1. Introduction

Total-internal-reflection fluorescence (TIRF) microscopy is an effective imaging method to observe the molecular mechanisms of subcellular processes [1]. This technique utilizes the evanescent wave generated by total internal reflection to illuminate the sample, which can limit the illumination area within a thin region near the surface of the sample [2]. In this case, fluorophores within the thin layer are excited, whereas fluorophores outside the layer are not affected. With surface selective illumination and unique polarization characteristics, TIRF microscopy has been widely used in several hot fields, such as exocytotic mechanism observation, environmental monitoring, and F-Actin visualization [3–5]. Compared with other conventional microscopy, TIRF microscopy is characterized by high contrast and high signal-to-noise ratio (SNR), which is suitable for molecular level imaging and detection [6]. In addition, TIRF devices are easy to combine with other imaging technologies, such as structured light illumination, fluorescence polarization, and fluorescence resonance energy transfer (FRET) [7–9].

TIRF microscopy can be generally categorized into two types according to the way to generate evanescent waves [10]: The first type is prism-based TIRF microscopy, which utilizes diverse geometrical prisms to couple the illumination beam with the total-internal-reflection (TIR) interface by using low cost and clean fluorescence excitation [11]. The second one is the popular objective-based TIRF microscopy in which a high numerical aperture (NA) objective is used to provide high angle TIR illumination [12]. Although these TIRF microscopy techniques have extensive use in several applications, the illumination is in single direction, which generates unavoidable shadows along the beam path [13]. Shadows and other artifacts attenuate image contrast [14] and degrade the image quality. To overcome shadow-related problems, illuminating the sample with a fast rotating beam is a straightforward method to weaken shadows effects. For instance, D. Axelord et al. set up a rotating optical-wedge-based system to allow uniform scanning in the exposure cycle [15], thereby repressing the anisotropic blur and interference fringes. M. Oheim et al. used acousto-optical deflectors instead of rotating wedges to scan a full circle with millisecond exposure time, thereby permitting multicolor alternating excitation [16]. Similar to the former, D. Hoppe et al. attempted to overcome the limitations posed by shadows by using a two-dimensional scan head to rotate laser beams rapidly around the back focal plane (BFP) of a high NA objective [17]. Another method involves using a circular disk or mask to obstruct parallel light. For example, M. Gu et al. proposed a scanning TIRF microscopy (STIRFM) with a high NA objective providing focused ring-beam illumination [18]. The angle of incidence was controlled by a circular disk in front of the objective lens to achieve illumination in all azimuthal directions. M. Lei and A. Zumbusch designed an afocal W-shaped axicon mirror to produce annular-shaped parallel light, with a transmittance of nearly 100% [19]. K. Gaus et al. manufactured a parabolic mirror that reflects the annular beam and focuses it at the bottom surface of samples [20].

As previously mentioned, the TIRF microscopy technique using the axisymmetric aspherical mirror is capable of avoiding the appliance jitter pertaining to the rotating beam; in the abovementioned methods however, the incident angle is maintained within a small range. Moreover, the incident angle cannot be adjusted continuously in a large range, which restricts the evolution of the three-dimensional (3D) image with axial super-resolution and molecule level localization [21–25]. In order to obtain a large range of the incident angle, galvanometers or scanners and large-size mirrors must be used. K. Stock et al. proposed a variable-angle TIRF (VA-TIRF) method involving a variable penetration depth by using a pair of adjustable and concave mirrors in a compact illumination device [26]. K. G. Heinze et al. developed an axicon-based TIRF microscopy (AxiTIRF-M) method using a laser ring focus system, in which one focus lens and two axicon lenses were used to control the ring diameter in order to tune the TIRF excitation angle [27]. C. Kuang et al. presented a polarized TIRF (P-TIRF) to overcome the challenges of multi-angle (MA)-TIRF, using a galvanometer to perform lateral scanning at BFP, in order to determine the 3D structure of cell proteins with isotropic resolution enhancement [28]. L. Chen et al. created a shadowless-illuminated variable-angle TIRF (siva-TIRF) instrument based on a dual-color DMD focusing the illuminating laser at six positions in the BFP of the objective thereby adjustingthe incident angle [29]. These methods can achieve convenient high-precision angle control; nevertheless, the angle adjustment range is still limited even using galvanometers, scanners, mirrors, etc.

