Ultrafast widefield optical sectioning microscopy by multifocal temporal focusing

Alipasha Vaziri; Charles V. Shank

doi:10.1364/OE.18.019645

1. Introduction

The invention of two-photon scanning microscopy [1] together with various fluorescence labeling techniques have revolutionized bio-imaging in the last 15 years and have created a wealth of new insights into biological structure and function. The power of this technique relies on its high optical sectioning capability which allows for axially highly localized excitation of fluorescent molecules in a biological sample. The high axial localization of excitation stems from the intensity squared dependence of excitation in the two-photon process and is achieved by focusing the light of an ultrafast laser to a diffraction limited spot using an objective with high numerical aperture. In order to generate an image, the focused spot has to be scanned across the sample typically by a pair of scanning mirrors. In this fashion series of images at different axial locations each separated by a fraction of the optical wavelength can be generated, allowing for a three dimensional reconstruction of the biological structure with diffraction limited resolutions in all dimensions.

However, the high optical sectioning in two-photon scanning microscopy is compromised by the point source excitation scheme. The need to scan a point source in order to generate an image introduces technical complexity and most notably imposes some limitations on a number of imaging applications where the achievable frame rates are below the time scales relevant for capturing the dynamics of the biological process under investigation. While the scanning time has recently been significantly reduced by the introduction of new methods that require scanning only along one dimension [2] or methods that rely on the excitation of the sample via multiple foci [3], all methods explored so far still rely on mechanical scanning of components. A method eluding that need would compel through its simplicity and could potentially achieve even higher scanning speeds which would have many applications, such as high-speed functional volume imaging. In order to achieve this, the ability to decouple the axial and the lateral beam parameters of the excitation light is desired. A “sculpted” beam with a spatial light distribution that exhibits a similar axial sectioning as the two-photon scanning technique while extending laterally over many microns, would overcome such issues with the finite scanning time. Hence, it could be used for high-speed imaging of biological processes with fast dynamics while maintaining the advantages of two-photon scanning microscopy.

Recently the technique of temporal focusing [4–6] has been shown to provide such a widefield excitation scheme with high optical sectioning, which has found applications amongst others in multilayer super-resolution imaging [7] and subcellular optogenetic control of neuronal circuitry [8]. In temporal focusing the axial localization of two-photon excitation is achieved by introducing a geometrical dispersion for the out of focus region in the sample and thereby reducing the spatial overlap of the spectral components of the pulse. This geometric dispersion in addition to the spatial divergence of the beam leads to the high axial sectioning of this technique. It has previously been shown [2] that the axial confinement of excitation for widefield temporal focusing is given by

T P E (Δ ​ z) = {[1 + {(\frac{Δ z}{z_{R}})}^{2}]}^{- \frac{1}{2}} ​,

with

T P E

describing the two-photon excitation probability as a function of the axial displacement

Δ z

from the focal point and

z_{R} = f^{2} λ / π D^{2}

the Rayleigh range of an optimally filled objective with a back focal aperture of D and a focal length of f for a beam with the central wavelength of λ. Experimentally, temporal focusing is achieved by dispersing the light from an ultrafast femtoscocond laser by a diffraction grating. The spot on the grating is then imaged via a telescope consisting of a lens and the microscope objective onto the specimen plane [4–6]. This geometry ensures that the beam at the specimen is geometrically dispersed everywhere except at the image plane where all spectral components are co-localized leading to its high optical sectioning despite of the widefield characteristic. In this configuration the lateral size of the beam at the sample is determined by the size of the spot on the grating and the demagnification factor of the telescope, while its axial width for a given pulse duration is determined by the geometric dispersion introduced by the grating and the numerical aperture of the microscope objective [2]. Using 10 fs and 140 fs pulsed lasers and microscope objectives with a numerical aperture of up to 1.2, we had previously demonstrated that axial confinements of excitation as short as ~1.6 µm can be achieved [7]. Although this value is far shorter than the depth of field of the same sized spot without temporal focusing, it is still about two times longer than typical axial confinements achieved by a two-photon scanning microscope [1]. This difference can be intuitively understood through the following argument. In widefield temporal focusing, the dispersion introduced by the grating leads to a line-shaped illumination of the back focal aperture. This is in contrast with the two-photon scanning microscope where the entire area of the back focal aperture is filled with a collimated beam and hence the full numerical aperture of the objective is utilized. This “underutilization” of the full numerical aperture in widefield temporal focusing leads to a lower axial confinement of excitation compared to the two-photon scanning technique. Improving the axial localization of temporal focusing to that of a two-photon scanning microscope would therefore require a complete filling of the back focal aperture. It has been shown [2] that a line scanning temporal focusing approach, i.e. a scheme in which the temporally focused spot forms a line in the sample that is scanned mechanically in one dimension, could achieve this goal by providing an axial confinement of excitation of

