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Abstract
In a total internal reflection fluorescence microscope, there is a 3D anisotropy in intensity of the excitation light. Using a mirror in a prism-based total internal reflection fluorescence microscope, we propose a very low-cost method to decrease the anisotropic property of the excitation light. Theoretically, we obtained the electric field of the transmitted light inside the sample as a function of the rotational angle of the mirror, polarization degree of the incident beam, and the refractive indices of the prism, immersion oil, cover glass, and sample. By using the refractive indices that are commercially available, proper practical combinations of the angle of mirror and polarization degree of the incident light are suggested to provide a merely 2D isotropic excitation light at the sample plane of a total internal reflection fluorescence microscope.
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1. Introduction
Total-internal-reflection-fluorescence (TIRF) microscopy is a powerful technique to investigate phenomena at the sub-diffracting axial distance of the sample-substrate interface [1–5]. In this method of microscopy, the incident angle of the illuminated light at the interface of sample and cover glass is greater than the critical angle and because of that a 2D propagating wave (inside the sample plane), and an evanescent wave (perpendicular to the sample plane) that does not propagate deeper than the penetration depth and excite fluorophore molecules [1–11]. Combination of a propagating wave and an evanescent wave provide an excitation light, which suffers of inequality in intensity along different directions [12] and causes a complexity in using of emission of fluorophore molecules in a quantitative study [2,13–17], where a sample typically contains a population of oriented fluorophore molecules, and investigating the density [18–20], the molecular orientation of single-molecules in 3D [6,17,21,22], and dynamic of single-molecules [21–31] are in interest.
A polarized light can excite those fluorophore molecules whose transition dipole moments (TDM) sufficiently overlap of a component of the excitation light (without perfect parallel alignment). Non-uniformity in the excitation electric field changes the probability of exciting individual molecules and consequently, this can lead to misinterpretation of the brightness in image processing of an image that is taken by a TIRF microscope [32].
Different solutions to increase the uniformity of the excitation field at the interface of the cover glass and sample have been proposed in a TIRF microscope like employing a flat-top TIR illumination [17], elliptical mirror [33] or by scanning the position of the focused light in the back focal plane of an objective based TIRFM [34–36]. Here, we suggest a very low-cost method of using a mirror at a specific angle regarding the polarization degree of the incident light. By using the refractive indices that are commercially available, we propose the proper angles of the mirror and polarization degree of the incident beam to have a 2D uniformity in the intensity of the excitation light at the interface of sample-substrate for two types of living and nonliving samples.
2. Theoretical approach
To manipulate the intensity of the excitation field in a typical upright prism-based TIRFM setup (see Fig. 1(a)), we start by assuming that the sample is in the $x-y$ plane and the two dielectric layers of oil immersion and cover glass are sandwiched between the sample and prism in the Cartesian coordinate system ($x,y,z$). The dielectric layers are semi-finite, nonmagnetic, optically isotropic and homogeneous media. The TIR occurs at the cover glass-sample interface, depending on the incidence angles of the beam regarding the prism-oil immersion ($\theta _{p}$), oil immersion-cover glass ($\theta _{o}$) and cover glass-sample ($\theta _{g}$) interfaces, as shown in Fig. 1(a). The incident beam (see Fig. 1(b)) propagates along the $x$-direction as:
where the beam is polarized in the $y-z$ plane, with an arbitrary angle, $\alpha$, regarding the $y$-axis ($0-90 ^{\circ }$; $E_{0y} \neq E_{0z}$). Therefore, the electric field of the incident beam is decomposed into $y$ and $z$ components as follows: where $E_{0y} = E_{0} \cos \alpha$ and $E_{0z} = E_{0}\sin \alpha$. Depending on the refractive indices and incident angles, if the beam’s incident angle at the cover glass-sample surface is larger than the critical angle, the TIR occurs at the cover glass-sample interface. We are interested in this condition. When the TIR occurs, the light beam in the sample will have three components along the $x$, $y$, and $z$ directions. The components along the $x$, $y$ directions are propagating waves, while the component along the $z$ direction is an evanescent wave. Fluorophore molecules located at the penetrated volume (the confined volume between $x-y$ plane and the penetration depth of the EW along the $z$-direction) are not excited uniformly. Those fluorophore molecules whose TDM have a component along the $z$-direction, are not excited uniformly since the EW has an exponential pattern along the $z$-direction (perpendicular to the sample plane) [12]. In addition, this anisotropy is held even at the sample’s surface (not inside the penetration depth). The anisotropy in intensity of the light beam at the surface of the sample happens even when the incident light has an equal polarization along $y$-axis and $z$-axis ($E_{0y}=E_{0z}$; $\alpha =45^{\circ }$) [12].
