1. Introduction

Light-sheet fluorescence microscopy (LSFM) is a microscopy technique that delivers wide-field optically sectioned images at high acquisition rates by splitting the illumination and detection of the fluorescence light into two orthogonal arms [1, 2]. One of the most common uses of the LSFM is to image embryos and organs, that tend to be in microscopic terms: thick, optically inhomogeneous and scattering samples.

As a result, LSFM suffers strongly from phase aberrations in both of its optical arms leading to a reduction in imaging quality. The aberrations in the imaging arm reduce the resolution of the resulting image. The aberrations in the illumination arm act in a more complicated manner. The effect of these aberrations changes over the field and can create strong non-uniformity in the illumination, slicing selectivity and image brightness over the image. Whilst correction of the phase aberrations in the imaging arm has been previously demonstrated [3], the problem of the correction in the illumination arm has yet to be solved. The reason for this is that there is currently no method for sensing the sample induced aberrations such that the light-sheet can be shaped to compensate for them. In this paper, a solution to the sensing and correction of these phase aberrations is presented. Direct wavefront sensing [4] on the fluorescent light emitted back in the direction of the source allows the optimal shape of the light-sheet to be found by utilizing a feedforward adaptive optics (AO) control system. This direct sensing is based on data from a Shack-Hartmann wavefront sensor [5] incorporated in an easily constructed epi-fluorescence arm. Once this aberration is known it can be corrected by applying the scaled conjugate phase to a spatial light modulator (SLM) controlling the illumination light.

This methodology is a departure from currently used methodologies where these aberrations are reduced by either chemically clearing the sample [6] or using biologically engineered organisms [7] to improve their optical quality. Whilst other approaches have modified the illumination of the microscope, they have not concentrated on correcting these aberrations, but rather using more complex methodologies that are less affected by them. They can be broadly grouped as methods changing the physical properties of the beam [8], the fusing of multiple datasets [2], or applying deconvolution [9] as means to improve the overall imaging result.

The drawback of these existing techniques is that aberrations are still present and it is necessary to infer the fluorescence signal, because it cannot be directly observed. Aberrations imply that fluorescence is in fact generated outside of the assumed sectioned plane, resulting in an increase in the background signal, a reduction in the signal-to-noise ratio, and features appearing in planes where they are not truly present.

To remove these spurious features the dataset must be deconvolved using its three-dimensional spatially variant point-spread function (PSF). Here noise corruption and the necessity to estimate the PSF over the field-of-view dictate that the output be an inference. Adaptive optics could allow for the correction of these phase aberrations, therefore, giving the direct observation of the fluorescence signal from the desired plane with no need for inference or extra post-processing.

2. Methodology for Feedforward Control

Adaptive optics has three main steps: wavefront sensing, reconstruction and correction. AO has been implemented in microscope systems in one of two ways [10]. One method, “direct sensing”, uses a device known as a wavefront sensor (WFS), which provides a signal that can be related to the spatiotemporal variation of the phase in a particular plane of the optical system. The strongest advantage for using a sensor is its speed and this is often necessary when the phase aberration has fast temporal dynamics; however, it generally applies constraints to what can be imaged (e.g. only point-sources), it can lead to anisoplanatic correction depending on the type of aberration, and it requires photons that could be used for imaging.

The second method, “indirect sensing” or “indirect optimisation”, uses an optimization procedure to iteratively improve the quality of the images. This second technique is known as sensor-less AO and is typically used in microscopy systems where the photon budget is low, or the object constraints for the sensor are not met. The advantage is that it can be always implemented with a suitable metric, however, if N is the number of modes used for the corrective element then the minimum number of steps to correct the aberration is N +1 [11], this leads to a lengthy and costly imaging process.

To sense the aberration in the illumination path, it was decided to use direct wavefront sensing, and since the back-scattered coherent illumination light would produce a speckle field at the wavefront sensor, the incoherent epi-fluorescent light was chosen to sense the aberration. It should be noted that the fluorescence light emitted orthogonally to the illumination is used for imaging, therefore, no light normally used for imaging is lost to sense and correct the aberration, see Fig. 1 for the layout of the experimental system.

