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Abstract
Structured illumination microscopy (SIM) requires polarization control to guarantee the high-contrast illumination pattern. However, this modulated polarization will induce artifacts in SIM when imaging fluorescent dipoles. Here we proposed the polarization weighted recombination of frequency components to reconstruct SIM data with suppressed artifacts and better resolving power. Both the simulation results and experimental data demonstrate that our algorithm can obtain isotropic resolution on dipoles and resolve a clearer structure in high-density sections compared to the conventional algorithm. Our work reinforces the SIM theory and paves the avenue for the application of SIM on a polarized specimen.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Structured illumination microscopy (SIM) is a rapidly evolving technique in super-resolution fluorescence imaging and has been widely used in biological studies. [1–5] SIM is superior to other techniques in terms of high photon efficiency. The efficient use of the available photon budget not only minimizes the excitation power used for rapid imaging but also maintains the long observation period of SIM with low photon toxicity, which is critical for live-cell imaging. In SIM, all photons are collected since no optical parts like pinhole [6,7] reject the signal. Moreover, the optical transfer function (OTF) of SIM has two peaks near the Abbe limit [Fig. 1(b)], which requires far fewer emitted photons than a Gaussian-like OTF to capture sample structures in the super-resolution regime under the same SNR [8]. This unique profile of the SIM OTF further guarantees efficient photon detection.
Fig. 1. Polarization-induced artifact in structured illumination microscopy (SIM). (a) Three orientations of patterns used in linear SIM are displayed, and each pattern orientation requires three shifted phase for 2D-SIM. To guarantee a high-contrast sinusoidal stripe, the laser beams generating the interference pattern are linearly polarized, and their polarizations are rotated to keep parallel to the pattern orientation. (b) Three components can be separated from images illuminated by patterns of each orientation and then recombined in the Fourier space. A higher modulation depth of the illumination patterns leads to more energies in the high-frequency information, which better preserves the super-resolved structures. (c, d) The full observable region of SIM (d) can be obtained by recombining the frequency components of each pattern orientation, and super-resolution image (c) is generated by inverse Fourier transform of (d). (e) When the sample of a fluorescent dipole is imaged by SIM, the amplitudes of the components in different pattern orientations are modulated by the dipole absorption efficiency of the polarized light (proportional to ${\cos ^2}(\theta - \alpha )$ where θ represents the polarization, α represents the dipole orientation). (f) When three separated components are combined, the amplitudes along the horizontal axis are significantly larger, which leads to an anisotropic resolution in the super-resolved image. (g) The partially super-resolved image for each pattern orientation can be obtained by applying inverse Fourier transform to the frequency information in (e). The polarization-related absorption efficiency results in a higher intensity of the first pattern orientation than the other two. (h) The super-resolution image of conventional SIM has an anisotropic resolution. Scale bar: 200 nm.
The additional peaks in the OTF of SIM are generated through the structured illumination with high-contrast stripes. [9,10] The sinusoidal pattern exciting the sample brings two frequency components beyond the cutoff frequency into the observable region. Higher the modulation contrast of the illumination stripe will result in higher proportion of high-frequency components to be detected. Therefore, the modulation contrast of the illumination stripes is the key to achieve the high-quantity super-resolution images of SIM. [11] Since S-polarized laser beams generate the highest contrast stripes within the same power, a polarization modulation part that rotates the polarization of the laser beams to keep it parallel to the stripes is embedded in most SIM systems,
The polarization control was emphasized in the hardware in various SIM publications, including components such as electro-optic devices [12], pizza-shaped [13], or vortex [14] half-wave plate. In the reconstruction process, nevertheless, all the previous algorithms assumed the scalar interaction between the electric field of light and the fluorophore, which means that the emission intensity is proportional to the excitation intensity. However, most fluorophores are dipoles, whose absorption efficiency of light is related to the dipole orientation and the polarization. [15–17] This anisotropic polarization response exists in most specimens labeled by fluorescent proteins or molecular probes, especially in the specimen of cytoskeletal filaments, lipid membranes, and bio- complex. [18–20] Since another benefit of SIM is its compatibility with standard fluorescence samples, the investigation on how this inherent polarization modulation will affect the SIM imaging results can reinforce the SIM theory and further broaden the application of SIM.