T P E (Δ ​ z) = {[1 + {(\frac{Δ z}{z_{R}})}^{2}]}^{- 1},

a value shorter by a factor of 3 compared to that of a widefield temporal focusing. However, as mentioned above, achieving such axial confinements without the need of mechanical scanning while providing higher speeds and larger fields of view would be highly desirable. In the following we have demonstrated the implementation of a method which overcomes the need for any mechanical scanning by using multifocal temporal focusing (MUTEF). In MUTEF at each time point one or several temporally focused diffraction limited spots are generated at the sample. These spots are then scanned across the sample as the laser beam propagates across two gratings; a diffraction grating and an Echelle grating; in picosecond time scale resulting in a widefield excitation area with diffraction limited axial resolution.

2. Method and theory

As discussed above, the main reason for the longer axial confinement of excitation in widefield temporal focusing is the underutilization of the numerical aperture of the objective. Thus, if one could use the entire numerical aperture, i.e. fill the back focal plane without sacrificing the lateral size of the excitation area, it would be possible to reduce the axial confinement of excitation to that of a two-photon scanning microscope. Complete two-dimensional filling of the back focal aperture in temporal focusing can be achieved by using diffraction in one dimension and spectral dispersion in the other dimensions. By preparing a beam at the diffraction grating for which the diffraction (i.e. divergence) is matched in its magnitude to that of the dispersion introduced by the grating but its direction is orthogonal, a spatially isotropically diverging beam can be prepared. Using the grating dispersion relation and the divergence of a Gaussian beam, the following constraint is imposed

\frac{Δ λ}{ε \sin α_{2}} = \frac{2 λ}{π ω_{0}^{z}},

where

Δ λ

is the spectral width of the pulsed source, ε is the grating period of the diffraction grating,

90 - α_{2}

is the diffraction angle and

ω_{0}^{z}

is the waist size of the collimated spot in the z-direction (i.e. parallel to the grooves) on the grating. In this fashion the spectral divergence in the y-direction and the spatial divergence in the z-direction are matched resulting in an uniform filling of the back focal aperture. As previously shown in the implementation of line-scanning temporal focusing [2], this requirement of matching the spatial and spectral divergence can be practically met by placing the diffraction grating at the focal point of a cylindrical lens. However, this approach will obviously lead to a line-shaped excitation area in the sample plane, as in temporal focusing the shape of the excitation beam is the demagnified image of the beam at the diffraction grating. Hence the line needs to be mechanically scanned in one dimension via a scanning mirror to generate a widefield excitation area. In our scheme instead of the mechanical scanning, a widefield area is generated by using an Echelle grating with lines orthogonal to that of the initial grating (Fig. 1 ). This design also resembles a scheme previously used for spectroscopy using resolved modes of a frequency comb [9].

Fig. 1 Overview of multifocal temporal focusing (MUTEF) for ultrafast high axial resolution widefield imaging. An Echelle grating is imaged via a telescope onto a diffraction grating with lines orthogonal to the former. In this fashion multiple beamlets each of which filling the backfocal aperture of an objective via dispersion in one dimension and via diffraction in the other dimension scan in picosecond time scale on the diffraction grating and the sample leading to a widefield excitation area.

