# Imaging across multiple spatial scales with the multi-camera array
microscope

Mark Harfouche  Ramona Optics Inc., 1000 W Main St., Durham, NC 27701, USA
These authors contributed equally to this work  Kanghyun Kim  Department of
Biomedical Engineering, Duke University, Durham, NC 27708, USA  These authors
contributed equally to this work  Kevin C. Zhou  Department of Biomedical
Engineering, Duke University, Durham, NC 27708, USA  Pavan Chandra Konda
Department of Biomedical Engineering, Duke University, Durham, NC 27708, USA
Sunanda Sharma  Ramona Optics Inc., 1000 W Main St., Durham, NC 27701, USA
Eric E. Thomson  Duke School of Medicine Department of Neurobiology, Durham,
NC 27708, USA  Colin Cooke  Department of Electrical and Computer Engineering,
Duke University, Durham, NC 27708, USA  Shiqi Xu  Department of Biomedical
Engineering, Duke University, Durham, NC 27708, USA  Lucas Kreiss  Department
of Biomedical Engineering, Duke University, Durham, NC 27708, USA  Amey
Chaware  Department of Biomedical Engineering, Duke University, Durham, NC
27708, USA  Xi Yang  Department of Biomedical Engineering, Duke University,
Durham, NC 27708, USA  Xing Yao  Department of Biomedical Engineering, Duke
University, Durham, NC 27708, USA  Vinayak Pathak  Department of Biomedical
Engineering, Duke University, Durham, NC 27708, USA  Martin Bohlen  Duke
School of Medicine Department of Neurobiology, Durham, NC 27708, USA  Ron
Appel  Ramona Optics Inc., 1000 W Main St., Durham, NC 27701, USA  Aurélien
Bègue  Ramona Optics Inc., 1000 W Main St., Durham, NC 27701, USA  Clare Cook
Ramona Optics Inc., 1000 W Main St., Durham, NC 27701, USA  Jed Doman  Ramona
Optics Inc., 1000 W Main St., Durham, NC 27701, USA  John Efromson  Ramona
Optics Inc., 1000 W Main St., Durham, NC 27701, USA  Gregor Horstmeyer  Ramona
Optics Inc., 1000 W Main St., Durham, NC 27701, USA  Jaehee Park  Ramona
Optics Inc., 1000 W Main St., Durham, NC 27701, USA  Paul Reamey  Ramona
Optics Inc., 1000 W Main St., Durham, NC 27701, USA  Veton Saliu  Ramona
Optics Inc., 1000 W Main St., Durham, NC 27701, USA  Eva Naumann  Duke School
of Medicine Department of Neurobiology, Durham, NC 27708, USA  Roarke
Horstmeyer  Ramona Optics Inc., 1000 W Main St., Durham, NC 27701, USA
Department of Biomedical Engineering, Duke University, Durham, NC 27708, USA
Department of Electrical and Computer Engineering, Duke University, Durham, NC
27708, USA  Corresponding author<EMAIL_ADDRESS>
###### Abstract

This article experimentally examines different configurations of a novel
multi-camera array microscope (MCAM) imaging technology. The MCAM is based
upon a densely packed array of “micro-cameras” to jointly image across a large
field-of-view at high resolution. Each micro-camera within the array images a
unique area of a sample of interest, and then all acquired data with 54 micro-
cameras are digitally combined into composite frames, whose total pixel counts
significantly exceed the pixel counts of standard microscope systems. We
present results from three unique MCAM configurations for different use cases.
First, we demonstrate a configuration that simultaneously images and estimates
the 3D object depth across a $100$ x $135$ $mm^{2}$ field-of-view (FOV) at
approximately 20 $\mu$m resolution, which results in 0.15 gigapixels (GP) per
snapshot. Second, we demonstrate an MCAM configuration that records video
across a continuous $83$ x $123$ $mm^{2}$ FOV with two-fold increased
resolution (0.48 GP per frame). Finally, we report a third high-resolution
configuration (2 $\mu$m resolution) that can rapidly produce 9.8 GP composites
of large histopathology specimens.

##  1 Introduction

A general challenge in the design of optical microscopes is to identify
strategies that overcome a fundamental trade-off between imaging resolution
and field-of-view (FOV). Optical microscopes range from FOVs of several
centimeters when resolving at multi-µm resolution, to less than a millimeter
when imaging at sub-µm resolution [1]. The total number of spatial points
resolvable by a standard optical microscope, commonly referred to as the
imaging system space-bandwidth product (SBP) [2], is generally between 10 and
50 million (10-50 megapixels) [3].

There are a number of compelling reasons why new microscope techniques with
increased SBP can be more useful than conventional microscopes. For example, a
large-SBP microscope would enable observation of multiple model organisms,
such as zebrafish (D. rerio), fruit flies (D. melanogaster), and nematodes (C.
elegans) during natural movement over a large area [4, 5, 6, 7]. In addition,
a high SBP system would assist with the rapid inspection of large electronics
components [8, 9], semiconductor wafers [10], microfluidic systems [11] and
various materials [12, 13] during manufacturing. Finally, high SBP microscopes
would also facilitate novel parallelized assays to increase the throughput of
high-content imaging and screening experiments common to the fields of
pharmacology, toxicology and drug discovery [14].

