Image scanning microscopy with a long depth of focus generated by an annular radially polarized beam

Weibo Wang; Weibo Wang; Weibo Wang; Baoyuan Zhang; Baoyuan Zhang; Biwei Wu; Biwei Wu; Xiaojun Li; Xiaojun Li; Jie Ma; Jie Ma; Pengyu Sun; Pengyu Sun; Shenghao Zheng; Shenghao Zheng; Jiubin Tan; Jiubin Tan

doi:10.1364/OE.413292

1. Introduction

Confocal scanning microscopy (CSM) is the most widely used modern optical microscopy technique. It was known that the lateral resolution of CSM can be improved by decreasing the diameter of the confocal pinhole [1,2], and the extreme case of a pinhole that is almost completely closed would nearly double the resolution [3]. In that case, however, the passing rate of light is drastically reduced, and the resolution improvement of the microscope is usually at the cost of reducing the signal-to-noise ratio (SNR) [4]. Therefore, it is of great significance to seek a microscopic imaging method that can realize high resolution and high SNR simultaneously. In [3], Sheppard first proposed an elegant solution to enhance the spatial resolution of CSM by replacing the point detector with an array detector. Based on this approach, Müller et al. proposed the concept of image scanning microscopy (ISM) [5], in which each pixel of the array detector acts as an independent tiny pinhole in confocal microscope and records its own image [6,7]. Experiments show that ISM can achieve the theoretical maximum resolution of confocal microscope with high collection efficiency [8,9].

In ISM, the photomultiplier tube is replaced with a pixelated detector array to image the light emitted from different excitation locations while scanning the sample, so as to obtain the whole information in the space domain. However, this process makes the excitation volume limited to the focal region, and the high resolution result only presented in the thin image plane. To image the whole sample volume, a stack of images at different depths has to be acquired, which reduces the efficiency of the acquisition for volume samples.

Since the limitation of ISM in volume imaging is growing ever more important, new imaging solutions are urgently needed. As with other microscopic imaging systems, the modulated beam can affect the nature of the focal point [10–13], thus improving the imaging result in ISM. In the various optical beam modes reported, the annular radially polarized beams have attracted much attention due to their unique possibilities of generating smaller spot and longer depth of focus [14–16]. If the depth of focus could be extended in axial direction while maintaining a smaller focus of high quality, the deeper interaction between the light field and the sample will be realized in ISM.

In this paper, we propose a method combining the annular aperture with standard ISM setup to generate strong longitudinally polarized beam with an axially extended excitation focus and tighter focused spot. An excitation focus with axially extended is scanned laterally in two dimensions to obtain a projected view of the volume specimen, which is defined by the axial extent of the focus and the scanning area. We first demonstrate a theoretical model of ISM with annular radially polarized beam (ISM-aRP) based on the confocal imaging principle and vectorial diffraction theory. Then, the improvement of spatial resolution and the extension of the depth of focus are evaluated by imaging the simulated lattice array sample, the hippocampal neurons specimen (Claudius Griesinger, Wellcome Images, London, UK) and the fluorescent beads suspension.

2. Method

2.1 Image formation in ISM with radially polarized beam

In contrast to a conventional CSM, which adopts a point detector, ISM images the fluorescence light onto a position-sensitive array detector. Every pixel of the array detector can be regarded as an individual confocal pinhole, acquiring an independent confocal image when a scan is performed. In this section, we derive the generalized expression for the vectorial electric field in the focal region of ISM illuminated by radially polarized beam, and illustrate the nature of ISM to enhance the resolution. Figure 1 shows the model of the illuminating and the detecting optical systems of radially polarized beam focused by a high numerical aperture (NA) objective.

Fig. 1. (a) Schematic sketch of the focusing of a radially polarized beam. The radially polarized beam produces electric fields with longitudinal component Ez and radial component Eρ. (b) Schematic diagram of the detection system. SP: specimen plane, OL: objective lens, DL: detector lens, DP: detector plane.

