Multi-photon attenuation-compensated light-sheet fluorescence microscopy

Attenuation of optical fields owing to scattering and absorption limits the penetration depth for imaging. Whilst aberration correction may be used, this is difficult to implement over a large field-of-view in heterogeneous tissue. Attenuation-compensation allows tailoring of the maximum lobe of a propagation-invariant light field and promises an increase in depth penetration for imaging. Here we show this promising approach may be implemented in multi-photon (two-photon) light-sheet fluorescence microscopy and, furthermore, can be achieved in a facile manner utilizing a graded neutral density filter, circumventing the need for complex beam shaping apparatus. A “gold standard” system utilizing a spatial light modulator for beam shaping is used to benchmark our implementation. The approach will open up enhanced depth penetration in light-sheet imaging to a wide range of end users.

where u is the normalized pupil coordinate corresponding to the − z axis of the microscope (see Fig. 1(a)), σ A is a real scaling factor, α controls the propagation-invariance of the Airy light-sheet 5 , σ dictates the degree of linear attenuation-compensation and the light-sheet propagates in the positive x direction. The first exponential term in Eq. (1) describes the phase modulation required to generate an Airy beam and the second exponent is the amplitude modulation required to combat attenuation. The NDF used in this study (Thorlabs, NDL-25C-4, Optical density: 0.04-4.0) has a neutral density which varies linearly along its length, therefore the transmission through the NDF varies exponentially along its length. γ u ( ) is a smoothly varying apodization function, the exact form of which is not critical. In ref. 12 , an SLM was used to set γ 8 , where . H( ) is the Heaviside step function, with an expanded beam. Here, to conserve laser power, we allow the natural Gaussian envelope of the laser to act as the apodization function.
We first tested the fidelity of attenuation-compensated Airy beams generated by the NDF-based approach. Airy light-sheet profiles in the presence of attenuation provided by an absorbing NIR dye (American Dye Source, Inc., ADS795WS, absorption coefficient: . × 1 6 10 5 L mol −1 cm −1 , 2 mM) were visualized in fluorescein. Figure 1(b) shows the Airy light-sheet profile with no attenuation-compensation. Figure 1(c,d) show the Airy light-sheet with NDF-based and SLM-based (σ = . 0 5) attenuation-compensation respectively. The peak intensity in the planes transverse to beam propagation ( − y z plane), normalized to the value at = x 0, as a function of longitudinal coordinate ( − x axis) ( Fig. 1(e)) clearly shows the intensity decay in the main lobe of the Airy beam without attenuation-compensation. We recover a nearly uniform intensity along the full extent of the light-sheet using either the NDF-or SLM-based compensation techniques.
Absorption and scattering are two key phenomena that impede deeper penetration of incident optical fields into tissue. While absorption and single-scattering yield exponential decay of the incident light intensity described by the Beer-Lambert law, the increasing contribution of multiple scattering with deeper penetration into the sample may yield strong deviations from the expected exponential decay. Prior studies on attenuation-compensation have only considered compensation of an exponential decay. However, it is possible to control the intensity evolution of the beam arbitrarily, and the decay profile may be compensated for with sufficient characterization of the specimen. Using MCmatlab 13 , an open-source Monte Carlo radiative transport program, we found that the intensity decay of the incident light field followed an exponential profile even in the presence of high scattering anisotropy (see Supplementary Note 1). This result means that compensation of the exponential intensity decay of light is sufficient, and arbitrary control of the intensity evolution of the beam is not required, for a wide range of specimens. Therefore, we are able to use a standard optical element, the NDF, for providing attenuation-compensation of the field. Two-Photon Airy LSFM Imaging Results. The two-photon Airy LSFM was set up to directly compare the image quality achieved between NDF-and SLM-based attenuation-compensation methods. A 3D suspension of 400 nm diameter green fluorescent beads was made in a 1% agarose gel, containing 2 mM NIR dye, to yield attenuation by absorption. Figure 2 shows maximum intensity projections of the recorded images of these samples and the normalized line intensity profiles taken through them, showing an enhancement in signal-to-background ratio (SBR) at depth when attenuation-compensation is used. Both NDF-and SLM-based methods achieved similar enhancements.
