1. INTRODUCTION

The control of beam propagation and imaging through turbid media remains a great scientific and technical challenge—especially in life science applications, since measurement time is limited and high spatial resolution is required. The deeper light propagates through scattering media, the more ballistic photons change to diffusive photons, such that their propagation directions or, respectively, their wavefronts become randomly distorted. However, several approaches have shown that wavefronts and photon propagation directions can be corrected to form a tight focus behind scattering media, if the transition properties (matrix) of the medium at a fixed time point can be measured [1,2]. In a similar way, angular phase correlations (phase memory) can be exploited to image simple structures through strongly scattering, opaque media onto a detector when certain boundary conditions are met [3–5]. In this regime, where light propagation is governed by diffusive photons, subsequent imaging from many directions becomes very time-consuming and computationally elaborate—a situation that is incompatible with most investigations of living matter.

But, image acquisition time and computational efforts can be significantly reduced if the number of ballistic photons can be enhanced relative to the number of diffusive photons. Ballistic photons propagate through the object and to the camera nearly without scattering, thus generating different spectral distributions regarding temporal or spatial frequencies from diffusive photons. By exploiting such principles, the image contributions between ballistic and diffusive photons can be separated on the detection side by image postprocessing [6,7] or by time gating [8,9].

However, the ratio between ballistic and diffusive photons along the optical beam axis can also be increased by controlling the phase profile on the illumination side, an effect that was unexpected, based on the picture of incoherent photon migration. If the overall dimensions and the scattering strengths of the objects can be roughly estimated, then Bessel beams—preferably generated by computer controlled spatial light modulators (SLM)—have shown to self-reconstruct their intensity profile in scattering media [10] by an amazingly strong constructive photon interference along the central intensity lobe of the Bessel beam, thereby increasing the number of ballistic photons relative to the diffusive photons.

Bessel beams seem to be especially advantageous in light sheet-based microscopy, since they penetrate deeper into inhomogeneous media, and their central beam lobe is much narrower than that of a Gaussian beam having the same depth of field. However, the concentric ring system of the Bessel beam illuminates the object above and below the focal plane and thereby reduces contrast. Several approaches have been applied to minimize the fluorescence in the ring system, such as multiple photon excitation [11,12], confocal line detection [13] or arranging Bessel beams to a lattice, leading to destructive interference in the ring systems, if phase disturbances induced by the biological medium are moderate [14].

An alternative approach to reduce the fluorescence in the Bessel beams ring system and to generate a very thin light needle by the remaining central lobe of the Bessel beam is to use stimulated emission depletion (STED) [15]. This idea has been investigated theoretically in idealized homogeneous media [16] and in more realistic scattering media [17]. Related approaches have been presented recently by reducing the beam width of a Gaussian beam propagating through water with a second harmonic generated STED beam [18]. Attempts to reduce the width of a complete light sheet remain difficult [19,20], since enormous STED beam powers would be required for efficient fluorescence depletion. Using the much slower fluorescence depletion process of RESOLFT, the spatial resolution in detection direction could be increased strongly by reducing the width of each fluorescence layer in light sheet microscopy [21].

In this paper, we demonstrate that the STED principle can be applied point-wise and also line-wise along 120-μm-long, self-reconstructing Bessel beams. Furthermore, we show that the spatial overlap of two Bessel beams with different orbital angular momenta and the resulting fluorescence depletion efficiency remains surprisingly stable, despite propagation through different scattering media, which may offer new applications in optical metrology or in microscopy.

2. BASIC PRINCIPLE

The combination of these two microscopy techniques requires two different non-diffracting (self-reconstructing) beams, which have to overlap perfectly over a propagation length of typically $\mathrm{\Delta }z>100\mathrm{\mu m}$ inside the object. Therefore, we use a 0th order ($\ell =0$) Bessel beam with a thin lobe in the center of the surrounding ring system for fluorescence excitation and a higher order ($\ell =3\dots 4$) STED Bessel beam with zero intensity in the center of the ring system with the same periodicity for fluorescence depletion [see top inset in Fig. 1(a)]. The vanishing intensity in the STED beam center results from a phase singularity of the helical phase profile $\exp (i\ell \tilde{\varphi })$, which is quantified by the charge number $\ell$ and counts the rotations of the $k$- vector around the Poynting-vector per wavelength. As shown in Fig. 1(a), both beams can be generated side by side by a single phase shaping element (SLM, Hamamatsu X10468-04).