Download Full Size | PDF

According to the theory of vector Debye integral [17], the electric field components of radially polarized beam are expressed in cylindrical coordinates (ρ,φ,z), where the beam propagates along the positive z-direction and z=0 at the focal plane, as shown in Fig. 1(a). For a pupil illuminated by radially polarized light, the electric fields near focus then have the following form [18]

(1)$${E_{ill}} = \left[ {\begin{array}{c} {{E_\rho }}\\ {{E_\phi }}\\ {{E_z}} \end{array}} \right] = \left[ {\begin{array}{c} {A\int\limits_0^\alpha {{{\cos }^{\frac{1}{2}}}\theta \sin (2\theta ){l_0}(\theta ){J_{^1}}(k\rho \sin \theta ){e^{ikz\cos \theta }}d\theta } }\\ 0\\ {2iA\int\limits_0^\alpha {{{\cos }^{\frac{1}{2}}}\theta {{\sin }^2}\theta {l_0}(\theta ){J_{^0}}(k\rho \sin \theta ){e^{ikz\cos \theta }}d\theta } } \end{array}} \right].$$

where α is the maximum divergence angle of the objective and α = arcsin(NA/n₁), NA is the numerical aperture of the objective lens, and n₁ is the refractive index in the object space. J_n(x) denotes a Bessel function of the first kind, of order n. k is the wavenumber (k=2π/λ) and l₀(θ) describes the apodization function given in the following form

(2)$${l_0}(\theta ) = exp \left[ { - \beta_0^2{{(\frac{{\sin \theta }}{{\sin \alpha }})}^2}} \right]{J_1}\left( {2{\beta_0}\frac{{\sin \theta }}{{\sin \alpha }}} \right).$$

where β₀ is the ratio of the pupil radius and the beam waist, which we set at β₀ = 3/2. In this paper, we set NA to 1.2 and refractive index to 1.33 between the objective lens and the sample, the wavelength to 532 nm. The excitation point spread function (PSF_exc) can be expressed as

(3)$$PS{F_{exc}} = {|{{E_\rho }} |^2} + {|{{E_z}} |^2}.$$

The emission fluorescence is collected by an objective lens with high aperture and then imaged onto the detector, as shown in Fig. 1(b). The expression with Cartesian components for the electric field at the detector plane in the focal region is given as [19]

(4)$${E_{\det }} = \left[ {\begin{array}{c} {{E_{dx}}}\\ {{E_{dy}}}\\ {{E_{dz}}} \end{array}} \right] = \left[ {\begin{array}{c} {{p_x}K_0^\textrm{{I} } - 2i{p_z}K_1^\textrm{{I} }\cos {\phi_d} + K_2^\textrm{{I} }({p_x}\cos 2{\phi_d} + {p_y}\sin 2{\phi_d})}\\ {{p_y}K_0^\textrm{{I} } - 2i{p_z}K_1^\textrm{{I} }\cos {\phi_d} + K_2^\textrm{{I} }({p_x}\cos 2{\phi_d} - {p_y}\sin 2{\phi_d})}\\ {{p_z}K_0^\textrm{{II} } - iK_1^\textrm{{II} }({p_x}\cos {\phi_d} + {p_y}\sin {\phi_d})} \end{array}} \right].$$

where the K functions are given by

(5)$$K_n^{\textrm{{I} ,{II} }} = \int\limits_0^{{\alpha _2}} {(\cos {\theta _1})} \sin {\theta _2}O_n^{\textrm{{I} ,{II} }}{J_n}({k_d}{r_d}\sin {\theta _2}){e^{i{k_d}{z_d}\cos {\theta _2}}}d{\theta _2}.$$

and the O functions can be represented by

(6)$$\begin{array}{c} O_0^\textrm{{I} }\textrm{ = }1\textrm{ + }\cos {\theta _1}\cos {\theta _2}\\ O_1^\textrm{{I} }\textrm{ = sin}{\theta _1}\cos {\theta _2}\\ O_2^\textrm{{I} }\textrm{ = }1\textrm{ - }\cos {\theta _1}\cos {\theta _2}\\ O_0^\textrm{{II} }\textrm{ = }\sin {\theta _1}\sin {\theta _2}\\ O_1^\textrm{{II} }\textrm{ = }\cos {\theta _1}\sin {\theta _2} \end{array}$$

where (r_d,ϕ_d,z_d) is the position in the detector plane in cylindrical polar coordinates. k_d is the wave number in the detector plane. (p_x,p_y,p_z)^T are the Cartesian components of the electric dipole moment and they are calculated as in [17]. The angular aperture of the collimating objective lens is α₁, and the angular aperture of the detector lens is α₂. The relationship between the azimuthal angle θ₁ and the azimuthal angle θ₂ is

