1. Introduction

In many biological applications, the capability of acquiring images with fine temporal resolution is essential and highly desired [1–3]. Laser scanning microscopy (LSM) is widely used in bioimaging. Unfortunately, conventional laser scanning devices are relatively slow, which limits its application in moving objects and dynamic imaging. With spatial dispersion of temporally stretched ultrashort pulses, Goda presented a new type of laser scanning that offers 1,000 times higher scanning rates than conventional scanners [4]. Since the ultra-high speed time-stretch approach employs near-infrared lasers, the imaging depth of biological tissue can be significantly increased. However, the resolution is reduced compared to visible light microscopy because both illumination and detection are in near-infrared region. An effective way to increase the resolution is to detect short wavelength emission, which can be achieved by combining ultra-high speed time-stretch scanning with multiphoton excitation process [5–9]. Yet, because of the small multiphoton absorption cross section, the multiphoton microscopy is suffered from the troublesome effect of high laser power and photobleaching, which is incapable for long-term imaging of biological tissues [10,11]. Superior to the conventional multiphoton material, rare-earth up-conversion nanoparticles (UCNPs) enable low excitation power, non-photobleaching, non-blinking, zero auto-fluorescence, large anti-Stokes shifts and narrow-band emission [12–15]. These unique properties make UCNPs being widely employed in biological imaging, and the ability for deep imaging with super-resolution has been confirmed [16].

Despite multiphoton process can extend the resolution, the resolution of emission light still be limited by the diffraction limit ($\def\upmu{\unicode[Times]{x00B5}}{\lambda }/({{2NA}})$). Recently, optical super-resolution microscopy has attracted a lot of interest because of its ability to break diffraction limit and to observe living sample at nanoscale [17–22]. Among these super-resolution microscopic techniques, structured illumination microscopy (SIM) stands out because of its high speed and low illumination intensity [23–25]. Typical SIM uses structured-illumination patterning, such as a sinusoidal pattern, are usually generated by the interference of two light beams emerging from a diffraction grating (2D-SIM) [19], or a spatial light modulator (SLM) [26]. Typical SIM is a wide-field microscopy that offers a shallow working depth (about 15 $\upmu$m imaging depth in the vertical direction) [27]. These characteristics cause wide-field SIM to be incompatible with multiphoton process which is based on point-scanning, and requires ultra-high laser density.

Based on a simple traditional laser point-scanning configuration, the concept of structured laser scanning microscopy was introduced by Lu [28]. This theory has also been applied in practical applications [29–32]. However, structured laser scanning microscopy has lower frame rates than wide-field structured microscopy. One of the reasons for the low imaging speed is due to point-by-point scanning process (e.g. through a pair of galvo mirrors). The other is the response time of temporal modulation device (e.g. through an acousto-optic modulator, AOM), which is typically on the order of kilohertz. In addition, to generate a steady structured illumination pattern, both the scanning procedure and the temporal excitation intensity modulation should be perfectly synchronized and coupled. Overall, an ultra-high speed structured light generation method that integrates scanning and modulation is highly desired for structured laser scanning microscopy.

In addition to ultra-high speed scanning proposed by Goda [4], ultra-high speed modulation that owing to the same principle is also verified. Wang introduces a time-encoded technique based on dispersive Fourier transform in optical fiber, to generate structured illumination patterns at a much higher speed of 50 MHz [33]. When both the modulation and scanning characteristics of dispersive Fourier transform are utilized, an ultra-high speed structured laser scanning microscopy can be realized.

In this paper we propose MUTE-SIM, that overcomes the limitations on imaging time and the resolution of laser scanning microscopy while maintaining low excitation power. The main idea of this strategy is generating a series of points with structured intensity and ultra-high speed to scan the sample, and improving the resolution by combining SIM with UCNPs. This is also the first time that UCNPs being used in SIM. According to the experimental results, it can be found that the resolution limit of near-infrared light is surpassed by a factor of $223.3\%$ with the scanning and modulation rate of 50 MHz while maintaining low illumination intensity. The scanning and modulation rate is equal to the repetition rate of the laser pulse, which is approximately 1000 times faster than traditional methods. According to this, the scanning and modulation rate could be further improved by increasing the repetition rate of the pulse laser. In addition, this technique reduces complexity and cost of the imaging system owing to the integration of scanning and modulation devices.

