1. Introduction

Selective plane illumination microscopy (SPIM) is a powerful technique used for 3D live fluorescence imaging in biological research [1–6]. Unlike conventional fluorescence imaging techniques based on the epi-illumination configuration, SPIM uses two objectives with optical axis orthogonal to each other for sample excitation and fluorescence detection separately. By confining the excitation light near the detection focal plane, SPIM allows high speed 3D imaging with high 3D spatial resolution, good optical sectioning capability, and minimal photobleaching and phototoxicity.

In order to maximize the benefit of SPIM, a key problem is how to create a thin and uniform excitation light sheet to cover the region of interest and confine the excitation light near the detection focal plane as much as possible. Different methods have been developed to create the excitation light sheet in SPIM, including the Gaussian light sheet created by cylindrical lenses or scanning Gaussian beams [1–3, 5, 6], the Bessel light sheet created by scanning Bessel beams [4, 7, 8], the Airy light sheet created by scanning Airy beams [9], and the optical lattice light sheet developed more recently created by dithering nondiffracting optical lattice patterns [10]. However, each of these methods has its own strengths and weaknesses, and it is very difficult to obtain a light sheet with thin thickness, large size and tight excitation light confinement at the same time. Therefore, tradeoffs must be made among these factors based on the desired performance and the sample to be imaged no matter what method is to be used to create the excitation light sheet.

The selection of the SPIM excitation light sheet and the optimization of its geometry are complicated. It involves the implementation of the appropriate method to create the light sheet and the tuning of the light sheet geometry based on the application and the specimen to reach the optimal balance between spatial resolution, optical sectioning capability and field of view (FOV). Here, we present a strategy to select, optimize and estimate the linear excitation light sheet in SPIM using the Gaussian light sheet, the Bessel light sheet, and the lattice light sheet as examples.

2. Results and discussion

The selection and optimization of the SPIM excitation light sheet are based on the desired spatial resolution, FOV, optical sectioning capability and the sample to be imaged. Experimental settings are usually tuned in the following sequence (Fig. 1). First, the combination of the excitation objective and the detection objective needs to be determined based on the desired spatial resolution and the size of samples to be imaged. Generally, it takes less effort to obtain higher spatial resolution with higher detection numerical aperture (NA), but it reduces the maximal FOV at the same time due to the Nyquist sampling requirement and the limited detection camera pixel number. For instance, a 0.4, 0.8 and 1.1 detection NA gives a lateral resolution of ~0.66 µm, ~0.33 µm and ~0.24 µm, but a maximum FOV of ~600 µm, ~300 µm and ~200 µm respectively with a 2k by 2k resolution camera. Obviously, a proper detection NA should be selected based on the specimen size, desired FOV and spatial resolution. Therefore, a 1.1 NA detection objective should be selected to image cultured cells, while a 0.4 or 0.8 NA detection objective should be selected to image a whole drosophila embryo or a zebrafish embryo. Meanwhile, it needs to be considered the SPIM alignment is more critical for higher detection NA, and its optical sectioning capability is worse than that with lower detection NA, which will be discussed below. The excitation objective can be selected afterwards based on the NA, working distance and geometry of the detection objective. The maximal excitation NA is usually 0.8 or smaller and the working distance has to be 3 mm or even longer.

 

Fig. 1 The procedure to select and optimize the SPIM excitation light sheet.

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Next, the minimal size of the excitation light sheet needs to be determined based on the region of interest to be imaged, and then the initial type and geometry of the excitation light sheet can be determined based on the required axial resolution. For example, a ~15 µm long light sheet is usually required to image a cultured cell. A submicron thin Bessel light sheet or optical lattice light sheet can be used for the initial test because a submicron axial resolution can be obtained and the requirement of the optical sectioning capability is usually not critical for imaging cultured cells. On the contrary, a light sheet of 100~200 µm is usually required to image a multicellular specimen, such as a drosophila embryo. The Gaussian light sheet is a better initial option for such samples because the optical sectioning capability is more important to image a large specimen and the excitation light is better confined by a Gaussian light sheet.