We further performed a comparison between attenuation-compensation methods in thick biological specimens of diameter between 300 μm-450 μm exhibiting attenuation from both absorption and scattering. Human embryonic kidney 293 (HEK-293) spheroids stably expressing Green Fluorescent Protein (GFP) were imaged. These samples were then fixed in 4% paraformaldehyde and embedded in 1% agarose gel for imaging. Figure 3(a-c) show images acquired with each method and intensity profiles through lines (1) and (2) are shown in Fig. 3(d,e). We performed a SNR analysis of these 3D image stacks in the spatial frequency domain, taking the Fourier transform of each − y z plane as a function of depth ( − x axis) into the specimen 6 . We identified spectral bands between = − f 10 50%(2 r NA λ / ) and = − f 80 100%(2 r NA λ / ) corresponding to "signal" and "noise" respectively, and summed the spectral magnitudes within these bands (see Supplementary Note 2 for more details). The trend in SNR across the FOV is shown for each method in Fig. 3(f), and the ratio of SNR in NDF-and SLM-based compensation relative to the case of no compensation is shown in Fig. 3(g). At a depth of 200 μm, these plots consistently show increases in SNR of ~39% with NDF-and ~27% with SLM-based attenuation-compensation in biological specimen, yielding similar image quality. Besides, a total of 8 HEK-293 spheroid image stacks were acquired, and increases in SNR between 15 45% − and 5 25% − in the NDF-and SLM-based attenuation-compensation cases were observed at a depth of 200 μm. The single bright spot observed at ~263 μm in Fig. 3(a-c) was due to an exceptional expression of GFP of a cell in the spheroid which manifests as a large spike in the SNR ratios as seen in Fig. 3(g). This spot was discarded while estimating the range of enhancement in SNR for the compensation schemes.
Single-Photon Airy LSFM Imaging Results. In addition, we also investigated the performance of attenuation-compensation in the single-photon excitation regime. The 1+1D Airy light-sheet profiles in the presence of attenuation were visualized in high concentration fluorescein dye (0.88 mM). Figure 4(a-c) show the corresponding Airy profiles with no attenuation-compensation, NDF-based, and SLM-based (σ = . 0 8) attenuation-compensation respectively. Uniform intensity in the Airy main caustic after attenuation-compensation can clearly be seen from Fig. 4(b,c) in contrast to the non-compensated case in Fig. 4(a). The analogous longitudinal intensity envelopes measured in the above three cases up to an imaging depth of 200 μm are shown in Fig. 4(d). The difference in area under the curves in this figure qualitatively represents the level of attenuation-compensation provided by both NDF and SLM over their non-compensated counterpart.
We made a 3D suspension of 2 μm diameter red fluorescent beads in 1% agarose gel containing 0.88 mM fluorescein, as a phantom acting as an attenuating medium. The attenuation coefficient was determined to be = . C 85 9 attn cm −1 . Figure 5 shows maximum intensity projections of the deconvolved images 5,6 of these samples and the line profiles taken through them, showing an enhancement in SBR at depth when attenuation-compensation is used. Both NDF-and SLM-based methods achieved similar enhancements.
Finally, we used a biological specimen in the single-photon attenuation-compensated Airy LSFM. Spheroids, comprising of human neuroblastoma (SH-SY5Y) cells stably expressing GFP, were studied. Figure 6 shows the − x z maximum intensity projections of the deconvolved images. Similar to the two-photon case, the spheroid was also imaged under three different conditions: no compensation, NDF-based attenuation-compensation, and SLM-based attenuation-compensation(σ = . 0 8). Similar to the two-photon scenario, the SNRs for the different compensation schemes were calculated after analysing the Fourier content of the deconvolved image stacks. Figure 6(f) plots the SNR against the propagation coordinate at the areas specified in Fig. 6(a-c,g) plots ratios of the data relative to the non-compensated case. These plots show increases in SNR of ~30% with NDF-and ~29% with SLM-based attenuation-compensation, in biological specimen, at a depth of 140 μm. Additionally, increases www.nature.com/scientificreports www.nature.com/scientificreports/ in SNR between 25-50% and 20-40% in the NDF-and SLM-based attenuation-compensation cases were observed at a depth of 140 μm, from a total of 4 SH-SY5Y spheroid image stacks acquired.

