Patent Application Publication Jan. 25,2024 Sheet 19 of 35. US 2024/0027680 Al

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US 2024/0027680 Al

between microparticle 225 and collimated light 204 main-
tained in product light 205, collected across time as well as
space, and has at least one spatial and one temporal property.
For example, an event in a spatio-temporal dataset describes
a spatial and temporal phenomenon that exists at a certain
time and location. Here, data acquired by spatio-temporal
profilometer 200 is collected for both physical space dimen-
sions and time of microparticle 225 in light-fluid interaction
volume 201.

[0054] Spatio-temporal profilometer 200 can be made of
various elements and components that are microfabricated,
Elements of spatio-temporal profilometer 200 can be various
sizes and can be made of a material that is physically or
chemically resilient in an environment in which spatio-
temporal profilometer 200 is disposed. Exemplary materials
include a metal, ceramic, thermoplastic, glass, semiconduc-
tor, and the like. The elements of spatio-temporal profilome-
ter 200 can be made of the same or different material and can
be monolithic in a single physical body or can be separate
members that are physically joined. In an embodiment,
elements are made of the same material. In an embodiment,
some elements include a different material than other ele-
ments.

[0055] In an embodiment, substrate 210 includes a cured
polymer. In an embodiment, flow of fluid 219 in fluid
channel 218 is parallel or orthogonal to propagation of
collimated light 204.

[0056] Substrate 210 can include a material that provides
flow in fluid channel 218. In an embodiment, substrate 210
is disposed in or included in a microfluidic device. Exem-
plary materials for substrate 210 include polymeric materials
such as elastomers (e.g., PDMS), epoxies and adhesives
(including tapes and photocurable adhesives), acrylics (¢.g..
PMMA), polycarbonates, polystyrenes, polyesters, polypro-
pylenes, cyclic olefin copolymers and hard materials, such
as glasses, semiconductor materials (e.g., pure and doped
silicon), and metals (e.g., aluminum). The region between
optical collimator exit wall 208 and fluid channel 218 is
transparent to collimated light 204. Substrate 210 can
include a combination of transparent, opaque, and reflective
boundaries to control light propagation in or through an
interior of spatio-temporal profilometer 200. In an embodi-
ment, substrate 210 includes light blocking member 270 that
absorbs, scatters, or reflects light out of the optical paths or
to prevent cross-talk between light paths.

[0057] _ It is contemplated that substrate 210 includes fluid
channel 218. In an embodiment, fluid channel 218 is made
in a curable polymer such as PDMS cast from a photoresist
pattern provided in a photolithographic process. In an
embodiment, fluid channel 218 is formed by laser oblation
or chemical etching of a material such as glass. Fluid
channel 218 can be made by milling, cutting, embossing,
and the like. Printing, e.g., 3D printing of substrate 210 can
form fluid channel 218 or other structural element of spatio-
temporal profilometer 200.

[0058] Dimensions of fluid channel 218 can be selected
based, e.g., on a type of flow through spatio-temporal
profilometer 200. Dimensions such as width (W) or height
(H) of fluid channel 218 (in direction X or Z) can be from
10 nm to | mm, specifically from 1 micrometer to 500
micrometers for fluid 219 such as liquid water. Dimensions
can depend on a speed of fluid 219 through flow controller
260 (e.g., a flow meter) or pressure on fluid 219. A shape of
fluid channel 218 can be, eg., rectangular, circular, or a

Jan. 25, 2024

combination thereof and can have a uniform or non-uniform,
cross section or can be confined to a straight line or fixed
within a single plane along its length. Fluid channel 218 can
include fluid channel sidewall 211 that bounds fluid channel
218 and that can curve, bend, split or include or a junction
that routes liquid in the flow system. It should be appreciated
that although FIG. 1 and other figures such as FIG. 7 show
straight fluid channel 218, such can be bent as indicated in
FIG. 12. A length (L) of fluid channel 218 can be selected
based on a size (e.g., a longest linear dimension or volume)
of light-fluid interaction volume 201 and that provides
selected convective or diffusion of fluid 219 between optical
interrogation zones. A length of fluid channel 218 can be
from 1 micrometer to 1 meter, specifically from 10 microm-
eters to 10 centimeters. In an embodiment, fluid channel 218
has a cross-section that is rectilinear, e.g., rectangular,
wherein a width and height are independently selected and
can be, e.g., 125 micrometers in one of the dimensions. In
an embodiment, fluid channel 218 is a glass capillary that
has an internal diameter of 150 micrometers.
[0059] Fluid channel entry 214 fluidically interconnects
fluid channel 218 to flow controller 260 that can be an
external source of fluid 219. Fluid channel exit 216 can
fluidically interconnect fluid channel 218 to a fluid sink.
Fluid channel entry 214 and fluid channel exit 216 can
transition in form and function to fluid channel 218 and can,
have similar cross-sectional dimensions. Additionally,
valves or bifurcations can control liquid flow to or in fluid
channel 218.

[0060] Fluid 219 flows through fluid channel 218 and can
be any suitable fluid that is compatible with fluid channel
218 such as a gas, liquid, or a combination thereof. It is
contemplated that fluid 219 includes microparticle 225 that
can include solid particles, compounds, or small molecules
disposed in a liquid or gas. Exemplary fluids 219 include
water, bodily fluids, and organic solvents such as alcohols
and fuels. The solid particles, compounds, and small mol-
ecules can include chemical compounds that absorb, scatter
or emit light such as fluorescent dyes, inorganic or organic
micro- or nano-particles, biological materials such as pro-
teins and protein aggregates. lipid vesicles, exosomes,
organelles and cells. Moreover, fluid 219 can include a
combination of a solution of different materials. In an
embodiment, fluid 219 includes microparticles 225. It
should be appreciated that microparticle 225 can be any size,
shape, or chemical compound including any of the previous
mentioned components, single molecules, conjugated mol-
ecules, polymers and the like, wherein microparticle 225 is
disposed in fluid 219, flows without obstructing fluid chan-
nel 218, and interacts in light-fluid interaction volume 201
with collimated light 204 to convert collimated light 204 to
product light 205 that exits light-fluid interaction volume
201 and is received by a detection waveguide (e.g., 230,
234).

[0061] Depending on substrate 210, fluid 219, or dimen-
sions of fluid channel 218, a pressure of fluid 219 in fluid
channel 218 can be from 0 Parscals (Pa) to 700 kPa,
specifically from 0 Pa to 130 kPa, and more specifically
from 0 Pa to 70 kPa. A viscosity of fluid 219 can be from
1x10-° to 1 Pa:s, specifically from 10x10-° to 0.1 Pa‘s, and
more specifically from 1x10~* to 0.01 Pa:s. Flow can be
unidirectional, and pressure can be positive or negative.
[0062] Fluid 219 can independently include reflective,
absorptive, fluorescent, reactive, or optically active mol-



US 2024/0027680 Al

SPATIO-TEMPORAL PROFILOMETER AND
PERFORMING TIME-RESOLVED SPATIAL
PROFILOMETRY FOR PRODUCING A
UNIFORM LIGHT PROFILE

CROSS REFERENCE TO RELATED,
APPLICATIONS

[0001] This application claims the benefit of U.S. Provi-
sional Patent Application Ser. No. 63/369,019 (filed Jul. 21,
2022), which is herein incorporated by reference in its
entirety.

STATEMENT REGARDING FEDERALLY
SPONSORED RESEARCH,
[0002] This invention was made with United States Gov-
ernment support from the National Institute of Standards and
‘Technology (NIST), an agency of the United States Depart-
ment of Commerce. The Government has certain rights in
this invention.

