Resolution-enhanced surface plasmon-coupled emission microscopy

Baoliang Ge; Ye Ma; Cuifang Kuang; Douguo Zhang; Kimani C. Toussaint; Shangting You; Xu Liu

doi:10.1364/OE.23.013159

1. Introduction

Surface plasmon-coupled emission (SPCE) has been proposed as an important imaging technique with high sensitivity, which makes use of a thin layer of metal deposited on glass slides to efficiently excite fluorophores [1–4]. Surface plasmon-coupled emission microscopy (SPCEM) has been successfully applied in biological imaging studies due to numerous advantages, such as improved signal-noise ratio, enhanced background suppression and reduced photobleaching by increasing the radiative decay rate of fluorophores [2, 5–7]. For example, SPCEM was used in the imaging of muscle fibrils to study the dynamics of the interaction between actin and myosin cross-bridges [8, 9]. Malicka et al. successfully used SPCEM for DNA hybridization measurements [10], and Borejdo et al. developed fluorescence correlation spectroscopy by introducing SPCE to improve the signal-to-noise ratio [11]. SPCEM has also been applied in other realms of biology research, such as aptamer-based protein sensing [12], and immunological detection [13, 14]. All of these applications demonstrate the great significance of SPCEM in investigations at the nanoscale.

In SPCEM, the radiation pattern of the fluorescence excited by surface plasmons (SPs) is highly directional, resulting in the enhancement of collection efficiency from 1% to 50% [2, 7]. Moreover, if a Kretschmann configuration is used, where fluorescent samples are excited by the incident light at the surface plasmon resonance (SPR) angle, a 10- to 40-fold-enhanced excitation field can be obtained due to the SPR effect, which can further increase the detection sensitivity. However, because of the highly directional polarization of the fluorescence in SPCEM, the point spread function (PSF) is modulated into an undesirable donut shape when the fluorescence is collected and focused onto the CCD by an imaging lens with a low numerical aperture (which equals the numerical aperture of the objective divided by its magnification). Generally, a donut-shaped PSF is undesired for conventional imaging applications and will require alternative imaging strategies for obtaining high spatial resolution. To enhance the imaging quality in SPCEM, several methods were proposed in previous work [5, 15–17]. A lateral resolution of around 200 nm can be obtained by introducing a vortex phase plate (VPP) or a polarization converter to convert the hollow PSF into a solid pattern [5, 17]. However, these approaches can further be improved in terms of resolution enhancement.

Fluorescence emission difference (FED) has been proposed as an easy and efficient method to break the diffraction limit in confocal microscopy [18]. In the FED method, two images scanned by different illumination patterns are obtained, and the subtraction of the two images with specific weights is used to reconstruct the super-resolution imaging result. One of the images is obtained by illuminating samples with a solid excitation spot, and the other image is obtained by scanning with a donut-shaped excitation pattern. Based on the intensity difference between two differently acquired images, an imaging result with a sharper effective PSF can be obtained, which demonstrates that the FED technique have the capability to break the diffraction barrier. The FED technique uses image subtraction to enhance resolution with low beam intensity and high imaging speed, thereby making the approach attractive for many imaging applications that seek higher spatial resolution.

In this paper, we apply the FED technique in SPCEM to further enhance its lateral resolution. Because of the highly directional polarization of fluorescence, phase modulation can be used in SPCEM to engineer its PSF. We will discuss the engineered PSF under different phase modulation and present the optimal imaging result based on the image subtraction technique. Results show that the lateral resolution in the proposed method can be enhanced by 33% and 20%, compared with that in conventional wide-field microscopy and the SPCEM with a single VPP [5], respectively.

2. Theory

2.1 Intensity distribution in the image plane of surface plasmon-coupled emission microscopy

The process of SPCE can be regarded as the reverse process of SPR [7], where the emission from fluorophores is coupled with SPs and then passes through the other side of the metal film with specific direction [6]. Based on vectorial diffraction theory [19], the PSF in SPCEM has been analyzed theoretically in Ref [6]. Figure 1 shows the orientation of a dipole and a diagram of the imaging process in SPCEM. Assume that the dipole locates in medium 1 (which we can regard as water) and emits fluorescence. The fluorescence passes through the metal film (medium 2) and the glass slide (medium 3), and is collected by the imaging system with a charge-coupled device (CCD) locating in the image plane in medium 4. The refraction indices of medium 1, 2, 3 and 4 are $n_{1}$ , $n_{2}$ , $n_{3}$ and $n_{4}$ , respectively. Assume that the orientation vector of the dipole is $(μ \sin θ_{d} \cos ϕ_{d}, μ \sin θ_{d} \sin ϕ_{d}, μ \cos θ_{d})$ , which is shown in Fig. 1(a), the electric field distribution in the image plane in the cylindrical coordinate $(r, φ, z)$ is $E$ , and the electric field near the tube lens is $E^{'}$ . The three components of $E^{'}$ can be written as:

