## Self-reconstructing sectioned Bessel beams offer submicron optical sectioning for large fields of view in light-sheet microscopy |

Optics Express, Vol. 21, Issue 9, pp. 11425-11440 (2013)

http://dx.doi.org/10.1364/OE.21.011425

Acrobat PDF (5416 KB)

### Abstract

One of main challenges in light-sheet microscopy is to design the light-sheet as extended and thin as possible - extended to cover a large field of view, thin to optimize resolution and contrast. However, a decrease of the beam’s waist also decreases the illumination beam’s depth of field. Here, we introduce a new kind of beam that we call sectioned Bessel beam. These beams can be generated by blocking opposite sections of the beam’s angular spectrum. In combination with confocal-line detection the optical sectioning performance of the light-sheet can be decoupled from the depth of field of the illumination beam. By simulations and experiments we demonstrate that these beams exhibit self-reconstruction capabilities and penetration depths into thick scattering media equal to those of conventional Bessel beams. We applied sectioned Bessel beams to illuminate tumor multicellular spheroids and prove the increase in contrast. Sectioned Bessel beams turn out to be highly advantageous for the investigation of large strongly scattering samples in a light-sheet microscope.

© 2013 OSA

## 1. Introduction

1. J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by Selective Plane Illumination Microscopy,” Science **305**(5686), 1007–1009 (2004). [CrossRef] [PubMed]

2. H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods **4**(4), 331–336 (2007). [CrossRef] [PubMed]

3. P. J. Keller, A. D. Schmidt, J. Wittbrodt, and E. H. K. Stelzer, “Reconstruction of Zebrafish early embryonic development by Scanned Light Sheet Microscopy,” Science **322**(5904), 1065–1069 (2008). [CrossRef] [PubMed]

4. F. O. Fahrbach and A. Rohrbach, “A line scanned light-sheet microscope with phase shaped self-reconstructing beams,” Opt. Express **18**(23), 24229–24244 (2010). [CrossRef] [PubMed]

6. 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), 417–423 (2011). [CrossRef] [PubMed]

7. F. O. Fahrbach and A. Rohrbach, “Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media,” Nat Commun **3**, 632 (2012). [CrossRef] [PubMed]

8. L. Silvestri, A. Bria, L. Sacconi, G. Iannello, and F. S. Pavone, “Confocal light sheet microscopy: micron-scale neuroanatomy of the entire mouse brain,” Opt. Express **20**(18), 20582–20598 (2012). [CrossRef] [PubMed]

9. E. Baumgart and U. Kubitscheck, “Scanned light sheet microscopy with confocal slit detection,” Opt. Express **20**(19), 21805–21814 (2012). [CrossRef] [PubMed]

10. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. **25**(20), 1493–1495 (2000). [CrossRef] [PubMed]

11. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. **195**(1-4), 35–40 (2001). [CrossRef]

## 2. Sectioned Bessel beams - shapes and dimensions

*Ẽ*, which consists of a thin ring of finite thickness. It can be described by

_{B}_{B}

*= n⋅*sin

*α*describes the maximum focusing angle of the Bessel beam. ε < 1 is the ring width parameter, i.e. the area ratio of the inner to the outer disc [4

4. F. O. Fahrbach and A. Rohrbach, “A line scanned light-sheet microscope with phase shaped self-reconstructing beams,” Opt. Express **18**(23), 24229–24244 (2010). [CrossRef] [PubMed]

*k*

_{0}NA

_{B}, the ring thickness is

*k*

_{0}NA⋅(1-√ε). For ε = 0, the back aperture is homogeneously illuminated and a conventional beam with a limited depth of field

*k*-plane. The red-shaded areas are projections of the Ewald-sphere onto the three orthogonal planes in k-space. In the

_{x}k_{y}*k*-plane the angular spectrum representation

_{x}k_{y}*Ẽ*(

*k*,

_{x}*k*) exhibits a point symmetry with respect to the optical z-axis. Mathematically, the spectrum can be sufficiently well described bywhere β is the angular width and rect is defined as rect(

_{y}*x*/

*b*) = 1 if |

*x*|≤

*b*/2 and 0 otherwise. β = 180° results in a conventional Bessel ring spectrum, since the rect-function does not cut-off any frequencies.