Discussion
We have utilized attenuation-compensation for Airy beam based LSFM to selectively deliver more light deeper into a specimen without increasing the peak illumination intensity, therefore minimizing photo-damage. We have demonstrated the utility of attenuation-compensation provided by a NDF in LSFM and, for the first time, demonstrated an attenuation-compensated two-photon Airy LSFM system. Attenuation-compensation was applied to a light-sheet using an SLM or an NDF, and the performance of the two methods was compared.  www.nature.com/scientificreports www.nature.com/scientificreports/ Through SNR measurements, we showed an enhanced feature contrast at depth for single-and two-photon Airy LSFM with attenuation-compensation employed using either SLM or NDF. We imaged multiple spheroids of SH-SY5Y and HEK-293 cells with diameter varying between µ µ − m m 300 450 . For brevity, only two sets of data, out of these, are presented here (Figs. 3 and 6). In two-photon Airy LSFM, increases in SNR at µm 200 deep in the HEK-293 spheroid were observed between − 5 150% and − 5 50% in the NDF-and SLM-based attenuation-compensation cases respectively. Similar SNR increases of − 15 65% and − 10 65% in the NDF-and SLM-based attenuation-compensation cases respectively at µm 140 depth in SH-SY5Y spheroid were observed in single-photon Airy LSFM. The spheroid in Fig. 3 is placed centrally with respect to the FOV, and the constituent cells are evenly distributed throughout the volume. The general increase in brightness near the centre of FOV could be attributed to the fact that there is a higher probability of finding a bright cell near the center since there are more cells along the projection in the middle. Figure 7 shows the sample-dependent improvement in SNR for NDF-and SLM-based attenuation-compensated single-and two-photon Airy LSFM, where the data correspond to eight multiple regions in different spheroid specimens. On average, the SNR corresponding to NDF-based two-photon Airy LSFM images of µm 450 diameter HEK-293 spheroid exceeds the non-compensated value by ~4% at a depth of µm 50 and then rises approximately linearly to a maximum improvement of ~22% at a depth of 200 m. Similarly, the SNR for SLM-based method mimics the non-compensated value at a depth of 50 m and then rises approximately linearly to a maximum improvement of ~20% at a depth of 200 μm.
We note that, in the single-photon image data (Fig. 6), attenuation-compensation results in a small reduction in SNR near the start of the FOV which was not observed in the two-photon experiments (Fig. 3). When considering the one-and two-photon light-sheet excitation profiles (Figs. 1 and 4), this can be understood by the considerable background present in the sidelobe region of the beam at the start of the FOV when attenuation-compensation is used. This large background component will reduce the contrast of the sidelobes and have an adverse effect on the deconvolution of the single-photon images. However, in two-photon excitation, the www.nature.com/scientificreports www.nature.com/scientificreports/ non-linear relationship between illumination intensity and fluorescence excitation will suppress this feature. This interesting effect, coupled with the fact that scattering generally reduces with increasing wavelength and absorption becomes the more dominant loss mechanism at the longer wavelengths used for multi-photon microscopy, suggest that attenuation-compensation may be most useful in the multi-photon regime. We have not discussed the detection direction of the fluorescence signal in this work, which also deserves attention as it may become a limitation for imaging at depth, particularly in single-photon LSFM.
It is interesting to consider applying attenuation-compensation to Bessel LSFM in a facile manner. Using a linear NDF would not be ideal in such a system since the required pupil function consists of concentric rings with varying amplitude and phase. This results in a smooth exponentially growing profile as we give a full wave-optics treatment of the problem. An exicon 14,15 would be the closest solution, but is not an off-the-shelf component. Although one could state that a cubic phase mask is also not an off-the-shelf element, it has an inherent simplicity compared to exicon or a quadratic phase element and thus is more amenable to an NDF.
Attenuation-compensation for an Airy beam relies on the application of both phase and amplitude modulation. By use of an NDF, a well defined amplitude modulation may be applied with the SLM imposing the required cubic phase for the resultant Airy profile. In the case of sole use of a single nematic SLM for both amplitude and phase modulation, we have applied the phase for the Airy profile and assumed a linear amplitude response for the device. However, in most cases this is not the case and a modest nonlinear modulation component is present which ideally would be accounted for by calibration. The absence of this amplitude calibration in our case leads to a small mismatch between the NDF + SLM and SLM-only cases for attenuation-compensation. The difference in SNR at depth in the sample as is seen in the data is attributed to this reason. It also highlights the fact that the NDF system avoids the requirement for amplitude modulation of the SLM adding an advantage to its use for attenuation-compensation.