Figure 1: The multi-camera array microscope (MCAM) for large field-of-view,
high-resolution imaging at video rate. (a) Photo of MCAM imaging unit
containing a 6 x 9 array of individual 13 megapixel CMOS sensors and
associated lenses (0.7 gigapixel per snapshot), with diagram of operation. (b)
Example image, created as a stitched composite of 54 simultaneously acquired
images from unique, slightly overlapping sample areas.

Unfortunately, large-SBP imaging cannot be easily achieved by directly
increasing the FOV of a microscope objective lens capable of a desired imaging
resolution. As specified by the lens scaling law [15], all lenses are affected
by optical aberrations, and the size of optical aberrations scale linearly
with the diameter of a lens. Large-diameter lenses must utilize additional
optical elements to correct for aberrations to maintain a fixed resolution
over a desired FOV. Additional elements must be added in a super-linear manner
[15, 16], which leads to a rapid increase in size, weight, complexity and cost
of large-SBP microscope objective lenses [17]. At the same time, the largest
currently available image sensors only contain several hundred megapixels
[18], which presents a second challenge to directly scaling up standard
single-lens microscope designs.

Instead of relying upon a single extremely large objective lens, most current
microscopes utilize mechanical scanning to overcome typical FOV limits.
Scanning systems capture multiple high-resolution images in a step-and-repeat
manner, which are then tiled together into a final large-area composite.
Scanning microscopes are available from a number of companies and form the
foundation of modern wide-area inspection and whole-slide imaging (WSI) [19].
Unfortunately, mechanical scanning is inherently slow. For example, a single
96 well plate (8 x 12 cm² in size) typically requires approximately 8 minutes
to scan [20, 21]. In addition, while sequential scanning works well for static
samples, it is not an option for rapidly moving samples.

An alternative to mechanical scanning is to scan a microscope’s illumination
while capturing images in a time-sequential manner. Structured illumination
microscopy [22] and Fourier ptychography [23, 24] process such variably
illuminated images into final, high-resolution image composites. Similar
strategies have also been employed utilizing speckle illumination [25]. Time-
sequential measurement of stochastic or photoactivated emission is also
standard practice in super-resolution microscopy [26, 27]. Finally,
alternative methods have utilized scanning spots produced by microlens arrays
[28, 29], as well as steering the illumination across large specimens via a
parabolic mirror [30], to observe a larger sample area. While such approaches
offer various merits over step-and-repeat scanning systems, the above methods
still must capture multiple images over time, and thus cannot easily record
large area, high-resolution synchronized video of dynamic objects.

A multi-aperture design can circumvent the lens scaling law by utilizing many
lenses and digital sensors to record images in parallel [31]. The first
demonstrations of digital multi-aperture imaging originated in standard
cameras designed for imaging distant objects and can be generally summarized
in two categories. The first “direct” category uses multiple cameras arranged
in a compact array with no additional collection optics. This design was
explored to decrease optical form-factor [32], to implement light-field
capture [33], to adopt hierarchical modular designs [34], and is now a common
feature in many smartphone camera systems. The second category of approach
adopts a cascaded or "multi-scale" lens design in which an array of cameras is
focused upon an intermediate image, typically produced by a large, primary
lens [35, 36, 31, 37]. This latter cascaded strategy has been implemented in
several interesting configurations [38], including a microscope that produces
images at sub-micrometer resolution over approximately one square centimeter
[39]. However, there has been limited work to date examining the direct use of
multiple imaging systems to record image and video across a continuous area at
high spatial resolution in parallel for applications in microscopy, which is
the focus of this work.

There are a variety of benefits of direct arrays for microscopic imaging
applications. For example, small optics exhibit fewer aberrations, and thus
simpler, more compact, and less expensive lenses can be used within the array
design. Similarly, smaller and inexpensive CMOS pixel arrays are now made in
large quantities for the smartphone camera market. Put together, these two
insights point to a relatively simple and inexpensive wide-area microscope
design. In this work, we demonstrate the ability to use such an array to
directly record images at micrometer-scale resolution over a FOV of several
hundred square centimeters in parallel. Our primary design, which we term a
multi-camera array microscope (MCAM), includes 54 micro-cameras that are
integrated into a regularly packed grid with a 13.5-mm center-to-center
spacing. In the following, we cover several configurations of this new
technology to achieve different functionalities: the ability to record 3D
snapshots across a 100 x 135 mm² area at approximately 20$\mu$m full-pitch
lateral resolution and 42$\mu$m axial sensitivity, video across a continuous
83 x 123 mm² area at 2X higher lateral resolution, and high-resolution image
with 9.8 GP over a similar area. As detailed below, each of these
configurations is a function of selected imaging magnification that one can
easily adjust using the same hardware.