BRIEF DESCRIPTION

[0003] Disclosed is a spatio-temporal profilometer for
performing time-resolved spatial profilometry, the spatio-
temporal profilometer comprising: a substrate; a tapered
optical collimator waveguide disposed on the substrate and
that receives diverging light, internally reflects the diverging
light by internal reflections on collimating sidewalls of
tapered optical collimator waveguide, collimates the diverg-
ing light in response to the internal reflections on collimating
sidewall, produces intermediate light from the diverging
light due to the internal reflections, produces collimated
light from the intermediate light that is communicated from
the tapered optical collimator waveguide, such that the
tapered optical collimator waveguide comprises: an optical
collimator entry wall that receives diverging light and com-
municates diverging light into an interior of the tapered
optical collimator waveguide; the collimating sidewalls dis-
posed obliquely to the optical collimator entry wall and
comprising a first collimating sidewall and a second colli-
mating sidewall that obliquely opposes the first collimating
sidewall, such that the first collimating sidewall and the
second collimating sidewall internally reflect the diverging
light inside of the tapered optical collimator waveguide and
convert the diverging light to the intermediate light; and an
optical collimator exit wall obliquely disposed to the colli-
mating sidewall and opposing the optical collimator entry
wall and that receives the intermediate light from the interior
of the tapered optical collimator waveguide, and communi-
cates the intermediate light as collimated light, such that the
collimated light is collimated; a fluid channel in optical
communication with the tapered optical collimator wave-
guide and comprising: a fluid channel entry that receives a
fluid comprising microparticles and communicates the
microparticles into an interior of the fluid channel; fluid
channel sidewalls disposed along a length of the fluid
channel and that constrain flow of the fluid to the interior of
the fluid channel; and a fluid channel exit that communicates
the fluid out of the fluid channel; and a light-fluid interaction
volume disposed in the fluid channel and provided by an
overlap within the fluid channel of the collimated light from.
the tapered optical collimator waveguide and the fluid; and
a light-fluid interaction volume boundary that bounds the
light-fluid interaction volume at a periphery of the colli-

Jan. 25, 2024

mated light that propagates in the fluid channel, such that the
fluid channel receives the fluid with the microparticles and
the collimated light in the light-fluid interaction volume,
produces product light from the collimated light in response
to the microparticles interacting with the collimated light in
the light-fluid interaction volume, and communicates the
product light out of the fluid channel.

[0004] Disclosed is a process for performing time-re-
solved spatial profilometry, the process comprising: receiv-
ing diverging light by an optical collimator entry wall of a
tapered optical collimator waveguide of a spatio-temporal
profilometer, the spatio-temporal profilometer comprising: a
substrate; the tapered optical collimator waveguide disposed
on the substrate and comprising: the optical collimator entry
wall; collimating sidewalls disposed obliquely to the optical
collimator entry wall and comprising a first collimating
sidewall and a second collimating sidewall that obliquely
opposes the first collimating sidewall; and an optical colli-
mator exit wall obliquely disposed to the collimating side-
wall and opposing the optical collimator entry wall; a fluid
channel in optical communication with the tapered optical
collimator waveguide and comprising: a fluid channel entry;
fluid channel sidewalls in fluid communication with the fluid
channel entry and disposed along a length of the fluid
channel; and a fluid channel exit that communicates the fluid
out of the fluid channel; and a light-fluid interaction volume
disposed in the fluid channel and provided by an overlap
within the fluid channel of the collimated light from the
tapered optical collimator waveguide and the fluid; and a
light-fluid interaction volume boundary that bounds the
light-fluid interaction volume at a periphery of the colli-
mated light that propagates in the fluid channel; communi-
cating the diverging light from the optical collimator entry
wall, into an interior of the tapered optical collimator
waveguide; internally reflecting the diverging light between
the first collimating sidewall and the second collimating
sidewall inside of the tapered optical collimator waveguide
and collimating the diverging light in response to the internal
reflections on the collimating sidewalls; producing interme-
diate light from the diverging light due to the internal
reflections; receiving, by the optical collimator exit wall, the
intermediate light from the interior of the tapered optical
collimator waveguide; communicating the intermediate light
as collimated light from the optical collimator exit wall, such
that the collimated light is collimated; receiving, by the fluid
channel entry of the fluid channel, a fluid comprising
microparticles and communicating the microparticles into
an interior of the fluid channel; receiving, by the fluid
channel entry, the collimated light from the tapered optical
collimator waveguide; subjecting the microparticles to the
collimated light in the light-fluid interaction volume; pro-
ducing product light from the collimated light in response to
the microparticles interacting with the collimated light in the
light-fluid interaction volume; communicating the product
light out of the fluid channel; detecting the product light
from the fluid channel; and determining a spatial profile and
a temporal profile of the microparticles flowing in the
light-fluid interaction volume from the product light.

BRIEF DESCRIPTION OF THE DRAWINGS,

[0005] The following description cannot be considered
limiting in any way. Various objectives, features, and advan-
tages of the disclosed subject matter can be more fully
appreciated with reference to the following detailed descrip-


US 2024/0027680 Al

tapered optical collimator waveguide 221, or by including
light blocking structures, as shown in FIG. 17.

[0092] In an embodiment, performing time-resolved spa-
tial profilometry can include: flowing fluid 219 including
microparticle 225 through fluid channel 218; communicat-
ing fluid 219 with microparticle 225 to light-fluid interaction
volume 201; providing light from light source 250; com-
municating diverging light 202 from light source 250;
optionally communicating diverging light 202 in optical
fiber 240 to tapered optical collimator waveguide 221;
making collimated light 204 from diverging light 202 in
tapered optical collimator waveguide 221; communicating
collimated light 204 through optical collimator exit wall
208; and communicating collimated light 204 through sub-
strate 210 to light-fluid interaction volume 201 in fluid
channel 218; subjecting microparticle 225 to collimated
light 204; producing pulses of product light 205 that includ-
ing light transmission, scattering, absorbance, or fluores-
cence interactions; communicating product light 205 from
light-fluid interaction volume 201 to optical detector 251 via
forward light detection waveguide 230 or back light detec-
tion waveguide 234; recording signal pulses from product
light 205 sensed by optical detector 251; and computing
properties of microparticle 225 that inchide fluorescence
intensity, size, or velocity from magnitudes or shapes of
signal pulses.

[0093] In an embodiment, operating spatio-temporal pro-
filometer 200 for serial optical interrogation of micropar-
ticles 225 includes providing spatio-temporal profilometer
200 with a plurality of light-fluid interaction volumes 201
arranged along a length of fluid channel 218 with each
light-fluid interaction volume 201 having an input light path,
fluorescence/scatter light path, and transmission light path
for detection of light; acquiring multiple measurements of
microparticles 225 for measurement replication; acquiring
multiple measurements for velocimetry determination via a
time-of-flight microparticles 225 in a selected light-fluid
interaction volume 201; acquiring multiple measurements
for detection and separation of microparticles 225 that enter
a selected light-fluid interaction volume 201 simultaneously
or are aggregated.

[0094] In an embodiment, operating spatio-temporal pro-
filometer 200 for projecting collimated light 204 with modi-
fied ray density patterns includes subjecting different beams
of diverging light 202 to different tapered optical collimator
waveguide 221 having different taper angles and lengths,
and optical fiber stops; modulating the profiles of collimated
light 204 in light-fluid interaction volumes 201; and option-
ally designing the angles, lengths, and tapers by empirical
studies or by computational ray tracing models.

[0095] In an embodiment, spatio-temporal profilometer
200 takes light from a source such as a multimode wave-
guide (MMW) and creates a rectangular light profile across
a micron-to-millimeter sized microchannels based on total
internal reflection (TIR) of light into a microfluidic wave-
guide, Waveguides and microchannels can be made from
photolithography to define photoresist structures that are
formed in a polymer (silicone poly(dimethylsiloxane) or
PDMS) to create microchannels. Such can include a 125 pm
diameter MMW with a 105 um core diameter such that the
waveguide is filled with an optical adhesive with refractive
index of about 1.56.