2. Methods and materials

In this work, a scanning and time-encoded patterning method is used to generate equivalent structured illumination. To get a high quality SIM image, influence factors and the origin of the resolution improvement are discussed. Materials used in this paper are $\beta \textrm {-}NaYF_4: 25\% Er^{3+} @ NaYF_4$ up-conversion nanoparticles.

2.1 Scanning and time-encoded patterns generation

The operation of the MUTE-SIM consists of three steps: time-to-wavelength conversion (i.e., temporal modulation), wavelength-to-space conversion (i.e., spatial scanning) and image reconstruction. The first two steps are shown in Fig. 1. Specifically, a broadband femtosecond laser is used as the light source.

 

Fig. 1. Generation of structured illumination with the MUTE-SIM geometry. (a)(b)(c) correspond to the time domain waveforms, spectrum, and spatial scanning spot of the broadband femtosecond laser, respectively. (d) shows the pulses are temporally stretched by the dispersive fiber, thus each wavelength will be separated in time. (f) The spectrum of the laser pulses is mapped into space by using a diffraction grating, different wavelengths correspond to different positions of the scanning spot. (g) Time domain waveforms of the pulses after modulation by a high-speed arbitrary waveform generator (AWG) together with a high-bandwidth optical modulator. (h)(i) The spectrum and spatial pattern correspond to the time domain modulation waveforms, respectively. Time coordinate t, spectral coordinate $\lambda$, spatial coordinate $x$ are one-to-one correspondence.

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In step 1, the temporal waveform is modulated onto the optical spectrum (wavelength) of the laser pulse with a predefined pattern (either in amplitude or phase) after the pulse is temporally stretched by the dispersive fiber. Time-stretch is a powerful technique in which the broadband spectrum of an optical pulse is mapped into a temporal waveform using group-velocity dispersion [34]. After this step, each wavelength will be separated in time and modulated with different intensities.

In step 2, the spectrum of the laser pulse with modulated pattern can be further mapped into a spatial illumination pattern by using a spatial disperser. In this paper we use a diffraction grating which maps the spectrum into a one-dimensional (1D) line pattern to perform a 1D line scan. During the scanning procedure, the modulated laser light was tightly focused on the specimen plane by a high NA objective. Above steps result in each wavelength of the optical pulse illuminating a different set of spatial coordinates on the target at a different time in series with different intensities. In addition, a cylindrical lens can be used to expand the field of view (FOV) in the non-raster scanning direction (y-axis) to avoid y-direction scanning. Since the excitation power of UCNPs is very low, UCNPs can be excited even with a cylindrical lens.

In step 3, the emission light of each scanning point with a predefined intensity modulation sequence is collected and integrated by a nondescanned EMCCD camera at the image plane. Several such EMCCD-images are captured with a set of intensity modulation sequences which are phase-shifted in space in order to reconstruct a super-resolution image of the specimen. After the images are acquired, the usual algorithm for WF-SIM can be applied to reconstruct the super-resolution image [35–38].

To obtain a high-quality SIM image, modulation contrast and spatial frequency of the illumination pattern are critical [39]. We provide a detailed explanation of MUTE-SIM, including a description of the mentioned influence factors and the origin of the resolution improvement. For simplifying but no loss of generality, we take the one-dimensional case into consideration. The detailed steps on how to achieve the desired structured illumination pattern is shown in appendix note 1.

