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Structured illumination microscopy with partially coherent illumination for phase and fluorescent imaging
1. Introduction . Optical microscopy is well known as a simple, easy-to-operate, and non-invasive imaging technique and has been widely used in life science and biomedicine. Yet, most biological samples are transparent or translucent and hence cannot be detected with a traditional brightfield microscope. Fluorescence microscopy can selectively visualize the structures of interest with high contrast by fluorescent tagging, yet its spatial resolution is limited by the emission wavelength (λ) and numerical aperture (NA) of the detection objective. In what follows, we evaluate the theoretical spatial resolution with 0.61λ/NA (Rayleigh criteria, ? 200?nm in general), which is defined by the distance between the peak and the first zero of the point-spread function [ 1 , 2 ]. Over the past three decades, various super-resolution optical microscopic technologies have been developed to meet the imperious demands of resolving the structures beyond the diffraction limit, such as stochastic optical reconstruction microscopy (STORM) [ 3 , 4 ], photoactivated localization microscopy (PALM) [ 5 ], stimulated emission depletion microscopy (STED) [ 6 – 8 ], and structured illumination microscopy (SIM) [ 9 – 11 ]. Among these super-resolution microscopic techniques, SIM is a fast (being wide-field), minimally-invasive technique and has no requirement on fluorescent markers and labeling procedures. SIM acquires the super-resolved image by utilizing the moiré effect between the illumination pattern and the sample, which downshifts the undetectable high-frequency information into the supporting area of the system [ 12 , 13 ]. The resolution enhancement in linear SIM is usually two-fold due to the linear response of fluorescence emission to the excitation intensity, while the resolution enhancement in nonlinear SIM can surpass two-fold by utilizing higher harmonics in the emission patterns [ 12 , 14 ]. Frame-rate SIM has been demonstrated for capturing the fast dynamics in live cells. Till yet, SIM has found extensive applications in life science [ 15 – 17 ]. In SIM, the illumination patterns are often generated by using gratings or optoelectronic devices, including spatial light modulator (SLM) and digital micro-mirror device (DMD) [ 18 – 22 ]. In general, the fringe patterns with high contrast are crucial to obtain super-resolved SIM images with a high signal-to-noise ratio (SNR). Often, monochromatic lasers [ 11 , 15 ] were employed as illumination sources to generate the fringe patterns with high fringe contrast. However, such high-coherence light sources will introduce moderate speckle noise and degrade the optical sectioning capability of SIM. Besides fluorescent microscopy, quantitative phase microscopy (QPM), as a label-free and non-invasive imaging method, can image transparent samples with high endogenous contrast and can achieve quantitative information on the 3D shape of the sample and the inner structure of transparent and translucent samples [ 23 – 25 ]. Yet, the spatial resolution of QPM (together with other coherent microscopic approaches) is also limited by the effective numerical aperture (NA) of the imaging system and the illumination wavelength λ in terms of 0.82λ/NA, with which two points with the identical phase can be justly resolved (the peak of the first point meets the first zero of the second point) [ 2 , 26 , 27 ]. Oblique illumination, speckle illumination, and structured illumination were applied to enhance the spatial resolution of QPM through synthetic aperture [ 28 , 29 ]. In general, the coherent illumination used in QPM also brings speckle noise and introduces other coherent artifacts. Hence, in both SIM-based fluorescent imaging and QPM, it is of great significance to seek a partially coherent illumination source that has low speckle noise on the one hand, and has a high temporal coherent length (to generate high-contrast fringes) on the other hand. Meaningful attempts have been conducted, for example, using light-emitting diodes (LEDs) [ 22 , 30 , 31 ], or using a rotating diffuser [ 32 ]. Specifically, a DMD-modulation based SIM was proposed for super-resolution imaging [ 22 ]. While, once a broad-band illumination is used for illumination in DMD-based SIM, the chromatic dispersion effect will intrinsically decrease the