3D-scanning microscopy with adaptive lenses and prisms for zebrafish studies

Abstract. Point-scanning-based microscopy systems require combination of axial and lateral scanning to obtain three-dimensional (3D) data. Axial scanning was commonly achieved by mechanical displacement of the objective or the sample. To improve, various adaptive lens-based solutions have been reported to circumvent the need for mechanically moving parts. The lateral scanning is predominantly implemented using galvanometric mirrors. Although the performance of such devices is flawless, they require bulky, folded beam-paths that make their incorporation in compact hand-held devices challenging. Recently, we introduced an adaptive prism as a transmissive device that enables lateral scanning. We demonstrate the first all-adaptive 3D scanning in laser scanning microscopes employing a compact in-line transmission geometry without mechanically moving parts and beam folding, combining an adaptive lens and a novel adaptive prism. Characterization of the all-adaptive microscope performance shows a lateral tuning range of approximately X  =  Y  =  130  μm and an axial tuning range of about Z  =  500  μm. We successfully demonstrate 3D raster scanning of the fluorescence of a thyroid of a zebrafish embryo.


Introduction
Adaptive optics technology has been employed in various systems to improve imaging properties, 1 correct aberrations, 2 and perform self-calibration. 3 Imaging techniques that acquire information in a point-wise manner, such as confocal microscopy 4,5 or optical coherence microscopy, 6,7 require point-scanning in three dimensions to obtain three-dimensional (3D) data. One possible way to accomplish the axial scanning is to mechanically translate the sample 8,9 or the microscope objective 10 in z-direction.
Several approaches employing adaptive lenses 11,12 have been introduced to realize axial scanning without the need for any mechanically moving parts in a variety of microscopes, such as confocal microscopy, 2,13 two-photon microscopy, 14,15 light-sheet microscopy, [16][17][18] structured illumination microscopy, 19,20 and standard wide-field microscopy. 21,22 More sophisticated adaptive lenses with 2 degrees of freedom enabled simultaneously tuning the focal position and correcting the spherical aberrations. This lens is committed to correct for specimen-induced spherical aberrations that occur in deep tissue applications 2 and systematic scan-induced aberrations. 12 The lateral scan is accomplished by mechanical translation of the sample or by reflective galvanometric mirrors. 23 The direction of the reflected beam can be regulated by turning the mirror. This type of scanner has a high resolution, good repeatability, and low drift values. It can approach both static and dynamic angles and can be operated at comparatively high speeds. However, galvanometer mirrors in reflective systems require a folded beam path, thus resulting in bulky optical setups. Adaptive prisms have the potential to improve and to allow for lateral scanning within an in-line compact setup. The first adaptive prisms reported were based on electrowetting on dielectric. [24][25][26] However, the scanning angle range of electrowetting-based prisms is too narrow to achieve a large field of view. Recently, we introduced a piezo-actuated adaptive prism with a large tuning range 27,28 as a suitable alternative to galvanometer mirror that enables an in-line transmissive configuration with large scanning angle range.
In this paper, we combine the adaptive prism with an adaptive lens, to realize the first all-adaptive 3D scanning in an in-line transmission geometry. To demonstrate the ability for biomedical 3D imaging of our approach, we conduct raster scanning of the thyroid of a cultured zebrafish embryo.

Adaptive Lens
The adaptive lens used in our all-adaptive scanning microscope consists of a transparent polydimethylsiloxan membrane, which is embedded in an annular piezo-bending actuator. Between the membrane and a glass substrate, an incompressible, transparent fluid is filled. When actuated, the bending actuator displaces the fluid underneath which generates a pressure inside the lens and deflects the membrane. We use a bimorph actuator (two piezo layers with opposite polarization) that provides large deflections in both directions. Such lenses have already been used in Refs. 13 and 19. As the numerical aperture (NA) of the adaptive lens is small (maximum 0.2), it has to be used in conjunction with an objective lens with high NA. The adaptive lens is imaged close to the objective back aperture as this is the best compromise between a reduction of systematic aberrations and the axial tuning range of the system. 29 The working principle of adaptive lens is illustrated in Fig. 1(a).