##  2 Multi-camera array microscope design

We will begin by deriving several key properties, such as the relationship
between magnification and pixel-limited resolution, for direct-array imaging
systems. Our starting assumption is that the array of interest is planar,
contains identical imaging systems that are arranged in a uniform grid, and is
imaging a large two-dimensional specimen of interest. We will scrutinize these
assumptions in later sections. As we aim to configure the entire array, and
thus each lens-sensor pair, to directly image at micrometer-scale resolution,
we will loosely refer to each lens-sensor pair as a microscope. It is useful
to begin by considering how only two such individual microscopes side-by-side
can be configured to image a continuous area (i.e., such that the FOV of each
microscope abuts the other, see Figure 2(a)). Naturally, one would aim to
place the microscopes as close as possible to one another. At the extreme
limit, the sensors for each microscope would ideally sit immediately adjacent
to one another.

Assuming this limit is achievable, we need to consider the objective lens
placed in front of each sensor. As shown in Figure 2(a), it is clear that a
lens with a magnification $M>1$ will result in a gap between FOVs of adjacent
microscopes. While it is possible to uniquely tilt each lens and sensor to
minimize or remove this gap [40], such a configuration introduces several
sources of experimental complexity that hinder large array development.
Instead, one can simply use a lens with $M\leq 1$ to ensure that the FOVs of
each imaging system directly touch one another (Figure 2(a)). This leads to a
first key property of direct array microscopy with a planar array - the
maximum magnification must be less than unity to ensure continuous imaging
across an extended FOV.

At first glance, this key property would appear problematic for achieving
high-resolution imaging. In such low-magnification conditions, the finite
sensor pixel size is critical for the overall resolution. The system’s pixel-
limited full-pitch resolution $r_{pix}$ is easily found by projecting the
finite pixel width $\delta$ onto the sample plane as $r_{pix}=2\delta/M$.
Historic CCD and CMOS sensors contained pixels on the order of
$\delta=5-10\mu$m in width, which suggests that even in an ideally tiled
array, the minimum full-pitch resolution would be $10-20\mu$m at best when
configured for continuous coverage, which precludes many applications. Over
the past years, however, the average pixel size of CMOS sensors has decreased
dramatically. It is now common to find CMOS pixels in the range of
$\delta=0.7-1\mu$m [41]. Alternative sensor designs likewise include even
smaller pixel widths [42]. Modern CMOS pixel arrays, typically found in most
smartphone cameras, achieve a minimum full-pitch resolution
$r_{pix}=2\delta/M$ between 1.4 and 2 $\mu$m when using a magnification of M =
1. This approximately matches the resolution offered by a current standard 4X
or 10X objective lens with numerical apertures in the 0.15-0.3 range.

In practice, placing individual image sensors immediately adjacent to one
another is challenging (in part due to mechanical packing and electrical
routing constraints). Considering an image sensor of an active area width $s$
in one dimension, this implies that the inter-camera pitch $p$ must satisfy
$p>s$ in practical MCAM implementation (Figure 2(b)). The sensor pitch $p$
also _defines the lateral separation_ between the optical axis of the adjacent
systems in a planar array design. This defines the physical separation between
the center of each image FOV. To fulfill our aim of imaging a contiguous
surface without any gaps, we must ensure that for each lens-sensor pair in the
array, the imaged FOV is equal to the sensor pitch: $FOV=p$ (see Figure 2(b),
green dashed line). When configured to image across a continuous object plane
without any gaps, the magnification of each imaging system, defined as the
ratio between its image FOV and an object FOV, is then given by:

$M=\frac{s}{p}.$ (1)

Inserting this required magnification into our definition of the imaging
system’s pixel-limited full-pitch resolution now provides a relationship in
terms of sensor width $s$ and pitch $p$:

$r_{pix}=\frac{2\delta}{M}=\frac{2\delta p}{s},$ (2)

for a configuration to image a continuous surface. Of course, the imaging
system magnification can also be selected to be greater than or less than Eq.
1, which will impact the total FOV coverage of the array microscope and its
resolution. We will detail these alternative configurations below. We plot
pixel-limited resolution as a function of magnification and for several common
sensor pixel widths in Figure 2(c), which also highlights the three
configurations of the MCAM investigated here.

Figure 2: (a) Diagram of two co-planar microscopes with immediately adjacent
sensors and lenses. A magnification $M>1$ leads to an unobserved gap (red
arrow), which is closed when $M=1$. (b) 1D MCAM diagram with sensor pitch $p$
larger than sensor width $s$. The MCAM can be configured to operate in three
regimes (Tiled, Continuous, Multi-View) depending upon selected magnification.
(c) MCAM pixel-limited resolution as a function of magnification for several
common pixel sizes (log-scale). Regimes of operation are noted at the top and
experimental demonstrations are marked with colored circles.