 

Fig. 1. Schematic of measurement principle. (a) Two phase holograms are used to generate the excitation beam (blue arrow and frame) and the depletion beam (yellow), with intensities $I_{\mathrm{EX}}(r)$ and $I_{\mathrm{ST}}(r)$. Both Bessel beams, differing in angular and radial momentum, are superimposed and focused by an objective lens onto a cluster of scattering spheres. After fluorescence depletion, a thin fluorescent light needle with intensity $I_{\text{tot}}(r)$ is generated and detected by a perpendicularly arranged objective lens (green arrow and frame). Theoretically obtained intensity line scans illustrate the depletion of the fluorescence in the Bessel beam’s ring system. (b) Numerical simulation of beam propagation and scattering at glass beads (in gray) by the excitation beam (in blue), the depletion beam (in orange) and the remaining needle-like fluorescence of the central beam lobe (in green).

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A. Description of Both Bessel Beams

The smaller the broadening of both beams during propagation, the narrower their radial angular spectrum widths $\mathrm{\Delta }{k}_r$. The smaller this radial momentum uncertainty, the more beam energy is carried in the Bessel beam’s ring system and the better the propagation stability (invariance). A perfect, but unrealistic Bessel beam has a thin annular Fourier spectrum, described by a delta function $\delta (k_r-k_0\mathrm{NA})$, and carries an infinite amount of energy in its ring system. A realistic Bessel beam has a smooth annular spectrum of thickness $\mathrm{\Delta }{k}_r$, and can be described by a 1D convolution (*) with a Gaussian function $\exp (-k_r^2/\mathrm{\Delta }{k}_r^2)$, where $\mathrm{\Delta }{k}_r$ defines the amount of energy in the ring system. Hence the beams’ electric field spectra

From the angular spectra, the electric field in the beam center is obtained, which is described by the Bessel function $J_{\ell }$ of order $\ell$, where the radial Bessel side lobes are damped by the Gaussian function:

Figure 1(a) shows side by side the intensities of the excitation beam $I_{\mathrm{EX}}(r,\varphi ,z)={|E_{\ell =0}(r,\varphi ,z)|}^2$ and the STED beam $I_{\mathrm{ST}}(r,\varphi ,z)={|E_{\ell =3}(r,\varphi ,z)|}^2$, which depletes the fluorescence only in the ring system, provided both beams are well adjusted relative to each other with help of the SLM. In the ideal case, fluorescence is emitted only in the central main lobe, such that a thin light needle is generated even inside a scattering medium [see cluster of spheres in Fig. 1(b)].

The overlap between both beams can be optimized by maximizing the product of both intensity cross-sections, $\rho (\ell ,\alpha )=\frac{1}{\sqrt{A}}·{\int }_{r_0}^{r_{\text{max}}}{I}_{\mathrm{EX}}(r^{\prime })·I_{\mathrm{ST}}(r^{\prime },\ell ,\alpha )r^{\prime }\mathrm{d}{r}^{\prime }$, which are integrated over the extent of their ring systems defined by the radii $r_0$ and $r_{\text{max}}\to \infty$, with $I_{\mathrm{EX}}(r_0)=0$. It turned out that the beam parameters in the absence of scatterers were $\alpha =({\mathrm{NA}}_{\mathrm{ST}}/{\lambda }_{\mathrm{ST}})/({\mathrm{NA}}_{\mathrm{EX}}/{\lambda }_{\mathrm{EX}})=1.1$ and helicity $\ell =3$ [17].

B. Quantifying Fluorescence and Depletion

The scenario illustrated in Fig. 1(b) is obtained from a computer simulation using the beam propagation method (BPM) [23,24] for two Bessel beams propagating through a cluster of spheres. The excitation beam intensity (in blue) and the depletion beam intensity (in orange), both distorted by scattering at the spheres, define the space variant depletion efficiency $\eta (\mathit{r})$, which defines the remaining fluorescence (in green).

The resulting fluorescence $F(\mathit{r})\approx C_{\text{ext}}(\mathit{r})·Q_{\mathrm{fl}}·\eta (\mathit{r})·I_{\mathrm{EX}}(\mathit{r})$ is approximately proportional to the extinction cross-section $C_{\text{ext}}(\mathbf{r})$ and the quantum efficiency $Q_{\mathrm{fl}}$ of the fluorophores and to the excitation intensity $I_{\mathrm{EX}}(\mathit{r})$ and the probability for spontaneous emission $\eta (\mathit{r})$. A good expression for this space variant distribution is $\eta (\mathit{r})=I_{\text{sat}}/(I_{\text{sat}}+I_{\mathrm{ST}}(\mathit{r}))$ [25], which depends on the intensity of the STED beam $I_{\mathrm{ST}}(\mathit{r})$ and the saturation intensity $I_{\text{sat}}=(hc·k_{\mathrm{fl}})/({\sigma }_{\mathrm{ST}}{\lambda }_{\mathrm{ST}})$ at which the rates of depletion ${\kappa }_{\mathrm{ST}}$ and fluorescence ${\kappa }_{\mathrm{fl}}$ equal each other [see inset of Fig. 1(a)]. ${\sigma }_{\mathrm{ST}}$ is the fluorophore-specific STED emission cross-section. Typical saturation intensities are in the range of $I_{\text{sat}}\approx 10–20\mathrm{mW}/{\mathrm{\mu m}}^2$.