\begin{matrix} E_{r}^{'} = \sqrt{\frac{\cos θ_{4}}{\cos θ_{3}}} {\frac{μ}{2} \sin θ_{d} \cos (ϕ_{d} - φ) [(\cos θ_{1} \cos θ_{4} τ_{p} + τ_{s}) + (\cos θ_{1} \cos θ_{4} τ_{p} - τ_{s}), \\ \times \exp (2 i (φ - ϕ))] - μ τ_{p} \cos θ_{d} \sin θ_{1} \cos θ_{4} \exp (i (φ - ϕ))} \end{matrix}

\begin{matrix} E_{φ}^{'} = \sqrt{\frac{\cos θ_{4}}{\cos θ_{3}}} {\frac{μ}{2} \sin θ_{d} \sin (ϕ_{d} - φ) [(\cos θ_{1} \cos θ_{4} τ_{p} + τ_{s}) - (\cos θ_{1} \cos θ_{4} τ_{p} - τ_{s}), \\ \times \exp (2 i (φ - ϕ))]} \end{matrix}

E_{z}^{'} = \sqrt{\frac{\cos θ_{4}}{\cos θ_{3}}} [μ \sin θ_{d} \cos (ϕ_{d} - φ) \cos θ_{1} \sin θ_{4} τ_{p} \exp (i (φ - ϕ)) - μ \cos θ_{d} \sin θ_{1} \sin θ_{4} τ_{p}] .

According to the vectorial diffraction theory [19], the relationship between

E

and

E^{'}

is:

Fig. 1 (a) Orientation of a single dipole. (b) Diagram of the imaging process in SPCEM.

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E = - \frac{i k_{4}}{2 π} \int_{0}^{2 π} \int_{0}^{σ} E^{'} \sin θ_{4} \exp (i k_{4} r \sin θ_{4} \cos (ϕ - φ)) \times \exp (i k_{4} z \cos θ_{4}) d θ_{4} d ϕ

Here $τ_{p}$ and $τ_{s}$ are the three-layer Fresnel coefﬁcient for p-polarized and s-polarized light, respectively. $θ_{1}$ , $θ_{3}$ and $θ_{4}$ are the semi-angle in medium 1, 2 and 3, respectively, and the relationship among them is established by using the Abbe sine condition. k₄ is the wave vector in medium 4. $ϕ$ is the azimuthal angle of the wave vector. The collection semi-angle σ can be obtained by

\frac{N A}{n_{4} \sin σ} = m a g,

where NA is the numerical aperture of the objective, and mag is the overall magnification for the imaging system.

Considering that the fluorescence is emitted by an ensemble of dipoles with random orientations, we calculate the PSF in SPCEM as the integral over all polar angles $θ_{d}$ and azimuthal angles $ϕ_{d}$ .

2.2 Point spread function and phase modulation

Assume that the numerical aperture of the objective is 1.45 and the magnification is 60X. The peak wavelength of fluorescence is 560 nm. The thickness of the metal layer is 50 nm, whose complex refraction index is 0.32 + 2.83i (Au). The dipole is assumed to be 20 nm away from the interface. All the parameters are set to be the same as those presented in Ref [5, 6]. Based on the equations shown above, we calculate the intensity contribution of the transverse components and the longitudinal components of the electrical field in the image plane, as is shown in Fig. 2. It can be seen that the transverse components interferes destructively in the center, while the longitudinal components interferes constructively in the center. Because the magnification of the imaging system is 60X, which indicates that the numerical aperture of the tube lens is 0.024 (since the NA of the tube lens is the quotient of the objective’s NA and the value of magnification), the longitudinal components E_z is negligible. Thus, the PSF of SPCEM is a hollow spot with doughnut shape.

Fig. 2 PSFs in SPCEM without and with vortex phase modulation. The intensity contribution of (a) the transverse components, and (b) the longitudinal components of the electrical field on the image plane without vortex phase modulation. (c) The PSF in SPCEM without a VPP. The intensity contribution of (d) the transverse components and (e) the longitudinal components of the electrical field on the image plane with vortex phase modulation. (f) The PSF in SPCEM when the VPP is introduced. The full size of each figure is 1μm × 1μm.

