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Point Spread Function of Objective-based Surface Plasmon Resonance Microscopy Yingyan Jiang, and Wei Wang Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.8b02800 • Publication Date (Web): 02 Jul 2018 Downloaded from http://pubs.acs.org on July 2, 2018
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Analytical Chemistry
Point Spread Function of Objective-based Surface Plasmon Resonance Microscopy Yingyan Jiang, and Wei Wang* State Key Laboratory of Analytical Chemistry for Life Science, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210093, China
ABSTRACT: Objective-based surface plasmon resonance microscopy (SPRM) is a novel optical imaging technique that can map the spatial distribution of local refractive index based on propagating surface plasmon polaritons (SPPs). Different from some other optical microscopy that shows a dot-like point spread function (PSF), nanosized object appears as a wave-like pattern containing parabolic tails in SPRM. Geometrical complexity of the wave-like pattern hampered the quantitative interpretation on the PSF of SPRM. Previous studies have shown that two adjacent rings were obtained in the frequency domain by applying a 2-dimensional Fourier transform to such patterns. In the present work, a ring fitting method was developed to extract geometrical features out of the dual-rings and to connect these features with several experimental parameters. It was found that the radius of ring equaled to the wavevector of SPPs. Its orientation revealed the propagation direction of SPPs. The coordinate distance of the center of ring gave the parallel component of the wavevector of the incident light, which was regulated by the incident angle. The ring broadening factor reflected the propagation length of SPPs in a reciprocal relationship. Systematical and quantitative interpretations in the frequency domain not only advanced the basic understanding on the PSF of SPRM, but also opened up the possibility to utilize these frequency-domain features for detection and sensing purposes in future.
Surface plasmon polaritons (SPPs) are electromagnetic waves propagating along a planar metal-dielectric interface that arise from the resonant oscillations of conduction electrons under particular light excitation.1-3 As an important form of light-matter interaction, SPPs exhibited several important strengths and have attracted intensive interests from broad scientific communities covering physics, chemistry and biology. From an optical point of view, the excitation of SPPs led to the significant confinement of electromagnetic waves at the interface of interest, which has enabled numerous applications in near-field optics,4 metamaterials and metasurfaces,5 surface enhanced spectroscopy,6 chemical and bio-sensing.7,8 Another important feature of SPPs is their capability to convert free-space photons to energetic electrons. It has recently advanced the scientific adventure in plasmon catalytic effect (SPPs-assisted chemical reactions)9-11 and plasmoelectric effect.12,13 The visualization of SPPs was mainly relied on near-field techniques such as scanning near-field optical microscopy,14 two-photon photoemission electron microscopy15,16 and photon scanning tunneling microscopy.17 They can directly map the electromagnetic field distribution of SPPs over a surface with the help of a scanning probe. Since the electromagnetic field of SPPs decayed exponentially along vertical direction from the surface, conventional far-field experiments were not able
to access the wavevector of SPPs unless transforming them into light by, for example, the interaction with an object. In the past decade, a far-field imaging system, termed surface plasmon resonance microscopy (SPRM), was developed by others and us to image nano-sized objects by wide-field imaging the reflected light with a camera.18-32 In contrast to the dot-like point spread function (PSF) observed in many other far-field microscopes such as fluorescence microscopy and dark-field microscopy, a wave-like PSF was experimentally observed in SPRM (Figure 1a).20,22-25,27,28 Any nano-sized object appeared as a wave-like pattern with periodic parabolic tails regardless its chemical composition and geometry as long as it is smaller than the diffraction limit. However, unlike the regular dot-like PSF that can be nicely fitted by 2-dimensional Gaussian function, directly fitting the wave-like pattern in the space domain has proven difficult despite of a few attempts.33,34 The wave-like pattern was first observed on 100200 nm virus nanoparticles by Tao and co-workers,24 which was further attributed to the scattering of plasmonic waves by nano-objects according to a simplified two-dimensional electromagnetic field model.20,35 Corn and co-workers reported a 2-dimensional Fourier transform (2D-FT) method to convert such wave-like patterns in the space domain to two adjacent rings in the frequency domain (Figure 1b).21 The theoretical basis of 2D-FT was recently established in details by Corn33
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Figure 2. (a) Temporal and (b) spatial approaches to achieve the image subtraction.