First, we present the imaging process of MUTE-SIM. The basic equations have been described in a previous publication [28] and we extend them to the multiphoton and saturation case. In the MUTE-SIM, each wavelength is tightly focused onto the specimen. Let $h_{\textrm {ex}}$ denote the excitation PSF, and $h_{\textrm {em}}$ the emission PSF. Assume the specimen has a fluorophore distribution of $S(r)$, and $M(t)$ is the predesigned temporal waveform. For a nondescanned setup the final images of the camera are equivalent to integration in time:

When the multiphoton process is combined with the MUTE-SIM, the effective excitation PSF $h_{\textrm {eff-ex}} (r)=[h_{\textrm {ex}} (r)]^n$, where $n$ is the order between excitation power and emission intensity. The $h_{\textrm {eff-ex}} (r)$ is narrowed as $n$ increases (i.e., a higher order multiphoton process), and the corresponding OTF ($\tilde h_{\textrm {eff-ex}}$) cutoff frequency becomes higher. However, the relationship in up-conversion process of UCNPs is not constant due to the power dependent nonlinearity (i.e., n decreases as the excitation power increases) [40]. Therefore, the highest spatial frequency of the modulation pattern decreases as the excitation power increases. Figure 2(a) shows the example curves of the $h_{\textrm {eff-ex}} (r)=[h_{\textrm {ex}} (r)]^n$ under different $n$ (from 1 to 4), $h_{\textrm {em}} (r)$ and saturated excitation PSF $h_{\textrm {sat}} (r)=[h_{\textrm {ex}} (r)]^{0.65}$ in the MUTE-SIM system, where the peak emission wavelength is set to 540nm, excitation wavelength is 1560nm, and NA of the objective is 0.6. In the simulations presented in Fig. 2(b), the cutoff frequency of $\tilde h_{\textrm {em}} (k)$ , $\omega _{\textrm {c,em}}$ is higher than the cutoff frequency of $\tilde h_{\textrm {eff-ex}} (k)$, $\omega _{\textrm {c,eff-ex}}$ and $\tilde h_{\textrm {sat-ex}} (k)$, $\omega _{\textrm {c,sat-ex}}$. This means that it is impossible to surpass the lateral resolution limit by a factor of 2 by using nonlinear effects in multiphoton scanning structured illumination systems. In order to better understand the deterioration effect, Fig. 2(c) shows the contrast of different pattern spatial frequency ($k_{\textrm {pattern}}$) in the MUTE-SIM system. Contrast refers to the ratio of the first-order frequency component to the DC component in the modulation pattern. For working at an appropriate contrast (contrast greater than 0.1), MUTE-SIM chooses 0.15 $\omega _{\textrm {c,em}}$ as a spatial frequency of illumination pattern under saturation conditions. The spatial frequency of illumination pattern that can be modulated at different values of n is shown in Fig. 2(c).

 

Fig. 2. Multiphoton process. (a) Normalized profiles of $h_{\textrm {em}} (k)$ and $h_{\textrm {eff-ex}} (k)$ under different relationship between excitation power and emission intensity. (b) Normalized profiles of $\tilde h_{\textrm {em}} (k)$ and $\tilde h_{\textrm {eff-ex}} (k)$ under different relationship between excitation power and emission intensity. (c) The contrast of different pattern spatial frequency in the MUTE-SIM system, and initial modulation (the modulation before the excitation pulse enters the objective) is set to 1.

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2.2 Materails

In this paper, $\beta \textrm {-}NaYF_4: 25\% Er^{3+} @ NaYF_4$ up-conversion material is used for experiment. The emission spectrum of UCNPs was measured under 1560nm laser excitation of 25mW and the results are shown in appendix note 2. Five up-conversion emission bands are clearly resolved and are maximal at 379, 408, 525, 540, and 660nm, respectively. An emission filter (Semeock FF01-940/SP-25) only allows 540nm to pass through. The details about the emission spectra and characterization of UCNPs are also shown in appendix note 2. It shows that the slope (nonlinearity) is not a constant: the larger the power density, the smaller the slope n. Then we can control the order n by controlling the excitation power. The details about the preparation of samples are shown in appendix note 3.