[0096] FIG. 15 to FIG. 21 show various properties of
spatio-temporal profilometer 200.

Jan. 25, 2024

[0097] In an embodiment, a process for measuring the
properties of microparticle 225 in spatio-temporal profi-
lometer 200 includes the following. For a step-function
patterned or collimated light, absorbance versus time signal
has three regions that can include: a monotone decreasing
region; a constant region: and a monotone increasing region
(FIG. 22). Boundaries between these regions can be found,
e.g., by piecewise polynomial regression, constrained opti-
mization, and the like, The radius R and velocity v of
microparticle 225 can be determined in relation to the widths
w,, W2, and w, of (temporal) regions (1), (2), and (3)
according to the formulas, for example:

2Rvw,
2Revws
L-2R=ww,
LevQwyte,)

Lev(wshe,),

wherein L is the length in the flow direction of the collimated
step-function light. These equations are solved to find v and
R.

[0098] In an embodiment, digital signals processing was
used to annotate signal pulses with approximate signal
boundaries, background level, integrated area, height, and
width. Several approaches were used to estimate the change
points K,, K;, K,, and K, marking, respectively, the signal
onset, plateau initiation, end of plateau, and disappearance
of signal. For all methods, initial guesses for K, and K,, were
provided by the annotated integration bounds; guesses for
K, and K, were

ee

fit a egies

wherein FWHM (full width half max) is the width annota-
tion. The constrained minimization

ty <p <a3 <a

nin fore {

Sx <5

[0099] was performed where y is the original data and yg,
is the data fitted by a piecewise discontinuous linear fit with
segment boundaries at x1, x2, x3, and x4 estimating K,, K,,
K,, and K,, respectively. The intersections between the
linear fit lines were chosen as K,, Ky, Ky, and K,. FIG. 23
shows some results.

[0100] Spatio-temporal profilometer 200 and processes
disclosed herein have numerous beneficial and fills a need
for many aspects of optics and photonics applications. For
example, beam shaping and collimating a diffractive Gauss-
ian beam into a flat-top profile provides an increase in laser
pulse energy without increasing the processed spot area or
line width. Such modifications permit dosage delivery of
light into, an optofluidic flow measurement system or
cytometer. Such provides calculation or compensation of
measurements dependent on aggregate signal integration


Patent Application Publication Jan. 25,2024 Sheet 13 of 35. US 2024/0027680 Al

i

i
'
i
"

a

Multimode
Optical
Waveguide

Cladding J Cladding] /~ Cladding

Multimode Fiber Multimode Fiber
FIG. 13


US 2024/0027680 Al

12. The spatio-temporal profilometer of claim 1, further
comprising an optical detector in optical communication
with the forward light detection waveguide and that receives
the product light from the forward light detection wave-
guide.

13. The spatio-temporal profilometer of claim 1, further
comprising an out-of-plane light collector in optical com-
munication with the forward light detection waveguide and
that receives the product light from the fluid channel.

14. The spatio-temporal profilometer of claim 1, further
comprising a lens disposed between the optical collimator
exit wall of the tapered optical collimator waveguide and the
fluid channel and that receives the collimated light from the
tapered optical collimator waveguide and communicates the
collimated light to the fluid channel.

15. The spatio-temporal profilometer of claim 1, wherein
flow controller in fluid communication with the fluid chan-
nel and that provides the fluid to the fluid channel.

16. The spatio-temporal profilometer of claim 1, wherein
a cross-sectional shape of the tapered optical collimator
waveguide is rectilinear.

17. The spatio-temporal profilometer of claim 1, wherein
a cross-sectional shape of the fluid channel is rectilinear.

18. The spatio-temporal profilometer of claim 1, wherein
the substrate comprises a cured polymer.

19. The spatio-temporal profilometer of claim 1, wherein
flow of fluid in fluid channel is parallel or orthogonal to
propagation of collimated light.

20. A process for performing time-resolved spatial profi-
lometry with a uniform light profile, the process comprising:

receiving diverging light by an optical collimator entry

wall of a tapered optical collimator waveguide of a

spatio-temporal profilometer, the spatio-temporal pro-

filometer comprising:
a substrate;
the tapered optical collimator waveguide disposed on
the substrate and comprising:
the optical collimator entry wall:
collimating sidewalls disposed obliquely to the opti-
cal collimator entry wall and comprising a first
collimating sidewall and a second collimating
sidewall that obliquely opposes the first collimat-
ing sidewall; and

an optical collimator exit wall obliquely disposed to
the collimating sidewall and opposing the optical
collimator entry wall;

a fluid channel in optical communication with the
tapered optical collimator waveguide and compris-
ing:

a fluid channel entry;

fluid channel sidewalls in fluid communication with
the fluid channel entry and disposed along a length
of the fluid channel; and

Jan. 25, 2024

a fluid channel exit that communicates the fluid out
of the fluid channel; and
a light-fluid interaction volume disposed in the fluid
channel and provided by an overlap within the fluid
channel of the collimated light from the tapered
optical collimator waveguide and the fluid; and
a light-fluid interaction volume boundary that bounds
the light-fluid interaction volume at a periphery of
the collimated light that propagates in the fluid
channel;
communicating the diverging light from the optical col-
limator entry wall, into an interior of the tapered optical
collimator waveguide;
internally reflecting the diverging light between the first
collimating sidewall and the second collimating side-
wall inside of the tapered optical collimator waveguide
and collimating the diverging light in response to the
internal reflections on the collimating sidewalls;
producing intermediate light from the diverging light due
to the internal reflections;
receiving, by the optical collimator exit wall, the inter-
mediate light from the interior of the tapered optical
collimator waveguide;
communicating the intermediate light as collimated light
from the optical collimator exit wall, such that the
collimated light is collimated and has a uniform light
profile;
receiving, by the fluid channel entry of the fluid channel,
a fluid comprising microparticles and communicating
the microparticles into an interior of the fluid channel;
receiving, by the fluid channel entry, the collimated light
from the tapered optical collimator waveguide;
subjecting the microparticles to the collimated light in the
light-fluid interaction volume;
producing product light from the collimated light in
response to the microparticles interacting with the
collimated light in the light-fluid interaction volume;
communicating the product light out of the fluid channel;
detecting the product light from the fluid channel; and
determining a spatial profile and a temporal profile of the
microparticles flowing in the light-fluid interaction
volume from the product light.
21. The process of claim 20, further comprising:
receiving diverging light by the optical collimator entry
wall of a tapered optical collimator waveguide;
constraining, by the fluid channel sidewalls, flow of the
fluid to the interior of the fluid channel; and
communicating, by the fluid channel exit, the fluid out of
the fluid channel.

+e eee


US 2024/0027680 Al

[0151] The entrance angles can be limited below 0... by
pre-filtering the ray with a fiber optic of sufficiently low
numerical aperture.

[0152] The processes described herein may be embodied
in, and fully automated via, software code modules executed
by a computing system that includes one or more general
purpose computers or processors. The code modules may be
stored in any type of non-transitory computer-readable
medium or other computer storage device. Some or all the
methods may alternatively be embodied in specialized com-
puter hardware. In addition, the components referred to
herein may be implemented in hardware, software, firm-
ware, or a combination thereof.

[0153] Many other variations than those described herein
will be apparent from this disclosure. For example, depend-
ing on the embodiment, certain acts, events, or functions of
any of the algorithms described herein can be performed in
a different sequence, can be added, merged, or left out
altogether (e.g, not all described acts or events are necessary
for the practice of the algorithms). Moreover, in certain
embodiments, acts or events can be performed concurrently,
e.g., through multi-threaded processing, interrupt process-
ing, or multiple processors or processor cores or on other
parallel architectures, rather than sequentially. In addition,
different tasks or processes can be performed by different
machines and/or computing systems that can function
together.