*E*

_{SeB}(

*x,y*)|

^{2}, |

*E*

_{SeB}(

*x,z*)|

^{2}and |

*E*

_{SeB}(y

*,z*)|

^{2}are shown in Fig. 1(b). Here and throughout this study

*x*is the beam scanning direction parallel to the light-sheet,

*y*is the direction of the detection optical axis perpendicular to the light-sheet.

*y*-direction because of the convolution with the sinc-function, which has a slightly different frequency than the

*J*

_{1}-functions (Eq. (2)) along

*y*. This has important implications for the application in light-sheet microscopy as will be shown below.

*dk*,

_{x}*dk*and

_{y}*dk*, as projections of the spectrum

_{z}_{B}. The outer-diameter of the ring-spectrum is 2

*k*

_{0}⋅NA

_{B}and is defined by the NA of the focusing lens, NA

_{B}. The inner diameter is 2√ε⋅

*k*

_{0}⋅NA

_{B}. The extent of the angular spectrum

*k*-direction is solely determined by the section’s angular extent, β, such that

_{y}*dk*= 2

_{y}*k*

_{0}⋅NA

*⋅sin(β/2), i.e. the width of the rect-function. The ring thickness determines the axial extent of the spectrum*

_{B}*dk*, which scales with the ring parameter ε such that

_{z}*dk*=

_{z}*k*

_{0}⋅(cosα - ε⋅cosα) ≈2

*k*

_{0}⋅NA

_{B}^{2}⋅(1-ε) in the paraxial approximation.

*k*-direction consists of two fragments of width

_{x}*dk*in an outer distance of Δ

_{x}*k*= 2

_{x}*k*

_{0}⋅NA

_{B}to each other. The frequency Δ

*k*defines the radial ring spacing of a Bessel beam. After projection in the pupil plane (angular spectrum), the (red) ring area on the Ewald sphere consists of the ring thickness (1-√ε) and the (1-cos(β/2)) part (see distance Δ

_{x}*k*indicated in green in Fig. 1(a)), such that

*dk*=

_{x}*k*

_{0}⋅NA

*⋅(1-√ε) + √ε⋅*

_{B}*k*

_{0}⋅NA

*⋅(1-cos(β/2)) =*

_{B}*k*

_{0}⋅NA

*⋅(1-√ε⋅cos(β/2)).*

_{B}*dk*defines the width of the beam envelope of the sectioned Bessel beam in scan direction as shown in Fig. 1(b).

_{x}*dj*⋅

*dk*= 2π (

_{j}*j = x,y,z*) we obtain the following extents of a sectioned Bessel beam with section angle β: These beam extents

*dx*,

*dy*and

*dz*represent effective widths and correspond to real space standard deviations obtained by the inverse of the standard deviations in

*k*-space [12

12. S. Grill and E. H. K. Stelzer, “Method to calculate lateral and axial gain factors of optical setups with a large solid angle,” J. Opt. Soc. Am. A **16**(11), 2658–2665 (1999). [CrossRef]

*dx*in scan direction describes the envelope of the modulated beam, but does not describe a Bessel beam with

*β*= 180°. Whereas

*dz*is independent of β, the dependency of the beam widths

*dx*and

*dy*on the section angle β is displayed in Fig. 2(a) (with ε = 0.8 and NA

_{B}= 0.4). It can be seen that

*dx*(β) and

*dy*(β) become minimal for β approaching 180°, which corresponds to a conventional Bessel beam with finite ring width. However, for a reasonable range of section angles β > 60°, it turns out that the width

*dy*in detection direction hardly changes with β, whereas

*dx*falls of strongly. In other words, the light sheet thickness

*dy*is nearly independent of β for β > 60°.

*dz*can be steered efficiently by varying the ring parameter ε = 0.7…0.95. This has a small effect on the lateral width

*dx*and no effect on

*dy*. By plotting

*dy*(NA) against

*dz*(NA) for the Gaussian beam (ε = 0 and β = 180°) as shown in Fig. 2(c), one finds that for a decreasing NA or increasing depth of field

*dz*(NA) the width

*dy*(NA) increases. For the conventional Bessel beam (β = 180°) and the sectioned Bessel beam (β = 100°), the widths

*dy*(ε) remain constant when increasing

*dz*(ε) via the ring parameter ε. As we will show below, this situation changes when the detection point-spread function PSF

_{det}(

*x*,

*y*,

*z*) is considered.