Figure 1. PSF of SPRM and Fourier space image. (a) PSF of SPRM (b) Fourier space image of the SPRM image in (a). (c) Correspondences between geometry feature of ring and experiment parameter.
and Tao34, respectively. 2D-FT processing has been adopted in several studies to enhance the image contrast by Fourier filtering,21,22,36 to extract the size information out of the wavelike pattern,37 and to improve the spatial resolution of SPRM via image deconvolution.34 Despite of brief theoretical perspective on the correlation between the radius of the ring and the wavevector of SPPs,22,34 how the PSF was determined by the experimental conditions remains unexplored so far. In the present work, we conducted the first systematic and quantitative study on the PSF of SPRM in order to clarify the dependence of the obtained wave-like pattern on various experimental conditions including wavelength, direction and angle of incident light, focus and the dielectric constant of solution. We proposed a ring-fitting method to quantitatively extract the geometrical features out of the dual-rings in the frequency domain (Figure 1b), because it was more difficult to fit the wave-like patterns in the space domain. As listed in Figure 1c, it was found that the radius of the ring equaled to the wavevector of SPPs, which was a function of wavelength of incident light, and the dielectric constant of metal film and solution. The broadening of the ring was determined by the propagation length of SPPs. The separation between these two rings was regulated by the incident angle. These quantitative dependences were all nicely explained by using a previously established theoretical model.34,35 The present work not only builds the solid experimental and theoretical framework for understanding the PSF of objective-based SPRM, it also points out a far-field approach to determine the wavevector of SPPs with high accuracy.
RESULTS AND DISCUSSION Apparatus and PSF of SPRM. The detailed descriptions on the apparatus of home-built SPRM can be found in a recent review article26 and the previous literatures.18,21,24 Briefly, a red or near-infrared monochromatic beam was collimated and focused at the back-focal plane (BFP) of an objective with high numerical aperture (Nikon Apo TIRF 60x NA 1.49 oil immersion objective), resulting in parallel illumination
towards a gold-coated coverslip with a certain incident angle. When this angle matched with the surface plasmon resonance (SPR) angle, it naturally created a Kretschmann configuration to excite SPPs propagating along the glass-metal-dielectric (air or solution) interface.1,2 The presence of a nano-sized object at the metal-dielectric interface interacted with the SPPs to generate a scattered wave centered at the location of this nanoobject. The interference between propagating SPPs, scattered wave and reflected wave altered the distribution of local reflectivity (see Ref. 35 for details). As a result, a wave-like pattern appeared in the differential SPRM image by subtracting the SPRM image in the absence of the nano-object from the one in the presence of the nano-object. Note that spherical polystyrene nanoparticles with a diameter of 150 nm was used as the nano-object throughout the work. The image subtraction can be achieved by either temporal or spatial approaches (Figure 2). In the temporal approach, the single nanoparticle collision events were continuously recorded. At certain moment, a single nanoparticle hit at the substrate and stayed on it. The SPRM image of the nanoparticle was obtained by subtracting the SPRM image just before the collision (t0) from the one just after the collision (t1). The subtraction removed the static background and delivered a wave-like pattern with excellent quality (Figure 2a). In the spatial approach, individual nanoparticles were preimmobilized on the gold film with an extremely low density, for instance, only several nanoparticles in a 60×80 µm2 region. At certain moment, the sample stage (piezo-stage or motorized stage) was horizontally moved by a distance (for instance, 20 µm) and stayed there (x0x1). Subtraction between the SPRM images captured at the two locations resulted in a differential SPRM image (Figure 2b). It contained a bright and a dark wave-like pattern that were separated by 20 µm. These two patterns are identical but with opposite signs, both representing the SPRM image of the nanoparticle itself. Temporal subtraction usually provided better quality but it involved the dynamic collision-and-stay of nanoparticles in solution. Spatial subtraction was more powerful for preimmobilized nanoparticles and for gas phase studies. In order to acquire wave-like patterns with high quality, temporal subtraction was utilized in the present work unless stated otherwise. The apparatus of SPRM was built on an inverted totalinternal reflection fluorescence microscopy (TIRFM) with the following modifications.18,21,24 First, because the reflected light and the incident light had the same wavelength, excitation and emission filters were removed from the filter cube and a 50/50 beam splitter was used instead of a dichroic mirror. Second, a