Fig. 1. a) Representation of the light path in an upright prism-based TIRF microscope, where $\theta _{a}$, $\theta _{p}$, $\theta _{o}$, and $\theta _{g}$ denote the incident angles of the beam regarding the air-prism, prism-oil immersion, oil immersion-cover glass, and cover glass-sample interfaces. b) The incident beam with polarization in the $y-z$ plane (an arbitrary angle, $\alpha$) propagates along the $x$-direction.
We obtain the three components of the excitation light in the sample plane, based on the degree of polarization of the incident beam, $\alpha$, and the incident angle at prism-oil immersion interface, $\theta _{p}$, using the Fresnel’s coefficients as [12,37]:
The anisotropy in the electric field across the sample surface is important, if the TIRF microscope is used to quantify single molecules. Here, we are interested in finding a method to decrease the anisotropy in intensity along the $y$ and $z$-directions. Our approach, as is shown in Fig. 1(b), is applying a mirror at a specific angle, $\gamma$, regarding the $x$-axis. For simplicity, we assume that the reflection coefficient of the mirror is ignorable and therefore, the mirror rotates the $z$-component of the incident electric field ($E_{0z}$) with an angle $2\gamma$ relative to $z$-axis. Meanwhile, the perpendicular component of the electric field on the incident plane, which is aligned with the $y$-axis, is reflected by the mirror without changing polarization (or changing the phase by $180^{\circ }$). Based on the geometry of our method, the incident angle of the beam from air to prism would be:
Therefore, the incident angle of the beam from prism to oil immersion medium, $\theta _p$, as a function of mirror’s angle is:
By using Snell’s law, all the other incident angles are written based on the mirror’s angle since:
We rewrite the angles $\theta _g$, $\theta _o$, and $\theta _s$ as a function of the geometrical configuration of the mirror, $\gamma$. Hence, Eqs. (3)–(5) as a function of the geometrical configuration of mirror, $\gamma$, are changed accordingly as:
and where $I_0$ is the intensity of the incident beam and $T_x(\gamma )$, $T_y(\gamma )$, and $T_z(\gamma )$, are in term of mirror’s angle, $\gamma$. We continue by evaluating the anisotropy in the polarized intensity along $x$ and $y$-directions ($I_{x}/I_{y}$; the sample plane) and $y$ and $z$-directions ($I_{y}/I_{z}$; perpendicular plane regarding the sample plane) as: and investigate whether it would be possible to find a condition that anisotropy approaches zero by approaching $I_{x}/I_{y}$ to unity, which only holds if:We repeat the same analysis by approaching $I_{y}/I_{z}$ to unity, which only holds if:
Therefore, the transition from anisotropy to 2D isotropy in the excitation light -either at the sample surface or perpendicular to the sample surface- can be done by fixing the polarization of the incident beam, $\alpha$, and then adjusting the angle of the mirror, $\gamma$, or fixing the mirror’s angle and tuning the polarization of the incident beam. In the next section, we investigate the applicability of two approaches from experimental point of view.
3. Analytical approach
In the previous section, the dependency between the polarized intensity of the excitation light in the sample medium, ($I_{x},I_{y},I_{z}$), the polarization degree of the incident beam, $\alpha$, and the rotational angle of the mirror, $\gamma$ was investigated. In this section, we are interested in studying the idea of using a mirror from experimental point of view and see which one is more practical: fixing the polarization of the incident beam, $\alpha$, and then adjusting the angle of the mirror, $\gamma$, or fixing the mirror’s angle and tuning the polarization of the incident beam.
