Abstract

Laser scanning microscopy is limited in lateral resolution by the diffraction of light. We show that we can obtain twenty percent improvement in the resolution of confocal microscopy using Bessel-Gauss beams with the right pinhole size compared to conventional Gaussian beam based confocal microscopy. Advantages of this strategy include simplicity of installation and use, linear polarization compatibility, possibility to combine it with other resolution enhancement and superresolution strategies. We demonstrate the resolution enhancement capabilities of Bessel-Gauss beams both theoretically and experimentally on nano-spheres and biological tissue samples without any residual artifacts coming from the Bessel-Gauss beam side lobes with a resolution of 0.39λ. We also show that the resolution enhancement of Bessel-Gauss beams yields a better statistical colocalization analysis with fewer false positive results than when using Gaussian beams. We have also used Bessel-Gauss beams of different orders to further improve the resolution by combining them in SLAM microscopy (Switching LAser Modes : Dehez, Optics Express, 2013) achieving a resolution of 0.2λ.

© 2017 Optical Society of America

1. Introduction

Bessel beams have a number of tantalizing properties that make them attractive for a broad range of applications. They possess a long depth of field with a small central focal spot and they self reconstruct in the presence of obstacles. However, Bessel beams carry infinite energy and as such, cannot physically exist. Bessel-Gauss beams have finite energy and maintain the most salient features of Bessel beams, namely extended depth of field, tight focal spot [1, 2] and self-reconstruction [3,4], but over a finite distance. Because of these features, Bessel-Gauss beams have been used in a variety of applications in microscopy such as augmented depth of field microscopy [5–9], light sheet microscopy [10–12] and in particle trapping [13].

Optical microscopy is a field where the resolution is limited by the diffraction of light. There is a sustained effort at developing strategies and methods to break the diffraction barrier and improve the resolution of optical microscopes. Because Bessel beams, and by extension Bessel-Gauss beams, have a tighter focal spot than the classic Gaussian beams, their use in laser scanning microscopy can lead to an increase in resolution. Our objective is to use Bessel-Gauss beams in confocal imaging systems to achieve such resolution improvement. One of our main goals is to keep the method as simple as possible. Some researchers have already used radially polarized Laguerre-Gauss beams of high order, which are asymptotically equivalent to Bessel-Gauss beams, for confocal imaging [14–16]. However the presence of residual side lobes often leads to degraded images. The solution we propose here is to use the pinhole of a confocal microscope to cut the fluorescence emission from the side lobes and keep only the fluorescence emission from the tight central spot. The rationale for using the pinhole is to preserve the optical sectioning of a confocal system.

In this study we provide theoretical and experimental results on nano-spheres and fixed tissue samples labelled with different staining approaches, to show that we can effectively use Bessel-Gauss beams to increase the resolution of a confocal microscope by ≈ 20%. This can be done by using a pinhole of the proper size (one Airy unit, the Airy unit corresponding to the diameter of the central disk of an Airy pattern) to keep the same depth of field as in confocal microscopy and reject the fluorescence coming from the side lobes. Moreover our method to create a Bessel-Gauss beam does not require a specific polarization state, meaning that we can use different polarization states to create Bessel-Gauss beams of different orders. We also show that Bessel-Gauss beams are compatible with the resolution enhancement method named SLAM (Switching LAser Modes) introduced in [17]; the donut version of the Bessel-Gauss beam leads to a better resolution than the TE01 (azimuthally polarized Laguerre-Gauss LG01 mode) donut mode due to the smaller size of its central lobe.

The paper is divided as follow. We first use the Richards-Wolf vectorial diffraction theory to characterize Gaussian and Bessel-Gauss beams. We then compare the theoretical beams with experimental measurements to prove that we can use Bessel-Gauss beams in a confocal microscope. Thirdly we show the resolution enhancement capability of Bessel-Gauss beams on different samples. Next we show an improvement of a statistical analysis on colocalization measurements of fluorescently labelled proteins in tissue samples; using a Bessel-Gauss beam for the image acquisition leads to fewer false positives than when a Gaussian beam is used for image acquisition. Finally we compare the use of Bessel-Gauss beams and Gaussian beams in SLAM microscopy [17].

2. Shaping of the Bessel-Gauss beam

2.1. Richards-Wolf vectorial diffraction theory

We used the vectorial diffraction theory of Richards and Wolf [18,19] to predict the focal spots of Gaussian and Bessel-Gauss beams, considering that the beams incident on the objective have vertical or azimuthal polarizations. This formalism provides the three electric field components in the focal plane considering the polarization state of the incident field and the high numerical aperture of the objective.

Using the expression of the angular spectrum representation of the electric field near the focus in cylindrical coordinates in [19] as a starting point we obtain the three electric field components of the beam in the focal plane. Assuming an incident beam linearly polarized along the x axis, the focused beam is calculated using the following equations:

Ex(ρ,φ,z)=E02n0θmaxcos12θl0(θ,φ)exp(ikzcosθ)sinθ×[(1+cosθ)J0(kρsinθ)+(1cosθ)J2(kρsinθ)cos(2φ)]dθ,Ey(ρ,φ,z)=E02n0θmaxcos12θl0(θ,φ)exp(ikzcosθ)sinθ×(1cosθ)J2(kρsinθ)sin(2φ)dθ,Ez(ρ,φ,z)=iE0n0θmaxcos12θl0(θ,φ)exp(ikzcosθ)sinθJ1(kρsinθ)cos(φ)dθ,
where, for an incident Gaussian beam, l0(θ)=exp((fsinθ)2w2) with f=Rsinθmax the focal length, R = 5mm the radius of the objective entrance pupil and w = 5mm the beam waist; E0 is the constant field amplitude, n = 1.47 the refractive index of the focusing medium (Dako mounting medium), θmax = 54 degrees and k the wavenumber. These parameters produce a numerical aperture NA = nsinθmax ≈ 1.2. For a Bessel-Gauss beam we illuminate the back aperture of the objective with an annular beam. We assume that the ring of light has a Gaussian profile of width Δθ, with l0(θ)=(πΔθ)1exp((θθ0)2Δθ2). J0, J1 and J2 represent the Bessel functions of order 0,1 and 2, respectively. In our case the values for θ0 and Δθ where 38 deg and 8.5 deg, respectively. The interface “coverslip - mounting medium” is taken into account by applying the boundary conditions [20] to the electric field distribution computed with the Richard and Wolf integrals. The longitudinal component of the electric field at a boundary verify the condition 1Ez1 = 2Ez2 where 1 is the permitivity of the first medium and 2 the permitivity of the second medium (mounting medium). Admitting the two mediums are non magnetic we have i=ni20 for i=1,2, 0 being the permitivity of vacuum. We can replace 21 by n12n22.

When using an incident beam with azimuthal polarization, the Richards and Wolf integrals lead to the following expressions of the electric fields components:

Ex(ρ,φ,z)=iE0n0θmaxcos12θl0(θ,φ)exp(ikzcosθ)sin2θJ1(kρsinθ)sin(φ)dθ,Ey(ρ,φ,z)=iE0n0θmaxcos12θl0(θ,φ)exp(ikzcosθ)sin2θJ1(kρsinθ)cos(φ)dθ,Ez(ρ,φ,z)=0.

Figure 1 shows calculations of the Gaussian, TE01 (azimuthally polarized Laguerre-Gauss LG01 mode) and Bessel-Gauss beams of order 0 and 1. We can see from the plots in Fig. 1 that the Full Width at Half Maximum (FWHM) of the Bessel-Gauss beam of order 0 central lobe is 20% smaller than the FWHM of the Gaussian beam. For azimuthal polarization the central peak to peak distance of the Bessel-Gauss beam of order 1 is 5% narrower than that of the TE01 donut beam; However the FWHM of the Bessel-Gauss beam of order 1 first lobe, i.e. width of the central annulus, is 20% smaller than that of the TE01 donut beam. We note the slight stretching of the Bessel-Gauss beam of order 0 along the vertical direction; this is due to the linear polarization of the annular beam which produces an axial electric field with two lobes along the polarization axis. On the contrary the azimuthally polarized Bessel-Gauss beam of order 1 is perfectly symmetrical.

 

Fig. 1 Comparison of Bessel-Gauss beams with their Gaussian beam counterparts in the focal plane (z = 0), as calculated by Eqs. (1) and (2). Left: theoretical Gaussian and TE01 beams. Middle: theoretical Bessel-Gauss beams. Right: Horizontal profiles with FWHM of the two beams. The coverslip refractive index is n2 = 1.5 and the mounting medium refractive index is n1 = 1.47. Numerical aperture of the focussing objective: NA = 1.2. Wavelength: λ = 532 nm

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These beam structures can be explained as follows. Let us consider analytical solutions of the Richards-Wolf integrals valid for the limit case of an infinitely thin incident annular beam defined by a Dirac delta function, i.e. l0(θ, φ) = δ(θθ0). When the incident field is linearly polarized along the x-axis, one can easily find the following expressions from Eq. (1):

Ex(ρ,φ,z)=E02ncos12θ0exp(ikzcosθ0)sinθ0×[(1+cosθ0)J0(kρsinθ0)+(1cosθ0)J2(kρsinθ0)cos(2φ)],Ey(ρ,φ,z)=E02ncos12θ0exp(ikzcosθ0)sinθ0×(1cosθ0)J2(kρsinθ0)sin(2φ),Ez(ρ,φ,z)=iE0ncos12θ0exp(ikzcosθ0)sinθ0J1(kρsinθ0)cos(φ),
It turns out that the contribution of the terms involving Bessel function J2 is significantly smaller than that of Bessel function J0 within the central lobe of the field structure. To a good approximation, the central part of the field structure reduces to:
Ex(ρ,φ,z)f(z)(1+cosθ0)J0(kρsinθ0),Ey(ρ,φ,z)0,Ez(ρ,φ,z)2if(z)J1(kρsinθ0)cos(φ),
with f(z)=E02ncos12θ0exp(ikzcosθ0)sinθ0.

