1. Introduction

Surface plasmon-coupled emission (SPCE) is an effective technique that takes the advantage of a thin layer of metal coated on glass slides to effectively intensify the fluorescence adjacent to the interface [1,2 ]. The fluorescence particle in the vicinity of the metal layer is able to excite the surface plasmonic wave which can be directly coupled and emitted highly directionally on the other side of the metal layer. This process is often comprehended as the reverse process of SPR [1,2 ]. Simply introducing SPCE is helpful for developing fluorescence correlation spectroscopy to improve the signal-to-noise ratio [3]. Besides imaging, SPCE has also been applied in other fields of biology research, such as aptamer-based protein sensing [4] and immunological detection [5,6 ]. Detection of the structure characteristics of material is also one of SPCE’s important applications [7]. An imaging technique called surface plasmon-coupled emission microscopy(SPCEM) is based on the process of SPCE and stands out as its improved signal-noise ratio, enhanced background suppression and reduced photo-bleaching, which all contribute to its successful application in biological imaging [8,9 ]. For example, SPCEM was properly used in the imaging of muscle fibrils to study the dynamics of the interaction between actin and myosin cross-bridges [10,11 ], and also be favorably used in DNA hybridization measurements [12]. All of these applications demonstrate the great significance of SPCEM in biological researches. However, one major flaw of this imaging method is that its instrumental PSF is donut-shaped and twice the size of the one of ordinary wide-field microscope, indicating that the lateral resolution of SPCEM is low and the image is distorted. This phenomenon derives from the radial polarization of the fluorescence in SPCEM and the low aperture of imaging lens [9]. There are several researches working on enhancing the resolution of SPCEM, including inserting a spiral phase plate [9] or liquid crystal plate [13]. Furthermore, we noticed that both the simulations and experiments indicate that the shape of transverse PSF is changeable along the axial positions, varying from a hollow spot to a solid spot. For convenience in statement, we called this particular phenomenon defocused surface plasmon-coupled microscopy (d-SPCEM) here. However, it should be noted that the variation of PSF’s shape happens when the whole image is not actually defocused and blurred. ‘Defocused’ in the title‘d-SPCEM’ only indicates we can change the transverse PSF by adjusting the axial position of the sample.

Fluorescence emission difference (FED) is a simple and convenient method to enhance the contrast and resolution in confocal microscopy [14]. Two images scanned by a solid illumination pattern and a hollow one respectively are obtained and then subtraction of these two images with a proper subtractive factor will create a better-performed image in the FED method. In fact, the difference of those two illumination patterns will reconstruct a sharper effective PSF leading to the increase of the weight of the high spatial frequency in the new image within the limit of the cut-off spatial frequency, which demonstrates that the FED technique may provide an alternative way to enhance the resolution, especially with extra optical modulation [15]. Based on the same optical principles, the technique can also be applied in wide-field microscope, especially SPCEM [16]. Since the PSF of SPCEM is donut shaped, the weight of high spatial frequency is attenuated and the whole image has low resolution, even if it still has the same cut-off frequency as conventional microscope. If we can properly apply the technique of FED to SPCEM, we can increase the weight of high spatial frequency and restore the resolution of diffraction limit.Therefore, the method of FED is suitable to enhance the resolution of SPCEM.

In this paper, we proposed a novel method to improve the lateral resolution of SPCEM combining d-SPCEM and the technique of FED. In d-SPCEM, we can obtain both the image with hollow spot PSF and an image with solid spot PSF by moving the sample’s axial postion over hundreds of nanometers. The mechanism of this phenomenon is precisely demonstrated with fundamental electromagnetic and optical theories. Furthermore,the subtraction process of the image of hollow-spot PSF and the image of solid-spot PSF will dramatically enhance the resolution and contrast, at least restoring the same resolution as conventional wide-field microscope with the same numerical aperture. The vadilty of our method has been verified with the simulation results of the spoke-like pattern sample and the experimental images of fluorescent particles. More importantly, our method does not requiry any additional revise of the conventional SPCEM configrertion. Therefore, we believe that our method will greatly enhance the resolution of SPCEM and have great potential for applications in biological observations.