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Analytical Chemistry linear polarizer was introduced to make sure the polarization direction was along the plane of incidence because only ppolarized light was capable of exciting SPPs. Third, instead of the electron multiplying CCD (EMCCD) camera that was often used in TIRFM to collect the weak fluorescent emission, an industrial CCD/CMOS camera was enough to capture the SPRM image as the reflected light carried sufficient photon flux. Forth, selection of suitable light source is one of the most critical factors to achieve high quality SPRM imaging. Laser diode with strong spatial coherence was often avoided as they induced obvious interference fringes in the image. The adoption of a rotating diffuser and multi-mode fiber was recommended when using laser diode in SPRM.31,38 In addition, laser diode also suffered from relatively large intensity fluctuation (~1% or higher). Super-luminescent diode was found to reach a balance between high beam quality and low spatial coherence, providing sufficient spatial homogeneity and temporal stability. Digital light projector has also been reported to be suitable light sources in SPRM.23,29 In contrast to the dot-like PSF in many far-field optical imaging techniques, SPRM exhibited a very special wave-like PSF. Existing studies have confirmed that the shape of the wave-like pattern was independent of the chemical identity and geometry of the nano-object. Similar pattern has been observed by different groups for various kinds of nano-objects including inorganic materials (metal,20,37 and metal oxide25), organic materials (polymer,22 and hydrogels36), and biological materials (virus,24 mitochondrion,39 and bacterium40,41). The shape was solely determined by the optical parameters such as the wavelength, dielectric constant of metal and solution, incident direction and angle. Therefore, one can conclude that the wave-like pattern represents the PSF of SPRM. Traditionally, the principle of SPR is described with a multilayer reflection model. It explains the relationship between resonance angle and a couple of optical properties.1 However, the conventional model does not provide information regarding the spatial distribution of local reflectivity induced by a single nano-object. In order to understand the physics behind this special wave-like PSF, several theoretical models have been proposed to describe the interaction between propagating SPPs and an isolated nanoparticle.33,35,42 Among them, the theory proposed by Tao and co-workers in 2014 was found to provide the best consistence on the experimental results.35 This theory involves interference among three components: the partially reflected wave, the propagating SPPs and the scattered wave of SPPs by the particle (a decaying cylindrical plasmonic wave). Readers are referred to the original paper for detailed descriptions on the theory.35 According to this model, one can calculate the distribution of reflectivity from the physical constants and experimental conditions (Figure 3a), which showed excellent agreement with the wave-like pattern experimentally observed for nanoobjects in SPRM (Figure 3b). 2-Dimensional Fourier transforms and ring fitting. In many far-field imaging techniques such as fluorescence microscopy and dark-field microscopy, 2-dimensional Gaussian distribution was often employed to directly fit the PSF in the space domain. The analogy turned out difficult for SPRM. Although the PSF in SPRM can be calculated from the theory, it remains challenging to directly fit the wave-like pattern in the space domain because of the lack of a simple algebraic expression. Fortunately, previous studies21,33,34,37 have revealed that 2-dimensional Fourier transform of the
Figure 3. Theoretical (a, c) and experimental (b, d) PSF in the space (a, b) and frequency (c, d) domain, respectively. Compared with theoretical ring (c), experimental result (d) displays intensity fading along the horizontal line connecting 90 degrees and 270 degrees (white arrows). In order to demonstrate the ring broadening effect, experimental results are extracted along four directions (45, 135, 225 and 315 degrees, white lines in (d)). They are fitted with Lorentz function to examine the robustness of thickness parameter, σ.