The transverse field is defined by a Bessel function of order 0 and it exhibits no angular variation. On the other hand the longitudinal electric field component is defined by a Bessel function of order 1; it has a zero at center and it exhibits an azimuthal variation due to the cosφ factor. This field component produces the beam stretching along the polarization axis.

When the incident beam is of azimuthal polarization, Eq. (2) simplifies to:

Eρ(ρ,φ,z)=0,Eφ(ρ,φ,z)=iE0ncos12(θ0)exp(ikzcosθ0)sin2(θ0)J1(kρsinθ0),Ez(ρ,φ,z)=0.
This field structure is defined by a Bessel function of order 1; it has no longitudinal component and it exhibits angular symmetry. The presence of a Gaussian envelope for the incident annular beam will translate into a Gaussian envelope for the field structure at focus [2]. Its main impact will be a cutoff of the outer sidelobes.

2.2. Experimental setup and measurements

To generate Bessel-Gauss beams we chose the design proposed by [6], using a refractive axicon [21] and a lens to create a thin Gaussian shaped ring. We used a high numerical aperture (NA = 1.2) objective for the focussing in order to achieve a very small spot size in the focal area. Figure 2 is a schematic view of the confocal microscope incorporating the axicon module. The axicon module that allows increasing image resolution is placed in the path of the laser beam before entering the confocal microscope. The lens after the axicon is used to produce the Fourier transform of the Bessel-Gauss beam at the galvanometer mirrors. The Fourier transform of the Bessel-Gauss beam has a Gaussian ring profile. The ring of light is then propagated to the back aperture of the objective. This objective then performs an inverse Fourier transform of the ring of light, generating a Bessel-Gauss beam focussed into the sample.

 

Fig. 2 Simplified schematic representation of the confocal microscope that uses Bessel-Gauss beams. The zoomed part depicts the beam transformation by the axicon. In the zoomed part w represents the Gaussian beam waist before entering the axicon and β is the angle of the cone formed by the rays refracted by the axicon. The laser used in our confocal microscope is a Compass 215M from Coherent Inc. (with a wavelength of 532 nm) delivering a maximum output power of 40 mW which is largely sufficient for all of the measurements reported here.

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In the following we provide a detailed description of the components used for the home made confocal microscope. The excitation laser we used is a Coherent DPSS (Diode Pumped Solid State) Compass 215M Laser at 532 nm. We also used a 60× UPlanSApo water immersion Olympus objective with a numerical aperture of 1.2. The PMT (Photomultiplier tube) was a Hamamatsu R3896 PMT mounted on the Hamamatsu C7950 PMT DAP-type socket. The mirrors, beamsplitter and ND filter are from Thorlabs : P01 mirrors, BS010 50 : 50 non-polarizing beamsplitter cube, 400 – 700 nm, 10 mm and NEK01 absorptive ND filter kits. The dichroics and excitation filters are from Semrock : FF580-FDi01-25×36 and FF509-FDi01-25×36 for the combination of the excitation lasers, Di01-R405/488/532/635-25×36 for the separation of the excitation and the emission and BLP01-488R-25, BLP01-647R-25 and BLP01-532R-25 as emission filters. To change the polarization from linear to azimuthal and create the donut shape we used an Arcoptix radial/azimutal polarization converter [22] with its electrical LC driver. The Arcoptix polarization converter is placed along a separate optical path; hence we can easily change from vertical to azimuthal polarization without realignment. We used the 50 : 50 non-polarizing beamsplitter cube to split and recombine the two different paths for vertical and azimuthal polarizations. We also used an iris to clean the beam before entering the axicon.

We chose to use a refractive axicon in our setup because of its low losses in converting a Gaussian beam into a Bessel-Gauss beam compared to the use of an annular aperture [23]. The axicon is also non specific to the polarization of the incident Gaussian beam, hence it can be used to create Bessel-Gauss beams with different polarization states and of different orders. Linear polarization creates a Bessel-Gauss beam of order 0 and azimuthal polarization a Bessel-Gauss beam of order 1 (see Fig. 3). For all our experiment we used an axicon with a deviation angle of β = 2.5 degrees. The diameter of the ring of light at the back aperture of the objective is 4.8 mm and it has a width of 0.7 mm.

 

Fig. 3 Calculations and experimental measurements of the vertically and azimuthally polarized Bessel-Gauss beams produced at the focus of the objective. The top row shows the vertically polarized Bessel-Gauss beam and the bottom row the azimuthally polarized Bessel-Gauss beam. The left column represents the simulated results, the middle one the experimental PSF (Point Spread Function) of the beams taken with 100-nm diameter nano-spheres (fluosphere carboxylate-modified microspheres, orange fluorescence 540/560 from Invitrogen molecular probes) and the right column compares the theoretical and experimental profiles and the corresponding FWHMs.

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Figure 3 shows calculations using Eqs. (1) and (2) and experimental measurements of the Bessel-Gauss beams for both vertical and azimuthal polarizations. We clearly see a good match between the simulations (left column) and experimental results (middle column). Deviations from azimuthal symmetry is present in the secondary lobes of the experimental beam and it is attributed to various aberrations [24,25].

Both Bessel-Gauss beams of order 0 and 1 have a smaller central lobe size or a smaller central hole size than their Gaussian or TE01 counterparts (see Fig. 4(A1–4)). This feature and their non-diffracting property make the Bessel-Gauss beams interesting alternatives to the Gaussian beams for several applications.

 

Fig. 4 A: Images of 100-nm diameter fluorescent nano-spheres (same as Fig. 3) observed with a confocal microscope having a pinhole of 15 μm. The nano-spheres are observed with a Gaussian beam of vertical polarization (A1), Bessel-Gauss beam of vertical polarization (A2), TE01 beam of azimuthal polarization (A3) and Bessel-Gauss beam of azimuthal polarization (A4). B: Focal spot of the Bessel-Gauss beam of vertical polarization for different pinhole diameters obtained using 100-nm fluorescent nano-spheres: 25 μm (B1), 15 μm (B2) and 10 μm (B3). Excitation wavelength: 532 nm. Scale bar: 500 nm

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Figure 4(B1–3) shows the effect of the pinhole size on the focal spot of the Bessel-Gauss beam. We see that a pinhole having a diameter of the size of one Airy Unit (10 μm) can effectively cut all the side lobes.

3. Characterization of the imaging system

To characterize the imaging system we fixed fluorescent nano-spheres of 100-nm diameter smeared on a glass coverslip and mounted on a slide using the DAKO mounting medium (with a refractive index of 1.47). We then observed them with a Gaussian beam and a Bessel-Gauss beam to compare the FWHM of the two PSFs. All the observations were made with a home made confocal system (see Fig. 2) using a water objective with a numerical aperture of 1.2.

Figure 5 illustrates the improvement in the size of the observed spheres achieved with the Bessel-Gauss beam. The FWHM of the spheres measured with the Gaussian beam is 292 ± 12 nm ≈ 0.55 λ (where λ is the wavelength in nanometers) and that observed with the Bessel-Gauss beam is 207 ± 6 nm ≈ 0.39 λ (only 4.5% larger than the theoretical value of 198 nm in Fig. 1). The measured relative reduction of the FWHM reaches ≈ 29%.

 

Fig. 5 Confocal image of a single and an average of ≈ 30 fluorescent nano-spheres for both Gaussian and Bessel-Gauss beams. Pinhole diameter: 10 μm. The right panel displays the normalized profiles of the nano-spheres along the horizontal axis (colored lines on the images). The traces with full lines are for the 30 nano-sphere average PSFs and the crosses are pixel values for the single nano-sphere measurements.

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The intensity profiles from Fig. 6 show an axial FWHM for the vertically polarized Gaussian beam of 1.0 ± 0.12 μm and an axial FWHM for the vertically polarized Bessel-Gauss beam of 1.2 ± 0.12 μm. Even if the Bessel-Gauss beam has a longer depth of field, the use of the confocal pinhole allows keeping the same axial sectioning (approximately 1 μm ≈ 2 λ) as with the Gaussian beam.

 

Fig. 6 Axial view of the PSF measured with nano-spheres. A) PSF of the vertically polarized Gaussian beam. B) PSF of the vertically polarized Bessel-Gauss beam. The left image displays an axial view of the PSF. The right curve is an intensity profile along the red dashed line of the axial PSF with the corresponding FWHM. The black dots on the curve represent the pixel data before interpolation. The red curves represent a plot of the interpolated values. Pixel size along the x axis: 24 nm. Pixel size along the z axis: 250 nm.

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4. Resolution enhancement in confocal microscopy

In this section we concentrate on determining the resolution of the Bessel-Gauss beam used in confocal microscopy compared to that using the classic Gaussian beam. We will do so by observing nano-spheres and small structures in biological samples (e.g. microtubules and synaptic markers) which are commonly used to test the resolution of a microscope.

4.1. Characterization of resolution using nano-spheres

For the resolution measurements on nano-spheres we used the same nano-spheres as for the PSF characterization (see Fig. 5). We can see in Fig. 7 the resolution improvement obtained with the Bessel-Gauss beam compared with the Gaussian beam. The central panel shows a resolution of ≈ 207 ± 12 nm (≈ 0.39 λ), which is below the theoretical resolution limit of our system with the same optics (the theoretical limit was defined by the Rayleigh criterion: 1.22λ2NA270nm0.51λ, which agrees with theoretical computations made with Gaussian beams incident on the objective). The relative improvement in resolution is ≈ 23%.

 

Fig. 7 Confocal images of a sample of 100-nm fluorescent nano-spheres observed with a Gaussian beam (left) and with a Bessel-Gauss beam (right). Center: normalized profiles along the coloured lines in the two images. The black line in the central panel corresponds to the resolution measured between the two maxima. Pinhole diameter: 10 μm. Scale bar: 510 nm. Images filtered with a Gaussian filter having a FWHM of one pixel.

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4.2. Resolution measurements with fixed biological samples

A better resolution between different fluorescently labelled proteins or proteins tagged by fluorescent antibodies is crucial in many aspects of biology, namely to count labels and distinguish structures. To show the resolution improvement given by the Bessel-Gauss beam we used two types of biological samples. First we detected microtubules with fluorescently labelled antibodies (monoclonal anti α-tubulin antibody) to see if we could distinguish microtubule bundles within small cellular compartments. Second, we detected proteins that form clusters (markers of neuronal synaptic junction) to verify if clusters are more easily resolved.