## 3. Measures for directional propagation stability

*I*(

*x*,

*y*,

*z*) = |

*E*

_{SeB}(

*x,y,z*) +

*E*

_{sca}(

*x,y,z*)|

^{2}is the interference of the unscattered field

*E*

_{SeB}(Eq. (1)) and the manifold scattered field

*E*

_{sca}. By normalizing the power of the beam propagating through a scattering sample

*P*

_{scat}to the power

*P*

_{ideal}of the corresponding unscattered beam one obtains

*Q*gives the relative power that a beam is able to maintain within a small radius

*R*around its axis in the presence of scatterers.

*Q*It is robust against natural beam spreading due to diffraction in homogeneous space and comparable for beams which differ in irradiance and total power. The power ratio averaged over Δ

*z*along the propagation axisallows to assess the beam's propagation stability with a single number – which means a reduction in data of >10

^{7}:1 in comparison to the full volume data.

*R*) relative to the ideal, unscattered beam as a function of propagation distance

*z*? This measure is relevant to microscopy: Good images with homogeneous illumination require that this power is independent of the perturbation of the beam. The change of the beam’s on-axis power at different positions in a sample that arises from different scattering of the beam is a major source of image artifacts. Its strength can be measured by the standard deviation of the position dependence of the on-axis power [5

5. F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics **4**(11), 780–785 (2010). [CrossRef]

## 4. Simulation results for directional propagation stability

13. M. D. Feit and J. A. Fleck Jr., “Light propagation in graded-index optical fibers,” Appl. Opt. **17**(24), 3990–3998 (1978). [CrossRef] [PubMed]

14. A. Rohrbach, “Artifacts resulting from imaging in scattering media: a theoretical prediction,” Opt. Lett. **34**(19), 3041–3043 (2009). [CrossRef] [PubMed]

*dz*≈100µm. Cross-sections of the beams are shown in Fig. 3.

*n*

_{scat}= 1.41 embedded in an aqueous gel with

*n*

_{med}= 1.33. A small imaginary refractive index (

*n*= 0.0004) is included to account for the beam energy that is lost due to backscattered light, which the BPM cannot account for otherwise. The simulations were performed for different parameters of the scattering sample, i.e. volume concentrations (ρ = 6%, ρ = 12%) and size (

_{i}*d*= 2µm,

*d*= 4µm). To obtain representative results, the beams were propagated at 9 different (

*x*

_{i},

*y*

_{i}) positions for 15 different arrangements of the spheres expressed by

*n*(

_{j}*x*,

*y*,

*z*). The stability ratio

*z*are inferior to those for the high-NA Bessel beam and surprisingly also the sectioned Bessel beam with a high NA. This result means that the relative power of the beam within a radius

*R*around the propagation axis is higher for (sectioned) Bessel beams if the NA of the beam is high. The penetration depth is higher for larger spheres for all illumination beams. These obstacles scatter more light in forward direction, i.e. they remove less light from the beams. This result qualitatively agrees with a rough estimate using the reduced scattering coefficient µ’

_{scat}= (1-

*g*)⋅µ

_{scat}where

*g*is the size-dependent scattering anisotropy factor (for λ = 488nm:

*g*

_{2µm}= 0.96,

*g*

_{4µm}= 0.99).

*i*(lateral axis) and the volume

*j*(vertical axis). The magnitude of

*i*= 1...9 in each of the volumes

*j*= 1...15 corresponding to 135 simulations for each beam type. While white represents

*i*= 1 in volume

*j*= 10 where

*i*= 9 in volume

*j*= 4 where

*i*= 1 &

*j*= 4, i.e. an average value of

## 5. Theoretical considerations on optical sectioning

*x*. If sectioned Bessel beams are used to illuminate a thin line and fluorescence along this line is detected using the confocal-line detection scheme [7

7. F. O. Fahrbach and A. Rohrbach, “Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media,” Nat Commun **3**, 632 (2012). [CrossRef] [PubMed]

