# Full-aperture extended-depth oblique plane microscopy through dynamic remote
focusing

Paolo Pozzi<EMAIL_ADDRESS>Dipartimento di Fisica, Politecnico di
Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy  Vipin Balan
Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32,
I-20133 Milano, Italy  Alessia Candeo  Dipartimento di Fisica, Politecnico di
Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy  Alessia Brix
Dipartimento di Biotecnologie Mediche e Medicina Traslazionale, Università
degli Studi di Milano, Via Festa del Perdono 7 - 20122 Milano, Italy  Anna
Silvia Pistocchi  Dipartimento di Biotecnologie Mediche e Medicina
Traslazionale, Università degli Studi di Milano, Via Festa del Perdono 7 -
20122 Milano, Italy  Cosimo D’Andrea  Dipartimento di Fisica, Politecnico di
Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy  Gianluca Valentini
Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32,
I-20133 Milano, Italy  Andrea Bassi  Dipartimento di Fisica, Politecnico di
Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy

###### Abstract

Oblique plane microscopy is a method enabling light-sheet fluorescence imaging
through a single microscope objective lens by focusing on a tilted plane
within the sample. To focus the fluorescence emitted by the oblique plane on a
camera, the light is imaged through a pair of remote objective lenses, facing
each other at an angle. The aperture mismatch resulting from this
configuration limits the effective numerical aperture of the system, reducing
image resolution and signal intensity.

This manuscript introduces an alternative method to capture the oblique plane
on the camera. Instead of relying on angled objective lenses, an electrically
tunable lens is employed. This lens adjusts the focal plane of the microscope
synchronously with the rolling shutter of a scientific CMOS camera. In this
configuration the entire aperture of the objective is effectively employed,
increasing the resolution of the system. Moreover, a variety of objective
lenses can be employed, enabling the acquisition of wider axial fields of view
compared to conventional oblique plane microscopy.

##  1 Introduction

Light-sheet microscopy is the gold standard method for fluorescence imaging of
complex three dimensional samples at high rates [1]. Due to the need for
multiple perpendicular microscope objectives around the sample, standard
light-sheet microscopy has significant geometric constraints for the shape and
mounting method of the observed sample. Although this three-dimensional
arrangement of sample mounting can sometimes be an advantage[2, 3], its use
with standard slides and Petri dishes, or in intravital applications in small
rodents can be challenging, requiring complex geometries [4] for the objective
lenses and for sample positioning.

Oblique plane microscopy (OPM) [5] is a variant of light-sheet microscopy, in
which a single objective lens is used both for light-sheet illumination and
fluorescence detection, greatly simplifying imaging of samples optically
accessible from a single direction. To achieve this, the excitation light is
confined to one edge of the objective aperture, so that the light sheet
propagates at an angle with respect to the optical axis. Since the illuminated
plane is tilted from the optical axis, only a small portion of it would be in
focus on a camera in a standard detection path. To have the oblique plane in
focus within the whole field of view of the microscope, a re-projection setup
is employed in the detection path, with a secondary microscope objective
forming a low magnification image of the sample, and a tertiary objective
observing such image at an angle.

While this configuration is effective and relatively simple to implement, the
aperture mismatch between the secondary and tertiary objectives constitutes a
significant drawback, limiting the performance and versatility of OPM. In
fact, as the angle between the light sheet and the optical axis decreases, the
fraction of fluorescence light coupled in the tertiary objective becomes
smaller, reducing both signal intensity and imaging resolution [6]. The
problem is visually represented in figure 1, which shows the effective
aperture angles for water immersion objectives on standard OPM for high and
low numerical apertures. The scheme assumes the rarely implemented ideal
scenario in which the tertiary objective has the same numerical aperture as
the primary, which would require the presence of an immersion medium between
the secondary and tertiary objective. Nonetheless, it can be observed that a
significant portion of the aperture of the primary objective is not employed
by the system, up to the extreme scenario of 0.5 NA objectives, in which the
two apertures have no overlap, and no fluorescence photons can be detected.

Figure 1: OPM apertures. Representation of OPM apertures for high and low
numerical aperture water immersion objectives. The angle $\alpha$ represents
the aperture of the primary objective, $\beta$ is the light-sheet aperture,
$\gamma$ is the aperture of an ideal tertiary objective in standard OPM with
the same numerical aperture as the primary. The effective aperture of the
system is the angle of the overlap between $\alpha$ and $\gamma$

As a result, only high numerical aperture primary objectives can be used
effectively in standard OPM, and the total aperture and resolution of the
system remain impaired from the re-projection setup.