[0154] Any logical blocks, modules, and algorithm el
ments described or used in connection with the embo
ments disclosed herein can be implemented as electronic
hardware, computer software, or combinations of both. To
clearly illustrate this interchangeability of hardware and
software, various illustrative components, blocks, modules,
and elements have been described above generally in terms
of their functionality. Whether such functionality is imple-
mented as hardware or software depends upon the particular
application and design constraints imposed on the overall
system. The described functionality can be implemented in
varying ways for each particular application, but such imple-
mentation decisions should not be interpreted as causing a
departure from the scope of the disclosure.

[0155] The various illustrative logical blocks and modules
described or used in connection with the embodiments
disclosed herein can be implemented or performed by a
machine, such as a processing unit or processor, a digital
signal processor (DSP), an application specific integrated
circuit (ASIC), a field programmable gate array (FPGA) or
other programmable logic device, discrete gate or transistor
logic, discrete hardware components, or any combination
thereof designed to perform the functions described herein.
A processor can be a microprocessor, but in the alternative,
the processor can be a controller, microcontroller, or state
machine, combinations of the same, or the like. A processor
can include electrical circuitry configured to process com-
puter-executable instructions. In another embodiment, a
processor includes an FPGA or other programmable device
that performs logic operations without processing computer-
executable instructions. A processor can also be imple-
mented as a combination of computing devices, e.g., a
combination of a DSP and a microprocessor, a plurality of
microprocessors, one or more microprocessors in conjunc-
tion with a DSP core, or any other such configuration.
Although described herein primarily with respect to digital
technology, a processor may also include primarily analog

Jan. 25, 2024
16

components. For example, some or all of the signal pro-
cessing algorithms described herein may be implemented in
analog circuitry or mixed analog and digital circuitry. A
computing environment can include any type of computer
system, including, but not limited to, a computer system
based on a microprocessor, a mainframe computer, a digital
signal processor, a portable computing device, a device
controller, or a computational engine within an appliance, to
name a few.

[0156] The elements of a method, process, or algorithm
described in connection with the embodiments disclosed
herein can be embodied directly in hardware, in a software
module stored in one or more memory devices and executed
by one or more processors, or in a combination of the two.
A software module can reside in RAM memory, flash
memory, ROM memory, EPROM memory, EEPROM
memory, registers, hard disk, a removable disk, a CD-ROM,
or any other form of non-transitory computer-readable stor-
age medium, media, or physical computer storage known in
the art. An example storage medium can be coupled to the
processor such that the processor can read information from,
and write information to, the storage medium. In the alter-
native, the storage medium can be integral to the processor.
The storage medium can be volatile or nonvolatile.

[0157] While one or more embodiments have been shown.
and described, modifications and substitutions may be made
thereto without departing from the spirit and scope of the
invention. Accordingly, it is to be understood that the present
invention has been described by way of illustrations and not
limitation. Embodiments herein can be used independently
or can be combined.

[0158] All ranges disclosed herein are inclusive of the
endpoints, and the endpoints are independently combinable
with each other. The ranges are continuous and thus contain
every value and subset thereof in the range. Unless other-
wise stated or contextually inapplicable, all percentages,
when expressing a quantity, are weight percentages. The
suflix (s) as used herein is intended to include both the
singular and the plural of the term that it modifies, thereby
including at least one of that term (e.g., the colorant(s)
includes at least one colorants). Option, optional, or option-
ally means that the subsequently described event or circum-
stance can or cannot occur, and that the description includes
instances where the event occurs and instances where it does
not. As used herein, combination is inclusive of blends,
mixtures, alloys, reaction products, collection of elements,
and the like.

[0159] As used herein, a combination thereof refers to a
combination comprising at least one of the named constitu-
ents, components, compounds, or elements, optionally
together with one or more of the same class of constituents,
components, compounds, or elements.

[0160] All references are incorporated herein by reference.
[0161] The use of the terms “a,” “an,” and “the” and
similar referents in the context of describing the invention
(especially in the context of the following claims) are to be
construed to cover both the singular and the plural, unless
otherwise indicated herein or clearly contradicted by con-
text. It can further be noted that the terms first, second,
primary, secondary, and the like herein do not denote any
order, quantity, or importance, but rather are used to distin-
guish one element from another. It will also be understood.
that, although the terms first, second, etc. are, in some
instances, used herein to describe various elements, these



US 2024/0027680 Al

Jan. 25, 2024 Sheet 23 of 35

Patent Application Publication

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US 2024/0027680 Al

ecules or particles that permit contrast in the presence of
collimated light 204. Fluid 219 can include fluorescein or
derivatives thereof. Specifically, a derivative can be fluo-
rescein-conjugated dextran or a CMNB-caged carboxyfluo-
rescein, or its derivatives. Fluid components can be selected
based on the wavelength of light to activate, deactivate, or
excite components of fluid 219. Components of fluid 219
can be selected on a diffusion coefficient, absorbance, or
emission spectra. Excitation, bleaching, and emission wave-
lengths independently can be from 240 nm and 1000 nm,
and specifically from 350 nm and 750 nm.

[0063] Waveguides (e.g., 220, 221, 230, 240) can be
disposed in substrate 210 as a microchannel, e.g., a void in
substrate 210. Optical fiber channel 220 and tapered optical
collimator waveguide 221 are in optical communication
with light source 250. back light detection waveguide 234
and forward light detection waveguide 230 can be in optical
communication with optical detector 251. Optical fiber 240
can be disposed along light paths. The light path can include
a bifurcation or optical element that changes a direction,
intensity, or spectrum of light along the light path.

[0064] Light source 250 can include a light-emitting diode
or laser that emits light at a desired wavelength. Properties
of diverging light 202 can be selected based on the desired
power density and spectral features or level of interaction
with microparticle 225 or other component of fluid 219.
[0065] Collimated light 204 can be used to induce fluo-
rescence, scatter, or absorption in fluid 219 in light-fluid
interaction volume 201. In an embodiment, fluid 219
includes fluorescein. Diverging light 202 that is used to
make collimated light 204 can be selected based on inter-
action with microparticle 225 and can have a wavelength
from 240 nm to 1000 nm, more specifically from 350 nm to
750 nm. In an embodiment, the wavelength of collimated
light 204 is from 450 nm to 500 nm, specifically from 470
nm to 490 nm. An intensity of collimated light 204 is
selected based on interaction with microparticle 225, nature
of flow of fluid 219, or desired characteristics of product
light 205. The intensity of collimated light 204 can be from
1 nanowatt (nW) to 1 W. In an embodiment, the intensity of
collimated light 204 is from 1 mW to 200 mW.

[0066] Tapered optical collimator waveguide 221 commu-
nicates collimated light 204 to light-fluid interaction volume
201 and is made from diverging light 202 via internal
reflection on collimating sidewall 207 that coverts diverging
light 202 to intermediate light 203 that ultimately is colli-
mated and leaves tapered optical collimator waveguide 221
from optical collimator exit wall 208 as collimated light 204.
Moreover, the light path can include a filter or bifurcation to
reduce intensity of collimated light 204 or direct part of
collimated light 204 to a light intensity meter. In an embodi-
‘ment, tapered optical collimator waveguide 221 is filled with
optical material that permits total internal reflection of
diverging light 202 and intermediate light 203. In an
embodiment, the optical material is a photocurable adhesive
that has a higher index of refraction than substrate 210. In an
embodiment, the optical material filling tapered optical
collimator waveguide 221 is dyed by a fluorescent com-
pound. In an embodiment, optical collimator exit wall 208.
In an embodiment, optical collimator exit wall 208 is curved
to shape collimated light 204 in light-fluid interaction vol-
ume 201. In an embodiment, tapered optical collimator
waveguide 221 has tapered collimating sidewalls 207 that
progressively increase a width of tapered optical collimator

Jan. 25, 2024

waveguide 221 along the propagation direction of diverging
light 202 in tapered optical collimator waveguide 221 to the
width of optical collimator exit wall 208. In an embodiment,
tapered optical collimator waveguide 221 has parabolic
collimating sidewalls 207. In an embodiment, collimated
light 204 has approximately uniform intensity across light-
fluid interaction volume 201. In an embodiment, an optical
element can be interposed between optical collimator exit
wall 208 and fluid channel 218 to modify a shape of
collimated light 204. The optical elements can be lenses that
narrow and focus collimated light 204 into a light sheet
through light-fluid interaction volume 201. In an embodi-
ment, optical fiber 240 is disposed in optical fiber channel
220 up to optical collimator entry wall 209. In an embodi-
ment, optical fiber 212 is inserted in tapered optical colli-
mator waveguide 221, e.g., to optical collimator exit wall
208. In an embodiment, optical fiber 212 is a 125-microm-
eter diameter multimode fiber that communicates visible
light.