With theoretical modeling, we simulated the point spread function (PSF) of an ideal fluorescent dipole. The dipole PSF appears as an ellipse-shaped pattern related to its dipole orientation instead of the isotropic Airy disk (Fig. 1), which will induce the “dipole artifact” in the SIM imaging results. In this paper, we identify the dipole artifact in both simulated results and experimental images. Furthermore, we proposed a novel algorithm termed Polarization Weighted Recombination SIM (PWR-SIM) addressing this problem. We demonstrated that a more definite structure could be resolved in the high-density specimen. Our model is validated both on simulation data and experiment data.
2. Principles and methods
2.1 Polarization-induced artifact in the SIM imaging of dipoles
The resolution of the wide-field microscope is limited by its optical transfer function (OTF). [21] In linear SIM imaging, the samples are excited with sinusoid stripe patterns of three directions. [9,10] This sinusoid pattern [Eq. (1)] will generate three frequency components (0th order and ± 1st order). The energy ratio of 0th order component to the ± 1st order components is determined by the modulation depth (m). The value of m is from 0 to 1, and a higher m means the stripe pattern has a higher contrast. With this illumination pattern, the ± 1st order components, which originally located outside the observable region of the wide-field microscope, are shifted in to this region, so that the observable region of SIM is expanded. Within the same illumination power, we should set m as high as possible to collect more signal that contributes to the resolution enhancement. When the modulation depth is decreased, the amplitude of two peaks in the SIM OTF descends [Fig. 1(b)]. Since the noise is rather uniform in the frequency domain, the high-frequency signals, which have a smaller amplitude due to the low-passing filtering of the optical system, are more vulnerable to noise. Therefore, generating the high-contrast pattern is essential for high-quality SIM imaging. Practically, to get the highest contrast illumination pattern, s-polarized laser beams are applied in most SIM setup, and the polarization of the laser beams rotates as the illumination stripes rotate, keeping the polarization parallel to the stripes [Fig. 1(a)].
The reconstruction of SIM is usually performed in the Fourier space and contains two steps. In the first step of components solving, the 0th order components and ± 1st order components are solved using the three images of the same direction. In conventional SIM, the sample is considered as monopoles, assuming that the emission intensity under any polarization excitation is uniform. Therefore, the intensity of the Fourier components of every direction is the same. [Figure 1(c)] In the second step of components assembling, the bands of different stripe directions are assembled to form a doubled region in the Fourier space [Fig. 1(e)], and the super-resolution image is correspondingly in spatial space [Fig. 1(d)].
However, most fluorophores are dipoles, which means that its absorption and emission property is strongly polarization-dependent. [15] Under linear polarization excitation, the absorption efficiency of the dipole E is determined by the angle between its natural orientation α and the polarization direction $\theta $, reaching the maximum when parallel and the minimum when perpendicular. The quantitative relationship is described as Eq. (2). [22]
Considering the inherent polarization modulation in the SIM setup, for a dipole sample, the intensity of the components of each direction is not uniform. [Figure 1(f)] When assembling them together, the entire spectrum in Fourier space is anisotropic. [Figure 1(g)] Because the resolution of the sample is determined by the high-frequency information in the Fourier space, the direction with higher intensity components will gain a higher resolution enhancement, and the direction with lower intensity components will achieve comparable a lower resolution enhancement. For a point dipole, the final image reconstructed by conventional SIM algorithm will become an ellipse.
This polarization-induced artifact will be more obvious when imaging dipole-filaments. Consider the two horizontal lines whose dipole orientation is parallel and perpendicular to its filament direction, respectively, and the resolution is mainly determined by how much the OTF is expanded along the vertical axis. For the line of parallel dipole orientation, the intensity of the components of this direction is the most powerful among all directions. On the contrary, that of perpendicular dipole orientation, the intensity of this direction is the weakest, result in less contribution to the resolution enhancement. More quantitative analysis is proposed in Section 3.2.
In summary, polarization control is a necessary part for SIM system. However, this inherent polarization modulation will affect dipole imaging. The PSF of a dipole will become elliptical and cause uneven resolution of lines with different dipole orientations. Since most fluorophores have dipole behavior, this anisotropic artifact will impair the broadness of application for SIM.
2.2 Principle of polarization weighted recombination SIM (PWR-SIM)
We proposed PWR-SIM addressing this polarization-induced artifact. We named the combination of the 0th order components and ± 1st order components for each direction as a polarization component [Figure 1(c)]. Then the intensity of each polarization component varies since they are under different polarization excitation. If we directly assemble them in Fourier space, the ensemble spectrum will be anisotropic, resulting in an elliptical detection image. PWR-SIM is to reweight these polarization components and recombine them to form an isotropic Fourier spectrum like Fig. 1(e). Considering the simplest situation that a single dipole with known the dipole orientation [Fig. 2(a)], the weight of each direction is ${\cos ^2}(\theta - \alpha )$, then we can directly divide this weight for the polarization component of corresponding orientation. Then this dipole artifact can be overcome.