The resolution of each imaging system within the array is also impacted by its
optics. Based on the specific pixel-limited resolution set by Eq. 2, it is
useful to match the optical resolution of each single lens to this limit. In
practice, this condition is relatively easy to satisfy for the compact imaging
optics used by each lens-sensor pair, as we demonstrate for a number of
configurations and as theoretically examined in prior work [43]. Each of the
micro-camera imaging lenses is relatively small, since the lens diameter must
be less than $p$, which is often on the order of 1 cm. Furthermore, small
lenses ensure tight array packing. Following the lens scaling law outlined in
Ref. [15], such small-diameter lenses are easily designed to offer high
performance (i.e., minimal aberrations) across a wide range of specifications.
While there are certainly optical limits on achievable resolutions and FOVs
for each micro-camera, a primary benefit of utilizing a multi-aperture imaging
arrangement is the ability to avoid many of the challenges associated with
large lens design. In other words, since the required SBP of each micro-camera
remains relatively small, designing a lens to meet pixel-limited resolution
requirements is much easier (and cheaper) than attempting to create a large
lens to capture a much larger SBP.

Finally, the number of individual lens-sensor pairs within the entire array
needs to be considered. This number is simply a function of the desired total
FOV for the array system. In this work, we first demonstrate a primary
configuration that covers an approximate 100 x 135 mm² area using a 6 x 9
array of 54 micro-cameras. We also demonstrate the ability to tile together
four individual multi-camera arrays to directly extend this total FOV by a
factor of four. This straight-forward scalability of the total FOV is a unique
benefit of arrayed microscopy, such as the MCAM system (see also Figure 7).

The selected magnification of all lens-sensor pairs within the array is a key
design choice that drives three primary regimes of operation (see Figure
2(b)). We summarize these three unique operation regimes next, before
experimentally demonstrating their benefits and trade-offs.

###  2.1 Configuration 1 - Multi-View Imaging

Using a large working distance and a low image magnification, the MCAM can be
configured for "multi-view" imaging. In this configuration, the FOVs of
individual lens-sensor pairs overlap so that each location in the sample is
imaged by at least two unique micro-cameras (see Figure 2(b), purple). As we
will show, a multi-view imaging geometry offers a number of interesting
benefits. For instance, this allows stereoscopic imaging to estimate the depth
of imaged objects, or to apply photogrammetry software to jointly reconstruct
a height map of the imaged object while stitching together the final large-
area composite. Alternatively, spectral or polarimetric multiplexing may be
utilized to capture additional specimen information from such overlapped
imagery. In the extreme scenario of all $N$ micro-cameras within the array
imaging the same object location, which is only possible when the object
distance is increased to a large stand-off distance, the micro-camera array
captures a light-field-type dataset [44], from which depth can be estimated
[45, 46, 47, 48]. We have found that a useful MCAM configuration is at the
opposite limit, where a small amount of inter-camera overlap between
immediately adjacent sensors can produce high-quality depth estimation, while
the entire array can still yield a significantly increased imaging FOV.

The magnification of an MCAM configured for multi-view imaging typically
satisfies,

$M_{m}\leq\frac{s}{2p}\leq\frac{1}{2}.$ (3)

which indicates that each micro-camera FOV has a width of $2p$ to ensure that
one point on the sample plane maps to at least two micro-cameras (except at
the boundaries). This will ensure that in two dimensions every point is imaged
by 4 micro-cameras with square image sensors. For example, inserting the
condition $M_{m}=1/4$ ($p=2s$) and a pixel size of $\delta=1.1\mu$m into
$r_{pix}=2\delta/M$ yields an 8.8 $\mu$m lower bound for full-pitch
resolution. This approximately matches the resolution provided by a 1.25X
microscope objective lens (with 21 mm FOV diameter) commonly used for
macroscopic (2D) inspection [1]. The number of micro-cameras required to image
a desired total sample plane FOV area $A$ in a multi-view configuration is
$\lceil$$A/4p^{2}$$\rceil$. We note that parts of the FOV of the corner micro-
cameras may not include more than one viewpoint per sample plane area, which
must be taken into account during post-processing analysis.

###  2.2 Configuration 2 - Continuous FOV Imaging

The Continuous FOV regime is entered when the magnification is increased past
the multi-view scenario, but the entire surface of an object is still viewed
by at least one micro-camera. This configuration has higher spatial resolution
than the multi-view geometry and requires the following magnification:

$M_{c}\leq\frac{s}{p}\leq 1.$ (4)

The continuous FOV configuration was the primary focus of our explanation at
the beginning of Section 2, where we explained how a continuous area (i.e.,
without any gaps in the FOV) is observed by a planar array when its
magnification is less than one. Typically, a small amount of inter-camera
image overlap (approx. 5-10%) is required for effective composite stitching.

###  2.3 Configuration 3 - Tiled High-Resolution Imaging

To obtain even higher image resolution, one can increase the magnification of
each single micro-camera such that a gap appears between adjacent FOVs (Figure
2(a)):

$M_{t}>\frac{s}{p}.$ (5)

Such a "tiled" configuration no longer images across a continuous sample area
in one snapshot. Instead, it captures data from a discrete, non-contiguous
sample area with a FOV width of $s/M$ along one dimension. The achievable
resolution of such a configuration depends on the selected magnification and
eventually the imaging optics. Based on $r_{pix}=2\delta/M$ and assuming
$M_{t}=2$ and a $\delta=1.1$ $\mu$m pixel size, we can estimate the full-pitch
pixel-limited resolution to 1.1 $\mu$m for a tiled imaging arrangement, which
matches the resolution achieved by a standard 10X microscope objective lens.