This drawback can be mitigated by tilting the direction of propagation of
fluorescence light through the use of a carefully positioned discontinuity in
refractive index between the secondary and tertiary objectives. This can be
achieved either through an immersion chamber with two separate liquids [7] or
through the use of a specialized axially asymmetric tertiary objective with
null working distance[8]. However, these modifications can be complex and
expensive to achieve, and still require the use of high numerical aperture
primary objectives in order to keep the angle between the light-sheet and the
optical axis suitably large. OPM with low NA objectives has been proven
possible through the use of a diffractive grating between the secondary and
tertiary objectives [9], which however introduces constraints on the maximum
usable NA, and restricts use for multi-color imaging.

This manuscript presents remote focusing oblique plane microscopy (RF-OPM), an
alternative approach to the oblique imaging problem. RF-OPM images the sample
through a single objective of arbitrary numerical aperture, presenting no
aperture mismatches in the detection path. Instead of using the standard OPM
re-projection method, an electrically tunable lens (ETL)[10] is introduced in
the back focal plane of the optical system, and a CMOS camera is positioned in
the image plane. In this configuration, at any given time, only a narrow
section of the oblique plane is in focus on the camera. The position of such
narrow section can be dynamically shifted along the oblique plane by changing
the focal power of the ETL. Through the linear modulation of the focal power
of the lens in sync with the rolling shutter exposure of the camera, images of
the oblique plane can be acquired entirely in focus. While limiting the
rolling shutter exposure to a small sub-region of the detector significantly
reduces the photon budget, the approach is already vastly employed in
conventional light-sheet imaging, either to increase axial confinement in
confocal light-sheet setups [11], or to enable wide fields of view with high
light-sheet numerical aperture [12]. These methods are generally considered a
standard procedure when imaging very large optically cleared samples[13].

##  2 Method

###  2.1 Working principle

While RF-OPM can in principle be implemented using any form of incoherent
remote focusing, including deformable lenses [14], deformable mirrors [15],
Alvarez lenses [16] or optical elements mounted on fast accelerating
translation stages [17], this manuscript reports an ETL based design. The ETL
was chosen mostly for simplicity of implementation and reproducibility of the
results, as it constitutes a relatively inexpensive and readily available
device that has performance compatible with the experimental design.

A simplified representation of the RF-OPM optical setup is reported in figure
2, panel B. The setup consists of a conventional epifluorescence microscope,
with a 4-f telescope conjugating the objective’s back focal plane with the
aperture of an ETL. The conventional dichroic and filter set is then
positioned between the ETL and the tube lens.

Figure 2: Method. A. Scheme of the imaging geometry in the axial direction for
different focal powers of the ETL. B. Simplified schematic of the optical
setup. FP - Objective focal plane, OL - Objective lens, PP - Pupil plane of
the system, L1, L2 - 4f telescope, DM1, DM2, DM3 - Dichroic mirrors, M1, M2 -
Image plane mirrors, ETL - Tunable lens, CL - Cylindrical lens, L3 - Tube
lens, CAM - Camera detector plane.

The laser light forming the light-sheet is focused by a cylindrical lens in
the center of the ETL. Between the two lenses of the 4-f telescope, a pair of
dichroic mirrors splits the excitation and detection paths, so that a manually
adjustable mirror in the image plane of the system can be tilted to move the
laser light at the edge of the objective aperture, achieving illumination
along an oblique plane.

In this configuration, the light-sheet remains positioned along a fixed
oblique plane, but its focus moves along the plane linearly with the focal
power of the ETL, as shown in figure 2, panel A. Neglecting the chromatic
aberrations of the ETL, the camera always remains focused on the horizontal
plane intersecting the light-sheet focus. As a result, at any given time, only
a thin strip of the camera detects details in focus, with the lateral position
of the strip shifting linearly with the ETL focal power. Using a rolling
shutter sensor with a short exposure, it is possible to linearly modulate the
focal power of the ETL so that the image is always in focus on the exposed
pixels. The final output of the detector will therefore be an image of the
light-sheet plane (indicated in red in panel A of figure 2), fully in focus.
Three-dimensional images can be acquired by either moving the sample through
the light-sheet with a translation stage or, in principle, by conjugating the
ETL plane with a galvanometric mirror, as is generally done in OPM.