Fig. 2. The principle of PWR-SIM. (a) Dipoles with different orientations reconstructed by conventional SIM, which has a lower resolution along the perpendicular direction. (b) By compensating the polarization weight factor ${\cos ^2}(\theta - \alpha )$, the reconstructed images acquired isotropic resolution. Scale bar: 100 nm
While the principle of PWR-SIM rather simple and straightforward, the implementation of this algorithm faces the following problems. Firstly, the weight factor ${\cos ^2}(\theta - \alpha )$ is close to zero when $\theta $ is perpendicular to α, so in this situation, the noise will degrade the reconstruction quality [Fig. 2(b)]; secondly, a real image contains multiple dipoles of different orientations, there is no such a uniform weight factor to compensate for each component. Therefore, PWR-SIM is implemented by an integrated spatial-angular deconvolution algorithm. We use ${\textrm{S}}({\mathbf r},\alpha )$ to model the dipole sample in spatial-angular hyperspace, where the value of ${\textrm{S}}({\mathbf r},\alpha )$ represents the intensify of a dipole at location r with orientation $\alpha $. Firstly, we calculated the 0th order components and 1st order components from raw SIM images [Fig. 3(a)] the same as the convention SIM algorithm does. Then for each direction, we combined its corresponding directional components together to get the polarization components ${{\textrm{P}}_\theta }({\mathbf r})$. [Figure 3(b)] The corresponding spatial image of a polarization component is formed as the convolution of ${\textrm{S}}({\mathbf r},\alpha )$ with a spatial kernel [directional PSF, ${\textrm{PS}}{{\textrm{F}}_\theta }({\mathbf r})$, Fig. 3(c)] and an angular kernel ${\cos ^2}(\theta - \alpha )$. [Equation (3)]
Fig. 3. The flowchart of PWR-SIM algorithm. (a) The nine raw images under structured illumination. (b) The polarization components, which are acquired by combining 0th order and ± 1st order spectrum components of the corresponding direction in Fourier space. (c) The directional PSF. (d) The resolved sample $S({\mathbf r},\alpha )$ after the spatial-angular deconvolution. (e) The wide field (WF) image. (f) The conventional SIM result. (g) The final PWR-SIM result, which is the integration along angular dimension of the result in (d).
2.3 Mathematical model of PWR-SIM
For a dipole sample $S({\mathbf r},\alpha )$, the detected image ${I_{\theta ,\phi }}({\mathbf r})$ under illumination direction $\theta $ and phase $\phi $ is represented as Eq. (4).
For convenient, we use ${\tilde{\textrm{D}}_{\theta ,{\textrm{m}}}}({{\mathbf k}_{\mathbf r}},\alpha )$ to denote $\sum\limits_\alpha {{{\tilde{{\textrm{S}}}}_{\theta, {\textrm{m}}}}({{\mathbf k}_{\mathbf r}} - {\textrm{m}}{{\mathbf k}_{\mathbf \theta }},\alpha )\cdot {\textrm{OTF}}({{\mathbf k}_{\mathbf r}})} \cdot {\cos ^2}(\theta - \alpha )$, where m represents the order of the spectrum component and ranges {-1,0,+1} for 2D SIM. Then ${{\textrm{I}}_{\theta ,\phi }}({\mathbf r})$ can be rewritten as ${\sum\nolimits_{\textrm{m}} {{{\textrm{e}}^{ - {\textrm{jm}}\phi }}{\textrm{D}}} _{\theta,{\textrm{m}}}}({{\mathbf k}_{\mathbf r}},\alpha )$, which is a linear combination of ${\tilde{D}_{\theta,{\textrm{m}}}}({{\mathbf k}_{\mathbf r}},\alpha )$. Therefore, for each $\theta $, with the measurement under three different $\phi $, each ${\tilde{{\textrm{D}}}_{\theta,{\textrm{m}}}}({{\mathbf k}_{\mathbf r}},\alpha )$ can be separated. In conventional SIM algorithm, with a generalized Wiener filter, all ${\tilde{{\textrm{D}}}_{\theta,{\textrm{m}}}}({{\mathbf k}_{\mathbf r}},\alpha )$ will be moved to the proper position in Fourier space and assembled together to form a super-resolution spectrum as Eq. (5). [9,10]
In PWR-SIM, each polarization component ${{\textrm{P}}_\theta }({\mathbf r})$ is assembled in a similar way. The spectrum is the combination of 0th order component and 1st order component of the corresponding direction. The spatial directional super-resolution is represented as Eq. (6).