Measurements of the resolution improvement with fluorescent immunostained microtubule samples are shown in Fig. 8. Because of their small diameter (≈ 25 nm), microtubules are typical structures used to illustrate resolution measurements. The profiles shown in Fig. 8 are integrated profiles along a 5-pixel width line. Here again we see a resolution improvement from the Gaussian beam to the Bessel-Gauss beam. The resolution measured with the Bessel-Gauss beam is of 207 ± 12 nm (≈ 0.39 λ) which is better than the theoretical resolution obtained with the Gaussian beam of ≈ 270 nm (≈ 0.51 λ). The relative resolution improvement is again ≈ 23%. With the Gaussian beam we cannot distinguish mincrotubule bundles; by contrast, they become visible when using the Bessel-Gauss beam.

 

Fig. 8 Confocal images of microtubules stained by immunohistochemistry (monoclonal anti α-tubulin primary antibody - revealed by a donkey anti-mouse Rhodamine RedX-labeled secondary antibody) observed with a Gaussian beam (left) and with a Bessel-Gauss beam (right). Center: normalized integrated profiles (5-pixel width line) along the coloured lines in the two images. The black line in the central panel corresponds to the resolution measured between the two maxima. Pinhole diameter: 10 μm. Scale bar: 510 nm. Images filtered with a Gaussian filter having a FWHM of one pixel.

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We also measured the resolution improvement due to the Bessel-Gauss beam on another biologically relevant sample. For the next sample we chose to use a neuronal synaptic staining. For this step, we detected by immunofluorescence the gephyrin protein which is a marker of inhibitory synaptic junction in neurons; it is thus present in the form of clusters at the cell membrane. We show improved resolution of gephyrin clusters with areas of dense synaptic contacts. In other words, more inhibitory postsynaptic sites can be resolved.

Figure 9 shows that when using the Bessel-Gauss beam, two adjacent synaptic gephyrin-positive sites that were not resolved with the Gaussian beam become distinguishable. Figure 9 shows a resolution of ≈ 219 ± 12 nm ≈ 0.41 λ with the Bessel-Gauss beam. The relative resolution improvement compared to the theoretical resolution of the Gaussian beam (of ≈ 270 nm) is ≈ 20%.

 

Fig. 9 Gephyrin immunodetected by a monoclonal mAb7a Oyster 550 coupled antibody, excitation maximum at 551 nm. Left: images obtained with a Gaussian beam. Center: normalized profiles along the coloured lines on the images. The black dotted line in the central panel corresponds to the resolution measured between the two maxima. Right: images obtained with a Bessel-Gauss beam. Pinhole diameter: 10 μm. Scale bar: 1000 nm. Images filtered with a Gaussian filter having a FWHM of one pixel.

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5. Resolution improvement between pre- and postsynaptic markers

One important challenge in optical microscopy and confocal microscopy is related to the ability to distinguish different structures within cells and organels. Most of these subcellular structures are smaller than the laser spot size and thus cannot be resolved. To measure the impact of improved resolution, we used fluorescent markers of two structures located on each side of neuronal synaptic junctions. We used the later paradigm because such structures are physically segregated but closely apposed. Indeed the pre- and postsynaptic sides are separated by an extracellular gap called the synaptic cleft which is typically ≈ 20–50 nm thick, making it difficult to distinguish between the two sides with a resolution of 270 nm.

For this we detected the pre- and postsynaptic structures by immunilabelling two different proteins. The first protein of interest is presynaptically localized: the Glutamic Acid Decarboxylase (GAD), which is an enzyme that transforms glutamate into GABA making the synapse inhibitory. The second protein of interest is gephyrin, which anchors GABAA receptors at inhibitory postsynaptic sites. To analyse the images and have an estimation on whether the two proteins are in the same area we used a statistical colocalization analysis [26]. The main issue with these two proteins is that image analysis reveals some degree of colocalization between them, meaning that they are interpreted to be in the same area, whereas in fact they are physically separated by the synaptic cleft. One reason for this problem is the lack of resolution.

Figure 9 shows that we could resolve more gephyrin-positive sites at the postsynaptic level using Bessel-Gauss beams. We now want to verify whether an increase in resolution between pre-and postsynaptic markers, GAD vs. gephyrin, reduces detection of false colocalization positives. Figure 10 displays a comparison of colocalization analysis between gephyrin and GAD labeling in neurons acquired with Gaussian beam versus Bessel-Gauss beam based confocal microscopy (see Fig. 10(a)).

 

Fig. 10 A: Two images of the same field taken with Gaussian and Bessel-Gauss beams with magnified sub-regions and their associated binarized masks (the mask creation is a step of the colocalization analysis [26]). The image contrast has been adjusted for better visibility but raw data were used for the analysis. B and C: comparison of the index obtained from Gaussian and Bessel-Gauss acquisitions with the same field. A lower index corresponds to a lower colocalization. The indexes are compared using a paired t-test.

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The colocalization analysis uses the resolution and signal to noise ratio to binarize the images and create a mask for each protein. This mask represents the area where the algorithm has detected the protein of interest. The algorithm then evaluates the overlap between the mask of the two proteins and use the size of each mask to normalize the colocalization results. This overlap is then compared to an overlap that we could expect from a purely random distribution of the same surface contained in the masks. The final value that illustrates the colocalization analysis is what we call the index. The index is calculated by taking the difference between the overlap of the masks and the overlap of a purely random distribution of the mask. This index is in normalized percentage of overlap; the lower the index the lower the colocalization.

Figure 10(a) displays some examples of resolution improvement achieved with the Bessel-Gauss beam: there is less overlap in the binarized mask when using the Bessel-Gauss beam. Figure 10(b) and (c) compare the index value obtained with the Gaussian beam versus the Bessel-Gauss beam. For both proteins (gephyrin in b and GAD in c) the index with the Bessel-Gauss beam is significantly smaller than the index obtained for the Gaussian beam. The index is smaller by ≈ 30 ± 5%, which is consistent with a reduction of the FWHM of the beam by ≈ 20% (the later yielding a reduction in beam cross section at half maximum of ≈ 36%), the index being calculated based on the surfaces. The results show that a 20% improvement in resolution using Bessel-Gauss beams yield an even greater improvement in image based colocalization analysis.

6. Superresolution with Bessel-Gauss beams : Bessel(B)-SLAM

In this section we apply the Bessel-Gauss beam to a superresolution strategy based on beam shaping in a confocal microscope. We chose this specific application because the required beam shaping is compatible with the beam shaping that leads to Bessel-Gauss beam confocal microscopy.

6.1. Principles of SLAM microscopy

SLAM stands for Switching LAser Modes. SLAM microscopy was introduced in [17] (also referred to fluorescence emission difference microscopy in [27] or Intensity Weighted Subtraction in [28]). SLAM can improve the resolution of confocal images by a factor of ≈ 2. This method uses two images taken with two different laser modes: one with a bright beam such as a Gaussian mode (TEM00) and one with a donut beam such as an azimuthally polarized mode (TE01). Here we replace the Gaussian mode by a vertically polarized Bessel-Gauss beam of order 0 and the TE01 beam by an azimuthally polarized Bessel-Gauss beam of order 1. The SLAM image is obtained by subtracting the image taken with the donut beam from the image taken with the bright beam.

ISLAM=Ibrightg×Idonut
Before subtraction, noise is filtered out from both images using a Gaussian filter with a FWHM of two pixels. In Eq. (6) g is a weighting factor that allows some adjustment of the processing. This weighting factor can have values ranging from 0 to 1. Most of the time the values of g will be hand tuned between 0.7 and 1. When the subtraction produce negative values, the value of ISLAM is set to zero [28].

The central spot of the Bessel-Gauss beam of order 0 is smaller than the Gaussian TEM00 spot and the central annulus of the Bessel-Gauss beam of order 1 is also smaller than the TE01 annulus (see Fig. 4(a)) leading to an improve resolution with the SLAM method. Here again we used the pinhole to keep the same depth of field and reject the light coming from some side lobes from all Bessel-Gauss beams.

6.2. Comparison of SLAM and B-SLAM on nano-spheres

By looking at the images and profiles in Fig. 11 we can see that the B-SLAM (SLAM with Bessel-Gauss beams) provides a better resolution than conventional SLAM. B-SLAM clearly resolves two nano-spheres that were not distinguished with SLAM. We measured a resolution of ≈ 105±12 nm with B-SLAM.

 

Fig. 11 Application of SLAM and B-SLAM to nano-spheres with Gaussian beams (top right image with g = 0.9) and Bessel-Gauss beams (bottom right image with g = 1.0). Left: confocal images. Center: normalized profiles along the coloured lines of the images. The black line in the central panel corresponds to the resolution measured between the two maxima. Pinhole diameter: 10 μm. Scale bar: 300 nm.

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6.3. Comparison of SLAM and B-SLAM with biological samples

We have also tested the resolution improvement achieved by B-SLAM on fluorescent stained α-tubulin. The profiles shown in Fig. 12 are integrated profiles along a 10-pixel width line. Here we can distinguish more physiologically relevant details with B-SLAM; two microtubule bundles that are not resolved with standard SLAM are resolved with B-SLAM.

 

Fig. 12 SLAM method applied to microtubules with Gaussian (top images) and Bessel-Gauss beams (bottom images). Left: confocal images. Right: SLAM (with g = 0.8) and B-SLAM (with g = 1.0) images. Center: normalized profile traces along the coloured lines in the images. The profiles are integrated along 10 pixels in width. Pinhole diameter: 10 μm. Scale bar: 1 μm.