2.3 Experimental setup

The schematic diagram of the proposed MUTE-SIM system is shown in Fig. 3. The optical source is a mode-locked femtosecond pulse fiber laser with a center wavelength of 1560 nm, 3 dB bandwidth of 10 nm, and a laser repetition rate of 50 MHz. A pulse from the laser enters a section of dispersive compensating fiber with a group-velocity dispersion of 1368 ps/nm in which the pulse is dispersed in the time domain. To modulate the predefined sinusoidal patterns onto the optical spectrum (i.e., the step1, time-to-wavelength conversion), high-speed arbitrary waveform generator (AWG) (40 GSa/s) together with high-bandwidth optical modulator (>10 GHz) are employed. Thus, each wavelength will be separated in time and modulated with different intensities. Afterward, a collimator (Thorlabs, F810APC-1550) cast the modulated optical pulse into free space, and the laser beam was expanded into a 7 mm diameter collimated beam. Next, the beam passing through a quarter wave plate (Thorlabs, WPQ10M-1550) and a half-wave plate (Thorlabs, WPH10M-1550) to adjust the polarization state for achieving the maximum diffraction efficiency of the grating. The laser beam is then spatially dispersed by a diffraction grating (Thorlabs, GR501210) with a groove density of 1200 lines/mm. To control aberrations, we imaged the grating face onto the back focal plane of an objective (40$\times$, 0.6 NA, $f$ = 5 cm) with lens pair L1 and L2 (Thorlabs, both AC508-150C-ML, $f$ = 150 mm) placed in a 4f configuration before the dispersed laser beam were focused via the objective. As an optional optical configuration, a cylindrical lens can be used with the objective to expand the FOV in the non-raster scanning direction (the cylindrical lens was not used in this experiment). The laser beam entering the objective was reflected off a dichroic beam splitter (Thorlabs, DMSP950L) and projected onto the sample. To collect fluorescence emission, we used a green band-pass filters (Thorlabs, MF535-22) before the EMCCD. We also used an adjustable magnification lens system to control the pixel size and imaging plane on the EMCCD. The EMCCD (ANDOR, iXon Ultra 897) used in Fig. 3 has a pixel size of 16$\upmu$m $\times$ 16$\upmu$m and active pixels of $512\times 512$. When the SIM images acquisition was completed, OpenSIM [37] is used for super-resolution reconstruction.

 

Fig. 3. The schematic diagram of the proposed MUTE-SIM system.

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3. Results

First, the performance of scanning and time-encoded pattern generation are verified (as shown in Fig. 4). Next, patterns with different phases shifts are generated to confirm the phase adjustment (as shown in Fig. 5). Finally, SIM image is reconstructed, and the resolution is improved from the diffraction FWHM of 1.586 $\upmu$m (the up-conversition is not used) to the measured FWHM of 0.71 $\upmu$m (reconstructed SIM image) with 50MHz scanning rate. To ensure a good signal to noise ratio (SNR), exposure time of the EMCCD is set to 0.05s (20Hz). Because images in three phases are needed to reconstruct one SIM image, the rate of the system is 6Hz. The FOV is 120$\upmu$m $\times$ 20$\upmu$m. Power at focus is 0.36 W. Thus, the power density is $0.36W/(120\mu m\times 20\mu m) = 150W/mm^2$.

 

Fig. 4. (a)-(c) The time domain waveforms. (d)-(f) The corresponding spectrum. (g)-(i) The corresponding spatial pattern whose periods are 8 $\upmu$m, 4 $\upmu$m, 2 $\upmu$m respectively.

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Fig. 5. Patterns with different phases. (a) Pattern with phase $\phi =0$. (b) Pattern with phase $\phi =\pi /2$. (c) Pattern with phase $\phi =\pi$. (d) The profile across the horizontal red line of (a)(b)(c).

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3.1 Time-encoded multiphoton structured illumination patterns

Figure 4 shows the time-domain waveform, spectrum, and spatial patterns of temporal-integrated scanning spots, respectively. Figures 4(a)–4(c) are time-domain waveforms of the modulated laser pulse at different modulation frequencies. Figures 4(d)–4(f) and Figs. 4(g)–4(i) are the corresponding spectrum and spatial pattern, respectively. When modulation frequency is higher, the spectrum and time-domain waveform maintains the modulation contrast, but the contrast of the spatial pattern is declined. The contrast of the spatial pattern is affected by the optical transfer function (OTF) of the microscopic objective. In addition, the unevenness of the wavelength intensity can be regarded as a ’background’. And by removing the ’background’, the real object shape can be easily obtained.