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Figure 2(d) and (e) show the simulated intensity distributions of the transverse and longitudinal components of the electrical field in the image plane when a one-fold VPP is introduced into the detection optical path. This VPP introduces a phase delay expressed by $\exp (i ϕ)$ [5, 20]. From Fig. 2(d) and (e), it can be noted that the transverse components interferes constructively at the focal point, while the longitudinal components interferes destructively. Likewise, the contribution of E_z can be ignored due to the low numerical aperture of the tube lens. Therefore, the PSF of SPCEM with vortex phase modulation can be modulated into a solid pattern.

This phenomenon shown in Fig. 2 can be attributed to the fact that SPCE displays a radial polarization pattern [5, 17]. Additionally, the tube lens with a low NA means that the transverse components are dominant and the longitudinal components are negligible. When a radial patterned light passes a tube lens with a low NA and focuses on the image plane, the intensity distribution is dominated by the transverse components, and therefore is donut-shaped.

2.3 Fluorescence emission difference in surface plasmon-coupled emission microscopy

The imaging process can be regarded as a superposition of the instrument PSF, each scaled and spatially translated by the object function, and thus the intensity distribution on the image plane is the convolution between the intensity distribution of the object and the PSF [21]

I_{i} (x, y) = I_{o} (x, y) \times P S F (x, y) .

Thus, in SPCEM with and without vortex phase modulation, the imaging results can be written as Eq. (11) and Eq. (12), respectively:

I_{S o l i d} (x, y) = I_{o} (x, y) \times P S F_{S o l i d} (x, y),

I_{H o l l o w} (x, y) = I_{o} (x, y) \times P S F_{H o l l o w} (x, y),

where

P S F_{S o l i d}

and

P S F_{H o l l o w}

are the two-dimensional PSF in SPCEM with and without phase modulation.

In the FED method numerical subtraction of images with different PSFs is used to obtain a reconstructed imaging result with higher resolution. The resulting image can be expressed by

I_{F E D} = I_{S o l i d} - s \times I_{H o l l o w},

where s is a subtractive factor [18, 22]

The effective PSF in SPCEM when the FED technique is used can be obtained by

P S F_{F E D} = P S F_{S o l i d} - s \times P S F_{H o l l o w} .

The subtraction of the two PSFs with different intensity distributions has the potential to create an imaging result with a sharper PSF, thus providing higher lateral resolution.

It is the special characteristics of SPCEM that allow us to apply the FED technique into a wide-field fluorescence microscopy to enhance its resolving ability. Firstly, the highly directional polarization of the fluorescence allows us to use the phase modulation technique to engineer the PSF. Plus, the collection efficiency of fluorescence has been dramatically enhanced by about 50 times in SPCEM [1], which allows us to split the collected fluorescence with acceptable signal strength.

3. Proposed configuration

Figure 3 shows a proposed experimental configuration. A continuous-wave laser source with wavelength of 532 nm is used to excite fluorescent samples. The sample is placed on a cover slip with a 50-nm thick gold-coated layer. The p-polarized excitation beam illuminates the coverslip with the SPR angle which equals to 45°. An objective lens with high numerical aperture (NA = 1.45) is used to collect the emission from the excited samples with peak wavelength of about 560 nm [6]. The collected fluorescence is split by a beam splitter. One part of the fluorescence is directly collected by a CCD placed on the image plane. The other part passes through a 0-2π VPP and then imaged by another CCD. A 4f system is inserted between the objective lens and the beam splitter to adjust the position of the back focal plane. The diaphragm and VPP are placed near the back focal plane of the tube lens.

Fig. 3 Schematic diagram of the proposed system.

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In the previous work on the FED method [22, 23], it is known that two characteristics of the effective PSF can lead to distortion in the FED resulting image. One characteristic is the positive side-lobe which may introduce some originally inexistent objects in the image due to the side-lobes. The other characteristic is the negative side-lobe that may cause information lost during the reconstructed process, because the positive intensity may be compensated by the negative intensity. Several methods have been proposed to minimize the appearance of positive and negative side-lobes [23]. One simple and efficient method is to use a diaphragm to narrow the aperture angle and increase the size of the solid PSF [22]. The diaphragm is placed on the back focal plane of the tube lens, so that no significantly negative impacts will be exerted on the field of view [24].