Finally, the excitation light sheet geometry can be tuned based on the spatial resolution requirement and signal to noise ratio (SNR) of the initial image results to reach the optimal balance between spatial resolution, FOV and the optical sectioning capability.

2.1 Spatial resolution

The lateral resolution of SPIM almost solely depends on the detection NA, given by ${\lambda }_{em}/2N{A}_{det}$, which is the same as that of the widefield microscopy, where ${\lambda }_{em}$ is the emission fluorescence wavelength and $N{A}_{det}$ is the detection NA. For a given SPIM system, the lateral resolution can be improved by combining SPIM with the structured illumination microscopy (SIM) [8, 11], but the improvement is usually minor and it is limited in one direction due to the relative low excitation NA and the constrained modulation direction [8].

Due to the axial confinement of the excitation light, an immediate benefit of SPIM is the improved axial resolution compared to the widefield detection. The point spread function (PSF) of SPIM can be considered as the product of the widefield detection PSF and the intensity profile of the excitation light sheet along the axial direction [7]. Thus, the axial resolution of SPIM is determined by both the excitation light sheet thickness $d_{ls}$ and the detection NA. When the excitation light sheet is in focus, the axial resolution is given by $1/(\frac{1}{d_{ls}}+\frac{n(1-\cos {\theta }_{det})}{{\lambda }_{em}})$, where n is the refractive index of the imaging buffer, and ${\theta }_{det}={\sin }^{-1}(N{A}_{det}/n)$ is the corresponding half-angle of light collection in the buffer. It must be noted that the excitation light sheet thickness is measured by the highest axial frequency $F_{ls}$ of the light sheet intensity profile in frequency space, where $d_{ls}=1/F_{ls}$ instead of the full width at half maximum (FWHM) of the light sheet in real space. In frequency space, the SPIM axial resolution corresponds to the highest axial frequency boundary of the SPIM optical transfer function (OTF), which is $F_{ls}+\frac{n(1-\cos {\theta }_{det})}{{\lambda }_{em}}$.

Figure 2(a) shows the dependence of the SPIM axial resolution on both the excitation light sheet thickness and the detection NA. Obviously, it is easier to improve the SPIM axial resolution by improving the coarser one between the light sheet thickness and the axial resolution of the detection objective, and the easiest way to increase the SPIM axial resolution is to use a higher detection NA. It also shows that the excitation light sheet thickness must be squeezed to a micron or thinner to obtain a ~0.5 µm or better axial resolution. Figure 2(b) shows the SPIM axial resolution obtained with excitation light sheets of different thicknesses and four commonly used detection NA of 0.6, 0.8, 1.05 and 1.1. The advantage of high detection NA in acquiring higher spatial resolution is shown clearly.

 

Fig. 2 (a) The contour map showing the dependence of the SPIM axial resolution on both the detection NA and the excitation light sheet thickness. (b) The SPIM axial resolution obtained with excitation light sheets of different thicknesses and detection NA of 0.6, 0.8, 1.05 and 1.1.

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2.2 Optical sectioning capability

The optical section capability is as important as axial resolution in 3D fluorescence imaging. It often determines SNR of acquired images and whether the theoretical spatial resolution can be obtained in practice [7]. Therefore, we studied how the optical sectioning capability of SPIM is affected by the excitation light sheet. In SPIM, the excitation light sheet can be considered as the sum of multiple arbitrary light sheets in focus and off focus (Fig. 3(a)), and the SPIM PSF is the sum of all sub PSFs produced by these sub light sheets while modulated by the intensity of each corresponding sub light sheet.