 

Fig. 1 A schematic representation of the optical system showing the major optical components for the addition of the sensor to the microscope design. The light from the spatial light modulator (SLM) is conjugated via the dichroic mirror (DCM) onto the illumination objective (IO). The light focuses into the sample that gives off uniform fluorescence into 4π steraradians. The fluorescence is captured in two paths, one through the detection objective (DO) and onto the camera for imaging; and epi-fluorescently through the IO via a optical relay to the wavefront sensor composed of a fluorescence filter (FF), a lenslet array (LA) and sCMOS camera. The iris (IR) allows the regulation of the spot sizes on the sensor. For explanatory purposes the orientation of the coordinate axes for the LSFM are shown on the right.

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A point-source in the centre of the microscope FOV in free space would produce a flat wavefront in the pupil plane of the illumination objective. Hence, by adding a wavefront sensor conjugated with this pupil plane it is possible to sense the phase aberration acquired in the optical path on the way out of the sample. By Babinet’s principle the illumination light will acquire the same phase aberration, scaled by the wavelength, on its way into the sample. Shaping the incident light with the conjugate aberration will, therefore, recover a point-source. A further advantage of this approach is if the illumination is restored to a Gaussian focus, then by definition, it cannot diverge faster from the focus. As a result any subsequent aberrations in the path will produce a light-sheet that is thinner, thus also increasing the axial resolution at the far side of the sample.

Unfortunately, LSFM is generally used to image extended sources and therefore, no point-source at the centre of the FOV is normally present. Whilst it would be possible to introduce so called ‘guide stars’ [12], practically this would be difficult implement and could interfere with biological processes. It is possible, however, to locate a region of fluorescence in a sample at the centre of the FOV. When a beam is used for illumination instead of a light-sheet, that is the cylindrical defocus is removed, fluorescence is generated throughout the Gaussian point-spread function (PSF) of the optical system.

With this extended incoherent source, the wavefront sensor reconstructs a weighted average of the anisoplanatic aberrations, that have been introduced by the sample in the vicinity of focal region, and the isoplanatic aberration of the system, including the pupil aberration and, to some extent, the aberration caused by the sample. The final correction from this sensor will be efficient because in a practical system the isoplanatic low-order component has a considerable weight. Moreover, the wavefront corrector conjugated to the system pupil plane is only capable of correction of this isoplanatic component of the aberration field.

A Shack-Hartmann wavefront sensor can be conjugated to this pupil plane showing an array of PSFs, or spots created by its lenslet array. The conventional procedure of wavefront correction by minimizing spot shifts from a known flat reference is not applicable for the case in discussion. The reason for this is that the epi-fluorescent light does not pass back via the corrector; even if it did, it is of the wrong wavelength and polarisation to have the desired effect. The system as a result can sense the aberration, but it cannot detect the effect of its own correction on the wavefront. It must instead operate in a blind single step feedforward mode, where the only means of verification of aberration correction is in the improvement found in a three-dimensional acquisition.

Following the usual procedure for this type of control, the spot displacements in each of the sub-apertures are linearly related to a modal decomposition of the wavefront in Zernike polynomials Z_n, where n is the Noll index. The stacked spot displacement vector s can be linearly related via the sensor geometry matrix G to the vector of Zernike coefficients z by:

To find the spot displacements s requires knowledge of the flat wavefront reference position r. The current measured centres c and the reference centres r are related to the displacement by the following expression: s = c − r. The reference spot positions, therefore, must be found before the control methodology can be applied. In this case, it is desirable to have a source in the centre of the FOV that has the similar properties as those found in the samples one desires to image (i.e. partially extended, same wavelength and intensity). Thus, a uniformly fluorescent medium of the correct wavelength and concentration is the most directly comparable.

Once s is calculable the inverse relationship of Eq. (1) is required, and since G is often not invertible, the Moore-Penrose left pseudo-inverse is used to define the Zernike coefficients at the sensor given the spot displacements:

The same Zernike polynomial modes Z_n are used for controlling the phase on the spatial light modulator (SLM), and once the wavefront reconstruction is done its conjugate is applied to the SLM. The vector of phases for every pixel φ^SLM is related to the sum of the Zernike polynomials at its position z^SLM by the following mathematical relationship:

Although β is theoretically calculable, it is better to make an experimental measurement. As previously mentioned the WFS is generally insensitive to the corrective phase, however, it is not completely and it is possible to make use of the translational Zernike modes (tip, tilt and defocus) for this purpose. As these modes correspond to the movement of the focal spot in three dimensions, the WFS is sensitive to their application on the SLM and β can be measured.