3.2 Patterns with different phases

The phase-shift of the spatial pattern can be achieved by changing the initial phase of the time-domain waveform. Figures 5(a)–5(c) shows spatial patterns in the focal plane of the objective with a period of 4 $\upmu$m and the three phases are $0$, $\frac {{\pi }}{{\textrm {2}}}$, $\pi$, respectively.

3.3 SIM imaging of UCNPs

To evaluate the super-resolution imaging of the MUTE-SIM, we used UCNPs as test samples. Figure 6 shows the resolution improvement using SIM. Figure 6(a) is a conventional illumination image of UCNPs sample. Figure 6(c) is a reconstructed SIM image from three images under patterns of three different phases. From the results, as shown in Fig. 6(f) and Fig. 6(h), the FWHM for the SIM is 0.71 $\upmu$m, and the FWHM of original multiphoton excitation image is 0.82 $\upmu$m, which demonstrates that the resolution is improved by a factor of $0.82/0.71=115.4\%$ through structured illumination. With improvements in the resolution, points which could not be distinguished in the red blocks in Fig. 6(b) can be separated in Fig. 6(d). According to theoretical calculations, $FWHM=0.61\lambda /Na$. When the up-conversion is not used, the FWHM is 1.586 $\upmu$m $(\lambda =1.56\upmu m, Na=0.6)$. So the final resolution is improved by a total factor of $1.586/0.71=223.3\%$.

 

Fig. 6. Multiphoton wide-field SIM super-resolution imaging with UCNPs. (a) Wide field image without pattern, scale bar: 10 $\upmu$m. (b) The intensity profile across the horizontal line of (a). (c) Reconstructed Linear SIM image, scale bar: 10 $\upmu$m. (d) The intensity profile across the horizontal line of (c). (e) The enlarge image of red box in (a), scale bar: 0.4 $\upmu$m. (f) The intensity profile across the red line of (e). (g) The enlarge image of red box in (c), scale bar: 0.4 $\upmu$m. (h) The intensity profile across the red line of (g).

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4. Discussions and conclusions

It should be noted that the SNR requirement for MUTE-SIM is higher than traditional multiphoton microscopy due to the frequency-domain reconstruction process, which is sensitive to noise. Increasing the excitation power is a straightforward way to get a better SNR. However, the relationship in up-conversion process of UCNPs is not constant due to the power dependent nonlinearity. When excitation power is higher than the saturation power, UCNPs degrades from multiphoton to one-photon or even saturation processes [40]. In this case, the cutoff frequency of the effective OTF becomes smaller, which causes a decrease in the contrast of the frequency domain components for image reconstruction as shown in Fig. 2. Therefore, this is a trade-off between the contrast and the SNR in UCNPs. Here, we get better SNR and fast image acquisition at the expense of lower cutoff frequency. This is one of the reasons why the resolution improvement is limited.

The reason for using 1560 nm as the center wavelength of the excitation light is based on the consideration that 1560 nm shows much lower tissue scattering, which can greatly enhance the penetration depth and focusing capability of light. Furthermore, dispersive fibers for dispersive Fourier transformation with high dispersion-to-loss ratio is most economical in the band centered at 1560 nm [4]. Although 1560 nm laser has higher water absorption which could result in damage to biological tissues due to overheating effect, the temperature does not rise significantly in the up-conversion nanoparticles due to its low excitation power [41]. In addition to 1560 nm, time-encoded can also be used in several discrete near-infrared (NIR) windows (e.g., 800 nm, 1.0 $\upmu$m, 1.3 $\upmu$m, and 1.7 $\upmu$m).

Furthermore, although the primary barrier of scanning and modulation speed is broken through, there are several other speed limit factors in the imaging system. First, the imaging speed is limited by the time needed to collect a sufficient number of photons. Compared to an organic luminescent substance, up-conversion materials can significantly increase the quantum yield of luminescence by increasing the intensity of the excitation light, thereby reducing the image acquisition time [42]. In addition, the inherent speed bottleneck of CCD or CMOS is also a limiting factor, which can be solved with the development of technology [43].