wave-like patterns delivered a dual-ring pattern in the frequency domain, as shown in Figures 3c and 3d. Another helpful feature for the frequency domain analysis is that, the amplitude pattern in the frequency domain is independent with its location in the space domain. No matter how the region-ofinterest was selected in the space domain, the shape and the location of the dual-ring is the same in the amplitude map in the frequency domain. That is because the information regarding the spatial location was carried in the phase component. In other words, the signal-to-background ratio of the dual-ring pattern in the frequency domain can be easily improved by averaging lots of individual nanoparticles. Such averaging was difficult in space domain because it was almost impossible to choose region-of-interests where different nanoparticles were precisely located at the same position. Note that Fourier transform is an equivalent conversion, which means wave-like patterns in the space domain can be completely and identically reconstructed from the dual-rings in the frequency domain through an inversed Fourier transform. Such reconstruction must apply to the complex value containing both amplitude and phase information. In order to match the requirement of discrete Fourier transform on the symmetry, image size (m×n) must be odd. Reconstruction of wave-like patterns from dual-rings has been demonstrated in previous studies, which more focused on the image filtering21 and deconvolution34. A ring-fitting method was developed herein to fit the dualrings in the frequency domain by using the following equation: z0 +a z= 2 ( x − x0 ) 2 + ( y − y0 ) 2 − r + σ 2
(
)
Eq. (1)
where x0 and y0 are the coordinates of the center of the ring, r is the radius, σ indicates the broadening effect (thickness) of the ring. The theory of spatial Fourier transform suggests that the radius r in the frequency domain is the wavevector of the SPPs in space domain. The broadening effect of the ring is due to the spatial damping of SPPs, i.e., the propagation length (Figure 3e). It was further found that the ring-fitting method worked
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Figure 4. (a) Three representative wave-like patterns in the space domain at three selected wavelengths, respectively. The corresponding rings in the frequency domain show reduced radius with the increasing wavelength. (b) The radius of ring gradually decreases with the increasing wavelength from 600 to 780 nm (black curve, left axis). This trend is well consistent with the calculated wavevector of SPPs (kspp, red curve, right axis).
well for both simulated and experimental results (Figure 3). Fitted result is shown in red curve in Figure 3d. The remaining disagreement at the present stage is that the intensity fading along the direction of 90 and 270 degrees (white arrows in Figure 3d). The amplitudes across this horizontal line are smaller compared with those along the vertical line (0 and 180 degrees). It is likely due to the depth of focus associated with the objective, which might cancel out some of reflected signals by also collecting the light from the out-of-focus planes. It is supported by the fact that the intensity fading was quite sensitive to the defocus of objective. However, the intensity fading only placed slight influence on the ring-fitting, and it did not affect the major parameters for describing the geometry of the ring. Dependence of ring geometries on experimental parameters. We subsequently examined the dependence ofring geometries (x0, y0, r and σ) on several important experimental parameters including wavelength (λ), angle (θ1) and direction (θ2) of incident light, dielectric constant of metal film (εm) and solution (εd). The radius r equaled to the wavevector of SPPs, which is a
Figure 5. (a) Increasing radius of ring is observed under solvent with higher refractive index (nair = 1.000, nPFH=1.252, nwater=1.331, nethanol=1.360). The refractive index of solution was experimentally determined with a refractometer. (b) The fitted radius (black curve) is quantitatively consistent with the calculated wavevector (red curve) under different solvents.
function of λ, εm and εd. Representative wave-like patterns in the space domain, and the ring-fitting results at three selected wavelengths are displayed in Figure 4a. While it is difficult to quantitatively tell the difference among the wave-like patterns, one can easily find that the radius of ring decreases with the increasing wavelength. Systematic measurements for a series of wavelengths from 600 to 780 nm further validate the trend (Figure 4b, black curve). It is expected because the radius of the ring equals to the wavevector of SPPs. Existing theory suggests the wavevector of SPPs can be calculated from the following equation:
kspp =
2π
λ
ε dε m ε d +ε m
Eq. (2) where λ is the incident light wavelength, εm is the dielectric constant of gold film and εd is the dielectric constant of solution. Because the wavelength-dependent εm,43 λ and εd are all known parameters, the wavevector of SPPs can be calculated as a function of wavelength (Figure 4b, red curve). These values are found to be nicely consistent with the fitted radius of the ring in the frequency domain (Figure 4b). The
Figure 6. (a) Illustrations on the angle (θ1) and direction (θ2) of incident light. BFP: Back focal plane of objective. Blue region represents the sample plane. (b) The linear dependence of the parallel component (kx=k0n0sinθ1) of the wavevector of free space incident light (k0) with the incident angle, sin(θ1).