In a tiled imaging configuration, the MCAM operates similarly to a large
number of individual microscopes configured to image in parallel [33]. To
observe a macroscopic area, mechanical scanning of either the specimen or the
array can be used to fill in the FOV gaps over multiple image acquisitions.
The number of scan locations required to fill in the FOV gaps across the
entire specimen plane in one dimension is $\lceil$$pM/s$$\rceil$ (i.e., the
number of micro-camera FOVs of size $s/M$ that fit within an inter-camera
spacing $p$). Assuming square image sensors and a square micro-camera packing
geometry, $($$\lceil$$pM/s$$\rceil$$)^{2}$ unique scan locations must be
visited during imaging.

Compared to standard step-and-repeat imaging with a single-lens microscope, an
array with $N$ micro-cameras can image a specified surface at least $N$ times
faster, since it has to scan $N$ times fewer locations, to increase imaging
throughput accordingly. A second benefit is a greatly reduced scanning travel
range. A tiled imaging MCAM only has to mechanically scan over the inter-
camera spacing distance $p$ to fill in missing FOV gaps, as opposed to
standard microscopes which must scan across the entire extent of the desired
aggregate FOV. In other words, $1/N$ less movement is required. In
applications where the throughput is important, this can result in rather
dramatic savings, e.g., in imaging of large histology slides or when
inspecting large semiconductor wafers for defects.

##  3 Results

To test each of the three imaging configurations, we constructed a prototype
MCAM system containing a 6 x 9 array of micro-cameras. The 54 individual 13
megapixel CMOS sensors (ONSemi AR1335, 3120 x 4208 pixels,
$\delta=1.1\leavevmode\nobreak\ \mu$m pixel width) were tiled at a $p=13.5$ mm
pitch on a single PCB board. We designed an optomechanical mount to hold a 6 x
9 array of customized lenses (25.05 mm effective focal length, f/4, 13 mm
outer diameter, fabricated by Edmund Optics). These lenses were separated by
the same $p=13.5$ mm pitch. Each lens can be focused individually via a custom
thread mount. To test all three imaging configurations, we used the same MCAM
design with all lenses focused to a common plane, and adjusted the distance
between the lenses and sensors by moving the optomechanical mount of the lens
array. For tiled imaging (configuration 3), an additional 6 x 9 array of
lenses was included to minimize aberrations (see details below). The sample
working distance was controlled via a 3-axis stage.

Image data from all micro-cameras was routed to a single Field-Programmable
Gate Array (FPGA) before transmission to a single desktop computer via a PCIe
link. The FPGA allows control over the settings of all 54 camera sensors,
e.g., exposure time and gain, through a global address. Once configured, a
single command initiates synchronized image or video acquisition across all
image sensors (approx. 0.7 GP per snapshot). Image and video data are
transmitted from all sensors to the FPGA via high-speed serial data lanes. The
FPGA then organizes and routes this data to a standard desktop computer with
128 GB of RAM and a 4TB solid-state drive for permanent storage. As detailed
below, the system enables full-frame video recording at seven frames per
second and higher frame rates at lower per-frame pixel counts.

We applied a standard image stitching software to create all composite images
post-capture unless stated otherwise. This customized software followed
procedures currently available within the open-source Hugin code base [49]. In
some experiments, it was beneficial to capture images of calibration targets
to identify optimal stitching parameters before executing the imaging
experiment. This pre-calibration step takes around two minutes for the first
two imaging configurations and an hour for the tiled imaging configuration and
then allows essentially instantaneous stitching of subsequent newly captured
frames (as long as the sample is flat and at the same depth).

###  3.1 Validation of optical resolution

We summarize the results of a first set of experiments designed to assess MCAM
system resolution in Figure 3. We imaged a custom-designed resolution target
with the printed area (green box in Figure 3) spanning 83 x 123 mm² at three
different working distances associated with each of the three configurations
(multi-view, continuous, and tiled design). For multi-view imaging, a working
distance of $WD_{m}=250$ mm yielded a magnification of $M_{m}=0.1$. For
continuous imaging, a working distance of $WD_{c}=140$ mm yielded a
magnification of $M_{c}=0.2$. Finally, for tiled imaging, we mounted a second
array of 6 x 9 matching lenses atop the existing lens array but flipped it to
produce a 4f imaging system for each micro-camera. This optical layout yielded
an approximate working distance of $WD_{t}=5$ mm and magnification $M_{t}=1$,
as seen in Table 1.