(7)$$\frac{{{n_1}\sin {\alpha _1}}}{{{n_d}\sin {\alpha _2}}} = \frac{{{n_1}\sin {\theta _1}}}{{{n_d}\sin {\theta _2}}} = \beta .$$

where β is the transverse magnification of the detector lens system, n_d is the refractive index of the detector plane, and we set them all to 1. Then, the detection point spread function (PSF_det) of this system can be expressed as follows

(8)$$PS{F_{\det }} = {|{{E_{dx}}} |^2} + {|{{E_{dy}}} |^2} + {|{{E_{dz}}} |^2}.$$

As for a photon emitted from a molecule at position r′ in the sample space and detected at position r on the point detector, the effective point spread function (PSF_eff) can be described as follow

(9)$$PS{F_{eff}}({\mathbf r},{\mathbf r^{\prime}},{\mathbf s}) = PS{F_{exc}}({\mathbf r} - {\mathbf r^{\prime}}) \times [{PS{F_{\det }}({\mathbf r} - {\mathbf r^{\prime}} + {\mathbf s}) \otimes p({\mathbf s})} ].$$

And the confocal image is given by

(10)$${I_{con}}({\mathbf r},{\mathbf s}) = S({\mathbf r^{\prime}}) \otimes PS{F_{eff}}({\mathbf r},{\mathbf r^{\prime}},{\mathbf s}).$$

where the function p(s) is the transmission function of the pinhole. “$\otimes$” denotes the 2D convolution operation. S(r′) is the intensity distribution of the analyzed sample.

The main difference between confocal microscope and ISM is the detector selection. In ISM, the final image produced by each excitation focus is recorded by a multi-pixels detector rather than a photomultiplier tube, and a stack of images are ultimately created to imitate a data stack collected during an ISM scan. To obtain the sharper image, the collected images need to be further processed, which is called “pixel reassignment”. The resolution of ISM coupled with pixel reassignment can be enhanced of times over the widefield microscope [20,21]. As shown in Fig. 2(a), the signals recorded at different pixel positions d in the detector plane gradually deviate with the increase of pixel positions, adding up these signals over the whole detector plane, a conventional image will be yielded, without resolution improvement. However, as shown in Fig. 2(b), shifting the off-axis signals to the midway between the excitation and detection maxima before adding them to the final image, a sharper signal can be generated [20]. Furthermore, the spatial resolution of ISM is improved to the same as the confocal microscope with nearly zero-size pinhole. Figure 2(c) and (d) are the normalized intensities of (a) and (b), respectively. Figure 2(e) depicts the principle of pixel reassignment from the perspective of the excitation PSF and the detection PSF in one-dimensional case. It can be seen that the distance between the excitation PSF and the detection PSF is p, with their respective axes as the center. Multiplying these two PSFs can yield an intermediate effective PSF of the imaging system which describes the scan image recorded by this single pixel [22]. Note that all the pixel positions are back-projected into sample space to achieve a better presentation. In this paper, we assume that there is no Stokes shift, and in order to make it more quantitative, we approximate the PSFs as Gaussian functions. The reassignment factor “o” of 1/2 is calculated by

(11)$$o = \frac{{\sigma _{exc}^2}}{{\sigma _{exc}^2 + \sigma _{\det }^2}} = {\left[ {1 + {{(\frac{{{\lambda_{\det }}}}{{{\lambda_{exc}}}})}^2}} \right]^{ - 1}}.$$

According to the above derivation, the super-resolution image of ISM with radially polarized beam can be constructed by summing the stack of multiple images which are reassigned to the half of the original distance from the excitation focus. This process can be expressed by

(12)$${I_{ISM}}({\mathbf r},{{\mathbf s}_{\mathbf i}}) = \sum\limits_{i = 0}^n {{I_{con}}({\mathbf r} - \frac{1}{2}{{\mathbf s}_{\mathbf i}},{{\mathbf s}_{\mathbf i}}{\mathbf )}} .$$

where s_i denotes the distance between the ith pixel and the optical axis. Since all the fluorescence light will be collected by the array detector during the whole stack process, ISM with radially polarized beam can achieve higher resolution without light losses.