4. Simulation results and discussions

4.1 Selection of the parameters for optimizing resolving ability

In order to maximize the resolving ability and avoid obvious distortion simultaneously, we need to optimize the related parameters in the proposed system: the aperture index and the subtractive factor. The aperture index is defined as the ratio between the aperture when the diaphragm is used and the aperture when the diaphragm is not used. The subtractive factor has been mentioned above. To describe the amount of the side-lobes in the effective PSF, we introduce the concept of the variance in the PSF, which means the integral of the square of the difference between the two PSFs in a certain area, in our work. It is obvious that a larger variance indicates more significant side-lobes, resulting in more obvious distortion in the imaging result.

The expression of the variance in the PSF is shown as follow:

V a r = {\int_{- \infty}^{\max} | P S F_{S o l i d +} (r) - s \times P S F_{H o l l o w} (r) |}^{2} d r .

Here, Var is the variance in the PSF of the two PSFs, and

s

denotes the subtractive factor. The variable r represents the lateral position in the imaging plane.

P S F_{S o l i d +} (r)

and

P S F_{H o l l o w} (r)

denote the normalized intensity of the extended solid PSF and the hollow PSF as the functions of lateral position, respectively. The value

\max

represents the lateral position of the left peak of the hollow PSF. Figure 4(a) shows the normalized intensities of the extended solid and hollow PSFs, respectively, as the functions of lateral position, and illustrates the integral range to calculate Var. The upper limit of the integral is shown as the position of the red dashed line which is also the boundary of the main side-lobe after subtraction.

Fig. 4 (a) The integral range to calculate Var. The upper limit of the integral is shown as the position of the red dashed line which is also the boundary of the main side-lobe after subtraction. (b) The relationship between Var and the aperture index with different subtractive factors. When the subtractive factor is given, an optimal value of the aperture index exists which can make the size of the extended solid PSF matches that of the hollow PSF to the greatest extent.

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In our simulation work, the interval between adjacent sampling points is 5 nm. In fact, because starting calculation from the minus infinite is impossible, we calculate the integral from −500 nm, considering that the intensity at the lateral position smaller than −500 nm is so weak as to be ignored.

The relationship between Var and the aperture index with different subtractive factors is shown in Fig. 4 (b). It is obvious that as the aperture index decreases, the size of the solid PSF will be extended. However, when the subtractive factor is given, an optimal value of the aperture index exists which can make the size of the extended solid PSF matches that of the hollow PSF to the greatest extent. In this situation, the distortion in the resulting image can achieve its minimum. From Fig. 4(b) we can see that when the aperture index equals to 0.6 and the subtractive factor is 0.5, the effective PSF will have the smallest side-lobes.

Figure 5(a) shows the variances of the peak value of positive side-lobes and the valley value of negative side-lobes as the functions of the subtractive factor when the aperture index is set to be 0.6. Figure 5(b) shows the relationship between the full width at half maximum (FWHM) and the subtractive factor. Due to the existence of negative side-lobes, FWHM might not be an effective criteria to measure resolution. Here, we presume that FWHM can be also applied to evaluate resolution within the range of negative side-lobe’s intensity from −0.1 to 0. When the subtractive factor is chosen from 0.5 to 0.55, when the intensity of negative side-lobes is higher than −0.1, as is shown in Fig. 5(a), we can obtain that the FWHM varies from 145 nm to 150 nm. Our simulation results show that the FWHM of the PSF in SPCEM with a single 0-2π VPP is 185 nm. Therefore, the resolving ability can be enhanced by about 20% by using the proposed method than that with a single 0-2π VPP.

Fig. 5 (a) Variances of the peak value of positive side-lobes and the valley value of negative side-lobes as functions of the subtractive factor when the aperture index is set to be 0.6. (b) Relationship between the FWHM and the subtractive factor.

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4.2 Point spread function of SPCEM with FED

The effective PSF in SPCEM by using the FED technique is shown in Fig. 6, in which the normalized intensity is a function of the lateral position. The aperture index is set to be 0.6, and the subtractive factor is 0.5. It is noted that the side-lobes are relatively small which will cause limited distortion. Moreover, the FWHM of the effective PSF is about 150 nm, which demonstrates that the resolving ability can be enhanced by about 20% compared with that in SPCEM with a single VPP.

Fig. 6 (a) The effective PSF by using the FED technique with the aperture index of 0.6 and the subtractive factor of 0.5. (b) The transvers cross section of the extended solid PSF (black dashed line), the hollow PSF (red dashed line), and the effective PSF by using the FED technique (blue solid line).