2. Theory

2.1 Evanescent field near a fluorosphore and surface Plasmon-coupled emission

According to basic optical theories, radiation emitted by an electric dipole consists of propagating and evanescent field. Usually, only the propagating field can be measured in the far field, since the evanescent field dies out over a length of approximately a wavelength from the sources [17]. The evanescent wave, however, can be converted to be observable when the radiation goes through an interface very close to the source. When the refraction index of the embedded medium is smaller than the refraction index of the medium on the other side of the interface, the evanescent wave can be turned into propagating wave, passing through under an angle larger than anti-critical angle [17,18 ].The similar phenomenon also appears when waves are propagating through a layer of metal with finite thickness, which is called surface plasmon-coupled emission (SPCE) and usually interpreted as the reverse process of surface plasma resonance (SPR) and caused by near field fluorescence [1].

The model of three layers that we used for verification is shown in Fig. 1(a) . The medium where the dipole embedded is air, whose refraction index is 1. The intermediate medium is an approximately 40 nm thick silver layer plated on a glass cover-slip, whose complex refraction index is 0.15 + 3.27i(when the wavelength of light is 560nm). The glass coverslip, which is on the other side of the metal layer, has the refraction index of 1.515 [8]. We suppose that the diameter of the fluorescence bead is approximately 150nm. Thus, we set the proximity between the metal interface and the dipole is 75nm. The electromagnetic waves passing through the metal layer can be separated into two orthographical components: p-polarized wave and s-polarized wave, which are corresponding to TM mode and TE mode, respectively [19]. Although the metal layer has a prodigious conductivity, the metal layer is too thin to make the electromagnetic field vanish. Figure 1(b) displays the transmission coefficient of both p-polarized and s-polarized light’s amplitude as a function of the emitting angle in the medium of glass. It is shown that the p-polarized light will be dramatically absorbed and emitted in a certain angle in the glass medium, while s-polarized wave simply transmits and decays in the metal layer.

 

Fig. 1 (a) Schemes for surface plasmon-coupled emission(SPCE). The propagation direction of SPCE is shown with green arrows. (b) The transmission coefficient of intensity as a function of the emitting angle in the medium of glass. The red line is for the s-polarized electromagnetic wave, while the blue line is for p-polarized waves. The minor flunctuation of the p-wave transmission curve derives from the calculation deviation. (c) the configuration of SPCEM $n_1$,$n_2$,$n_3$,$n_4$are the refraction index of the corresponding part of the system, ${\theta }_4$is the aperture angle, while $\phi$is the azimuthal angle).

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The condition for the occurrence of SPCE is that the magnitude of incident wave vector matches the wave number that can excite surface plasmonic wave:

where $k_0$denotes the wave number in the vacuum when the wavelength is$\lambda$.${\epsilon }_1$, ${\epsilon }_2$ are the permittivity of the medium where the dipole embedded and the metal, respectively. In general,${\epsilon }_2<0$ and${\epsilon }_2<\left|{\epsilon }_1\right|$ [19], and $k_{spp}$, the wave number of surface plasma wave, is constantly larger than the wave number in medium where the dipole submerged in, which could be denoted as $k_1$, and

This principle means that only the evanescent field near an electric dipole can excite surface plasmonic of the metal. Thus, the propagating waves pass through under the angle smaller than the anti-critical angle while the evanescent waves travel under angles larger than the anti-critical angle. ${\theta }_c$, the anti-critical angle can be shown as:

where $n_1$ and $n_3$ represent the refraction index of air and glass, respectively [20–22 ]. The evanescent field will excite SPCE, while the propagating field will simply pass through the metal layer. Therefore, in this case, the fluorescence is the amalgamation of SPCE wave and ordinary propagating waves.

2.2 Surface plasmon-coupled emission microscopy (SPCEM)

Based on those principles above, the evanescent field near a fluorescent bead which is quite adjacent to the interface can excite the surface plamon-coupled emission. This part of light is enhanced and propagates at the particular angle of ${\theta }_{spp}$, which is shown in Fig. 1(a). Meanwhile, propagating field is passing through the metal layer directly and propagate under the critical angle ${\theta }_c$. These two parts are both collected and imaged on CCD by a microscope configuration shown in Fig. 1(c). This technique is called surface plasmon-coupled emission microscopy [8, 9 ]. An TIRF objective with a high NA is utilized to collect the fluorescence of SPCE and to image them on a CCD. The fluorescent beads were excited by a laser beam from the other side of the metal layer, which is the so-called RK configuration [2].The peak wavelength of the fluorescence is 560nm, and the wavelength of the exciting light is 532nm. Most of the SPCE wave is p-polarized, which means this part of light is radial-polarized, while the propagating field stays unpolarized as regular fluorescence does.