fringe contrast of the projected stripes [ 33 ]. An alternative approach to reduce the coherent noise is to place a rotating optical diffuser on a monochromatic laser, and it was applied to an SLM-based SIM to reduce coherent noise [ 32 ]. Whether in medical imaging or biological optical microscopy, it is an emerging trend to combine different techniques (modalities) in an imaging platform, as researchers seek to extract more and complementary information from the same sample. In biological studies, there is a need for label-free imaging, which provides structural or morphological images of living samples without staining or fluorescence labeling. There is also a need for fluorescence imaging, which reveals specific functions of subcellular structures after staining with exogenous fluorophores. Several imaging modalities combining optical diffraction tomography (3D-resolved phase imaging) and super-resolved fluorescence microcopy have been reported [ 34 , 35 ]. This study presents a partially coherent illumination based (PCI-based) SIM apparatus for multi-modality microscopic imaging. Different from the prior works, quantitative DIC phase imaging and fluorescence imaging that utilizes the same structured illumination are performed in a simple setup, providing morphological super-resolved/sectioned functional images of the same sample. The partially coherent illumination enhances the SNR of all the imaging modalities, and provides a sound optical-sectioning capability for fluorescent SIM imaging. 2. Methods . The schematic diagram of the PCI-based SIM apparatus is shown in Fig.? 1 , where a diode laser with the wavelength of 561?nm (MLL-U-561, Changchun New Industries Optoelectronics Technology Co., Ltd., China) is used as the illumination source. The intensity of the illumination beam is tuned by a neutral density filter (NF). The illumination beam is expanded by a beam expander (BE) to have a diameter of 1?cm. And the beam is relayed by a telescope system L 1 -L 2 to a digital micromirror device (DMD). A diffuser (the diffusing angle is 15°) is placed close to the focal plane of the telescope system (L 1 and L 2 ), and the diffuser is fixed on a motor (KN335714, Huatong Electronics Co., Ltd., China), of which the rotation speed is around 2000 revolutions per minute (RPM) at a voltage of 4.5?V. Thus, the coherent speckle intrinsically with lasers can be suppressed by time-averaging of the diffusor, as shown in the inset in Fig.? 1 (a). To be specific, the focused light beam ( λ 1 , k 1 ) is scattered transiently after passing through the rotating diffuser, and the scattering extent changes at the same time, meaning that any point that is irradiated on the sample plane experiences a time-varying phase modulation with different propagation vectors ( λ 1 , k 1 - k n ). When the diffusor is kept still (not rotating), the generated speckles in the sample plane have an averaged diameter of 51?±?19 μm (mean?±?s.d.). Ultimately, the speckle noise at a point on the image plane varied with time and is eliminated by the superimposing and averaging, and the final result (using the USAF as the sample) is shown in Fig.? 1 (a). ? Fig. 1. The schematic diagram of the proposed structured illumination microscopy with partially coherent illumination. (a) The experimental apparatus. The inset shows the principle of speckle-noise reduction by using a rotating optical diffuser. (b) Fringe patterns along the x - and y - directions loaded sequentially to DMD for super-resolution imaging. BE, beam expander; DM, dichroic mirrors; DMD, digital micromirror device; L 1 -L 6 , achromatic lens; MO 1 -MO 2 , microscopic objectives; M 1 -M 2 , mirrors; NF, neutral density filter. Download Full Size PPT Slide PDF After being temporally modulated by the rotating diffusion, the illumination beam becomes a partially coherent beam. The beam, guided by the mirror M 1 , illuminates the DMD (1920×1080 pixels, pixel size 7.56 μm, DLP F6500, UPOLabs Co., Ltd., China) at an incidence angle of 24°. The modulated light by the DMD, namely structured illumination, propagates along the normal direction of the DMD and enters the microscope system. In this situation, the stripes with a contrast of 80% are achieved. It is worth noting that the stripe contrast can be further improved by satisfying the blaze and diffraction conditions of the DMD by illuminating the DMD at a blaze angle [ 36 – 38 ]. To enhance the spatial resolution isotropically, two