Fig. 2. Schematic diagram explaining the principles of pixel reassignment. (a) PSF of the conventional confocal microscopy recorded at different detector element positions in the detector plane; (b) PSF of the conventional ISM with radially polarized beam recorded at different positions of detector elements in the detector plane; (c) Normalized intensities of (a). (d) Normalized intensities of (b). (e) The conception of pixel reassignment in one-dimensional case. The distance between PSF_exc (green curve) and PSF_det (blue curve) is p, with their respective axes as center. When neglecting the Stokes shift, PSF_eff (black curve) occurs at the distance of p/2 from the excitation focus.

Download Full Size | PDF

2.2 Extended depth of field

In the pursuit of the axially extended excitation focus, which is dominated by the longitudinal component, a binary optical element of an annular aperture is used to tailor the beam, as can be seen in Fig. 3(a). Figure 3(b) shows the schematic sketch of the focusing of a radially polarized beam with narrow annular. The total electric field of the radially polarized beam consists of the longitudinal component E_z and the radial component E_ρ, in which the longitudinal component can produce a strong intensity along the beam axis, while the direction of the radial component is perpendicular to the optical axis. If the radial component can be suppressed and the proportion of longitudinal component gets increased, a longer focal depth and sharper focal spot will be obtained [23]. Since the longitudinal component is mainly generated by the outer part of the input beam, we introduce an annular mask to modulate the incident radial polarized beam, and the modified beam can be computed by updated apodization function l (θ) using a pupil filter function T(θ) as follows

(13)$$l(\theta ) = T(\theta ){l_0}(\theta )$$

where

(14)$$T(\theta ) = \left\{ {\begin{array}{cc} 0 & (0 \le \theta \le {r_1})\\ 1 & ({r_1} \le \theta \le {r_2}) \end{array}} \right.$$

Here, r₁ and r₂ are the inner radius and the outer radius of the narrow annular aperture, respectively, and r₂ is the same size as the back aperture of the objective. Introducing the updated apodization function into Chapter 2.1, the complete theoretical model of ISM-aRP is constructed. Due to the introduction of the narrow annular mask, all of the incident rays have almost the same incidence angles and well matched phases, resulting in effective interference along the optics axis even far away from the focus. Figure 3(c) shows the cross-sectional intensity profiles of the electric field components at the focus without the annular mask and with the annular mask (r₁/r₂ = 0.85), which further shows the strong longitudinal component generated by the modulated beam.

Fig. 3. (a) Schematic sketch of the narrow annular beam. (b) Schematic sketch of the focusing of a radially polarized beam with a narrow annular. The longitudinal component E_z is parallel to the optical axis, and the radial component E_ρ is perpendicular to the optical axis. (c) The cross-sectional intensity profiles of electric field components at the focal point with r₁ = 0 and r₁/r₂ = 0.85, respectively. The longitudinal component intensity profile (red curve) of narrow annular beam can produce a stronger intensity along the beam axis, and the overall electric field intensity profile (black curve) becomes sharper.

Download Full Size | PDF

3. Result

The basic schematic of the set-up is shown in Fig. 4. A linear polarized beam with $\mathrm{\lambda }$=532 nm is expanded and collimated towards the microscope. The collimated linearly polarized light is converted into the annular radially polarized light by a polarization converter and an annular aperture before entering the objective lens. The tailored beam focused by the objective lens images onto a position-sensitive camera, and a whole image for excited region can be recorded for each position of the scanning focus. The traditional ISM setup was implemented with a camera, which seems straightforward, but slower imaging speed limited its development. Afterwards, some scholars also found that good detection performance can be obtained by using a small number of detector elements, such as photomultipliers or avalanche photodiodes [24–26]. Thus, we construct a 5×5 array detector with a pixel size of 0.2 AU (where AU denotes the size of the Airy Disk) to simulate the ISM imaging.

Fig. 4. The schematic of modified radially polarized ISM system. The ISM signal is recorded by a position-sensitive camera. Each scan focus will record a complete image of the excitation region

Download Full Size | PDF

Based on the above theoretical calculation about ISM-aRP, the comparison of excitation PSFs is given in Fig. 5. The simulation results show the depth of focus has been significantly extended in ISM-aRP. To quantify the effect of the promotion, we set the length of full width at half maximum (FWHM) intensity of the PSF along the propagation direction as the depth of focus. For the conventional ISM with circularly polarized beam (ISM-CP), the depth of focus is approximately 1.821λ, whereas the depth of focus is longer than 6.239λ for ISM-aRP, which shows a promising application in volumetric imaging. Besides, as can be seen in Fig. 5(e), the focus spot is sharper than that generated by the circle polarized beam, which can further improve the resolution of conventional ISM.