Figure 3: MCAM resolution and FOV assessment. Custom-designed resolution target imaged by three MCAM configurations (multi-view, continuous, tiled - labeled with purple, green, and blue, respectively). Gigapixels (GP) were reported for final stitched composites. Red boxes denote full-pitch resolutions of approximately 20, 10, and 2 $\mu$m. Table 1: MCAM specifications Design | FOV (cm2) | Res ($\mu$m) | M | WD (mm) | GP | # snaps
---|---|---|---|---|---|---
Multi-View | 135 | 20 | 0.1 | 250 | 0.15 | 1
Continuous | 100 | 10 | 0.2 | 140 | 0.48 | 1
Tiled | 96 | 2 | 1 | 5 | 9.8 | 25

The total array FOV varied slightly for each imaging configuration, which we
denote with colored box outlines (purple, green, and blue) in Figure 3.
Additional key specifications for each design are highlighted in Table 1.
Maximum full-pitch resolution limits for each setup were 20 $\mu$m, 10 $\mu$m,
and 2 $\mu$m for multi-view, continuous, and tiled imaging, respectively. The
trend in achieved resolution follows the mathematical derivation in section 2.
We also demonstrate that the resolution changes very little across different
camera positions and across different image regions of a single camera for the
multi-view and continuous configurations, as shown in supplementary Figure S1.
Tiled imaging (configuration 3), however, exhibits limited aberrations at the
corner of each micro-camera FOV, as a working distance of the lenses utilized
for this demonstration was $90-\infty$ mm, not the 5 mm used here. Future
designs can utilize customized lens designs for tiled imaging, or crop such
aberrated areas at the expense of requiring additional scanning. In the
following subsections, we demonstrate MCAM imaging performance in each regime
in a set of experiments.

###  3.2 3D imaging with multi-view

Stereo imaging is a standard technique in computer vision that can estimate
object depth based on imaging from multiple views [50]. Through a similar
principle, the multi-view imaging configuration of the MCAM (with 50 % or more
overlap between the FOV of adjacent cameras) can be used to estimate the 3D
height of specimens. The most direct explanation of stereoscopic-based depth
estimation follows the principle of triangulation. As sketched in Figure 4(a),
a point on the object plane will map to two image plane locations on two
unique sensors in a multi-view setup configured with 50 % overlap. Each imaged
location will be at certain a lateral disparity, $d_{1}$ and $d_{2}$, with
respect to the optical axes of camera 1 and 2. From these measurable lateral
disparities and known optical setup parameters, such as inter-camera pitch $p$
and image plane distance $I_{d}$, object depth can be computed as,

$Object\ depth=\frac{pI_{d}}{d_{1}+d_{2}},$ (6)

To verify this principle with our multi-view MCAM, we performed an experiment
to measure the accuracy of this depth estimation by recording images of a
standard USAF resolution target at a range of object distances. After
calibrating the multi-view MCAM to exhibit slightly more than 50% overlap in
each dimension ($WD_{m}=250$ mm), we axially displaced the resolution target
from -3 to 3 mm from the originally calibrated focal plane and captured images
at 10 $\mu$m increments. From two acquired camera images per depth plane, we
then used standard stereoscopic methods to 1) find common features across both
images, 2) compute disparity distances $d_{1}$ and $d_{2}$ from corresponding
optical axes, and 3) apply Eq. 6 to estimate object depth. As plotted on the
y-axis in Figure 4(b), we observe accurate performance across the 6 mm range
with an experimental RMSE of 42.4 $\mu$m with respect to ground-truth depth.

Figure 4: (a) Diagram of multi-view MCAM. FOV of each lens-sensor pair is
$FOV_{m}=32$ mm. (b) Plot of stereoscopic height measurement accuracy (c)
Example stitched composite with a jointly estimated 3D height map. Full
gigapixel-scale results can be found at gigazoom.rc.duke.edu.

Photogrammetric 3D reconstruction algorithms can also be used to produce
dense, pixel-wise 3D surface height maps that are co-registered with the
stitched photometric images (Figure 4(c)). The problem of estimating 3D
information from a collection of multi-view 2D images has been extensively
studied in the computer vision community at macroscopic scales [51, 52] and
more recently at smaller, mesoscopic (mm) scales [53]. Here, we adapted the
algorithmic approach laid out in [53] to jointly reconstruct a stitched
composite and 3D surface height map for all individual 54 MCAM sub-images. The
central idea behind this computational procedure is to jointly match and
register sample features viewed from multiple perspectives while converting
parallax distortions to an estimated sample height. Unlike light-field
microscopes, the multi-view MCAM can jointly provide a significantly enlarged
image FOV with hundreds of resolved megapixels per snapshot, in addition to a
3D height map with an estimated axial sensitivity of 42 $\mu$m. Figure 4(c)
demonstrates 3D surface height map formation for a leaf across a 135 cm2 area,
from which the 3D nature of the midrib is clearly highlighted.

###  3.3 Gigapixel video over a continuous area

For the next demonstration of MCAM imaging, we arranged the multi-camera array
for continuous area imaging at a working distance of $WD_{c}=140$ mm, which
creates a small amount (approx. 5-10%) of inter-camera overlap (Figure 5(a)).
As shown in Figure 2, This configuration provides a higher magnification and
spatial resolution for contiguous area imaging as compared to the multi-view
arrangement.