Herein, we propose an e-TIRF microscopy method based on a large-sized elliptical mirror [30], which achieves shadowless illumination similar to that by a shadowless lamp, and a wide range of adjustable penetration depth achieved by using a large aperture mirror. In this work, we characterize the shadowless performance of the proposed method and compare it with that of conventional TIRF microscopy. In addition, we analyze the evanescent field of focusing characteristics based on the vectorial diffraction theory, and demonstrate the adjustable excitation depth with beam modulation.

2. Theoretical model

In this section, we (i) model the theory of e-TIRF microscopy, (ii) demonstrate the simulation of the lateral intensity field distribution near the focal region and the axial distribution of the evanescent field (iii) compare the characterizes of e-TIRF microscopy with that of conventional TIRF microscopy.

2.1 Intensity distribution in the focal region based on elliptical mirror

Figure 1 shows the schematic of the illumination device involving a high-NA objective and that of the elliptical mirror. Figure 1(a) shows the schematic of the illumination device based on high-NA objective. By controlling the radius of the obstruction, the size of the inner diameter of the ring beam can be changed; this can control the minimum incident angle (θ_min) of the incident light at the interface, which can then adjust the penetration depth of the evanescent field. θ_min increases with the extension of the obstruction; when θ_min increases to the critical value, the incident angle of all the rays is larger than the critical angle θ_c and TIR occurs. The index of refraction of both the cover glass (K9 glass) and the immersion oil is n = 1.518. However, owing to the limitations of the device structure, the maximum incident angle cannot approach 90°. Figure 1(b) shows the schematic of the illumination device based on the elliptical mirror. In this case, the minimum incident angle (θ_min) corresponding to the outer radius of the ring beam can be controlled by modulating an aperture. Points A and B are the two foci of the elliptical mirror. A collimated laser beam passes through a circular obstruction to form a ring beam. After being focused on point A by the focusing lens, a 360°-illuminated hollow-cone is collected by the elliptical mirror. Owing to the property of two-foci conjugation of the elliptical mirror, the rays emitted from one focal point of the elliptical mirror are focused on another focal point without aberration, readily able to obtain an incidence angle close to 90° at the interface.

 

Fig. 1 Schematic of the illumination device involving (a) the high-NA objective, (b) the elliptical mirror.

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For high-NA objectives, when the numerical aperture is greater than 0.7, the polarization state of the incident light can significantly affect the distribution of the focused spot [31]. This effect becomes more significant as the convergence angle further increases. The e-TIRF microscope is a high-NA system, where the effects of apodization, depolarization and aberration cannot be ignored, thus, the paraxial approximation theory is inapplicable, and the Debye vectorial theory is employed [31]. It is assumed that the incident polarization is in the x direction, and the spot focused on focal point B on the elliptical mirror no longer polarizes in the x direction. Its electric field $E$ is a vector superposition of $E_x$,$E_y$and$E_z$,which is called the depolarization effect. The distribution of the electric field vector of the converging rays near the focal point B can be expressed in the Cartesian coordinate system as [32]:

In Fig. 1, θ_max and θ_min are the upper and lower bounds of the convergence angles at the interface, respectively; $P({\theta }_1)$ is the apodization factor of the illumination system; ${\theta }_1$and ${\theta }_2$ are the incident and refraction angles at the interface, which are linked via Snell’s law; k₀, k₁, and k₂ denote the wave numbers in vacuum, the first medium, and the second medium, respectively; J₀(x), J₁(x) and J₂(x) are the zero-order, first-order, and second-order Bessel functions of the first kind; and t_s and t_p are the Fresnel amplitude transmission coefficients for s and p polarization states, which can be formally expressed as:

The aberration function $\Phi ({\theta }_1)$ caused by two interfaces can be expressed as:

 

Fig. 2 Schematic of elliptical mirror system.