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7. Discussion

We have taken advantage of the fact that the diffraction-limited spot of a Bessel-Gauss beam remains smaller than that of a Gaussian beam for improving the resolution of laser scanning confocal microscopy. It is also advantageous to use Bessel-Gauss beams because their width is constant over the depth of field of the microscope which is not the case for Gaussian beams that tend to diverge, even within the 1-μm depth of field achieved with a 1-AU pinhole. This feature contributes in reducing the blur due to the diffraction limited focal spot. Moreover Bessel-Gauss beams are naturally resistant to scattering, thanks to their self reconstruction properties, and can therefore be used for deeper imaging in confocal microscopy. The effect of small pinhole on radially polarized high order Laguerre-Gauss beams has been theoretically investigated [29] but previous attempts in confocal microscopy kept some side lobe residuals [15,16] that degraded the images. A slit has also been used to cut the background fluorescence in a Bessel light sheet imaging system [30]. By using the Bessel-Gauss beam in confocal microscopy with a small pinhole we were able to measure a ≈ 20% resolution improvement in different types of samples confirming the effectiveness of the Bessel-Gauss beam as an alternative to the Gaussian beam. The use of Bessel-Gauss beams yields improvement in colocalization analysis beyond the linear increase in resolution.

Our methods can be used to generate Bessel-Gauss beams of different orders. This feature has allowed to improve the resolution of SLAM microscopy down to ≈ 105nm. This adds to the capability of the Bessel-Gauss beams to be integrated in a variety of other modalities used in microscopy. SLAM is not restricted to modalities based on fluorescence, but can also be used with any type of laser scanning microscopy. Some researchers have recently used Bessel-Gauss beams in CARS (Coherent Anti-stokes Raman Scattering) microscopy to improve the resolution [31]; since CARS and two photon excited microscopies are compatible with the SLAM method ([17, 32]), Bessel-Gauss beams could further enhance the resolution of these modalities.

The measured resolution enhancement factor is of ≈ 1.3 for Bessel-Gauss beam confocal microscopy and of ≈ 2.5 for B-SLAM, compared to the theoretical resolution of Gaussian beam based confocal microscopy. The method described herein does not yield a resolution as small as STimulated Emission Depletion (STED [33]), STochastic Optical Reconstruction Microscopy (STORM [34]) or Photo Activated Localization Microscopy (PALM [35]); however, its design is simple enough that it can be adjusted on a standard confocal microscope. STED microscopy needs pulsed and high power lasers, making the microscopy setup more complex than that of a confocal microscope. STORM and PALM are incompatible with deep imaging and inherently slower due to the need of multiple acquisitions. Moreover the proposed method relies only on beam shaping and thus it is not specific to fluorescent staining required by STED, STORM and PALM. The main limitation of SLAM, mentioned in [28]], is the generation of negative values due to the subtraction; a method of correction is proposed in that reference.

Because of the presence of side lobes in the Bessel-Gauss beam, a fraction of laser power is lost. To keep the same image quality (signal to noise ratio) the laser power must be increased in such way as to generate sufficient power in the central lobe of the Bessel-Gauss beam as to keep the same power density as with the Gaussian beam. The power losses due to the side lobes and the stretching of the beam along its axis are not important enough as to require a high laser power. Typical observations with the Gaussian beam require between 2 and 20 μW depending on the sample; the corresponding observations with the Bessel-Gauss beam require between 5 and 50 μW. All the power measurements were made right before the objective. Commercial confocal microscopes typically use lasers with power between 5 mW and 50 mW, which is more than sufficient for the approach presented here. One solution to the side lobe problem has been to use two-photon effects and incorporate Bessel-Gauss beams in a two-photon microscope. In this case side lobe excitation is greatly reduced and imaging is achieved without compromising on lateral resolution and with an extended depth of field [5,6].

8. Conclusion

The proposed method allows for an improvement of the resolution of a confocal microscope (with a correct size pinhole) of ≈ 20% at the cost of just adding a minimal number of optical elements in the optical path. It also offers opportunity for confocal microscopy in deeper tissues. The method uses beam shaping and thus does not rely on properties of specific fluorophores nor several acquisitions (except for the B-SLAM technique where only two images are required). The beam shaping method we used is flexible and allows generating Bessel-Gauss beams of order 1 with azimuthally polarized incident beams. We also showed that we can improve the efficiency of SLAM microscopy using Bessel-Gauss beams of order 0 and 1 to replace the Gaussian and TE01 beams previously used for the SLAM microscopy. This adds to the versatility of the Bessel-Gauss beams that have already been used in other microscopy contexts. Moreover the design used here with the axicon can be retrofitted in a confocal/two-photon commercial microscope [7].

Funding

Natural Sciences Engineering Research Council of Canada(NSERC)(371078-2010, 171034-05); Canadian Institutes of Health Research(CIHR)(STP-53908); NSERC-CIHR Collaborative Health Research Projects(CGP-140190); Canada Research Chair in Chronic Pain and Related Brain Disorders(950-230938).

Acknowledgments

The authors would like to thank Antoine G. Godin for his help with the code for the colocalization analysis, Charleen Salesse for providing cell cultures, Annie Castonguay, Martin Cottet, Cleophace Akitegetse and Alicja Gasecka for helpful discussions.

References and links

1. K.B. Rajesha, N. Veerabagu Sureshb, P.M. Anbarasanc, K. Gokulakrishnanb, and G. Mahadevand, “Tight focusing of double ring shaped radially polarized beam with high NA lens axicon,” Opt. Laser Technol. 43(7), 1037–1040 (2011). [CrossRef]  

2. 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), 14891–14905 (2012). [CrossRef]   [PubMed]  

3. G. Milione, A. Dudley, T.A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R.R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams,” J. Opt. 17(3), 035617 (2015). [CrossRef]  

4. F.O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010). [CrossRef]  

5. P. Dufour, M. Piché, Y. De Koninck, and N. McCarthy, “Two-photon excitation fluorescence microscopy with a high depth of field using an axicon,” Appl. Opt. 45(36), 9246–9252 (2006). [CrossRef]   [PubMed]  

6. G. Thériault, Y. De Koninck, and N. McCarthy, “Extended depth of feld microscopy for rapid volumetric two-photon imaging,” Opt. Express 21(8), 10095–10104 (2013). [CrossRef]   [PubMed]  

7. G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell. Neurosci. 8, 139 (2014).

8. 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,” Microscopy (Oxf) 63(1), 23–32 (2014). [CrossRef]  

9. W. Yu, Z. Ji, X. Yang, Z. Gong, Y. Xiao, P. Xi, and K. Shi, “STED imaging by using hollow Bessel beam,” in Frontiers in Optics 2015, paper FTu3D.6.

10. T.A. Planchon, L. Gao, D.E. Milkie, M.W. Davidson, J.A. Galbraith, C.G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–426 (2011). [CrossRef]   [PubMed]  

11. M. Zhao, H. Zhang, Y. Li, A. Ashok, R. Liang, W. Zhou, and L. Peng, “Cellular imaging of deep organ using two-photon Bessel light-sheet nonlinear structured illumination microscopy,” Biomed. Opt. Express 5(5), 1296–1308 (2014). [CrossRef]   [PubMed]  

12. P. Zhang, P.M. Goodwin, and J. H. Werner, “Fast, super resolution imaging via Bessel-beam stimulated emission depletion microscopy,” Opt. Express 22(10), 12398–12409 (2014). [CrossRef]   [PubMed]  

13. J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4–6), 239–245 (2001). [CrossRef]  

14. Y. Kozawa and S. Sato, “Sharper focal spot formed by higher-order radially polarized laser beams,” J. Opt. Soc. Am. A 24(6), 1793–1798 (2007). [CrossRef]  

15. Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, and S. Sato, “Lateral resolution enhancement of laser scanning microscopy by a higher-order radially polarized mode beam,” Opt. Express 72(6),15947–15954 (2011). [CrossRef]  

16. J. Kim, D.C. Kim, and S.H. Back, “Demonstration of high lateral resolution in laser confocal microscopy using annular and radially polarized light,” Microsc. Res. Techniq. 19(17), 441–446 (2011).

17. H. Dehez, M. Piché, and Y. De Koninck, “Resolution and contrast enhancement in laser scanning microscopy using dark beam imaging,” Opt. Express 21, 7128–7141 (2013). [CrossRef]  

18. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. 2. structure of the image field in an aplanatic system,” Proc. R. Soc. A 253(1274), 358–379 (1959). [CrossRef]  

19. L. Novotny and B. Hecht, Principles of Nano-Optics, (Cambridge University, 2006), Chap.3. [CrossRef]  

20. J.D. Jackson, Classical Electrodynamics, (Wiley, 1998).

21. J.H. McLeod, “The axicon: A new type of optical element,” J. Opt. Soc. Am. 44(8), 592–597 (1954). [CrossRef]  

22. Arcoptix Switzerland, “Radial/aximuthal polarisation converter,” <http://www.arcoptix.com/radial_polarization_converter.htm>.