 

Fig. 3 (a) The excitation light sheet is a sum of multiple arbitrary light sheets in focus and off focus. (b) The max projection of SPIM PSFs in the lateral and axial directions obtained with 0.8 and 1.1 detection NA and a 0.32 µm thick Gaussian light sheet at different light sheet off focus distances. Scale bar: 1 µm.

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Figure 3(b) shows the max projection of the SPIM PSFs in the lateral and axial directions obtained with 0.8 and 1.1 detection NA using an arbitrary Gaussian light sheet of 0.32 µm thick created with 0.8 excitation NA at 488 nm excitation wavelength. It is almost the thinnest light sheet can be created practically in SPIM, due to the physical constrain between the excitation objective and the detection objective. SPIM PSFs were calculated with the excitation light sheet deviated from the detection focal plane from 0 µm to 1.6 µm with 0.4 µm intervals at 525 nm detection wavelength. It can be observed that off focus excitation light sheets don’t contribute anything positive to SPIM performance. SPIM PSF disrupts quickly as the light sheet moves away from the detection focal plane, especially when the off distance is larger than half of the depth of the detection focus (detection axial resolution). It can also be concluded that the off focus light reduces the optical sectioning capability of SPIM by increasing the fluorescence background. The higher the energy carried by the off focus light sheets the worse the optical sectioning capability of SPIM, especially when the excitation light is out of the depth of the detection focus. Therefore, no matter what method is used to create the excitation light sheet, the off focus excitation light should be reduced as much as possible. The result also suggests that the excitation light sheet must stay in focus to prevent the central peak of the excitation light sheet from producing fluorescence background rather than in focus fluorescence signal. Obviously, the requirement is more critical for higher detection NA and thinner excitation light sheets, because the depth of focus of a higher detection NA is narrower than that of a lower detection NA, and the imaging performance decays quicker for a thinner excitation light sheet as it becomes off focus. For the same reason, SPIM with higher detection NA has worse optical section capability for a given excitation light sheet, because the narrower depth of focus makes more excitation light contributes to the fluorescence background.

Nevertheless, the amount of the fluorescence background produced by the off focus excitation light also depends on the sample structure. For a densely labeled specimen, the majority of the off focus excitation light produces fluorescence light that contributes to the fluorescence background, hence an excitation light sheet with better light confinement should be used to image such specimen. On the other hand, a thinner light sheet, although could contain more off focus excitation light, can be adopted to push the axial resolution with less worrying about the fluorescence background if the specimen structure is sparse.

2.3 Tradeoffs between axial resolution, field of view and optical sectioning capability

We further compared several excitation light sheets used in the latest SPIM techniques through numerical simulation, including the Gaussian light sheet, the Bessel light sheet and the lattice light sheet following the proposed strategy in terms of axial resolution, FOV and optical sectioning capability. The refractive index of n = 1.33 and the excitation wavelength of 488 nm were used in all calculations and numerical simulations unless otherwise specified. We first studied the SPIM axial resolution can be obtained using the Gaussian light sheet of different lengths, because the Gaussian light sheet is the simplest and most commonly used method for sample excitation in SPIM. The thickness and length of a Gaussian light sheet are given by ${\lambda }_{exc}/2N{A}_{exc}$ and $\frac{{\lambda }_{exc}}{n(1-\cos {\theta }_{exc})}$ respectively, where $N{A}_{exc}$ is the excitation NA, and ${\lambda }_{exc}$ is the excitation laser wavelength.

Figure 4(a) shows the relationship between the length and thickness of the Gaussian light sheet, and Fig. 4(b) shows the SPIM axial resolution obtained using the Gaussian light sheet of different lengths and detection NA of 0.6, 0.8, 1.05 and 1.1 at 488 nm excitation wavelength and 525 nm detection wavelength. As expected, SPIM axial resolution becomes worse as the length of the Gaussian light sheet increases due to the tradeoff between the Gaussian light sheet length and thickness. However, this problem is only significant when the desired SPIM axial resolution is less than a micron. Therefore, the Gaussian light sheet satisfies both requirements of axial resolution and filed of view if the required axial resolution is only about 1-2 micron level. The problem of the Gaussian light sheet arises when a submicron axial resolution is required within a relative large FOV. For example, in order to reach a half micron axial resolution with 1.1 detection NA, a one micron or thinner Gaussian light sheet must be used, which is corresponding to ~0.25 or higher excitation NA, giving less than 20 µm FOV.