It should be noted that the camera output obtained in this configuration
consists of the projection of the oblique plane in the horizontal direction,
and as such the magnification of the final image will be different for the $x$
and $y$ axes of the camera. An appropriate affine transformation should be
applied to obtain an unwarped image.

###  2.2 Field of view

As discussed in the previous section, the magnification of the system is
different along the axes parallel and perpendicular to the propagation
direction of the light-sheet. When the light-sheet is correctly aligned at the
edge of the pupil aperture, the angle of the beam from the optical axis is

$\alpha=\arcsin{\left(\frac{{NA}_{obj}}{n}\right)}-0.5\arcsin{\left(\frac{{NA}_{ls}}{n}\right)}$
(1)

where ${NA}_{obj}$ and ${NA}_{ls}$ are the numerical apertures of the
objective and of the light-sheet beam respectively, and $n$ is the refractive
index of the sample. For simplicity in the design of the system, this can also
be approximated as

$\alpha=\arcsin{\left(\frac{D_{obj}-R_{ls}}{2fn}\right)}$ (2)

.

Where $f$ is the focal length of the objective lens, $D_{obj}$ is the diameter
of the back aperture of the objective, and $R_{ls}$ is the radius of the
light-sheet beam at the objective back focal plane.

Given the magnification $M$ of the system and assuming the use of a square
detector of side $D$, the dimensions of the field of view of the acquired
images is

${FOV}_{\bot},{FOV}_{\parallel}=\frac{D}{M},\frac{D}{M\sin{\alpha}}$ (3)

where ${FOV}_{\bot}$ is the size in the direction perpendicular to the
propagation of the light-sheet, and ${FOV}_{\parallel}$ is the one along the
propagation direction of the light-sheet. As a consequence, the total axial
distance covered by the field of view is

${FOV}_{axial}=\frac{D}{M\tan{\alpha}}$ (4)

.

It is important to notice that the final pixel size along the propagation
direction of the light-sheet increases with the tangent of the angle,
approaching infinity as the light-sheet becomes vertical. In principle, an
extremely wide field of view can be achieved in the axial direction by using a
very low numerical aperture objective or by moving the light-sheet beam
towards the center of the objective’s aperture, but very low pixel sampling
would be obtained in this situation.

A second limit to the achievable axial size of the field of view is given by
the effective dioptric power range of the ETL, and its ability to linearly
modulate it at a frequency compatible with the desired frame rate. To ensure
the most effective use of the ETL focal power range, the telescope conjugating
it to the objective back focal plane should precisely match the two apertures.
In this configuration, the required achievable focal length (both converging
and diverging) of the ETL is

${f}_{tl}=\frac{2M_{tel}^{2}f_{obj}^{2}}{{FOV}_{axial}}$ (5)

.

where $f_{obj}$ is the focal length of the objective lens and $M_{tel}$ is the
magnification of the telescope between the objective and the ETL.

###  2.3 Resolution and frame rate

The estimation of the resolution of a standard OPM can be complex due to the
dependence of the effective numerical aperture of the system on the angle
between the secondary and tertiary objectives. A complete and exhaustive
analysis can be found in Ref. [18]. In principle, RF-OPM images can achieve
the nominal resolution of the objective in the oblique plane, while the
resolution in the direction perpendicular to the oblique plane is given by the
thickness of the light-sheet at its focus.

However, a limit to the performance is imposed by optical aberrations
introduced by the ETL. When mounted horizontally, a conventional ETL
introduces aberrations from the desired spherical phase with an RMS amplitude
of less than $200\,nm$, which can generally be neglected in light-sheet
microscopy, since typical samples often introduce more severe aberrations [19,
20]. However, when the ETL is operated at increasing frequencies, secondary
modes other than pure defocus begin to be excited, which generally introduce
spherical-like aberrations. For readily available commercial ETLs, such
secondary modes exhibit a resonant frequency at approximately $400\,Hz$,
therefore precluding applications at extremely high frame rates. At more
conventional light-sheet frame rates of tens of $Hz$, these effects can be
considered negligible.

In addition to the excitation of secondary modes in the ETL, a second
limitation to the maximum frame rate achievable in RF-OPM is given by the
capability of the ETL to linearly modulate focal power over time. If a
detector capable of alternating the direction of the rolling shutter at each
frame is employed, the ETL can be synchronized with the detector through a
triangular waveform. Triangular waveforms are relatively trivial to generate
with ETLs, and nonlinear behavior is limited to short intervals between frames
in which the direction of the scan is reversed. However, most detectors
generally utilised in light-sheet microscopy are not capable of alternating
rolling shutter direction at each frame. In this case, the ETL must generate a
sawtooth waveform, which presents a critical point at the discontinuity
between frames. Since the ETL cannot instantly switch from a large positive
focal power to a large negative one or vice versa, a significant interval
between frames is necessary to allow the ETL to reset its position. Hence, as
the microscope frame rate increases, the fraction of time in which the
detector is actually exposed decreases, which could lead to an insufficient
signal-to-noise ratio.