7. F. O. Fahrbach and A. Rohrbach, “Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media,” Nat Commun **3**, 632 (2012). [CrossRef] [PubMed]

*p*

_{CL}obtained by confocal-line detection (CL) from a fluorophore distribution

*c*(

_{F}**r**) can be approximated bywhere the symbol ’*‘ designates a convolution. In Fourier space Eq. (8) is the convolution of the corresponding transfer functions:where

*Ẽ*

_{ill}(

**k**) and

*Ẽ*

_{det}(

**k**) are the Fourier transforms of the illuminating field (Eq. (2)) and of the coherent detection PSF. AC{..} designates the auto-correlation.

*H*

_{sys}(

**k**,β) for various section angles. The first row illustrates projections of the angular spectrum

*Ẽ*

_{ill}(

*k*,

_{x}*k*,β) along the beam propagation axis

_{y}*z*. The second row shows

*H*

_{ill}(

*k*β) = AC[

_{x},k_{y},*Ẽ*

_{ill}(

*k*β)], whereas

_{x},k_{y},*H*

_{sys}(

*k*β) is shown in the third row. From the shape of

_{x},k_{y},*H*

_{sys}(

*k*β), the beam’s sectioning capability can be estimated. It is roughly expressed by the ratio of high spatial frequencies (HSF) to medium/low high spatial frequencies (LSF) of the MTF. The LSF components lie close to the center of the axis which appears in yellow and white for all beams indicating the largest amplitudes. Medium amplitudes are shown in red and extend to the highest frequencies (i.e. largest distances to the center) for the conventional Bessel beam. The line-profiles shown to the right of Fig. 6 confirm that the Bessel beam MTF contains the highest spatial frequencies. However, the support for medium frequencies (see extent of yellow areas in

_{x},k_{y},*H*

_{sys}(

*k*)) is smaller in comparison to the sectioned Bessel beam for β = 0.6…0 8π. This finding indicates the different sectioning capability for sectioned Bessel beams as analyzed in detail below.

_{x},k_{y}*h*

_{sys}(

**r**) (see Eq. (7)), can be measured in 3D when

*c*(

_{F}**r**) corresponds to a small fluorescent sphere. The integral over

*h*

_{sys}(

**r**) is a measure for the total fluorescence signal. To quantify the optical sectioning performance we compute the total fluorescence as a function of the detection axis, such thatThe latter equality results from Parseval’s theorem, where

*H*

_{sys}(

*k*,

_{x}*k*) is the modulus transfer function of

_{z}*h*

_{sys}(

*x*,

*z*). The normalized integral of

*F*(

*y*),corresponds to the fluorescence-sea method [16

16. M. Schrader, U. G. Hofmann, and S. W. Hell, “Ultrathin fluorescent layers for monitoring the axial resolution in confocal and two-photon fluorescence microscopy,” J. Microsc. **191**(2), 135–140 (1998). [CrossRef] [PubMed]

17. G. Vicidomini, M. Schneider, P. Bianchini, S. Krol, T. Szellas, and A. Diaspro, “Characterization of uniform ultrathin layer for z-response measurements in three-dimensional section fluorescence microscopy,” J. Microsc. **225**(1), 88–95 (2007). [CrossRef] [PubMed]

*dy*

_{OS}of the optical section is defined such thatand gives the range along the detection axis out of which the majority of the fluorescence is collected. Alternatively, it is useful to investigate the signal-to background ratio SBG. Here the signal

*G*(-δ)) /

*G*(-δ) for

*F*(

*y*) =

*F*(-

*y*).

## 6. Influence of the section angle β on optical sectioning

*dy*

_{OS}for a series of angles β using numerically computed distributions of

*h*

_{sys}(

*x*,

*y*,

*z*). The simulation was performed using a discretization of 23nm in a cube with a side length of 4096 pixels (≈94µm). The wavelength λ

_{0}= 488nm corresponds to 8 pixels in a medium with

*n*= 1.33. Examples for the cross-sections

*h*

_{ill}(

*x*,

*y*) of a sectioned Bessel beam for β = 20° and β = 110° and a conventional Bessel beam are shown in Figs. 7(a)-7(c). The ring parameter is ε = 0.9 so that the depth of field is

*dz*

_{1/e}≈80µm. The detection point-spread function is shown in Fig. 7(d).

