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Abstract
Various techniques in microscopy are based on point-wise acquisition, which provides advantages in acquiring sectioned images, for example in confocal or two-photon microscopy. The advantages come along with the need to perform three-dimensional scanning, which is often realized by mechanical movement achieved by stage-scanning or piezo-based scanning in the axial direction. Lateral scanning often employs galvo-mirrors, leading to a reflective setup and hence to a folded beam path. In this paper, we introduce a fully refractive microscope capable of three-dimensional scanning, which employs the combination of an adaptive lens, an adaptive prism, and a tailored telecentric f-theta objective. Our results show that this microscope is capable to perform flexible three-dimensional scanning, with low scan-induced aberrations, at a uniform resolution over a large tuning range of $X=Y=6300\ \mathrm {\mu m}$ and $Z=480\ \mathrm {\mu m}$ with only transmissive components. We demonstrate the capabilities at the example of volumetric measurements on the transgenic fluorescence of the thyroid of a zebrafish embryo and mixed pollen grains. This is the first step towards flexible aberration-free volumetric smart microscopy of three-dimensional samples like embryos and organoids, which could be exploited for the demands in both lateral and axial dimensions in biomedical samples without compromising image quality.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Point-wise imaging methods such as confocal microscopy [1] or two-photon microscopy [2] require the focus to be scanned in three dimensions to measure volumetric data. This can be achieved by moving the sample with a stage. Faster scans can be accomplished by the usage of galvo-mirrors for the lateral and piezo drivers to move the microscope objective for the axial scanning.
In recent years, it was shown by several groups that adaptive lenses can take over the axial scanning, removing the need for mechanical axial translation of the objective [3–6]. Furthermore, it was shown that the use of adaptive lenses offers both faster and more flexible scanning. The main drawback is that there is a trade-off between scanning range and scan-induced aberrations [7–9] which depends on the choice of the adaptive lens position within the setup. The best compromise is to use a quasi telecentric setup [10]. Furthermore, it was shown that adaptive lenses with more versatile surface actuation, i.e. with several degrees of freedom were able to correct higher orders of induced aberrations and minimize system and sample induced aberrations while performing the axial scanning [9,11–13].
For the scanning perpendicular to the beam path, reflective components are generally employed to achieve lateral scanning having the advantage of large tilt angle and mature technology, such as piezo-actuated mirrors, microelectromechanical systems (MEMS) mirrors [14], and galvanometer mirrors [15]. However, these non-transmissive components lead to a folded beam path, resulting in a bulky setup. In this sense, a fully refractive 3D raster scanning microscope could help to improve both scanning speed and flexibility. 3D scanning is also possible employing spatial light modulators (SLM). However, these commonly suffer from low scan rates, low light efficiency as light is lost in the diffraction orders, and, in the case of the broadly used liquid crystal on silicon SLMs, the polarisation sensitivity. Other drawbacks are, that they have to use phase-wrapping and have a limited stroke.
In former works, we have successfully introduced adaptive prisms [16] as a possible solution to replace galvo-mirrors, and combined them with adaptive lenses to create a 3D scanning system [17]. As all components are transmissive, this approach can be realized in an unfolded and compact in-line geometry. However, this cascading of adaptive elements leads to scanning-dependent aberrations and field curvature in the region of interest. Especially astigmatism was found to be responsible for the degradation [17].
For instance, rays enter a regular scan lens with an angle $\theta$ to the axis and focus at a distance $d=f*\tan \theta$ from the optical axis, when the beam is scanned laterally across their input pupil. In combination with adaptive prisms and adaptive lenses, strong astigmatism occurs when all are used together to perform 3D scanning, which results in blurred or distorted images and lower resolution.
As a result, employing regular scan lenses to achieve homogeneous resolution is challenging. A laser scanning microscope with a telecentric f-theta scan lens has been proposed to image planar targets in [18]. Recently, some telecentric f-theta scan lenses have been presented in a variety of applications, including terahertz imaging [19,20], 3D imaging [19,21], confocal microscopy [18] and space environment mapping [22]. However, the distortions caused by the imperfect scan lenses themselves need to be compensated. Some other designs of telecentric f-theta scan lenses [22–24] performed well, but it is difficult to manufacture and use them directly in standard optical laboratories since they have uncommon shapes and require multiple distance alignment in such lenses.