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However, Fig. 6 shows the effective PSF which has the smallest side-lobes. In most cases, relatively larger side-lobes can be allowed when FED technique is used to enhance the resolution. Previous research on FED [22, 23] has shown that the valley value of negative side-lobe can be −0.2 or even larger without too much distortion of the image. Our simulation results of larger subtractive factors shown in the following part also verify this feasibility.

The choice of the subtractive factor depends on the specific situations where we apply the FED technique [25]. If we want to minimize the existence of distortion with a plausible enhancement of resolution, we should choose a smaller subtractive factor, as is shown in Fig. 6. If the resolution and contrast ratio are required to be better, while the distortion is permitted to be slightly larger, a larger subtractive factor could be chosen. However, when aperture index is set to be 0.6, the subtraction factor should be less than 0.8 to avoid too obvious distortion.

4.3 Estimation of resolution enhancements

Here, we use a 4μm × 4μm spoke-like sample which is shown in Fig. 7(a) to evaluate the lateral resolution as an alternative to the FWHM. Figure 7(b)-(f) show the imaging results of the introduced sample by using different imaging methods. The image obtained using a conventional wide-field microscope is shown in Fig. 7(b), and the diameter of the unresolved round area is about 450 nm. Figure 7(c) shows the image by using SPCEM with a single 0-2π VPP, and the diameter of the unresolved region is roughly 370 nm. The image obtained using SPCEM with the FED technique is shown in Fig. 7(d) when the aperture index is set to be 0.6 and the subtractive factor is selected as 0.5, and the unresolved round area’s diameter is about 300 nm. Figure 7(e) and (f) show the images obtained using the proposed method with larger subtractive factors which are 0.7 and 0.8, respectively. Their diameters of unresolved area are also ~300 nm.

Fig. 7 Simulation results of a sample with a spoke-like pattern. (a) Spoke-like sample. (b) Imaging result by using a conventional wide-field microscope. (c) Imaging result in SPCEM with a 0-2π VPP. (d)-(f) Imaging result in SPCEM by using the FED technique when the aperture index is 0.6 and subtractive factor is selected as 0.5, 0.7 and 0.8, (which are denoted as FED¹, FED² and FED³), respectively. The full size of the sample is 4μm × 4μm.

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The resolving ability can be estimated by measuring the size of the unresolved area. When the aperture index is set to be 0.6 and the subtractive factor is 0.5, the lateral resolution can be enhanced by about 20% than that in SPCEM with a 0-2π VPP, and by nearly 30% compared with that in a conventional wide-field microscope. These results are quite similar to those we obtain by calculating the FWHM. However, as the subtractive factor further increases, the area of the unresolved region is not obviously reduced. That is to say, the further increased subtractive factor does not necessarily lead to the better lateral resolution, but the contrast radio will be better when a larger subtractive factor is used. Additionally, it is found that the distortion in the imaging result with the aperture index of 0.6 is not serious when the subtractive factor is less than 0.8. Thus, we can adjust the subtractive factor within the range from 0.5 to 0.8 in order to obtain a resulting image with the highest resolution and contrast.

4.4 High resolution with less distortion

In this section, we will show two simulation results to demonstrate the ability of the proposed method to provide imaging results with high resolution and less distortion. First, we design a sample to verify the improvements in lateral resolution and to test the extent of distortion in the resulting image obtained by using the proposed method. The imaging performance is tested by imaging a sample with a nine-point array, with each point being << λ. The clearance of the nearest points is 200 nm, and the full size of the sample is 1μm × 1μm, as is shown in Fig. 8(a). The imaging result obtained by using a conventional wide-field microscope is shown in Fig. 8(b). It is noted that the nine points can hardly be resolved. Figure 8(c) shows the imaging result in SPCEM with a 0-2π VPP. Although the resolving ability is enhanced by introducing a VPP to engineer the PSF, the enhancement is not significant enough to completely separate the image of each point. By applying the FED technique in SPCEM, further improvements in lateral resolution can be obtained. When the aperture index is set to be 0.6 and the subtractive factor is selected as 0.8, the nine points can be clearly resolved without obvious distortion, as is shown in Fig. 8(d).