*dy*

_{OS}for scanned illumination beams and wide-field detection in a light-sheet microscope. In this case,

*dy*

_{OS}depends only on the thickness of the light-sheet. The intensity of the light-sheet is constant along the scan axis (

*h*(

_{LS}*y,z*) ∝ ∫

*h*

_{ill}(

*x*,

*y*,

*z*)d

*x*) and within the depth of field of the beam (

*h*

_{LS}(

*x*,

*y,z*) ≈

*h*

_{LS}(

*y*)), so that one can write

*F*(

*y*) = ∫∫

*h*

_{LS}(

*y*) ·

*h*

_{det}(

*x*,

*y*,

*z*) d

*x*d

*z*=

*h*

_{LS}(

*y*) · ∫∫

*h*

_{det}(

*x*,

*y*,

*z*) d

*x*d

*z.*As the detection lens collects equal amounts of light from each plane, i.e. ∫∫

*h*

_{det}(

*x*,

*y*,

*z*) d

*x*d

*z*=const, the proportionality

*F*(

*y*) ∝

*h*

_{LS}(

*y*) holds. The section thickness

*dy*

_{OS}(β) is shown in Fig. 7(j). With NA = 0.4 and ε = 0.9, a minimum thickness of

*dy*

_{OS}≈2.5µm is achieved for β = 30° and increases significantly for larger values. At the same NA, thinner light-sheets can only be generated by shorter beams having a smaller ε. For e.g. ε = 0.8 and a Bessel beam with

*dz*

_{1/e}≈40µm,

*dy*

_{1/}

*≈1.7µm is possible for β = 50°.*

_{e}_{det}= sin(NA

_{det}/

*n*). As described by Eqs. (7) and (10), the optical sectioning depends on the overlap between the illumination beam and the point-spread-function of the detection objective lens. This overlap can be steered for sectioned Bessel beams by adapting the value β relative to α

_{det}. The system-point-spread functions

*h*

_{sys}corresponding to the beams shown in Figs. 7(a)-7(c) are displayed below in Figs. 7(e)-7(g) for a detection PSF with NA = 0.8 (Fig. 7(d)). It can be seen, that the small value of β = 20° results in a grating-like structure that is only poorly confined along

*y*. Accordingly,

*F*(

*y*), shown in Fig. 7(h) is very broad. For the conventional Bessel beam (Fig. 7(e)), even though the main signal is confined well, the ring structure leads to strong sidelobes of

*F*(

*y*). The best result, i.e. a small extent of

*h*

_{sys}along the

*y*-axis (Fig. 7(h)) and weak side-lobes is obtained for the sectioned Bessel beam with β = 100° (Fig. 7(f)).

*G*(

*y*) is plotted in Fig. 7(i) and exhibits the steepest and narrowest step for the sectioned Bessel beam. Figure 7(j) shows the optical sectioning

*dy*

_{OS}for various angles β = 0…180°. The thinnest sections are obtained for angles β in the range of 80° to 140°. Therefore, the optical sectioning for equal depth of field (ε = 0.9) is improved by a factor of ≈4 from

*dy*

_{OS}= 2.4µm to

*dy*

_{OS}= 0.6µm relative to conventional Bessel beams with confocal-line detection or sectioned Bessel beams with wide-field detection.

## 7. Optical sectioning dependency on the depth of field

*y*and its waist diameter Δ

*z*(Fig. 2(c)). Optical sectioning provided by a Bessel beam increases linearly, as can be seen by the good agreement of the values with a fitted line. The steps in the

*dy*

_{OS}(

*dz*) originate from the Bessel beam’s rings. In contrast, optical sectioning for the sectioned Bessel beams is completely independent on the depth of field. The sectioned Bessel beam’s cross-section mainly increases on the sides (along the

*x*-axis) where no light is collected by the detection lens, i.e. the only overlap between the illumination PSF

*h*

_{ill}and the detection PSF

*h*

_{det}is in the thin beam center around the beam’s axis.