Then we apply spatial-angular deconvolution algorithm on ${{\textrm{P}}_\theta }({\mathbf r})$. Since the convolution is a linear operation, we use $H{}_\theta$ to represent the matrix form of the convolution kernel ${\textrm{PS}}{{\textrm{F}}_\theta }({\mathbf r})\cdot {\cos ^2}(\theta - \alpha )$. From a guess sample distribution ${S_{guess}}({\mathbf r},\alpha )$, we set the mean-squared-error between the guessed images and detected images $\sum\nolimits_\theta {{{|{{P_\theta } - {H_\theta }{S_{guess}}} |}^2}}$ as the optimization function. Since optimization function is convex, this optimization problem can work in the Richardson-Lucy iterative scheme. [23,24] From an initial guess of the sample ${S^{(0)}}$ in spatial-angular hyperspace, we update the ${S^{(k)}}$ iteratively following the gradient descent until ${S^{(k)}}$ is converged [Eq. (8)]. The final PWR-SIM result is the integration along angular dimension $\sum\nolimits_\alpha {S({\mathbf r},\alpha )} $.
3. Simulations
3.1 Simulation condition
We built a simulation model for PWR-SIM. The basic SIM parameter is set as objective NA = 1.4, emission wavelength $\mathrm{\lambda }$=528 nm, and shifted wave factor ${k_p} = 5\mu {m^{ - 1}}$. The direction of three illumination patterns are $0^\circ ,60^\circ ,120^\circ $, respectively. The PSF of the optical system is defined as a Gaussian function [Eq. (9)], and the OTF is its Fourier Transform correspondingly.
The specimen is modeled in spatial-angular hyperspace. For most SIM setup, only three direction of pattern is applied, equivalent to three measurement point in angular dimension. Therefore, during the spatial-angular deconvolution, we also apply three sample points in angular dimension to avoid the oversampling issue.3.2 Simulation of polarization-induced artifact
We simulate the dipole filaments to validate the polarization-induced artifact. (Fig. 4) The dipole orientation of the line is indicated by the white arrow. The width of both line is 20 nm. To quantify the resolution of the line sample, we apply Gaussian fitting to the intensity profile of its normal line. [Equation (10)] The relation between the full width at half maximum (FWHM) and the standard deviation $\sigma $of Gaussian fitting result is $FWHM = 2.355 \cdot \sigma $
where X is the spatial position, Y is the intensify, A, $\mu $, $\sigma $ is the parameter to be fit.Fig. 4. Simulation of dipole filaments of different orientations. (a) SIM and PWR-SIM result of a line sample of 20 nm width with parallel dipole orientation and perpendicular dipole orientation, respectively. The dipole orientation is indicated by the white arrow. (b) The intensity profile of the lines in (a). From the Gaussian fitting result, the width of these dipole lines in SIM image is 87 nm, 114 nm, respectively, suggesting that the resolution of the line of parallel dipoles is higher than that of the perpendicular dipoles. While in PWR-SIM image, the width of both lines is close to the ground truth (20 nm). Scale bar: (a) 200 nm.
In the conventional SIM result, the FWHM of these two lines is 87 nm and 114 nm, respectively, suggesting that the resolution of line with parallel dipole orientation in conventional SIM is 1.31 higher than that of perpendicular dipole orientation. While in the PWR-SIM, after enough deconvolution iterations, the width of both lines will reach ∼20 nm, which is close to the ground truth, suggesting the dipole effect is overcome this by PWR-SIM.
3.3 Simulation of crossed dipole lines
Wide-field microscopy cannot distinguish several dipoles overlapped in a diffraction-limited area. However, since their emission intensity shows different peaks under polarization excitation, polarization demodulation provides more information to distinguish them and improves the spatial resolution [25]. Inherit from the embedded polarization deconvolution, PWR-SIM is able to provide a higher spatial resolvability, especially in high density labeled samples.