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A collimated excitation beam with a diameter of $d_{0}$ is diffracted off of an Echelle grating with a periodaand a step depth b (Fig. 2 ). The zero-order beam is then imaged via a telescope with magnification $M_{1}$ onto the grating with a periodε. The dispersed first order diffraction of the grating is then imaged via a second telescope consisting of the microscope objective and the coupling lens with the focal length $f_{2}$ onto the specimen. In order to understand how the combination of the Echelle grating and temporal focusing can be used for fast high axial resolution imaging and to develop an insight for the requirements and limitations of such a system, it is instructive to consider a picture where the parameters of the excitation beam and the geometry of the optical system are mapped into the spatial domain (Fig. 2). In such a picture the temporal delay introduced by the step depth b of the Echelle grating generates a series of copies of the initial pulse that are each separated by $2 b$ in the axial direction and propagate towards the grating. Each pulse itself extends over a spatial distance equivalent to the pulse coherence length of $σ = 2 λ \ln 2 / π Δ λ$ . These series of pulses each separated by $a / M_{1}$ in the z-direction are falling at an angle $α_{1}$ onto the grating and scan across it along the y-direction. In this fashion at each moment in time the grating is illuminated by multiple “beamlets” which are forming spots of a size $σ / \sin α_{1}$ in the y-direction and $a / M_{1}$ in the z-direction with their centers separated by $Δ = \sqrt{{(2 b / \sin α_{1})}^{2} + {(a / M_{1})}^{2}}$ . In order to achieve the highest axial confinement of excitation the size of these “beamlets” has to be smaller or equal to the projected size of a magnified diffraction limited spot onto the grating. At the same time the separation between these beamlets has to be such that the axial position of the first Talbot image at $Δ^{2} / 2 λ M_{2}^{2}$ is at least about two Rayleigh ranges away from the focal plane of the objective [10]. The Talbot length is a consequence of the Fresnel diffraction and is the axial period at which a self constructive focusing of light passing through a periodic structure occurs. It was shown in [10] the above condition can be practically met when the ratio between the separation of the beamlets and the magnified diffraction limited spot is ~20. Altogether this poses the following constrains:

\frac{σ}{\sin α_{1}} \leq \frac{M_{2} s}{\sin α_{2}},

\frac{a}{M_{1}} \leq M_{2} s,

2 b / \sin α_{1} \geq \frac{20 M_{2} s}{\sin α_{2}},

withsthe size of the diffraction limited spot and

M_{2}

the magnification of the second telescope. In addition, the combined choice of

f_{2}

and ε must be such that the dispersion of the “beamlets” in the y-direction leads to the filling of the backfocal aperture D, i.e:

Fig. 2 Details of the pulse propagation and the geometry in MUTEF at the diffraction and the Echelle grating.

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\frac{Δ λ f_{2}}{ε \sin α_{2}} = D .

While Eqs. (2.2), (2.3) and (2.5) are defining the conditions for using the entire numerical aperture of the objective for the individual beamlets and hence achieving a diffraction limited axial confinement of excitation, Eq. (2.4) is defining the minimal required condition for achieving distinguishability between these beamlets over a sufficient axial extent around the focal plane at the sample and hence avoiding interference that would otherwise result in a deterioration of the axial confinement.

In many ways this is similar to the basic idea of multifocal microscopy [3] where fast high axial resolution imaging is achieved by exciting the sample with multiple foci which are mechanically scanned in at least one dimension. However the lack of any mechanical moving parts in our scheme results in significantly higher scanning speeds which are equivalent to the time required for light to scan across an area of the size of the spot.

As shown in Fig. 2 an important feature of our scheme is that at each moment in time the grating and hence the sample can be illuminated with multiple beamlets, as long as they are separated by an amount given by Eq. (2.4). This also means that there is not a direct tradeoff between the imaged field of view and the axial confinement or the imaging speed. Increasing the field of view based on the above picture would mean adding more beamlets in Fig. 2 which would not affect their required minimal separation. However as the field of view increases other limiting factors come into play which ultimately pose a tradeoff between the imaged field of view, the axial resolution and its uniformity across the imaged area. One limiting factor stems from the underlying assumption that the spot on the Echelle grating is imaged onto the grating which in turn is imaged onto the specimen. This condition can theoretically be only satisfied at a single axial position, however our implementation relies on the approximation that all reflective surfaces of the Echelle grating are imaged onto the grating. In order for this approximation to be valid it is required that the demagnified axial distance over all Echelle grating axial steps $n b / M_{_{1}}^{2}$ with $n = d_{3} / s$ the number of Echelle grating lines covered by the excitation spot, to be smaller than the Rayleigh length of the magnified diffraction limited spot on the grating, i.e.