groups of binary fringes along the x - and y -orientations, and five-phase shifts ( δ m =2( m -1)π/5, m =1, …, 5.) for each, were loaded to the DMD in sequence (as shown in Fig.? 1 (b)). The illumination light is diffracted by the binary fringes, forming the structured light with its intensity periodically modulated. The structured light is further relayed by the telescope systems L 3 -L 4 and L 5 -MO 1 to the sample plane. A home-made mask containing four circular filtering holes (the diameter of each hole is about 1?mm, and the spacing of the ±1 st diffraction orders is 2.5?mm) was fabricated by a 3D printer, and was placed in the middle focal plane of L 3 -L 4 to block the spectrum of the structured light except the ±1 st orders. The interference of the ±1 st orders produces ideal cosine fringe patterns on the sample plane. Both phase and fluorescence imaging can be performed with the proposed PCI-based SIM apparatus. For quantitative phase imaging, the transmit light through the sample is imaged by the telescope system MO 2 -L 6 to the CCD 1 plane (4000×3000 pixels, pixel size 1.85 μm, DMK 33UX226. The Imaging Source Asia Co., Ltd., China) in a defocused manner. Both the amplitude and phase images of the sample can be reconstructed from the recorded diffraction patterns under different structured illuminations. Moreover, the sample can also be imaged in a focused manner by using the transmission SIM mode [ 21 ]. For fluorescent imaging, being excited by the structured illumination, the signal from the sample is imaged sequentially by the telescope system MO 1 -L 5 to the CCD 2 plane (4096×3000 pixels, pixel size 3.45 μm, Basler ace acA4112-20um, Basler Vision Technology (Beijing) Co., Ltd., China). 3. Experiments and results . 3.1 Characteristics of PCI in beam uniformity and speckle noise reduction . The first experiment was carried out to prove the capability of reducing the speckle noise by rotating an optical diffuser. For this experiment, plane wave illumination was used by loading a plain image with the gray value of 1 onto the DMD. Figure? 2 (a) and 2 (b) are the images obtained under the coherent (without the rotating diffuser) and partially coherent illumination (with the rotating diffuser), respectively. Figure? 2 (c) shows the normalized intensity distributions along the orange and green lines in Fig.? 2 (a) and 2 (b). The comparison indicates that the illumination becomes more uniform by using a rotating optical diffuser. For a quantitative evaluation, the beam flux contrast (BFC) BFC= $\sqrt {\sum {{({{I_i} - {I_{avg}}} )}^2}/N} /{I_{avg}}$ was calculated to quantitively analyze the beam uniformity within the whole field of view (FOV). Here, I i ( x , y ) is the intensity distribution in the image, I avg is the average intensity of I i ( x , y ), and N is the total number of pixels. Usually, the smaller the BFC is, the higher the uniformity of the illumination is. The calculated BFC are 0.52 and 0.11 for the coherent illumination and the partially coherent illumination, respectively. Moreover, the intensity histograms of the images in Fig.? 2 (a) and 2 (b) were calculated and shown in Fig.? 2 (g) and 2 (h). The fit of the histograms to the gaussian function tells the half-width is 0.5?±?0.05 for the CI and 0.1?±?0.01 for the PCI. The results mentioned above imply that the beam uniformity can be significantly enhanced by using a rotating optical diffuser. ? Fig. 2. The comparison of image quality under coherent and partially coherent illumination. (a) and (b) are the intensity distributions under the CI and PCI without sample, respectively. (c) is the intensity profiles along the orange/green lines in (a)-(b). (d) and (e) are the images of USAF under the above two illumination methods, and intensity profiles along the origin/green solid lines are shown in (f). (g) and (h) are the intensity histograms in (a) and (b). Download Full Size PPT Slide PDF At the same time, the signal-to-noise ratio (SNR) was compared by extracting two lines from the UASF-1951 (R3L3S1P, Thorlabs, America) images in Figs.? 2 (d) and 2 (e), which were imaged with CI and PCI, respectively. The intensity distributions along the two lines are plotted in Fig.? 2 (f), showing that PCI has a lower noise level (fluctuation) and higher spatial resolution than CI. Meanwhile, we calculated the standard deviation (STD) of the intensities within the orange and green square area in Figs.? 2 (a) and 2 (b) to quantify the level of coherent noise. And the final results are 0.13 for the CI case and 0.07 for the PCI case, respectively. 