To validate this capability, we simulated the specimen of triple close crossing dipole lines. (Fig. 5) The width of all three lines is 20 nm and their dipole orientation is indicated as the white arrow in Fig. 5(a) (parallel to line direction). Gaussian white noise is added and the peak signal-to-noise ratio (PSNR) is as indicated. In SIM images, the gap surrounded by the lines is hard to observe, while in PWR-SIM images, the structure is quite clear. We also compared our PWR-SIM result with non-polarization deconvolution [Fig. 5(c)], which is implemented by directly applying spatial deconvolution on ${P_\theta }({\mathbf r})$ without the angular kernel ${\cos ^2}(\theta - \alpha )$. While in this situation, the detailed information will be lost quickly as the iteration number goes higher and cannot contribute to resolve the tiny structure. The quality of PWR-SIM image is still acceptable even when the PSNR is 5. This improved resolving power will broaden the application of PWR-SIM.
Fig. 5. Simulation results of triple crossing lines as an example of high-density sample. (a) The ground truth of the simulated sample. The dipole orientation of the lines is parallel to the filament direction as indicated. (b) Conventional SIM result of (a). (c) Non-polarization deconvolution result of (a). (d-f) PWR-SIM result of the (a) under different signal-to-noise ratios. Scale bar: (a-f) 200 nm
4. Experiments
4.1 Experimental setup
All experimental SIM data in this paper are collected on commercial system DeltaVision OMX SR from GE, US. The objective is 60x 1.4NA oil immersion from Olympus, Japan. The excitation wavelength and emission wavelength of the green channel are 488 nm and 528 nm, respectively. The excitation wavelength and emission wavelength of the red channel are 561 nm and 609 nm, respectively. The pixel size of all raw SIM captured images is 80 nm. And the pixel size of all super-resolved SIM image is 40 nm.
4.2 SIM reconstruction
The conventional SIM result in this paper was reconstructed either directly by open-source software fairSIM [26] (www.fairsim.org) or by a home-written MATLAB code based on fairSIM framework. The key parameter in fairSIM is set as: OTF estimated parameter a = 0.30, wiener filter parameter = 0.02, the apodization bend = 0.9, and apodization cutoff = 2. For sparse labeled in vitro specimens, due to the limited signal-to-noise ratio of the raw SIM images, we additionally apply exponential OTF damping and zero-frequency suppression [27] to reduce the ripple effect. The ripple effect in all SIM images is lower than 10%.
The polarization components and directional PSF are generated as intermediate output during the conventional SIM reconstruction. Then the spatial-angular deconvolution is further implemented with a home-written code. The related code and example dataset is uploaded on https://github.com/chenxy-thu/pwr-sim/.
4.3 Validation of the polarization-induced artifact
We imaged sparse labeled in vitro specimens to validate the aforementioned polarization-induced artifact. DNA filaments labeled by molecular probes such as SYTOX or Hoechst shows perpendicular dipole orientation [28], which would lose resolution with SIM imaging according to our theory and simulation results. We imaged SYTOX-orange labeled lambda-DNA in vitro with SIM. [Fig. 6(a)] The curve in Fig. 6(c) shows the average of 10 selected regions across the filaments. The spatial resolution of the SIM result is 197 nm from the Gaussian fitting result [Eq. (10)]. The k vector of the structured illumination is $4.858\mu {m^{ - 1}}$, resulting in a theoretical SIM resolution of 105 nm. The achieved resolution of lambda-DNA filaments with convention SIM reconstruction is lower than that in theory, due to the perpendicular polarization.
Fig. 6. Experimental result of in vitro filaments with parallel dipole orientation and vertical dipole orientation. (a-b) The SIM and PWR-SIM results of the lambda-DNA filament labeled by SYTOX-orange are compared. The ensemble dipole orientation is vertical since the dye molecule is perpendicularly inserted to the filament, which leads to a significantly lower resolution in the conventional SIM result. (d-e) The SIM, and PWR-SIM result of the actin filaments labeled by Alexa-488-Phalloidin are compared. The ensemble dipole orientation is parallel to the filament due to the binding mode between the fluorophore and the target. (c, f) The statistic result of 10 selected regions of each sample. The SIM resolution of lambda-DNA is 197 nm, and that of actin is 85 nm, suggesting that the resolution of the dipole line of perpendicular orientation is lower than that of parallel orientation, which is consistent with our simulation result. With PWR-SIM, the resolution of lambda-DNA is 105 nm, and the resolution of actin is 66 nm, which is closer to the theoretical resolution. Scale bar: (a,b,d,f) 1 um.
In contrast, we also imaged the in-vitro actin filament labeled by Alexa-Phalloidin-488, which shows parallel polarization. [29] The averaged curve of 10 selected regions is shown in Fig. 6(f) and the resolution of the SIM result is 85 nm. The k vector of the structured illumination is $5.078\mu {m^{ - 1}}$, resulting in a theoretical SIM resolution of 90 nm. The resolution of actin filaments with parallel polarization achieves the theoretical resolution of with conventional SIM algorithm.