Adaptive Prism
In Fig. 1(b), the working principle of adaptive prism is illustrated. The adaptive prism consists of a fixed glass substrate and a tiltable glass window that sandwich a fluid. The upper glass of the adaptive prism can be tilted by three piezo-bimorph bending transducers (see Fig. 2). As the wavefront tilt is induced by the adjustment of the controlled path-length caused by the refractive index transition from the fluid in the prism to air (approximately 1.48 to 1), a surface tilt of 1 deg is required to induce a wavefront tilt of 0.48 deg. It has been verified that the prism is capable to induce wavefront tilts up to AE6.4 deg and achieves response times of 2.5 ms. 27 3 Characterization of All-Adaptive 3D Scanning Microscope

Digital Holography for Characterization of Adaptive Components
The characterization of the individual adaptive lens and prism is performed using digital off-axis holography. 30 The adaptive element is illuminated (green beam) and the transmitted light is imaged onto the camera. There it is overlapped with a coherent plane wave, which acts as a reference beam (marked in red) Fig. 3. The change of the wavefront angle upon actuation is measured holographically. The reconstructed results are summarized in Fig. 4. The tuning range of the adaptive lens is in the range of −23 to 19 dpt. We show the wavefront tilt angle of the adaptive prism amounts to a scanning range of 12.8 deg. As the mounting of the adaptive prism is not perfectly aligned, tilting in the x-axis also leads to a small tilt in the y-axis direction.

Digital Holography for Characterization of the 3D Scanning
The characterization of the 3D scanning is performed with the in-line digital holographic system shown in Fig. 5. The laser beam (TCLDM9) at an output wavelength of 532 nm is expanded by a beam expander and illuminates the adaptive lens. A 4f imaging system consisting of two lenses with focal length of both 75 mm images the adaptive lens to the adaptive prism, which is again imaged to the front lens by two 50-mm lenses. In the first characterization measurements, the scanning lens has a focal length of 25.4 mm.
A reference beam marked in red is split, magnified, and is overlapped on the digital camera with the object beam. The object beam is the scanned focus, which acts as a point source. The region of interest is imaged to the camera together with the reference beam. The resulting interference rings allow to reconstruct the origin of the point source in 3D by digital propagation, employing the angular spectrum propagation. 30 The setup is designed in in-line geometry, which is sufficient to reconstruct the amplitude information of the scanned region. Hence, we can track the scanning of the focus position numerically and can characterize the system.
The all-adaptive 3D scanning system is driven as shown in Fig. 6. In these experiments, just a single lateral scan in the x-direction is performed with the adaptive prism. As a first step, the actuation voltages of the adaptive elements are tuned as follows: the voltage of the adaptive lens U is kept constant at −40 V, while the whole voltage range of the adaptive prism is tuned, resulting in a lateral scan at constant axial position. The voltage U 1 on the adaptive prism is driven from −50 V to þ150 V and the decreasing voltage of the adaptive prism U 2 is from þ150 V to −50 V. Then, U increased by 10 V and again U 1 and U 2 are driven over the whole voltage range, until the static voltage U is tuned over the whole range. For each voltage pair, Fig. 5 The sketched digital holographic setup is used to characterize the scanning system. The green beam acts as an object beam, while the red beam is the reference beam. Actuation of the adaptive elements results in a shifting focus, which acts as a point-source. a digital holographic measurement is performed, resulting in 360 measurements in total in this experiment. Figure 7 shows cross-sections of the amplitude reconstructions for different propagation distances at different voltages.
The trajectory of lateral scanning is shown in Fig. 8. For each hologram, the propagation is performed, resulting in a cross-section amplitude image for each voltage configuration. The example in the figure shows the superposition of all reconstructions for scanned voltages on the adaptive prism, and for a constant axial position, at a voltage of 40 V on the adaptive lens.
The resulting scanned 3D area is shown in Fig. 9. The overall axial scan-range in this configuration is approximately 10.8 mm.
It is noteworthy that the z distance is measured relative to the camera position. The lateral scanning range amounts from −3.47 to þ3.47 mm when U AL ¼ −40 V, from −2.67 to þ2.67 mm when U AL ¼ 0 V, and from −2.31 to þ2.33 mm when U AL ¼ þ40 V, respectively. The results are consistent with analytical geometric considerations.
Using simple trigonometric calculations, the effective lateral scan angle can be determined and is displayed in Fig. 10(a). The standard deviation of the lateral tilt angles along each voltage  pair is shown in Fig. 10(b), the maximum standard deviation appears for the maximum angles and amounts to 1%, while for small angles, the standard deviation appears to be 0.05%.
For large tilt-angles of the adaptive prism, the focus quality and the peak intensity degrade due to aberrations. The by far greatest contribution to the aberrations, induced by tuning of the adaptive elements, is astigmatism. As in these experiments the scan lens has a comparably low refractive power, the spherical aberrations have a small effect in this configuration. Images of the resulting point-spread functions are shown in Fig. 11(a). The change of the astigmatism of the whole system during scanning is shown in Fig. 11(b). All other aberrations do not show significant contributions. Due to hysteresis, the axial displacements of the focal spot behave differently for decreasing and increasing voltages.

