Alternative Methods to Enhance the Axial Resolution of Total Internal Reflection Fluorescence–Structured Illumination Microscopy

Abstract

Total internal reflection fluorescence–structured illumination microscopy (TIRF-SIM) can enhance the lateral resolution of fluorescence microscopy to twice the diffraction limit, enabling subtler observations of activity in subcellular life. However, the lack of an axial resolution makes it difficult to resolve three-dimensional (3D) subcellular structures. In this paper, we present an alternative TIRF-SIM axial resolution enhancement method by exploiting quantitative information regarding the distance between fluorophores and the surface within the evanescent field. Combining the lateral super-resolution information of TIRF-SIM with reconstructed axial information, a 3D super-resolution image with a 25 nm axial resolution is achieved without attaching special optical components or high-power lasers. The reconstruction results of cell samples demonstrate that the axial resolution enhancement method for TIRF-SIM can effectively resolve the axial depth of densely structured regions.

1. Introduction

Fluorescence microscopy is an essential technique for resolving the three-dimensional (3D) subcellular structures of microtubules and mitochondria. However, the resolution of conventional microscopy is limited by the diffractive nature of optics, which is known as a diffraction limit. In general, the resolution limit can be expressed as λ/2NA in the horizontal direction and 2λ/NA² in the vertical direction, where λ is the working wavelength, and NA is the optical system’s numerical aperture (NA) [1]. To overcome the diffraction limit, various super-resolution microscopy (SRM) techniques have been proposed, such as stimulated emission depletion (STED) microscopy [2,3], photoactivated localization microscopy (PALM) [4], stochastic optical reconstruction microscopy (STORM) [5,6], structured illumination microscopy (SIM) [7,8,9], and so on. Among all of these SRM techniques, SIM, especially total internal reflection fluorescence SIM (TIRF-SIM), has become the most successful commercial SRM due to its low phototoxicity, high spatiotemporal resolution, and relatively low cost [10].

Despite its popularity, SIM’s relatively low spatial resolution compared to other SRM techniques is its biggest drawback. Nevertheless, recent work demonstrated that by combining sparsity and continuity features in fluorescence imaging, SIM can achieve a lateral spatial resolution of 60 nm and fast super-resolution imaging at 564 Hz in live cells [11]. However, the improvements in axial resolution enhancement still lag behind existing methods in terms of lateral resolution.

In our previous works based on variable-angle total internal reflection fluorescence microscopy (VA-TIRF), we explored the axial distribution of fluorophores by acquiring TIRF images at different incident angles. Based on VA-TIRF, we developed multi-angle interference microscopy (MAIM) and demonstrated that by obtaining a TIRF image stack at 20 TIRF excitation angles, the axial resolution of SIM can be enhanced to 20 nm. Hence, the 3D reconstruction of fluorophores can be achieved [12,13]. Despite improved axial resolution, the complex multi-angle illumination system may affect both the temporal resolution and operational efficiency [14,15,16]. Therefore, simultaneous two-angle axial ratiometry (STARII) is proposed to reduce the number of incident angles to only two-angle TIRF images [13]. As the intensity distributions of the two TIRF images are different, the axial depth can be calculated. However, it still requires angle switching and mode switching during the reconstruction process, which leads to decreased temporal resolution and increased complexity in the SIM setup.

Herein, building on our previous work, we present an alternative method to enhance the axial resolution of TIRF-SIM without the need for angle or mode switching. Our method can leverage both lateral information and depth information directly from TIRF-SIM images, thus having no impact on the temporal resolution and device complexity of the TIRF-SIM system. By exploiting quantitative information regarding the distance between fluorophores and the surface within the evanescent field, the relative distances between fluorophores can be determined. An axial resolution within 50 nm was achieved while maintaining a lateral resolution comparable to that of TIRF-SIM. Simulations and calibration were conducted to evaluate our method’s superiority in terms of axial resolution improvement. This method can be applied to commercial TIRF-SIM and provides a practical tool for exploring the 3D subcellular structure of cells.

