Analysis of the surface plasmon resonance interferometric imaging performance of scanning confocal surface plasmon microscopy.

Here, we apply rigorous coupled-wave theory to analyze the optical phase imaging performance of scanning confocal surface plasmon microscope. The scanning confocal surface plasmon resonance microscope is an embedded interferometric microscope interfering between two integrated optical beams. One beam is provided by the central part around the normal incident angle of the back focal plane, and the other beam is the incident angles beyond the critical angle, exciting the surface plasmon. Furthermore, the two beams can form an interference signal inside a confocal pinhole in the image plane, which provides a well-defined path for the surface plasmon propagation. The scanning confocal surface plasmon resonance microscope operates by scanning the sample along the optical axis z, so-called V(z). The study investigates two imaging modes: non-quantitative imaging and quantitative imaging modes. We also propose a theoretical framework to analyze the scanning confocal surface plasmon resonance microscope compared to non-interferometric surface plasmon microscopes and quantify quantitative performance parameters including spatial resolution and optical contrast for non-quantitative imaging; sensitivity and crosstalk for quantitative imaging. The scanning confocal SPR microscope can provide a higher spatial resolution, better sensitivity, and lower crosstalk measurement. The confocal SPR microscope configuration is a strong candidate for high throughput measurements since it requires a smaller sensing channel than the other SPR microscopes.


Introduction
Surface plasmon resonance (SPR) is an electromagnetic wave phenomenon on a noble metal surface that can be excited by a coherent p-polarized light source. The SPR is a label-free measurement technique responding to change in refractive indices on the noble metal surface. It has been utilized in thin-film based optical sensors and fiber-based optical sensors. Each platform has different advantages; the thin-film based optical sensors allow a convenient integration to a conventional microscope setup, whereas the fiber-based sensor has the advantage of light-weight optical transducer [1] and waveguide fabrication [2]. It has been demonstrated and employed in a wide range of applications, including protein binding and kinetics [3], small-molecule detection [4], small chemical ions [5], ultrasonic detection [6], voltage sensing [7], and refractive index sensing [8]. Recently, research groups studied the infection mechanism of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) or the deadly COVID-19 virus and reported binding kinetics between the virus and Angiotensin-converting enzyme 2 (ACE2) [9], and tracking its dynamics [10] using SPR microscopic imaging.
The first SPR microscope was developed under a prism-based Kretschmann configuration [11], which Yeatman and Ash later improved in 1987 [12]. In the experiment, when the light was incident on noble metal, the reflectance reflected off the metal surface, and there was a dark band appeared in the detector due to the coupling process of the SPR. The dark band can be utilized in sensing to indicate refractive index change on the metal surface. However, there are several limitations in such a prism-based system, including the oblique illumination leading to an optical aberration in the image [13] and the long working distance reducing the imaging lens's numerical aperture (NA) [14]. In addition, Yeatman [15] reported a critical trade-off between resolution and sensitivity. The excited surface plasmons (SPs) can propagate several microns away on the sample surface from the excitation point. So, suppose there is an imaging sample at an SP excitation position, the SPs propagate and measure several microns of sample and provide an averaged and blurry image leading to a poor resolution but good sensitivity. Meanwhile, a high-resolution SPR microscope can be achieved by reducing the SPs' propagation length. This technique has been demonstrated and achieved in means, including using a lossy metal such as aluminum [16] and a rough metal surface [17].
The combination between the SPR and a standard optical microscope enables optical imaging and sensing thanks to high NA objective lenses. There are several high NA objective lens-based SPR microscopes reported in the literature. These imaging techniques can be categorized into two main types: non-interferometric microscopy capable of imaging an SP intensity image and interferometric microscopy imaging an SP phase image. The phase imaging, of course, requires an interferometer [18,19].
The SPR microscopes can also be further classified as non-quantitative and quantitative imaging due to the quantitative measurement nature of the SPR. The difference between the two imaging modes is that quantitative imaging reports the image as plasmonic angles or equivalent refractive indices [20] for each spatial image position, whereas the non-quantitative mode provides an optical intensity image.