The PWR-SIM result of these two samples is also displayed in Fig. 6(b), and Fig. 6(e). The FWHM of lambda-DNA and actin is 105 nm and 66 nm, respectively, which is closer to the theoretical SIM resolution. This result suggests PWR-SIM acquired uniform resolution enhancement with both parallel dipoles and perpendicular dipoles, meaning that the polarization-induced artifact is decreased substantially.
4.4 Demonstration of the improved resolving power with PWR-SIM
We further validated the improved resolving power of PWR-SIM experimentally. We imaged Alexa-488-Phalloidin labeled actin in BAPE cells [Figs. 7(a)–7(c)] and Atto-633-Phalloidin labeled actin in U2OS cells [Figs. 7(d)–7(f)]. The ensemble dipole orientation of Alexa-Phalloidin-488 labeled actin is parallel to the filament, while that of Atto-633-Phalloidin labeled actin is perpendicular to the filament, which has been proved elsewhere. [29,30] Compared with conventional SIM, PWR-SIM is able to provide a clearer view in high-density region. And compared with the non-polarization deconvolution result, which is implemented by directly applying spatial deconvolution on ${P_\theta }({\mathbf r})$ without the angular kernel ${\cos ^2}(\theta - \alpha )$, PWR-SIM result is more smooth and contains fewer artifact.
Fig. 7. Experimental demonstration of the improved resolving power of PWR-SIM. (a-c) Experimental result of Alexa-488-Phalloidin labeled actin in BAPE cell. (d-f) Experimental result of Atto-633-Phalloidin labeled actin in U2OS cell. SIM result, non-polarization deconvolution result and PWR-SIM result are compared and zoomed in view are provided in the white square. The ensemble dipole orientation of (a-c) should be parallel to the filament while the ensemble dipole orientation of (d-f) should be perpendicular due to the binding mode between the fluorescent dye and the target. PWR-SIM is able to provide a clear view compared to SIM result, and contains less artifact compared to non-polarization deconvolution result, suggesting the resolving power of PWR-SIM is substantially improved in the high-density region. Scale bar: (a-f) outer: 5 um, inner: 1 um.
5. Discussion and conclusion
Structured illumination microscopy is a powerful tool for biological imaging, however, its reconstruction artifact sometimes degraded its performance substantially. [27] Although some advanced algorithms have been developed for precise parameter estimation [31,32] or reconstruction under imperfect experimental condition [33,34], seldom of them focused on the polarization effect caused by SIM setup. In this paper, we studied a novel aspect of SIM, that the polarization excitation used in most SIM systems will affect the image quality. We theoretical built SIM model considering the polarization effect and discovered the polarization-induced artifact when imaging dipoles. We proposed the polarization components recombination (PWR-SIM) algorithm to compensate for this artifact. Furthermore, with the help of spatial-angular deconvolution, PWR-SIM is able to provide a clearer structure in the region of crossed filaments.
PWR-SIM works for the sample with dipole properties. Although most fluorescent molecules are dipoles, if they are randomly wobbling, we cannot observe the dipole effect with a SIM system. But if fluorescent dipoles rigidly bind to the target structure, their orientation will be in a regular spatial distribution, then the ensemble dipole effect will be obvious. Specimen exhibiting strong anisotropic polarization response includes some small molecule dyes such as SYTOX, Hoechst or YOYO-1 [28,29] and some fluorescent proteins with rigid linkers [18]. Moreover, the polarization modulation property of the optical system will affect the quality of PWR-SIM since the directional PSF is calculated with the assumption that the polarization ratio of the excitation beam is 1. Then for the SIM setup with no or low polarization modulation, such as instant SIM [35,36], PWR-SIM is not applicable.
Although our model only includes the 2D dipole model, it can be applied to the 3D dipole as well. Because the illumination beam of SIM contains no axial polarization, the axial component of the 3D dipole will not be excited so that it would not bring dipole artifact. Similarly, our model is also compatible with 3D-SIM or TIRF-SIM [12]. Moreover, most commercial SIM setups only provide patterns of three different directions, which limits the orientation resolvability of dipoles. For some home-built SIM system, if more polarization illumination patterns are applied, the performance of PWR-SIM can be further improved.
Funding
Shenzhen Technology Development Program (KQTD20170810110913065); Natural Science Foundation of Beijing Municipality (18JQ019); National Natural Science Foundation of China (61327902, 61475010, 61729501); National Key Research and Development Program of China (2017YFC0110202).
