2.1.

Theory of dmdSTED

For traditional STED [Fig. 1(a)], the excitation and depletion lasers are continuous wave or pulsed with a certain repetition frequency, so the final fluorescent signal remains the same. When the modulation of frequency $f_{m1}$ is applied only to the excitation light, the corresponding fluorescence signal also has a frequency of $f_1$ [Fig. 1(b)], as published in the literature called modulated STED (mod-STED).¹⁸

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.

For dmdSTED, we applied different modulation frequencies $f_{m1}$ and $f_{m2}$ to the excitation and depletion beams, respectively [Fig. 1(c)]. When two lasers of different frequencies are focused on the sample, via Fourier transform, the fluorescence signals with multiple frequencies are obtained. As seen from Fig. S1(b) in the Supplementary Material, the fluorescent signals are mainly distributed at four frequencies along the frequency spectrum: $f_1-f_2$, $f_1,f_2$, and $f_1+f_2$. Frequency intensity $\xi (f)$ is defined to measure the relative strength of each discrete frequency component. The spatial- and frequency-domain characteristics of different fluorescent signal components when applying dual modulation to the excitation and depletion beams are shown in Fig. 1(d). Here, “dark green” represents the fluorescence in the central area, “light green” represents the fluorescence in the outer ring area, and “yellow” represents the AStEx fluorescence in the outer ring area. The upper part of Fig. 1(d) shows that there is no AStEx, and the fluorescence in the center area only has a frequency of $f_1$, while the outer ring area is a combination of four frequency components at the same time. The lower part of Fig. 1(d) shows the condition in the presence of AStEx, and the fluorescence with a frequency of $f_2$ occurs due to re-excitation. Therefore, for actual imaging, detected fluorescence signals will present specific frequency characteristics, as shown in Fig. 1(e), where $\xi (f_1)$ contains the fluorescence in the center and outer ring area, and $\xi (f_2)$ corresponds to the fluorescence in the outer ring area, including the AStEx signal. Therefore, by demodulating a specific frequency, fluorescent signals of different components can be achieved, and then the background signal can be removed by the difference between $\xi (f_1)$ and other frequency intensities, such as $\xi (f_2)$, $\xi (f_1-f_2)$, or $\xi (f_1+f_2)$. Strong anti-Stokes fluorescence mainly exists at the frequency $f_2$. Therefore, the anti-Stokes background is removed in the demodulation stage using lock-in hardware, and then the nondepleted background can be further removed through the difference between $\xi (f_1)$ and the sum frequency $\xi (f_1+f_2)$ or the difference frequency $\xi (f_1-f_2)$ using a carefully selected subtracting coefficient. To this end, for mod-STED, nondepleted fluorescence is mixed with the effective fluorescence at frequency $f_1$ in the frequency spectrum.¹⁸ The detailed calculation of the proposed method is illustrated in Note S2 in the Supplementary Material.

Different frequency components are analyzed experimentally, as shown in Fig. 2(a). The frequency component $\xi (f_1)$ corresponds to the fluorescence in the center area and a part of the fluorescence in the outer circle. Whereas, owing to the combined effect of excitation light and depletion light with different modulation frequencies, the fluorescence in the outer ring area will contain four frequency components: $\xi (f_1)$, $\xi (f_2)$, $\xi (f_1-f_2)$, $\xi (f_1+f_2)$. The prominent difference between the imaging results of four frequency components is the signal intensity, as shown in Fig. 1(c). In particular, when the anti-Stokes fluorescence is not obvious, $\xi (f_2)$ can be mainly considered as the background signal. In addition, the modulation contrast CM also has a significant effect on $\xi (f_1)$ and $\xi (f_2)$ imaging. Here, we define the modulation contrast $CM=(I_{\max }-I_{\min })/(I_{\max }+I_{\min })$, where $I_{\max }$ or $I_{\min }$ is the maximum intensity or minimum intensity of the excitation beam or depletion beam. While, $C{M}_1$ and $C{M}_2$ are the modulation contrast of the excitation and depletion beams, respectively. The influence of $C{M}_2$ is characterized by the experimental imaging in Fig. 2(b), which is also evidenced by the results in Figs. S2–S4 in the Supplementary Material. Specifically, as $C{M}_2$ increases, the signal-to-noise ratio (SNR) of $\xi (f_2)$ imaging increases, but the resolution of $\xi (f_1)$ imaging decreases accordingly [Fig. 2(b)]. Therefore, in actual imaging, the most appropriate $C{M}_2$ value should be selected considering both aspects. We also numerically and experimentally investigate the influences of either excitation beam intensity $I_{\mathrm{exc}}$ or depletion beam intensity $I_{\mathrm{dep}}$ against the signal intensities of different frequency components (see Figs. S5 and S6 in the Supplementary Material). In addition, the influence of the applied modulation frequencies is discussed (see Figs. S7 and S8 in the Supplementary Material).