2.3 3D point spread function & defocused surface plasmon-coupled emission microscopy(d-SPCEM)

Since the electromagnetic wave transmitted through a thin layer of metal is composed of ordinary fluorescence and surface plasmon-coupled emission wave, the intensity distribution of the beam will be unusual, leading to a distinctive point spread function in SPCEM. Electromagnetic wave derived from surface plasmon-coupled emission is radial polarized; therefore, it will focus into a donut-like spot on focus plane. Meanwhile, the ordinary fluorescence originated from propagating field can be focused into a solid spot. Based on vectorial diffraction theory [23], and the theoretical work before [8], we design a computer program to simulate the PSF of SPCEM in different situations via Matlab, and the simulation results are shown in Figs. 2(a)-2(c) . The fluorescence transmitting above the critical angle, which is believed to be the surface plasmon-coupled emission, is focused into a hollow 3D PSF, which is shown in Fig. 1(a). The propagating field, passing through under the critical angle, is forming a solid 3D PSF, just like what Fig. 2(b) is showing. It is found that surface plasmon-coupled emission and regular fluorescence are uneven distributed along the axial direction, which results in the 3D point spread function to be tweezer shaped shown in Fig. 2(c). Figs. 2(d)-2(g) show the simulated transverse PSF on the focal plan when the imaging axial position is 0nm, 100nm, 200nm, 300nm away from the ideal image plane. It is demonstrated that while the imaging position only moved 300nm near the focus plane, its image of fluorescent bead can change from a donut-like spot into a solid spot. Different from other wide-field fluorescence microscopy, this defocus phenomenon is very sensitive along the axial position. We called the technique that moving the axial position of the sample to change the PSF into a solid one ‘defocused surface plasmon-coupled emission microscopy’. Actually, it is different from the ordinary defocus, since the shape of transverse PSF only changed within the range of 3D PSF. With d-SPCEM, we can easily modify the shape of SPCEM’s PSF without the decrease of image quality and resolution.

 

Fig. 2 (a)The three dimensional PSF calculated with the fluorescence above the critical angle; (b) the three dimensional PSF calculated with the fluorescence under the critical angle; (c) Three dimensional point spread function of surface plasmon-coupled emission microscopy. For (a)-(c),the axial range is 700nm in objective space. The transverse range is also 1200nm in objective space. The scale bar shows the length of 200nm and the yellow dashed line shows the position of focus plane. (b)-(e) The simulated transverse point spread function when the imaging axial position is 0nm, 100nm,200nm,300nm away from the ideal image plane on the right side. The scale bar shows the length of 200nm.

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2.4 Fluorescence emission difference with d-SPCEM

The imaging process can be regarded as a superposition of the instrument PSF, thus the intensity distribution on the image plane is the convolution between the intensity distribution of the object and the PSF [24]

 

Fig. 3 (a) the cross-section profile of transverse PSF when the imaged particle is 0,400nm away from the focal plane(the solid-spot PSF and the hollow-spot PSF), and the cross-section profile of transverse PSF of FED when the subtraction factor is 0.4. (b) The normalized magnitude of OTF of solid spot PSF, hollow-spot PSF and the PSF of FED with the subtraction factor of 0.4. (c)-(e)the transverse PSF of d-SPCEM in-focus and 400nm away from focal plane, the transverse PSF of FED with subtraction factor of 0.4, respectively. The scale bar is 200nm.

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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

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

Combining d-SPCEM with FED could effectively restrain the emergence of negative values in FED technique. Negative values derive from the artificial procedure of setting the negative value to be zero and will cause the distortion of the image. In d-SPCEM, the defocused solid-spot PSF has a profile that is more suitable with the hollow-spot PSF. Therefore, the subtraction will create less negative value. In Figs. 3(a) and 3(e), we can see that the negative values of the combined technique are negligible with the subtraction factor of 0.4.

Furthermore, applying FED in d-SPCEM, it is unnecessary to insert a vortex phase plate or a liquid crystal plate to improve the resolution. The defocus process only requires the movement of the sample’s axial position that can be accomplished by precisely controlling the microscope’s sample stage. It will remarkably decrease the complexity of experimental setup. The remarkable improvement of lateral resolution can be further verified by simulations and experimental results in the following parts of this paper.