A video of a viscous fluid mixture (areas dyed red and green for
visualization) was recorded at a frame rate of 5 Hz for a duration of 21
seconds (115 frames were recorded within 128GB RAM). Two exemplary frames
highlighting liquid movement are in Figure 5(b) and an example recording is in
Visualization 1, wherein the dynamics of small particulate matter is clearly
observable. As detailed in the Discussion, current MCAM frame rates are
limited by FPGA-to-workstation data transmission. Video data can be acquired
at higher frame rates across the same contiguous area, by reducing per-frame
data with on-chip pixel binning, wherein adjacent pixel values are combined
pre-transmission for a reduced final frame pixel count. For example, with the
CMOS sensors and electronics utilized in the current configuration, an
approximate 28 frame rate is achieved with the use of 2X pixel binning, at the
expense of a 2X lower pixel-limited resolution.

Figure 5: (a) Diagram of continuous FOV MCAM. FOV of each lens-sensor pair is
$FOV_{c}=16$ mm. (b) Continuous FOV MCAM video of a dynamic fluid mixture.
Full gigapixel-scale results can be found at gigazoom.rc.duke.edu.

###  3.4 9.8 gigapixel tiled imaging

Finally, to demonstrate higher resolution MCAM imaging, we created a slightly
modified optical arrangement and outfitted the specimen plane for limited
translation scanning. For each of the 54 micro-cameras in the tiled imaging
configuration, we arranged two of the same lenses used for multi-view and
continuous imaging in a 4f configuration. This produced 54 unique 1x
magnification images, each with an approximate 2 $\mu$m full-pitch resolution
limit. The maximum lateral travel distance for MCAM tiled imaging is specified
by $p$, the inter-camera spacing, which here is 13.5 mm Figure 6(a)). This
particular tiled imaging setup requires 5 x 5 scans (25 snapshots) to cover
the entire FOV, where each snapshot’s FOV overlaps with adjacent snapshots by
approximately 10% for effective stitching. The resulting dataset from our 25
scans contains 1350 unique micro-camera images (13 megapixels per image).

Figure 6(b) shows a set of two macaque brain slices (75 $\mu$m thick) arranged
on slides, which were simultaneously imaged using the tiled MCAM configuration
to produce final composites with 9.8 GP in total. In this example, along with
lateral scanning to fill in inter-camera FOV gaps, we also executed axial
scanning (10 slices at 10 $\mu$m increment) to account for the uneven surface
of the relatively thick tissue specimens. For each micro-camera at each
lateral scan position, we selected the most in-focus image via a Laplacian-
based contrast metric for final composite synthesis. The bottom-left images in
Figure 6(b) show the CA2 region of the hippocampus, while the bottom-right
images highlight an area exhibiting gliosis.

Figure 6: (a) Diagram of tiled high-resolution MCAM. FOV of each lens-sensor
pair is $FOV_{t}=3.5$ mm. (b) Large-area simultaneous scan of multiple brain
slices. Full gigapixel-scale results can be found at gigazoom.rc.duke.edu.
Figure 7: To demonstrate the straight-forward scalability of the MCAM system,
four MCAMs (24 micro-cameras each, 10 megapixel sensors, $p=19$ mm pitch) were
tiled together to image a 4X larger FOV. (a) Optical arrangement for acquiring
example stitched composites with 0.96 gigapixels per snapshot of (b) large
collection of butterfly wings and (c) collard green leaf.

##  4 Discussion and Conclusion

The three configurations of the MCAM system, presented in this work are a
natural starting point for exploring the utility of parallelized acquisition
in microscopy. By providing gigapixel-scale single-snapshot throughput, the
MCAM technology opens up new possibilities for wide-area high-resolution 3D
imaging and video. There is a number of existing challenges and future
directions for MCAM technology improvement that will likely lead to exciting
follow-up work, which we summarize below.

One primary challenge faced by multi-aperture microscope designs is data
management. In this work, we utilized a single FPGA to aggregate Mobile
Industry Processor Interface (MIPI) data directly from all sensors, which led
to several key benefits. First, the single FPGA allowed us to directly
synchronize video capture across all 54 cameras within the array, leading to
the ability to record gigapixel-scale video data without motion artifacts.
Second, we were able to achieve a maximum data transmission rate of
approximately 5 GB/sec, which corresponds to approximately 7 frames per second
video (8 bits/pixel) with our 54-camera arrangement. It is possible to crop
the sensors or reduce the camera count to increase the frame rate; for
example, a 3072$\times$3072 square crop yields $\sim$10 frames per second.
Transfer at such high data rates must account for limitations both in
transmission links and in drive write speeds. In our prototype, we utilized a
PCIe connection between the computer and the MCAM and stored data on pre-
allocated RAM space before moving to a solid-state drive, which enabled
approximately 249 seconds of video capture at full resolution. As solid-state
storage volumes and write speeds continue to improve, we anticipate the
ability to increase data transmission rates, and thus imaging frame rates,
using the current array. We also anticipate that improved data transmission
will open the door to novel MCAM designs that offer even larger full-frame
sizes. Compression methods are likewise available to dramatically reduce video
sizes in a lossless manner, for example [54, 55, 56], and we see the FPGA as a
key means to pre-process image data for additional future speed-up.