The resolution is improved with only one orientation in current strategy, because the scanning system is based on a one-dimensional grating. But it can be easily upgraded to 2D by using 2D dispersion devices, such as the commercially available virtually imaged phased array (VIPA) [44], to achieve two-dimensional scanning and resolution improvement in two orientations. We also noticed that in addition to the laser point-scanning configuration, there are also some configurations that combine line-scanning and SIM, which can improve the imaging speed [45,46]. In these configurations, the refresh rate of the illumination pattern can be increased to 200ns (limited by the response time of AOM), which is slower than the MUTE-SIM (20ns).

In this paper, we propose a new scheme of laser scanning microscopy based on time-wavelength-space conversion. This method overcomes the speed limitation on image acquisition with scanning and modulation rate of 50 MHz and reduces complexity to the imaging system by integrating scanning and modulation devices. For the first time, we combined multiphoton up-conversion process with SIM to achieve super-resolution. It can be found that surpasses the resolution limit at 1560 nm excitation by a factor of $223.3\%$ and maintaining a low illumination power density of 150 $W/mm^2$.

As a new scheme of ultra-high speed, high resolution technology, MUTE-SIM can help to detect high dynamic phenomena beyond the diffraction limit. Although the longer wavelength 1560 nm beam can penetrate deep into the biological tissue, the depth imaging capability of it has not been exploited in this work. We believe that when combined with the low illumination intensity of UCNP, MUTE-SIM could be applied for deep organ imaging at cellular level resolution in live animals.

Appendix

Note 1: generate the structured pattern

First, the process of generating structured illumination pattern is discussed. The smaller the modulation period of the illumination pattern that is used in SIM (i.e., the higher modulation frequency), the more resolution enhancement that can be achieved. The period of the illumination pattern is related to the wavelength-to-space conversion. The basic principle is that the diffraction grating has a spectroscopic effect on broadband optical pulses, with the result that each wavelength diffracted along a different direction. After each wavelength is focused by the objective, the spatial distance is the period of the illumination pattern. The period is given by Eq. (4):

(4)$$\Delta X = \frac{f}{{d \cdot \cos \beta }}\cdot\Delta \lambda$$

Here, $\Delta X$ denotes the spatial period, $f$ is the focal length of the objective, $d$ is the grating constant, $\beta$ is the diffraction angle and $\Delta \lambda$ is the encoding period in the wavelength, which is determined by the encoding period $\Delta t$ in the time-to-wavelength conversion. The time-to-wavelength conversion that based on temporal modulation is relatively straightforward because the time-to-wavelength mapping is highly linear [34]. This relationship can be described by dispersive fibers with group-velocity dispersion (GVD):

(5)$$\Delta \lambda {\textrm{ = }}\frac{{\Delta t}}{{\operatorname{GVD}}}$$

In theory, due to the diffraction effect, the period of the illumination pattern is limited by the effective point spread function (PSF) of the imaging system. Here, the diffraction effect is determined by the grating and the objective, and the effective PSF depends on the larger one (N denotes the total number grooves and NA is the numerical aperture of objective) :

(6)$$\Delta x_{\textrm{ grating}} {\textrm{ = }}\frac{f}{{N\cdot{d}\cdot\cos \beta }}\cdot\lambda$$

(7)$$\Delta x_{\textrm{objective}} {\textrm{ = 0}}{\textrm{.61}}\frac{\lambda }{{NA}}$$

For higher resolution enhancement, it is necessary to produce an illumination pattern that approximates the diffraction limit of the objective, which imposes requirements on the length of the laser incident on diffraction grating:

(8)$$f\cdot{NA} \leqslant l\cdot{\cos \beta}$$

Under the premise of reasonably using grating, we get the minimum coding period of MUTE-SIM, in which the finest illumination pattern can be realized:

(9)$$\Delta t_{\textrm{min}} = {\textrm{0}}{\textrm{.61}}\frac{\lambda}{{NA}}\cdot\frac{{d\cdot\cos \beta}}{f}\cdot\operatorname{GVD}$$

On the other hand, a high-speed arbitrary waveform generator (AWG) together with high-bandwidth optical modulator are employed to generate the predefined patterns in the time domain.

