figure table

# Ultra-miniature dual-wavelength spatial frequency domain imaging for micro-
endoscopy

Jane Crowley  University of Nottingham, Department of Electrical and
Electronic Engineering, Optics and Photonics Group, University Park,
Nottingham, United Kingdom, NG72RD  George S.D. Gordon  University of
Nottingham, Department of Electrical and Electronic Engineering, Optics and
Photonics Group, University Park, Nottingham, United Kingdom, NG72RD

###### Abstract

There is a need for a cost-effective, quantitative imaging tool that can be
deployed endoscopically to better detect early stage gastrointestinal cancers.
Spatial frequency domain imaging (SFDI) is a low-cost imaging technique that
produces near-real time, quantitative maps of absorption and reduced
scattering coefficients, but most implementations are bulky and suitable only
for use outside the body. We present an ultra-miniature SFDI system comprised
of an optical fiber array (diameter $0.125$ mm) and a micro camera ($1\times
1$ mm package) displacing conventionally bulky components, in particular the
projector. The prototype has outer diameter $3$ mm, but the individual
components dimensions could permit future packaging to $<1.5$ mm diameter. We
develop a phase-tracking algorithm to rapidly extract images with fringe
projections at $3$ equispaced phase shifts in order to perform SFDI
demodulation. To validate performance, we first demonstrate comparable
recovery of quantitative optical properties between our ultra-miniature system
and a conventional bench-top SFDI system with agreement of $15$% and $6$% for
absorption and reduced scattering respectively. Next, we demonstrate imaging
of absorption and reduced scattering of tissue-mimicking phantoms providing
enhanced contrast between simulated tissue types (healthy and tumour), done
simultaneously at wavelengths of $515$ nm and $660$ nm. This device shows
promise as a cost-effective, quantitative imaging tool to detect variations in
optical absorption and scattering as indicators of cancer.

###### keywords:

spatial frequency domain imaging, miniaturization, optical properties, optical
fibers

<EMAIL_ADDRESS>
##  1 Introduction

Gastrointestinal cancers account for one quarter of the global cancer
incidence and over one third of all cancer related deaths [1]. Wider
population-based endoscopic screening can significantly decrease mortality
[2], but miss rates for some types of polyps during diagnostic colonoscopies
can be as high as $26$% [3]. There is therefore a need for an improved
contrast imaging device that is minimally invasive and can be deployed
endoscopically. To be deployed via the instrument channel of a standard
colonoscope it must have an outer diameter $<3$ mm, and to be suitable for
population screening programmes it must be relatively low-cost to manufacture
and operate.

Spatial frequency domain imaging (SFDI) is a low-cost imaging technique that
returns quantitative maps of absorption and reduced scattering coefficients in
close to real time [4, 5]. SFDI requires a $2$D illumination pattern of known
spatial frequency to be generated and projected onto a sample of interest,
with the result captured on a standard CMOS camera. Demodulation is then
performed to obtain the high and low frequency modulation amplitudes by
capturing three separate patterns equally shifted in phase ($I_{1},I_{2}$,and
$I_{3}$) using the equations:

$I_{AC}(x_{i})=\frac{\sqrt{2}}{3}[(I_{1}(x_{i})-I_{2}(x_{i}))^{2}+(I_{2}(x_{i})-I_{3}(x_{i}))^{2}+(I_{3}(x_{i})-I_{1}(x_{i}))^{2}]^{1/2}$
(1) $I_{DC}(x_{i})=\frac{1}{3}[I_{1}(x_{i})+I_{2}(x_{i})+I_{3}(x_{i})]$ (2)

This is repeated on a reference material of known optical properties (and
hence known diffuse reflectance values) such that the modulation transfer
function of the imaging system can be corrected for, and diffuse reflectance
values obtained. Diffuse reflectance values are then used to estimate
absorption and reduced scattering coefficients using a look-up table generated
from either the Diffusion Approximation or Monte Carlo simulation as solutions
to the radiative transfer equation. Obtaining the optical properties at more
than one wavelength allows for the extraction of additional tissue
information, such as chromophore concentration via the Beer-Lambert law. This
addition of endogenous contrast information is an aid in diagnosing tissue
types, and has been used during breast reconstructive surgery for oxygenation
imaging [6].

Performing SFDI at more than one wavelength simultaneously is advantageous for
several reasons. Firstly, it gives the opportunity to penetrate to different
depths in the sample of interest with different wavelengths[7]. Secondly, it
introduces the capability to obtain chromophore information, such as
oxyhaemoglobin and deoxyhaemoglobin concentration, by measuring the variation
in absorption coefficient at more than one wavelength[8][9]. Blood oxygenation
SFDI systems often operate in the Red/IR e.g. [10], but most fiber bundle
systems operate in the green to avoid too much cross-coupling between fibers
[11]. Also, using just one individual wavelength (e.g. $515$ nm), one can
obtain different structural tissue information.