3.2 Analysis of stripe contrast . Reducing the coherence of the illumination source usually results in the reduction of the stripe contrast, which may, in turn, affect the SNR of the super-resolved SIM image. In order to quantitatively analyze the stripe contrast, we loaded binary fringe patterns on DMD to illuminate the sample and monitored the generated fringes under different illumination settings, CI by using monochromatic laser, PCI by using a rotating optical diffuser, or LED (470/30?nm central-wavelength/width, 8° divergence angle, Shenzhen Paranormal Technology Co., Ltd, China). In this experiment, different illumination conditions were obtained from the same optical setup (shown in Fig.? 1 (a)) but only switching the illumination among LEDs, laser, and laser with rotating diffusor. For different illumination methods, the illumination is filtered by a mask in their Fourier plane to block the unwanted diffraction orders except the ±1 st orders. The coherence lengths of different illumination settings are calculated with L coh =2ln(2)λ 2 /π△λ, where λ and △λ are the central-wavelength and wavelength width, respectively. The calculation turns out that L coh =46.3?mm and L coh =3.25 μm for the laser illumination and LED illumination, respectively. The PCI based on a rotating optical diffuser has the same L coh as the laser illumination but has reduced a lateral coherence length by superimposing and averaging different speckles varying with time. The generated sinusoidal stripes under different illumination settings are shown in Figs.? 3 (a)–3(c), respectively. The comparison shows that, compared with the CI using monochromatic laser, the PCI based on a rotating optical diffuser and LED has significantly reduced speckle noise. Meanwhile, the stripe contrast of the three cases is 80.3%, 70.0%, and 16.6%, respectively. There are two reasons for the low fringe contrast of the LED illumination. First, the LED illumination has a spatially expanded spectrum in the Fourier plane, and the fringe contrast will be reduced when the high spatial frequencies of the spectrum are attenuated by the OTF of the imaging system. Second, the LEDs with broad wavelength-spectrum suffers from dispersion when being modulated by DMD, which will in turn reduce the fringe contrast [ 33 ]. It is worth mentioning that the fringe contrast can be improved by using a color filter to narrow the LED bandwidth or using a pinhole to enhance the spatial coherence if a high-power LED source is used. ? Fig. 3. The illumination stripes were generated by using a high-coherence laser (a), embedding a rotating optical diffuser into the illumination path (b), and using LED illumination (c). (d) The intensity distribution along the lines in (a), (b), and (c), respectively. Download Full Size PPT Slide PDF In contrast, the reduction of the spatial coherence of the illumination by rotating an optical diffuser can greatly suppress the speckle noise but does not lose much stripe contrast, which will guarantee good quality of super-resolution image reconstruction. 3.3 Quantitative differential phase contrast (qDIC) imaging of PCI-based SIM . A confirmatory experiment was carried out to demonstrate the capability of the proposed technique for qDIC imaging of transparent samples with high endogenous contrast. Mouse adipose stem cells (ADSC) were used as phase samples while experimenting. For the qDIC imaging mode, the magnification and numerical aperture of the imaging system MO 2 -L 6 are 10× and 0.32, respectively. Two groups of binary patterns with the orientation along the x - and y - directions were loaded on the DMD in sequence. The period of the binary patterns corresponds to ten pixels on DMD and the modulation depth was 1. The x - and y - orientated fringe patterns on DMD were shifted by five times, generating a phase shift of 2 i π/5 with i ?=?0, 1, 2,?