When $\Delta t_{\textrm {min}}$ is small enough to approach the bandwidth of the modulator, the modulation contrast is significantly reduced. In order to obtain an illumination pattern of the same spatial period while maintaining the modulation contrast, this can be achieved by adjusting the grating parameters, for example using a grating with a higher grating constant. This ensures maximal modulation contrast at a cost of a narrowing in the FOV of the microscope, which is also a very important technical indicator for the microscope. The FOV of the MUTE-SIM is given by:

(10)$$\textrm{FOV} = \frac{f}{{d\cdot\cos \beta }}\cdot\Delta\lambda _{\textrm{band}}$$

Where $\lambda _{\textrm {band}}$ is the spectral width of the light source. This is a trade off between the encoding period and the FOV of microscopy. In practical applications (i.e., high NA objective), it is advisable to obtain a better modulation contrast by narrowing the FOV. Next, we present the imaging process of MUTE-SIM. The basic equations has been described in a previous publication [28] and we extend them to the multi-photon and saturation case. In the MUTE-SIM, each wavelength is tightly focused onto the specimen. Let $h_{\textrm {ex}}$ denote the excitation PSF, and $h_{\textrm {em}}$ the emission PSF. Assume the specimen has a fluorophore distribution of $S(r)$, and $M(t)$ is the predesigned temporal waveform. For a nondescanned setup the final images of the camera is equivalent to integration in time:

(11)$$I_{\textrm{camera}} (x) = \iint {M(t)\cdot{h_{\textrm{ex}}} (r - t)\cdot}S(r)\cdot{h_{\textrm{em}}} (x - r)drdt$$

Note 2: spectrum of UCNPs

In this paper, $\beta \textrm {-}NaYF_4: 25\% Er^{3+} @ NaYF_4$ up-conversion material is used for experiment. The emission spectrum of UCNPs was measured under 1560nm laser excitation of 25mW and the results are shown in Fig. 7(a). Five up-conversion emission bands are clearly resolved and are maximal at 379, 408, 525, 540, and 660nm, respectively. The 540nm is the strongest emission band which identified by the red circle in Fig. 7(a). In this paper, an emission filter only allows 540nm to pass through and block other four peaks. Figure 7(b) shows the core-shell of this material with transmission electron microscopy (TEM), the diameter is $\sim$22.1nm [as shown in Fig. 7(c)], which is small enough for super-resolution experiment. Figure 7(d) shows the energy level diagram of $\beta \textrm {-}NaYF_4: 25\% Er^{3+} @ NaYF_4$ nanocrystals which fits to Fig. 7(a). Figure 8(a) shows pump-power dependence of $\beta \textrm {-}NaYF_4: 25\% Er^{3+} @ NaYF_4$ with 1560 excitation from experiment. Figure 8(b) shows the relationship between slope n and power density. It shows that the slope (nonlinearity) is not a constant: the larger the power density, the smaller the slope n.

 

Fig. 7. Emission spectrum and core-shell. (a) The emission spectrum of UCNPs measured under 1560 nm laser of 25mW. ①CWL:379nm,FWHM:4nm. ②CWL:408nm,FWHM:8nm. ③CWL:525nm,FWHM:12nm. ④CWL:540nm,FWHM:5nm. ⑤WL:660nm,FWHM:8nm. (b) TEM images of core-shell nanostructure of $\beta \textrm {-}NaYF_4: 25\% Er^{3+} @ NaYF_4$ with the size of 22.1 nm, scale bar 0.05$\upmu$m. (c) Size distribution histograms corresponding to TEM image (b), $22.1 \pm 0.9 nm$, respectively. Histograms of the crystals sizes are drawn from analysis of >150 crystals. (d) Energy level diagram of $\beta \textrm {-}NaYF_4: 25\% Er^{3+} @ NaYF_4$ nanocrystals.

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Fig. 8. (a) Pump-power dependence of $\beta \textrm {-}NaYF_4: 25\% Er^{3+} @ NaYF_4$ with 1560nm excitation, 540nm emission in log-log scale. (b) The relationship between slope n and power density.