## 8. Images of tumor multicellular spheroids

*p*(

*x*,

*y*

_{i},

*z*) for

*y*= 100 μm, located approximately in the center of the spheroid. The images reveal that confocal-line detection is able to improve visually perceived contrast well above the level of scanned Gaussian beams. However, in the case of Gaussian beam illumination, the signal for large penetration depth (right side) becomes very weak and the structure of the cell walls is hardly visible anymore. We quantitatively investigated the penetration depth by integrating the images shown in Figs. 7(b)-7(d), along the

_{i}*x*-axis to obtain

*p*

_{avg}(Fig. 7(e)). This measurement quantifies the beam’s on-axis power similar to the

*Q*-Values computed from numerical data in Section 4. We could confirm the simulation results and found that sectioned Bessel beams perform better than Gaussian beams and equally well as conventional Bessel beams regarding penetration into a scattering medium.

17. G. Vicidomini, M. Schneider, P. Bianchini, S. Krol, T. Szellas, and A. Diaspro, “Characterization of uniform ultrathin layer for z-response measurements in three-dimensional section fluorescence microscopy,” J. Microsc. **225**(1), 88–95 (2007). [CrossRef] [PubMed]

*p*(

_{y}*x*,

*z*) was Fourier transformed to

*k*= (

_{r}*k*

_{x}^{2}+

*k*

_{z}^{2})

^{1/2}≥

*k*) and low (LSF, where

_{F}*k*<

_{r}*k*) contributions separated by the corner frequency

_{F}*k*

_{F}= 1.1/µm. The ratio of the integrated high- and low-frequency contributionsprovides a quality parameter for image contrast

*C*as previously in [7

**3**, 632 (2012). [CrossRef] [PubMed]

*C*(

*y*) for all image planes

_{i}*p*(

*x*,

*y*

_{i},

*z*). The measurement confirms the visual perception: confocal-line detection increases image contrast for all illumination modes. The contrast

*C*(

*y*) depends also on the plane

_{i}*y*of the image inside the spheroid which is due to scattering of the fluorescence on the detection side. Figure 9(f) also reveals that sectioned Bessel beams offer better contrast than conventional Bessel beams. The values

_{i}*C*(

*y*) are similar to Gaussian beam illumination. However by comparing Fig. 9(b) and 9(d) one can directly see that the sectioned Bessel beam yields a more favorable combination of overall image contrast and image detail at large penetration depths.

## 10. Discussion

*dx*,

*dy*,

*dz*of a sectioned Bessel beam (SBB) in free space were described by evaluating the extents

*dk*,

_{x}*dk*,

_{y}*dk*of its finite width ring spectrum in

_{z}*k*-space, which is mainly defined by the sectioning angle β and the ring width parameter ε. These criteria give a good estimate for the dimensions of the illumination beams when scattering is negligible.

*Q*we were able to directly quantify many important beam properties that are of great interest to microscopy: the penetration depth into inhomogeneous media and the influence of the position of the beam in the scattering medium on the beam shape. Beams that show superior directional propagation stability are beneficial to light-sheet microscopy in two ways: an increased penetration depth and reduced artifacts. In contrast to the self-similarity of the transverse beam profile [18

18. T. V. Truong, W. Supatto, D. S. Koos, J. M. Choi, and S. E. Fraser, “Deep and fast live imaging with two-photon scanned light-sheet microscopy,” Nat. Methods **8**(9), 757–760 (2011). [CrossRef] [PubMed]

4. F. O. Fahrbach and A. Rohrbach, “A line scanned light-sheet microscope with phase shaped self-reconstructing beams,” Opt. Express **18**(23), 24229–24244 (2010). [CrossRef] [PubMed]

**3**, 632 (2012). [CrossRef] [PubMed]

*P*/

*E*of the beam energy

*P*within a circular region with radius

*R*around the propagation axis

*z*(

*P*(

*z*;

*R*) according to Eq. (4)) and the total beam energy

*E = P*(

*z,∞*), is a useful measure for the fraction of the beam’s energy that excites fluorophores within the confocal volume. It is expected that this illumination efficiency η decreases for β<180°, especially for small values as for β = 20° (shown in Fig. 7(c)). However, within the range β>100° (Fig. 7(b)) that improves optical sectioning, the decrease in efficiency η in comparison to conventional Bessel beams (Fig. 7(a)) is small, especially for higher NAs and ring widths ε. For example, for NA = 0.4, ε = 0.8, the efficiency decreases by ≈30% for β = 100°, but for NA = 0.4 and ε = 0.9, the decrease of η for values of β>100° is only <10% in comparison to the conventional Bessel beam. These values were obtained from simulated data for