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.

In dmdSTED, the nondepleted background can be removed through the difference between $\xi (f_1)$ and $\xi (f_1+f_2)$ or $\xi (f_1-f_2)$ using a subtracting coefficient, shown in the graph of Figs. S9 and S10 in the Supplementary Material. As is known, subtraction will cause negative values. The influence of the subtracting coefficient is investigated in order so that the negative value should be around 0, and we numerically demonstrate that the optimal subtracting coefficient is about 1.56 (Fig. S11 in the Supplementary Material). Numerical results on nanoparticles and microtubes show that dmdSTED affords higher discernment ability with respect to conventional STED (Figs. S12 and S13 in the Supplementary Material). Thus, given the acquired spatial resolution, dmdSTED has the potential of lower required depletion light power. The modulation transfer function (MTF) along the radial direction of the PSF is simulated. It is seen from Fig. S14 in the Supplementary Material that dmdSTED with relatively lower depletion power, such as $40\mathrm{MW}/{\mathrm{cm}}^2$, could have even larger spatial frequency in parallel to the conventional STED scenario with $100\mathrm{MW}/{\mathrm{cm}}^2$ depletion power. In our perspective, dmdSTED has the ability to reduce the applied depletion light doses, which may have the potential to alleviate the photobleaching issue. In the future, the experimental works are expected to further verify this advantage of dmdSTED. Thus, in the case of conventional STED with $100\mathrm{MW}/{\mathrm{cm}}^2$ depletion power, 40-nm spatial resolution is revealed. With our dmdSTED when $C{M}_2=0.9$, only $40\mathrm{MW}/{\mathrm{cm}}^2$ depletion power is entailed. This simulation result verifies the ability of dmdSTED in the reduction of light doses (Fig. S15 in the Supplementary Material).

The optics setup of dmdSTED is shown in Fig. S16 in the Supplementary Material. Notably, as shown in Fig. S17 in the Supplementary Material, the demodulation signal intensity is negatively correlated to the applied modulation frequency $f_m$. This is limited by our acousto-optic and electro-optic modulators. Meanwhile, in the experimental setup, the time constant (TC) of the lock-in amplifier is recommended to be longer than the modulation period ($T_m$), which is equal to $1/f_m$.¹⁸ In addition, the pixel dwell time $T_d$ should be equal to or greater than TC. That is, for 100-kHz modulation, the pixel dwell time should be longer than $10\mu \mathrm{s}$. Thus, if $f_m$ is too small, $T_m$ becomes too large, and $T_d$ is even longer. Furthermore, a high value for $T_d$ will induce greater noise, which results in contamination of the image quality, as well as reduced acquisition speed. We have experimentally demonstrated that the values of $f_m$ in the range of 10 to 150 kHz are appropriate for this imaging modality, and this represents the optimal trade-off between acquisition speed and image quality. In the future, an optical modulator with even higher working frequency is highly recommended to further increase the acquisition speed and to inhibit the $1/f_m$ background noise due to laser intensity undulation.²⁷

3.1.