Typical commercial scan lenses must strike a balanced compromise between short focal length, high performance, and a large field of view. Among them, focal length has a substantial impact on spatial resolution, and the high performance includes important parameters such as f-theta distortion and field curvature. This holds true, for example, for the scan lens LSM03-VIS (Thorlabs) with the shortest effective focal length of $39\mathrm {mm}$, but it is difficult to provide a low f-theta distortion over the visible wavelength range. Scan lenses with the lowest f-theta distortion (such as FTH100-1064, FTH160-1064, and FTH254-1064 of Thorlabs) do not allow for telecentric performance, and their focal lengths are typically larger than $100\mathrm {mm}$. Hence, in order to realize a fully refractive raster scanning microscope, we designed a tailored telecentric f-theta scan objective with a short focal length of $30\mathrm {mm}$ and with an extremely low f-theta distortion of $0.2{\%}$ over input angles $\pm 18^{\circ }$, which has a great benefit over some commercial scan lenses such as FTH160-1064-M39 (f-theta distortion of $1{\%}$ over input angles $\pm 18^{\circ }$) and LSM03-VIS (f-theta distortion of $0.5{\%}$ over input angles $\pm 12^{\circ }$). In this paper, we show that the combination of our scan objective and the adaptive prism and lenses enables to achieve near aberration-free 3D scanning over a large three-dimensional range.
2. Components of the fully refractive scanning microscope
2.1 Adaptive prisms and adaptive lenses
The adaptive prism used in our fully refractive scanning microscope consists of a fixed glass substrate and a tilt-adjustable glass window with an optical fluid in between, sealed in an elastic cavity. Three individually controllable piezo-bimorph bending transducers enable a 2D tilt of the upper glass of the adaptive prism when a voltage is applied. It has been demonstrated that the surface tilt of the glass window can reach more than 12 degrees, which corresponds to a wavefront tilt up to around $\pm 6^{\circ }$ at response times of $2.5\ \mathrm {ms}$ [16]. In Fig. 1(a), the working principle of lateral scanning using an adaptive prism and a scan lens is illustrated.
Fig. 1. (a) Schematic of the lateral scanning system using an adaptive prism. (b) Schematic of the axial scanning system with an adaptive lens. The adaptive lens is placed at a conjugate plane of the scan lens.
The adaptive lens used in our scanning microscope consists of a transparent elastomer (PDMS) membrane with an embedded annular piezo-bending actuator. Below this membrane, there is incompressible and transparent fluid in the fixed volume. The bending actuator displaces the fluid and hence deforms the membrane, resulting in a shift of the axial focal spot position of the adaptive lens [3]. The working principle of the axial scanning using an adaptive lens is illustrated in Fig. 1(b), which is in a 4f configuration. In this paper, the focal tuning range of the microscope is $Z=480\ \mathrm {\mu m}$ within a voltage range of 0 to $\pm 40\ \mathrm {V}$.
2.2 Design of the scan objective
The designed telecentric f-theta scan objective consists of four independent commercial lenses: Thorlabs LC1715-A, Thorlabs AC254-050-A, Thorlabs AC254-075-A, and Thorlabs AC254-075-A mounted in sequence, as shown in Fig. 2(a). We assembled the four lenses in one lens tube, to guarantee good alignment. Retaining Rings were incorporated to avoid any tilt. Considering that the distance between the lenses is zero, the accuracy of the lens distance did not pose a concern in our setup. The diameter of the incident beam is set to $4\ \mathrm {mm}$, which is the same as the input settings in the datasheet of most commercial scanning lenses, so that it later allows for performance comparisons, such as f-theta distortion and field curvature. In Fig. 2(b), a lateral scan range of $6.3\ \mathrm {mm}$ is given when the input half-angle is set as $\pm 6^{\circ }$, which is the maximum half-tilt angle that the adaptive prism can generate.
Fig. 2. (a) The composition of the designed telecentric f-theta scan objective. (b) The scanning range after employing an adaptive prism with the aperture of $8\ \mathrm {mm}$.
To summarize, the scan objective derived from the optical software Zemax OpticStudio shows the following distinct advantages:
- • The scan objective is capable of performing flat-field scanning with near-zero field curvature. Furthermore, it has the ability of f-theta scanning, which means linear displacement and constant scan rate in the lateral scanning plane;
- • The property of being telecentric (the converging cone of rays is always perpendicular to the specimen plane) leads to a uniform spot size in the image plane at each scan position, which is essential to realize nearly aberration-free scanning spots independent of the lateral position.