The ratios between applied Zernike coefficient on the SLM and the measured coefficient on the WFS for each of the translation modes are averaged together. With β now known, the corrective phase ${\widehat{\phi }}^{\text{SLM}}$ applied to the SLM can be directly related to the spot displacements on the sensor by:

In summary, the main reason for the use of the feedforward control strategy is that it is not possible to image the laser line directly in an aberrating sample and obtain feedback. While this methodology senses and corrects the aberration introduced between the objective lens and the focal plane, any images of the shape of the light-sheet itself would be affected by a different aberration, which could not be corrected by the wavefront corrector. Even a perfectly corrected light-sheet would, therefore, appear aberrated if imaged directly. For these reasons, it is impossible to image the light-sheet inside an aberrating sample in this optical configuration, thus feedforward control is used.

3. Experimental Design and Calibration

For the purpose of experimental verification, a light-sheet fluorescence microscope has been realized in the configuration shown in Fig. 1, here the illumination is provided by a 488nm laser (100mW Sapphire LP, Coherent Inc., U.S.) followed by polarization optics (WPH10M-488 and GT5-A, Thorlabs, U.S.) to produce linearly polarized light for the following spatial light modulator (SLM) (512×512, Meadowlark Optics, U.S.) with the additional benefit of providing a fixed intensity attenuator.

The light from the SLM is optically conjugated to the back aperture of an NA= 0.3 objective lens (UMPLFLN 10x Olympus, Japan) via a beam expander (AC508-180-A-ML and AC508-200-A-ML, Thorlabs, U.S.) of $1.1\dot{1}\times$ thus utilising the full numerical aperture (NA) of the microscope objective. To form the light-sheet a cylindrical lens pattern is applied to the SLM, thus cancelling the focusing power of the lens in the y-direction, such that it is possible to have a light-sheet across the vertical field-of-view of the detection camera of around 400 μm.

The detection of fluorescence follows the standard LSFM design and is orthogonal to the light-sheet propagation direction. The fluorescence light is conjugated from the NA= 0.5 imaging objective (UMPLFLN 20× Olympus, Japan) to a deformable mirror (DM) (DM69, ALPAO, France), which used for changing the imaging plane in step with the SLM, via a 1:1 telescope (AC508-180-A-ML, Thorlabs, U.S.). The fluorescence at the mirror is then focused onto the imaging camera (Orca Flash v2, Hamamatsu Photonics, Japan) through a fluorescence filter (MF525-39, Thorlabs, U.S.). Hereby, obtaining a optically sectioned image at a desired plane in the sample. Three-dimensional imaging is obtained by scanning the SLM and DM in synchronous motion after a calibration procedure described in the author’s previous work [13].

To this base a Shack-Hartmann wavefront sensor (SH-WFS), made of a lenslet array (300 μm rectangular array, Flexible Optical B.V., Netherlands) and a camera (UI-3060CP Rev. 2, IDS, Germany) has been added to record the wavefront of the epi-fluorescent light. The light incident to the microscope is reflected from a dichroic mirror (DCM) (MD498, Thorlabs, U.S.) such that the epi-fluorescent light from the sample can be collected via an optical relay (AC254-150-A-ML and AC254-100-A-ML, Thorlabs, U.S.) onto this wavefront sensor. A tunable iris (IR) (SM1D12D, Thorlabs, U.S.) for regulating the out-of-focus fluorescence is implemented in the image plane of the optical relay to help with the sensing procedure.

The feedforward calibration is practically done as follows. A reference sample is mounted on the setup, this must be uniformly fluorescent and have the same systematic aberrations as the regular samples. For this purpose, fluorescein in low density agarose (0.5%) is chosen and mounted in a square sided 1×1mm capillary tubes (Vitrotubes™ 1×1mm, VitroCom, U.S.). The laser beam is focused to a spot via the SLM into the fluorescent agarose and aligned with the centre of the FOV of the imaging camera.

This defines the reference position of the Shack-Hartmann spots and it is regarded as virtually aberration free. The wavefront sensor uses the brightest 350 sub-apertures and reconstructs the wavefront using 50 Zernike modes. The sensor geometry matrix G is calculated based on these reference positions and the Zernike phase constructor for the SLM Φ is constructed based on the device properties.

To this reference position a fixed and known amount of tip, tilt and defocus are applied to the SLM sequentially and the displacement of the spots on the Shack-Hartmann are recorded. The scaling parameter β between the applied Zernike coefficient for the SLM and the measured coefficient is recorded and stored in memory. The expression found in Eq. (5) can now be applied to calculate the correction.