Imaging of Nanoparticles

We tested our method using 40-nm fluorescent particles (Abberior). Practically, bias intensity is defined: $I_{\mathrm{bias}}=(I_{\max }+I_{\min })/2$. The specific experimental parameters were determined as follows: for the excitation beam, the bias intensity $I_{\text{bias}}$ was $7\mu \mathrm{W}$, $C{M}_1$ was 1, and the modulation frequency was 50 kHz; for the depletion beam, $I_{\text{bias}}$ was 470 mW, $C{M}_2$ was 0.35, and the modulation frequency was 75 kHz. The pixel dwell time is $50\mu \mathrm{s}$. Here, the choice of $I_{\text{bias}}$ and $C{M}_2$ of the depletion beam not only guarantees the imaging resolution when the depletion intensity is at the minimum value, but also ensures that the fluorescence signal of $\xi (f_2)$ is as large as possible. Meanwhile, the depletion intensity for STED was selected at $I_{\mathrm{STED}}=I_{\text{bias}}=470\mathrm{mW}$, ensuring a fair comparison between STED and dmdSTED. The experimental results are presented in Fig. 3. Figures 3(a)–3(c) show the imaging results of confocal, STED, and dmdSTED. It can be seen that the resolutions of STED and dmdSTED are basically the same, but for dmdSTED the halo around the particles caused by the background signal at the periphery is relatively weakened. Signal levels are measured, and SNRs of confocal, STED, and dmdSTED are 8.96, 9.25, and 18.17, respectively. This is due to the background signal originating from the excitation beam, which can be filtered out in dmdSTED. Here, the re-excitation caused by the depletion beam is very weak owing to the selected depletion wavelength and sample. The subtracted background for dmdSTED is shown in Fig. S20(a) in the Supplementary Material. A partially enlarged view in Figs. 3(d)–3(f) and the intensity profiles in Fig. 3(g) verify the above-mentioned result in a clearer way. In both cases, the resolving ability can completely resolve 40-nm particles, and thus the FWHM values of the two profiles are almost the same. However, for STED, a part of the additional background signal is clear in the lower middle of the profile, but these signals nearly disappear in dmdSTED. Figure 3(h) shows the statistical results of the particle size distribution of the nanoparticles, with a mean value of 61 nm for dmdSTED and that of 77 nm for STED. Fourier ring correlation (FRC) analysis is also conducted, and the results show that the resolutions of confocal, STED, and dmdSTED are 211, 77, and 61 nm, respectively [Fig. S18(a) in the Supplementary Material]. A spatial transverse resolution of $\lambda /8$ is reached.

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.

3.2.

Cell Imaging of dmdSTED

Furthermore, we tested the effectiveness of the method using cell experiments. The sample was Hela cell vimentin labeled with Star Green (Abberior). The experimental parameters are generally similar to those of the nanoparticles. The $C{M}_1$ value of the excitation laser was maintained at 1, and that of the depletion laser was 0.35. The modulation frequencies of the excitation and depletion lasers were 50 and 80 kHz, respectively. Figures 4(a)–4(c) show the imaging results of confocal, STED, and dmdSTED, respectively. In order for fair comparison, the STED image is already subtracted by the optics system background (refer to Fig. S19 in the Supplementary Material). Via the demodulation at the frequency ($f_1+f_2$), the subtracted background for dmdSTED is shown [Fig. S20(b) in the Supplementary Material]. Also, SNRs of confocal, STED, and dmdSTED are characterized to be 8.79, 8.86, and 11.55, respectively, where 30.4% improvement of SNR is revealed in contrast to conventional STED. The results show that dmdSTED can effectively remove the undesired background in STED, and the partially enlarged images in Figs. 4(d)–4(f) show the corresponding results more clearly. We further verified the influence of $C{M}_2$ on the signal frequency intensities of the sum and difference frequencies. The experimental results are consistent with the previous theoretical analysis. Here, the most suitable $C{M}_2$ value was $\sim 0.5$ to 0.7 (evidenced by Figs. S3 and S4 in the Supplementary Material). For a small $C{M}_2$, the desired signal strength is weakened, affecting the imaging SNR. When $C{M}_2$ is too large, the depletion intensity will decrease to a very low level, and the imaging resolution will be influenced. The results indicate that the imaging contrast and resolution can be enhanced for a reasonable $C{M}_2$. FRC analysis is conducted, and the results show that the spatial resolutions of confocal, STED, and dmdSTED are 225, 91, and 74 nm, respectively [Fig. S18(b) in the Supplementary Material]. That is, 22.9% enhancement of spatial resolution is reached in contrast to conventional STED.