23. W.T. Welford, “Use of annular apertures to increase focal depth,” J. Opt. Soc. Am. 50(8), 749–752 (1960). [CrossRef]  

24. X. Zeng and F. Wu, “Effect of elliptical manufacture error of an axicon on the diffraction-free beam patterns,” Opt. Eng. 47(8), 083401 (2008). [CrossRef]  

25. R. Arimoto, C. Saloma, T. Tanaka, and S. Kawata, “Imaging properties of axicon in a scanning optical system,” Appl. Opt. 31(31), 6653–6657 (1992). [CrossRef]   [PubMed]  

26. L.E. Lorenzo, A.G. Godin, F. Wang, M. St-Louis, S. Carbonetto, P. W. Wiseman, A. Ribeiro-da-Silva, and Y. De Koninck, “Gephyrin clusters are absent from small diameter primary afferent terminals despite the presence of GABAA receptors,” J. Neurosci. 34(24), 8300–8317 (2014). [CrossRef]   [PubMed]  

27. C. Kuang, S. Li, W. Liu, X. Hao, Z. Gu, Y. Wang, J. Ge, H. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep. 3, 1441 (2013). [CrossRef]  

28. K. Korobchevskaya, C. Peres, Z. Li, A. Antipov, C.J.R. Sheppard, A. Diaspro, and P. Bianchini, “Intensity weighted subtraction microscopy approach for image contrast and resolution enhancement,” Sci. Rep. 6, 25816 (2016). [CrossRef]   [PubMed]  

29. Y. Kozawa and S. Sato, “Numerical analysis of resolution enhancement in laser scanning microscopy using a radially polarized beam,” Opt. Express 23(3), 2076–2084 (2015). [CrossRef]   [PubMed]  

30. P. Zhang, M.E. Phipps, P M. Goodwin, and J.H. Werner, “Confocal line scanning of a Bessel beam for fast 3D imaging,” Opt. Lett. 39(12), 3682–3685 (2014). [CrossRef]   [PubMed]  

31. S. Heuke, F.B. Legesse, D. Akimov, U. Hubner, J. Dellith, M. Schmitt, and J. Popp, “Bessel beam coherent anti-Stokes Raman scattering microscopy,” J. Opt. Soc. Am. B 32(9), 1773–1779 (2015). [CrossRef]  

32. A. Gasecka, A. Daradich, H. Dehez, M. Piché, and D. Côté, “Resolution and contrast enhancement in coherent anti-Stokes Raman-scattering microscopy,” Opt. Lett. 38(21), 4510–4513 (2013). [CrossRef]   [PubMed]  

33. S.W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19(11), 780–782 (1994). [CrossRef]   [PubMed]  

34. E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hes, “Imaging intracellular fluorescent proteins at nano-meter resolution,” Science 313(5793), 1642–1645 (2006). [CrossRef]   [PubMed]  

35. M.J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–795 (2006). [CrossRef]   [PubMed]  

References

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  1. K.B. Rajesha, N. Veerabagu Sureshb, P.M. Anbarasanc, K. Gokulakrishnanb, and G. Mahadevand, “Tight focusing of double ring shaped radially polarized beam with high NA lens axicon,” Opt. Laser Technol. 43(7), 1037–1040 (2011).
    [Crossref]
  2. 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), 14891–14905 (2012).
    [Crossref] [PubMed]
  3. G. Milione, A. Dudley, T.A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R.R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams,” J. Opt. 17(3), 035617 (2015).
    [Crossref]
  4. F.O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
    [Crossref]
  5. P. Dufour, M. Piché, Y. De Koninck, and N. McCarthy, “Two-photon excitation fluorescence microscopy with a high depth of field using an axicon,” Appl. Opt. 45(36), 9246–9252 (2006).
    [Crossref] [PubMed]
  6. G. Thériault, Y. De Koninck, and N. McCarthy, “Extended depth of feld microscopy for rapid volumetric two-photon imaging,” Opt. Express 21(8), 10095–10104 (2013).
    [Crossref] [PubMed]
  7. G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell. Neurosci. 8, 139 (2014).
  8. 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,” Microscopy (Oxf) 63(1), 23–32 (2014).
    [Crossref]
  9. W. Yu, Z. Ji, X. Yang, Z. Gong, Y. Xiao, P. Xi, and K. Shi, “STED imaging by using hollow Bessel beam,” in Frontiers in Optics 2015, paper FTu3D.6.
  10. T.A. Planchon, L. Gao, D.E. Milkie, M.W. Davidson, J.A. Galbraith, C.G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–426 (2011).
    [Crossref] [PubMed]
  11. M. Zhao, H. Zhang, Y. Li, A. Ashok, R. Liang, W. Zhou, and L. Peng, “Cellular imaging of deep organ using two-photon Bessel light-sheet nonlinear structured illumination microscopy,” Biomed. Opt. Express 5(5), 1296–1308 (2014).
    [Crossref] [PubMed]
  12. P. Zhang, P.M. Goodwin, and J. H. Werner, “Fast, super resolution imaging via Bessel-beam stimulated emission depletion microscopy,” Opt. Express 22(10), 12398–12409 (2014).
    [Crossref] [PubMed]
  13. J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4–6), 239–245 (2001).
    [Crossref]
  14. Y. Kozawa and S. Sato, “Sharper focal spot formed by higher-order radially polarized laser beams,” J. Opt. Soc. Am. A 24(6), 1793–1798 (2007).
    [Crossref]
  15. Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, and S. Sato, “Lateral resolution enhancement of laser scanning microscopy by a higher-order radially polarized mode beam,” Opt. Express 72(6),15947–15954 (2011).
    [Crossref]
  16. J. Kim, D.C. Kim, and S.H. Back, “Demonstration of high lateral resolution in laser confocal microscopy using annular and radially polarized light,” Microsc. Res. Techniq. 19(17), 441–446 (2011).
  17. H. Dehez, M. Piché, and Y. De Koninck, “Resolution and contrast enhancement in laser scanning microscopy using dark beam imaging,” Opt. Express 21, 7128–7141 (2013).
    [Crossref]
  18. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. 2. structure of the image field in an aplanatic system,” Proc. R. Soc. A 253(1274), 358–379 (1959).
    [Crossref]
  19. L. Novotny and B. Hecht, Principles of Nano-Optics, (Cambridge University, 2006), Chap.3.
    [Crossref]
  20. J.D. Jackson, Classical Electrodynamics, (Wiley, 1998).
  21. J.H. McLeod, “The axicon: A new type of optical element,” J. Opt. Soc. Am. 44(8), 592–597 (1954).
    [Crossref]
  22. Arcoptix Switzerland, “Radial/aximuthal polarisation converter,” < http://www.arcoptix.com/radial_polarization_converter.htm >.
  23. W.T. Welford, “Use of annular apertures to increase focal depth,” J. Opt. Soc. Am. 50(8), 749–752 (1960).
    [Crossref]
  24. X. Zeng and F. Wu, “Effect of elliptical manufacture error of an axicon on the diffraction-free beam patterns,” Opt. Eng. 47(8), 083401 (2008).
    [Crossref]
  25. R. Arimoto, C. Saloma, T. Tanaka, and S. Kawata, “Imaging properties of axicon in a scanning optical system,” Appl. Opt. 31(31), 6653–6657 (1992).
    [Crossref] [PubMed]
  26. L.E. Lorenzo, A.G. Godin, F. Wang, M. St-Louis, S. Carbonetto, P. W. Wiseman, A. Ribeiro-da-Silva, and Y. De Koninck, “Gephyrin clusters are absent from small diameter primary afferent terminals despite the presence of GABAA receptors,” J. Neurosci. 34(24), 8300–8317 (2014).
    [Crossref] [PubMed]
  27. C. Kuang, S. Li, W. Liu, X. Hao, Z. Gu, Y. Wang, J. Ge, H. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep. 3, 1441 (2013).
    [Crossref]
  28. K. Korobchevskaya, C. Peres, Z. Li, A. Antipov, C.J.R. Sheppard, A. Diaspro, and P. Bianchini, “Intensity weighted subtraction microscopy approach for image contrast and resolution enhancement,” Sci. Rep. 6, 25816 (2016).
    [Crossref] [PubMed]
  29. Y. Kozawa and S. Sato, “Numerical analysis of resolution enhancement in laser scanning microscopy using a radially polarized beam,” Opt. Express 23(3), 2076–2084 (2015).
    [Crossref] [PubMed]
  30. P. Zhang, M.E. Phipps, P M. Goodwin, and J.H. Werner, “Confocal line scanning of a Bessel beam for fast 3D imaging,” Opt. Lett. 39(12), 3682–3685 (2014).
    [Crossref] [PubMed]
  31. S. Heuke, F.B. Legesse, D. Akimov, U. Hubner, J. Dellith, M. Schmitt, and J. Popp, “Bessel beam coherent anti-Stokes Raman scattering microscopy,” J. Opt. Soc. Am. B 32(9), 1773–1779 (2015).
    [Crossref]
  32. A. Gasecka, A. Daradich, H. Dehez, M. Piché, and D. Côté, “Resolution and contrast enhancement in coherent anti-Stokes Raman-scattering microscopy,” Opt. Lett. 38(21), 4510–4513 (2013).
    [Crossref] [PubMed]
  33. S.W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19(11), 780–782 (1994).
    [Crossref] [PubMed]
  34. E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hes, “Imaging intracellular fluorescent proteins at nano-meter resolution,” Science 313(5793), 1642–1645 (2006).
    [Crossref] [PubMed]
  35. M.J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–795 (2006).
    [Crossref] [PubMed]

2016 (1)

K. Korobchevskaya, C. Peres, Z. Li, A. Antipov, C.J.R. Sheppard, A. Diaspro, and P. Bianchini, “Intensity weighted subtraction microscopy approach for image contrast and resolution enhancement,” Sci. Rep. 6, 25816 (2016).
[Crossref] [PubMed]

2015 (3)

2014 (6)

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell. Neurosci. 8, 139 (2014).

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,” Microscopy (Oxf) 63(1), 23–32 (2014).
[Crossref]

M. Zhao, H. Zhang, Y. Li, A. Ashok, R. Liang, W. Zhou, and L. Peng, “Cellular imaging of deep organ using two-photon Bessel light-sheet nonlinear structured illumination microscopy,” Biomed. Opt. Express 5(5), 1296–1308 (2014).
[Crossref] [PubMed]

P. Zhang, P.M. Goodwin, and J. H. Werner, “Fast, super resolution imaging via Bessel-beam stimulated emission depletion microscopy,” Opt. Express 22(10), 12398–12409 (2014).
[Crossref] [PubMed]

P. Zhang, M.E. Phipps, P M. Goodwin, and J.H. Werner, “Confocal line scanning of a Bessel beam for fast 3D imaging,” Opt. Lett. 39(12), 3682–3685 (2014).
[Crossref] [PubMed]

L.E. Lorenzo, A.G. Godin, F. Wang, M. St-Louis, S. Carbonetto, P. W. Wiseman, A. Ribeiro-da-Silva, and Y. De Koninck, “Gephyrin clusters are absent from small diameter primary afferent terminals despite the presence of GABAA receptors,” J. Neurosci. 34(24), 8300–8317 (2014).
[Crossref] [PubMed]

2013 (4)

C. Kuang, S. Li, W. Liu, X. Hao, Z. Gu, Y. Wang, J. Ge, H. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep. 3, 1441 (2013).
[Crossref]