###  2.4 Experimental setup

Images were acquired on a custom RF-OPM setup. The setup is designed for a
60X, $1.1\,NA$ water-dipping objective (LUMFL N 60XW, Olympus, Japan), with a
back focal plane aperture diameter of $6.6\,mm$. In order to prove the
versatility of the method, additional experiments were performed with a 20X,
$0.5\,NA$ water-dipping objective (UMPlanFL N 20XW, Olympus, Japan).

The back focal plane of the objective is conjugated with the $16\,mm$ aperture
of the ETL (EL-16-40-TC-VIS-5D with ECC-1C controller, Optotune, Switzerland)
through two lenses of $125\,mm$ and $300\,mm$ focal respectively (AC254-125-A
and AC508-300-A, Thorlabs, USA), forming a 2.4X 4-f telescope. This resulted
in perfect matching of the aperture of the 60X objective, while the numerical
aperture of the 20X objective was cropped down by the ETL diameter to
approximately $0.37$.

In order to image green fluorophores, long-pass dichroic mirrors with a cutoff
wavelength at around $500\,nm$ are used to split the path between the two
lenses of the telescope. Dichroic mirrors with mm-scale thickness are employed
(DMLP505L, Thorlabs, USA, $5\,mm$ thick, and Di03-R488-t3-25x36, Semrock, USA,
$3\,mm$ thick) in order to minimize aberrations in the light-sheet path
introduced by their curvature.

Excitation light is provided by a $40\,mW$, $473\,nm$ diode laser
($\lambda$-beam, RGB laser systems, Germany) coupled to a single-mode fiber.
Light from the fiber is collimated to a beam diameter of $8\,mm$ with a
reflective collimator (RC08SMA-P01, Thorlabs, USA), focused through a
$400\,mm$ focal cylindrical lens (LJ1363RM-A, Thorlabs, USA) in a light-sheet
conjugated to infinity by a $150\,mm$ focal length lens (AC254-150-A,
Thorlabs, USA), and then reflected through the center of the ETL by a dichroic
mirror (DMLP505L, Thorlabs, USA). This configuration led to a final ratio of
$0.18$ between the aperture diameters of the light-sheet and the objective at
the back focal plane of the system.

An additional 0.5X 4-f telescope (AC508-200-A and AC508-100-A, Thorlabs, USA)
is present in the fluorescence light optical path between the ETL and the
tube-lens of the system. This addition serves two purposes: firstly, to extend
the optical path length, allowing the horizontal mounting of the ETL; and
secondly, to accommodate potential future upgrades, such as the integration of
a galvanometric mirror at the system’s back focal plane, which would enable
faster dynamic imaging. A fluorescence filter (MF525-39, Thorlabs, USA) is
present after the relayed back focal plane, and a $200\,mm$ focal length tube
lens (MXA20696, Nikon, Japan) is employed to conjugate the image plane of the
system to an sCMOS camera (Orca Flash 4.0 v2, Hamamatsu, Japan), with a final
effective magnification of 55.55X when using the 60X objective, and of 16.66X
when using the 20X objective. Images were acquired on a 2048 by 1024 pixels
subregion of the detector. The active region was cropped vertically to 1024
pixels, since the 60X objective showed significant spherical aberration
outside this range, while the axial field of view achievable with the 20X
objective was considered more than adequate for most available samples. Given
the geometry of the setup, the final field of view of raw images for the 60X
objective span $240\,\mu m$ on the horizontal plane by $156\,\mu m$ along the
oblique plane, at an angle of $48^{\circ}$ with the optical axis, for a total
axial range of $104\,\mu m$. For the 20X objective, the field of view span
$720\,\mu m$ on the horizontal plane by $1020\,\mu m$ along the oblique plane,
at an angle of $20^{\circ}$ with the optical axis, for a total axial range of
$958\,\mu m$.