Stabler et al. [21] reported that for SPR microscopes, the resolution depended on the SP's propagation direction and shape of the sample, as shown in Fig. 1. Pechprasarn and Somekh [22] explained imaging mechanisms in SPR microscopes that a radial polarization should be employed for scattering-based samples, such as cells and point objects, since the radial polarization can excite more of the SPs than linear polarization. On the other hand, for structured samples where diffraction orders are well defined, as shown in Fig. 1(a)-(c), such as flow channels, microfluidic channels, and protein binding arrays, the image's resolution depended strongly on the geometry of the sample. Therefore, linear polarization is recommended for the latter case.  The incident polarization relative to the grating sample direction is shown in Fig. 1. Here, the x-polarization is the electric field direction along the x-axis and perpendicular to the grating stripes, as depicted in Fig. 1(a). On the other hand, the y-polarization is defined as the electric field direction parallel to the y-axis and the grating stripes, as depicted in Fig. 1(b). It will be explained later that the confocal SPR microscope operates by defocusing the sample along the optical axis, z defocus, towards the objective lens. Thus, the z defocus of 0 means the sample is at the objective lens' focal plane, the negative z means defocusing the sample towards the objective lens, and on the other hand, the positive z means moving the sample away from the objective lens outwards the focal plane.
There are several configurations for non-interferometric SPR microscopes [23][24][25][26]; the operating principle of such microscopes is that they require an amplitude aperture to block the incident light except around the SPR reflectance dip, enhancing the image contrast. Otherwise, the SPR image has no optical contrast due to the strong reflectance of non-SPR angles. There are two types of apertures widely employed in SPR microscopes: annulus aperture [27] and point illumination [24], which can be controlled using a physical aperture or an amplitude spatial light modulator. Although in this paper we quantify the performance of the scanning confocal SPR microscope, the performance of the non-interferometric microscope will be compared and discussed later in the results and discussion section.
Somekh et al. [28] proposed an interferometric heterodyne V(z) SPR microscope. The microscope forms an image using interference between two beams: one beam is reflected off the plasmonic sample, and a mirror provides the other. The signal is measured as the sample is defocused towards the objective lens, the so-called V(z) measurement. Of course, a stable and repeatable axial scanning measurement requires a high precision motorized stage and a closed-loop control position for the sample stage. Zhang et al. [29]. employed a phase spatial light modulator providing the defocused phase transfer function to modulate the relative phase of the incident beam instead of physically moving the sample. The crucial advantage of the microscope configuration is that the resolution does not depend on the propagation length of the SPs but the NA of the objective lens without losing the SPR sensitivity [22]. A research group in French has demonstrated the technique's capability by imaging neural cells [30] and locating a single nanoparticle with a particle radius of 100 nm [31].
Pechprasarn and Somekh [22] reported a theoretical study to quantify the quantitative imaging performance of the heterodyne V(z) SPR microscope by estimating the plasmonic angles from the average ripple period of the first 3 V(z) ripples, as highlighted in yellow in Fig. 2(c). covering the z defocus distance of -1.5 µm and estimated the plasmonic angle by the V(z) ripple period ∆z to λ / 2n(1 − cos θ p ) .