[0067] Light-fluid interaction volume 201 is where colli-
mated light 204 interacts with microparticle 225 or other
components of fluid 219 to produce product light 205 that
can include fluorescence, bleaching, scattering, or absorp-
tion. In an embodiment, collimated light 204 induces
microparticle 225 to emit fluorescence. In an embodiment,
collimated light 204 causes microparticle 225 to emit fluo-
rescent light and microparticle 225 to bleach (e.g., be
optically changed by collimated light 204 to stop emitting
fluorescence). The intensity of collimated light 204 with the
amount of time microparticle 225 spends in light-fluid
interaction volume 201 (e.g., the speed of fluid 219) can
determine an amount of bleaching versus emitted fluores-
cence. In an embodiment, optical detector 251 is in optical
communication with, e.g. forward light detection wave-
guide 230, by optical fiber 240. In an embodiment, optical
fiber 240 is a 125-micrometer diameter multimode fiber that
carries a visible wavelength of light.

[0068] _ In spatio-temporal profilometer 200, microparticle
225 can be a deactivated state of microparticle 225, an
excited state of microparticle 225, or a modified variant of
microparticle 225. The type of microparticle 225 can be
selected based on an interaction time with input light, color
of emitted or scattered light, or an increase in signal to noise
ratio in photodetector 248.

[0069] Forward light detection waveguide 230 or other
detection waveguide, e.g, back light detection waveguide
234 or out-of-plane light collector 237, receives product
light 205 from light-fluid interaction volume 201 in fluid
channel 218 and can communicate product light 205 to
optical detector 251 or to some other member for analysis or
use either on substrate 210 or external to substrate 210.
Optical modification members such as a filter or bifurcation
can be included with, in, or after these waveguides and can
reduce the intensity of product light 205 or direct part of
product light 205 to optical detector 251 that can include,
e.g., a light intensity meter, spectrometer, and the like. In an
embodiment, forward light detection waveguide 230, back
light detection waveguide 234, or out-of-plane light collec-
tor 237 can be filled with optical material that permits total
internal refection of light. In an embodiment, the optical
material is a photocurable adhesive that has a higher index
of refraction than substrate 210. In an embodiment, forward.
light detection waveguide 230 includes a lens to focus
product light 205 into forward light detection waveguide



Patent Application Publication Jan. 25, 2024 Sheet 4 of 35 US 2024/0027680 Al

200
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26S
amr
Lato
m m 2 ?
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Patent Application Publication Jan. 25, 2024 Sheet 34 of 35 US 2024/0027680 Al

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cod <s < eS 3

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FIG. 31

Ohr

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US 2024/0027680 Al

Jan. 25, 2024 Sheet 20 of 35

Patent Application Publication

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Patent Application Publication

Length Experimental

Jan. 25, 2024 Sheet 26 of 35

US 2024/0027680 Al

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|
Relative Ray Density

0.5mm

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1.5mm

27mm

Effective Waveguide

Length

3.8mm

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Length

Eu

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Effective Waveguide

Length

Relative Ray Density

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Patent Application Publication Jan. 25,2024 Sheet 22 of 35. US 2024/0027680 Al



Patent Application Publication Jan. 25,2024 Sheet 35 of 35. US 2024/0027680 Al

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Patent Application Publication Jan. 25,2024 Sheet 17 of 35. US 2024/0027680 Al

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Patent Application Publication Jan. 25,2024 Sheet 9 of 35 US 2024/0027680 Al

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Patent Application Publication Jan. 25,2024 Sheet 32 of 35. US 2024/0027680 Al



US 2024/0027680 Al

Jan. 25, 2024 Sheet 29 of 35

Patent Application Publication

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Jan. 25, 2024 Sheet 18 of 35

US 2024/0027680 Al

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Patent Application Publication Jan. 25,2024 Sheet 8 of 35 US 2024/0027680 Al

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as) United States
a2) Patent Application Publication co) Pub. No.: US 2024/0027680 Al

Cooksey et al.

US 20240027680A1

(43) Pub. Date: Jan. 25, 2024

G4)

(7)

(72)

@)

(22)

(60)

SPATIO-TEMPORAL PROFILOMETER AND
PERFORMING IE-RESOLVED SPATIAL
PROFILOMETRY FOR PRODUCING A
UNIFORM LIGHT PROFILE

Applicant: Government of the United States of
America, as represented by the
Secretary of Commerce, Gaithersburg,
MD (US)

Inventors: Gregory Alan Cooksey, Gaithersburg,
MD (US); Paul Nathan Patrone,
Washington Grove, MD (US); Matthew
DiSalvo, Gaithersburg, MD (US); Jalal
Sadeghi, Gaithersburg, MD (US)

Appl. No.: 18/225,002
Filed: Jul. 21, 2023

Related U.S. Application Data

Provisional application No. 63/369,019, filed on Jul.
21, 2022.

200

Publication Classi

(51) Int. Cl.

cation

GO2B 6/10 (2006.01)
GO2B 6/42 (2006.01)
GO2B 2728 (2006.01)

(52) US.
exe G02B 6/105 (2013.01); GO2B 6/4206

(2013.01); G02B 27/283 (2013.01)

(57) ABSTRACT

A spatio-temporal profilometer performs time-resolved spa-
tial profilometry and includes a substrate, a tapered optical
collimator waveguide, a fluid channel, and a light-fluid
interaction volume. The tapered optical collimator wave-
guide receives diverging light, internally reflects it, and
collimates it. The fluid channel receives a fluid comprising
microparticles and communicates the microparticles into the
fluid channel. The light-fluid interaction volume is disposed
in the fluid channel and provided by an overlap within the
fluid channel of the collimated light from the tapered optical
collimator waveguide and the fluid. The spatio-temporal
profilometer produces product light from the collimated
light in response to the microparticles interacting with the
collimated light in the light-fluid interaction volume from
which is determined a spatial and temporal profile of
microparticles in the fluid channel.



US 2024/0027680 Al

th

propagation angle 8,, of rays prior to the m” successive
internal reflection, can be modeled (see Supplemental for
derivation) as

w
Q

Bm = 8 = 20m = Ve

mmo = {la m
0,

lee

lal<e

defining 6, as the initial positive angle of the ray, @ as the
sidewall angle of a waveguide of length L, and m,,, is the
maximum possible number of reflections the ray can
undergo before becoming effectively collimated. This model
assumes that the waveguide walls are perfectly smooth and
that incoming rays were angled below the critical angle of
the waveguide. The scenario of waveguides with a converg-
ing taper, that is, a2<a,, was not considered since it would
act to increase the ray angles, which would be detrimental in
applications requiring collimated light.