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Analytical Chemistry
Figure 7. Representative rings in the frequency domain (top panel) and the corresponding zoom-in (bottom panel) at three incident angles. Best resonance is achieved at 68.86 degrees. (b) Ring radius remains constant at different incident angles. Note that the axis ranges are identical to those in Figure 6b.
slight difference was attributed to the inaccurate wavelengthdependent εm because of the thickness and roughness of gold film as well as the influence from a 2-nm Cr adhesion layer.4446 As a matter of fact, because the determination of ring radius is straightforward and accurate, the present work provides a simple far-field approach method to experimentally determine the wavevector of SPPs. The influence of dielectric constant of solvent was also examined by introducing a series of solvent with different refractive index. Ring with increasing radius is observed when increasing the refractive index of solution (Figure 5). Because of the difficulty in handling nanoparticle collision under different types of solvents (particularly in air), a spatial approach was adopted to obtain the PSF from pre-immobilized polystyrene nanoparticles. Fitted radius is consistent with the calculated wavevector of SPPs in a broad refractive index range from 1.000 (air) to 1.360 (ethanol). The results demonstrate that the radius of ring in the frequency domain is capable of determining the wavevector of SPPs. There are two parameters regulating the angle (θ1) and direction (θ2) of incident light, respectively, depending on the position of light beam being focused at the back focal plane (BFP) of objective (Figure 6a). This is achieved by adjusting the position of light source at the plane perpendicular to the beam. Altering the distance between focus and the center of the back focal plane changed the incident angle (θ1). The
interface, the resonance angle was ~68.86 degrees. Figure 7 shows the fitted results at three different incident angles (θ1). It was found that the two rings are tangent to each other when the incident angle perfectly matches the resonance angle. Intersected and separated rings were obtained when the incident angle was lower and higher than the resonant angle, respectively (Figure 7a). The incident angle dependence strongly indicates the participant of reflected wave in the PSF, as this is the only field that is affected by the incident angle. The radius, r, is independent with θ1 (Figure 7b). The propagation direction of SPPs (θ2) can be adjusted by focusing the incident beam at the circumference in the BFP with a particular distance. In this case, the direction of polarizer should be accordingly adjusted. The alteration on θ2
coordinate distance of the center of ring (ටx02+y02 ) gives the parallel component (kx) of the wavevector of the incident light. In the theory of total internal reflection and mathematical description of the evanescent wave,47 kx can be expressed as kx=k0n0sinθ1. In the case of incident light wavelength is 720 nm, we plot kx against sinθ1 (Figure 6b) and fit it with a directly proportional function (red curve). The refractive index of glass coverslip is calculated to be 1.512 from the slope of red curve in Figure 6b. This value is in good agreement with the value (1.515) provided by the manufacturer. SPPs can be excited only when θ1 dropped into a narrow range (~3 degrees) around the particular resonance angle. For example, when a 720 nm beam was utilized at a gold-water
Figure 8. (a) A representative wave-like pattern of single polystyrene nanoparticles at 720 nm. (b) Damping constant in the space domain is calculated by exponentially fitting the intensity curve along the vertical direction as indicated by the white line in (a). (c) Ring width is obtained by fitting the ring in the frequency domain with a Lorentz function. (d) A linear dependence is observed between the damping constant and the reciprocal of the ring width under a series of wavelengths.
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higher than the focal plane, the pattern tended to be more flat (U-shape), as shown in Figure 9b. The radius of dual-ring in all cases are identical to each other, suggesting that de-focus does not change the wavevector of SPPs. Meanwhile, the intersection of the two rings was similar for lower-plane and higher-plane situations at certain incident angle. However, the intensity distributions on the ring are different at high frequency area as indicated by white arrows in Figures 9c and 9d. These results further supported the argument that the reflected wave was involved in the PSF of SPRM.