 

Fig. 4 (a) The relationship between the length and thickness of the Gaussian light sheet. (b) The SPIM axial resolution obtained with Gaussian excitation light sheets of different lengths and detection NA of 0.6, 0.8, 1.05 and 1.1.

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Bessel SPIM using Bessel light sheets created by scanning Bessel beams was developed to provide a solution for the tradeoff between the axial resolution and the FOV in SPIM [4, 7, 8], especially when a submicron axial resolution is required. Bessel beam, among the category of the nondiffracting beams, propagates indefinitely without changing its cross-sectional intensity profile, which follows the square of a zero-order Bessel function of the first kind [12]. Near nondiffracting beams can be created by limiting the wave vector difference of the excitation light in the propagation direction, and a near Bessel beam can be created by sending a uniform annular excitation light to the back pupil of the excitation objective in practice. A Bessel light sheet created by scanning a Bessel beam can therefore maintain a uniform thickness over a long distance due to the nondiffracting property. However, besides the central peak, Bessel beam contains a series of concentric side lobes of decreasing intensity surrounding the central peak, but with equal integrated energy in each lobe. In consequence, Bessel light sheet consists of not only a thin central light sheet created by the Bessel beam central peak, but also tails on both sides of the central light sheet created by Bessel beam side lobes leading to more off focus excitation light.

We first studied the dependence of the Bessel beam thickness and length on the excitation annulus outside and inside excitation NA, $N{A}_{OD}$ and $N{A}_{ID}$. The thickness of the Bessel beam is given by ${\lambda }_{exc}/2N{A}_{OD}$, and the length of the Bessel beam is determined by the maximal difference of the excitation light wave vector along the propagation direction, given by $\frac{{\lambda }_{exc}}{n(\cos {\theta }_{ID}-\cos {\theta }_{OD})}$, where ${\theta }_{OD}={\sin }^{-1}(N{A}_{OD}/n)$ and ${\theta }_{ID}={\sin }^{-1}(N{A}_{ID}/n)$. Figure 5(a) shows the length of the Bessel beam created by different excitation $N{A}_{OD}$ and $N{A}_{ID}$. Clearly, for a given $N{A}_{OD}$ or Bessel beam thickness, the larger the $N{A}_{ID}$, or the thinner the excitation annulus, the longer the Bessel beam.

 

Fig. 5 (a) The contour map showing the dependence of the Bessel beam length on the excitation $N{A}_{OD}$and $N{A}_{ID}$. (b) The contour map showing the dependence of Bessel beam side lobes range on the excitation $N{A}_{OD}$and $N{A}_{ID}$. (c) The ratio of the excitation energy carried by the central peak of Bessel beams created by different excitation $N{A}_{OD}$and $N{A}_{ID}$. (d) The ratio of the excitation energy carried by the central peak of Bessel beams of different lengths and thicknesses. (e) The ratio of the excitation energy carried by the central light sheet of Bessel light sheets created by different excitation $N{A}_{OD}$ and $N{A}_{ID}$. (f) The ratio of the excitation energy carried by the central light sheet of Bessel light sheets of different lengths and thicknesses. (Note that the ripples in (d) and (f) are due to the limited sampling density of the excitation beam parameters for numerical simulations.)