To improve speed of SFDI systems towards real-time operation, a single phase
image can be used instead of three: a technique termed single snapshot of
optical properties (SSOP)[12]. SSOP uses a Fourier demodulation method to
perform spatial frequency demodulation which typically results in poorer image
quality, although a method to retain more spatial resolution has been proposed
using a Hilbert Transform instead [13], and emerging convolutional neural
network techniques can improve resolution [14, 15]. SSOP has been shown to
successfully quantify bowel ischaemia[16].

SFDI has shown to return successful contrast between healthy and malignant
resected esophageal and colon tissue [17, 18]. _Sweer et al._ imaged resected
esophageal tissue from eight patients undergoing esophagectomy. By comparing
regions imaged with a commercially available SFDI system from _Modulim_ [19]
with results from histological analysis of tissue, it was determined that
healthy esophageal tissue has a reduced scattering coefficient higher than the
reduced scattering coefficient of both invasive squamous cell carcinoma and
Barrett’s esophagus with mild chronic inflammation, in the red wavelength
region $\sim 660$ nm. The absorption coefficient of healthy esophageal tissue
is lower than invasive squamous cell carcinoma and analogous to that of
Barrett’s esophagus with mild chronic inflammation, at a wavelength of $\sim
660$ nm. _Nandy et al._ found that healthy colon tissue has a higher reduced
scattering coefficient than malignant colon tissue and a lower absorption
coefficient across the wavelength range $460-630$ nm.

SFDI is an attractive choice for an imaging modality because it does not
require high-powered lasers, sensitive detectors (mobile phone cameras are
sufficient) or complex optical components. It is therefore relatively low-cost
to manufacture and operate devices, and they can be miniaturized easily. As a
result, a number of SFDI systems exist, such as large commercial systems[19],
portable handheld systems[20], handheld $3$D printed systems[21], compact
multispectral imaging systems[22]. However, in most existing systems the
projector element remains costly and difficult to miniaturize, being typically
comprised of either a digital micromirror device (DMD) projector [20], a
motorized grating [21, 22], or a static spatial frequency transparency [23].

There have been a number of approaches to miniaturize SFDI projectors to make
them suitable for endoscopic deployment. Fixed gratings have been used to
achieve SSOP via rigid endoscopes [24]. While SSOP is advantageous as it
reduces acquisition times, it poses several disadvantages, such as reduced
image quality due to the use of filtering a single image. The previously
developed probe is rigid in nature and not suitable for imaging in the
gastrointestinal tract. Fixed gratings have also been used for optical
sectioning via flexible imaging fiber bundles [25]. The use of a micro camera
is advantageous over imaging through a fiber bundle as an imaging fiber bundle
is highly sensitive to vibrations, cross coupling and fiber movements, making
the reconstruction of images challenging. Phase-shifted illumination has been
demonstrated via an imaging fiber bundle [26], but the use of DMDs is
relatively high cost, and commercial fiber bundles projection only support
high fidelity fringes at green wavelengths due to increased cross-coupling
between cores in red wavelengths[11]. Ultra-thin fiber arrays have been used
to create fringe patterns interferometrically for profilometry but not, to our
knowledge, for SFDI[27].

None of these existing systems are suitable for routine endoscopic deployment
in the gastrointestinal tract because they either use DMD-based projectors
which are costly and cannot be sufficiently miniaturized; use fiber bundles
which produce low-quality fringe patterns at a limited set of wavelengths and
only record low resolution images; or use rigid endoscopes which are not
flexible enough.

We have therefore developed an ultra-miniature SFDI system, with an outer
diameter $3$ mm that uses a fiber array to interferometrically produce fringe
patterns at green ($515$ nm) and red ($660$ nm) wavelengths and records images
at $320\times 320$ pixel resolution using a micro camera. The prototype
packaging is sufficiently small that is it compatible with the instrument
channel of a standard colonoscope. This makes the device comparable to the
thinnest previous SFDI system designs that used fiber bundles to achieve a
total diameter of $2.7$ mm[25].

We first compare optical property measurements in our ultra-miniature system
to that of a conventional bench-top system and find agreement between
absorption and reduced scattering coefficients of $15$% and $6$% respectively.
We show the potential to operate the system at more than one wavelength
simultaneously, enabling rapid tissue property measurements. This device
therefore shows potential to be deployed endoscopically for _in-vivo_
gastrointestinal imaging to detect optical properties as potential indicators
of cancer.

##  2 Methods

###  2.1 Component design and selection

The primary components needed for an SFDI system are a source of pattern
projection and an image detector to capture the projected patterns on a sample
of interest. We chose to use an optical fiber array as the source of
projection patterns and a micro camera as the detector.

Figure 1: Proposed ultra-miniature SFDI system (a) Schematic of fiber array in
ultra-miniature SFDI system showing dual wavelength illumination
simultaneously. Light passes from the two lasers into the fiber array via a
selection of 7 single-mode fiber input ports. At the tip of the fused taper,
the fibers are spaced in a hexagonal array, providing three possible spacings.
Crossed polarizers are placed in front of the fiber tip and the micro camera
to reduce specular reflections from the imaging sample. (b) Photograph of
experimental set up. (c) Prototype device package of $3$ mm diameter with
inset showing zoomed in view of fiber tip and camera.