During propagation, both beams are scattered at the spheres, such that the total intensity of the beams is characterized by the interference of unscattered (index u) and scattered (index s) light, $I_{\mathrm{EX}}(\mathit{r})={|E_{\mathrm{EX},u}(\mathit{r})+E_{\mathrm{EX},s}(\mathit{r})|}^2$ and $I_{\mathrm{ST}}(\mathit{r})={|E_{\mathrm{ST},u}(\mathit{r})+E_{\mathrm{ST},s}(\mathit{r})|}^2$. Both beams can be separated in an ideal unscattered term and an additive term due to scattering [24] such that $I_{\mathrm{EX}}(\mathit{r})=h_{\mathrm{EX},u}(\mathit{r})+h_{\mathrm{EX},s}(\mathit{r})$ and $I_{\mathrm{ST}}(\mathit{r})=h_{\mathrm{ST},u}(\mathit{r})+h_{\mathrm{ST},s}(\mathit{r})$. Using the separation into unscattered and scattered beams for both excitation and depletion, the expected fluorescence can also be split into a term without and with scatterers:

Thus, the total fluorescence splits into four terms. In the absence of scatterers, the probability for spontaneous emission ${\eta }_u(\mathit{r})=I_{\text{sat}}/(I_{\text{sat}}+h_{\mathrm{ST},u}(\mathit{r}))$ is determined by the ideal, unscattered STED beam $h_{\mathrm{ST},u}(\mathit{r})$. In the presence of scatterers, however, three additional terms occur, among which two terms are beneficial to the image quality and only one is bad, where scattered light from the STED beam depletes fluorescence from the center of the unscattered excitation beam.

The space-dependent fluorescence depletion efficiency $Q_D(\mathit{r})=1-\eta (\mathit{r})=I_{\mathrm{ST}}(\mathit{r})/(I_{\text{sat}}+I_{\mathrm{ST}}(\mathit{r}))$ expresses the probability of the depletion process and can also be separated in terms of unscattered and scattered light:

For large intensities of the STED beam, $I_{\mathrm{ST}}\gg I_{\text{sat}}$, the depletion efficiency reaches $Q_D(\mathit{r})\to 1$.

3. EXPERIMENTAL SETUP

The setup developed and constructed in our lab is based on two continuous wave (cw) lasers: a 25-mW excitation laser (Cobolt Calypso 04-01 491 nm) and a 2-W STED laser (MPB Communications, VFL-P-2000-560). As depicted in Fig. 2, both beams are first expanded and then combined by beam splitters such that their beam phases are modulated independently by the left and right halves of a SLM (Hamamatsu X10468-04) operating in reflection mode. After overlapping both beams, these are deflected with a galvanometric scan mirror and focused with the illumination objective (IO, ${\mathrm{NA}}_{\text{ill}}=0.35$) to be scanned through the focal plane of the detection objective (DO, ${\mathrm{NA}}_{\text{det}}=1.0$). This lens images the fluorescence light onto a sCMOS camera (Andor Neo 5.5). Coherent light from both lasers transmitted through the object is collected by a scattering objective lens (SO, ${\mathrm{NA}}_{\text{sca}}=0.35$) and projected onto the second camera (PhotonFocus DS1-D1024-80-CL-10), which enables analysis of the power spectra ${|{\tilde{E}}_{\ell =0}(k_x,k_y)|}^2$ and ${|{\tilde{E}}_{\ell =3}(k_x,k_y)|}^2$ of the transmitted beams and thus facilitates the alignment of both beams.

 

Fig. 2. Photos and sketch of the experimental setup. The excitation beam and the STED beam are projected onto the left and right halves of a SLM and are then superimposed by beam splitters (BS). The angular spectra of both beams are projected by a lens ${\mathrm{L}}_1$ onto a scanning mirror (SM) with zeroth order beam block (B). Two lenses (SL and TL) project the tilted angular spectra onto the back focal plane (BFP) of the IO, which focuses the Bessel beams into the sample chamber. The SO images the angular spectrum of the scattered laser light onto a camera (${\mathrm{Cam}}_{\text{sca}}$), whereas the fluorescence generated in the sample chamber is collected by the detection objective (DO) and imaged onto another camera (${\mathrm{Cam}}_{\text{det}}$).