Due to the inability of the detector to image with an alternating direction
rolling shutter, a sawtooth function is used for modulating the ETL focal
power in time. The maximum usable imaging rate achievable is $50\,Hz$, with a
duty cycle of exposure of approximately $60\%$, while higher duty cycles can
be achieved at lower frame rates, up to $90\%$ at $10\,Hz$. Higher frequencies
or better duty cycles could be achieved by vertically cropping the active
region of the detector, reducing the axial size of the field of view.

Three-dimensional datasets were acquired by translating the sample
horizontally with a servo-controlled actuator (M-405.CG, Physik Instrumente,
Germany). A custom software script was used to correct the dataset shearing
and stretching through an affine transform.

##  3 Results

###  3.1 Microbeads imaging

In order to evaluate the performance of the system, a $3\,mm$ thick sample of
$0.17\mu m$ yellow-green fluorescent microbeads (P7220 PS-Speck Point Source
Kit, Thermo Fisher Scientific, USA) embedded in agarose gel was imaged with
the two objectives. Representative datasets are reported in figure 3.

Figure 3: Microbeads imaging A x-z maximum intensity projection (where z is
the direction of the optical axis of the objective) over a $25\,\mu m$ range
in y of a microbead image, acquired with the 20X objective. Scale bar is
$100\,\mu m$. B x-z maximum intensity projection over a $100\,\mu m$ range in
y of a microbead image, acquired with the 60X objective. Scale bar is $25\,\mu
m$. C,D images on a horizontal and vertical plane of a single microbead,
acquired with a 60X objective. Scale bar is $1\,\mu m$. E estimation of the
full width at half maximum of the size of a single bead at the optimal working
distance of the 60X objective. Lines are spline interpolation of data.

A first, important observation is that high aperture objectives are generally
optimized for diffraction-limited imaging within a relatively short axial
range of operation. This can be clearly observed in figure 3, panels A and B,
which show how the axial resolution of the system is conserved throughout the
axial field of view with the 0.5 NA 20X objective lens, but is only optimal
within a range of approximately $30\,\mu m$ for the 1.1 NA 60X objective.
Within the optimal range of the objective, the full width at half maximum of
the psf of the system is sub-micrometric laterally and around $1\,\mu m$
axially. The resolving power is slightly worse than the nominal diffraction
limit of the objective, and a slight star shape can be observed in the PSF.
Both these effects are, most likely, due to slight astigmatism introduced in
the detection path by the three dichroic mirrors utilised in the system. To
avoid the introduction of vignetting in the system at high defocusing power of
the ETL, large dichroics (2-inch diameter) were employed, which introduced
non-negligible wavefront distortion. Moreover, the employed objectives are not
optimized for use with a coverslip, which is necessary for imaging beads in an
inverted microscope. A more optimized layout of the system using a coverslip-
optimized objective and smaller, higher-quality dichroics should solve this
issue.

###  3.2 Mouse kidney imaging

The main advantage of OPM systems over traditional light-sheet microscopy is
its ability to image samples conventionally mounted on a microscopy slide. In
order to show this capability, a commercially available and fairly widespread
sample, a $16\,\mu m$ cryostat section of mouse kidney with immunofluorescence
staining (Fluocells prepared slide #3, Invitrogen, USA), was imaged with the
setup.

Figure 4: Prepared mouse kidney slide imaging. A. Geometry of the acquisition,
not to scale. The green plane represents the objective’s focal plane, the red
plane represents the raw field of view of the system, and the blue plane
represents the axial field of view of the system. The orange arrow show the
direction of the sample translation. B. Representative images of the sample.
Image border colors report their geometry referring to the scheme in panel A.
Images in the horizontal and vertical plane are obtained through affine
transform of the raw data. Scale bar for the horizontal and the vertical image
is $50\,\mu m$, scale bars in raw image are $20\,\mu m$, and intensity scale
bar is in arbitrary units.

The glomeruli and convoluted tubules, stained with Alexa 488, were visible
with the laser and filter set present in the setup. Due to the thin nature of
the sample, only the 60X objective was utilised. Figure 4 shows the
acquisition geometry and a representative image of the sample. Raw planes were
acquired at $50\,Hz$, with a $0.4\,\mu m$ spacing between planes, on a 2048 by
256 pixels sub-region of the detector. The dataset shows good optical
sectioning, and resolution performance comparable to those measured in the
microbeads test. The images produced are also comparable to those reported in
literature or on commercial microscopes documentation for the same sample. The
main drawback of the current setup is the single-channel acquisition, which
limits the amount of information that can be retrieved. Future upgrades with
multi-edge dichroics could easily enable the use of multiple excitation
wavelengths. The widely available dual rolling shutter feature of sCMOS
cameras, together with the use of an image splitter, could also allow the
simultaneous acquisition of two channels, doubling the acquisition pixel rate
of the system.