CONCLUSIONS The PSF of SPRM was experimentally investigated in a systematical and quantitative manner. While it is challenging to fit the PSF in space domain, a ring fitting method was developed to extract geometrical features from the dual-rings in the frequency domain. It was found that the radius of ring (r) equaled to the wavevector of SPPs. Its orientation (θ2) gave the propagation direction of SPPs. The coordinate distance of the center of ring (ටx02+y02 ) gave the parallel component (kx) Figure 9. Representative wave-like patterns in the space domain (a, b), and the corresponding rings in the frequency domain (c, d) when the sample plane is lower (a, c) and higher (b, d) than the objective focal plane.
led to the rotation of dual-ring in the frequency domain (Figure 1), while maintaining its radius and other geometrical parameters. It is a well-known fact that the damping in the time or space domain leads to the broadening effect in the frequency domain, which can be fitted by Lorentz function according to a previous literature.48 The width of Lorentz function, σ, can be extracted from the ring fitting to quantify the damping constant. The damping of SPPs is highly wavelength dependent, which can be described with the propagation length using the equation below: 3
1 λ ε d + ε m 2 ε m2 Lspp = = 2ki 2π ε mε d ε mi Eq. (3) We accordingly investigated the relevance between damping constant in the space domain and the ring width in the frequency domain at different wavelengths. Figure 8a shows a representative wave-like pattern of single polystyrene nanoparticles at 720 nm. As shown in Figure 8b, the damping constant was estimated to be 4.128 µm by exponentially fitting the intensity decay along the vertical direction (white line in Figure 8a). In the frequency domain, ring fitting reveals a ring width of 0.0448 µm- 1 (Figure 8c). It was found that the σ value from ring fitting was in reciprocal to the damping constant (Figure 8d). The relationship can be described by the formula: Lspp=1/(2πσ). A longer damping distance quantitatively corresponds to a narrower ring. The influence of objective focus was finally investigated. All the discussion above was conducted when the sample was perfectly placed at the front focal plane of objective. When we intendedly change the vertical distance between sample and objective to achieve de-focus conditions, the wave-like pattern was found to dramatically change. In particular, when the sample was placed lower than the focal plane, the originally V-shaped pattern became more symmetrical (X-shape), as shown in Figure 9a. In contrast, when the sample was placed
of the wavevector of the incident light, which was regulated by the incident angle (θ1). The ring broadening factor (σ) reflected the propagation length of SPPs in a reciprocal relationship. These results not only advanced the fundamental understanding on the theory of SPPs and SPRM, they also pave solid ways towards potential applications based on the ring-fitting method. For example, because the ring-fitting is a straightforward and reliable method to determine the wavevector, one may use this value to calibrate the wavelength-dependent dielectric constant of metal film. The latter is a fundamental constant that is essential for many SPPs-based applications. Similarly, the precise determination on the incident angle is also desired in objective-based SPRM. Because of the complicated light path, the conversion model between light source position and incident angle is not accurate enough with geometrical optics estimation. Measuring the ring-ring distance provided a novel way to precisely determine the incident angle. Furthermore, while SPR-based techniques are often powerful in measuring the change of solution refractive index, the determination on the absolute refractive index in a microscopic region is a more difficult task. Because the ring radius is also dependent on the refractive index of solution, this number could be used to determine the absolute value of refractive index of solution. The present work also opens up the possibility for frequency domain-based chemical and bio-sensing by using the ring geometry as the read-out signal.
AUTHOR INFORMATION Corresponding Author * E-mail:
[email protected]. (W.W.)
ORCID Yingyan Jiang: 0000-0002-5367-1225 Wei Wang: 0000-0002-4628-1755
Notes The authors declare no competing financial interest.
ACKNOWLEDGMENT We thank financial supports from the National Natural Science Foundation of China (Grants No. 21522503 and 21527807), the
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Analytical Chemistry Natural Science Foundation of Jiangsu Province (BK20150013), and State Key Laboratory of Analytical Chemistry for Life Science (5431ZZXM1802).
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