- • The maximum design numerical aperture (NA) of the scan objective can be calculated from the maximum half-angle in the simulation, as shown in Fig. 3. Hence, the design image-side NA is 0.36. The simulated focal length (referred to as distortion focal length in Zemax) is $30\ \mathrm {mm}$, which is significantly less than the focal length of most commercial f-theta scan lenses (usually more than $100\ \mathrm {mm}$), resulting in a small spot size and a high resolution.
- • The design of the scan objective is based on fixed lenses placed at a distance of $0\ \mathrm {mm}$ apart from each other, thus eliminating the difficulty of accurate positioning.
Fig. 3. The maximum half-angle of the scan objective to the light beam and the beam path in different situations.
2.3 Theoretical and simulated results
The most critical parameters for an f-theta objective are the f-theta distortion and field curvature. The f-theta distortion of a lens is defined in Eq. (1):
where $f$ indicates the effective focal length, $\theta$ represents the incidence angle, and $y_{\text {Bun}}$ is the lateral position of the bundle ray, respectively.As shown in Fig. 4(a), the maximum f-theta distortion over input angles up to $\pm 18^{\circ }$ for different wavelengths within the visible wavelength range is marked in this figure. When the wavelength is $470\ \mathrm {nm}$, the maximum f-theta distortion remains less than $0.181{\%}$. When the wavelength is $532\ \mathrm {nm}$, the maximum f-theta distortion remains less than $0.086{\%}$. When the wavelength is $635\ \mathrm {nm}$, the maximum f-theta distortion remains less than $0.199{\%}$. In our experiments, we use a wavelength of $532\ \mathrm {nm}$. Considering that the maximum lateral scan angle of our adaptive prism is around $\pm 6^{\circ }$, the maximum f-theta distortion in our setup is less than $0.029 {\%}$ as shown in the figure.
Fig. 4. (a) The f-theta distortion of our scan objective over the visible wavelength range. (b) Field curvature of designed scan objective over the visible wavelength range. In both figures, blue represents the wavelength of $470\ \mathrm {mm}$, green represents the wavelength of $532\ \mathrm {mm}$, and red represents the wavelength of $635\ \mathrm {mm}$.
Figure 4(b) shows the distribution of field curvature over an input tilt angle range of $\pm 12^{\circ }$ for different wavelengths within the visible wavelength range. The maximum sagittal field curvature and tangential field curvature are $0.244\ \mathrm {mm}$ and $0.057\ \mathrm {mm}$ at the wavelength of $532\ \mathrm {nm}$. In our setup at an input tilt angle range of $\pm 6^{\circ }$, the maximum sagittal field curvature and tangential field curvature are only around $60\ \mathrm {\mu m}$ and $1.8\ \mathrm {\mu m}$, respectively. These performances guarantee the feasibility of distortion-free lateral scanning progress in our system.
In a scanning system, the scan field diameter (SFD) is strongly influenced by the focal length $f$ of the scan lens. In a square scan field, the SFD is given by
where $\theta _{max}$ is the maximum deflection half-angle in radians. Considering that the maximum lateral half-angle offered by the adaptive prism is around $6^{\circ }$, the maximum lateral SFD in the experiments is approx. $6.3 \times 6.3 \mathrm {~mm}^{2}$.The main goal of the f-theta objective is to produce a constant spot size appropriate for the required resolution, and precisely position those spots anywhere in a flat image plane. The $\frac {1}{{e}^{2}}$ beam diameter width is given by
where $C=1.83$ for a Gaussian beam, $\lambda$ is the wavelength of the laser source, and $D$ is the diameter of the entrance beam. Therefore, the spot size depends only on the diameter of the entrance beam. Besides, the theoretical lateral resolution is defined by the Rayleigh criterion as the minimum distance between resolvable points as $R_{\text {Lateral}}={0.61\lambda }/{\mathrm {NA}}$. The objective has a design-NA of 0.36, giving a best possible resolution of $0.9\ \mathrm {\mu m}$. However, with the aperture diameter of $8\ \mathrm {mm}$ of the adaptive prism, we achieved a resolution of $2.2\ \mathrm {\mu m}$.The Strehl ratio within the input scan angle range of $\pm 6^{\circ }$ is shown in Fig. 5. In the simulation, the Strehl ratio is greater than $90.6{\%}$ over the whole quadratic field of $\pm 6^{\circ }$, and remains greater than $98{\%}$ within the largest circular field of view.