Later in 2012, Zhang et al. [32] have introduced a scanning confocal SPR microscope, which can provide a similar microscope transfer function to the heterodyne V(z) microscope and also embedded interferometry through a single optical beam illumination, in which the V(z) signal is formed by reference beam labeled as 'Ref' and the reradiated surface plasmons labeled as 'SP' in Fig. 2(a). The 'Ref' beam illuminates the noble metal surface reflecting off the surface with no SPs excited, whereas the 'SP' beam is at the higher incident angles around the SP dip; hence it can excite the SPs. The SPs then reradiated from the metal surface, returning to the objective lens and captured under a camera. The camera pixels within 0.25λ/NA of the point spread function Airy disc can be integrated as the signal allowing confocal detection using an artificial pinhole [32]. The pinhole provides a well-defined SP propagation path in which the SPs that appeared to come from the focal point contribute to the V(z) signal within the pinhole. Therefore, the SP signal in the image plane can be limited to the footprint size of 2ztanθ sp for a z defocus, and the footprint size can be larger than the sample size, as depicted in Fig. 1(c), degrading the sensitivity of the V(z) measurement. The interference between the 'SP' beam and the 'Ref' beam can be measured as the sample is defocused along the z defocus, appearing as ripples as depicted in    [31] also discuss the essential requirement of the incident beam profile's smooth amplitude pupil function; sharp edges can generate an undesired ripple frequency in the V(z) curve.
Common issues of employing a high NA objective lens are that the objective lens usually has a Gaussian amplitude profile modulation due to the total internal reflection reducing the lens's optical throughput [33] and the spherical phase aberration [34] around the edge of the lens. However, the amplitude distortion is not a problem to the V(z) measurement since the smooth edge amplitude function is preferred. In addition, the spherical phase distortion does not affect the V(z) measurement much. As shown in Fig.2b, the V(z) signal is contributed by two beams, which occupy narrow wave vector spaces in the Fourier plane. Therefore, the deviation in phase curvature due to the spherical aberration will only introduce a slight systematic measurement error to the V(z) curves by scaling the z-axis, which can be readily calibrated.
In addition, Zhang et al. [35] have employed a phase spatial light modulator (phase-SLM) to perform phase stepping measurement with the phase pupil function, as shown in Fig. 2(b). The phase stepping can be employed to recover plasmon phase shift for any z defocus, as shown in Fig. 2(c), with no need to measure a few cycles of V(z) ripples. Later Pechprasarn and Somekh [36] reported the detection limit of the confocal SPR microscope for quantitative imaging that with 100 µJ energy on the image plane, the confocal system should be able to detect a single molecule of 100 kDa and discuss that z defocus degrades the sensitivity.
The confocal SPR microscope has demonstrated its potential in several applications, including thin film thickness measurement [35], protein binding [37], and attenuation coefficient measurement [38].
The following points were not investigated: (1) the non-quantitative imaging of V(z) microscopes for each z defocused imaging plane. Here, the image contrast and resolution for different flow channel sizes and polarization direction relative to the grating sample were investigated. (2) Performance characterization of quantitative imaging of V(z) microscopes for each z defocused imaging plane. (3) There is no direct performance comparison between the quantitative imaging and non-quantitative imaging mode. Here we propose a theoretical framework to analyze the scanning confocal SPR microscope and apply the rigorous couple-wave analysis (RCWA) to quantify the microscope performance compared to scanning annulus aperture SPR microscope [27], a non-interferometric microscope reported in Tontarawongsa et al. [23].

RCWA and microscope simulation
A microscope simulation software based on RCWA [39] computation was developed in-house under the Matlab 2019a environment utilizing parallel computing to calculate reflection coefficients. There were three types of samples investigated in this study, which were (1) a bare gold sensor with thickness d m of 50 nm and refractive index n m of 0.18344 + 3.4332i for 633 nm wavelength extracted from Johnson and Christy 1972 [40] in water backing with water refractive index n w of 1.33; (2) a uniform Bovine Serum Albumin (BSA) protein layer with the layer thickness of 10 nm and the BSA refractive index n p of 1.4 [41] coated on a 50 nm uniform gold layer, and (3) 5 Bovine Serum Albumin (BSA) protein grating samples with grating periods λ g of 5 µm, 10 µm, 15 µm, 20 µm, and 25 µm; 50% fill-factor, protein height d g , and the BSA refractive index n p of 1.4, as depicted in Fig. 2(a); the protein grating was deposited on a 50 nm uniform gold layer. It will be shown in the result section later that the non-interferometric microscope and the scanning confocal SPR microscope can perform a low crosstalk measurement when the sample size is at least 12.5 µm corresponding to a 25 µm grating period and 5 µm corresponding to a 10 µm grating period, respectively. Therefore the chosen grating periods are the optimal range to explain and compare the performance of the two microscopes.