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4. RESULTS

In point scanning STED, the stronger the depletion efficiency and the reduction of the width of the point-spread function, the higher the intensity of the STED beam at the fluorophore, which is expressed as a multiple of the fluorophores saturation intensity, that is, $I_{\text{STED}}/I_{\text{sat}}\approx 6$ in our case. This is achieved best with shorter laser pulses with high peak intensities, often leading to strong fluorophore bleaching. However, since we seek to achieve efficient depletion along the focus line with propagation lengths $\mathrm{\Delta }z>100\mathrm{\mu m}$, the challenge is different. Because the central maximum of the Bessel beam is much narrower than that of a comparable Gaussian beam, the goal is to suppress the fluorescence most efficiently in the ring system of the Bessel beam. This goal becomes more and more difficult the more strongly the two beams run out of phase relative to each other; they thereby generate new interference distributions along the propagation length. The decay of the depletion efficiency $Q_D(x,y,\mathrm{\Delta }z)$ with propagation length $\mathrm{\Delta }z$ therefore depends on the strength of the scattering and the loss of the phase correlations between the coherent photons in each beam. In the following, three different classes of the refractive index inhomogeneities are investigated.

A. Bessel Beam Depletion of Isolated Beads

In a first experiment, we imaged isolated 0.75-μm large, fluorescing polystyrene beads embedded in an agarose gel. These beads were smaller than the ring period of both Bessel beams. As illustrated in Fig. 3(a), a first scan was performed by moving a single bead in the lateral $x$-direction through the excitation Bessel beam ($\ell =0$) alone, resulting in the fluorescence image (blue frame) displayed in Fig. 3(b). A second scan was performed with a STED Bessel beam ($\ell =3$) alone, resulting in a fluorescence image indicating the central zero intensity (red frame). The third scan was performed with both beams switched on, resulting in a fluorescence image, where the intensity in the ring system is efficiently suppressed (green frame). This is quantified by four line scans shown in Fig. 3(c), where the fluorescence in the first Bessel ring with STED beam switched on is reduced by up to 80%. The usual subtraction of the fluorescence excited by the STED beam (see inset) has only a minor effect (curve shown in cyan). Figure 3(d) shows the mean depletion efficiency $Q(x_b)$, which varies both in space and with the STED intensity and was averaged over 19 beads, as well as the standard deviation from the mean. It is highest at the first ring of the Bessel beam and well below 20% in the beam center at $x_b=0$. Fluorescence is not affected in a distance $|x_b|>5\mathrm{\mu m}$.

 

Fig. 3. Beam profiling. (a) A 0.75-μm fluorescent bead embedded in agarose gel is scanned laterally with different beams. (b) Resulting fluorescence images of the 0th order excitation Bessel beam (blue), the 3rd order STED Bessel beam (red) and the combination of both beams (green). (c) Fluorescence line profiles show fluorescence depletion only in the Bessel ring system and small fluorescence excitation by the STED beam itself, which is typically subtracted (-S) in postprocessing from the combination of both beams (Exc/STED-S). (d) Space-dependent probability for spontaneous emission $Q(x_b)$ averaged over 19 beads (solid line), and the standard deviation from the mean (shaded area).

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B. Resolution Enhancement in Bead Images

In a second experiment, we performed one sweep of the Bessel beams in lateral $x$-direction during the integration time of the camera and moved the bead cluster in detection direction $y_b$ to record a stack of images [see sketch in Fig. 4(a)]. The projected bead images in the $yz$-plane are shown in Fig. 4(b) and a magnification of two bead images in Fig. 4(c). The corresponding line scans in the detection direction in Fig. 4(d) reveal a significant reduction in the $1/e$ widths, which are on average nearly 50% with STED Bessel beam switched on [green profile in Fig. 4(e)]. It should be emphasized that the ring intensity oscillations visible in Fig. 3(c) are invisible in Fig. 4(d), since the elongated width of the point-spread function in detection direction has a strong averaging effect.

 

Fig. 4. Single bead imaging. (a) Different beams are scanned in lateral $x$-direction across isolated 0.75-μm beads. (b) Bead images in the $yz$-plane without (blue frame) and with (green frame) fluorescence depletion (STED). (c) Magnification of marked area in (b). (d) Normalized image intensity profiles F(y) without STED beam (blue), with STED beam (green), and the fluorescence bead image of the STED beam alone (red). (e) The $1/e$ Image widths $\delta y(z)$ from different bead images at propagation distances between $z=12$ and $z=42\mathrm{\mu m}$ without (blue) and with (green) STED beam.