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.

3.3.

Eliminating the Anti-Stokes Background

To date, STED has been successfully applied to many samples, including organic fluorophores, fluorescent proteins, quantum dots, and color centers in diamond. However, the practical feasibility depends on the emitter’s intrinsic properties of the emitter, which sometimes hampers the applicability of STED imaging. Organometallic halide perovskites are attracting considerable research interest as a promising candidate for next generation solar cells. Currently, the dominant observation method for this material is scanning electron microscopy. The as-published literature has reported the successful utilization of STED on ${\mathrm{CsPbBr}}_3$ quantum dots.²⁸ In this study, we attempted to observe perovskite using our optical system. A remarkable feature of perovskite is its high fluorescence brightness, including anti-Stokes fluorescence. Hence, we introduce it to the experiments here to verify our method for removing anti-Stokes fluorescence noise.

Figures 5(a)–5(c) show the confocal, STED, and dmdSTED images, respectively. For the STED modality, the perovskite exhibits strong absorption of the depletion light and produces strong anti-Stokes fluorescence, exhibited in Fig. 5(d), which is even stronger than the effective fluorescence and severely hinders the application of STED imaging on this material.

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: $2.5\mu \mathrm{m}$.

Figure 5(e) shows the respective intensities of confocal, STED, dmdSTED, and anti-Stokes fluorescence, which indicates that the anti-Stokes background is comparable to the confocal image. For the reason that the normalized intensities of the four images are similar and the subdiffraction effect of the perovskite is not obvious, it is caused by two aspects. First, an obvious feature of perovskite is its high fluorescence brightness, which can emit strong fluorescence under extremely weak excitation light intensity (here we employ $1\text{-}\mu \mathrm{W}$ $I_{\mathrm{exc}}$, which is 1/10 of the applied excitation power for common fluorescent samples). Hence, it also shows decent brightness in the dmdSTED condition. Second, because of the large size of the sample used here, perovskites are agglomerated possibly in the order of hundreds of nanometers. Thus, the fluorescence signal intensity is further enhanced. Therefore, the signal intensity decline of dmdSTED is limited in Fig. 5(e). In addition, the anti-Stokes fluorescence exhibited fluorescence intensity close to that of confocal, but the STED intensity was slightly lower than the two, which we believe is mainly due to the relatively higher photobleaching in STED, resulting in a decrease of the mean intensity of STED imaging.

By demodulating at the specific frequency $f_2$, the anti-Stokes fluorescence can be effectively filtered. Here, the nondepletion background signal was obtained by demodulating the frequencies $f_1\pm f_2$, which is also the subtracted background, as shown in Fig. S20(c) in the Supplementary Material, where hollow features in some areas are presented. This phenomenon confirms to a certain extent that the solid and hollow beams work at the same time, and the stimulated emission effect indeed occurs. The FWHM with the line plot is 273 nm with dmdSTED imaging, as shown in Fig. 5(f), achieving the imaging of the perovskite coating. FRC analysis is conducted, and the results show that the spatial resolutions of confocal, STED, and dmdSTED are 320, 241, and 205 nm, respectively [Fig. S18(c) in the Supplementary Material]. To this end, dmdSTED can effectively separate different types of signals and enhance the imaging resolution.