As an example, we start with the condition that the polarization degree of the incident beam, $\alpha$, is fixed at $\alpha = 45^{\circ }$, where $E_{0y}=E_{0z}$, and see what would be the possible variation range in the angle of the mirror, $\gamma$. By using the refractive indices from Table 1 in Eqs. (3)–(5), the polarized intensity of the excitation light in the sample medium, $n_{s}=1.33$ (an aqueous medium as a non-living sample) and , $n_{s}=1.38$ (a living sample), along $x$, $y$, and $z$-directions, vs. the mirror’s angle, $\gamma$, are shown in Fig. 2, where the refractive indices of the cover glass are $n_{g}=\{1.46, 1.52\}$ and the apex angle of the prism $\epsilon$, is $60{^{o}}$. Four curves with the oil immersion, $n_{o}=1.48$ (see Table 1) are plotted by dashed lines (different dashes), and four other curves with the oil immersion, $n_{o}=1.5$ (see Table 1) are plotted by markers (different markers). The polarized intensity of $I_{x}$, $I_{y}$, $I_{z}$, and the intensity ratio of $I_{x}/I_{y}$ and $I_{y}/I_{z}$ vs. the angle of the mirror, $\gamma$, are shown in Fig. 2(a)-(c), and Fig. 3(a),(b), respectively. The polarized intensity along the $x$-direction, $I_{x}$, (see Fig. 2(a)) reaches its minimum at the critical angle [12,13,16], which is correspondent to the mirror’s angle, $\gamma$, less than $5-10^{\circ }$, and starts to increase by increasing the supercritical angle. The amplitude of the component along $x$-direction, $E_{x}$, is coupled to the amplitude of the excitation light in the $z$-direction, and the “primary" polarization state of the incident light does not hold at the TIR condition. As a result, the confined light in the penetrated volume (inside the sample) suffers from an anisotropy in the intensity of the excitation light in three dimensions (compare the vertical axes in three panels of Fig. 2). From Fig. 3(b), where when $\alpha = 45^{\circ }$, the mirror’s angle, $\gamma$, should be less than $5-10^{\circ }$ to be able to decrease the 2D anisotropy along $y$, and $z$-directions. In general, the typical mirror’s angle should be tuned at a small angle regarding the horizontal direction in the laboratory frame (the $x$-axis) and in an experiment is not an easy task. Therefore, we ignore the idea of tuning the mirror in a prism-based TIRF microscope, $\gamma$, for a specific polarization degree of the incident beam, $\alpha$. Instead, we move to the other method of fixing an angle for the mirror, then tuning the polarization degree of the incident beam, $\alpha$ with a polarizer, for example.
Fig. 2. The polarized intensity in the sample medium along a) $x$-direction, $I_{x}$, b) $y$-direction, $I_{y}$, and c) $z$-direction, $I_{z}$. vs. the rotational angle of the mirror, $\gamma$, in the presence of sample, cover-glass, and oil immersion with different refractive indices, as are listed in Table 1. The polarization degree of the incident beam, $\alpha$, is fixed at $\alpha = 45^{\circ }$ ($E_{0y}=E_{0z}$) and at this condition, the polarized intensity along the $x$-direction, $I_{x}$, reaches its minimum, when the mirror’s angle is less than $10^{\circ }$. The apex angle of the prism $\epsilon$, the refractive index of air, $n_{a}$, prism, $n_{p}$, oil immersion, $n_{o}$, cover-glass, $n_{g}$, and sample, $n_{s}$, are $(\epsilon,n_{a},n_{p})=(60{^{o}},1,1.43)$, $n_{s}=\{1.33, 1.38\}$, $n_{o}=\{1.48,1.5\}$, and $n_{g}=\{1.46, 1.52\}$, respectively. Dashed lines and markers represent the data with $n_{o}=1.48$, and $n_{o}=1.5$, respectively.