A second challenge is reaching a higher resolution. Following section 2’s
analysis, it is clear that resolution can be improved beyond our initial
demonstrations. For tiled imaging, custom-designed lenses with superior
magnification could match the resolution performance of standard high-NA
objective lenses over the demonstrated 8 x 12 cm² FOV. For continuous and
multi-view imaging, one primary driver of resolution is the inter-camera
spacing $p$. Future MCAM designs can readily be created with $p<13.5$mm for a
proportional increase in resolution performance. Smaller pixels and/or
alternative single-photon detector arrays [42, 57, 58] may also be adopted.
Our demonstrated design likewise utilized 4:3 format CMOS sensors. It is
alternatively possible to utilize perfectly square sensors for uniform overlap
in x and y. Or, highly rectangular sensors can be utilized for multi-view
imaging with an overlap in just one spatial dimension (i.e., to facilitate
stereoscopic imaging with just two views per sample plane location), which may
lead to improved resolution multi-view imaging. Finally, a non-rectangular
(e.g., hexagonal) micro-camera packing geometry may also yield future
performance gains.

It is also desirable to ensure that the macroscopic objects imaged here remain
in sharp focus. We used standard calibration processes to first focus all 54
lenses within our prototype array for the three demonstrated configurations
onto a common plane. However, afterward, care was required to ensure each
macroscopic sample was placed and remained in-focus. As the MCAM transitions
to higher resolution designs with shallower depths of field, several
strategies may prove helpful. For example, a phase mask may be included for
extended depth of field imaging [59]. A per-lens autofocus capability would
enable imaging at high focus across curved specimens, or even surfaces that
variably change in height as a function of time.

In terms of imaging FOV, a particular MCAM design’s coverage is simply
proportional to the number of micro-cameras included within an array. If a
larger FOV is required, then it is possible to directly join multiple MCAMs to
form a larger aggregate array. An example of such an aggregate MCAM array to
image over a significantly larger FOV is shown in Figure 7(a). In this
demonstration, we combined four identical, separately constructed 4 x 6 micro-
camera arrays into an aggregate 8 x 12 array that contained 96 individual
lens-sensor pairs (10 megapixels each, 0.96 GP per snapshot). As demonstrated
in Figure 7(b, c), such a configuration can provide high-resolution continuous
image capture over a large, macroscopic area covering approximately 18 x 24
cm². Additional details about this design can be found in Ref. [60].

The MCAM can also be configured for a wide variety of alternative imaging
configurations. We have recently demonstrated multi-aperture fluorescence
imaging [60]. Polarization [61], phase contrast [62] and aperture coding [63]
techniques can also be easily implemented to extract additional specimen
information. Likewise, while it has been previously explored in tiled imaging
configurations that do not image a continuous area [64], variable-angle dark-
field and bright-field illumination is an alternative direction for novel
configurations of continuous and multi-view MCAM setups. As with all digital
microscopes, software will continue to play an increasingly important role in
the pre-processing and analysis of the MCAM’s terapixel-sized datasets. While
this work performed all processing post-capture, future implementations may
benefit from on-the-fly or hardware-accelerated image stitching and/or surface
height estimation. For application-specific scenarios such as object tracking
and feature detection, various methods may be used to significantly reduce
acquired file sizes on-the-fly while still maintaining salient image
information.

##  5 Funding

Research reported in this publication was supported by the Office of Research
Infrastructure Programs (ORIP), Office Of The Director, and the National
Institute Of Environmental Health Sciences (NIEHS) of the National Institutes
of Health under Award Number R44OD024879, by the National Cancer Institute
(NCI) of the National Institutes of Health under Award Number R44CA250877, by
the National Institute of Biomedical Imaging and Bioengineering (NIBIB) of the
National Institutes of Health under Award Number R43EB030979, the National
Science Foundation under Award Number 2036439, and the Duke Coulter
Translational Partnership Award.

##  6 Acknowledgments

The authors would like to thank Dr. Benjamin Judkewitz, Dr. Florian Engert and
Dr. Michael Orger for helpful guidance during project development.

##  7 Disclosures

MH: Ramona Optics Inc. (F,I,P,S), KCZ: Ramona Optics Inc. (C), SS: Ramona
Optics Inc. (C), CC: Ramona Optics Inc. (C), RA: Ramona Optics Inc. (I,E,P),
CC: Ramona Optics Inc. (I,E,P), JD: Ramona Optics Inc. (I,E,P), GH: Ramona
Optics Inc. (I,E,P), JP: Ramona Optics Inc. (I,E,P), PR: Ramona Optics Inc.
(I,E,P), VS: Ramona Optics Inc. (I,E,P), RH: Ramona Optics Inc. (F,I,P,S).

##  8 Data availability

Data underlying the results may be obtained from the authors upon reasonable
request.

##  9 Supplemental document

See Supplement 1 for supporting content.

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##  Appendix A Supplementary Figure S1 Resolution analysis

Figure 8: Experimental results of MCAM resolution assessment across camera and
FOV. Zoom-ins at four marked locations in Figure 3 for each MCAM
configuration. Red boxes denote full-pitch resolutions of approximately 20,
10, and 2 $\mu$m.