Fig. 5. (a), (b) Excitation PSFs for the radially polarized beam with an annular aperture (aRP beam) in x-y plane and ρ-z plane, respectively. (c), (d) Excitation PSFs for the circularly polarized beam (CP beam) in x-y plane and ρ-z plane, respectively. (e) Normalized intensity distribution of the PSFs of (a) (red curve) and (c) (blue curve). (f) Normalized intensity distribution of (b) (red curve) and (d) (blue curve).

Download Full Size | PDF

The simulation results of lattice sample are given to further illustrate the improved resolution of ISM-aRP. As shown in Fig. 6(a), the sample is a square lattice of 49 points with 208 nm interval between two adjacent points. The illumination beam is then scanned one pixel of the lattice sample at a time and repeated at each point, ultimately resulting in as many images as the pixels number of the detector, i.e. 25 images in this example. Then the final ISM signal can be yielded by shifting each of the recorded images with proper displacements. Figure 6(b) and (c) are the comparison of images generated by ISM-CP and ISM-aRP. Figure 6(d) depicts the normalized intensity distribution of PSFs for the confocal microscopy (black curve), ISM-CP (blue curve) and ISM-aRP (red curve). The corresponding FWHM are 0.454λ, 0.309λ and 0.297λ, respectively, which shows that the resolution of ISM-aRP is enhanced by 4% compared with that in ISM-CP. Figure 6(e) and (f) are the corresponding normalized intensity profiles along the green line and blue line in Fig. 6(b) and (c), respectively. Results show the slightly enhanced resolution of ISM-aRP.

Fig. 6. (a) The lattice sample. The distance between the two adjacent points is 208 nm. (b), (c) ISM images of ISM-CP and ISM-aRP, respectively. Scale bar: 300 nm. (d) the normalized intensity distribution of PSFs for the confocal microscopy (black curve), the ISM-CP (blue curve) and the ISM-aRP (red curve), respectively. (d) corresponding normalized intensity profiles along the green line and blue line in Fig. 6(b) and Fig. 6(c), respectively.

Download Full Size | PDF

To evaluate the image intensity of ISM-aRP at different depths, a simulated hippocampal neurons specimen is imaged. The intensity images at the focus plane of conventional confocal microscope, ISM-CP and ISM-aRP are shown in Fig. 7(a), (b) and (c) respectively. The insets (b-1) and (c-1) are the magnified views of the region outlined by the blue box and red box in Fig. 7(b) and (c). Figure 7(d) and (e) demonstrate the image results at the depth of 0.5λ, 1λ, 2λ and 4λ in ISM-CP and ISM-aRP. The red and blue bars from dark to light indicate a gradual increase in depth. The comparison of imaging results at different depths can be observed visually according to the intensity profiles shown in Fig. 7(f) and (g). It can be seen that the image intensity of ISM-CP decreases dramatically with the increase of the defocus distance, while ISM-aRP maintains a relatively high image intensity over a considerable distance. The simulation results show that the ranges of imaging in depth in ISM-CP and ISM-aRP are -λ ∼ λ and -3λ ∼ 3λ, respectively, which are consistent with the theoretical calculation in previous.

Fig. 7. The imaging results of simulated hippocampal neurons specimen. (a)-(c) The intensity images at the focus plane of conventional confocal microscope, ISM-CP and ISM-aRP. The insets (b-1) and (c-1) are the magnified views of the region outlined by the blue box and red box in (b) and (c). (d), (e) Image results at the depth of 0.5λ, 1λ, 2λ and 4λ in the ISM-CP and ISM-aRP. Scale bar: 1 µm. (f) The corresponding intensity profiles along the horizontal lines in (d). (g) The corresponding intensity profiles along the horizontal lines in (e).

Download Full Size | PDF

To further demonstrate the imaging capability of the ISM-aRP in volumetric imaging, we test the specimen of simulated fluorescent beads suspension as shown in Fig. 8. With conventional ISM system, only a few fluorescent beads can be imaged in each focus plane, as shown in Fig. 8(a)-(c), and multiple imaging at different depths is required to obtain more information about other fluorescent beads. However, in ISM-aRP, an excitation focus with axially extended is scanned laterally in two dimensions to obtain a projected view of the fluorescent beads suspension, which contains the information about all the fluorescent beads. It shows that the entire volume of interest was scanned in only one frame, and the transverse resolution to be constant throughout different depths.