3. Fully refractive telecentric f-theta system
3.1 Description of the system
The fully refractive telecentric f-theta system is shown in Fig. 6(a). The adaptive lens is located at the conjugate pupil of the scan objective in a quasi 4f configuration. The optimum position of the adaptive prism was derived by optimization of all parameters during the Zemax simulation and is located at $12.6\ \mathrm {mm}$ in front of the lens plane of the scan objective.
Fig. 6. (a) Illustration of the fully refractive telecentric f-theta system combined with lateral scanning and axial scanning. (b) The additional digital holography configuration that is used for the characterization of the system.
In the characterization setup, we used a laser with an output wavelength of $532\ \mathrm {\mu m}$ (Thorlabs-CPS532) and a beam expander (GBE10-A) to increase the beam’s diameter, thus decreasing the focal spot size and increasing resolution according to Eq. (3). A tuneable aperture is placed behind the beam expander to precisely adjust the beam diameter. For the characterization of the fully refractive telecentric f-theta system, the 4f system is extended by an additional digital holographic interferometer, as shown in Fig. 6(b). Digital holography is chosen as it allows to numerically determine the shift of the focus position in three dimensions. The beam passing the adaptive lens, adaptive prism, and scan objective interferes with a plane reference wave, generating holograms in the camera plane, thus leading to a different interference signal depending on the axial focus position without the need to move the camera. Numerical propagation allows to quantitatively determine the relative focus shift induced by the applied voltages on the adaptive lens and prism. The determination of the three-dimensional position of the focus by the principle of digital holography is shown on the left of Fig. 7(a). The cross-section across amplitude reconstructions for different axial depths, i.e. different focus positions, at a constant lateral position is shown on the right. Furthermore, the lateral scanning ability at a constant axial depth at the example of $40\ \mathrm {V}$ applied to the lens is shown in Fig. 7(b). This shows lateral scanning with near-zero field curvature in great agreement with the simulation results as shown in Fig. 4(b), which also demonstrates the remarkable improvement in astigmatism correction of this system compared to our previous results in [17].
Fig. 7. (a) Digital holographic propagation enables the determination of the 3D focus position and exemplary cross-section across amplitude reconstructions for different propagation distances at a constant lateral position. (b) The lateral scanning at a constant axial depth where the voltage of the adaptive lens is kept at $40\mathrm {V}$.
3.2 Characterization results
One of the main quality criteria for the adaptive scanning system is the uniformity of the scanning focus throughout the whole scan range. Adaptive elements, such as the adaptive lenses and prisms our system is based on, have made significant progress over the years. These adaptive elements have been demonstrated to effectively correct spherical aberration [9,13] and chromatic aberration [25], and have made preliminary progress in achieving comprehensive second-order and third-order Zernike aberrations along with spherical aberration correction. Despite these advancements, generating a consistently uniform scanning focus throughout the whole scan range remains a challenge. While commonly the application of adaptive lenses and prisms can be tuned with the desired defocus and tilt into a microscope setup, it is always accompanied by undesired aberrations. Such additional variable aberrations induced by the scanning procedure would degrade the focus quality, i.e. shape and peak width of the point spread function, especially for large angles. The results in Fig. 8 show that the spot quality remains constant over the whole lateral scanning field. Here, for each voltage step of the adaptive lens, a full lateral scan of the adaptive prism was conducted. As the camera was kept constantly in its axial position, the spot diameter increases as we tune the focus of the lens. The performance is well maintained when additionally the voltage applied on the adaptive lens is tuned and thus the focus position is axially shifted. This can be observed by the highly uniform intensity distribution of the scanning spots for a constant focus position.
Fig. 8. A camera located at a fixed position was used to measure the intensity distribution of a scanning focus for different voltages applied at the adaptive lens and adaptive prism, i.e. at different positions in 3D. The values of $60\ \mathrm {\mu m}-420\ \mathrm {\mu m}$ represent the axial distance between the focus and camera plane, controlled by tuning the voltages applied on the adaptive lens, while the angles $0^{\circ }-6^{\circ }$ represent the angle of the adaptive prism.