To create an ultra-miniature fringe projector without using DMD elements, we
designed a customized two-dimensional pitch-reducing optical fiber array
(PROFA™, _Chiral Photonics_ , NJ) to create fringes interferometrically, shown
in Fig. 1. The fiber array was designed to produce interference patterns
within a widely used spatial frequency range ($0.1-0.3$ mm-1 [28, 29]) at an
initial test working distance of $50$ mm when two adjacent channels are
illuminated by the same laser source. To compute the required fiber spacings,
we used a double slit equation:

$m\lambda=d\sin{\theta}$ (3)

where $m$ is the number of the interference line spacings from the central
point, $\lambda$ is the wavelength of light, $d$ is the distance between slits
and $\theta$ is the angle of projection. The desired wavelength was chosen to
be $660$ nm. The distance from slit to projection pattern, i.e. the working
distance, was chosen initially to be $50$ mm, which is the maximum working
distance of the camera. Using Eqn 3, we can therefore determine the spacing
$d$ required to produce our spatial frequencies of interest. The fabricated
fiber array has spacings of $5$, $8.66$ and $10$ $\mu$m, which will produce
spatial frequencies of $0.15$, $0.25$, $0.3$ mm-1 at 660nm, as shown in Fig. 2
a. We can then determine the spatial frequency projection at varying fiber to
sample working distances, shown in Fig 2 (b). Typical endoscope working
distances are $20-30$ mm [30], which is achievable using the 5$\mu$m spacing
option of our array with $0.3$ mm-1 spatial frequency, though in future
designs a 2.5$\mu m$ spacing could enable even shorter working distances. The
7 fiber channels are spaced at the tip as shown in Fig 1. The light sources
used are a $5$ mW $660$ nm laser diode (LPS-660-FC, _Thorlabs_) and a $3$ mW
$515$ nm laser (LP515-SF3, _Thorlabs_).

Figure 2: Determining desired fiber spacing to produce spatial frequencies
within our range of interest $0.1-0.3$ mm-1 (a) Addressable spatial frequency
projection at working distances (WD) of $50$ mm (solid lines) and $30$ mm
(dashed lines). The dotted lines represent the three possible fiber tip
spacings of $5$, $8.66$ and $10$ $\mu$m (b) proposed design of spatial
frequency projection at various working distances for fiber tip spacing (d) of
$5$ $\mu$m (solid lines) and $2.5$ $\mu$m (dashed lines), useful for smaller
working distances.

The camera chosen is a $1\times 1$ mm micro camera module (Osiris M module,
_OptaSensor_ , Germany). The camera has a resolution of $320\times 320$
pixels, with an individual pixel size of $2.4$ $\mu$m. An in-built lens placed
in front of the sensor provides horizontal and diagonal field of views of
$68^{\circ}$ and $90^{\circ}$ respectively, accompanied by a depth of focus of
$5-50$ mm. The camera module produces a $12$ bit RGB raw image output. The
camera is accompanied by software to control camera parameters such as
exposure, gamma correction and black level correction. The automatic exposure
correction was disabled so that all image frames contain the same optical
power ranges. The micro camera has a frame rate of up to $50$ fps, but here we
typically operate it at $10$ fps due to capture software limitations. However,
$10$ fps is the minimum rate required for proper endoscopic visualization[31].

To minimize specular reflections present on the imaging sample, adhesive-
backed polymer polarizer sheets and placed in front of the camera and fiber
tip to create cross-polarization. The camera is also placed at a small angle
of $4^{\circ}$ to the fiber to further limit specular reflections on the
imaging sample. This angle is smaller than conventional SFDI systems[6], but
is more amenable to miniaturization. Previous work has shown that this angle
can still produce high quality optical property maps[32]

###  2.2 Phase-tracking algorithm

An inherent property of an interferometer such as our fiber array is that the
sinusoidal pattern produced will shift over time due to mechanical drifts,
vibrations, temperature and intensity variations [33]. Conventional wisdom may
suggest using a complex set up consisting of a phase-shifting control system
and a piezoelectric transducer driver to stabilize and control this phase
shift[27]. However, we exploit the natural phase drift to our advantage via a
phase-tracking algorithm.

Figure 3: Characterization of fringes and phase tracking (a) image of selected
zeroth frame and average of all frames, where $N$ is the total number of all
frames within video capture, and corresponding cross sections. The single
frame - averaged frames has had a smoothing filter applied (b) image of zeroth
frame, $120^{\circ}$ shifted frame and $240^{\circ}$ shifted frame and
corresponding cross sections, all with smoothing filters applied.

A video, typically $10-20$ s, is first recorded of the shifting sinusoidal
pattern on a sample of interest. This timeframe is purely selected for
experimental convenience but in practice only the first second or so of
recorded frames is required. To determine which frames to use for
demodulation, we first take an average of all frames within the video and
subtract this from each individual frame. This allows us to visualize the
spatial frequency pattern with reduced noise (see Fig 3 a).