The modeled confocal SPR microscope consisted of a linearly polarized coherent source with the wavelength λ 0 of 633 nm, a 1.7NA oil immersion objective lens with the oil immersion index n 0 of 1.78, as shown in Fig. 2(a). A conjugate plane of the objective lens's back focal plane (BFP) was projected on an amplitude spatial light modulator and a phase spatial light modulator for amplitude pupil function modulation and phase stepping measurement.
Here the BFP was modeled by 651×651 pixels; the number of pixels can provide sufficient sampling of the SPR reflectance curves, the SPR dips, and phase transitions for all the samples in this study. This study investigated two polarization directions: the x-polarization and the y-polarization, which defined the electric field direction relative to the grating stripes, as shown in Fig. 1(a)-(b). Their corresponding wave-vectors were then assigned to each pixel in the BFP array along the x-axis k x , the y-axis k y , and the z-axis k z , representing plane waves at the exit pupil of the objective lens illuminating the sample. The maximum k x and k y that the objective lens can accommodate are 2πNA/λ 0 and the k z can be calculated by the relationship for each position in the BFP array, as depicted in Fig. 3. Then each position on the BFP can then be converted to an incident plane wave for RCWA calculation. The RCWA calculation defines the incident plane wave direction by the incident angle θ 0 azimuthal angle ϕ and the polarization angle φ. The θ 0 can be related to k x and k y by sin −1 Fig. 3(a). For the x-polarization, the φ is identical to ϕ; whereas, for the y-polarization, the φ has an additional offset of π/2 rad accounting for 90 degrees difference in the incident electric field direction. The RCWA computations with 271 diffraction orders were then calculated for each incident plane wave defined by the parameters θ 0 , ϕ, and φ; 423,801 RCWA calculations correspond to each array position in the BFP array. It is crucial to point out that the RCWA accuracy and  convergence depend on the number of diffraction orders included in the computation. The 271 diffracted orders can provide accurate and convergent results with numerical stability of 7.17×10 −8 ; the convergence tests for extreme cases in the study are discussed and reported in the Supplement 1. The RCWA computes the complex reflected electric fields for s-polarization E s,m and complex reflected magnetic fields for p-polarization H p,m for each diffraction order, where m is the m th diffraction order. The E s,m and H p,m fields were then stored in a 651×651×271 pixels array in which the 3 rd dimension stored each of the diffracted orders, as depicted in Fig. 3(b).
The objective lens can collect some reflected diffraction orders depending on the diffraction angles and the NA. The wave-vectors along the x-axis for each diffracted orders k x,m can be computed using the Floquet equation as expressed in Eq. (1) [42]. For these 1D grating samples, there were the diffracted orders along the x-axis k x,m only, as depicted in Fig. 3(b); therefore, for this study, the wave vector along the y-axis of the reflected beam remained k y . The wave-vectors for each diffracted order along the z-axis k z,m can also be determined as expressed in Eq. (2).
The diffracted angles θ 0,m can be determined from the sin −1 Only the diffraction angles within the NA of the objective lens and non-imaginary k z,m (propagating waves) can be collected by the objective lens as depicted in Fig. 3(a).
The collected reflected magnetic field BFPs H p,m (k x,m , k y ) and the reflection electric field E s,m (k x,m , k y ) were then converted back to the rectangular coordinate system using Equations (3) to (4) for the electric field component along the x-axis and the y-axis, respectively, as shown in Fig. 4(a).
where ϕ m is given by tan −1 (︂ k y k x,m )︂ .  Each diffraction order was then multiplied by a smooth BFP amplitude pupil function P(k x , k y ) as shown in Fig. 4(b); this can be modulated using an amplitude SLM. The design and detailed analysis of the amplitude pupil function is reported in the Supplement 1. The V(z) ripple for any x and z position can be calculated using Eq. (5).