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The factor e is the eccentricity of the elliptical mirror, a is the semi-major axis of the elliptical mirror, and z is the axial coordinate of point M. Therefore, the total apodization factor of the e-TIRF microscopy can be expressed as the product of the elliptical mirror’s apodization factor p(θ) and the aplanatic lens’ apodization factor$\sqrt{\cos \alpha }$:

2.2 Transverse intensity field distribution

2.2.1 Linearly polarized light illumination

In the case where the incident beam is linearly polarized in the x direction, the contour plots of normalized intensity |E|² and its components |E_x|², |E_y|² and |E_z|² near the focus (z = 0) of the elliptical mirror at the interface (d = 0) between K9 glass (n₁ = 1.518) and water (n₂ = 1.333) are shown in Fig. 3.

 

Fig. 3 Contour plots of intensity within 2λ radius near the evanescent focus of the elliptical mirror illuminated by the beam linearly polarized in the x direction (a)|E_x|²,(b) |E_y|²,(c) |E_z|²,(d) |(E)|².Peak intensities of |(E)|² have been normalized to 100; critical angle corresponding to the interface K9 glass (n₁ = 1.518) and water (n₂ = 1.333) is 61.4°; incident angular range: 62°–89°; long axis: 2a = 100 mm, eccentricity e = 0.8.

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By selecting an appropriate size of the obstruction and aperture, the incident angle range of the hollow illumination cone can be controlled. When the minimum value of the incident angle corresponding to the outer radius of the ring beam is equal to the critical angle of total internal reflection, it can be ensured that all the incident rays in the cone of light can stimulate the evanescent field at the interface. Due to the conjugate characteristics of the two focal points of the elliptical mirror, the maximum angle of incidence can theoretically reach 90°; considering the elliptical mirror processing errors and other assembly errors, the maximum angle of incidence is taken as 89°.

Obviously, the focused spot at the interface contains not only the polarization component along the x-axis but also the polarization components along the y-axis and the z-axis, which is caused by the depolarizing effect. The |E_z|² component is more significant than the |E_y|² component, and its intensity is even closer to the |E_x|² component. It is clear that the patterns of |E_x|², |E_y|²and |E_z|² respectively exhibit one, four and two lobes, which is caused by the factors cos(2φ_s), sin(2φ_s) and cos(φ_s) in Eq. (1) and the relative strength of the Bessel functions, J₀(x), J₁(x) and J₂(x) [35]. As shown in Fig. 3, there is one single peak in the |E_x|² component and twin peaks in the |E_z|² component. This phenomenon can be explained by the interference of the plane components of focusing light; destructive interference vanishes the E_z component and constructive interference enhances the E_x component at the focus [18]. Because of the intensity distribution of electric field components |E_x|² and |E_z|², the total electric field intensity shows a bimodal distribution in the focal plane, which is also called the focus splitting phenomenon. This distribution is quite different from the lateral intensity distribution of Airy spot obtained by scalar theoretical calculations.

2.2.2 Circularly polarized light illumination

When the incident light is left-handed circularly polarized, the electric field near the focal point B of the elliptical mirror is represented by:

In this case, the contour plots of normalized intensity |E|² and its components |E_x|², |E_y|² and |E_z|² near the focus (z = 0) of the elliptical mirror at the interface (d = 0) between K9 glass (n₁ = 1.518) and water (n₂ = 1.333) are shown in Fig. 4. From the results of circular polarization, one can see that the total light field |E|²is distributed in a circular symmetry, and the distribution directions of |E_x|², |E_y|² are perpendicular to each other. As expected, because of the Fresnel amplitude transmission coefficients t_s, t_p and the aplanatic lens’ apodization factor$\sqrt{\cos \alpha }$, the distribution of |E_x|²and |E_y|² is rotated counterclockwise with a certain angle. In addition, in the case of circular polarization, different from linear polarization, the intensities of the three electric field components are almost similar.