We then take an average across several rows within the frame, applying a
smoothing filter, and plot the sinusoidal pattern. We select a zeroth frame
and designate the phase of the extracted sinusoid to be $0^{\circ}$. Next, we
calculate the average distance between adjacent maxima of this sinusoid in
pixels. This value gives the period of the pattern, in pixel units. Custom
_Python_ code then cycles through all frames in the captured video and selects
frames of equal intensity variation whose sinusoidal projections have relative
phases of $(120\pm 10)^{\circ}$ and $(240\pm 10)^{\circ}$ from the selected
zeroth frame (see Fig 3 b). Frames where the sine wave is non-discernible or
the intensity variation between peak and trough is low relative to the zeroth
frame are disregarded. This eliminates frames where coherence is temporarily
disturbed while perturbations are still in progress. We then select these
frame numbers from the initial video and demodulate the images using Eqns 1
and 2.

###  2.3 Imaging homogeneous tissue-mimicking phantoms

In order to perform initial validation of the system, we fabricated tissue
mimicking co-polymer in oil phantoms with tunable optical properties by
controlling concentrations of TiO2 and Nigrosin dye [34]. The fabricated
phantoms had a thickness of $30$ mm and were ensured to be non-transparent so
as to meet the semi-infinite thickness requirement of SFDI [35]. We fabricated
two phantom batches; one with increasing amounts of dye stock solution from
$0.5-1$ g ($0.0015-0.0030$ w/v%) corresponding to an absorption coefficient
range of $0.006-0.017$ $mm^{-1}$ at $660$ nm and the second with increasing
amounts of TiO2 from $0.07-0.13$ g ($0.07-0.13$ w/v%) corresponding to a
reduced scattering coefficient range of $0.52-0.99$ $mm^{-1}$ at $660$ nm. The
batch with increasing dye stock solution each had $0.1$ g of TiO2 and the
batch with increasing TiO2 each had $0.5$ g of dye stock solution to ensure
the semi-infinite material requirement was met. We chose these optical
property ranges as they lay within optical properties of interest of typical
gastrointestinal tissue samples [17] and they had previously been calibrated
for in literature using a double integrating sphere (DIS) [34].

For purposes of comparison, we imaged phantoms in both our ultra-miniature
system and a standard bench-top SFDI system. The bench-top system was built
in-house using a commercial projector (_LG Minibeam PH150g HD ready mini
projector_), a Raspberry Pi camera, crossed polarizers placed in front of the
camera and projector, and a $635$ nm filter placed in front of the camera to
ensure only red light was captured. The system was validated against phantoms
with optical properties measured in a double integrating sphere system and
found to be in agreement with a margin of error around 20%, which is within
the typical expected range [36].

The phantoms were placed in the bench-top system such that the projector is
placed at a $6^{\circ}$ angle to the plane of the camera, the projector-camera
distance is fixed at $35$ mm, and the distance from the projector-camera plane
to the base breadboard is $220$ mm. The Diffusion Approximation was used to
generate a look-up table to recover the optical properties of the phantoms.
Because our ultra-miniature system uses a laser at $660$ nm and the bench-top
system uses white-light source with a camera filter at $635$ nm, a small
adjustment for wavelength is required. First, separate LUTs are computed for
each of the wavelengths. Second, an adjustment based on multiwavelength
measurements from a double integrating sphere system is applied [34]. For
these particular phantoms, the measured difference via DIS between absorption
and reduced scattering coefficients from $635$ nm to $660$ nm is $14$% and
$3$% respectively. Therefore, we adjust reference optical properties for
optical property calculation depending whether we were using the bench-top or
ultra-miniature system. When imaging phantoms at $515$ nm in the ultra-
miniature system, the LUT and reference optical properties were also adjusted
for accordingly.

We placed the phantoms such that the top of the phantom was $50$ mm from the
distal end of the imaging probe and the projection pattern was in the center
of the sample. We took videos of the shifting projection pattern on the
phantom for $10-20$ s. The video was then input to _Python_ phase-tracking
code for processing described in Sect 2.2 to find the exact frames needed to
calculate the optical properties. We imaged each phantom at three different
spatial frequencies by illuminating three different fiber channel
combinations. We calculated the optical properties using a look-up table
generated from the Diffusion Approximation. For each phantom, we calculated
the optical property maps a total of $18$ times, using every other phantom as
a reference in turn for each spatial frequency. This approach helps to average
out errors arising from mismatches in expected optical properties of phantoms,
which arises in turn due to discrepancies between DIS and SFDI measurements,
which can be up to $20$% [36]. Finally, the mean of all $18$ optical property
maps is used to determine the absorption and reduced scattering coefficients.
A 2D Gaussian filter with standard deviation of $5$ pixels was applied to
resultant optical property maps using _scipy.ndimage.gaussian_filter_.