Fig. 8. The specimen of fluorescent beads suspension. (a)-(c) The conventional ISM fluorescence images acquired at different depths. (d) An ISM-aRP image acquired in a single scan. Scale bar: 2 µm.

Download Full Size | PDF

4. Conclusions

In summary, we introduce the annular radially polarized beam into ISM, which opens a new perspective of volumetric imaging. We first demonstrate a theoretical model for ISM-aRP, and study the focus spot size and the depth of focus. To evaluate the improvement of spatial resolution and the extension of the depth of focus, the lattice array sample and the simulated hippocampal neurons specimen are computational imaged. Results show that the resolution can be enhanced by 4% compared with conventional ISM with circular polarized beam, and the depth of focus can be extended to more than 6λ. The simulation results of the fluorescent beads suspension intuitively illustrate the ability of ISM-aRP to acquire all information of the volume sample. The extended depth of field opens new possibilities for in-vivo imaging, as tiny vertical movements (such as those induced by respiration) no longer defocus the plane of interest. We believe that this approach will be a critical progress towards enabling neuroscientists to decipher the functional organization of complex neuronal networks, such as rapid imaging of neural circuits at cellular synaptic resolution. And we also believe that the combination of ISM-aRP with two-photon excitation (2PE) will further produce more extensive applications. The combination of resonant scanner and fast photomultiplier facilitates the further realization of in vivo imaging, which requires high frame rate. Moreover, the proposed scheme can be easily integrated into the commercial laser scanning microscopy systems because of its adaptability and technical simplicity to existing microscopic systems. Tighter focal spots and longer depths of focus with strong longitudinal polarization, combined with ISM of high resolution, contribute to promote new possibilities for high quality imaging of thick specimen and volume sample.

Funding

National Natural Science Foundation of China (51775148, 51975161); Natural Science Foundation of Heilongjiang Province (QC2018079); China Postdoctoral Science Foundation (2017T100235).

Disclosures

The authors declare that there are no conﬂicts of interest related to this article.

References

1. G. Cox and C. J. R. Sheppard, “Practical Limits of Resolution in Confocal and Non-Linear Microscopy,” Microsc. Res. Tech. 63(1), 18–22 (2004). [CrossRef]

2. T. Wilson and C. Sheppard, “Theory and practice of scanning optical microscopy,” J. Opt. Soc. Am. A 4(3), 551–560 (1987). [CrossRef]

3. C. J. R. Sheppard, “Super-resolution in confocal imaging,” Opt. 80(2), 53–54 (1988).

4. E. A. Ingerman, R. A. London, R. Heintzmann, and M. G. L. Gustafsson, “Signal, noise and resolution in linear and nonlinear structured-illumination microscopy,” J. Microsc. 273(1), 3–25 (2019). [CrossRef]

5. C. B. Müller and J. Enderlein, “Image scanning microscopy,” Phys. Rev. Lett. 104(19), 198101 (2010). [CrossRef]

6. C. J. R. Sheppard, M. Castello, G. Tortarolo, G. Vicidomini, and A. Diaspro, “Image formation in image scanning microscopy, including the case of two-photon excitation,” J. Opt. Soc. Am. A 34(8), 1339 (2017). [CrossRef]

7. I. Gregor and J. Enderlein, “Image scanning microscopy,” Curr. Opin. Chem. Biol. 51, 74–83 (2019). [CrossRef]

8. A. G. York, S. H. Parekh, D. D. Nogare, R. S. Fischer, K. Temprine, M. Mione, A. B. Chitnis, C. A. Combs, and H. Shroff, “Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy,” Nat. Methods 9(7), 749–754 (2012). [CrossRef]

9. J. Huff, “The Airyscan detector from ZEISS: confocal imaging with improved signal-to-noise ratio and super-resolution,” Nat. Methods 12(12), i–ii (2015). [CrossRef]

10. Y. Xue, C. Kuang, S. Li, Z. Gu, and X. Liu, “Sharper fluorescent super-resolution spot generated by azimuthally polarized beam in STED microscopy,” Opt. Express 20(16), 17653 (2012). [CrossRef]

