Light-sheet microscopy with length-adaptive Bessel beams.

In light-sheet microscopy, a confined layer in the focal plane of the detection objective is illuminated from the side. The illumination light-sheet usually has a constant beam length independent of the shape of the biological object. Since the thickness and the length of the illumination light-sheet are coupled, a tradeoff between resolution, contrast and field of view has to be accepted. Here we show that scanned Bessel beams enable object adapted tailoring of the light-sheet defined by its beam length and position. The individual beam parameters are obtained from automatic object shape estimation by low-power laser light scattered at the object. Using Arabidopsis root tips, cell clusters and zebrafish tails, we demonstrate that Bessel beam light-sheet tailoring leads to a 50% increase in image contrast and a 50% reduction in photobleaching. Light-sheet tailoring requires only binary amplitude modulation, therefore allowing a real time illumination adaptation with little technical effort in the future.

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A conical phase is required in order to form a Bessel beam, where the phase slope k 0 ·NA defines the NA of the beam (at wave number k 0 = 2π/λ 0 with vacuum wavelength λ 0 ). Remarkably, the phase of the hologram is independent from the axial beam profile, i.e. the phase and the NA are not changed during the measurement. To adapt the beam length Δz(x) and axial beam position z 0 (x), only an amplitude modulation is required. Figure 3(a) shows how amplitude and phase of the hologram displayed on the SLM define the beam shape.
We assume the typical case that the distance z 0 between axial beam center position and hologram position is larger than the beam length Δz. Then the transmission function T(x,y) and the amplitude A(x,y) of the hologram have an annular shape [30,31]: With 2 2 r x y = + and circ(r-r 0 ) = 1 for r ≤ r 0 and = 0 otherwise. The center diameter R 0 of the ring defines the axial beam position according to 0 0 NA z n R = ⋅ with n being the refractive index. The beam length is given by the width ΔR of the ring according to NA z n R Δ = ⋅Δ . The magnification of the illumination system has been set to M ill = 1 in order to keep things simple. To avoid oscillations of the axial beam profile a low-pass filtering of the amplitude A(x,y) is required.
The SLM used in the current setup is a pure phase shifting element, although we used an algorithm to modulate the amplitude as well by transforming the continuous amplitude modulation into a binary pattern [30]. Therefore, in order to modulate beam length and axial beam position, a dynamic binary amplitude modulation in combination with a static phase modulation can replace the often slow SLMs. Hence, an axicon can be used as static phase element and a digital micromirror device (DMD) for dynamic binary amplitude modulation. The framerate of the currently used SLM is limited to 60 Hz, which is not enough to enable real time light-sheet adaptation. In contrast, DMDs feature framerates of more than 10 kHz [32][33][34]. Thus, for a field of view of 500 µm and a framerate of 50 Hz, totally 200 beams can be adapted laterally in steps of 2.5 µm within only 20 ms. This step size is small enough to sample all relevant object shapes. Also binary phase SLMs have been used for fast Bessel beam position control [35]. In this study, beams were rapidly shifted axially to enabled tiled light-sheets of rectangular shape, hence, light-sheets were not adapted to the shape of the object. Figure 1 shows a confocal detection based on the rolling shutter technique, which requires a minimum scanning speed (minimum speed of rolling shutter). For the proof of principle measurements presented in this work, a DMD has not been available, so that beam adaptation could not be realized at the scanning speed required for rolling shutter based confocal detection. To circumvent this problem, individual images were captured automated at each lateral scan position. The final image was calculated by multiplying the individual images with a mask representing the confocal slit and subsequently summing up all images [13] length the total beam power and therefore the amount of bleaching increase. In other words, a reduction in beam length is proportional to a reduction in bleaching.
The bar chart in Fig. 3(b) shows the fraction q 0 of photons that form a useful light-sheet image i.e. photons excited in the main maximum. This fraction q0(Δz) depends on the beam length Δz and, in the case of confocal detection, on the slit width d s . For a slit width of d s = 1 µm, one finds q 0 = 54% for Δz = 200 µm and q 0 = 42% for Δz = 600 µm. Assuming that only the photons excited in the main maximum contribute to the useful signal, whereas all photons from the Bessel rings form the image background, the signal-to-background ratio is given by Therefore, the SBR increases by 62% if the beam length is reduced from 600 µm to 200 µm. Figure 3(c) shows the decay of SBR(Δz) with beam length Δz for conventional and confocal detection mode. In conventional mode, the relative improvement achieved by keeping the illumination beam short is more pronounced than in the confocal case. Nevertheless, the absolute SBR is always higher if confocal detection is applied.