###  2.4 Dual wavelength imaging

Multi-wavelength imaging is possible with this system as the fiber array
consists of seven channels and only two are needed per wavelength to produce
an interference pattern. Therefore, this system has the potential to explore
up to tri-wavelength simultaneous illumination. We imaged three phantoms with
$660$ nm projection only, then $515$ nm projection only, and finally with
$660$ nm and $515$ nm projected simultaneously. We perform dual-wavelength
imaging by illuminating channels $1\&7$ with $660$ nm and channels $2\&5$ with
$515$ nm, producing spatial frequency patterns of $0.3$ mm-1 and $0.2$ mm-1
respectively at a $50$ mm working distance. A video is captured of both
illumination patterns simultaneously, and analysis is carried out by
extracting the red and green channels from the video capture. Following the
same process in Sect 2.2, fringes of interest are selected and optical
properties calculated. Expanding the existing system to tri-colour would be
possible either by adding an additional laser of, say $\sim 450$ nm, to two
available illumination channels will produce a spatial frequency of $0.22$
mm-1, and could be analysed from the blue channel of the captured video.
Multi-wavelength imaging would probe different depths and could be used to
image optical properties of layered material.

###  2.5 Extrapolating performance to clinical applications

The ultra-small size of our prototype device may incur performance penalties
compared to standard bench-top SFDI. Qualitatively, this appears as noise in
measured images. However, the ultimate goal of the tool is to provide
sufficient contrast for identifying diseased tissue compared to healthy
tissue. To assess this, we post-process our optical property measurements to
estimate the sensitivity and specificity that could be achieved in a clinical
device. This is then compared against American Society of Gastrointestinal
Endoscopy (ASGE) guidelines, which require a new device to demonstrate $90$%
sensitivity and $80$% specificity in order to be used in lieu of biopsy
sampling [37].

To extrapolate our device’s potential clinical performance we simulate random
measurements based on previously measured absorption and scattering statistics
of healthy esophageal tissue, Barrett’s esophagus and squamous cell carcinoma
(SCC) [17]. Because of the non-negativity and underlying multiplicative nature
of absorption and scattering processes, a log-normal distribution is used to
generate samples[38]. A baseline model is first created that estimates
performance under the assumption that intra-sample variation is purely
biological in origin. To adapt this into the model used here, we add an
additional term to the variance based on error measurements observed from our
ultra-miniature system.

500 random training samples are generated for the healthy, Barrett’s and SCC
tissue types, and two binary linear support vector machine classifiers are
trained (healthy vs. Barrett’s and healthy vs SCC). A further 500 validation
samples are then generated for each of the 3 classes and passed through the
trained classifiers. Based on the classification error rates, sensitivity and
specificity for the baseline and ultra-miniature system are estimated.

##  3 Results

###  3.1 Projector performance

The expected spatial frequency of the projected illumination pattern is
comparable to the desired spatial frequency with $12$% and $7$% error for
$660$ nm and $515$ nm respectively. Some channels produce clearer interference
patterns than others, due to cross talk between fibers. This also results in
the interference pattern from some channels being more stable than others in
time, with interference patterns being stable for $<1$ s under typical
operating conditions, but $>10$ s if the fibers are kept still.

Through imaging a resolution target (R3L3S1N - Negative 1951 USAF Test Target,
3” x 3”, _Thorlabs_ , UK), we determined the resolution of the imaging system
to be $0.793$ lp/mm at a working distance of $50$ mm, shown in Fig 4 a. Fig 4
b shows the raw performance of the projection fiber with green and red
wavelengths onto an absorbing and scattering phantom. This represents a
typical raw image required from the camera. Finally, Figure 4c shows a direct
capture on a CMOS image sensor of the projected pattern from the fiber. This
shows that clear fringes are produced within an envelope, but that there is
also some noise arising from aperture and cross-talk effects forming a ring
around the target area. We therefore restrict our analysis to regions within
this ring where fringes are projected with high quality.

Figure 4: Raw performance of camera and projector (a) Image of USAF target
captured with mini camera module taken with room lights on (b) image captured
with mini camera module of dual wavelength projection from fiber tip showing
extracted red and green channels respectively, (c) Direct capture on image
sensor of projected fringe pattern, showing good fringe contrast within a
region of circular interference.

###  3.2 Phase-tracking stability

We analysed the fringe phase shift and contrast for 15 recorded videos, during
which we continually perturbed the fiber by hand to simulate realistic usage.
An example trace of fringe phase vs. time is shown in Fig 5 (a) which
indicates that the required 3 phases can be obtained under 1s. Fig 5 (b) shows
the calculated difference from maximum to minimum of the interference fringes
as a function of time, i.e. the fringe contrast. The contrast appears
relatively stable over the $3$ s time interval. To further analyse the
combined effect, we used Poisson statistics across these 15 captures to
estimate the expected time at maximum frame rate required to obtain 3 usable
frames (defined as having sufficiently high contrast across 3 phases) with 99%
probability. We found this varied from 0.42 s to 2.34 s with a mean of 1.17 s.
This may be sufficient for practical imaging provided the probe can be held
within the same field of view for 1-2 s.