2. Theory

When an incident beam travels from a medium with a high refractive index (n₁) to a medium with a low refractive index (n₂), total internal reflection occurs if the incident angle exceeds the critical angle, which is defined as θ_c = arcsin(n₂/n₁). This results in the generation of an evanescent wave (Figure 1a). The evanescent wave excitation intensity at a distance, z, from the interface, can be expressed as follows:

$$I\left(z\right)=I\left(0\right)e^{-z/d\left(\theta \right)}$$

(1)

where θ is the incident beam of the angle, and I(0) is the intensity at the interface. The evanescent wave penetration depth d(θ) $=\lambda /\left(4\pi \sqrt{n_1^{2}si{n}^2\theta -n_2^2}\right)$ is the distance from the interface at which the intensity decays to 1/e of I(0) [17]. d(θ) typically ranges from 30 to 300 nm, depending on the refractive index contrast (n₁/n₂), incident angle (θ), and excitation beam wavelength of the (λ).

According to Equation (1), the intensity of evanescent wave decays exponentially with increasing depth, as shown in Figure 1b. Because of this property, the evanescent field is confined to a thin layer close to the coverslip, which enables a high signal-to-noise ratio (SNR) by suppressing defocus information. Considering the continuity and sparsity of fluorescence images, the relationship between intensity and depth can be used to estimate the axial relative distance directly. The fluorescence intensity $E_{x,y}\left(z\right)$ in the evanescent field is equivalent to the following:

$$E_{x,y}(z)=E_0{\int }_{\delta }^{\mathrm{\infty }}{D}_{x,y}\left(z\right)e^{-z/d\left(\theta \right)}dz$$

(2)

where D_{x, y}(z) is the axial distribution of fluorophore. Under the simple two-layer model, this distribution is assumed to be spatially uniform, i.e., D_{x, y}(z) = D [18]. E₀ represents the evanescence wave intensity at the interface, and δ is the axial relative distance, as shown in Figure 1b. E₀ can be determined by coherently superposing the incident and reflected beams while solving Maxwell’s equations with appropriate boundary conditions. Since we use s-polarization light, the boundary values are as follows [17]:

$$E_0\left(\theta \right)={\left|A_s\right|}^2{\displaystyle \frac{4co{s}^2\theta }{1-{\left(n_2/n_1\right)}^2}}$$

(3)

To avoid mode switching and keep the lateral super-resolution information, we proposed obtaining both lateral and axial super-resolution information just in the TIRF-SIM mode. The overall process of our method is shown in Figure 1c. The TIRF-SIM raw images $I_{{\varphi }_i,{\alpha }_j}\left(x,y\right)$ were captured in three different phases ${\varphi }_i$ (i = 1, 2, 3) and three directions ${\alpha }_j$ (j = 1, 2, 3) which can be expressed as follows:

$$I_{{\varphi }_i,{\alpha }_j}\left(x,y\right)=\left[H_{{\varphi }_i,{\alpha }_j}\left(x,y\right)\cdot S\left(x,y\right)\right]\otimes PSF$$

(4)

where S(x, y) is the sample distribution and $H_{{\varphi }_i,{\alpha }_j}\left(x,y\right)$ is the structured illumination pattern in different phases and directions. Then, the TIRF image can be generated by averaging the raw images:

$$I_{\mathrm{T}\mathrm{I}\mathrm{R}\mathrm{F}}=\sum I_{{\varphi }_i,{\alpha }_j}\left(x,y\right)/9$$

(5)

To avoid potential artifacts arising from out-of-focus background signals that may confound the axial reconstruction by introducing spurious intensity values, TIRF-SIM was used as a pre-processing step before reconstruction, as shown in Figure 1c. Since the SIM image may distort the intensity information during the reconstruction process, the TIRF image is needed to obtain axial information. Trainable Weka Segmentation (TWS) was used for structure extraction [19]. TWS utilizes Fiji’s built-in feature-extraction modules to generate multi-layer features, including Gaussian blur filters with varying kernel sizes and Sobel filters. The resulting feature maps are then fed into a classifier. These features are concatenated into high-dimensional vectors to train the classifier, ultimately yielding a binary mask as follows:

$$I_{mask} = \left\{\begin{array}{c}1, \sigma \left[f_{w,b}\left(I\right)\right]\ge t\\ 0, \sigma \left[f_{w,b}\left(I\right)\right]<t\end{array}\right.$$

(6)

where σ denotes the sigmoid activation function applied to the last fully connected layer. When the output result is below the threshold t, the pixel is considered noise or background. f_w,b represents a neural network with trainable parameters w and b. The Hadamard product was applied to the TIRF image using the following mask:

$$E=I_{\mathrm{T}\mathrm{I}\mathrm{R}\mathrm{F}}\otimes I_{mask}$$

(7)