 

Fig. 4 Contour plots of intensity within 2λ radius near the evanescent focus of the elliptical mirror illuminated by the left-handed circularly polarized beam (a) |E_x|²,(b) |E_y|²,(c) |E_z|²,(d) |(E)|². Peak intensities of |(E)|² have been normalized to 100; critical angle corresponding to the interface K9 glass (n₁ = 1.518) and water (n₂ = 1.333) is 61.4°; incident angular range: 62°–89°; long axis: 2a = 100 mm, eccentricity e = 0.8.

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In general, in the e-TIRF illumination setup, when the illumination light is linearly polarized in x direction, the total intensity at the interface is bimodal along the x-direction, and the full width at half maximum in the x-direction is larger than that of the circular polarized case. Therefore, a large field of view can be obtained by employing the linear polarized illuminated beam. In the case of circular polarization, the total intensity distribution is more uniform, which can well suppress the artifact effects.

The relative intensity distribution of the |E_z|²and |E_x|² components is determined by the degree of depolarization. Figure 5(a) presents the peak intensity ratio |E_z|²/|E_x|² with respect to the minimum incident angle (θ_min). As can be seen from the plots, when the medium above the interface changes from air to water, the peak of the curve moves to the upper right. Limited by the structure of the illumination device, the maximum convergence angle of high-NA objective (NA = 1.49) θ_max1 is about 78°. Different from high-NA objective, the maximum convergence angle of the elliptical mirror θ_max2 can be close to 90°. As θ_min becomes large, the |E_z|²/|E_x|² ratio increases and peaks at the critical incident angle θ_c; then, the |E_z|²/|E_x|² ratio starts to decrease as θ_min continues to increase. This indicates that the depolarization effect is most pronounced when the minimum convergence angle θ_min is equal to the critical angle θ_c. The distribution of component |E_z|² is mainly contributed by the incident plane wave satisfying the evanescent field excitation condition, and the distribution of component |E_x|² is mainly contributed by the plane wave components with a small incident angle [35]. Therefore, |E_x|² continues to decrease as θ_min increases from 0 to the θ_c, which causes |E_z|²/|E_x|² to increase to the peak value. The ratio |E_z|²/|E_x|² starts to decrease after the critical angle θ_c, which is caused by the fact that |E_z|² decreases much faster than |E_x|² when all incident rays meet the evanescent field excitation condition.

 

Fig. 5 Plots of (a) the peak intensity ratio |E_z|²/|E_x|², (b)the focus separation $\Delta x$and (c) the normalized dip depth $\eta$ versus minimum incident angle (${\theta }_{min}$). The red and blue lines correspond to the device of high-NA objective (NA = 1.49) and elliptical mirror, respectively. The solid and dashed lines correspond to the interfaces between immersion oil (n = 1.518) and air (n = 1), and between immersion oil (n = 1.518) and water (n = 1.333), respectively. The illuminated beam is polarized along the x direction.

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To characterize the shape of the intensity distribution at the interface, the plots of the two-focus separation Δx and the normalized dip depth η with respect to θ_min are presented in Fig. 5(b) and 5(c), respectively. Similarly, separation Δx peaks at the critical angle θ_c; this indicates that the focus splitting effect is most pronounced when θ_min is close to θ_c. In addition, the focal splitting phenomenon occurs after a certain threshold angle in both cases of high-NA objective and elliptical mirror. For the same interface, the threshold in the case of elliptical mirror is larger than that in the case of high-NA objective. For two different interfaces in Fig. 5(b), the two peaks are almost equal, but the threshold at the interface between immersion oil and water is larger than that at the other interface.

The normalized dip depth η is defined as the difference between normalized intensity peak and trough in the x direction. As shown in Fig. 5(c), η reaches the peak at the critical angle θ_c, and the peak at the interface between water and immersion oil is larger than the peak at the other interface. Similarly, there also exists a certain threshold in the plots, and the threshold becomes larger as the medium above the interface changes from air to water.