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Note 3: prepareation of samples

Materials

YCl$_3\cdot$6H$_2$O (99.99%), ErCl$_3\cdot$6H$_2$O (99.99%), NH$_4$F (>98%), NaOH (>97%), oleic acid (OA, 90%), and 1-octadecene (ODE, 99%) were purchased from Sigma-Aldrich and used as received without further purification.

Synthesis of hexagonal-phase NaYF$_4$ nanocrystals

NaYF$_4$ nanocrystals were synthesized using a typical method as previous work. Typically, methanol solution of 0.25 mmol ErCl$_3$, 0.75 mmol YCl$_3$ were mixed with 8 ml OA and 8 ml ODE in a 50 ml round bottom flask. The mixed solution was heated up to 150℃ for 30 min until it became clear. With gentle flow of argon gas through the reaction flask, the solution cooled slowly to room temperature. Methanol solution dissolved with 4 mmol NH$_4$F and 2.5 mmol NaOH was added into the flask with vigorous stirring for more than 30 min. Then, the mixed solution was heated up to 90℃ to evaporate methanol and to 150℃ to evaporate all the residual water. Finally, the solution was heated to 300℃ in an argon atmosphere and kept at this temperature for 90 min for complete reaction and crystal formation. After reaction and cooling down to room temperature, the synthesized nanocrystals were washed with cyclohexane/ethanol for several times and dispersed in cyclohexane for use.

Synthesis of hexagonal phase core-shell structure and sandwich structure nanocrystals

For the synthesis core-shell structure nanocrystals, typically, $\beta \textrm {-}NaYF_4: 25\% Er^{3+} @ NaYF_4$ nanocrystal. A modified hot-injection method was used for growing shells onto the core nanocrystals. 0.2 mmol $NaYF_4: 25\% Er^{3+}$ nanocrystals were dispersed in cyclohexane and mixed with OA (3mL) and ODE (8mL) in a 50mL three-neck flask. The mixture was degassed under Ar flow and kept at 100℃ for 30 min to completely remove cyclohexane. Then heated up to 150℃ and kept at this temperature for 15 min to remove the any possible water. The mixture solution was quickly heated to 300℃ and $NaYF_4$ source solution was injected to the core nanocrystals mixture solution using syringe. The injection rate is 0.05 ml/2 min. After the reaction, the precipitate was washed with cyclohexane/ethanol for several times and dispersed in cyclohexane for use.

Samples for microscope

Samples for microscope are prepared step by step. Firstly, the coverglass was washed with ethanol to remove the oil on top of it. Secondly, the coverglass was rinsed with Poly-L-Lysine so that a negative charge can be formed on it. Then the coverglass was rinsed with de-ionized water and the excessive water on it was blowed off with compressed air. After that, the UCNPs solution was diluted with cyclohexane and 40uL solution was dropped onto coverglass. The excessive UCNPs solution was rinsed with cyclohexane. At last, the coverglass was put onto a slide,and nail polish was used to seal the sample on the corners.

TEM Characterization

The morphology of the synthesize nanocrystals was characterized using transmission electron microscopy (TEM) imaging (Philips CM10 TEM) with an operating voltage of 100 kV. The samples were prepared by placing a drop of a dilute suspension of nanocrystals onto the formvar-coated copper grids (300 meshes) and allowing it to dry in a desiccator at room temperature.

Funding

National Natural Science Foundation of China (61729501, 61771284, 31971376); Natural Science Foundation of Beijing Municipality (JQ18019, L182043, Z181100008918011); National Key Research and Development Program of China (2017YFC0110202, 2019YFB1803501).

Acknowledgments

C.H., Z.W., P.X. and H. C. designed the experiments. C.H., Z.W., W.Z. performed the experiments. X.Y., C.M. prepared UCNPs. P.X. and H. C. supervised the project. C.H., Z.W., P.X. and H. C. analyzed the data. C.H., Z.W., X.Y., P.X. and H. C. wrote the manuscript with contributions from all authors.

Disclosures

The authors declare no conflicts of interest.

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