11. S. Ipponjima, T. Hibi, Y. Kozawa, H. Horanai, H. Yokoyama, S. Sato, and T. Nemoto, “Improvement of lateral resolution and extension of depth of field in two-photon microscopy by a higher-order radially polarized beam,” Reprod. Syst. Sex. Disord. 63(1), 23–32 (2014). [CrossRef]

12. G. Thériault, Y. De Koninck, and N. McCarthy, “Extended depth of field microscopy for rapid volumetric two-photon imaging,” Opt. Express 21(8), 10095 (2013). [CrossRef]

13. R. Lu, Y. Liang, G. Meng, P. Zhou, K. Svoboda, L. Paninski, and N. Ji, “Rapid mesoscale volumetric imaging of neural activity with synaptic resolution,” Nat. Methods 17(3), 291–294 (2020). [CrossRef]

14. L. Yang, X. Xie, S. Wang, and J. Zhou, “Minimized spot of annular radially polarized focusing beam,” Opt. Lett. 38(8), 1331 (2013). [CrossRef]

15. X. Xie, H. Sun, L. Yang, S. Wang, and J. Zhou, “Effect of polarization purity of cylindrical vector beam on tightly focused spot,” J. Opt. Soc. Am. A 30(10), 1937 (2013). [CrossRef]

16. H. Dehez, A. April, and M. Piché, “Needles of longitudinally polarized light: guidelines for minimum spot size and tunable axial extent,” Opt. Express 20(14), 14891 (2012). [CrossRef]

17. T. Computing, “Electromagnetic diffraction in optical systems, II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A 253(1274), 358–379 (1959). [CrossRef]

18. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77 (2000). [CrossRef]

19. P. D. Higdon, P. To, E. Science, P. Road, and O. Ox, “Imaging properties of high aperture multiphoton,” J Microsc. 193(2), 127–141 (1999). [CrossRef]

20. C. J. R. Sheppard, S. B. Mehta, and R. Heintzmann, “Superresolution by image scanning microscopy using pixel reassignment,” Opt. Lett. 38(15), 2889 (2013). [CrossRef]

21. C. J. R. Sheppard, M. Castello, G. Tortarolo, T. Deguchi, S. V. Koho, G. Vicidomini, and A. Diaspro, “Pixel reassignment in image scanning microscopy: a re-evaluation,” J. Opt. Soc. Am. A 37(1), 154 (2020). [CrossRef]

22. J. E. McGregor, C. A. Mitchell, and N. A. Hartell, “Post-processing strategies in image scanning microscopy,” Methods 88, 28–36 (2015). [CrossRef]

23. K. Kitamura, K. Sakai, and S. Noda, “Sub-wavelength focal spot with long depth of focus generated by radially polarized, narrow-width annular beam,” Opt. Express 18(5), 4518 (2010). [CrossRef]

24. M. Castello, C. J. R. Sheppard, A. Diaspro, and G. Vicidomini, “Image scanning microscopy with a quadrant detector,” Opt. Lett. 40(22), 5355 (2015). [CrossRef]

25. M. Castello, G. Tortarolo, M. Buttafava, T. Deguchi, F. Villa, S. Koho, L. Pesce, M. Oneto, S. Pelicci, L. Lanzanó, P. Bianchini, C. J. R. Sheppard, A. Diaspro, A. Tosi, and G. Vicidomini, “A robust and versatile platform for image scanning microscopy enabling super-resolution FLIM,” Nat. Methods 16(2), 175–178 (2019). [CrossRef]

26. S. Koho, E. Slenders, G. Tortarolo, M. Castello, M. Buttafava, F. Villa, E. Tcarenkova, M. Ameloot, P. Bianchini, C. J. R. Sheppard, A. Diaspro, A. Tosi, and G. Vicidomini, “Two-photon image-scanning microscopy with SPAD array and blind image reconstruction,” Biomed. Opt. Express 11(6), 2905–2924 (2020). [CrossRef]

Image scanning microscopy with a long depth of focus generated by an annular radially polarized beam

Abstract

1. Introduction

2. Method

2.1 Image formation in ISM with radially polarized beam

2.2 Extended depth of field

3. Result

4. Conclusions

Funding

Disclosures

References

Cited By

Figures (8)

Equations (14)

Optics Express