###  3.3 Zebrafish imaging

Tg(kdrl:eGFP)s843 zebrafish embryos, expressing a green fluorescent protein in
the vascular structure [21] were imaged at 3 to 5 days post fertilization
(dpf). The pigmentation was suppressed through 1-phenyl-2-thiourea (PTU)
treatment [22]. To immobilize the larvae, 0.016% tricaine anesthetic solution
was used. The inverted nature of the microscope allowed convenient horizontal
mounting of the larvae on a coverslip. A layer of 1% w/v agarose was laid on
the coverslip, in which a $0.8\,mm$ wide groove cast with a 3D-printed comb
was created to hold the larvae during imaging, as described in ref [23].
Experiments were conducted with both objectives. High-resolution details of 3
dpf embryos were obtained with the 60X objective, while images of the full
vascular system of a 5 dpf embryo were collected in a single sweep of the
translation stage with the 20X objective. Images at 60X magnification were
recorded at $20\,Hz$ on the full 2048 by 1024 pixel active region, with a
total data throughput of approximately $42\times 10^{6}\,pixels/s$, while 20X
datasets were acquired at $50\,Hz$ on a 2048 by 768 pixel active region, with
a total data throughput of approximately $78\times 10^{6}\,pixels/s$. Three-
dimensional datasets were captured by moving the translation stage, with
horizontal spacing between frames of $0.4\,\mu m$ for 60X images, and of
$1\,\mu m$ for 20X images.

Figure 5: Zebrafish larvae imaging A, B. Representative raw images from the
detector during stack acquisition, with 60X and 20X objectives respectively.
Scale bars are $50\,\mu m$ in A and $100\,\mu m$ in B. C. Typical two-
dimensional lateral image after affine transform for a 60X image of the larva
tail vasculature. Scale bar is $50\,\mu m$. D. Typical two-dimensional lateral
image after affine transformation for a 20X image of the larva vasculature.
Scale bar is $50\,\mu m$.E, F. Depth encoded projection of full dataset of the
eye and tail vasculature respectively in 3 dpf larvae, acquired with the 60X
objective at $20\,Hz$, scale bars are $100\,\mu m$. G. Maximum intensity
projection of an entire 5 dpf larva acquired with the 20X objective at
$50\,Hz$, scale bar is $200\,\mu m$.

Typical datasets are reported in figure 5. Images acquired with the 60X 1.1 NA
objective showed fine details in the vascular structure, both in the
relatively clear tail sections and in the more complex and optically dense
vasculature of the eye. The 20X objective produced, as expected, lower
brightness and lower resolution images, but its wide field of view enabled the
acquisition of images of the entire $3.5\,mm$ long larva in a single sweep of
the actuator in approximately one minute. Although the numerical aperture is
lower, and therefore the quality of the images is not comparable, the field of
view and pixel throughput of the microscope are comparable to state-of-the-art
OPM with custom tertiary objectives [24].

##  4 Discussion

This manuscript introduces a novel approach to the visualization of tilted
planes in OPM, employing an ETL and the detector rolling shutter to replace
the reprojection setup of standard OPM. The proposed setup presents several
advantages compared to a standard OPM, namely:

  * •

The system collects photons from the full aperture of the objective. While the
gain in terms of effective signal is reduced by the need to have an exposure
time shorter than the frame time to synchronize the rolling shutter with the
ETL scan, this still enables imaging at higher resolution than standard OPM
[25]. Similar performance can be achieved with discontinuities in the
refractive index between the secondary and tertiary objectives of standard
OPM, but the presented method is arguably simpler and cost-effective.

  * •

The proposed method allows great flexibility in the selection of the
microscope objective. Unlike in standard OPM, low-aperture objectives can be
used. Moreover, the objective can be rapidly switched during experiments,
without the need to realign the optical system. The only limitation to the
capability of operation with different objectives lies in the need to match
the diameter of the back aperture of the objective with the diameter of the
ETL. When the aperture diameter of the chosen objectives differs, as it did in
the case of the ones employed here, the setup should be designed to either
crop the pupil of the objectives with larger back apertures, or to underfill
the ETL aperture when using objectives with smaller back apertures. Since,
from equation 5, reducing the magnification of the objective pupil at the ETL
plane results in smaller axial shifts for the same lens current input, the
presented setup was designed to always use the full aperture of the ETL and
maximize the axial field of view when using the 60X objective, cropping the
aperture of the 20X objective as a tradeoff. Different experimental needs may
require different tradeoffs. Ideally, alternative remote focusing approaches
with faster actuators and longer ranges may allow the use of the full aperture
of any objective needed.