\frac{d_{3} b}{s M_{1}^{2}} \leq \frac{s^{2} M_{_{2}}^{2} π}{4 λ},

with

d_{3}

the sizes of the field of view at the sample. Further, a similar condition to Eq. (2.6) must be met for the different illuminated areas on the grating at different axial positions. As the grating is tilted in the x-y-plane it must be ensured that the axial range corresponding to this tilt angle is small compared to the Rayleigh range. For a desired field of view at the sample and a given choice of other variables in order to fulfill Eq. (2.6)

M_{1}

and

M_{2}

have to be maximized. However large magnification and hence a large spot size at the gratings become at some point experimentally impractical. Further, a large spot size on the grating will also lead to a situation that Eq. (2.5) cannot be satisfied for all points, which in turn will result in an inhomogeneous axial resolution across the field of view with higher resolution at the center and gradually decreasing for points on the perimeter. This effect is closely related to the achievable depth resolution with a patterned illumination as discussed in [10]. However as discussed further below, since in our scheme the choice of all experimental parameters for a desired target field of view is not uniquely defined by constrains in Eqs. (2.1)–(2.6) for realizing large fields of view it would be desirable to minimize

M_{2}

and the spot size

d_{1}

on the grating while maximizing

M_{1}

in order to satisfy Eq. (2.6).

3. Experimental realization

For the experimental implementation of MUTEF we used a 140 fs pulsed laser source with 80 MHz repetition rate at a center wavelength of 800 nm and an average power of ~100mW at the sample. A collimated beam with $d_{0} ~ 6 m m$ was directed towards the Echelle grating with a period of $a ~ 290 μ m$ and a step depth of $b ~ 500 μ m$ . A larger grating period was used to avoid any “shadowing” effects from neighboring lines, i.e. a situation in which the divergence of the reflected beam leads to a partial blocking of the propagating beam by the neighboring grating lines. This ensured that Eq. (2.4) was satisfied. A three times demagnifying telescope was used to image the surface of the Echelle grating onto that of the grating at an angle of $α_{1} ~ 10^{\circ}$ . In this fashion the set of delayed pulses generated beamlets on the grating with spot sizes of $97 μ m$ and $247 μ m$ respectively in the z- and y-direction. As required by Eqs. (2.2) and (2.3) this value is below the size of the projection of a magnified diffraction limited spot onto the grating generated by our 60X, NA = 1.2 objective and $f_{2} = 600 m m$ . Using Eq. (2.4) this configuration also gave a separation of $5.7 m m$ between the beamlets on the grating which practically means that the grating is never illuminated by more than a single beamlet at a time and is well above the size of the magnified diffraction limited spot. Using a grating with a period $ε = 0.83 μ m$ ensured complete filling of the backfocal aperture of our objective in combination with our coupling lens with $f_{2} ~ 600 m m$ . Further, by inserting our parameters into Eq. (2.6) we verified that the conditions for imaging of the Echelle grating surface onto that of the diffraction grating and further onto the sample via the two telescopes were satisfied.

Two-photon excitation was induced on fluorescent beads with a diameter of ~200 nm, on a thin fluorescent sheet, on fluorescently labeled pollen grains and on fixed mouse kidney cells labeled with Alexa flour conjugated to WGA labeling apical surface. The fluorescence light was collected in the epi-configuration, separated from the excitation bema via a dichroic beam splitter and detected on a CCD camera.

4. Results and discussion

We started by comparing the axial confinement of excitation in different two-photon techniques using fluorescent beads. Before measuring the axial resolution of our MUTEF imaging, we first verified that a line shaped beam at the grating for which dispersion and the spatial diffraction were matched according to Eq. (2.1), is indeed resulting in a shorter axial confinement of excitation than the widefield temporal focusing. This was done by focusing the incoming beam via a cylindrical lens to generate a focused line of ~95 μm in the z-direction with the beam waist positioned at the grating. In this fashion the cylindrical lens generated a single similarly sized beamlet to what would be produced by the Echelle grating. This line-shaped beam at the grating led as expected to a diffraction limited axial confinement. Next we introduced the Echelle grating and measured the axial confinement of excitation of our MUTEF technique. Figure 3a shows a comparison of the axial confinement of this line shaped temporal focusing, standard widefield temporal focusing two-photon widefield imaging (i.e. without any temporal focusing when both the spectral and the spatial gratings were replaced by mirrors) and the MUTEF imaging.