2.3 Axial light field distribution based on elliptical mirror

The penetration depth of the evanescent field is an important characteristic. To demonstrate that the adjustable range of penetration depth based on elliptical mirror is larger than that based on high-NA objective, we present the relationship of normalized intensity and axial position of the evanescent field in Fig. 6, it is clear that the intensity is exponentially decaying with the penetration depth increasing.

 

Fig. 6 Normalized intensity versus evanescent field depth of (a) elliptical mirror; (b) high-NA objective (NA = 1.49)

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In e-TIRF microscopy, the incident angle range of the hollow cone can be controlled by adjusting the aperture and the obstruction, which makes the penetration depth of the evanescent field adjustable. In Eq. (1), d and ρ is assumed to be zero, then we can derive the axial distribution of the evanescent field. Figure 6(a) shows the plots with three different incident ranges based on elliptical mirror; the critical angle θ_c at the interface between immersion oil (n = 1.518) and water (n = 1.333) is 61.4°. When the incident angle is in the range of 62°-67°, 84°-89° and 62-89°, the penetration depths of the evanescent field are z_E1 = 215.89 nm, z_E2 = 89.69 nm and z_E3 = 125.73 nm, respectively. As expected, z_E3 is between z_E1 and z_E2. Therefore, the adjustable range of the penetration depth based on elliptical mirror is 89.69-215.89 nm.

In the case of high-NA objective (NA = 1.49), the minimum and the maximum incidence at the interface between immersion oil (n = 1.518) and water (n = 1.333) are 62°and 78°, respectively. Figure 6(b) demonstrates the plots with three different incident ranges based on objective (NA = 1.49); the critical angle θ_c at the interface between immersion oil (n = 1.518) and water (n = 1.333) is 61.4°. The penetration depths of the evanescent field are z_O1 = 215.89 nm, z_O2 = 104.37 nm and z_O3 = 138.67 nm corresponding to the incident angles 62°–67°, 73°–78° and 62°–78°. Thus, the adjustable range of penetration depth based on high-NA objective is 104.37–215.89 nm.

By comparing the subplot of e-TIRF with that of high-NA objective, we can conclude that the range of penetration depth has been extended by utilizing e-TIRF microscopy, which is potentially useful in three-dimensional imaging and high axial resolution applications. The principle of 3D TIRF can be referred to [22].

3. Experiment

3.1 Experimental setup

The basic schematic of e-TIRF microscopy is demonstrated in Fig. 7(a), linearly polarized 532 nm laser (MW-SGX, 532 nm, CLASS IIIb) is used as the light source. The obstruction is used to adjust the inner radius of the annular beam, which is placed in front of lens and obstructs the central part of the beam. The aperture is used to control the outer radius of the annular beam. As the key part of this system, the lower focus of the elliptical mirror coincides with the focus of the condenser lens, the upper focus of the elliptical mirror coincides with the spherical center of the half-ball lens(diameter 5 mm, Edmund Optics), and it is located at the interface between the immersion oil (n = 1.518) and water (n = 1.333). The half-ball lens is glued to the glass slide by the microscope’s immersion oil (Oil, n = 1.518, Olympus Type F), matching the refractivity of the glass slide and the half-ball lens. A long-pass filter (562 nm, 25.0 mm diameter, Dichroic Filter, Edmund) blocks the excitation laser beam. The spherical wave emitted by the point source propagates through the obstruction and is collimated by the lens; the aperture modulates the annular beam to a proper size, which is compatible to the minimum incident angle. Then, the condenser lens reshapes the annular beam to a hollow cone and it is collected by the elliptical mirror; the focused incident light excites the evanescent field, and then the fluorescence emitted by the sample is collected by the objective lens(NA = 0.75, Olympus, RMS40X-PF). In the experimental setup, the image is collected on the other side of illumination. This scheme is easy to realize and alignment, which requires the samples be thin otherwise the image will be blurred by the sample. We can also install imaging lens on the same side of illumination to observe thick samples, however this will constrain the range of incident angle when utilizing a high NA objective.