…, 4, and the generated diffraction patterns were recorded by the CCD 1 camera, as shown in Fig.? 4 (a) and 4 (b), respectively. The fringe patterns in Fig.? 4 (a) and 4 (b) were magnified and compared with that obtained with the CI-based qDIC approach reported in Ref. [ 21 ]. The comparison implies that the stripes under PCI are more homogeneous and have a higher signal-to-noise ratio (SNR) than that under CI. Then, both the amplitude and phase derivatives of the sample can be obtained by using the phase-shifting reconstruction algorithm described in Ref. [ 21 ]. The amplitude image of the sample is shown in Fig.? 4 (e), and the phase derivatives are shown in Fig.? 4 (c) and 4 (d), respectively. Eventually, the phase distribution of the mouse ADSC in Fig.? 4 (f) was determined by integrating the phase derivatives along the x - and y - orientations. Compared to the amplitude image, PCI-based qDIC can visualize the transparent samples with high contrast and high SNR. More preferably, it provides us the chance to quantitatively assess the optical path difference (OPD) of the sample. Note that the PCI generated by the rotating diffusor can enhance the SNR of both the reconstructed amplitude and phase images. Compared to the CI-based qDIC approach [ 21 ], PCI-based qDIC has much lower coherent noise and resultantly a higher SNR in the reconstructed amplitude and phase images, as shown in Fig.? 4 (g) and 4 (h). We further demonstrate with Fig.? 5 dual-modality imaging (including qDIC and fluorescent imaging) can be implemented for the same sample with pixel-to-pixel correspondence. In this experiment, mouse ADSC cells were stained with Plasma membrane Stain (CellMask Orange, ThermoFisher) following the protocol in Ref. [ 39 ]. The cells were imaged with both qDIC and fluorescent imaging modalities. The qDIC image (Fig.? 5 (a)) and fluorescent image (Fig.? 5 (b)) show the same structure of the cells at this staining setting. While, different intracellular organelles of the cells can be further visualized with high contrast by using a specific fluorescent labeling strategy. ? Fig. 4. qDIC imaging of mouse adipose stem cells (ADSC). (a) and (b) are the intensity images of the sample recorded under the fringe patterns along the x - and y - directions. (c) and (d) are the reconstructed phase derivatives of the cells along the x - and y - directions, respectively. (e) and (f) the reconstructed amplitude (normalized) and phase (unit: rad) images of the ADSC cells, respectively. (g) and (h) the enlarged images (the dash-box in (e) and (f)) obtained with CI and PCI. The scale bar in (e), 60 μm. Download Full Size PPT Slide PDF ? Fig. 5. qDIC and fluorescence imaging of mouse adipose stem cells (ADSC). (a) qDIC image of the cells. (b) fluorescence image of the cells stained with plasma membrane stain (CellMask Orange). The scale bar in (a) and (b), 60 μm. Download Full Size PPT Slide PDF 3.4 Synthetic-aperture non-fluorescent imaging of PCI-based SIM . We further demonstrate the preponderances of the PCI-based SIM to image the non-fluorescent samples along the transmission beam path. SiO 2 beads with a diameter of 500?nm were used as the sample. Limited by the numerical aperture (NA detect =0.32) of the detection objective MO 2 , the spatial resolution is δ =0.82λ/NA detect =1.44 μm under on-axis plane wave illumination. To enhance the spatial resolution, binary gratings with a period of five pixels were loaded onto DMD, and the ±1 st orders of the grating were selected by the filter-mask to form sinusoidal fringes on the sample plane. The illumination angle of the ±1 st diffraction orders of the sinusoidal patterns is θ illum =0.30?rad, and thus the theoretical lateral resolution can be estimated with δ str =0.82λ/(sin θ illum +NA detect )?=?0.75 μm, implying a resolution enhancement factor of 1.9. The binary fringe patterns were shifted by five times along the grating vector direction, the generated in-focus intensities with the phase shift increment of 2π/5 were recorded in sequence by CCD 1 . Then, the whole process was repeated after rotating the binary fringe patterns for 90° in DMD. Eventually, the resolution-enhanced image was obtained with the method elaborated in Ref. [ 40 ], and the result is shown in Fig.? 6 (b). Compared with the conventional bright-field image in Fig.? 6 (a), the beads in the PCI-based non-fluorescent SIM image are much sharper and better resolved. The same sample was also imaged by the same method as Fig.? 6 (a) but using a high-NA objective (40×/0.6), as shown in Fig.? 6 (c). The beads image in Fig.? 6 (b) and 6 (c) agree with each other, implying the PCI-based non-fluorescent SIM can enhance the spatial resolution of a low-NA objective and visualize the proper structures of the sample. Furthermore, the comparison of Fig.? 6 (b) and 6 (c) also tells that PCI-based SIM has a better de-blurring capability due to averaging of multiple images along the ±1 st order of structured illuminations. The comparison of the two intensity profiles (Fig.? 6 (d)) that cross the center of the same bead in Fig.? 6 (a) and 6 (b) highlights the resolution enhancement capability of PCI-based transmission SIM. The lateral-resolution evaluation of PCI-based transmission SIM and the conventional bright-field microscopy using plane-wave illumination was conducted by randomly choosing 15 SiO 2 beads and fitting the intensity profiles crossing their centers with Gaussian functions. The statistics tell that the averaged full width at half maximum (FWHM) is 1.82?