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The red fluorescence image profile from the STED beam, which is not the STED beam profile, has been normalized to $F(y)=1$ to visualize this effect.

C. Fluorescence Depletion Behind Two Large Scatterers

In a third experiment, we embedded unlabeled 8-μm glass spheres in a fluorescing gel, such that the fluorescence excited (at $P_{\mathrm{EX}}=0.6\mathrm{mW}$) and depleted (at $P_{\mathrm{ST}}=1\mathrm{W}$) by the beams can be well examined. In the example presented in Fig. 5, different beams are incident from the left and are scattered at two spheres, which appear as black circular areas. The fluorescence image in Fig. 5(a) shows the propagation behavior of a conventional Gaussian beam (all beams have the same depth of field), which is strongly focused and deflected by the two spheres, such that no fluorescence signal is visible in the back part of the image along the optical axis.

 

Fig. 5. Beam self-reconstruction behind two 8-μm glass spheres. Images $F(x,z)$ of propagating and scattering beams exciting fluorescence in a labeled agarose gel. Image width corresponds to a propagation length of 140 μm. Two unlabeled beads appear dark. (a) Fluorescence image of the Gaussian beam reveals its large diameter and strong deflection at the spheres. Two hypothetic round objects (yellow circles) are images in detection direction, indicated by two elongated PSFs. The real and the ideal images differ significantly. (b) Zeroth order Bessel beam reconstructs its intensity profile after scattering at both spheres. Hypothetic real images are more like the ideal images. (c) In combination with a 3rd order STED Bessel beam, the fluorescence in the ring system can be depleted, despite strong scattering with a reasonable efficiency, as indicated in (f) by the two line scans taken at $z_1=20\mathrm{\mu m}$ and $z_2=90\mathrm{\mu m}$. Hypothetic real images resemble the ideal images as also visible in Fig. 5(d) without scatterers. (e) Distribution $Q_D(x,z)$ illustrates the space-dependent efficiency of fluorescence depletion. Scale bar: 10 μm.

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The focal plane images $F(x,z)$ in Fig. 5 approximate the fluorescence intensity within the object. Because the unscattered beams and the scatterers are both rotationally symmetric, it is valid to assume that the fluorescence distribution in the focal plane may also correspond to the fluorescence distribution perpendicular to it, that is, $F(x,z)\approx F(y,z)$. To illustrate the space-dependent appearance of two hypothetical roundish fluorescent objects (indicated by yellow circles) caused by the deflected and imperfect illumination, we took the hypothetic fluorescence image at $z\approx 80\mathrm{\mu m}$ in different heights along $y$ relative to each other, but both within the depth of field of the detection $\mathrm{PSF}(y,z)$. The two resulting real and ideal roundish images taken in the ($x$, $z$) plane are completely different for Gaussian, Bessel and STED Bessel beams.

By exciting fluorescence with a 0th order Bessel beam, Fig. 5(b) shows that this beam self-reconstructs behind both spheres and is able to illuminate both hypothetic spheres differently, although a perfect beam would not illuminate the upper sphere, as shown in the ideal image. Figure 5(c) shows the result of additional fluorescence depletion with the self-reconstructing 3rd order Bessel beam, resulting in an efficient depletion, even behind the scatterers. This is demonstrated by the bright (right) and hardly (left) fluorescing images of the hypothetical objects and by the intensity line scans of Fig. 5(f). In the experimental imaging process, the convolution of the 3D detection point-spread function with the 3D fluorescence emission distribution results in a strong background generation and image blur. Therefore, we subtracted a Gaussian shaped background intensity from the Bessel beams [see dashed line in Fig. 5(f)] leading to an increase in contrast in the images of Figs. 5(b)–5(d) (for details see Supplement 1 and Visualization 1). A 3D deconvolution was not possible, since the required 3D image was not available.

Whereas Fig. 5(d) illustrates the fluorescence $F(\mathit{r})\sim C(\mathit{r})·\eta (\mathit{r})·I_{\mathrm{EX}}(\mathit{r})$ generated by the excitation intensity $I_{\mathrm{EX}}(\mathit{r})$ and the depletion $\eta (\mathit{r})=I_{\text{sat}}/(I_{\text{sat}}+I_{\mathrm{ST}}(\mathit{r}))$ in the absence of scatterers, Fig. 5(e) displays the depletion efficiency $Q_D(\mathit{r})=1-\eta (\mathit{r})$ in the presence of scatterers according to Eq. (4). $Q_D(\mathit{r})=(F_{\mathrm{EX}}(\mathit{r})-F_{\text{tot}}(\mathit{r}))/F_{\mathrm{EX}}(\mathit{r})$ is obtained by the images of the fluorescence distributions without and with depletion, $F_{\mathrm{EX}}(\mathit{r})$ and $F_{\text{tot}}(\mathit{r})$.