The maximum fluorescence intensity in the evanescent field was used to estimate the fluorophore distribution and axial distances. In Equation (2), the fluorescence intensity is the highest at δ = 0:

$$E_{max}=E_{0}Dd\left(\theta \right)$$

(8)

E_max (θ) can be obtained from the maximum pixel value in a TIRF image. Therefore, the equation can be simplified as follows:

$$E\left(\theta \right)=E_{0}Dd\left(\theta \right)e^{-\mathsf{\delta }/d\mathsf{\theta }}$$

(9)

By rearranging the exponential term, the relative axial distance is the following:

$$\delta =d\left(\theta \right)ln\left({\displaystyle \frac{E_{max}}{E+ϵ}}\right)$$

(10)

Here, we added a small positive constant ε to prevent the denominator from becoming zero. Then, by combining the axial reconstruction information with the lateral super-resolution information of TIRF-SIM, the 3D super-resolution image can be obtained.

3. Results and Discussion

3.1. Simulations

First, a 3D microtubule sample was generated to validate the effectiveness of the proposed method. By controlling the SNR and sample depth, the factors affecting the axial resolution were systematically analyzed. The variations and bending trends of the microtubule were simulated using exponential and trigonometric functions, respectively. The imaging process was simulated via projection onto the x-y plane and adding noise at varying levels. We compared the reconstruction results under different SNR values and visualized them using the x-y-z coordinate system.

In Figure 2, the green line represents the true microtubule distribution at a depth of 220 nm, while the red points denote the reconstruction results. Figure 2a–c show the reconstruction results under simulated SNR conditions of 30, 20, and 10, respectively. At lower SNR levels, the reconstruction results exhibit a higher prevalence of outliers. Nevertheless, even under low-signal-intensity conditions, our method successfully reconstructed the microtubule morphology.

As the axial depth increased, deviations in the reconstruction results became more pronounced owing to fluorescence intensity decay in the evanescent field. However, the maximum deviation remained within 25 nm, confirming the axial resolution of the proposed method. Furthermore, quantitative analysis using the root mean squared error (RMSE) indicated that as the microtubule axial depth increased, the resolution gradually decreased (Figure 2d). By comparing the different curves in Figure 2d, we observed that when the SNR was sufficiently high, the axial resolution reached approximately 5 nm at all depths. This suggests that with sufficiently long exposure times or high excitation light intensities, the axial resolution can be maintained within 10 nm. These results indicate that the axial resolution decreases with increasing emitter depth and decreasing SNR; nevertheless, it remains within 25 nm.

3.2. Experiments

3.2.1. Calibration

Next, we performed an experimental calibration using an Alexa Fluor 488-labeled silica sphere deposited centrally on a coverslip surface and immersed in a refractive-index-matched medium. The silica sphere, with its well-defined axial geometry, serves as a standard sample for calibration. As shown in Figure 3a, the sphere radius is 4.86 ± 0.47 μm. Based on this known radius, the axial distance of fluorophores located on the outer shell of the sphere relative to the coverslip surface was calculated using trigonometry. The computed axial distances were then compared with the true depths to further validate the model. The system we used was a typical TIRFM, which was inverted on a vibration-isolation stage. The system was based on a Nikon-Ti microscope using three polarized excitation beams of 488, 561, and 639 nm and collimated using a coupler (Nikon LU4A) and collimation lens (CL) [12]. TIRF-SIM imaging was performed using a 100X/NA1.49 Nikon objective lens to acquire nine raw SIM images.

Figure 3b shows the reconstruction results for the relative distances δ from Figure 3a, ranging from 0 to 220 nm. Color coding was applied to the reconstruction results, which was implemented using the imagesc method in MATLAB R2022b. The reconstruction results were compared with the ground truth to further validate the accuracy of the proposed method. An intensity profile line was drawn on the reconstruction results using ImageJ software 1.54p, and the intensity profile was generated from the center of the sphere to its edge. As shown in Figure 3d, the reconstructed average height profile agrees well with the ground truth. As the axial position increases, the evanescent wave intensity decreases exponentially. A lower light intensity indicates a lower SNR and higher divergence. As can be seen, our method achieves an axial resolution of 25 nm within the illumination volume.