Fig. 3. a,b) The intensity ratio of $I_{x}/I_{y}$ and $I_{y}/I_{z}$ in the sample medium vs. the mirror’s angle, $\gamma$, of data in Fig. 2, which are a measure of anisotropy in the intensity of the transmitted light at the interface in a TIRF microscope, where the polarization degree of the incident beam, $\alpha$, is fixed at $\alpha = 45^{\circ }$ ($E_{0y}=E_{0z}$). c,e) The possible combinations of the mirror’s angle and the degree of polarization of the incident beam, $\alpha$, which holds c) $I_{x}/I_{y}=1$ (Eq. (14)), or e) $I_{y}/I_{z}=1$ (Eq. (15)). d) The intensity ratio of the excitation light at the sample and cover glass interface, $I_{x}/I_{y}$, vs. the degree of polarization of the incident beam, where the angle of mirror, $\gamma$, is assumed $4^{\circ }$ (using panel (c) to hold $I_{x}/I_{y}=1$; see the inset curve.). f) The intensity ratio of the excitation light at the sample and cover glass interface, $I_{y}/I_{z}$, vs. the degree of polarization of the incident beam, where the angle of mirror, $\gamma$, is assumed $4^{\circ }$ (using panel (e) to hold $I_{y}/I_{z}=1$; see the inset curve.). The apex angle of the prism $\epsilon$, the refractive index of air, $n_{a}$, prism, $n_{p}$, oil immersion, $n_{o}$, cover glass, $n_{g}$, and sample, $n_{s}$, are as $(\epsilon,n_{a},n_{p})=(60{^{o}},1,1.43)$, $n_{s}=\{1.33, 1.38\}$, $n_{o}=\{1.48,1.5\}$, and $n_{g}=\{1.46, 1.52\}$, respectively. Dashed lines and markers represent the data with $n_{o}=1.48$, and $n_{o}=1.5$, respectively.
Table 1. Refractive indices of the prism, $n_{p}$, oil immersion, $n_{o}$, cover glass, $n_{g}$, and sample, $n_{s}$, at 500 nm wavelength [12].
By setting up a mirror and manipulating the mirror’s angle and polarization degrees of the incident beam, we are interested in the condition that the intensity ratio of $I_{x}/I_{y}$ and $I_{y}/I_{z}$ would approach unity. We start with an incident beam with an arbitrary polarization degree, $\alpha$, and plot the possible combinations of the mirror’s angle and the degree of polarization of the incident beam, $\alpha$, (Eq. (15)), while the anisotropy of the excited light in the sample plane approaches zero by approaching $I_{x}/I_{y}$ to unity. Depending on the refractive indices of a sample, if one chooses a proper combination of a prism, a cover glass, and an oil immersion, then proper (or desired) polarization of the incident beam would be selected from the curve in Fig. 3(c), in the manner that $I_{x}/I_{y}=1$. Figure 3(d) shows the intensity ratio of $I_{x}/I_{y}$ in the sample plane if the mirror’s angle, $\gamma$, is assumed $4^{\circ }$. The inset curve in Fig. 3(d), clearly shows the isotropy in the excitation light at the sample plane for different combinations of optical elements and samples.
We can repeat the similar approach and plot variation of the degree of polarization of the incident beam, $\alpha$ vs. the mirror’s angle $\gamma$ (Eq. (15)), while the anisotropy of the excited light in the vertical plane (regarding the sample plane) approaches zero by approaching $I_{y}/I_{z}$ to unity. Again, depending on the refractive indices of a sample, if one chooses a proper combination of a prism, a cover glass, and an oil immersion, then proper polarization of the incident beam would be selected from the curve in Fig. 3(e), in the manner that $I_{y}/I_{z}=1$. Figure 3(f) shows the intensity ratio of $I_{y}/I_{z}$ in the sample plane if the mirror’s angle, $\gamma$, is assumed $4^{\circ }$. The inset curve in Fig. 3(f), clearly shows the 2D isotropy in the excitation light in the prependicular plane (regarding the sample plane) for different combinations of optical elements and samples.
At the experimental condition that the intensity along $x$ and $y$ directions inside the sample (or $y$ and $z$ directions perpendicular to the sample plane) are getting equal, the probability of exciting a fluorophore molecule in 2D along the $x$ and $y$ directions (at the sample surface and not penetrated volume) would be identical, and this would help using the brightness of emitted fluorescence in a quantitative study and have less complexity in image analysis. Based on our findings, this can be done either by fixing the polarization of the incident beam, $\alpha$, and then tuning the angle of the mirror, $\gamma$, or fixing the angle of the mirror and tuning the polarization of the incident beam, which the latter on is the easiest method.
4. Conclusion
Illuminating samples in a TIRF microscope is a combination of a propagating wave (at the sample surface in 2D) and an evanescent wave (perpendicular to the sample surface), which does not propagate deeper than the subdiffraction-penetration depth inside the sample. There is a known inequality in the intensity of the propagating wave and the evanescent wave, which leads to an unequal probability of excitation of fluorophore molecules. Here, by fixing a mirror at a specific angle and manipulating with the polarization degree of the incident beam, we propose a simple but effective method to convert the 3D anisotropy in the intensity of the illuminated light to a 2D isotropic light either at the sample plane or perpendicular to the sample plane.