±?0.27 μm for conventional bright-field microscope and 1.05?±?0.14 μm for PCI-based non-fluorescent SIM. It is meant that the lateral resolution has been improved by a factor of 1.7. Beside using two groups of perpendicular 1D fringe patterns, 2D patterns (grids) can be used, which will bring cross-correlation terms between orthogonal frequency to the detectable bandwidth and hence providing a more isotropic resolution enhancement [ 41 ]. The enhancement in spatial resolution is the contribution of synthetic aperture, and it will not surpass the physical diffraction limit elaborated by the Abbe criterion. And it should be mentioned that the deviation between the experimental and theoretical resolution is due to the existence of aberrations in the imaging system. ? Fig. 6. PCI-based SIM imaging of SiO 2 beads. (a) Bright-field images (10×/0.32) of SiO 2 beads under plane-wave illumination. (b) PCI-SIM (10×/0.32) image of the scatting sample. (c) Bright-field image (40×/0.6) of SiO 2 beads under plane-wave illumination. (d) The intensity profiles along the origin/green lines in (a) and (b). The symbols are the experimental data, and the lines in (d) are the Gaussian fits. The scale bar in (a), 60 μm. Download Full Size PPT Slide PDF Then, we imaged a rat tail crosscut with both traditional bright-field microscopy (Fig.? 7 (a)), CI-based non-fluorescent SIM (Fig.? 7 (b)), and PCI-based non-fluorescent SIM (Fig.? 7 (c)). The comparison of these three images confirms that both the CI- and PCI-based structured illumination can enhance the spatial resolution and the image contrast, while PCI-based non-fluorescent SIM can further improve the image quality by suppressing the speckle noise (via time-averaging). The latter is reflected by the standard deviation calculated from a plain area within the rectangular boxes in 7(b) and 7(c), which is 0.11 and 0.07 for CI-based and PCI-based transmission SIM, respectively. ? Fig. 7. The scattering images of a rat tail crosscut under bright-field optical microscopy with plane-wave illumination (a), CI-based non-fluorescent SIM (b), and PCI-based non-fluorescent SIM (c). The scale bar in (a), 60 μm. Download Full Size PPT Slide PDF 3.5 Super-resolution fluorescence imaging of PCI-based SIM . We further demonstrate the preponderances of the PCI-based SIM to image fluorescent samples in the reflected beam path. First, the spatial resolution enhancement was proved by imaging fluorescent beads with a diameter of 500?nm (RF500C, emission-peak wavelength 620?nm, Shanghai Huge Biotechnology Co., Ltd, China). The numerical aperture (NA detect =0.4) of the detection objective MO 2 limits the lateral resolution under epi-illumination to δ plan? =?0.61λ em /NA=0.95 μm, and λ em ?=?620?nm is the emission-peak wavelength of the fluorophore used. We set the period of the binary patterns loaded onto DMD as seven pixels, yielding sinusoidal fringes with the period of P SIM ?=?1.32 μm at the sample plane. The binary fringe patterns were shifted by seven times along the grating vector directions with one pixel at a time, the generated raw intensity images with the phase shift 2π/7 were recorded in sequence by CCD 2 located at the image plane. Later, the same procedure was repeated after the binary grating on the DMD was rotated by 90°. Eventually, the super-resolved images of the sample can be obtained with the Open-SIM reconstruction algorithm [ 40 ] and are shown in Fig.? 8 -right, in comparison with the conventional wide-field image in Fig.? 8 -left. It is distinct that the SIM image has dramatically enhanced spatial resolution compared to the conventional wide-field image, which is further confirmed by analyzing the intensity profiles in Fig.? 8 (d) and 8 (g). The theoretical lateral resolution of wide-field fluorescence microscopy in terms of FWHM is 0.51λ em /NA=0.79 μm, and the theoretical enhancement on the lateral resolution of SIM is [(2×NA/λ em )?