Comparative performance parameters
Here, the following microscope imaging performance parameters were defined using the definitions as in Tontarawongsa et al. [23] to compare the confocal V(z) microscope's capability to non-interferometric SPR microscopes.
(1) 10-90% resolution (Res 10−90% ) is the spatial distance that has the image intensity between 0.1 to 0.9 of a normalized image transition between the two materials of the grating when the image was normalized to 0 to 1 intensity level, as depicted in Fig. 5(a).
(2) Contrast (C) is computed by taking the image intensity difference between the two centers of grating samples of any images divided by their maximum intensity value as depicted in Fig. 5(b).
(3) Sensitivity (S) calculated for the quantitative imaging mode is defined as the difference in plasmonic wave vectors at the two centers of the grating sample over product between the refractive index difference and the grating thickness as expressed in Eq. (6) and depicted in Fig. 5(c). S = k sp,BSA grating − k sp,water grating (n g − n w )d g    show the V(x,z) images of the five grating samples for the x-polarization and the y-polarization, respectively, when each V(x,z) image was normalized with its maximum intensity value for the optical contrast calculation as shown in Fig. 5(b). At the focal plane z of 0 µm, there was virtually no contrast for the two regions. The two materials' V(z) curves had a slightly different ripple period of 480 nm and 440 nm for the water and protein regions. The difference in the ripple period gave rise to the imaging contrast mechanism of the microscope when the sample was defocused along the optical axis. The highest optical contrast was at the z defocus of -1.2 µm and later degraded when the sample was defocused to the negative defocus side. Figure 7(a) shows V(z) curves corresponding to the two centers of grating materials for the 25 µm grating sample for the x-polarization case. Fig.7b-c shows the image contrast between the two centers of the five grating samples for the x-polarization and the y-polarization, respectively. The microscope can also provide contrast reversal images corresponding to the negative contrast values. The z defocuses with a decent contrast were at -5.92 µm, -5.68 µm,   Fig. 6. The microscope cannot resolve the 5 µm grating, especially for the x-polarization. The y-polarization performed better than the x-polarization for all grating samples, similar to the non-interferometric results extracted from Tontarawongsa et al. [23], highlighted in a star symbol '⋆' in Fig. 7(b)-(e). A more detailed table for all the grating periods can be found in Table S1 in the Supplement 1. The spatial resolution degraded when the sample was negatively defocused beyond -1.64 µm.     non-interferometric microscope, the scanning confocal SPR microscope resolution was better than the non-interferometric microscope by 2.28 times and 2.43 times for the x-polarization and y-polarization, respectively, when the z defocus was within -3 µm. Moreover, the optical contrast of the scanning confocal microscope was significantly higher than the non-interferometric microscope by 8.20 times for the x-polarization and 7.02 times for the y-polarization.

Quantitative imaging performance
The quantitative phase imaging was computed by computing the V(x,z) images employing the phase stepping as depicted in Fig. 2(c). to work out the relative phase ψ(x,z) between the 'SP' and the 'Ref' beams using phase stepping relationship [35] Figure 8(a). shows the ψ(z) phases of the two uniform cases. The gradient of the ψ(z) phase for the uniform BSA case shown in solid blue is slightly higher than the bare gold case shown in solid red. The local phase gradient of the relative phase dψ(x,z)/dz allows us to work out the plasmonic wave vector k sp (x,z) contour corresponding to each spatial pixel in the image from θ sp (x,z) using Eq. (9) and shown in Fig. 8(b).