[0111] According to equation (1), the rate of change of ray
angle 6 proceeds at a constant velocity —29 rad per reflec-
tion. Intuitively, as reflecting rays lose inclination angle,
more travel distance is needed to reach subsequent reflec-
tions. The behavior of inter-reflection distances L,, can be
modeled by the recursive equation

hy re)

tang, +tangtang,.2% 2 | 1
SO a
liam, * tae)

[0112] Equation (3) describes the span of the m‘ reflection
of aray for the specific scenario where the ray initially enters
the waveguide positioned at its centerline and with a positive
angle of inclination. When ray angles approach the sidewall
angle, they cannot reflect again within the waveguide and
become effectively collimated. This asymptotic phenom-
enon is reproduced in the model, since mathematically the
limit of L,, approaches infinity as 8,,, approaches cp. Com-
plete model equations and derivations that consider arbitrary
ray entrance angles and entrance positions are presented in
the Supplemental.

[0113] An initial observation from equation (3) is that, due
to diminishing returns, complete collimation of a single ray
can require meter-long distances (FIG. 31). Yet, substantial
reductions in ray angle can be seen over only millimeters of
slightly tapered waveguides. For example, rays entering a
slightly diverging (25 mrad) waveguide at typical critical
angles (440 mrad) would reflect 8 times and exit the wave-
guide at 215 mrad, approximately half their initial angle.
Steeper incoming rays received the most reflective correc-
tions, and steeper waveguide tapers were more effective at
collimating over shorter distances. The results on single rays
were a preliminary validation of the 2D model.

[0114] Uniform Beam Shaping: Simulation & Validation
[0115] Hypothetical beam properties were explored using
raytracing simulations of the diverging waveguide model.
Beams were represented as ensembles of 10° single rays
exiting the waveguide, allowing them to be characterized via
Monte Carlo simulations (FIG. 25A). Periodic inhomoge-
neities in ray densities were observed in all simulations with
straight or angled waveguide tapers (FIG. 25A-C). Upon

Lm =

‘anf, — tang

Jan. 25, 2024

closer inspection, it was observed that rays initially near the
waveguide wall reflect much earlier than centrally posi-
tioned rays. This causes a depletion in rays near the wall and
concentration at the center. This imbalance is reversed
further down the waveguide, ultimately resulting in an
oscillatory pattern. Interestingly, these inhomogeneities
became less frequent for tapered waveguides, evidenced
both by simulations and experimental light field mapping
(FIG. 25C). Hypothetically, by maintaining uniform ray
densities over prolonged distances, tapered waveguides offer
an opportunity to tailor the geometries to emit more uniform
beams (FIG. 25D).

(0116] To characterize the effects of geometric factors on
beamshaping, five properties of simulated beams were quan-
tified: variability, divergence, sharpness, collimation, and
width (FIG. 26A). The frequency and magnitude of beam
variations decreased for longer waveguides, suggesting
damped oscillatory behavior (FIG. 26B). Greater taper
angles increased the oscillation magnitude. The simulated
beams with the least divergence were observed at greater
waveguide lengths and taper angles (FIG. 26C). With at least
1 mm of waveguide length, simulated beams had sharp
edges with <8 pm rise/fall distances (FIG. 26D). As
expected, the beams became wider and more collimated in
longer and more tapered waveguides (FIG. 26E-F). To
validate these findings, 3D COMSOL raytracing simulations
and optical experiments were performed. The number of
reflections, distances to reflections, and mixing phenomenon
were qualitatively in agreement between the 3D COMSOL
and 2D analytical simulations. Overall, the simulated beam
behavior was surprisingly complex given the simple geom-
etry of the diverging waveguide model.

[0117] Real-world beam profiles were characterized and
compared to simulations to address the predictive power of
the simulations. An uncertainty quantification (FIG. 27A) of
one representative uniform beam was simulated with various
uncertainties in geometries, including a profile variability
with divergence, sharpness, collimation, and width with a
mean metric value and standard error of the metric. These
uncertainties indicate theoretical limits to prediction accu-
racy. Experimental measurements from real-world beams
emitted by various different waveguides and microscopi-
cally profiled using fluorescent tracer dyes were generally
consistent with these theoretical limits (FIG. 27B). Initially,
some experimental beam profiles were observed with minor
asymmetry; similar asymmetries were recovered in simu-
lated profiles with minor misalignments (shifts/skews) in the
fiber positioning (FIG. 32). Thus, fiber alignment features
were added to waveguide designs to reduce the likelihood of
imperfect alignments. These results indicate the predictive
power of the model and ability to generate real-world CoLs
with different defined properties.

[0118] Simplified Beam Geometry Enables Optimized
Particle Size Analysis

[0119] The utility of CoLs for optofluidic measurements
was tested by incorporating tapered waveguides into an
optofluidic particle size analyzer (FIG. 29A). Two types of
CoLs were selected: a “high precision” CoL with an excep-
tionally sharp, collimated, and wide beam and “high
throughput” CoL with a narrower beam. The device
included a straight flow cell that was illuminated with a
series of eight perpendicular beams emitted by MMSMCs.
Microspheres flowed through the microchannel, passing the
excitation beam and obscuring the light being transmitted



Patent Application Publication Jan. 25,2024 Sheet 11 of 35 US 2024/0027680 Al

200

N\

n>
head

a2 <2)



Patent Application Publication Jan. 25, 2024 Sheet 10 of 35

US 2024/0027680 Al

210

=

7
oy Ne
aA]
06
12 aor at / 2)
\ a oo
nt
7 7 L__,--
m me of af ,
206
at
2
|
19-4
212


US 2024/0027680 Al

intensity across light-fluid interaction volume 201. In an
embodiment, tapered optical collimator waveguide 221 has
a rectilinear cross-section.

[0077] Light-fluid interaction volume 201 is a volume in
fluid channel 218 where collimated light 204 interacts with
fluid 219 and particularly, microparticle 225. In an embodi-
ment, collimated light 204 modifies microparticle 225. A
modification of microparticle 225 can include a chemical
modification such as uncaging or caging, fluorescence acti-
vation, photobleaching, and the like. In an embodiment,
microparticle 225 is a fluorophore or a caged-fluorophore
such as fluorescein or caged-fluorescein.

[0078] Spatio-temporal profilometer 200 can be made in
various ways. It should be appreciated that spatio-temporal
profilometer 200 includes a number of optical, electrical, or
mechanical components, wherein such components can be
interconnected and placed in communication (e.g., optical
communication, electrical communication, mechanical
communication, fluid communication, and the like) by
physical, chemical, optical, or free-space interconnects. The
‘components can be disposed on mounts that can be disposed
on a bulkhead for alignment or physical compartmentaliza-
tion. As a result, spatio-temporal profilometer 200 can be
disposed in a terrestrial environment or space environment.
Elements of spatio-temporal profilometer 200 can be formed
from suitable materials. According to an embodiment, the
elements of spatio-temporal profilometer 200 are formed
using chemical processing, microfabrication, or 3D printing
although the elements of spatio-temporal profilometer 200
can be formed using other methods, such as injection
molding or machining a stock material such as block of
material that is subjected to removal of material such as by
cutting, laser oblation, and the like. Accordingly, spatio-
temporal profilometer 200 can be made by additive or
subtractive manufacturing. The various layers thus formed
can be subjected to joining by bonding to form spatio-
temporal profilometer 200.

[0079] The process for making spatio-temporal profilome-
ter 200 can include defining fluid channel 218 and wave-
guides. The process for defining the flow channel can
involve subtractive manufacturing (eg. laser ablation,
engraving, cutting, etching, etc.) or additive manufacturing
(e.g. 3D printing, controlled deposition, templated substrate
growth, and the like) or photolithography to define topo-
graphic features that will become or will be used to produce
constituent elements of the flow meter. In an embodiment,
topographic features were produced on silicon wafers using
photolithography. A negative photoresist. polymer (e.g.,
SU8) was used as the photosensitive polymer to produce the
topographic patterns on a silicon wafer. In an embodiment,
the SU8 features were approximately the same height as the
optical fiber diameter. The SU8 features are typically treated
with a silane to facilitate removal of substrates after casting.
Alternative methods to produce topographic features include
milling and embossing of metals or plastics and/or etching
materials such as glass and silicon.