 

Fig. 7 (a) The basic schematic of e-TIRF microscopy; (b) the photograph of the experimental setup.

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Figure 7(b) shows the photograph of the experimental setup, and the photograph of the elliptical mirror (long axis: 2a = 100 mm, focal distance: 2c = 80mm, eccentricity e = 0.8) is showed in the top right corner of the picture. The surface roughness of the elliptical mirror is rms 0.1μm. In Fig. 7(b), the first lens (${\varphi }_1$ = 12.7mm, f₁ = 40mm, Thorlabs, LB1378) and the second lens (${\varphi }_2$ = 25.4mm, f₂ = 200mm, Thorlabs, LB1954) constitute a beam expander system, which expands the beam size for 5 times and makes the adjustment of the beam size much easier. By adjusting the diameter of the aperture and the position of mask1, we can modulate the inner radius and the outer radius of the ring beam independently. According to the geometric ray tracing principle, we can easily conclude that ${\theta }_{max}$ and ${\theta }_{min}$ vary approximately linearly with mask position and aperture diameters respectively. In practice, we usually use an 8mm mask to adjust the incident angle, and the minimum position increment of the mask is 1mm, corresponding to incident angle of 0.5 degree approximately. The size of mask2 is constant, which corresponds to the incident angle of $90°$at the interface and ensures all incident rays can be collected by the elliptical mirror. Both mask1 and mask2 are pasted on transparent glass bases. The third lens (${\varphi }_3$ = 25.4mm, f₃ = 200mm, Thorlabs, LB1954) and the forth lens (${\varphi }_4$ = 12.7mm, f₄ = 40mm, Thorlabs, LB1378) reduce the diameter of the annular beam for 5 times, which matches the aperture size of condenser lens. In our experimental setup, we utilize an objective (NA = 0.75, Olympus, RMS40X-PF) to couple the ring beam into elliptical mirror.

3.2 Experimental results

3.2.1 Auto-fluorescence imaging of pollen by e-TIRF

To demonstrate the shadow-suppressed effect in the elliptical mirror-based TIRF method, this experiment utilizes the pollen fluorescence particles as samples. Figures 8(a), (b), and (c) exhibit the images of fluorescence pollen particle in inclined illumination method, the prism-based TIRF method, and the e-TIRF method, respectively. From the result of inclined illumination, we can see the one-sided fluorescence image of the pollen, and the image has strong fluorescence background noise. The results of Fig. 8(b) indicate that the fluorescence pollen particle image is still one-sided. However, compared with the inclined illumination method in Fig. 8(a), the pollen fluorescence image in the prism-based TIRF method has more abundant details, the pollen fluff is clearly visible, the entire image has a higher SNR, and the image quality is clear and pure; Fig. 8(c) demonstrates the fluorescence pollen particle image in the e-TIRF method. With the illumination of the evanescent waves generated by the hollow cone, a clear and homogeneous pollen image is presented in Fig. 8(c). It retained all the superiority of Fig. 8(b), one can even see the clear ring outline containing the pollen fluff details.

 

Fig. 8 (a) Fluorescence pollen particle image in the inclined illumination method. (b) Fluorescence pollen particle image in the prism-based TIRF method, (c) Fluorescence pollen particle image in the e-TIRF method.

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Comparing the three different illumination methods, we can easily come to the conclusion that shadows and artifacts can be well suppressed by utilizing the e-TIRF method.