3. Configuration and preparation

3.1 SPCEM configuration

The scheme for experiments is shown in Fig. 4 . A laser beam with wavelength of 532nm is passing through an objective lens with NA of 0.8 to focus on the sample to excite the fluorescence. The sample is a group of sparsely distributed fluorescent beads of approximately 150nm diameter which are placed on the thin layer of metal. The metal layer for the excitation of SPCE is a silver layer of 40 nm thickness plated on a glass coverslip. An oil objective lens, which has a NA of 1.49 and a magnification of 100 is used to collect the fluorescence on the other side of the metal layer. The fluorescence, propagating through a filter used for eliminating the exciting light, is refocused by a tube lens on the image plane, where a CCD is placed to obtain the image of the sample. The tube lens increased the magnification to about 220. The peak wavelength of the fluorescence is 560 nm. In SPCEM, we only care about the images derived from the fluorescence in the vicinity of the interface (within a wavelength). In fact, the KR configuration, which excite the fluorescence and collect it on the same side of the metal [1], can better suppress the interference from the fluorescence in the deeper layer. The sample in our experiment is just a thin layer of fluorescence beads. Therefore, the RK and KR configuration will have the same image performance.

 

Fig. 4 the experimental SPCEM scheme for nanoparticle tracking.

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3.2 Experiment preparation

We chose 150nm diameter fluorescent beads as our sample and diluted them with 1000 volume water. Since the size of the bead is quite large, the fluorescence is not obviously quenched on the metal layer. The diluted sample is placed on a coverslip coated with 40nm thick silver. When the water is evaporated, all fluorescent beads are sparsely distributed. With the experiment setup in Fig. 4, we can capture the image of those fluorescent beads. We set the focal plane on the interface of metal and air, and move the sample away from the objective gradually. Every time we moved 10nm, we took an image. In this way, we moved the sample several micrometers and applied these images to analyze the variation of point spread function along axial positions.

4. Simulation and experiment results

4.1 The different shape of transverse PSF along axial positions

We display our images of sparsely distributed fluorescent beads (150nm, 532nm/560nm) in Fig. 5 . Because the number of images is large, we only show 4 images of a 9.3μm × 8.5μm zone of detected area, which were captured when the sample was moved 50nm, 150nm, 250nm and 350nm from the focal plane, which are shown in Figs. 5(a)-5(d). The focal plane is deliberately fixed to be overlapped with the surface of metal. The images of a single bead are shown in Figs. 5(e)-5(h) from which we can easily tell the donut-shaped spot changing into a solid one.

 

Fig. 5 (a)-(d) Fluorescent beads’ images of a 9.3μm × 8.5μm zone of our detected area when the sample was moved 50nm, 150nm, 250nm and 350nm. The length of the scale bar is 1μm. (e)-(h) The images of a single bead at the axial position of 50nm,150nm, 250nm,350nm.This bead is shown in (a) by a yellow arrow. The whole size of each image is 1.2μm × 1.2μm.The length of the scale bar is 400nm.

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4.2 Simulation results for FED with d-SPCEM

A sample of 4μm × 4μm spoke-like sample, which is shown in Fig. 6(a) , is used to evaluate the lateral resolution of our method. The image of hollow-spot PSF is shown in Fig. 6(b). We can clearly see two unresolved areas: the central circle disk is close to the diffraction limit, but the outer ring degrades its resolution and distorts the image. The image of off-focused solid-spot PSF, which is shown in Fig. 6(c), has lower resolution and less cut-off spatial frequency. Fig. 6(d) shows the imaging result of Tang’s method to enhance SPCEM’s resolution. It is believed that the resolution of diffraction limit has been restored. Figs. 6(e) and 6(f) are the deconvolution results of Figs. 6(b) and 6(c) with 30 iritations. We see that the deconvolution method does not create satisfactory results. The results of FED with subtraction of 0.5 and 0.7 are shown in Figs. 6(g) and 6(h). The diffraction limit is also restored, and the contrast of the images can be improved. Compared to SPCEM with VPP, our method does not required additional optical element and the image’s contrast can be increased. To evaluate the resolving ability roughly, we can measure the diameter of unresolved area. The diameter of the outer ring in Fig. 6(b) is 3.4μm, while the diameter of its central unresolved area is 1.7μm. The diameter of the unresolved area of Figs. 6(g)-6(h) are both close to 1.5μm. Therefore, our method can reach the resolution at least twice that of conventional SPCEM, and optimize the resolve potential of hollow-spot PSF.