To test this calibration an amount of tip, tilt and defocus are applied to the SLM and the system is run in a closed-loop mode, for only these modes. The system is found to return to the reference position after a few iterations (depending on the size of the feedback parameter), therefore, the calibration is verified for these modes.

In order to test the calibration for higher order Zernike modes it is possible to place a low-power cylinder in the pupil plane of the focusing objective. By imaging the fluorescent agarose it is possible to test if the adaptive system is able to correct modes higher than tip, tilt and defocus. If this lens is placed tilted and off-axis it will introduce further low order Zernike modes above astigmatism. The results of this test, shown in Fig. 2, demonstrate the corrective ability of the feedforward system. The limitations of single step correction are also visible in this data. It shows that the system is unlikely to return to the diffraction-limit in a single step, however, significant improvement of the beam profile is observed.

 

Fig. 2 (a) Beam profile in fluorescent agarose without added aberration. (b) Beam profile with a low power cylinder placed off-axis in the pupil plane of the focusing objective. (c) The corrected beam profile using the wavefront sensor system.

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The wavefront sensor is now calibrated for use with any sample. A further note is that when a sample is mounted in the microscope, it is necessary to disable the correction of the translational modes, as they effect the three-dimensional imaging process. In Fig. 3, a demonstration of the reconstruction of the wavefront for a sample is shown. The reconstructed wrapped phase is displayed next to the decomposition of modes from the wavefront sensor. The source here was a microbead after a Tg(fli:GFP) zebrafish embryo as described in the following section. The limiting factor in the speed of the correction is the exposure time of the camera for sufficient signal-to-noise ratio, typically of the order of a few hundred milliseconds.

 

Fig. 3 On the left the corrective phase based on the data from the wavefront sensor applied to the corrector when imaging a microbead through a Tg(fli:GFP) zebrafish embryo as seen in Fig. 6 is shown. The phase is wrapped in the range, 0 to 2π or 0 to λ, the wavelength of the light is shown. The right side shows the decomposition of this phase in the peak-to-peak Zernike coefficients in radians ordered by Noll index starting at index 5, astigmatism, below which is uncorrected by the system.

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4. Biological Imaging Results

To test the wavefront sensor technique on biological samples a number of fixed Tg(fli:GFP) zebrafish embryos three days post-fertilization (dpf) were imaged on the microscope. Three-dimensional stacks of 400 × 400 × 100 μm were recorded by scanning the sheet and the focus with the DM and the SLM respectively before and after adaptive correction. The specimens were sampled axially at the Nyquist sampling rate of the objective of 1 μm. The raw data was acquired in the xy-plane and later re-sliced for visualization as explained by Fig. 4.

 

Fig. 4 The axes definition and imaging form of the microscope. The raw images are acquired in the xy plane and then are re-sliced to form images in xz and yz planes, which can be used for axial comparison.

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It may be noted that the field-of-view of the detection microscope along the illumination path, x-axis, is much larger than the region over which the light-sheet is thinner than the detection objective depth-of-focus, in this case around ≈23 μm. Outside of this region the sectioning ability and the axial resolution are worse. The divergence of the beam can be seen in Fig. 2 as this is acquired over the same field-of-view.

The z-stack without any correction was acquired using a Gaussian light-sheet. Afterwards, the cylindrical focus was turned off and the wavefront from the sample was measured in the epi-fluorescent signal. Using the ratio of feedback determined in the calibration the conjugate phase is applied to the SLM and a second dataset was acquired without tip, tilt and defocus mode correction. These datasets were re-sliced into xz-orientation and yz-orientation for axial comparison and maximum intensity projections of the central 512 planes are shown side by side in Fig. 5.

 

Fig. 5 (a) A raw slice from the corrected dataset showing the region of interest (ROI.) (b) Maximum intensity projections through the ROI to give xz-images and yz-images from a 3 dpf Tg(fli:GFP) zebrafish larvae for a standard non-adaptive light-sheet. (c) The same ROI with adaptive correction. (d) The line profiles taken through these projections along the white lines shown in (b) and (c).

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It is expected that if the aberrations in the light-sheet are reduced then the sheet thickness will decrease, therefore, an increase in the axial resolution should be observed. Furthermore, in a suitable regions of the samples, features that were not visible with the aberrated light-sheet should become visible with the corrected light-sheet.