*R*= 1µm. In conclusion, to maximize the efficiency η, the largest value of β that still enables good optical sectioning should be used. For example, as can be seen in Fig. 9, β = 140° already provides much better optical sectioning than the conventional Bessel beams for NA

_{det}= 0.8. We expect that even higher values of β are suited for lower detection NAs that are often used for light-sheet microscopy of samples with a size of several hundred microns.

*P*/

*E*of a suitable SBB (large β) is slightly lower than that of a Bessel beam. However, the optical sectioning of a SBB is much better than that of a conventional BB. For example, for NA = 0.4 and ε = 0.9, one needs to increase the illumination intensity by 10% to gain a factor of 2 in sectioning (SBG) by using a SBB with β = 100°. This SGB value was computed according to Eq. (13) with

*G*(

*y*) shown in Fig. 7(i) for a depth of field of the detection lens of 4µm.

3. P. J. Keller, A. D. Schmidt, J. Wittbrodt, and E. H. K. Stelzer, “Reconstruction of Zebrafish early embryonic development by Scanned Light Sheet Microscopy,” Science **322**(5904), 1065–1069 (2008). [CrossRef] [PubMed]

5. F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics **4**(11), 780–785 (2010). [CrossRef]

*S*is created by all fluorophores within a slice around the focal plane of the detection lens (with thickness corresponding to its depth of field). For this case, using numerical data, we computed an efficiency η, that is approx. 3-5 times higher than for confocal-line detection [7

**3**, 632 (2012). [CrossRef] [PubMed]

## 11. Summary and conclusion

## Acknowledgments

## References and links

1. | J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by Selective Plane Illumination Microscopy,” Science |

2. | H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods |

3. | P. J. Keller, A. D. Schmidt, J. Wittbrodt, and E. H. K. Stelzer, “Reconstruction of Zebrafish early embryonic development by Scanned Light Sheet Microscopy,” Science |

4. | F. O. Fahrbach and A. Rohrbach, “A line scanned light-sheet microscope with phase shaped self-reconstructing beams,” Opt. Express |

5. | F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics |

6. | 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 |

7. | F. O. Fahrbach and A. Rohrbach, “Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media,” Nat Commun |

8. | L. Silvestri, A. Bria, L. Sacconi, G. Iannello, and F. S. Pavone, “Confocal light sheet microscopy: micron-scale neuroanatomy of the entire mouse brain,” Opt. Express |

9. | E. Baumgart and U. Kubitscheck, “Scanned light sheet microscopy with confocal slit detection,” Opt. Express |

10. | J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. |

11. | J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. |

12. | S. Grill and E. H. K. Stelzer, “Method to calculate lateral and axial gain factors of optical setups with a large solid angle,” J. Opt. Soc. Am. A |

13. | M. D. Feit and J. A. Fleck Jr., “Light propagation in graded-index optical fibers,” Appl. Opt. |

14. | A. Rohrbach, “Artifacts resulting from imaging in scattering media: a theoretical prediction,” Opt. Lett. |

15. | T. Ersoy, B. Yalizay, and S. Akturk, “Self-reconstruction of diffraction-free and accelerating laser beams in scattering media,” J. Quantum Spec. Rad. Trans. |

16. | M. Schrader, U. G. Hofmann, and S. W. Hell, “Ultrathin fluorescent layers for monitoring the axial resolution in confocal and two-photon fluorescence microscopy,” J. Microsc. |

17. | G. Vicidomini, M. Schneider, P. Bianchini, S. Krol, T. Szellas, and A. Diaspro, “Characterization of uniform ultrathin layer for z-response measurements in three-dimensional section fluorescence microscopy,” J. Microsc. |

18. | T. V. Truong, W. Supatto, D. S. Koos, J. M. Choi, and S. E. Fraser, “Deep and fast live imaging with two-photon scanned light-sheet microscopy,” Nat. Methods |