  * •

The use of the same ETL for both excitation and fluorescence light ensures the
light-sheet is always at its thinnest point in the region of the exposed
rolling shutter. This greatly improves resolution at the axial edges of the
field of view, and provides imaging of wider fields of view when compared to
standard OPMs, or even traditional light-sheet microscopes with fixed
cylindrical lenses. While this feature could be fully exploited in the
presented data with the lower aperture objective, the narrow optimal axial
range of higher performance objectives does hinder this capability of the
system, due to the appearance of non-negligible spherical aberration when
focusing further from the objective’s focal plane. This position-dependent
aberration could be reduced through the implementation of multi-conjugate
aberration correction in the system [19].

##  5 Funding

The research has received funding from LASERLAB-EUROPE (grant agreement no.
871124, European Union’s Horizon 2020 research and innovation programme) and
the European Union’s NextGenerationEU Programme with the I-PHOQS
Infrastructure (IR0000016, ID D2B8D520, CUP B53C22001750006) “Integrated
infrastructure initiative in Photonic and Quantum Sciences.” The PhD student
Alessia Brix was supported by the PhD program in Experimental Medicine of the
University of Milan, Milan.

##  6 Data availability

All the raw data for the images presented in the manuscript, together with
software for affine transformation are available as an open dataset on Zenodo
[26].