Figure 5: Fiber array performance (a) phase of frames vs time (b) fringe
contrast, defined as difference from maxima to minima of interference fringes
detected vs time

To examine the stability of the fringe envelope we averaged all frames
together for individual video captures and plotted the a cross-sectional
envelope profile. By repeating this across 5 separate video captures using a
range of different phantoms, we observed how the fringe envelope varies. Given
that the envelope shape is largely determined by the fibre exit aperture we
would expect the shape to be relatively uniform across different samples,
although effects such as cross-talk between fibres may cause a variation.
Additionally, fluctuations in laser power, laser polarization state or small
transients in relative power in different fibres due to manual perturbations
may influence the envelope.

From our results, shown in 6, we observe that the shape of the envelope is
fairly consistent across different captures, though the absolute scale does
appear to change within a range of $\pm$10%. In future systems, this could be
partially compensated by having a power meter recording laser output which can
be used later used for normalization.

We therefore expect that there may be some variation between the reference
phantom envelope and the measurement: the envelope will be approximately
correct but the amplitudes may vary which could be a contributing source to
the overall system error, in the region of 10%.

Figure 6: Plot of average fringe envelope for 5 different captures using
phantoms with different optical properties. Though the amplitude of the
envelop varies in intensity, the position and shape stay relatively constant.

###  3.3 Comparing ultra-miniature SFDI system to bench-top SFDI system

We then compared optical property measurements from our conventional bench-top
SFDI system to our ultra-miniature SFDI system. The results are shown in Fig 7
a & b. We found that the average standard error in absorption and reduced
scattering coefficients between the ultra-miniature system and the bench-top
system were $15$% and $6$% respectively. However, we note that the slope of
the absorption graph is much less than unity, reaching as high as 60% in the
high absorption range. This may be due to a range of factors including stray
background light, non-ideal sinusoid shapes and the resulting mismatch in the
LUT, or varying envelope amplitudes. Because the absorption is consistently
underestimated, this may be rectified using additional calibration steps, for
example phantom-based LUT generation [39] or realistic simulation of the fibre
imaging set up [32].

Figure 7: Comparison of bench-top SFDI system and ultra-miniature system: (a)
absorption coefficient and (b) reduced scattering coefficient measured from
bench-top system ($x$ axis) and ultra-miniature system ($y$ axis). Error bars
represent the standard deviation across the image.

###  3.4 Imaging typical gastrointestinal conditions with ultra-miniature SFDI
system

We fabricated two phantoms to simulate gastrointestinal tissue states: one
with optical properties mimicking squamous cell carcinoma, and the second with
optical properties mimicking healthy esophageal tissue, and placed them side
by side. SFDI imaging of this sample was then performed at 660nm, with the
resulting optical property maps shown in Fig 8 c & f, and resultant optical
property maps with filtering applied shown in Fig 8 d & g.

Figure 8: Imaging a phantom simulating esophageal tissue at 660nm: (a) white
light image of two phantoms with different optical properties side by side (b)
expected and (c) measured absorption coefficient of phantoms (d) measured
absorption coefficient with smoothing filter applied (e) expected and (f)
measured reduced scattering coefficient of phantoms (g) measured reduced
scattering coefficient with smoothing filter applied. Expected optical
properties are computed from the mean measured values of the individual
phantoms measured in bench-top SFDI system.

To illustrate the effect of speckle averaging, we compared the optical
properties of the same phantoms measured with just a single spatial frequency
to three spatial frequencies averaged together. The results are shown in Fig
9: Fig 9(a & d) represent the expected optical properties of the phantoms, Fig
9 (b & e) show the optical properties measured from a single spatial frequency
projection and Fig 9 (c & f) show the optical properties measured by taking
the average over three different spatial frequency projections. The standard
deviation of pixels in the absorption coefficient maps reduces from $0.0049$
to $0.0044$ from Fig 9 (b) to (c). The standard deviation of pixels in the
reduced scattering coefficient maps reduces from $0.32$ to $0.15$ from Fig 9
(e) to (f).

Figure 9: Visual representation of averaging over several spatial frequencies
to reduce speckle noise.

Using our post-processing simulation, we found that for detecting Barrett’s
esophagus vs. healthy we could achieve a sensitivity of 76.2% and a
specificity of 82.8%. This falls just short of the ASGE guidelines [37].
However, for SCC vs. healthy we find $>$99% sensitivity and 89.6% specificity.
This meets the ASGE guidelines and is in agreement with experimental pre-
clinical SFDI studies that typically achieve values $>$90% for both
sensitivity and specificity when comparing healthy and cancer tissue [40, 41].

###  3.5 Dual-wavelength imaging

Finally, we characterized the performance across the two wavelengths. We found
that the recovered optical properties varied by $\leq 10\%$ when the two
wavelengths are measured simultaneously, compared to measuring them
sequentially. This demonstrates the capability of the system to image optical
properties at two wavelengths simultaneously with relatively low cross-
coupling.