A. Gasecka, A. Daradich, H. Dehez, M. Piché, and D. Côté, “Resolution and contrast enhancement in coherent anti-Stokes Raman-scattering microscopy,” Opt. Lett. 38(21), 4510–4513 (2013).
[Crossref] [PubMed]

G. Thériault, Y. De Koninck, and N. McCarthy, “Extended depth of feld microscopy for rapid volumetric two-photon imaging,” Opt. Express 21(8), 10095–10104 (2013).
[Crossref] [PubMed]

H. Dehez, M. Piché, and Y. De Koninck, “Resolution and contrast enhancement in laser scanning microscopy using dark beam imaging,” Opt. Express 21, 7128–7141 (2013).
[Crossref]

2012 (1)

2011 (4)

K.B. Rajesha, N. Veerabagu Sureshb, P.M. Anbarasanc, K. Gokulakrishnanb, and G. Mahadevand, “Tight focusing of double ring shaped radially polarized beam with high NA lens axicon,” Opt. Laser Technol. 43(7), 1037–1040 (2011).
[Crossref]

T.A. Planchon, L. Gao, D.E. Milkie, M.W. Davidson, J.A. Galbraith, C.G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–426 (2011).
[Crossref] [PubMed]

Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, and S. Sato, “Lateral resolution enhancement of laser scanning microscopy by a higher-order radially polarized mode beam,” Opt. Express 72(6),15947–15954 (2011).
[Crossref]

J. Kim, D.C. Kim, and S.H. Back, “Demonstration of high lateral resolution in laser confocal microscopy using annular and radially polarized light,” Microsc. Res. Techniq. 19(17), 441–446 (2011).

2010 (1)

F.O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[Crossref]

2008 (1)

X. Zeng and F. Wu, “Effect of elliptical manufacture error of an axicon on the diffraction-free beam patterns,” Opt. Eng. 47(8), 083401 (2008).
[Crossref]

2007 (1)

2006 (3)

P. Dufour, M. Piché, Y. De Koninck, and N. McCarthy, “Two-photon excitation fluorescence microscopy with a high depth of field using an axicon,” Appl. Opt. 45(36), 9246–9252 (2006).
[Crossref] [PubMed]

E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hes, “Imaging intracellular fluorescent proteins at nano-meter resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

M.J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–795 (2006).
[Crossref] [PubMed]

2001 (1)

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4–6), 239–245 (2001).
[Crossref]

1994 (1)

1992 (1)

1960 (1)

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. 2. structure of the image field in an aplanatic system,” Proc. R. Soc. A 253(1274), 358–379 (1959).
[Crossref]

1954 (1)

Akimov, D.

Alfano, R.R.

G. Milione, A. Dudley, T.A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R.R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams,” J. Opt. 17(3), 035617 (2015).
[Crossref]

Anbarasanc, P.M.

K.B. Rajesha, N. Veerabagu Sureshb, P.M. Anbarasanc, K. Gokulakrishnanb, and G. Mahadevand, “Tight focusing of double ring shaped radially polarized beam with high NA lens axicon,” Opt. Laser Technol. 43(7), 1037–1040 (2011).
[Crossref]

Antipov, A.

K. Korobchevskaya, C. Peres, Z. Li, A. Antipov, C.J.R. Sheppard, A. Diaspro, and P. Bianchini, “Intensity weighted subtraction microscopy approach for image contrast and resolution enhancement,” Sci. Rep. 6, 25816 (2016).
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April, A.

Arimoto, R.

Arlt, J.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4–6), 239–245 (2001).
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Ashok, A.

Back, S.H.

J. Kim, D.C. Kim, and S.H. Back, “Demonstration of high lateral resolution in laser confocal microscopy using annular and radially polarized light,” Microsc. Res. Techniq. 19(17), 441–446 (2011).

Bates, M.

M.J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–795 (2006).
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Betzig, E.

T.A. Planchon, L. Gao, D.E. Milkie, M.W. Davidson, J.A. Galbraith, C.G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–426 (2011).
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E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hes, “Imaging intracellular fluorescent proteins at nano-meter resolution,” Science 313(5793), 1642–1645 (2006).
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Bianchini, P.

K. Korobchevskaya, C. Peres, Z. Li, A. Antipov, C.J.R. Sheppard, A. Diaspro, and P. Bianchini, “Intensity weighted subtraction microscopy approach for image contrast and resolution enhancement,” Sci. Rep. 6, 25816 (2016).
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Bonifacino, J.S.

E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hes, “Imaging intracellular fluorescent proteins at nano-meter resolution,” Science 313(5793), 1642–1645 (2006).
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L.E. Lorenzo, A.G. Godin, F. Wang, M. St-Louis, S. Carbonetto, P. W. Wiseman, A. Ribeiro-da-Silva, and Y. De Koninck, “Gephyrin clusters are absent from small diameter primary afferent terminals despite the presence of GABAA receptors,” J. Neurosci. 34(24), 8300–8317 (2014).
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G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell. Neurosci. 8, 139 (2014).

Chakraborty, O.

G. Milione, A. Dudley, T.A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R.R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams,” J. Opt. 17(3), 035617 (2015).
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Cottet, M.

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell. Neurosci. 8, 139 (2014).

Daradich, A.

Davidson, M.W.

T.A. Planchon, L. Gao, D.E. Milkie, M.W. Davidson, J.A. Galbraith, C.G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–426 (2011).
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E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hes, “Imaging intracellular fluorescent proteins at nano-meter resolution,” Science 313(5793), 1642–1645 (2006).
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De Koninck, Y.

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell. Neurosci. 8, 139 (2014).

L.E. Lorenzo, A.G. Godin, F. Wang, M. St-Louis, S. Carbonetto, P. W. Wiseman, A. Ribeiro-da-Silva, and Y. De Koninck, “Gephyrin clusters are absent from small diameter primary afferent terminals despite the presence of GABAA receptors,” J. Neurosci. 34(24), 8300–8317 (2014).
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H. Dehez, M. Piché, and Y. De Koninck, “Resolution and contrast enhancement in laser scanning microscopy using dark beam imaging,” Opt. Express 21, 7128–7141 (2013).
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G. Thériault, Y. De Koninck, and N. McCarthy, “Extended depth of feld microscopy for rapid volumetric two-photon imaging,” Opt. Express 21(8), 10095–10104 (2013).
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P. Dufour, M. Piché, Y. De Koninck, and N. McCarthy, “Two-photon excitation fluorescence microscopy with a high depth of field using an axicon,” Appl. Opt. 45(36), 9246–9252 (2006).
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Dellith, J.

Dholakia, K.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4–6), 239–245 (2001).
[Crossref]

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K. Korobchevskaya, C. Peres, Z. Li, A. Antipov, C.J.R. Sheppard, A. Diaspro, and P. Bianchini, “Intensity weighted subtraction microscopy approach for image contrast and resolution enhancement,” Sci. Rep. 6, 25816 (2016).
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G. Milione, A. Dudley, T.A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R.R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams,” J. Opt. 17(3), 035617 (2015).
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Dufour, P.

Fahrbach, F.O.

F.O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[Crossref]

Forbes, A.

G. Milione, A. Dudley, T.A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R.R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams,” J. Opt. 17(3), 035617 (2015).
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T.A. Planchon, L. Gao, D.E. Milkie, M.W. Davidson, J.A. Galbraith, C.G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–426 (2011).
[Crossref] [PubMed]

Galbraith, J.A.

T.A. Planchon, L. Gao, D.E. Milkie, M.W. Davidson, J.A. Galbraith, C.G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–426 (2011).
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T.A. Planchon, L. Gao, D.E. Milkie, M.W. Davidson, J.A. Galbraith, C.G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–426 (2011).
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Garces-Chavez, V.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4–6), 239–245 (2001).
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Ge, J.

C. Kuang, S. Li, W. Liu, X. Hao, Z. Gu, Y. Wang, J. Ge, H. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep. 3, 1441 (2013).
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L.E. Lorenzo, A.G. Godin, F. Wang, M. St-Louis, S. Carbonetto, P. W. Wiseman, A. Ribeiro-da-Silva, and Y. De Koninck, “Gephyrin clusters are absent from small diameter primary afferent terminals despite the presence of GABAA receptors,” J. Neurosci. 34(24), 8300–8317 (2014).
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K.B. Rajesha, N. Veerabagu Sureshb, P.M. Anbarasanc, K. Gokulakrishnanb, and G. Mahadevand, “Tight focusing of double ring shaped radially polarized beam with high NA lens axicon,” Opt. Laser Technol. 43(7), 1037–1040 (2011).
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Goodwin, P.M.

Gu, Z.

C. Kuang, S. Li, W. Liu, X. Hao, Z. Gu, Y. Wang, J. Ge, H. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep. 3, 1441 (2013).
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C. Kuang, S. Li, W. Liu, X. Hao, Z. Gu, Y. Wang, J. Ge, H. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep. 3, 1441 (2013).
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Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, and S. Sato, “Lateral resolution enhancement of laser scanning microscopy by a higher-order radially polarized mode beam,” Opt. Express 72(6),15947–15954 (2011).
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Hes, H.F.

E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hes, “Imaging intracellular fluorescent proteins at nano-meter resolution,” Science 313(5793), 1642–1645 (2006).
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Hibi, T.

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,” Microscopy (Oxf) 63(1), 23–32 (2014).
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Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, and S. Sato, “Lateral resolution enhancement of laser scanning microscopy by a higher-order radially polarized mode beam,” Opt. Express 72(6),15947–15954 (2011).
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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,” Microscopy (Oxf) 63(1), 23–32 (2014).
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Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, and S. Sato, “Lateral resolution enhancement of laser scanning microscopy by a higher-order radially polarized mode beam,” Opt. Express 72(6),15947–15954 (2011).
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Ipponjima, S.

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,” Microscopy (Oxf) 63(1), 23–32 (2014).
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W. Yu, Z. Ji, X. Yang, Z. Gong, Y. Xiao, P. Xi, and K. Shi, “STED imaging by using hollow Bessel beam,” in Frontiers in Optics 2015, paper FTu3D.6.

Karimi, E.