Increasing contrast with adaptive light sheets
To demonstrate the contrast enhancement capabilities of tailored LSM, we imaged an Arabidopsis root tip with (LTi6b:eGFP) membrane labeling and a fixed spherical cell cluster of T47D breast cancer cells stained with propidium iodide DNA labeling. The ideal lightsheet and the reference light-sheet -without object adaptation -used for the Arabidopsis root are presented in Fig. 2(c),(d). The NA of the illumination beam has been set to 0.13, resulting in a FWHM of the first maximum of 1.36 µm. Figure 4 shows a comparison of the corresponding fluorescent images using the reference light-sheet and a tailored light-sheet (both using line-confocal detection). The magnified image sections A and B underline the improvement in image contrast. To determine the contrast enhancement quantitatively, the reduces with increasing frequency because noise becomes more dominant in this range. The contrast improvement is more pronounced in the lower right part of the image. This can be explained by the shorter beam length which was applied in this area for tailored imaging. This effect is especially pronounced in the conventional detection mode. Although contrast improvement is better for the conventional detection, the pure image contrast with confocal detection is still much better than with conventional detection -with and without adaptive Bessel beams.

Adapting the beam length to the penetration depth
The line-confocal light-sheet fluorescence images of the cell cluster are shown in Fig.  5(a),(b). The cells had been in culture for 28 days, growing to a diameter of roughly 500 µm of the cell clu due to scatteri  The value dependency o twice as many  Furthermore, most light-sheet microscopes allow a rotation only around the x-axis (perpendicular to both optical axes). By rotating the root by 90° around x, light-sheet tailoring becomes unnecessary, but at the same time the size of the object in detection direction would increase and thus also the number of frames per 3D-stack.
According to the bar chart shown in Fig. 3(b), it was expected that bleaching is proportional to the beam length. The experimental data presented in Fig. 6 shows that the percentage of bleached fluorophores increases by a factor of 2, if the beam length is scaled up by a factor of 2.5. This can be explained by the fact that the light-sheet images have been captured with line-confocal detection, where the influence of the bleached areas far away from the focal plane is reduced. This is more relevant for longer beams, which are significantly broader than the shorter beam. Nevertheless, we could demonstrate a tremendous effect of the beam length on fluorophore bleaching. Therefore, we expect that the possible acquisition time of biological specimen sensitive to fluorophore bleaching can be doubled by light-sheet tailoring. This nearly compensates the main disadvantage of Bessel beams relative to Gaussian beams, which is enhanced bleaching, but maintains the strong advantages of Bessel beam illumination such as higher axial resolution and more homogeneous illumination.

Conclusion and outlook
We presented a concept for object adapted light-sheet tailoring. Adapting the Bessel beams lengths and positions to the space variant extent of the biological object result in a significant improvement in contrast and reduced photo bleaching. The image improvement depends on the shape and orientation of the object, which was estimated by a pre-scan using low-power scattered laser light. Light-sheet tailoring can be added to any system using Bessel beams, which are generated by either a static phase axicon or spatial light modulators, and this without any drawbacks or compromises. Especially photobleaching is expected to be reduced by light-sheet tailoring, although this effect has to be validated with different specimen in long term imaging experiments in the future.
Due to the characteristics of Bessel beams, light-sheet tailoring requires only binary amplitude modulation, which is also possible by phase-only SLMs. Due to the low frame rate of conventional SLMs, the proof of principle measurements presented in this article have been captured with a very limited frame rate. However, because only binary amplitude modulation is required, the phase-only SLM can be replaced by a fast DMDs or binary SLM. These devices feature frame rates, which enable tailored light-sheet microscopy at the maximum imaging speed of modern sCMOS cameras. With pure amplitude modulation, it is not possible to adapt Gaussian beams, which require a phase modulation in order to optimize the focal position and the depth of field.
Beside the automated object adapted light-sheet tailoring, the shape of the light sheet can also be defined by the user. In this way, parts of the object can be excluded from illumination. It is also possible to create light-sheets with user defined intensity distributions. In scanned LSM this is easily achieved in scanning direction by modulating the illumination intensity. In addition, the presented technique allows adaptation along the illumination direction. This enables the compensation of a varying fluorophore density as well as the correction of the intensity drop due to absorption of the illumination beam.
In summary, the simple and straightforward automation of tailored light-sheets enables this concept promising to become a standard feature in LSM with Bessel beams.

Method
Simulating the contribution q i of the individual Bessel rings onto the image formation a) Calculate the 3D intensity distribution of Bessel beams with different lengths by the angular spectrum wave propagation method. b) Separate the beam into its rings. c) Separate convolution of the Beam rings with the 3D-Detection-PSF in order to get the images of the individual beam rings for the case the object is a homogeneous distribution of fluorophores. d) Cut the focal plane out of the 3D images. e) Calculate the ratio q i of the power inside a slit of width ds for a certain ring i and the total power in the image of all rings.