To quantify the uniformity of the focal spots during lateral scanning, we took the on-axis picture recorded of the focus as a reference and use a normalized 2D cross-correlation of each focus for larger scan angles to track the variation. The results are plotted in Fig. 9. Compared to the commercial scan lens a significant improvement in the uniformity of the scanning focus can be observed when the optical system employs the present scan objective. As can be seen in Fig. 9(b), the values of cross-correlation stay above $95{\%}$ throughout the lateral scan range and show a comparable behavior to the simulated theoretical PSF. Most importantly, the high quality is also maintained for the largest angles. This can be also seen in the simulated Fig. 9(c) of the focal spots.
Fig. 9. Normalized cross-correlation between the intensity distribution of the focus without actuation of the adaptive prism and for actuation from $-6^{\circ }$ to $6^{\circ }$. (a) Using a commercial lens, (b) Using the designed f-theta scan objective. The measured data agree well to the simulation. (c) Simulated Huygens PSF, which is the diffraction PSF using direct integration of the Huygens wavelets method.
The uniform spot quality indicates that the tunable aberrations the adaptive elements induced are small, as astigmatism shows only small effects in this system. In the simulation of Seidel coefficients, the value of the astigmatism coefficient of the designed scan objective proves this point as $0.062\ \mathrm {\mu m}$. With all the same settings (wavelength: $532\ \mathrm {nm}$, input angle: $\pm 6^{\circ }$, beam diameter: $2\ \mathrm {mm}$), the contribution of the astigmatism coefficient of several commercial scan lenses is shown in Fig. 10 as $0.399\ \mathrm {\mu m}$ of LSM03-VIS (Thorlabs), $0.342\ \mathrm {\mu m}$ of SL50-CLS2 (Thorlabs), and $0.260\ \mathrm {\mu m}$ of CLS-SL (Thorlabs), respectively. The comparison demonstrates the ability of the designed scan objective to minimize astigmatism. Even the sum of the Seidel coefficients for astigmatism, coma, and spherical aberration, of our designed scan objective is lower than the astigmatism of the commercial objectives.(Fig. 10).
4. Experimental validations
The fully refractive telecentric f-theta microscope employed for biomedical measurements is shown in Fig. 11. We scanned the focal spot across the specimen in 3D by tuning the voltages of the adaptive lens and adaptive prism. It provides a maximum tuning range of approximately $X=Y=6300\ \mathrm {\mu m}$. The overall axial tuning range is $Z=480\ \mathrm {\mu m}$, and the axial step size can be altered for various biomedical samples. The fluorescence light that is excited in the sample passes through a long-pass filter with the cut-off wavelength of $550\ \mathrm {nm}$ and a lens in front of a digital camera, to filter out the excitation light. A camera with the pixel size of $2.2\ \mathrm {\mu m}$ detects the resulting intensity distribution for each voltage combination.
Fig. 11. Illustration of the fully refractive telecentric f-theta microscope with lateral scanning and axial scanning for the biomedical specimen.
Just like for the characterization measurements, the whole range of the voltages applied to the adaptive prism is tuned first, before the voltage on the adaptive lens is changed. This is repeated until all required axial depths have been scanned. Before the experiments, a calibration related to the position of each focal spot and each voltage pair should be performed. The setting of the scanning step size in the experiment will directly affect the final imaging quality achieved from the point-wise scanning. The step size may be equal to or smaller than the focus, creating either a non-overlapping or overlapping scan pattern. By the principle of optimal scanning using the least number of steps or pixels that can provide adequate spatial resolution [26], the criteria for choosing a suitable scanning step size in our experiment is that adjacent focal points are connected without overlapping to achieve the best imaging quality.
4.1 Experimental results for a fluorescent thyroid of the zebrafish embryo
As a demonstration application, we use the microscope for measurements on a transgenic zebrafish embryo. The fluorescent proteins within the thyroid of the zebrafish embryo are excited by the laser wavelength of $532\ \mathrm {nm}$. The voltage on the adaptive lens is tuned from $0\ \mathrm {V}$ to $-3\ \mathrm {V}$, corresponding to an axial scanning of $36 \ \mathrm {\mu m}$ range. In Fig. 12 we show data of the measured thyroid for a voltage step size of $0.5\ \mathrm {V}$, corresponding to 7 layers. The 7 layers of images can be superimposed finally to a 3D view after all the scanning is accomplished.