There are two types of operating z defocus ranges, which were (1) from z of -6 µm to -2 µm and (2) z of -1.1 µm. The nature of the two operating ranges differed due to the different contrast of the recovered k sp between the two samples ∆k sp , as shown in Fig. 8(b). The z defocus range of -6 µm to -2 µm can accurately measure the plasmonic angle, whereas the z of around -1.1 µm can enhance sensitivity and contrast due to the interference of the defocused BFP. The following section quantifies the two operating ranges. The recovered k sp values for the bare gold and the uniform BSA were 14.22 rad/µm and 14.31 rad/µm at z of -4 µm, respectively.       Figure 9(a)-(e). and Fig. 9(f)-(j). show the recovered k sp (x, z) of the five grating samples for the x-polarization and the y-polarization, respectively. The z defocus with the highest k sp contrast between the two centers of the gratings was different depending on the grating period, which was z of -2.72 µm (2ztanθ sp of 7.63 µm) for λ g of 5 µm, which was the first z defocus operating position before the region with no optical contrast as depicted in Fig. 9; z of -3.76 µm (2ztanθ sp of 10.54 µm) for all the other grating periods. Thus, the z defocuses with the defocused optical beam size more expansive than the grating stripes yielded blurry images. The y-polarization had better contrast and spatial resolution than the x-polarization, summarized in Fig. 11.  show the k sp (x,z) for the z defocus around -1.1 µm. The operating position can enhance the optical contrast, in other words, the sensitivity by 5.46 times and 5.61 times for 25 µm grating period with the x-polarization and the y-polarization, respectively, compared to the operating z defocuses between -6 µm to -2 µm, as shown in Fig.11a and Fig.11c. The z defocus position did provide the additional sensitivity and the spatial resolution by 2.4 times compared to the z defocus of -2 µm, as shown in Fig.11b for the x-polarization and Fig.11d for the y-polarization. It is essential to point out that the operating position is not applicable for absolute k sp value measurement; it, however, is a strong candidate for relative k sp measurement with enhanced sensitivity. The two operating ranges can be summarized in terms of their performance in the spatial resolution, as shown in Fig.11a, sensitivity in which directly proportional to the optical contrast in Fig.11b, and measurement crosstalk at the protein region and the water region in Fig.11c-d in comparison to non-interferometric SPR response extracted from Tontarawongsa et al. [23]. Table S2 and Fig S3 in the Supplement 1 provide a detailed analysis of the microscope's performance parameters for the quantitative imaging mode of the two operating ranges compared to the non-interferometric microscope. For the spatial resolution, the z of -1.1 µm provided a consistent performance regardless of the sample size with the spatial resolution of 2.85 µm and 1.75 µm for the x-polarization and the y-polarization, respectively. The resolution degraded as the sample size increased for the other z operating points for the scanning confocal SPR and the non-interferometric SPR microscopes. For the 25 µm grating, the scanning confocal SPR microscope had a worse spatial resolution for the x-polarization and a slightly better resolution for the y-polarization when compared to the non-interferometric microscope. The z of -1.1 µm can enhance sensitivity performance by 7.8 times for the x-polarization and 5.7 times for the y-polarization compared to the non-interferometric microscope and the other z operating points. The z operating positions other than the z of -1.1 µm had a similar sensitivity to the non-interferometric microscope. Fig.11c-d shows one of the critical advantages of the scanning confocal SPR microscope, which has a superior crosstalk performance for both polarizations. At z of -1.1 µm, the scanning confocal SPR microscope can provide a low crosstalk measurement for the 10 µm grating period (5 µm protein size) in contrast to the non-interferometric microscope, which requires the grating sample with the size of at least 25 µm (12.5 µm protein size) and the y-polarization for the crosstalk of 0.05. Having discussed that although the z of -1.1 µm can provide a measurement enhancement; it is not a feasible operating position for measuring absolute plasmonic angle since the recovered k sp differed from the two uniform cases. However, the operating position is a strong candidate for measuring relative k sp . The scanning confocal SPR microscope did not show a classic trade-off between sensitivity and resolution [12], unlike the non-interferometric SPR microscope.