Experimental Validation
For the final all-adaptive scanning microscope, a 40× Olympus microscope objective (effective focal length ¼ 4.5 mm, NA ¼ 0.65) is employed as a scanning lens to further increase the NA and magnification of the system. The resulting axial scan range is reduced to around 500 μm. Laterally, the usable scan range amounts to approximately 130 μm. The theoretical axial and lateral resolutions of the system are 2.5 μm and 500 nm, respectively.  As a first step in the experiment, a USAF resolution test chart (Thorlabs R1DS1P) is used as a target. The all-adaptive scanning setup is applied in transmission geometry in a comparable way as shown in the characterization setup. Only the scanning lens is replaced by the abovementioned microscope objective. The sample plane is imaged to a digital camera by a lens system. Without any voltage on the adaptive optical elements, the microscope objective creates a focus on the sample. By applying voltage trajectories on the adaptive prism, a lateral scanning is accomplished resulting in a shifting focus on the camera. For each voltage constellation, an image is acquired. By superposition of the individual single-focus images, the image of the USAF test target is obtained, as displayed in Fig. 12. The smallest elements (element 6 of group 7) of our USAF test chart is clearly resolved, which corresponds to a lateral resolution of 2.2 μm. A slight tilt of the scans is observable, which is induced by a slightly rotated mounting of the adaptive prism, the optical setup, and camera.

3D Scanning of the Fluorescence of a Thyroid in Transgenic Zebrafish Embryos
The setup we used for the first all-adaptive 3D scanning experiments is shown in Fig. 13. The setup is used in reflection geometry. An LED is used for flood-illumination during alignment of the setup. The laser beam is scanned across the sample in three dimensions by just changing the voltages on the adaptive elements. The fluorescence is excited within the thyroid of a transgenic  zebrafish larvae. A long-pass filter in front of the camera in the detection path separates the fluorescence signal from the excitation. For each voltage combination, an image is recorded with the digital camera. As described earlier, the lateral scan is performed for a constant voltage on the adaptive lens. Then, the adaptive lens is tuned and the lateral scan is repeated for a different axial position. These individual scans are shown in Fig. 14(c). After scanning is completed, the data can be superimposed to the 3D view shown in the upper right of the figure. For future experiments, the setup is to be realized in a confocal geometry to reduce the out-of-focus signals by optical sectioning. Additionally, the detection geometry has to be adjusted, to keep the detection focused at the excitation, as currently tuning of the adaptive elements leads to a slight detuning of the setup.

Discussion
We demonstrate first all-adaptive 3D scanning, combining two adaptive scanning elements. This configuration has high potential to enable a compact and cost-effective in-line laser scanning microscope, without beam folding. The advantages of our approach in comparison to scanning using a spatial light modulator (SLM) are the large tuning range and the potentially high tuning  speed. Additionally, the refractive elements have a higher efficiency than the diffractive SLM versions. These advantages promise faster measurements in the sub-ms range and are thus important for fluorescence microscopy as they may result in a reduced exposure of the sample, minimizing bleaching effects. In the final microscope, the focus size in lateral dimension is approximately 1 μm. The scan range in air amounts to approximately X ¼ Y ¼ 130 μm in lateral direction and about Z ¼ 500 μm in axial direction. However, there is still room for improvement. While the lateral full-width half maximum point-spread function-size of the system is below 2 μm over the whole tuning range, the axial resolution is in the range of 10 μm. This could be improved by changing the setup to a confocal alignment. The precise control and orchestration of the adaptive elements is highly demanding, requiring either closed-loop iterations or system monitoring, e.g., using wavefront sensing techniques. 12 To ensure a high resolution in all-dimensions during scanning and to reduce the astigmatism, a multi-segmented lens is required to enable non-symmetric tuning. This further increases the difficulty for a precise control. Nevertheless, the presented approach has a high potential to improve the performance and increase the scanning flexibility for all point-scanning-based microscopy systems, paving the way to smart, computational microscopes.