+?1/ P SIM ]/[2×NA/λ em )]=1.6 [ 38 ], implying a theoretical resolution of 0.49 μm for PCI-based SIM. To experimentally evaluate the lateral resolution, fifteen fluorescent beads were randomly chosen, and the intensity distributions along the line crossing the bead centers were extracted and fitted with Gaussian functions. The statistics tell that the averaged FWHM is 0.93?±?0.02 μm (mean?±?s.d.) for the conventional wide-field image and 0.48?±?0.01 μm for PCI-based SIM image. The deviation between the theoretical and measured values is mainly due to the aberration of the system. In addition, we also use the decorrelation analysis [ 42 ] to quantitively calculate the lateral resolution of the wide-field and SIM images, and the results obtained are 1.01 μm and 0.48 μm for the two modalities. As mentioned above in section 3.4 , the aberration in the imaging system will contribute to the difference between the experimental resolution and theoretical resolution. ? Fig. 8. Super-resolution imaging of 500?nm-diameter fluorescent beads. The left and right of (a) are obtained by conventional wide-field microscopy and PCI-based SIM, respectively. The conventional wide-field image and PCI-based SIM image of the enlarged areas indicated with (a1) and (a2) are magnified and shown in (b-c) and (e-f), respectively. The intensity profile along the lines in (b-c) and (e-f) are plotted and compared in (d) and (g), respectively. The scale bar in (a), 20 μm. Download Full Size PPT Slide PDF Then, we imaged wheat anther that is sandwiched between two coverslips through a conventional wide-field microscope and PCI-based SIM, and the results are shown in the left and right of Fig.? 9 (a), respectively. Once the conventional wide-field and PCI-based SIM images of a rectangular area on the sample are magnified and shown in Fig.? 9 (b) and Fig.? 9 (c), the latter one shows finer structures and clearer background. Furthermore, a line from the same locations in Fig.? 9 (b) and Fig.? 9 (c) was analyzed in Fig.? 9 (d), and the result confirms once again that the PCI-based SIM modality can show the more refined structure of the same sample, compared to the wide-field microscopy. It is also worthy to point out that, in order to endow the SIM system with a certain spatio-temporal resolution and for its successful application in the measurement the rapid dynamics, we restrict the orientation of the structured patterns to two directions that are orthogonal to each other. A more isotropic resolution enhancement can be achieved by using fringe patterns in more directions (i.e., three or even more pattern directions). For instance, the result obtained with four-direction fringe patterns (Fig.? 9 (f)) shows more refined details along the diagonal direction of the box than what obtained with two-direction fringe patterns (Fig.? 9 (g)). ? Fig. 9. Imaging of wheat anther with conventional wide-field microscopy and PCI-based SIM. (a) The composite image of the wide-field microscopy (upper-left) and PCI-based SIM (lower-right). (b) and (c) are the enlarged wide-field and PCI-based SIM images from the region within the dash-white frames in (a). (d) The intensity profiles along the white-dash line are indicated in (b) and (c). (e) and (f) are the enlarged views of the super-resolved images obtained by using the fringe patterns along two directions and four directions, respectively. The insets in (e) and (f) show the synthesized frequency-spectra using 2-direction and 4-direction fringe patterns. The scale bar in (a), 40 μm. Download Full Size PPT Slide PDF 3.6 Optical sectioning imaging of PCI-based SIM . Apart from super-resolution, optical sectioning (OS) is another function of structured illumination microscopy [ 43 ]. Different from super-resolution SIM, OS-SIM just needs one-directional fringe illumination, and the optimal frequency of the stripes is half of the cut-off frequency of the optical system to obtain the best sectioning effect [ 44 ]. As a result, the fringe period was set to 3.4 μm at the sample plane (the period of the binary patterns loaded onto DMD was set as nine pixels). Three-step phase-shifting with the interval of 2π/3 was performed by translating the binary patterns for three pixels each time. Resultantly, three intensity images ( I 0 , I 2π/3 , I 4π/3 ) with the phase-shift of 2π/3 were generated. The fluorescence excited by the structured illumination was imaged to CCD 2 after being filtered by a color filter (600/50?nm, central-wavelength/FWHM), and the final optical sectioning image is calculated as [ 43 ]: (1) $$I = {[{{{({I_0} - {I_{2\pi /3}})}^2} + {{({I_0} - {I_{4\pi /3}})}^2} + {{({I_{2\pi /3}} - {I_{4\pi /3}})}^2}} ]^{1/2}}. $$ With this operation, the out-of-focus blurring can be eliminated. Figure? 