[0080] In an embodiment, features in substrate 210 are
produced by casting and curing a liquid material, such as
poly(dimethylsiloxane) (PDMS) against the topographic
features. Other exemplary casting materials include epoxy,
adhesives or curable polymers or melts. Alternative means
of fabricating a substrate in the milli or micro or nanoscale
size range include 3D printing, cutting, milling, laser writ-
ing, and embossing.

Jan. 25, 2024

[0081] In an embodiment, substrate 210 is bonded to
another substrate so as to form a bottom of the channel
features and to form open-ended microchannels that include
the flow member and light paths. In an embodiment, the
substrate is bonded to a flat surface of the same material as
the cast substrate so that the index of refraction of the
material is the same around the exterior of the light guides.
In an embodiment, the substrate and bonded layer were
PDMS and the bonding was performed by oxygen plasma
treatment of both layers prior to placing them together. In an
embodiment, the PDMS layers are bonded together using a
layer of liquid PDMS and the device bond following heat
treatment to cure the liquid PDMS. Other methods to form
the enclosed channels include using an adhesive such as
epoxies, double-sided tape, or a mechanical force provided
by a device such as a clamp or vacuum pump.

[0082] In an embodiment, the light paths (e.g., wave-
guides) are filled with a suitable material such as an optical
liquid or adhesive or matching fluid to produce total-internal
reflection and carry light along the waveguide. Alternatively,
the light paths can be formed by modifying the optical
properties of the substrate, e.g. by chemical, thermal, or
optical manipulation, such that these regions become
capable of confining and transmitting light as a waveguide.
As waveguides, the light paths then function to deliver light
to and collect light from material in light-fluid interaction
volume 201 of fluid channel 218. In an embodiment, the
light paths are filled with PDMS that has a higher crosslinker
ratio (e.g. 1:5). In an embodiment, the material filling the
light paths was a UV curable optical adhesive (c.g., com-
mercially available as Norland Optical Adhesive 88), which
has a higher index of refraction compared to PDMS.
[0083] In an embodiment, a process for making spatio-
temporal profilometer 200 includes incorporating optical
fiber 240 to transmit light from sources and detectors to and
from spatio-temporal profilometer 200. In an embodiment,
the height of waveguides for light paths was set to match the
diameter of bare optical fiber, and the width at the entrance
of the light path waveguide where the fiber is inserted is a
factor (e.g. 3 times) larger than the diameter of the fiber. In
an embodiment, the width of the light path channel tapers
down to width of the fiber or includes a partial closing of the
channel that is narrower than the fiber (e.g. 110 microm-
eters) to stop the fiber insertion at a certain point. Following
insertion of the fibers into the light path, curing was per-
formed for the coupling fluid with ultraviolet light or heat to
lock the fibers in place. Alternatively, waveguides can be
solid, and light can be launched into the such by gluing fibers
to the ends of light paths or focusing light into light paths
using optical elements.

[0084] In an embodiment, a process for making spatio-
temporal profilometer 200 includes casting hollow air-pock-
ets within PDMS substrate 210 located between tapered
optical collimator waveguide 221 and fluid channel 218. The
curvature of the interfaces between the PDMS and air
pockets formed lenses that narrowed and focused light
beams into light-sheet beams.

[0085] Spatio-temporal profilometer 200 has numerous
advantageous and unexpected benefits and uses. In an
embodiment, a process for performing time-resolved spatial
profilometry with a uniform light profile includes: receiving
diverging light 202 by an optical collimator entry wall 209
of a tapered optical collimator waveguide 221 of a spatio-
temporal profilometer 200, the spatio-temporal profilometer



Patent Application Publication Jan. 25,2024 Sheet 31 of 35. US 2024/0027680 Al

vamewmrady

Transmit
FIG. 28A
004 a a
= 008 J = 003F “3
20m } = 002} ;
> >
0.01 J 0.01F a
y ! ! f n |) ae re rae ar
05. 4 15 2 05. 4 15 2
Time (Samples) xo! Time (Samples) xi!
FIG. 28B
e Velocity
o Diameter | |

MAD error (%)

mo wo fF MO @&

f—)

Diameter (um)

FIG. 28C


US 2024/0027680 Al

through the channel. The time course of light transmission,
measured by silicon photodiodes, manifested as trapezoidal
pulse shapes with rounded comers. These shapes were
within a shape produced by convolution of a moving circle
with the laser profile. The pulse shapes were charactered as
consisting of three pronouncedly linear phases: a rise, pla-
teau, and fall phase with change points k,, k,, k,, and k,
marking, respectively, the signal onset, plateau initiation,
end of plateau, and disappearance of signal (FIG. 29B). For
an ideal CoL laser profile of width w as in FIG. 24, particle
velocity y and diameter D can be calculated as

@

6)

[0120] To accommodate the noise and uncertainty in real-
world systems, a linear model modifying equations (4-5)
was proposed:

Qk, + Kz + O3K3 + O4ky = AK = ©

Bins + Bats + Boks + Bans = OR = °

y

where the a and B are eight constants determined by
empirical calibration and the K are four estimates of the true
change points k. We note that “change points” refers to
instants of time at which some property of a signal changes
abruptly. Changepoint detection is an open problem in
signals processing, and the optimality of a suitable method
(inflection points, kneepoints, statistical thresholding, and
the like) is situation dependent, Thus, calibrations of equa-
tions (6-7) will likely depend on the method chosen to
determine K.

[0121] The metrology method was calibrated for accuracy
in determining the diameter and velocity of reference poly-
styrene microspheres. Particle sizes were obtained from a
linear calibration curve of obscuration magnitude to manu-
facturer’s specified sizes. Time-averaged particle velocities
were obtained from their time-of-flight between consecutive
interrogation beams.

[0122] This metrology approach was applied to a mixed
microparticles sample. The sample included polystyrene,
silica, polymethacrylate, and melamine resin microparticles
with nominal sizes within the 8 microns to 30 microns range.
These analytes have diverse, unspecified, and potentially
inhomogeneous optical properties (absorbance, index of
refraction) or shape (in the case of the silica particles) and
would be challenging to assess using scatter- or absorbance-
methods.

[0123] Simulation

[0124] All 2D ray simulations were calculated in MAT-
LAB using equations (sI-s6). Monte Carlo simulations of
beams were performed by modeling between 10* and 10°
individual rays in the waveguide with randomly sampled
initial positions and angles. Assuming the rays entering the
waveguide are guided rays at the near field of a step index
multimode fiber, the ray angles and positions be uniformly
distributed in 3D space. The uniform position distribution in

Jan. 25, 2024

3D can be projected across the waveguide cross-section to
arrive at the 1D distribution model

®

where r is the radius of the circular cross-section of the fiber
optic and x is the transverse distance across the fiber optic
along the plane of the coupled waveguide. Beams produced
by the waveguide were modeled over a 200 um span beyond
the top of the waveguide, where microfluidic channels
would be situated. Constraints to the waveguide geometric
parameters were added based on real-world fabrication
limitations. To fabricate the waveguides using our previ-
ously developed lithographic approaches, the waveguide
depth, length, and breadth would be limited to =100 ym, <2
cm, and <500 um. The 100 pm depth allows butt-coupling
of a typical 105 um diameter 0.1 NA fiber directly to the
waveguide channel in a single-layer device. The 2 cm length
matches the maximum device footprints that are practical for
standard wafer processing. Lastly, the breadth limit of 500
hm maintains structurally sound channel aspect ratios below
Sih.