Fig. 8 Simulation results of a sample with nine points. The clearance between the nearest points is 200 nm, and the intensity of each point is set to be equal. (a) The nine-point sample. (b) Imaging result obtained by using a conventional wide-field microscope. (c) Imaging result in SPCEM with a 0-2π VPP. (e) Resulting image by applying the FED technique in SPCEM with the aperture index being 0.6 and the subtractive factor being 0.8. The full size of the sample is 1μm × 1μm.

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Second, an array of thin gratings is designed for simulation test. The size of each line is 5 nm $\times$ 200 nm, and the grating period is 200 nm, as is shown in Fig. 9(a). The conventional wide-field microscope’s image is shown in Fig. 9(b), in which the lines cannot be resolved. After placing a vortex phase plate in front of the CCD, the resolving ability is enhanced, as is shown in Fig. 9(c). However, the five lines are still not able to be completely resolved. Figure 9(d) is the imaging result of the proposed method. The subtractive factor is chosen as 0.8, and the aperture index is set to be 0.6. We find that the five lines are clearly resolved without obvious distortion.

Fig. 9 Simulation results of a grating consisting of five lines. (a) The geometrical image of the sample. The clearance between the adjacent lines is 200 nm. (b) The image of a conventional wide-field microscope. (c) The image using SPCEM with 0-2π VPP’s modulation. (d) The image using SPCEM with the FED technique. The aperture index is chosen as 0.6 and the subtraction factor is set to be 0.8.

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4.5 Simulation results of imaging microtubule

To test the performance of the proposed method in imaging biological samples, a simulated microtubule sample shown in Fig. 10(a) is introduced. The microtubule sample is simulated as randomly distributed lines with the width of 25 nm. The sample with the full size of 3μm × 3μm has 18 microtubules. The image by using conventional SPCEM is shown in Fig. 10(b), from which we can see that the imaging pattern is unresolved and distorted due to the irregular PSF. Figure 10(c) shows the imaging result when a 0-2π VPP is introduced to modulate the irregular PSF into a solid spot. Figure 10(d) shows the imaging result by using the FED technique in SPCEM with the aperture index of 0.6 and the subtractive factor of 0.7. It is noted that resolution is further enhanced without obvious distortion in the image. Furthermore, it can be seen that the FED method has the ability not only to improve the resolution, but to reduce the inexistent image caused by the side-lobes of the PSF in SPCEM with a 0-2π VPP. The FED method can also decrease the distortion of imaging results using SPCEM in certain situations.

Fig. 10 Simulation results of a microtubule sample. (a) Microtubule sample. (b) Imaging result by using the conventional SPCEM. (c) Imaging result by using the SPCEM with a 0-2π VPP. (d) Imaging result by using the FED technique in SPCEM with the aperture index of 0.6 and the subtractive factor of 0.7. The full size of the sample is 3μm × 3μm.

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5. Conclusion

In this paper, a novel method to enhance the lateral resolution in SPCEM by using the FED technique is proposed. In our method, the difference between the image with phase modulation by using a 0-2π VPP along with a diaphragm and the original SPCEM imaging result is used to estimate the spatial information of the analyzed sample. By optimizing the size of the diaphragm and the subtractive factor, the lateral resolution can be improved by 20% and 33%, compared with that in SPCEM with a single VPP and in the conventional wide-field fluorescence microscopy, respectively, when the distortion is minimized. Simulation results are presented to verify the ability of the proposed method to improve lateral resolution and reduce imaging distortion.

The proposed method expands the application of the FED technique from confocal microscopy into wide-field SPCEM. With its satisfactory performance in the enhancement of resolution and avoidance of distortion, it is believed that the proposed method is promising and practical for application in biological observation and research.

Acknowledgments

This work was financially supported by grants from the National Basic Research Program of China (973 Program) (No.2015CB352003) and the National Natural Science Foundation of China (No. 61205160, 61377013, 61378051, 61335003, 11374286 and 61427818).

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Resolution-enhanced surface plasmon-coupled emission microscopy

Abstract

1. Introduction

2. Theory

2.1 Intensity distribution in the image plane of surface plasmon-coupled emission microscopy

2.2 Point spread function and phase modulation

2.3 Fluorescence emission difference in surface plasmon-coupled emission microscopy

3. Proposed configuration

4. Simulation results and discussions

4.1 Selection of the parameters for optimizing resolving ability

4.2 Point spread function of SPCEM with FED

4.3 Estimation of resolution enhancements

4.4 High resolution with less distortion

4.5 Simulation results of imaging microtubule

5. Conclusion

Acknowledgments

References and links

Cited By

Figures (10)

Equations (11)

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