**OCIS Codes**

(110.0180) Imaging systems : Microscopy

(140.3300) Lasers and laser optics : Laser beam shaping

(290.0290) Scattering : Scattering

**ToC Category:**

Microscopy

**History**

Original Manuscript: February 12, 2013

Revised Manuscript: April 8, 2013

Manuscript Accepted: April 12, 2013

Published: May 2, 2013

**Virtual Issues**

Vol. 8, Iss. 6 *Virtual Journal for Biomedical Optics*

**Citation**

Florian O. Fahrbach, Vasily Gurchenkov, Kevin Alessandri, Pierre Nassoy, and Alexander Rohrbach, "Self-reconstructing sectioned Bessel beams offer submicron optical sectioning for large fields of view in light-sheet microscopy," Opt. Express **21**, 11425-11440 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-9-11425

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### References

- J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by Selective Plane Illumination Microscopy,” Science305(5686), 1007–1009 (2004). [CrossRef] [PubMed]
- H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods4(4), 331–336 (2007). [CrossRef] [PubMed]
- P. J. Keller, A. D. Schmidt, J. Wittbrodt, and E. H. K. Stelzer, “Reconstruction of Zebrafish early embryonic development by Scanned Light Sheet Microscopy,” Science322(5904), 1065–1069 (2008). [CrossRef] [PubMed]
- F. O. Fahrbach and A. Rohrbach, “A line scanned light-sheet microscope with phase shaped self-reconstructing beams,” Opt. Express18(23), 24229–24244 (2010). [CrossRef] [PubMed]
- F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics4(11), 780–785 (2010). [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. Methods8(5), 417–423 (2011). [CrossRef] [PubMed]
- F. O. Fahrbach and A. Rohrbach, “Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media,” Nat Commun3, 632 (2012). [CrossRef] [PubMed]
- L. Silvestri, A. Bria, L. Sacconi, G. Iannello, and F. S. Pavone, “Confocal light sheet microscopy: micron-scale neuroanatomy of the entire mouse brain,” Opt. Express20(18), 20582–20598 (2012). [CrossRef] [PubMed]
- E. Baumgart and U. Kubitscheck, “Scanned light sheet microscopy with confocal slit detection,” Opt. Express20(19), 21805–21814 (2012). [CrossRef] [PubMed]
- J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett.25(20), 1493–1495 (2000). [CrossRef] [PubMed]
- J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun.195(1-4), 35–40 (2001). [CrossRef]
- S. Grill and E. H. K. Stelzer, “Method to calculate lateral and axial gain factors of optical setups with a large solid angle,” J. Opt. Soc. Am. A16(11), 2658–2665 (1999). [CrossRef]
- M. D. Feit and J. A. Fleck., “Light propagation in graded-index optical fibers,” Appl. Opt.17(24), 3990–3998 (1978). [CrossRef] [PubMed]
- A. Rohrbach, “Artifacts resulting from imaging in scattering media: a theoretical prediction,” Opt. Lett.34(19), 3041–3043 (2009). [CrossRef] [PubMed]
- T. Ersoy, B. Yalizay, and S. Akturk, “Self-reconstruction of diffraction-free and accelerating laser beams in scattering media,” J. Quantum Spec. Rad. Trans.113(18), 2470–2475 (2012). [CrossRef]
- M. Schrader, U. G. Hofmann, and S. W. Hell, “Ultrathin fluorescent layers for monitoring the axial resolution in confocal and two-photon fluorescence microscopy,” J. Microsc.191(2), 135–140 (1998). [CrossRef] [PubMed]
- G. Vicidomini, M. Schneider, P. Bianchini, S. Krol, T. Szellas, and A. Diaspro, “Characterization of uniform ultrathin layer for z-response measurements in three-dimensional section fluorescence microscopy,” J. Microsc.225(1), 88–95 (2007). [CrossRef] [PubMed]
- T. V. Truong, W. Supatto, D. S. Koos, J. M. Choi, and S. E. Fraser, “Deep and fast live imaging with two-photon scanned light-sheet microscopy,” Nat. Methods8(9), 757–760 (2011). [CrossRef] [PubMed]

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