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. D. Axelrod, “Cell-substrate contacts illuminated by total internal reflection fluorescence,” J. Cell Biology 89(1), 141–145 (1981). [CrossRef]
2. B. P. Olveczky, N. Periasamy, and A. Verkman, “Mapping fluorophore distributions in three dimensions by quantitative multiple angle-total internal reflection fluorescence microscopy,” Biophys. J. 73(5), 2836–2847 (1997). [CrossRef]
3. D. Axelrod, “Total internal reflection fluorescence microscopy in cell biology,” Traffic 2(11), 764–774 (2001). [CrossRef]
4. D. Axelrod, E. H. Hellen, and R. M. Fulbright, “Total internal reflection fluorescence,” in Topics in Fluorescence Spectroscopy, vol. 3 (Springer, 2002), pp. 289–343.
5. D. Axelrod, Total Internal Reflection Fluorescence Microscopy, 1st ed., vol. 89 (Elsevier, 2008).
6. D. Axelrod, “Evanescent excitation and emission in fluorescence microscopy,” Biophys. J. 104(7), 1401–1409 (2013). [CrossRef]
7. M. Milosevic, “On the nature of the evanescent wave,” Appl. Spectrosc. 67(2), 126–131 (2013). [CrossRef]
8. M. Martin-Fernandez, C. Tynan, and S. Webb, “A pocket guide to total internal reflection fluorescence,” J. Microsc. 252(1), 16–22 (2013). [CrossRef]
9. Y. Fu, P. W. Winter, R. Rojas, V. Wang, M. McAuliffe, and G. H. Patterson, “Axial superresolution via multiangle TIRF microscopy with sequential imaging and photobleaching,” Proc. Natl. Acad. Sci. 113(16), 4368–4373 (2016). [CrossRef]
10. S. Pendharker, S. Shende, W. Newman, S. Ogg, N. Nazemifard, and Z. Jacob, “Axial super-resolution evanescent wave tomography,” Opt. Lett. 41(23), 5499–5502 (2016). [CrossRef]
11. G. E. Cragg and P. T. C. So, “Lateral resolution enhancement with standing evanescent waves,” Opt. Lett. 25(1), 46–48 (2000). [CrossRef]
12. E. Sheykhi, B. Sajad, S. Tavaddod, H. Naderi-Manesh, and N. Roostaiei, “Tuning fluorophore excitation in a total-internal-reflection-fluorescence microscopy,” Appl. Opt. 58(29), 8055–8060 (2019). [CrossRef]
13. S. Wakelin and C. R. Bagshaw, “A prism combination for near isotropic fluorescence excitation by total internal reflection,” J. Microsc. 209(2), 143–148 (2003). [CrossRef]
14. S. L. Reck-Peterson, N. D. Derr, and N. Stuurman, “Imaging single molecules using total internal reflection fluorescence microscopy (TIRFM),” Cold Spring Harb. Protoc. 2010(3), pdb.top73 (2010). [CrossRef]
15. J. F. Beausang, Y. Sun, M. E. Quinlan, J. N. Forkey, and Y. E. Goldman, “The acquisition and analysis of polarized total internal reflection fluorescence microscopy (polTIRFM) data,” Cold Spring Harb. Protoc. 2012(6), pdb.prot069419 (2012). [CrossRef]
16. A. E. Knight, “Single-molecule fluorescence imaging by total internal reflection fluorescence microscopy (IUPAC technical report),” Pure Appl. Chem. 86(8), 1303–1320 (2014). [CrossRef]
17. F. Stehr, J. Stein, F. Schueder, P. Schwille, and R. Jungmann, “Flat-top TIRF illumination boosts DNA-PAINT imaging and quantification,” Nat. Commun. 10(1), 1268 (2019). [CrossRef]
18. D. Loerke, B. Preitz, W. Stuhmer, and M. Oheim, “Super-resolution measurements with evanescent-wave fluorescence-excitation using variable beam incidence,” J. Biomed. Opt. 5(1), 23–31 (2000). [CrossRef]
19. D. Loerke, W. Stühmer, and M. Oheim, “Quantifying axial secretory-granule motion with variable-angle evanescent-field excitation,” J. Neurosci. Methods 119(1), 65–73 (2002). [CrossRef]
20. E. Sheykhi, B. Shojaedin-Givi, B. Sajad, H. Naderi-Manesh, and S. Tavaddod, “Quantifying F-actin patches in single melanoma cells using total-internal reflection fluorescence microscopy,” Sci. Rep. 12(1), 19993 (2022). [CrossRef]
21. J. N. Forkey, M. E. Quinlan, and Y. E. Goldman, “Protein structural dynamics by single-molecule fluorescence polarization,” Biology at the Single Molecule Level, S. H. Leuba and J. Zlatanova, eds. Schliwa, ed. (Elsevier Science Ltd., 2001), pp. 1–36.