G. Milione, A. Dudley, T.A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R.R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams,” J. Opt. 17(3), 035617 (2015).
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Kim, D.C.

J. Kim, D.C. Kim, and S.H. Back, “Demonstration of high lateral resolution in laser confocal microscopy using annular and radially polarized light,” Microsc. Res. Techniq. 19(17), 441–446 (2011).

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J. Kim, D.C. Kim, and S.H. Back, “Demonstration of high lateral resolution in laser confocal microscopy using annular and radially polarized light,” Microsc. Res. Techniq. 19(17), 441–446 (2011).

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K. Korobchevskaya, C. Peres, Z. Li, A. Antipov, C.J.R. Sheppard, A. Diaspro, and P. Bianchini, “Intensity weighted subtraction microscopy approach for image contrast and resolution enhancement,” Sci. Rep. 6, 25816 (2016).
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Y. Kozawa and S. Sato, “Numerical analysis of resolution enhancement in laser scanning microscopy using a radially polarized beam,” Opt. Express 23(3), 2076–2084 (2015).
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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,” Microscopy (Oxf) 63(1), 23–32 (2014).
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Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, and S. Sato, “Lateral resolution enhancement of laser scanning microscopy by a higher-order radially polarized mode beam,” Opt. Express 72(6),15947–15954 (2011).
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Y. Kozawa and S. Sato, “Sharper focal spot formed by higher-order radially polarized laser beams,” J. Opt. Soc. Am. A 24(6), 1793–1798 (2007).
[Crossref]

Kuang, C.

C. Kuang, S. Li, W. Liu, X. Hao, Z. Gu, Y. Wang, J. Ge, H. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep. 3, 1441 (2013).
[Crossref]

Kurihara, M.

Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, and S. Sato, “Lateral resolution enhancement of laser scanning microscopy by a higher-order radially polarized mode beam,” Opt. Express 72(6),15947–15954 (2011).
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Li, H.

C. Kuang, S. Li, W. Liu, X. Hao, Z. Gu, Y. Wang, J. Ge, H. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep. 3, 1441 (2013).
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Li, S.

C. Kuang, S. Li, W. Liu, X. Hao, Z. Gu, Y. Wang, J. Ge, H. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep. 3, 1441 (2013).
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Li, Y.

Li, Z.

K. Korobchevskaya, C. Peres, Z. Li, A. Antipov, C.J.R. Sheppard, A. Diaspro, and P. Bianchini, “Intensity weighted subtraction microscopy approach for image contrast and resolution enhancement,” Sci. Rep. 6, 25816 (2016).
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Lindwasser, O.W.

E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hes, “Imaging intracellular fluorescent proteins at nano-meter resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Lippincott-Schwartz, J.

E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hes, “Imaging intracellular fluorescent proteins at nano-meter resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Liu, W.

C. Kuang, S. Li, W. Liu, X. Hao, Z. Gu, Y. Wang, J. Ge, H. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep. 3, 1441 (2013).
[Crossref]

Liu, X.

C. Kuang, S. Li, W. Liu, X. Hao, Z. Gu, Y. Wang, J. Ge, H. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep. 3, 1441 (2013).
[Crossref]

Lorenzo, L.E.

L.E. Lorenzo, A.G. Godin, F. Wang, M. St-Louis, S. Carbonetto, P. W. Wiseman, A. Ribeiro-da-Silva, and Y. De Koninck, “Gephyrin clusters are absent from small diameter primary afferent terminals despite the presence of GABAA receptors,” J. Neurosci. 34(24), 8300–8317 (2014).
[Crossref] [PubMed]

Mahadevand, G.

K.B. Rajesha, N. Veerabagu Sureshb, P.M. Anbarasanc, K. Gokulakrishnanb, and G. Mahadevand, “Tight focusing of double ring shaped radially polarized beam with high NA lens axicon,” Opt. Laser Technol. 43(7), 1037–1040 (2011).
[Crossref]

McCarthy, N.

McLeod, J.H.

Milione, G.

G. Milione, A. Dudley, T.A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R.R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams,” J. Opt. 17(3), 035617 (2015).
[Crossref]

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T.A. Planchon, L. Gao, D.E. Milkie, M.W. Davidson, J.A. Galbraith, C.G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–426 (2011).
[Crossref] [PubMed]

Nemoto, T.

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,” Microscopy (Oxf) 63(1), 23–32 (2014).
[Crossref]

Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, and S. Sato, “Lateral resolution enhancement of laser scanning microscopy by a higher-order radially polarized mode beam,” Opt. Express 72(6),15947–15954 (2011).
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G. Milione, A. Dudley, T.A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R.R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams,” J. Opt. 17(3), 035617 (2015).
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L. Novotny and B. Hecht, Principles of Nano-Optics, (Cambridge University, 2006), Chap.3.
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E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hes, “Imaging intracellular fluorescent proteins at nano-meter resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Patterson, G.H.

E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hes, “Imaging intracellular fluorescent proteins at nano-meter resolution,” Science 313(5793), 1642–1645 (2006).
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Peng, L.

Peres, C.

K. Korobchevskaya, C. Peres, Z. Li, A. Antipov, C.J.R. Sheppard, A. Diaspro, and P. Bianchini, “Intensity weighted subtraction microscopy approach for image contrast and resolution enhancement,” Sci. Rep. 6, 25816 (2016).
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Piché, M.

Planchon, T.A.

T.A. Planchon, L. Gao, D.E. Milkie, M.W. Davidson, J.A. Galbraith, C.G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–426 (2011).
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Rajesha, K.B.

K.B. Rajesha, N. Veerabagu Sureshb, P.M. Anbarasanc, K. Gokulakrishnanb, and G. Mahadevand, “Tight focusing of double ring shaped radially polarized beam with high NA lens axicon,” Opt. Laser Technol. 43(7), 1037–1040 (2011).
[Crossref]

Ribeiro-da-Silva, A.

L.E. Lorenzo, A.G. Godin, F. Wang, M. St-Louis, S. Carbonetto, P. W. Wiseman, A. Ribeiro-da-Silva, and Y. De Koninck, “Gephyrin clusters are absent from small diameter primary afferent terminals despite the presence of GABAA receptors,” J. Neurosci. 34(24), 8300–8317 (2014).
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F.O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[Crossref]

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M.J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–795 (2006).
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Sato, A.

Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, and S. Sato, “Lateral resolution enhancement of laser scanning microscopy by a higher-order radially polarized mode beam,” Opt. Express 72(6),15947–15954 (2011).
[Crossref]

Sato, S.

Y. Kozawa and S. Sato, “Numerical analysis of resolution enhancement in laser scanning microscopy using a radially polarized beam,” Opt. Express 23(3), 2076–2084 (2015).
[Crossref] [PubMed]

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,” Microscopy (Oxf) 63(1), 23–32 (2014).
[Crossref]

Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, and S. Sato, “Lateral resolution enhancement of laser scanning microscopy by a higher-order radially polarized mode beam,” Opt. Express 72(6),15947–15954 (2011).
[Crossref]

Y. Kozawa and S. Sato, “Sharper focal spot formed by higher-order radially polarized laser beams,” J. Opt. Soc. Am. A 24(6), 1793–1798 (2007).
[Crossref]

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Sheppard, C.J.R.

K. Korobchevskaya, C. Peres, Z. Li, A. Antipov, C.J.R. Sheppard, A. Diaspro, and P. Bianchini, “Intensity weighted subtraction microscopy approach for image contrast and resolution enhancement,” Sci. Rep. 6, 25816 (2016).
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Shi, K.

W. Yu, Z. Ji, X. Yang, Z. Gong, Y. Xiao, P. Xi, and K. Shi, “STED imaging by using hollow Bessel beam,” in Frontiers in Optics 2015, paper FTu3D.6.

Sibbett, W.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4–6), 239–245 (2001).
[Crossref]

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F.O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[Crossref]

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E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hes, “Imaging intracellular fluorescent proteins at nano-meter resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

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L.E. Lorenzo, A.G. Godin, F. Wang, M. St-Louis, S. Carbonetto, P. W. Wiseman, A. Ribeiro-da-Silva, and Y. De Koninck, “Gephyrin clusters are absent from small diameter primary afferent terminals despite the presence of GABAA receptors,” J. Neurosci. 34(24), 8300–8317 (2014).
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Thériault, G.

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell. Neurosci. 8, 139 (2014).

G. Thériault, Y. De Koninck, and N. McCarthy, “Extended depth of feld microscopy for rapid volumetric two-photon imaging,” Opt. Express 21(8), 10095–10104 (2013).
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Wang, Y.

C. Kuang, S. Li, W. Liu, X. Hao, Z. Gu, Y. Wang, J. Ge, H. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep. 3, 1441 (2013).
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Werner, J. H.

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Wiseman, P. W.

L.E. Lorenzo, A.G. Godin, F. Wang, M. St-Louis, S. Carbonetto, P. W. Wiseman, A. Ribeiro-da-Silva, and Y. De Koninck, “Gephyrin clusters are absent from small diameter primary afferent terminals despite the presence of GABAA receptors,” J. Neurosci. 34(24), 8300–8317 (2014).
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[Crossref]

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[Crossref]

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W. Yu, Z. Ji, X. Yang, Z. Gong, Y. Xiao, P. Xi, and K. Shi, “STED imaging by using hollow Bessel beam,” in Frontiers in Optics 2015, paper FTu3D.6.

Xiao, Y.

W. Yu, Z. Ji, X. Yang, Z. Gong, Y. Xiao, P. Xi, and K. Shi, “STED imaging by using hollow Bessel beam,” in Frontiers in Optics 2015, paper FTu3D.6.

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W. Yu, Z. Ji, X. Yang, Z. Gong, Y. Xiao, P. Xi, and K. Shi, “STED imaging by using hollow Bessel beam,” in Frontiers in Optics 2015, paper FTu3D.6.