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The Bessel beam side lobes problem is another factor must be considered in Bessel SPIM. For Bessel beams of the same length, a thinner Bessel beam can be obtained with thinner excitation annulus and higher $N{A}_{OD}$, but it contains more side lobes, results in worse excitation light confinement. The range of Bessel beam side lobes can be estimated approximately by the maximal difference of the wave vector propagating to the same lateral direction, given by $\frac{{\lambda }_{exc}}{2(N{A}_{OD}-N{A}_{ID})}$, which is also the length of the corresponding Bessel light sheet tails. Figure 5(b) shows its relationship to the excitation $N{A}_{OD}$ and $N{A}_{ID}$.

To estimate the confinement of the Bessel beam on the excitation light, we also studied the ratio of the excitation energy carried by the central peak of Bessel beams created by different excitation $N{A}_{OD}$ and $N{A}_{ID}$ (Fig. 5(c)). The result shows that for a given $N{A}_{OD}$, the thinner the excitation annulus, the less the excitation energy carried by the central peak. To reveal the relationship more straightforward, this ratio is plotted against the Bessel beam length and thicknesses in Fig. 5(d). For example, for a Bessel beam with 50 µm length and half micron thick central peak, the central peak only carries less than 5% of the excitation energy. Apparently, although Bessel beam is capable to maintain a thin central peak over a long distance, the confinement on the excitation light is poor, and it becomes worse as the beam length increases.

The ratio of the excitation energy carried by the central light sheet of the Bessel light sheet is higher than that of the corresponding Bessel beam, because part of the energy carried by side lobes is in focus. Figure 5(e) shows the ratio of the excitation energy carried by the central light sheet of the Bessel light sheet created by different excitation $N{A}_{OD}$and $N{A}_{ID}$, and Fig. 5(f) shows its dependence on the Bessel light sheet length and thickness. The result shows that the energy carried by the Bessel light sheet tails is still significant. Therefore, although Bessel SPIM gives high axial resolution theoretically, it is often difficult to be obtained practically by Bessel sheet scan, and Bessel SPIM must be combined with SIM to take the full benefit of the think central light sheet thickness to reach submicron or better axial resolution. Meanwhile, the thickest Bessel beam that is long enough to cover the region of interest and give the required axial resolution should be used to minimize the Bessel beam side lobes energy because the optical sectioning capability can’t be improved by using SIM.

Lattice light sheet microscopy was developed more recently [10], in which a lattice light sheet created by dithering a nondiffracting optical lattice is used for sample excitation. The nondiffracting optical lattice is able to confine the excitation light closer to the detection focal plane while overcome the tradeoff between the light sheet length and thickness in the same way as the Bessel beam does, which is limiting the wave vector difference of the excitation light in the propagating direction. Instead of using a uniform excitation annulus, the annulus is only partially filled with periodic stripes. A nondiffracting optical lattice can also be considered as a coherent Bessel beam array, in which all Bessel beams interfere with each other coherently [10]. The length and thickness of the lattice light sheet are also determined by the excitation $N{A}_{OD}$ and $N{A}_{ID}$ of the annulus constraining the excitation light wavefront, and can be calculated use the same equations used for the Bessel light sheet calculation.

The coherent Bessel beam array (nondiffracting optical lattice) intensity profile is affected by both the individual Bessel beam geometry and the beam array period. We first studied the relationship between the coherent Bessel beam array intensity profile and the beam array period for a given Bessel beam. A Bessel beam created with excitation $N{A}_{OD}=0.5$ and $N{A}_{ID}=0.46$, giving ~30 µm beam length, was used to create coherent Bessel beam arrays with beam period from 0.96 µm to 5 µm. The intensity profile of the obtained coherent Bessel beam arrays and the corresponding lattice light sheets are shown in Media 1. We compared the ratio of the excitation energy carried by the central light sheet of different lattice light sheets, and the result is plotted in Fig. 6(a). The beam array intensity profile, the corresponding lattice light sheet and the excitation light intensity profile at excitation objective pupil at the above periods are shown in Fig. 6(b). The result shows that the off focus side lobes of different Bessel beams interfere with each other destructively at array periods of 1.06 µm, 2.1 µm, 3.16 µm and 4.2 µm, which are roughly integer multiples of ${\lambda }_{exc}/N{A}_{ID}$, so that the off focus excitation light is heavily suppressed. The central light sheet carries the maximal excitation energy, which is ~50% of the total energy, at the periods of 1.06 µm, around ${\lambda }_{exc}/N{A}_{ID}$.