D. Beam Penetration and Fluorescence Depletion in Sphere Clusters

Most relevant to applications in metrology and microscopy is the situation where beams have to propagate through turbid media, often consisting of diffusing aerosols, water droplets, complex fluids or, in the extreme, inhomogeneous biological material. To investigate the nonlinear interplay between the two self-reconstructing Bessel beams and the resulting fluorescence depletion in strongly, but homogeneously, scattering media, we used 0.35-μm fluorescing spheres embedded in an agarose gel in different concentrations.

To avoid the strong averaging effect by the 3-D imaging process, the change of the beam cross-section and, thereby, the propagation behavior can be better investigated by using the beads both as coherent scatterers and as point-like fluorescing probes $C(\mathit{r})=C_0·{\sum }_j\delta (\mathit{r}-{\mathit{r}}_j)$ randomly distributed across the beam volume. A series of $N=121$ images was taken by moving the bead cluster through the beam. From this stack of images, the maximum selection (projection) was performed. In this way, the ring system of an averaged Bessel beam, and also the effect of the fluorescence depletion, can be well visualized and quantified, and the effective penetration depth into scattering media can be extracted.

The beam propagation behavior from left to right through the scattering medium is illustrated in Figs. 6(a)–6(d) for two bead volume concentrations of $c_1=0.13\%$ and $c_3=0.52\%$. The mean fluorescent response was also measured for a third volume concentration $c_2=0.26\%$, which is shown in Supplement 1. The 0th order Bessel beam excites fluorescence both in its narrow beam center and in the surrounding ring system. In combination with the 3rd order Bessel beam, the fluorescence in the ring system is also efficiently depleted after more than 100-μm propagation through the scattering medium. The result is a thin fluorescing light needle, which hardly spreads out. The third image shows the Gaussian beam with the same depth of field, revealing the much broader beam diameter and a stronger decay in fluorescence. The fourth image displays the space variant depletion efficiency $Q_D(x,z)$, according to Eq. (4), which is very small in the beam center and strongest at the location of the first Bessel ring. In order to compensate for the discrete nature and random position of the scatterers, a gliding average over a region of $\mathrm{\Delta }z=6\mathrm{\mu m}$ has been performed before computing $Q_D(x,z)$. Remarkably, the lateral periodic ring structure in the depletion efficiency is also visible by the parallel horizontal lines, indicating very good self-interference of the beam, despite a strong local phase disturbance induced by the scatterers.

 

Fig. 6. Beam propagation over 120 μm through a cluster of beads, fluorescence generation, and STED efficiency. Fluorescing polystyrene beads with 0.35-μm diameter are embedded in agarose gel at concentrations $c_{\text{vol}}=0.13\%$ (left) and $c_{\text{vol}}=0.52\%$ (right). Maximum projections of images revealing the intensity profile of (a) a single Bessel beam, (b) a Bessel beam with the STED beam and (c) a Gaussian beam. (d) Space varying depletion efficiency $Q_D(x,z)$ derived from (b) reaching efficiencies at the first Bessel ring of up to 60%, which is shown by the bright yellow areas. Central parts of (a)–(d) are magnified in (e) and (f) for $c_{\text{vol}}=0.13\%$ and $c_{\text{vol}}=0.52\%$, respectively. (g) Average depletion efficiencies along $z$ in the center and the ring system for the three bead concentrations. (h) Fluorescence line profiles $F(x,z_0)$ at $z_0=30\mathrm{\mu m}$ (solid line) and $z_0=75\mathrm{\mu m}$ (dashed line), and corresponding depletion efficiencies $Q_D(x,z_0)$. Profiles are averaged over 60 pixels, that is, $\mathrm{\Delta }z\approx 6\mathrm{\mu m}$. (i) Axial fluorescence profiles $F(x=0,z)$ for two different concentrations of scatterers averaged over the beam centers of the Bessel beam (left), the Bessel beam with STED (center) and the Gaussian beam (right). (j) Comparison of decay constants for all beam types at three different bead concentrations.