We then imaged two phantoms with different optical properties placed adjacent
to one another, one mimicking the optical properties of squamous cell
carcinoma and the other mimicking the optical properties of healthy esophageal
tissue. The results are shown in Fig 10 (a-l). The difference in optical
properties is visible from both the red and green channels. The optical
properties measured from the red and green channel are not expected to be the
same as the phantom properties shift with wavelength [34]. We expect the
phantom optical properties measured from the green channel to be higher than
phantom optical properties measured from the red channel.

Figure 10: Optical properties measured from dual-wavelength imaging
experiment: (a) expected absorption coefficient from red channel (b) measured
absorption coefficient from red channel with (c) filtering applied (d)
expected absorption coefficient from green channel (e) measured absorption
coefficient from green channel with (f) filtering applied. (g) expected
reduced scattering coefficient from red channel (h) measured reduced
scattering coefficient from red channel with (i) filtering applied (j)
expected reduced scattering coefficient from green channel (k) measured
reduced scattering coefficient from green channel with (l) filtering applied.

##  4 Discussion

We have developed an ultra-miniature SFDI system and shown its capability to
quantitatively image differences in optical properties of typical
gastrointestinal conditions simulated in tissue-mimicking phantoms, providing
enhanced contrast. It is sufficiently small to fit in the instrument channel
of a standard colonoscope ($<3$mm). This work could therefore form the basis
of new devices suitable for cost-effective endoscopic deployment for screening
of gastrointestinal cancers.

This work has limitations that need further investigation before clinical
translation. The first limitation is the choice of wavelengths, which in these
experiments was $660$ and $515$ nm. By evaluating the absorption coefficient
at two wavelengths tissue information such as chromophore concentration can be
determined. Oxyhaemoglobin (HbO2) and deoxyhaemoglobin (Hb) are important
tissue optical properties because they can detect perfusion, which enables
differentiation between malignant and benign tumours[42] though wavelengths of
$670$ and $850$ nm are more commonly used [9]. Our system has two constraints
which make it challenging to extend to the NIR e.g. $850$ nm. First, the micro
camera module has an IR filter that blocks light in this range but future
versions may remove this. Secondly, the fiber array was designed for $660$ nm,
and therefore very lossy when using a $850$ nm laser, with $<$ 1% efficiency.
In future, a fiber array could be designed to operate successfully at both
$660$ and $850$ nm: indeed fiber arrays with low-coupling between cores and
that operate well into the NIR ($1550$ nm) are routinely used in
telecommunications[43].

The second limitation is the need for real time operation for clinical
application. Our analysis shows that it typically takes between 0.42s and
2.34s to obtain 3 suitable frames for SFDI (sufficient contrast with 3 shifted
phases) while the fiber is being manually perturbed. Though this gives an
effective SFDI frame rate of at most 2.4 fps, faster frame-rate cameras could
likely improve this: $>100$ fps cameras are widely available. If the system
were kept still it would take longer to acquire the 3 desired frames, but in
this case artificial phase perturbation could be introduced by means of a
phase-shifter or a mode scrambler on one of the fiber arms. However, the phase
tracking algorithm is currently relatively slow and runs offline (taking
several minutes), so does not allow for real-time operation. This could be
addressed by implementing the algorithm on a fast GPU that processes images as
they arrive. Alternatively, images with non-optimal phases could be used for
sinusoid fitting instead of waiting for 3 equispaced phases [44].

The third limitation is image quality, which is somewhat reduced by the non-
ideal illumination patterns produced by the fiber array. This causes both
noise and some inaccuracies in optical properties. The noise has been
partially addressed by varying the spatial frequency but could be further
improved by normalizing for laser power, using AI[45] for noise-reduction
reconstruction or building custom LUTs based on non-ideal projection
patterns[32]. The underestimation of absorption at larger absorption levels
can be up to 60%, though this too may be reduced by alternative calibration
procedures [39]. This does not appear to significantly impact the quantitative
maps of tissue produced, and, more importantly, still permits a suitably high
theoretical sensitivity and specificity. According to the American Society of
Gastrointestinal Endoscope (ASGE) guidelines, a new device requires $90$%
sensitivity and $80$% specificity in order to be used in lieu of biopsy
sampling [37]. Post-processing analysis of our data suggest the detection of
Barrett’s esophagus may fall just short of this, although this could be
improved by binning together pixels at the expense of spatial resolution.
However, we show that it is possible to exceed these values when comparing
healthy and squamous cell carcinoma models, achieving $>$99% sensitivity and
89.6% specificity. This shows that even in the presence of visually
perceptible noise, absorption and scattering when used in combination remain
sufficiently robust to provide maps of squamous cell carcinoma. However, we
note that our simulated values of sensitivity and specificity are probably
higher than what would be expected in a preclinical study as they do not
consider other confounding pathologies such as neoplasias or inflammation.