 

Fig. 6 (a) The ratio of the excitation energy carried by the central light sheet of lattice light sheets created by the same excitation $N{A}_{OD}=0.5$ and $N{A}_{ID}=0.46$ at different lattice periods from 0.96 µm to 5 µm. (b) The coherent Bessel beam array (optical lattice) intensity profile, the corresponding lattice light sheet and the excitation light intensity profile at the excitation objective pupil at lattice periods of 1.06 µm, 2.1 µm, 3.16 µm and 4.2 µm. (c) The ratio of the excitation energy carried by the central light sheet of lattice lights and Bessel light sheets created with the same excitation $N{A}_{OD}=0.5$ and $N{A}_{ID}$ from 0.3 to 0.49. (c) The ratio of the excitation energy carried by the central light sheet of lattice lights and Bessel light sheets of the same thickness ($N{A}_{OD}=0.5$, $d_{ls}=0.488 \text{µ}m$) and different lengths from 10 µm to 100 µm. (Note that the ripples in (c) and (d) are due to the limited pixel size and filed of view for numerical simulations.)

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Finally, we compared the maximal ratio of the excitation energy carried by the central light sheet of lattice light sheets and Bessel light sheets created with the same excitation $N{A}_{OD}$ = 0.5 and $N{A}_{ID}$ from 0.3 to 0.49 (Fig. 6(c)). The ratio is also plotted against the light sheet length in Fig. 6(d). The result shows that the lattice light sheet offers significantly better excitation light confinement than the Bessel light sheet of the same length and thickness. However, the excitation light confinement by the lattice light sheet also becomes worse as the light sheet thickness decreases and the length increases, but the energy carried by the central light sheet is still more than 40% for a half micron thick, ~60 µm long lattice light sheet. Therefore, the lattice light sheet is a generally a better option compared to the Bessel light sheet to get submicron axial resolution in a large FOV without using SIM, despite the experimental generation of the lattice light sheet is more complex than that of the Bessel light sheet. The same rule used to choose the appropriate Bessel light sheet is also valid for choosing the lattice light sheet in SPIM imaging. In comparison with the Gaussian light sheet, the lattice light sheets also holds its advantage of higher axial resolution, but with a little worse optical sectioning capability for sub-hundred micron length, while its advantage vanishes as the length increases.

3. Conclusions

In summary, we present a strategy to select and optimize the linear excitation light sheet in SPIM based on spatial resolution, FOV and optical sectioning capability. We show that the spatial resolution of SPIM is determined by both the detection NA and the thickness of the excitation light sheet. However, whether the theoretical resolution can be obtained practically is determined by the optical sectioning capability of SPIM. We also show that the excitation light sheet should always stay in focus in SPIM, and the off focus excitation light should be reduced as much as possible. The alignment of SPIM using higher detection NA and thinner excitation light sheet is more critical, and the optical sectioning capability is worse with higher detection NA than that with lower detection NA, although the spatial resolution is generally higher. By using a detection NA of 1.0 or above, the Gaussian light sheet satisfies general requirements for spatial resolution, FOV and optical sectioning capability when the required SPIM axial resolution is above a micron, and the lattice light sheet should be used when a submicron axial resolution is required because it is thinner than the Gaussian light sheet of the same length and confines excitation light better than the Bessel light sheet of the same thickness. Meanwhile, the thickest and shortest light sheet that is able to give the required axial resolution and FOV should always be used for all types of the excitation light sheet to minimize the off focus excitation light in SPIM.