Acknowledgment
The authors thanks to Dr. Chunyan Shan for the assistance in SIM experiment.
Disclosures
The authors declare no conflicts of interest.
References
1. P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009). [CrossRef]
2. L. Shao, P. Kner, E. H. Rego, and M. G. Gustafsson, “Super-resolution 3D microscopy of live whole cells using structured illumination,” Nat. Methods 8(12), 1044–1046 (2011). [CrossRef]
3. X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, and P. Xi, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Biotechnol. 36(5), 451–459 (2018). [CrossRef]
4. J. Nixon-Abell, C. J. Obara, A. V. Weigel, D. Li, W. R. Legant, C. S. Xu, H. A. Pasolli, K. Harvey, H. F. Hess, and E. Betzig, “Increased spatiotemporal resolution reveals highly dynamic dense tubular matrices in the peripheral ER,” Science 354(6311), aaf3928 (2016). [CrossRef]
5. Y. Guo, D. Li, S. Zhang, Y. Yang, J.-J. Liu, X. Wang, C. Liu, D. E. Milkie, R. P. Moore, and U. S. Tulu, “Visualizing intracellular organelle and cytoskeletal interactions at nanoscale resolution on millisecond timescales,” Cell 175(5), 1430–1442.e17 (2018). [CrossRef]
6. S. W. Paddock, “Principles and practices of laser scanning confocal microscopy,” Mol. Biotechnol. 16(2), 127–150 (2000). [CrossRef]
7. R. Gräf, J. Rietdorf, and T. Zimmermann, “Live cell spinning disk microscopy,” in Microscopy techniques (Springer, 2005), pp. 57–75.
8. D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, and M. Pasham, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015). [CrossRef]
9. M. G. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000). [CrossRef]
10. M. G. Gustafsson, L. Shao, P. M. Carlton, C. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008). [CrossRef]
11. G. Ball, J. Demmerle, R. Kaufmann, I. Davis, I. M. Dobbie, and L. Schermelleh, “SIMcheck: a toolbox for successful super-resolution structured illumination microscopy,” Sci. Rep. 5(1), 15915 (2015). [CrossRef]
12. L. J. Young, F. Ströhl, and C. F. Kaminski, “A guide to structured illumination TIRF microscopy at high speed with multiple colors,” J. Visualized Exp. (111), 53988 (2016). [CrossRef]
13. H.-W. Lu-Walther, M. Kielhorn, R. Förster, A. Jost, K. Wicker, and R. Heintzmann, “fastSIM: a practical implementation of fast structured illumination microscopy,” Methods Appl. Fluoresc. 3(1), 014001 (2015). [CrossRef]
14. K. Zhanghao, X. Chen, W. Liu, M. Li, Y. Liu, Y. Wang, S. Luo, X. Wang, C. Shan, H. Xie, J. Gao, X. Chen, D. Jin, X. Li, Y. Zhang, Q. Dai, and P. Xi, “Super-resolution imaging of fluorescent dipoles via polarized structured illumination microscopy,” Nat. Commun. 10(1), 4694 (2019). [CrossRef]
15. R. Camacho, D. Täuber, and I. G. Scheblykin, “Fluorescence Anisotropy Reloaded—Emerging Polarization Microscopy Methods for Assessing Chromophores’ Organization and Excitation Energy Transfer in Single Molecules, Particles, Films, and Beyond,” Adv. Mater. 31(22), 1805671 (2019). [CrossRef]
16. T. Chandler, H. Shroff, R. Oldenbourg, and P. La Rivière, “Spatio-angular fluorescence microscopy I. Basic theory,” J. Opt. Soc. Am. A 36(8), 1334–1345 (2019). [CrossRef]
17. K. Zhanghao, J. Gao, D. Jin, X. Zhang, and P. Xi, “Super-resolution fluorescence polarization microscopy,” J. Innovative Opt. Health Sci. 11(01), 1730002 (2018). [CrossRef]
18. A. M. Vrabioiu and T. J. Mitchison, “Structural insights into yeast septin organization from polarized fluorescence microscopy,” Nature 443(7110), 466–469 (2006). [CrossRef]
19. M. Kampmann, C. E. Atkinson, A. L. Mattheyses, and S. M. Simon, “Mapping the orientation of nuclear pore proteins in living cells with polarized fluorescence microscopy,” Nat. Struct. Mol. Biol. 18(6), 643–649 (2011). [CrossRef]
20. J. Lazar, A. Bondar, S. Timr, and S. J. Firestein, “Two-photon polarization microscopy reveals protein structure and function,” Nat. Methods 8(8), 684–690 (2011). [CrossRef]