## References

  * [1] John M Girkin and Mariana Torres Carvalho.  The light-sheet microscopy revolution.  Journal of Optics, 20(5):053002, 2018.
  * [2] Alessia Candeo, Fabrizio G Doccula, Gianluca Valentini, Andrea Bassi, and Alex Costa.  Light sheet fluorescence microscopy quantifies calcium oscillations in root hairs of arabidopsis thaliana.  Plant and Cell Physiology, 58(7):1161–1172, 2017.
  * [3] Alessia Candeo, Ilenia Sana, Eleonora Ferrari, Luigi Maiuri, Cosimo D’Andrea, Gianluca Valentini, and Andrea Bassi.  Virtual unfolding of light sheet fluorescence microscopy dataset for quantitative analysis of the mouse intestine.  Journal of Biomedical Optics, 21(5):056001–056001, 2016.
  * [4] Adam K Glaser, Kevin W Bishop, Lindsey A Barner, Etsuo A Susaki, Shimpei I Kubota, Gan Gao, Robert B Serafin, Pooja Balaram, Emily Turschak, Philip R Nicovich, et al.  A hybrid open-top light-sheet microscope for versatile multi-scale imaging of cleared tissues.  Nature methods, 19(5):613–619, 2022.
  * [5] Christopher Dunsby.  Optically sectioned imaging by oblique plane microscopy.  Optics express, 16(25):20306–20316, 2008.
  * [6] Jeongmin Kim.  Recent advances in oblique plane microscopy.  Nanophotonics, 0, 2023.
  * [7] Bin Yang, Xingye Chen, Yina Wang, Siyu Feng, Veronica Pessino, Nico Stuurman, Nathan H Cho, Karen W Cheng, Samuel J Lord, Linfeng Xu, et al.  Epi-illumination spim for volumetric imaging with high spatial-temporal resolution.  Nature methods, 16(6):501–504, 2019.
  * [8] Etai Sapoznik, Bo-Jui Chang, Jaewon Huh, Robert J Ju, Evgenia V Azarova, Theresa Pohlkamp, Erik S Welf, David Broadbent, Alexandre F Carisey, Samantha J Stehbens, et al.  A versatile oblique plane microscope for large-scale and high-resolution imaging of subcellular dynamics.  Elife, 9:e57681, 2020.
  * [9] Maximilian Hoffmann and Benjamin Judkewitz.  Diffractive oblique plane microscopy.  Optica, 6(9):1166–1170, 2019.
  * [10] Florian O Fahrbach, Fabian F Voigt, Benjamin Schmid, Fritjof Helmchen, and Jan Huisken.  Rapid 3d light-sheet microscopy with a tunable lens.  Optics express, 21(18):21010–21026, 2013.
  * [11] Eugen Baumgart and Ulrich Kubitscheck.  Scanned light sheet microscopy with confocal slit detection.  Optics express, 20(19):21805–21814, 2012.
  * [12] Kevin M Dean, Tonmoy Chakraborty, Stephan Daetwyler, Jinlong Lin, Gerard Garrelts, Ons M’Saad, Hannahmariam T Mekbib, Fabian F Voigt, Martina Schaettin, Esther T Stoeckli, et al.  Isotropic imaging across spatial scales with axially swept light-sheet microscopy.  Nature protocols, 17(9):2025–2053, 2022.
  * [13] Hiroki R Ueda, Hans-Ulrich Dodt, Pavel Osten, Michael N Economo, Jayaram Chandrashekar, and Philipp J Keller.  Whole-brain profiling of cells and circuits in mammals by tissue clearing and light-sheet microscopy.  Neuron, 106(3):369–387, 2020.
  * [14] Jun Jiang, Dapeng Zhang, Steven Walker, Chenglin Gu, Ya Ke, Wing Ho Yung, and Shih-chi Chen.  Fast 3-d temporal focusing microscopy using an electrically tunable lens.  Optics express, 23(19):24362–24368, 2015.
  * [15] Terry Wright, Hugh Sparks, Carl Paterson, and Chris Dunsby.  Video-rate remote refocusing through continuous oscillation of a membrane deformable mirror.  Journal of Physics: Photonics, 3(4):045004, 2021.
  * [16] M Bawart, A Jesacher, S Bernet, and M Ritsch-Marte.  Remote focusing in confocal microscopy by means of a modified alvarez lens.  Journal of Microscopy, 271(3):337–344, 2018.
  * [17] Edward J Botcherby, R Juškaitis, Martin J Booth, and Tony Wilson.  An optical technique for remote focusing in microscopy.  Optics Communications, 281(4):880–887, 2008.
  * [18] Jeongmin Kim, Tongcang Li, Yuan Wang, and Xiang Zhang.  Vectorial point spread function and optical transfer function in oblique plane imaging.  Optics Express, 22(9):11140–11151, 2014.
  * [19] T Furieri, A Bassi, and S Bonora.  Large field of view aberrations correction with deformable lenses and multi conjugate adaptive optics.  Journal of Biophotonics, page e202300104, 2023.
  * [20] Dean Wilding, Paolo Pozzi, Oleg Soloviev, Gleb Vdovin, and Michel Verhaegen.  Adaptive illumination based on direct wavefront sensing in a light-sheet fluorescence microscope.  Optics express, 24(22):24896–24906, 2016.
  * [21] Suk-Won Jin, Dimitris Beis, Tracy Mitchell, Jau-Nian Chen, and Didier Y. R. Stainier.  Cellular and molecular analyses of vascular tube and lumen formation in zebrafish.  Development, 132(23):5199–5209, 12 2005.
  * [22] Johnny Karlsson, Jonas Von Hofsten, and Per-Erik Olsson.  Generating transparent zebrafish: a refined method to improve detection of gene expression during embryonic development.  Marine biotechnology, 3:522–527, 2001.
  * [23] Abdullah R Ahmed, Alessia Candeo, Sofia D’Abrantes, Sarah R Needham, Rahul B Yadav, Stanley W Botchway, and Anthony W Parker.  Directly imaging the localisation and photosensitization properties of the pan-mtor inhibitor, azd2014, in living cancer cells.  Journal of Photochemistry and Photobiology B: Biology, 213:112055, 2020.
  * [24] Bin Yang, Merlin Lange, Alfred Millett-Sikking, Xiang Zhao, Jordão Bragantini, Shruthi VijayKumar, Mason Kamb, Rafael Gómez-Sjöberg, Ahmet Can Solak, Wanpeng Wang, et al.  Daxi—high-resolution, large imaging volume and multi-view single-objective light-sheet microscopy.  Nature methods, 19(4):461–469, 2022.
  * [25] Venkatakaushik Voleti, Kripa B Patel, Wenze Li, Citlali Perez Campos, Srinidhi Bharadwaj, Hang Yu, Caitlin Ford, Malte J Casper, Richard Wenwei Yan, Wenxuan Liang, et al.  Real-time volumetric microscopy of in vivo dynamics and large-scale samples with scape 2.0.  Nature methods, 16(10):1054–1062, 2019.
  * [26] Paolo Pozzi.  Raw data from the manuscript ”full-aperture extended-depth oblique plane microscopy through dynamic remote focusing”, https://zenodo.org/doi/10.5281/zenodo.10036881, 2023.