3.2.2. Multi-Color Cell Imaging

We applied our method to fixed-cell imaging in order to reconstruct the 3D structure of U2OS cells in a GATTA-Cells 4C sample. The incident beam angle was set to 72°, and TIRF-SIM raw images were obtained for reconstruction. Then, we applied color coding to the reconstruction results of Alexa Fluor 555-labeled microtubules and Alexa Fluor 488-labeled mitochondria, mapping different depth values to different colors for a more intuitive axial depth representation.

The fluorophores experienced excitation in the TIRF-SIM mode. Figure 4a,b show the TIRF and TIRF-SIM imaging results of the microtubule. By reconstructing raw images using our method, a 3D super-resolution image was obtained, as shown in Figure 4c. To further analyze the distribution of the microtubules, the 3D volumetric image in Figure 4d provides a more intuitive depth-coded image representation. When measuring the fluorophore axial depth in TIRF images, distinguishing the axial distribution in dense regions is challenging owing to the lateral diffraction limit. The regions of interest (ROI) show two microtubules located at approximately the same lateral position but at different axial positions. At a low lateral resolution, the two microtubules are regarded as an axial ensemble. This can lead to confusion in the reconstruction results. By combining lateral super-resolution information for structure extraction and background subtraction, the axial overlap issue can be effectively resolved. By drawing a profile line in ROI, the intensity of the white line indicates a lateral resolution of 195 nm, as shown in Figure 4e. The frequency histogram of the normalized axial depth is shown in Figure 4f. The microtubule axial depth was within 220 nm and gradually decreased outward, corresponding to the downward slope observed in the fixed sample cells.

Similarly, Figure 5a,b present the TIRF and TIRF-SIM imaging results of mitochondria. The reconstruction results for the mitochondria also exhibit a downward cell slope, and the tubular structure of the mitochondria is clearly visible, as shown in Figure 5c,d. The inner cristae structures of the mitochondria are also clearly observed in the ROI. After optical sectioning, the 3D volumetric image shown in Figure 5d was obtained. In Figure 5e, the pixel intensity values on the white line are normalized, and the TIRF and TIRF-SIM normalized intensity values are compared. The TIRF-SIM results clearly reveal an intensity difference of 98 nm caused by the inner ridge structure. These results indicate that our method can enhance both the lateral and axial direction resolutions. The axial depth above the coverslip was normalized, and a frequency histogram was plotted in Figure 5f.

4. Conclusions

In this paper, we present an alternative method for achieving 3D super-resolution imaging. Unlike previous methods, our approach does not require a complex optical system or high-power lasers. We achieved an axial super-resolution based on TIRF-SIM without the need for a multi-angle illumination system in MA-TIRF, thus avoiding errors caused by angle or mode switching. We conducted calibration experiments on a silica sphere with known axial depths. The deviation between the axial distribution reconstructed by this method and the true distribution of the microspheres was <25 nm. Additionally, we calculated the RMSE of the axial depths of synthetic microtubules under different SNRs. These experiments confirmed the accuracy of the proposed method. Although the axial resolution varied slightly under different imaging conditions—such as changes in emitter brightness, fluorophore density, and sample depth—it remained consistently within 25 nm across a range of signal-to-noise ratios (SNRs) and axial positions. These results demonstrate the robustness of the method under practical conditions and highlight its potential for high-precision axial localization in complex biological samples. Because of its simple reconstruction process, our method can be combined with existing commercial TIRF SIM microscopes. Beyond resolution enhancement, the proposed method preserves the intrinsic advantages of TIRFM through an evanescent field. A shallower excitation depth of the evanescent field implies that a larger out-of-focus background is removed during the imaging process. Fewer incident angles result in a higher reconstruction speed, which also leads to lower photobleaching and phototoxicity and higher temporal resolution. The samples demonstrated broad compatibility with standard fluorescently labeled specimens, including, but not limited to, chemically fixed cells and cryo-preserved tissue sections.

The proposed method prioritizes simplicity over theoretical resolution, making it particularly suitable for 3D super-resolution in commercial TIRF microscopes. However, due to experimental limitations, we were unable to perform axial localization experiments on live-cell samples. In addition, owing to the limitations of the traditional SIM algorithm used for fast reconstruction, the current reconstruction speed is primarily constrained by the SIM reconstruction rate. In future work, we aim to improve the proposed method by incorporating faster lateral super-resolution techniques and conducting reconstruction experiments on live-cell samples. These will serve as key directions for further development. We hope that the method presented in this paper can provide a different perspective on TIR-based 3D super-resolution.