 

Fig. 6 Simulation results of a sample with spoke-like pattern. (a) the spoke-like sample. (b)the imaing results of exactly in-focus SPCEM(hollow-spot PSF) ;(c) the imaing results of d-SPCEM when the imaged pattern is 300nm away from focal plane(solid-spot PSF) ;(d)the imaging result of SPCEM with vortex phase plate(VPP); (e)-(f) the imaging results of deconvolution process of Figs. 6(b) and 6(c); (g)-(h) The imaging results of FED with subtraction factor of 0.5and 0.7. The whole size of the sample is 4μm × 4μm.The length of the scale bar is 1μm .

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4.3 Experiment results

To test the practicl performance of d-SPCEM with the technique of FED, we conducted our method on the sample of sparsely distributed fluorescence beads . We picked images right on the focal plane and 400nm away from the focal plane, which are shown in Figs. 7(a) and 7(b) , respectively. Obviously, the image on the focal plane (with donut-shaped PSF)is distorted, and its resolution is compromised. At the same time, the quality of image nearly 400nm away is improved since the PSF turned into a solid one, but the resolution is also degraded since the solid spot is extended. The de-convolution result with 30 iterations of Fig. 7(a) is shown in Fig. 7(c). The PSF used in this de-convolution process is simulated with program we mentioned in the former part of this article. The quality of the image has been improved. However, the distortion has not been completely eliminated and resolution of diffraction limit has not been totally retrieved. According to the principle of FED, we subtracted the Fig. 7(b) with Fig. 7(a) and set the subtraction factor to be 0.6, whose result is shown in Fig. 7(d). We can see that not only the resolution is improved, but the distortion and noise has been wiped out. The area zoomed in and the profiles in Fig. 7(e) show that four particles which cannot be distinguished in d-SPCEM, in a small area of the whole image, is clearly distinguished with FED. Furthermore, the noise of image has also been suppressed a lot by the method of FED. Based on these experimental results, we can assure that the resolution and contrast of SPCEM can be significantly improved by employment of FED.

 

Fig. 7 Experimental results of fluorescence beads. (a) the image of SPCEM right on focal plane (hollow-spot PSF); (b) the image when the particle is 400nm away from the focal plane (solid-spot PSF);(c) the deconvolution result of Fig. 7(a) with 30 iterations. (d) the image of d-SPCEM combined with FED with a subtraction factor of 0.6. A particular area in Figs. 7(a)-7(d) is zoomed in and four particles are marked with dashed line to be further investigated;(e) Intensity profiles along the white dashed line in Figs. 7(a)-7(d). The whole size of each image is 9.3μm × 8.5μm. The scale bar denotes 1μm.

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Furthermore, the FED process can be utilized to localize the position of a single particle without massive numerical processing. SPCEM has the potential of realizing single particle tracking(SPT). The application of FED in SPCEM can actually help us pinpoint the actual location of a particle without complex numerical calculation(like PALM and STORM), which could prompt the development of SPT. That is what we are working on and pursuing in the future.

5. Conclusion

In this paper, we illustrate the mechanism of changeable shapes of transverse PSFs along axial positions in d-SPCEM. When the sample is exactly at the focal plane in object space, we can take an image with donut-like PSF. What is novel is that we can also obtain an image which has solid spot PSF when the sample deviated from the focal plane about 400nm. With the application of FED which conducts the subtraction process of the image with solid-spot PSF and the image with the PSF of hollow-spot PSF, we can increase the weight of high spatial frequency, dramatically improve the lateral resolution of SPCEM and at least restore the resolution of diffraction limit. Based on theoretical simulations and experimental result, we verified that d-SPCEM combined with FED can effectively improve the contrast and resolution with better performance than deconvolution method. We also proved that our method can reach the same or even better resolution enhancement of SPCEM with VPP without additional optical element in the conventional setup.

Supported by the superior performance of simulations and experiment results, it is not groundless to say that the application of FED in d-SPCEM will be an effective method to enhance the lateral resolution and extend the application of SPCEM with simple configuraions. It is believed that our method has a great potential to be applied in the future biological research.