For an example of the performance of the system, a section from the body region of one of the zebrafish has been included in Fig. 5. Looking at the projections found here, one sees agreement with these expectations. The spreading of the features along the axial z direction is smaller in the corrected beam, thus verifying that aberrations have been corrected by the system. It should be noted that this was done using only the central plane as the reference for the correction due to the need for a centrally aligned region of fluorescence for the wavefront sensing. This correction is likely to only be good for a limited range in three dimensions depending on the structure of the sample, however, it is found that the correction appears to have a positive effect throughout the z-range here of 100 μm and in the visible y-range of around 200 μm. A sample with intensely varying refractive index would be expected to fare worse, nevertheless, with an SLM conjugated to the system pupil only the isoplanatic aberrations from the centre of the FOV can be efficiently corrected.

Line profiles in the axial direction have been taken, denoted by the white lines in the images, and are displayed next to the corrected images. From these it can be clearly seen that the correction has increased the resolution and brought out features not visible in the original images. The contrast between regions of no fluorescence and fluorescence are increase also, in keeping with the prediction of better optical sectioning.

In order to quantify the increase in resolution, a zebrafish was included in agarose containing fluorescent microbeads. A microbead is subsequently placed in the centre of the FOV after the light has passed through the zebrafish. In this way, the image of the microbead is affected by an aberration comparable to the one affected images of the biological sample. A three dimensional acquisition is done with and without correction and in Fig. 6 the results of this test show conclusively that the adaptive system improves the axial resolution of the system from an aberrated FWHM of 9.2 ± 0.1 μm to a corrected 3.4 ± 0.1 μm.

 

Fig. 6 Imaging a microbead sample to demonstrate axial resolution improvement. (a) A xz-slice from a dataset where a microbead is used as the guide star after an aberrating sample. (b) The same field of view as in (a) with the adaptive correction applied. (c) Line profile through the microbead to show the improvement made by the adaptive system. The light is incident from the right.

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Notice here that the quality of the image in the zebrafish is not as high as previously shown, as the system is sensing the light from the microbead placed behind it and correcting for that, however, there is still some improvement as the labelled vascular structure can be more clearly seen in this region of tail with the AO on.

5. Discussion

By direct wavefront sensing on the epi-fluorescent light from a sample, the phase aberrations have been determined and corrected by using feedforward control. The benefits of the correction of phase aberrations as outlined in the introduction are many, and with the methodology presented it has been possible to implement them in the illumination arm of the light-sheet fluorescence microscope.

As a result of this feedforward control the images produced by the adaptive microscope are better than those produced by the same microscope without the adaptive control applied. The methodology lies in the same stream of adaptive optics control that is also being implemented in astronomical telescopes [14] as an alternative to the more traditional feedback based systems. The use of the epi-fluorescent light appears to be the only available information source for the correction of the phase aberrations in the illumination arm of this type of microscope.

This paper has focused on how to sense and correct these phase aberrations, but it should be noted that the methodology is also compatible and parallelizable with any modifications to the shape of the beam as demonstrated by multiple groups [8, 13, 15, 16], which if used together would potentially allow for an even greater increase imaging quality.

The technique is not perfect and does have a drawback that is common to all wavefront sensor methods, it is expected to produce strongly anisoplanatic correction. The correction is calculated only for the centre of the field-of-view and then it is applied for imaging over an entire volume meaning that the quality of the correction should decrease with increasing displacement from this position. From our imaging experiments, however, it is found that the effect is not large enough to require continuous (and problematic) feedforward control to the SLM, despite imaging in a zebrafish that is optically inhomogeneous.

The wavefront sensor is a relatively simple addition to the adaptive LSFM system, being the replacement of the mirror with a dichroic mirror and a 4- f system to the sensor. If it is possible to build and implement in a light-sheet microscope, it would guarantee an improvement in image quality, signal-to-noise ratio and axial resolution. The use of a wavefront sensor means that the system is fast, robust and accurate as long as an area of fluorescence can be located in the centre of the field of view. As the fluorescent areas of the sample are generally of interest, it does not apply a particularly stringent constraint on the regions that can be imaged.

From an additional user perspective, the technique is fast and non-invasive, meaning it can work seamlessly in the background once the calibration is done, and as long as the system does not change the calibration will be valid over a long timespan. Moreover, it does not require the use of cleared or genetically engineered samples as the adaptive components work to overcome the optical inhomogeneities.

In summary and conclusion, this paper has demonstrated that the aberrations present within a sample can be sensed and corrected in the illumination arm of a light-sheet fluorescence microscope, using a feedforward control methodology. As a result, the images from the microscope are improved compared with the non-adaptive case, this is due to a better axial resolution and beam quality produced by the correction of phase aberrations.