3.2.2 Imaging of fluorescent microsphere by e-TIRF

To verify that the penetration depth of the evanescent field in the elliptical mirror-based TIR method is controllable, we applied the fluorescent microspheres (Lumisphere, 5μm, Polystyrene, BaseLine) as experimental samples, and the fluorescence microsphere images at different ranges of incident angles are shown in Fig. 9. In this experiment, the outer radius of the ring beam can be controlled by adjusting the radius of the aperture, therefore, the maximum incident angle of the hollow cone corresponding to the inner radius of the ring beam remain unchanged, while the minimum incident angle of the hollow cone corresponding to the external radius of the ring beam changes. Figure 9 shows the fluorescent microsphere images at different incident angle ranges, with details in the enlarged region indicated by the white box in Fig. 9, region 2. In Fig. 9(a), the incidence range is 75–85°; and one can see the fluorescence profile of the microsphere although the brightness of the fluorescent sample is low. The incidence range in Fig. 9(b) is 65–85°, the fluorescence microspheres are clearer and brighter with clear outlines and better contrast, and the details of the boxed fluorescence microsphere is presented in region 2. Furthermore, comparing the two subfigures of region 3 in Fig. 9(a) and 9(b), it shows that the red curve has a larger width at the bottom, which indicates that the fluorescence microsphere in Fig. 9(b) has a larger excitation area. The penetration depth has nothing to do with the incident intensity, it is only related to the range of the incident angle. Therefore, according to the geometric relationship, deeper excitation depths can be obtained with an incident angle range of 65–85°. This experiment demonstrates that the e-TIRF method has the characteristics of controlled penetration depth, which has been confirmed by our previous conclusion. The selective excitation with different penetration depths has potential application value in three-dimension imaging.

 

Fig. 9 Fluorescent microsphere images with different ranges of incident angles (a) 75–85° (b) 65–85°.

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We can see from Fig. 9 (a), when the incident angle ranges from 75 degrees to 85 degrees, the diameter of the emission region of the microsphere is 2.69μm. With 580nm fluorescent wavelength, the FWHM (full width at half maximum) of the PSF (point spread function) of an NA0.75 objective is about 0.4μm. In consideration of the convolution effect of the imaging system, the actual diameter of the region of the microsphere illuminated by the evanescent wave is roughly 2.69-2*0.4 = 1.89 μm. According to the geometrical relationship, the TIRF penetration depth is $2.5-\sqrt{{2.5}^2-{(1.89/2)}^2}\text{=}185\text{nm}$. Similarly, when the incident angle ranges from 65 degrees to 85 degrees, the TIRF penetration depth is 255nm. The theoretical penetration depths of e- TIRF are 97nm and 123nm according to the analysis in section 2.3, and the deviation maybe caused by disturbance of stray light and aberration in imaging system. We cannot obtain accurate penetration depth based on imaging method. To measure the penetration depths of evanescent field precisely, a fibre with a nanoscale tip is utilized to couple the evanescent light into photoelectric detector, which is drived by a high-resolution PZT to record axial intensity of evanescent field. This work will be done in our future research.

4. Conclusion

Based on Debye vectorial diffraction theory, we analyze the evanescent field distribution generated by circularly polarized and linearly polarized laser in the focal region of the elliptical-mirror-based total-internal-reflection fluorescence (e-TIRF) microscopy. According to the simulation results, we can conclude that a large field of view can be acquired by employing the linear polarized illuminated beam. Moreover, in the case of circular polarization, the total intensity distribution is more uniform, which can well suppress the artifact effects. The simulation also demonstrates that the intensity of evanescent field generated by elliptical-mirror decreases exponentially with the penetration depth, and the polarization characteristic of the evanescent in various direction is given. We build up an e-TIRF microscopy set up utilizing a focused hollow-cone illumination with all-direction and large range of incidence. The e-TIRF microscopy can modulate the penetration depth of the evanescent field, whose adjustable range is larger than the high-NA objective. Though it is not a substantial improvement, evanescent field with continuously adjustable penetration depth in large range is not easy to realize by a high-NA objective. E-TIRF is easy to calibrate to generate an annular illumination compared with high-NA objective TIRF. In this manuscript, we calculate the intensity distributions of the e-TIRF excitation field. This is helpful since TIRF illumination under multiple overcritical angles is not usual compared to collimated illumination in classical TIRF approaches. Moreover, unlike the single-direction illumination in the prism method and objective method, all the azimuthal-direction illumination is utilized in the e-TIRF method, which can improve the imaging quality and suppress the shadow effect. Three-dimension imaging of biological samples illuminated by various penetration depth of evanescent light will be reported in our further work.