Fig. 3 a) Comparison of the axial localization of excitation in different two-photon imaging schemes for a spot size of ~6µm. While regular two-photon excitation (green trace) with such a beam size only leads to a poor axial confinement (FWHM~7µm) and the widefield temporal focusing (blue line) to a confinement of ~1.6µm, both the line scan temporal focusing (black trace) and the MUTEF imaging (red) curve yield the same axial confinement (~0.85µm) as a two-photon scanning microscope. However only in MUTEF imaging a wide field of view can be achieved without any mechanical scanning. b) Lateral intensity distribution of the MUTEF excitation

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We observed an improvement of the axial confinement in the line-shaped temporal focusing to widefield temporal focusing from ~1.6 $μ m$ to ~0.8 $μ m$ . Using the MUTEF technique with the parameters discussed above we found a very similar axial confinement with a FWHM of ~0.85 $μ m$ , however in this case the beamlets scanning the grating in tens of picoseconds generated a widefield excitation. The fact that the axial confinement is very close to that of the line-shaped temporal focusing also shows that the amount of the introduced delay between the neighboring beamlets by the Echelle grating was sufficient to avoid interference. In order to verify that the scanning beamlets resulted in a homogeneous excitation area on the sample, we used a thin (~100 nm) florescent sheet to capture the lateral intensity distribution. As shown in Fig. 3b this resulted in an excitation area on the sample with a diameter of ~6 $μ m$ for which the intensity distribution along the y- and z-directions followed a Gaussian. The measurement of the lateral intensity distribution in Fig. 3b also ensured the lack of any shadowing effects as mentioned above. The measured values for the axial confinement of the line-shaped temporal focusing and the MUTEF imaging are also comparable to the expected value of ~0.7 µm for a confocal or two-photon scanning microscope based on $Δ z = 0.32 λ / n \sin^{2} θ / 2$ [11] and represents ~9-fold improvement compared to the widefield two-photon excitation (i.e. when both gratings are replaced by mirrors.)

In the current work the size of our field of view was limited by the available laser power and the efficiency of the gratings. However, larger fields of view at the sample can in principle be generated with this scheme as long as the requirements in section 2 are fulfilled. As an example a field of view of $d_{3} ~ 50 μ m$ can be generated for a system using the same laser source and microscope objective as in our case. Using a coupling lens with $f_{2} ~ 120 m m$ the filling of the backfocal aperture can be achieved by a higher dispersive grating with $~ 2000$ grooves per millimeter and the Eqs. (2.3), (2.4), and (2.5) can be satisfied by choosing $M_{1} ~ 14$ . This will result in a spot size of $d_{0} ~ 56 m m$ on the Echelle grating which is, although a large spot, still an experimentally manageable size.

Once we had characterized the excitation parameters of our beam, we applied the high axial sectioning capability of the MUTEF technique to the imaging of biological samples. We imaged fluorescently labeled pollen grains and fixed mouse kidney cells labeled with Alexa flour conjugated to WGA labeling apical surface. Figure 4a shows a fluorescent image of a pollen grain generated by one photon excitation from a Xenon lamp. In order to compare the axial sectioning capability of MUTEF to the widefield temporal focusing and widefield two-photon excitation, we focused on an area between two spikes shown in Fig. 4a while translating the sample axially via a piezoelectric stage in 50 nm steps. Figure 4b shows the improved axial localization of the MUTEF imaging. While the high axial localization of excitation in MUTEF induces fluorescence either on the upper or on the lower spike, the temporal focusing excitation results in the simultaneous excitation of both spikes. The widefield two-photon excitation results in addition to a significant amount of out of focus fluorescence stemming from the excitation of spikes at lower and higher axial locations. The improved axial localization of MUTEF was also demonstrated on a single spike with a directional component along the axial direction (Fig. 4c). When the stage was displaced by steps of 100 nm, we observed for MUTEF that the excitation area on the spike moved from the bole to the tip of the spike (left to right). However the temporal focusing excitation over most of the same range led to an almost homogeneous excitation of the entire spike, while the widefield two-photon excitation led to a high out of focus fluorescence and resulted in images that barely changed over the range of our axial scan. Expectedly, a three-dimensional representation of the entire image stacks for each of the three illumination approaches led to similar findings (Fig. 4d). While individual spikes could clearly and individually be identified in the three-dimensional representation of MUTEF, they were less clear in the temporal focusing excitation and almost not resolvable in the widefield two-photon excitation.