The gold-standard approach using an SLM offers dynamic control over the degree of attenuation-compensation. However, in the system we demonstrated, the compensation module in Fig. 1 consisting of an NDF exhibits virtually identical performance with that of the SLM for a fixed set of parameters. Flexibility to change the strength of compensation may be achieved by combining the NDF with cylindrical zoom lenses 16 for variable (de-)expansion. Figure 8 illustrates this concept, using a double-pass through the cylindrical zoom unit to ensure identical (de-)expansion. Such a system would enable dynamically reconfigurable attenuation-compensation without the need for complex diffractive optics. We expect that our approach will open up enhanced depth penetration using propagation-invariant beams in optical manipulation, optical coherence tomography, extended-depth multi-photon microscopy, and other imaging modalities.

Methods
Attenuation-compensated Airy light-sheet microscope setup. Our two-photon attenuation-compensated Airy LSFM is based on the OpenSPIM design 17 in a digitally scanned light-sheet microscope (DSLM) configuration 18 as shown in Fig. 1(a). The Ti:Sapphire ultrashort pulsed laser (Coherent Chameleon Ultra II, www.nature.com/scientificreports www.nature.com/scientificreports/ central wavelength 810 nm, 140 fs pulse duration, 80 MHz repetition rate) is spatially filtered and expanded before being directed onto a spatial light modulator (SLM; Hamamatsu, LCOS X10468-04) or cubic phase mask (CPM; PowerPhotonic, custom LightForge mask) to generate the phase profile required to generate a 2+1D Airy profile 12,19 . The SLM (CPM) is then imaged onto a galvo mirror (GM; Thorlabs GVS001) by lenses L1 and L2 and then onto the back aperture of the illumination objective (O1; Nikon, N10XW-PF, 0.30/10x, water immersion) by lenses L3 and L4.
Attenuation-compensation can be implemented on the SLM or by the addition of the compensation module (red dashed box in Fig. 1(a)). The compensation module comprises a linear graded neutral density filter (NDF; Thorlabs, NDL-25C-4, Optical density: 0.04-4.0) and two cylindrical telescopes oriented to elongate the beam along the − z axis (CL1, LJ1810L1-B, f = 25 mm, Thorlabs and CL2, LJ1567RM-B, f = 100 mm, Thorlabs) incident onto the NDF and then contract it to the original beam dimensions (CL3, LJ1567RM-B, f = 100 mm, Thorlabs and CL4, LJ1810L1-B, f = 25 mm, Thorlabs). The NDF has a neutral density which varies linearly along its length, therefore the transmission through the NDF varies exponentially along its length. The focal lengths of the cylindrical lenses were chosen to give magnifications of 4x and 0.25x respectively. The compensation module is positioned such that there is an imaging relation between the NDF and the SLM/CPM along the − z axis. Different sizes of beam incident on the NDF will yield different intensity (amplitude) gradients across the beam and therefore achieve different strengths of intensity modulation along the beam. For our system parameters (NA ill = 0.24, α = 7) the compensation achieved with the NDF closely matches the SLM-based compensation with σ = .
0 5 ( Fig. 1(b-e)). Note that for the implementation of SLM-based attenuation-compensation, the phase modulation on SLM was calibrated experimentally, and a linear amplitude modulation was assumed.

Fluorescent attenuating phantoms.
For testing the performance of two-photon attenuationcompensating Airy LSM, green fluorescent beads (400 nm in diameter, Thermo Fisher Scientific, G400) were added to 4 mM NIR dye (American Dye Source, Inc., ADS795WS, absorption coefficient: . × 1 6 10 5 L mol −1 cm −1 ) and later mixed with an equal volume of 1% low-melting point agarose to make a strongly attenuating (absorbing) phantom. This suspension was injected into an FEP tube (Adtech Polymer Engineering Ltd., FT1.3 × 1.6), which was sealed with putty (Hawksley, Crystaseal) at both ends, and imaged under the microscope. The final concentration of NIR dye in the phantom was 2 mM.
We made strongly attenuating phantoms for single-photon attenuation-compensating Airy LSM by adding fluorescent red beads (2 m in diameter, Thermo Fisher Scientific, R0200) to high concentration fluorescein dye (1.76 mM, Thermo Fisher Scientific, FITC) and mixing this with an equal volume of 1% low-melting point agarose.
A variable number of cells (e.g. 500, 1000, 2000) depending on the wanted spheroids size were plated in ultra-low attachment 96-well round bottom cell culture plates (Corning Costar 7007). After a 48 hours period (or when