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The magnifications shown in Figs. 6(e) and 6(f) from the marked areas in the center of the beams allow a direct comparison of the four distributions $F_{\mathrm{Be}}(x,z,I_{\mathrm{ST}}=0)$, $F_{\mathrm{Be}}(x,z,I_{\mathrm{ST}}>0)$, $F_{\mathrm{Ga}}(x,z,I_{\mathrm{ST}}=0)$ and $Q_D(x,z,I_{\mathrm{ST}}>0)$. The corresponding line scans (averaged over $\mathrm{\Delta }z\approx 6\mathrm{\mu m}$) at propagation distances of $z=30\mathrm{\mu m}$ and $z=75\mathrm{\mu m}$ are shown in Fig. 6(h). The decay of the fluorescence intensity $F_j^{(\mathrm{rel})}$ (with $j=\mathrm{2,3}$ representing the respective volume concentrations) relative to the fluorescence intensity in the bead sample $c_1$ is plotted in Fig. 6(i) along the propagation direction, averaged over the center of the Bessel beam. By exponentially fitting with $\exp (-({\mu }_j-{\mu }_1)·z)$, one can extract the decay coefficients ${\mu }_j$ (or penetration depths $d_j=1/{\mu }_j$ for the sample with volume concentration $c_j$ [see Figs. 6(i) and 6(j) and Supplement 1]. This fluorescence decay has been analyzed for the Bessel and the Gaussian beam and for the combination of both Bessel beams enabling the propagation variant STED effect. Figure 6(j) reveals that the average penetration depth of the Bessel beam is about 19% higher than the average penetration depth of the Gaussian beam. The penetration of the Bessel beam with the STED beam switched on is even about 27% higher than that of the Gaussian beam.

It can be seen from Fig. 6(h) that the 50% width (FWHM) $\mathrm{\Delta }x\approx 0.95\mathrm{\mu m}$ of the Bessel beam with STED is three times narrower than the Gaussian beam over the whole propagation distance. The fluorescence decay for the Bessel beam (central lobe, position $r_0$) with STED beam switched on is slightly smaller than without STED. We compared the unwanted depletion efficiency of $Q_D(z,r_0)$ $<0.2$ at the central lobe, relative to $Q_D(z,r_1)$ $<0.6$ along the lateral position $\pm r_0$ of the first ring [see Fig. 6(g)] and found a stronger decay in depletion efficiency along the first ring because of a loss of STED photons in this area mainly due to scattering. The scattered STED light also depletes the fluorescence in the central lobe, as described by Eq. (3). Further, it can be seen in Fig. 6(h) that the lateral profiles of the depletion efficiencies $Q_D(x,z=30\mathrm{\mu m})$ and $Q_D(x,z=75\mathrm{\mu m})$ still reveal a peak in depletion at the position of the first ring.

5. DISCUSSION AND CONCLUSION

In this study, we addressed the question of whether the propagation stability and the overlap of a 0th order and 3rd order Bessel beam propagating in inhomogeneous materials can exploit the STED principle for the generation of thin fluorescent light needles.

We discuss the design of the experiments, the unexpected nature of the results and how they can be explained, and what is necessary to apply these principles to light sheet microscopy or other optical measurement technologies.

Light sheet microscopy (LSM) has its main advantages in the fast and efficient acquisition of large 3D data stacks, where fluorescence bleaching is minimized through an efficient photon budget. STED microscopy, on the other hand, is a point scanning technique with modest acquisition speed, strong fluorescence bleaching, and very high spatial resolution (mostly in 2D images). The combination of these two techniques could result in an advantageous compromise regarding imaging speed, resolution, contrast, and bleaching. Since a very good overlap between the excitation and depletion beam, even in inhomogeneous media, is required, Bessel beams with their extraordinary propagation stability are much better suited than Gaussian beams [6,13]. The Bessel STED beam, however, must have sufficient power to be distributed over the volume of the first rings of the Bessel beam. It has been shown in many publications that the fluorescence depletion (and thereby the width of the illumination focus) can be increased with a higher STED intensity. To verify that this is also true for fluorescence depletion along a line (and not a point) was not the intention of the study. The application of a cw power of $P_{\mathrm{ST}}=1\mathrm{W}$, available in our STED beam—resulting in a ratio of $I_{\mathrm{ST}}/I_{\text{sat}}\approx 6$—was already so high that bleaching was an issue in some experiments. Hence, the main intention of our study was to demonstrate that efficient fluorescence excitation and depletion is possible along a line, even in large, inhomogeneous media. Our results indicate that the usage of higher intensities should not result in thinner light needles (the beam’s central lobe is only little affected by depletion) but generate less background through a more efficient fluorescence depletion in the ring system. In this way, thin and propagation stable light needles should be possible that can be scanned laterally in the plane of focus to achieve extraordinary image quality through very thin light sheets in LSM. This cannot be achieved with the cw beam photon densities available in our configuration, but it could be achieved with a pulsed STED setup with a sufficiently low repetition rate. This, however, usually comes with increased costs and complexity of the optical setup. If imaging speed is less of an issue then fluorophore bleaching, it is useful to replace the STED principle by the RESOLFT principle using switchable fluorophores [21], when their switching speed will have been improved in the future.