10 (a) shows a stack of sectioned images of a pollen grain at different axial sections, obtained by using PCI-based SIM. In Fig.? 10 (b-d), the sectioned images of the pollen grain were obtained by using conventional wide-field microscopy, CI-based SIM (Fig.? 10 (b)), and PCI-based SIM (Fig.? 10 (c)) are compared in parallel. The comparison implies PCI-based SIM is superior to CI-based SIM in optical sectioning for that the contrast of the partially-coherent fringe illumination decays faster with the axial defocusing distance. Meanwhile, PCI-based SIM image has higher SNR and fewer artifacts that are from the out-of-focus region. ? Fig. 10. Optical sectioning images of the pollen grain. (a) a stack of sectioned images of an autofluorescent pollen grain at three different axial positions. (b) Comparison of the images obtained at the different axial planes by using (b)conventional microscopy, (b) CI-based SIM, and (d) PCI-based SIM. The scale bar in the third row, 30 μm. Download Full Size PPT Slide PDF 4. Conclusion and discussion . This study presents a PCI-based SIM apparatus, with which quantitative phase imaging and super-resolved/sectioned fluorescent imaging are performed, providing multi-modality, complementary information for the same sample. Under the partially coherent illumination (PCI) generated by placing a rotating diffuser on a monochromatic laser beam, the fringe patterns with high-contrast and low speckle-noise are generated using a DMD, avoiding the intrinsic dispersion problem in conventional LED-illumination based SIM. It was found from our experiments that the PCI can enhance the signal-to-noise ratio (SNR) of QPI images dramatically, and it endows SIM with a sound sectioning capability, although the SNR enhancement on super-resolved fluorescence imaging is not apparent. It is worth mentioning that we used five-step phase-shifting for non-fluorescent SIM in the transmission beam path and seven-step phase-shifting for fluorescent SIM in the reflected beam path to achieve a higher signal-to-noise (SNR) of the reconstruction by trading with time. However, it is more advantageous to utilize three-step phase-shifting when imaging dynamic samples, for which the temporal resolution is demanding. Although the current dual-modality images presented in the paper were taken separately (in sequence), we will upgrade the imaging system in the future to acquire phase and fluorescence images simultaneously, providing both morphological and functional information for the same sample. Furthermore, the imaging system can be upgraded to measure polarimetric samples as well. Funding . National Natural Science Foundation of China (62075177); Natural Science Foundation of Shaanxi Province (2020JM-193, 2020JQ-324, 2021JQ-184); Fundamental Research Funds for the Central Universities (JB210513, JC2112, XJS210503, XJS210504); Guangdong Basic and Applied Basic Research Foundation (2020A1515110590); State Key Laboratory of Transient Optics and Photonics; Key Laboratory of Image Processing and Pattern Recognition . Acknowledgments . P. Gao conceived and supervised the project. K. Wen, Z. Gao, and X. Fang performed experiments and data analysis. M. L, Z. Z, and J. Zheng contributed to data analysis. K. Wen, M. Y, J. Zheng, and P. Gao wrote the draft of the manuscript; All the authors edited the manuscript. Disclosures . The authors declare that there are no conflicts of interest related to this article. Data availability . Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request. References . 1. R. Heintzmann and C. Cremer, “Laterally modulated excitation microscopy: Improvement of resolution by using a diffraction grating,” Proc. SPIE 3568 , 185–196 (1999). [ CrossRef ] ? 2. M. Born and E. Wolf, Principles of optics , 7th ed. (Cambridge University, 2013), Chap.8. 3. M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3 (10), 793–796 (2006). [ CrossRef ] ? 4. J. F?lling, M. Bossi, H. Bock, R. Medda, C. A. Wurm, B. Hein, S. Jakobs, C. Eggeling, and S. W. 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