Fig. 4 Demonstration of the axial confinement of MUTEF imaging and its comparison to temporal focusing and widefield 2-photon excitation for a spot size of ~6µm on fluorescently labeled pollen grains. a) Overview fluorescence image of a pollen grain using a fluorescence lamp. b) Comparison between MUTEF, and wide-field 2-photon imaging at two axial planes separated by 50nm. While the MUTEF imaging clearly leads to the excitation of either the upper or the lower spike, the temporal focusing imaging leads to the excitation of both spike at x = 0nm and the widefield temporal focusing in addition to significant amount of out of focus florescence. c) Excitation of a spike with a directional component in the axial direction when the sample is moved by steps of 100nm. One can clearly see that the excitation area on the spike moves from the bole to the tip of the spike for the MUTEF imaging, whereas in the temporal focusing the spike is more homogenously excited over the entire range of the axial range and the widefield two-photon imaging almost does not give any sectioning. d) The three-dimensional representation of an image stack over a range of ~20µm shows clearly the higher optical section capability of the MUTEF imaging compared to the two other alternative methods. The integration time for all two-photon images was 100ms.

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We further demonstrated the sectioning capability of our MUTEF technique on fixed mouse kidney cells labeled with Alexa flour conjugated to WGA labeling apical surface. Figure 5a shows an overview of the fluorescence image of these cells. We focused on a contact area between two of these cells and compared the results of the MUTEF imaging to the images produced by the other two alternative techniques. Figure 5b shows a comparison between the three excitation techniques when the sample was displaced axially over a range of 100 nm. The MUTEF excitation revealed an inverted v-shape structure for which the two “arms” can be individually identified. The intensity along these “arms” changed continuously as a function of the axial displacement. While the same v-shape structure was to some extent recognizable in the temporal focusing excitation and exhibited some changes in the locations and intensities of the fluorescence as a function of displacement, the widefield two-photon excitation did not show any structure at all. Figure 5c shows a three-dimensional representation of the respective image stacks in which the improved axial resolution in MUTEF is apparent.

Fig. 5 Demonstration of axial confinement of MUTEF imaging and its comparison to temporal focusing and widefield 2-photon excitation for a spot size of ~6µm on fixed mouse kidney cells labeled with Alexa flour conjugated to WGA labeling apical surface. a) Overview fluorescence image of the fixed kidney cells b) Comparison between MUTEF, temporal focusing and wide-field 2-photon imaging at three axial planes separated by 50nm. In the MUTEF imaging an inverted V-shape structure is excited at x = 0nm for which the excitation moves to the tip of the structure at x = 50nm and is significantly reduced on the right hand side tip at x = 100nm. Imaging the same region using temporal focusing leads to a more unspecific excitation of a region which remains almost unchanged over the axial range. Using just 2-photon excitation without any temporal focusing leads in addition to a significant amount of out of focus background. c) The three-dimensional representation of an image stack over a range of ~20µm shows clearly the higher optical section capability of the MUTEF imaging compared to the two other alternative methods. The integration time for all two-photon images was 100ms.

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In summary we have shown that the axial confinement of excitation in the widefield temporal focusing can be improved by about a factor of two to ~0.85 $μ m$ using the Multifocal Temporal Focusing (MUTEF) imaging technique. This is a value comparable to the axial confinement of excitation that would be typically achieved by using two-photon scanning or confocal microscopy [11]. This improvement in axial confinement of temporal focusing was achieved for a widefield excitation area that was generated by a set of diffraction limited beams produced by an Echelle grating and scanning across a second tilted diffraction grating in picosecond time scale. The simplicity of MUTEF, the lack of any moving mechanical components and its high axial sectioning; is expected to make it a versatile tool for a large number of imaging applications. All areas in which two-photon scanning microscopy is used could potentially benefit from this method, opening up a wide range of future possibilities.

Acknowledgments

We thank G. Shtengel, H. Shroff and A. York for helpful discussions and G. Shtengel for advice and help with the metal evaporator. This work was supported by Howard Hughes Medical Institute.

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Ultrafast widefield optical sectioning microscopy by multifocal temporal focusing

Abstract

1. Introduction

2. Method and theory

3. Experimental realization

4. Results and discussion

Acknowledgments

References and links

Cited By

Figures (5)

Equations (8)

Optics Express