For the other z operating positions, the crosstalk performance degraded as the sample defocused further away. For z of -3 µm, the x-polarization was worse than the y-polarization in terms of crosstalk. For the 20 µm grating, the scanning confocal SPR had lower crosstalk than the non-interferometric microscope for both polarizations. The y-polarization with the 15 (7.5 µm protein size) µm sample size can provide low crosstalk of 0.05. Table 1 summarizes the key findings in this study compared to the non-interferometric microscope performance reported in Tontarawongsa et al. [23] for the non-quantitative and quantitative imaging modes.

Effect of fill factor
In this section, the effect of the fill factor is investigated. The fill factor for the 25 µm grating period sample was varied from 0.1 to 0.9 to test the performance of y-polarization at z of -1.2 µm, as shown in Table 2. The measurement crosstalk depends on the actual width of the protein channel. Note that the S parameter depends on the measurement accuracy of both the uncoated and the coated regions. For the higher fill factor, the accuracy of the protein measurement increased; on the other hand, it decreased in the water region leading to the unbalanced accuracy between the two regions. The highest S was at the 50% fill factor and degraded for the other fill factors due to the measurement accuracy tradeoff between the two regions. The fill-factor did not affect the spatial resolution like in the varying grating period case discussed earlier. For biological measurements, the measurement accuracy in the active binding site region or the protein region is more crucial than the gap region or the water region. The higher fill factor allows us to reduce the grating period further without losing the measurement accuracy in the sensing region.
The analysis enables us to determine a proper SPR sample size for an accurate quantitative SPR measurement, and the recommended sizes of liquid flow channel or active site for high throughput microscopic measurements [43][44][45] are 5 µm, 7.5 µm for the confocal SPR microscope for the two z operating ranges with the y-polarization, whereas a significantly larger size of 12.5 µm for the non-interferometric microscope. Therefore, the number of measurement channels for multiple binding sites or high throughput screening included in each type of microscope differs. For example, a 100x microscope objective with its field of view of 200 µm can incorporate 13 Table 1. Summarizes the key findings in this study comparing the performance of the confocal scanning SPR microscope and the non-interferometric microscope for the non-quantitative and quantitative imaging modes.
x-polarization λg (µm) to 20 parallel flow channels for channels with 50% fill factor under the confocal scanning SPR microscope, whereas the field of view can only accommodate 4 flow channels to perform an accurate SPR measurement.

Conclusions
The rigorous coupled-wave analysis was applied to analyze the sensing and imaging performance of the scanning confocal SPR microscope. The scanning confocal SPR microscope operates by defocusing the sample towards the objective lens. The reradiated surface plasmons and the embedded reference beam form a V(z) interference signal inside the confocal pinhole, allowing a well-defined path for surface plasmon propagation. We analyzed both non-quantitative and quantitative imaging modes and compared them to the annulus aperture scanning SPR microscope.
For the non-quantitative imaging, the scanning confocal SPR microscope performed better than the non-interferometric microscope by 2.43 times and 7.02 times in terms of spatial resolution and image contrast for the y-polarization, respectively. There were two regimes of operating points for the quantitative imaging: z of -1.1 µm, where there was still a strong influence of the reference beam, and the z of -6 µm to -2 µm. For the z of -1.1 µm, the confocal microscope can enhance the spatial resolution by 2.42 times, sensitivity by 5.68 times, and crosstalk by 7.95 times compared to the non-interferometric microscope. For the -6 µm to -2 µm, the performance of the confocal SPR microscope degraded at a larger z defocus. At z of -3 µm, the sensitivity and resolution of the confocal SPR microscope were similar to the non-interferometric microscope; however, the crosstalk performance of the confocal SPR microscope was better than the angular scanning SPR microscope. The recommended optical setup for scanning confocal SPR microscope is the y-polarization with the flow channel and the molecular active site of 5 µm to 7.5 µm, which is around two times smaller than the size recommended of 12.5 µm in the intensity-based SPR microscope.