Further miniaturization of the device could look at the use of metasurfaces
for polarizers on the fiber tip[46], various fiber tip filters to image
different reflected wavelengths[47], or patterned surfaces to produce a
concentric circle illumination pattern required for wide-field imaging inside
tubular lumen.

##  5 Conclusion

We have shown the capability of an ultra-miniature ($3$ mm diameter) SFDI
system to detect quantifiable variances in absorption and reduced scattering
coefficients in tissue mimicking phantoms with errors of $15$% and $6$%
respectively, compared to a conventional bench-top SFDI system. Our device has
the capability to project two wavelengths simultaneously, enabling extraction
of additional properties such as tissue chromophore information. We fabricated
tissue-mimicking phantoms simulating typical gastrointestinal condition of
squamous cell carcinoma adjacent to healthy esophageal tissue, where the
absorption coefficient of squamous cell carcinoma is much greater than that of
healthy tissue and the reduced scattering coefficient is lower. We have shown
the capability of our system to image this variation at both one and two
wavelengths simultaneously, providing enhanced contrast between the two tissue
types. Because of its small size and therefore compatibility with endoscopic
deployment, we envisage this system could be used for cost-effective
endoscopic screening of gastrointestinal cancers.

### Disclosures

The authors declare no conflict of interest

### Acknowledgements

The authors acknowledge support from a UKRI Future Leaders Fellowship
(MR/T041951/1) and an EPSRC Ph.D. Studentship (2268555).

### Data, Materials, and Code Availability

The data presented in this study are available from the following source: [DOI
to be inserted later].

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###### List of Figures

  1. 1 Proposed ultra-miniature SFDI system (a) Schematic of fiber array in ultra-miniature SFDI system showing dual wavelength illumination simultaneously. Light passes from the two lasers into the fiber array via a selection of 7 single-mode fiber input ports. At the tip of the fused taper, the fibers are spaced in a hexagonal array, providing three possible spacings. Crossed polarizers are placed in front of the fiber tip and the micro camera to reduce specular reflections from the imaging sample. (b) Photograph of experimental set up. (c) Prototype device package of $3$ mm diameter with inset showing zoomed in view of fiber tip and camera.
  2. 2 Determining desired fiber spacing to produce spatial frequencies within our range of interest $0.1-0.3$ mm-1 (a) Addressable spatial frequency projection at working distances (WD) of $50$ mm (solid lines) and $30$ mm (dashed lines). The dotted lines represent the three possible fiber tip spacings of $5$, $8.66$ and $10$ $\mu$m (b) proposed design of spatial frequency projection at various working distances for fiber tip spacing (d) of $5$ $\mu$m (solid lines) and $2.5$ $\mu$m (dashed lines), useful for smaller working distances.
  3. 3 Characterization of fringes and phase tracking (a) image of selected zeroth frame and average of all frames, where $N$ is the total number of all frames within video capture, and corresponding cross sections. The single frame - averaged frames has had a smoothing filter applied (b) image of zeroth frame, $120^{\circ}$ shifted frame and $240^{\circ}$ shifted frame and corresponding cross sections, all with smoothing filters applied.
  4. 4 Raw performance of camera and projector (a) Image of USAF target captured with mini camera module taken with room lights on (b) image captured with mini camera module of dual wavelength projection from fiber tip showing extracted red and green channels respectively, (c) Direct capture on image sensor of projected fringe pattern, showing good fringe contrast within a region of circular interference.
  5. 5 Fiber array performance (a) phase of frames vs time (b) fringe contrast, defined as difference from maxima to minima of interference fringes detected vs time
  6. 6 Plot of average fringe envelope for 5 different captures using phantoms with different optical properties. Though the amplitude of the envelop varies in intensity, the position and shape stay relatively constant.
  7. 7 Comparison of bench-top SFDI system and ultra-miniature system: (a) absorption coefficient and (b) reduced scattering coefficient measured from bench-top system ($x$ axis) and ultra-miniature system ($y$ axis). Error bars represent the standard deviation across the image.
  8. 8 Imaging a phantom simulating esophageal tissue at 660nm: (a) white light image of two phantoms with different optical properties side by side (b) expected and (c) measured absorption coefficient of phantoms (d) measured absorption coefficient with smoothing filter applied (e) expected and (f) measured reduced scattering coefficient of phantoms (g) measured reduced scattering coefficient with smoothing filter applied. Expected optical properties are computed from the mean measured values of the individual phantoms measured in bench-top SFDI system.
  9. 9 Visual representation of averaging over several spatial frequencies to reduce speckle noise.
  10. 10 Optical properties measured from dual-wavelength imaging experiment: (a) expected absorption coefficient from red channel (b) measured absorption coefficient from red channel with (c) filtering applied (d) expected absorption coefficient from green channel (e) measured absorption coefficient from green channel with (f) filtering applied. (g) expected reduced scattering coefficient from red channel (h) measured reduced scattering coefficient from red channel with (i) filtering applied (j) expected reduced scattering coefficient from green channel (k) measured reduced scattering coefficient from green channel with (l) filtering applied.