21. T. Williams, The optical transfer function of imaging systems (CRC Press, 1998).
22. K. Zhanghao, L. Chen, X.-S. Yang, M.-Y. Wang, Z.-L. Jing, H.-B. Han, M. Q. Zhang, D. Jin, J.-T. Gao, and P. Xi, “Super-resolution dipole orientation mapping via polarization demodulation,” Light: Sci. Appl. 5(10), e16166 (2016). [CrossRef]
23. W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. A 62(1), 55–59 (1972). [CrossRef]
24. D. Fish, A. Brinicombe, E. Pike, and J. Walker, “Blind deconvolution by means of the Richardson–Lucy algorithm,” J. Opt. Soc. Am. A 12(1), 58–65 (1995). [CrossRef]
25. N. Hafi, M. Grunwald, L. S. Van Den Heuvel, T. Aspelmeier, J.-H. Chen, M. Zagrebelsky, O. M. Schütte, C. Steinem, M. Korte, and A. Munk, “Fluorescence nanoscopy by polarization modulation and polarization angle narrowing,” Nat. Methods 11(5), 579–584 (2014). [CrossRef]
26. M. Müller, V. Mönkemöller, S. Hennig, W. Hübner, and T. Huser, “Open-source image reconstruction of super-resolution structured illumination microscopy data in ImageJ,” Nat. Commun. 7, 10980 (2016). [CrossRef]
27. C. Karras, M. Smedh, R. Förster, H. Deschout, J. Fernandez-Rodriguez, and R. Heintzmann, “Successful optimization of reconstruction parameters in structured illumination microscopy–a practical guide,” Opt. Commun. 436, 69–75 (2019). [CrossRef]
28. A. S. Backer, M. Y. Lee, and W. Moerner, “Enhanced DNA imaging using super-resolution microscopy and simultaneous single-molecule orientation measurements,” Optica 3(6), 659–666 (2016). [CrossRef]
29. S. B. Mehta, M. McQuilken, P. J. La Riviere, P. Occhipinti, A. Verma, R. Oldenbourg, A. S. Gladfelter, and T. Tani, “Dissection of molecular assembly dynamics by tracking orientation and position of single molecules in live cells,” Proc. Natl. Acad. Sci. 113(42), E6352–E6361 (2016). [CrossRef]
30. C. A. V. Cruz, H. A. Shaban, A. Kress, N. Bertaux, S. Monneret, M. Mavrakis, J. Savatier, and S. Brasselet, “Quantitative nanoscale imaging of orientational order in biological filaments by polarized superresolution microscopy,” Proc. Natl. Acad. Sci. 113(7), E820–E828 (2016). [CrossRef]
31. K. Wicker, O. Mandula, G. Best, R. Fiolka, and R. Heintzmann, “Phase optimisation for structured illumination microscopy,” Opt. Express 21(2), 2032–2049 (2013). [CrossRef]
32. K. Wicker, “Non-iterative determination of pattern phase in structured illumination microscopy using auto-correlations in Fourier space,” Opt. Express 21(21), 24692–24701 (2013). [CrossRef]
33. N. Patwary, A. Doblas, and C. Preza, “Image restoration approach to address reduced modulation contrast in structured illumination microscopy,” Biomed. Opt. Express 9(4), 1630–1647 (2018). [CrossRef]
34. T. Lukeš, P. Křížek, Z. Švindrych, J. Benda, M. Ovesný, K. Fliegel, M. Klíma, and G. M. Hagen, “Three-dimensional super-resolution structured illumination microscopy with maximum a posteriori probability image estimation,” Opt. Express 22(24), 29805–29817 (2014). [CrossRef]
35. A. G. York, P. Chandris, D. Dalle Nogare, J. Head, P. Wawrzusin, R. S. Fischer, A. Chitnis, and H. Shroff, “Instant super-resolution imaging in live cells and embryos via analog image processing,” Nat. Methods 10(11), 1122–1126 (2013). [CrossRef]
36. M. Guo, P. Chandris, J. P. Giannini, A. J. Trexler, R. Fischer, J. Chen, H. D. Vishwasrao, I. Rey-Suarez, Y. Wu, and X. Wu, “Single-shot super-resolution total internal reflection fluorescence microscopy,” Nat. Methods 15(6), 425–428 (2018). [CrossRef]