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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,” Microscopy (Oxf) 63(1), 23–32 (2014).
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X. Zeng and F. Wu, “Effect of elliptical manufacture error of an axicon on the diffraction-free beam patterns,” Opt. Eng. 47(8), 083401 (2008).
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G. Milione, A. Dudley, T.A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R.R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams,” J. Opt. 17(3), 035617 (2015).
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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,” Microscopy (Oxf) 63(1), 23–32 (2014).
[Crossref]

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Nat. Photonics (1)

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Opt. Commun. (1)

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Opt. Eng. (1)

X. Zeng and F. Wu, “Effect of elliptical manufacture error of an axicon on the diffraction-free beam patterns,” Opt. Eng. 47(8), 083401 (2008).
[Crossref]

Opt. Express (6)

Opt. Laser Technol. (1)

K.B. Rajesha, N. Veerabagu Sureshb, P.M. Anbarasanc, K. Gokulakrishnanb, and G. Mahadevand, “Tight focusing of double ring shaped radially polarized beam with high NA lens axicon,” Opt. Laser Technol. 43(7), 1037–1040 (2011).
[Crossref]

Opt. Lett. (3)

Proc. R. Soc. A (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. 2. structure of the image field in an aplanatic system,” Proc. R. Soc. A 253(1274), 358–379 (1959).
[Crossref]

Sci. Rep. (2)

C. Kuang, S. Li, W. Liu, X. Hao, Z. Gu, Y. Wang, J. Ge, H. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep. 3, 1441 (2013).
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Figures (12)

Fig. 1
Fig. 1 Comparison of Bessel-Gauss beams with their Gaussian beam counterparts in the focal plane (z = 0), as calculated by Eqs. (1) and (2). Left: theoretical Gaussian and TE01 beams. Middle: theoretical Bessel-Gauss beams. Right: Horizontal profiles with FWHM of the two beams. The coverslip refractive index is n2 = 1.5 and the mounting medium refractive index is n1 = 1.47. Numerical aperture of the focussing objective: NA = 1.2. Wavelength: λ = 532 nm
Fig. 2
Fig. 2 Simplified schematic representation of the confocal microscope that uses Bessel-Gauss beams. The zoomed part depicts the beam transformation by the axicon. In the zoomed part w represents the Gaussian beam waist before entering the axicon and β is the angle of the cone formed by the rays refracted by the axicon. The laser used in our confocal microscope is a Compass 215M from Coherent Inc. (with a wavelength of 532 nm) delivering a maximum output power of 40 mW which is largely sufficient for all of the measurements reported here.
Fig. 3
Fig. 3 Calculations and experimental measurements of the vertically and azimuthally polarized Bessel-Gauss beams produced at the focus of the objective. The top row shows the vertically polarized Bessel-Gauss beam and the bottom row the azimuthally polarized Bessel-Gauss beam. The left column represents the simulated results, the middle one the experimental PSF (Point Spread Function) of the beams taken with 100-nm diameter nano-spheres (fluosphere carboxylate-modified microspheres, orange fluorescence 540/560 from Invitrogen molecular probes) and the right column compares the theoretical and experimental profiles and the corresponding FWHMs.
Fig. 4
Fig. 4 A: Images of 100-nm diameter fluorescent nano-spheres (same as Fig. 3) observed with a confocal microscope having a pinhole of 15 μm. The nano-spheres are observed with a Gaussian beam of vertical polarization (A1), Bessel-Gauss beam of vertical polarization (A2), TE01 beam of azimuthal polarization (A3) and Bessel-Gauss beam of azimuthal polarization (A4). B: Focal spot of the Bessel-Gauss beam of vertical polarization for different pinhole diameters obtained using 100-nm fluorescent nano-spheres: 25 μm (B1), 15 μm (B2) and 10 μm (B3). Excitation wavelength: 532 nm. Scale bar: 500 nm
Fig. 5
Fig. 5 Confocal image of a single and an average of ≈ 30 fluorescent nano-spheres for both Gaussian and Bessel-Gauss beams. Pinhole diameter: 10 μm. The right panel displays the normalized profiles of the nano-spheres along the horizontal axis (colored lines on the images). The traces with full lines are for the 30 nano-sphere average PSFs and the crosses are pixel values for the single nano-sphere measurements.
Fig. 6
Fig. 6 Axial view of the PSF measured with nano-spheres. A) PSF of the vertically polarized Gaussian beam. B) PSF of the vertically polarized Bessel-Gauss beam. The left image displays an axial view of the PSF. The right curve is an intensity profile along the red dashed line of the axial PSF with the corresponding FWHM. The black dots on the curve represent the pixel data before interpolation. The red curves represent a plot of the interpolated values. Pixel size along the x axis: 24 nm. Pixel size along the z axis: 250 nm.
Fig. 7
Fig. 7 Confocal images of a sample of 100-nm fluorescent nano-spheres observed with a Gaussian beam (left) and with a Bessel-Gauss beam (right). Center: normalized profiles along the coloured lines in the two images. The black line in the central panel corresponds to the resolution measured between the two maxima. Pinhole diameter: 10 μm. Scale bar: 510 nm. Images filtered with a Gaussian filter having a FWHM of one pixel.
Fig. 8
Fig. 8 Confocal images of microtubules stained by immunohistochemistry (monoclonal anti α-tubulin primary antibody - revealed by a donkey anti-mouse Rhodamine RedX-labeled secondary antibody) observed with a Gaussian beam (left) and with a Bessel-Gauss beam (right). Center: normalized integrated profiles (5-pixel width line) along the coloured lines in the two images. The black line in the central panel corresponds to the resolution measured between the two maxima. Pinhole diameter: 10 μm. Scale bar: 510 nm. Images filtered with a Gaussian filter having a FWHM of one pixel.
Fig. 9
Fig. 9 Gephyrin immunodetected by a monoclonal mAb7a Oyster 550 coupled antibody, excitation maximum at 551 nm. Left: images obtained with a Gaussian beam. Center: normalized profiles along the coloured lines on the images. The black dotted line in the central panel corresponds to the resolution measured between the two maxima. Right: images obtained with a Bessel-Gauss beam. Pinhole diameter: 10 μm. Scale bar: 1000 nm. Images filtered with a Gaussian filter having a FWHM of one pixel.
Fig. 10
Fig. 10 A: Two images of the same field taken with Gaussian and Bessel-Gauss beams with magnified sub-regions and their associated binarized masks (the mask creation is a step of the colocalization analysis [26]). The image contrast has been adjusted for better visibility but raw data were used for the analysis. B and C: comparison of the index obtained from Gaussian and Bessel-Gauss acquisitions with the same field. A lower index corresponds to a lower colocalization. The indexes are compared using a paired t-test.
Fig. 11
Fig. 11 Application of SLAM and B-SLAM to nano-spheres with Gaussian beams (top right image with g = 0.9) and Bessel-Gauss beams (bottom right image with g = 1.0). Left: confocal images. Center: normalized profiles along the coloured lines of the images. The black line in the central panel corresponds to the resolution measured between the two maxima. Pinhole diameter: 10 μm. Scale bar: 300 nm.
Fig. 12
Fig. 12 SLAM method applied to microtubules with Gaussian (top images) and Bessel-Gauss beams (bottom images). Left: confocal images. Right: SLAM (with g = 0.8) and B-SLAM (with g = 1.0) images. Center: normalized profile traces along the coloured lines in the images. The profiles are integrated along 10 pixels in width. Pinhole diameter: 10 μm. Scale bar: 1 μm.

Equations (6)

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E x ( ρ , φ , z ) = E 0 2 n 0 θ max cos 1 2 θ l 0 ( θ , φ ) exp ( i k z cos θ ) sin θ × [ ( 1 + cos θ ) J 0 ( k ρ sin θ ) + ( 1 cos θ ) J 2 ( k ρ sin θ ) cos ( 2 φ ) ] d θ , E y ( ρ , φ , z ) = E 0 2 n 0 θ max cos 1 2 θ l 0 ( θ , φ ) exp ( i k z cos θ ) sin θ × ( 1 cos θ ) J 2 ( k ρ sin θ ) sin ( 2 φ ) d θ , E z ( ρ , φ , z ) = i E 0 n 0 θ max cos 1 2 θ l 0 ( θ , φ ) exp ( i k z cos θ ) sin θ J 1 ( k ρ sin θ ) cos ( φ ) d θ ,
E x ( ρ , φ , z ) = i E 0 n 0 θ max cos 1 2 θ l 0 ( θ , φ ) exp ( i k z cos θ ) sin 2 θ J 1 ( k ρ sin θ ) sin ( φ ) d θ , E y ( ρ , φ , z ) = i E 0 n 0 θ max cos 1 2 θ l 0 ( θ , φ ) exp ( i k z cos θ ) sin 2 θ J 1 ( k ρ sin θ ) cos ( φ ) d θ , E z ( ρ , φ , z ) = 0 .
E x ( ρ , φ , z ) = E 0 2 n cos 1 2 θ 0 exp ( i k z cos θ 0 ) sin θ 0 × [ ( 1 + cos θ 0 ) J 0 ( k ρ sin θ 0 ) + ( 1 cos θ 0 ) J 2 ( k ρ sin θ 0 ) cos ( 2 φ ) ] , E y ( ρ , φ , z ) = E 0 2 n cos 1 2 θ 0 exp ( i k z cos θ 0 ) sin θ 0 × ( 1 cos θ 0 ) J 2 ( k ρ sin θ 0 ) sin ( 2 φ ) , E z ( ρ , φ , z ) = i E 0 n cos 1 2 θ 0 exp ( i k z cos θ 0 ) sin θ 0 J 1 ( k ρ sin θ 0 ) cos ( φ ) ,
E x ( ρ , φ , z ) f ( z ) ( 1 + cos θ 0 ) J 0 ( k ρ sin θ 0 ) , E y ( ρ , φ , z ) 0 , E z ( ρ , φ , z ) 2 i f ( z ) J 1 ( k ρ sin θ 0 ) cos ( φ ) ,
E ρ ( ρ , φ , z ) = 0 , E φ ( ρ , φ , z ) = i E 0 n cos 1 2 ( θ 0 ) exp ( i k z cos θ 0 ) sin 2 ( θ 0 ) J 1 ( k ρ sin θ 0 ) , E z ( ρ , φ , z ) = 0 .
I SLAM = I bright g × I donut

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