)–(f) Partially enlarged view of the area marked by the blue dashed box in (a)–(c). Scale bar: 300 nm. (g) Image intensity change curve at the position along the blue dotted line in (d)–(f). The blue and red lines represent STED and dmdSTED, respectively, where the FWHM of dmdSTED is 63 nm. (h) Distribution of the statistical results of the FWHM of nanoparticles.

Fig. 4. Biological cell imaging results. The imaging results of (a) confocal, (b) STED, and (c) dmdSTED. Scale bar: $2\mu \mathrm{m}$. (d)–(f) Partially enlarged view of parts indicated by the blue dashed box in (a)–(c). Scale bar: $1\mu \mathrm{m}$. (g) Image intensity variation curve along the blue dotted line. The blue, red, and yellow lines correspond to confocal, STED, and dmdSTED, respectively. The sample used here is vimentin labeled with Star Green.

Fig. 5. Imaging of perovskite coating. Imaging results of (a) confocal, (b) STED, and (c) dmdSTED. (d) Anti-Stokes fluorescence through demodulating the frequency $f_2$. (e) Signal intensity bars of confocal, STED, dmdSTED, and anti-Stokes fluorescence. (f) Intensity profiles along the blue dashed lines in (a)–(c). Scale bar: $2.5\mu \mathrm{m}$.