22. J. N. Forkey, M. E. Quinlan, and Y. E. Goldman, “Measurement of single macromolecule orientation by total internal reflection fluorescence polarization microscopy,” Biophys. J. 89(2), 1261–1271 (2005). [CrossRef]
23. D. Axelrod, T. P. Burghardt, and N. L. Thompson, “Total internal reflection fluorescence,” Annu. Rev. Biophys. Bioeng. 13(1), 247–268 (1984). [CrossRef]
24. N. L. Thompson, H. M. McConnell, T. P. Burhardt, and T. P. Burghardt, “Order in supported phospholipid monolayers detected by the dichroism of fluorescence excited with polarized evanescent illumination,” Biophys. J. 46(6), 739–747 (1984). [CrossRef]
25. S. E. Sund, J. A. Swanson, and D. Axelrod, “Cell membrane orientation visualized by polarized total internal reflection fluorescence,” Biophys. J. 77(4), 2266–2283 (1999). [CrossRef]
26. R. M. Dickson, D. J. Norris, and W. E. Moerner, “Simultaneous imaging of individual molecules aligned both parallel and perpendicular to the optic axis,” Phys. Rev. Lett. 81(24), 5322–5325 (1998). [CrossRef]
27. J. Oreopoulos and C. M. Yip, “Combinatorial microscopy for the study of protein–membrane interactions in supported lipid bilayers: order parameter measurements by combined polarized TIRFM/AFM,” J. Struct. Biol. 168(1), 21–36 (2009). [CrossRef]
28. A. Anantharam, D. Axelrod, and R. W. Holz, “Polarized TIRFM reveals changes in plasma membrane topology before and during granule fusion,” Cell. Mol. Neurobiol. 30(8), 1343–1349 (2010). [CrossRef]
29. V. Kiessling, M. K. Domanska, and L. K. Tamm, “Single snare-mediated vesicle fusion observed in vitro by polarized TIRFM,” Biophys. J. 99(12), 4047–4055 (2010). [CrossRef]
30. A. T. Ngo, Z. J. Jakubek, Z. Lu, B. Joós, C. E. Morris, and L. J. Johnston, “Membrane order parameters for interdigitated lipid bilayers measured via polarized total-internal-reflection fluorescence microscopy,” BBA - Biomembr. 1838(11), 2861–2869 (2014). [CrossRef]
31. A. Yildiz and R. D. Vale, “Total internal reflection fluorescence microscopy,” Cold Spring Harb. Protoc. 2015(9), pdb.top086348 (2015). [CrossRef]
32. J. C. Waters, “Accuracy and precision in quantitative fluorescence microscopy,” (2009).
33. J. Liu, Q. Li, M. Li, S. Gao, C. Liu, L. Zou, and J. Tan, “Elliptical mirror-based TIRF microscopy with shadowless illumination and adjustable penetration depth,” Opt. Lett. 42(13), 2587–2590 (2017). [CrossRef]
34. R. Fiolka, Y. Belyaev, H. Ewers, and A. Stemmer, “Even illumination in total internal reflection fluorescence microscopy using laser light,” Microsc. Res. Tech. 71(1), 45–50 (2008). [CrossRef]
35. D. S. Johnson, J. K. Jaiswal, and S. Simon, “Total internal reflection fluorescence (TIRF) microscopy illuminator for improved imaging of cell surface events,” Curr. Protoc. Cytom. 61(1), 12–29 (2012). [CrossRef]
36. D. S. Johnson, R. Toledo-Crow, A. L. Mattheyses, and S. M. Simon, “Polarization-controlled TIRFM with focal drift and spatial field intensity correction,” Biophys. J. 106(5), 1008–1019 (2014). [CrossRef]
37. M. Born and E. Wolf, Principles of Optics5th ed. (Pergamon, 1975).