Fig. 12. Excited fluorescence of thyroid in transgenic zebrafish embryo along with different voltage pairs, and superimposed 3D view of the excited fluorescence of the thyroid.
To further test the practical ability of the axial scanning in our microscope, we perform measurements on mixed pollen grains (item: 304264 from Carolina Biological Supply Company). As shown in Fig. 13, for the axial scanning of mixed pollen grains, the voltage applied to the adaptive lens is tuned from $0\ \mathrm {V}$ to $-1.4\ \mathrm {V}$ with the voltage decreasing in steps of $0.2\ \mathrm {V}$. After the scanning, 8 images at different depths are recorded sequentially with each axial step depth of $2.4\ \mathrm {\mu m}$ and could be superimposed to create a 3D view. As a result, the maximum axial size of the mixed pollen grains is around $16.8\ \mathrm {\mu m}$.
Fig. 13. Excited fluorescence of mixed pollen grains along with different depths. Scale bar: $20\mathrm {\mu m}$.
All layers of information obtained from the scanned pollen grains are systematically illustrated in Fig. 14(a). Utilizing this data, we proceeded to generate a three-dimensional reconstruction of the pollen grains. By setting the axial step size to $2.4\ \mathrm {\mu m}$, we successfully created a superimposed view of the excited fluorescence in the 3D reconstruction, as depicted in Fig. 14(b).
Fig. 14. Layers information (a) and superimposed view (b) of the excited fluorescence of the mixed pollen grains in 3D scanning.
In this experiment, the lateral resolution has been enhanced to a uniform $2.2\ \mathrm {\mu m}$. In conjunction with an axial step size of $2.4\ \mathrm {\mu m}$, the image quality demonstrates a remarkable improvement compared to our previous results in [17]. Our approach allows to acquire fully 3D images of biomedical samples without any mechanical movement and any beam folding in a microscope set-up based on the adaptive lens, adaptive prism, and our new scan objective.
5. Conclusions
In this paper, we have introduced a fully refractive 3D raster scanning microscope, which combines an adaptive prism, an adaptive lens, and a specially designed telecentric f-theta scan objective in a 4F configuration. This microscope enables high-quality 3D scanning of biological samples without the need for any mechanical movement, beam folding, and without field curvature. It enables a uniform focus spot size over the whole scanning range and the maximum tuning range of approximately $X=Y=6300\ \mathrm {\mu m}$ in the lateral direction and $Z=480\ \mathrm {\mu m}$ in the axial direction.
Although the preliminary results show the high potential of our approach, there is still much room for improvement. The systematic aberrations were almost removed by the f-theta objective. However, sample-induced aberrations can still degrade the measurement. Thus, an adaptive lens with more degrees of freedom can be applied to account also for these. But still the main drawback is, that the more complexity is introduced to the system, the harder it is to tune the voltages to obtain the desired lens-reaction. Here, a machine learning-based approach to self-parameterization can offer a solution [25]. The key advantage of the scanning approach is that the scans have the potential to be very flexible and can achieve high scan rates compared to stage scanning and piezo-based axial scanning [27]. The incorporation of adaptive prisms and adaptive lenses eliminates the need for bulky and reflective mechanical scanning systems, resulting in a more compact microscope design with only transmissive components. Furthermore, the absence of mechanical scanning components avoids mechanical vibrations, leading to improved stability in the imaging process. However, still there is a trade-off between system complexity and the increase in scan rate, which has to be considered depending on the exact application. If the above-mentioned tasks are solved, the presented system has the potential to enable fast and gentle high resolution smart microscopy.
Funding
Funded by the Deutsche Forschungsgemeinschaft (CZ55/32-2, WA1657/6-2); and the China Scholarship Council (201706500012).
Acknowledgments
The Article Processing Charges (APC) were funded by the joint publication funds of the TU Dresden, including Carl Gustav Carus Faculty of Medicine, and the SLUB Dresden as well as the Open Access Publication Funding of the DFG.
Disclosures
The authors declare that there is no conflict of interest regarding the publication of this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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