Our experimental concept of using a single SLM for the parallel and independent manipulation of the phases of both illumination beams turned out to be quite advantageous. By observing the propagation behavior in a fluorescing solution in the object plane and by recording their transmitted angular (Fourier) spectra, the SLM turned out to be the best solution to control the overall overlap of both beams. In a recent theory study, we evaluated the optimal beam parameters numerically, and these parameters were also optimal in the experiments with beam propagation lengths of at least 100 μm. In conventional point scanning STED, the beam overlap length is less than 1 μm, and the STED beam consists of only one ring. For line STED, focusing lenses with numerical apertures in the range of $\mathrm{NA}=0.2–0.3$ are required and epsilon values $ϵ<0.8$ that do not distribute too high photon energies in the Bessel beams’ ring systems ($\text{ideally}<30\%$). Using these beam parameters, we found that our depletion efficiencies of $Q_D=0.6–0.8$, achieved in the important first Bessel ring, coincide well with those predicted by our theory study. As predicted by the theory and confirmed in our experiments, fluorescence depletion in the second and outer rings dropped to $Q_D=0.3–0.5$, provided that scattering or the propagation length were small (Figs. 3–6). For imaging applications, it might be helpful to use confocal line detection (i.e., a rolling shutter of a camera) to additionally block the remaining fluorescence emitted from the outer beam rings.

The space variant depletion efficiency. The most striking results in this paper are the self-reconstructing properties of both Bessel beams and the resulting fluorescence distribution. Figures 5(a) and 5(b) demonstrate the known effect that Gaussian beams are strongly deflected by larger refractive index inhomogeneities, while Bessel beams remain propagation stable. Phase shifts induced from obstacles, such as glass spheres, can easily displace a constructive beam interference by a fraction of a wavelength. It is, therefore, surprising that the electric field and the intensity overlaps of both beams are so precise, even after strong scattering, that efficient fluorescence depletion occurs only at the desired positions. The intensity distributions of each first ring in both the excitation and the STED beam, in Figs. 5(c)–5(e), reveal that the central Bessel lobe is hardly depleted, while the first ring at around $z=90\mathrm{\mu m}$ is significantly depleted, especially on the upper side. Exemplarily, the significance for potential imaging applications can be illustrated by two hypothetical objects, one within the main lobe, and another within the first side lobe (first ring). In a Gaussian beam with limited optical sectioning (spatial resolution), both objects would be illuminated and detected with nearly the same low intensity while with a Bessel beam with a similar bright intensity. However, only by switching on the STED Bessel beam are the intensities of both objects clearly different and can be separated with superior optical sectioning. An additional effect is important, when the beam intensities can be separated in unscattered and scattered parts: according to Eq. (3), the fluorescence terms due to scattering, $F_s\sim ({\eta }_s{h}_{\mathrm{EX},u}+{\eta }_u{h}_{\mathrm{EX},s}+{\eta }_s{h}_{\mathrm{EX},s})$, destroy the desired fluorescence of the unscattered illumination beam $h_{\mathrm{EX},u}(\mathit{r})$ by the scattered STED beam $h_{\mathrm{ST},s}(\mathit{r})$ or the term ${\eta }_s(\mathit{r})=I_{\text{sat}}/(I_{\text{sat}}+h_{\mathrm{ST},s}(\mathit{r}))$. Therefore, the propagation stability (little scattering and deflection) of the STED beam is of utmost importance.

The beam propagation through a homogeneous distribution of scatterers, illustrated in Fig. 6, shows once more that beam spreading is much larger with Gaussian beams than with Bessel beams. While the decay of the central Bessel lobe is hardly affected by the depletion beam, even in large propagation distances $z=75\mathrm{\mu m}$ [Fig. 6(h)], the decay of fluorescence depletion in the first ring is smaller than the decay along the centers of other beams. This can be explained by the dependency of the depletion efficiency according to Eq. (4), which decays non-exponentially, as visible in the depletion behavior $Q_D(r_0,z)$ at the location $r_0$ of the first ring. This effect demonstrates that the nonlinear interaction of different beams can result in beneficial ratios of excitation and depletion rates when acting on the same fluorophores. These two rates—and thereby the STED efficiency—are heavily influenced by the local phase differences of the incident photons.

Despite the strong scattering of the beams during propagation through inhomogeneous media, resulting in individual and relative phase delays of photons (or plane waves) and thereby in spatial shifts of the interference intensities, the STED principle along a 100-μm-long line works surprisingly well. The resulting fluorescence light needles are unexpectedly propagation stable in inhomogeneous media and may open a range of new applications in bio-photonic and related technologies.