[0125] Beam width was measured by the full width half
max (FWHM). Beam divergence was quantified by the
fraction of total ray density falling within the exit aperture
of the diverging waveguide. Beam rise time was calculated
as the distance taken for the beam profile to rise from 2% to
50% of the beam intensity. Beam variability was quantified
by the coefficient of variation of the beam profile between
the FWHM crossing points. To reduce the effect of ray shot
noise on estimates of beam variability, the profile was first
smoothed by a central moving average filter with width
equal to 4% the signal FWHM. Beam collimations was
calculated as the proportion of actual ray reflections to the
maximum possible ray reflections m,,,, according to equa-
tion (2).

[0126] 3D simulations were performed by COMSOL Mul-
tiphysics following the assumptions from the 2D model.
[0127] | Microfabrication

[0128] The 2D-taper-based MMSMC and the microfluidic
channels were formed as a single layer using photolithog-
raphy and soft lithography as reported previously. Templates
were created from SU-8 2100 negative photoresist that was
spin-coated on silicon wafers and exposed using a 395 nm
laser writer (MLA 150, Heidelberg Instruments). After
development and thermal curing at 200° C., the templates
were functionalized by vapor deposition with trichloro (1H,
1H,2H,2H perfluorooctyl) silane. Devices were cast in poly
(dimethylsiloxane) (PDMS, Sylgard 184, refractive
index» 1.42) by pouring PDMS over the master wafer and
curing for 3 hours at 70° C. Fluidic inlets and outlet
were formed by punching 0.75 mm diameter bores through
the mold. A flat PDMS substrate was bonded to the mold to
seal the waveguides and microfluidic channel. Bonding was
performed by mating both surfaces either after 30 s oxygen
plasma treatment (Plasma Preen, Plasmatic Systems Inc.) or
alternatively after contact ping both surfaces with
PDMS crosslinker. The waveguide channels were filled with
optical adhesive (refractive index of 1.56 when cured) and
degassed. Stripped and cleaved multimode optical fibers
(105 um core diameter and 125 ym cladding diameter) with
0.1 or 0.22 numerical aperture were inserted into the wave-



US 2024/0027680 Al

Jan. 25, 2024 Sheet 30 of 35

Patent Application Publication

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US 2024/0027680 Al

[0032] FIG. 27 shows, according to some embodiments,
formation of high-quality Col. despite uncertainty in in
silico predictions for simulated 2D ray heatmaps and 1D
profiles for a selection of CoL beams of different widths.
[0033] FIG. 28 shows, according to some embodiments,
particle velocimetry and size analysis facilitated by CoLs.
(A) Photograph of an optofluidic microdevice with inte-
grated tapered waveguides. Inset below: Annotated fluores
cence microscopy image of optical interrogation regions
with labeled liquid flowing past the CoL beam. (B) Analysis
of transmission signals produced as a flowing particle
occludes the CoL beam. (C) Calibration results.

[0034] FIG. 29 shows, according to some embodiments,
particle velocimetry and size analysis of heterogenous
mixed samples, particularly, brightfield microscopy images
of microparticle beads.

[0035] FIG. 30 shows, according to some embodiments,
geometric optics model for propagating rays in a diverging
waveguide. (A) Schematic and coordinate system for mod-
cling sequential reflections of a ray (solid black arrow)
traveling through a diverging waveguide (grey trapezoid)
via total internal reflection. (B) Detailed cutaway schematics
for an initial reflection (left of axis break) as well as for an
arbitrary m-th reflection (right of axis break). Only the top
half of the waveguide is shown.

[0036] FIG. 31 shows, according to some embodiments,
single-ray simulation results with plots of the relationship
between propagation angle, waveguide length, entrance
angle, and taper angle.

[0037] FIG. 32 shows, according to some embodiments,
simulated beam profiles emitted from tapered waveguides of
different lengths with a 0.5 degree bias to the alignment axis
of the fiber.

DETAILED DESCRIPTION.

[0038] A detailed description of one or more embodiments
is presented herein by way of exemplification and not
limitation.

[0039] The collimation of light is an important concept in
optics. It is used in a wide variety of applications, such as
laser alignment, microscopy, spectroscopy, and cytometry.
Collimated light is light that propagates in parallel rays,
while divergent light spreads out during propagation. Con-
ventional ways to make collimated light from divergent light
include using a lens, a mirror, or combination of lenses and
mirrors. A lens is a curved optic that bends light rays. When
a divergent light beam passes through a lens, the lens bends
the rays to attempt to produce rays that travel in parallel. The
focal length of the lens determines how well the light is
collimated. The longer the focal length, the higher the degree
of collimation. A mirror includes a surface that reflects light
rays. When a divergent light beam is incident on a mirror, the
mirror reflects the rays to attempt to produce lights rays that
propagate in parallel. The type of mirror that is used affects
how well the light is collimated. A parabolic mirror has been
found to one of the most effective type of mirror for
collimating light. In some cases, a combination of lenses and
mirrors are used to attempt to collimate light, e.g., when the
light source is large or for increased collimation. Some of the
factors that affect the collimation of light include: the size of
the light source, wherein the smaller the light source, the
better the collimation; distance between the light source and
the collimating device, wherein the closer the light source is
to the collimating device, the better the collimation; or focal

Jan. 25, 2024

length of the collimating device, wherein the longer the focal
length, the better the collimation. However, conventional
technology including just mirrors or lenses, alone or in
combination, fail to provide high degree of collimation
suitable for acquiring highly resolved temporal and spatial
data from flowing microparticles. Spatio-temporal profi-
lometer 200 overcomes the technical limitations of such
conventional technology and provides highly-resolved tem-
poral and spatial data for flowing microparticles.
[0040] | It is technically challenging to make uniform light
profiles inside microfluidic devices. Controlling the unifor-
mity and spatial extent of light within microsystems permits
robust fabrication and improves measurement capabilities.
Conventional optical interfaces to microscopes involve
cumbersome optics or spatial light modulators that can have
limited adaptability and high fabrication or computational
complexity. There is a long-standing an unmet need to
improve the measurement of materials in optofluidic devices
used in flow cytometry and imaging with uniform light
profiles that have sharp boundaries. Spatio-temporal profi-
lometer 200 fills this need, is easy and inexpensive to make,
is adaptable to many systems, is durable, and is small in size
and does not require additional optical components.

[0041] It has been discovered that spatio-temporal profi-
lometer 200 receives and modifies light from an input source
with eflicient output and proj a uniform light beam
across a microfluidic interrogation region. Spatio-temporal
profilometer 200 has an integrated structure that can include
an optical waveguide of a particular shape that creates a
collimated and uniform light beam in an absence of certain
optical elements such as lenses to produce collimated light
that is free from common sources of aberration. Spatio-
temporal profilometer 200 solves the problem of creating
wide, optical beams that have uniform intensity through
their cross section. Spatio-temporal profilometer 200 and
such light profiles are useful in optical measurement sys-
tems, including optofluidic applications such as cytometry
and imaging. Advantageously, spatio-temporal profilometer
200 provides optical output that is a uniform top-hat or
flat-top illumination profile emanating in 3 dimensions.
[0042] Spatio-temporal profilometer 200 performs time-
resolved spatial profilometry. In an embodiment, with ref-
erence to FIG. 1, FIG. 2, FIG. 3, FIG. 4, FIG. 5, FIG. 6, FIG.
7, FIG. 8, FIG. 9, FIG. 10, FIG. 11, and FIG. 12, spatio-
temporal profilometer 200 includes: substrate 210; tapered
optical collimator waveguide 221 disposed on substrate 210
and that receives diverging light 202, internally reflects
diverging light 202 by internal reflections on collimating
sidewalls 207 of tapered optical collimator waveguide 221,
collimates diverging light 202 in response to the internal
reflections on collimating sidewall 207, produces interme-
diate light 203 from the diverging light 202 due to the
internal reflections, produces collimated light 204 from
intermediate light 203 that is communicated from tapered
optical collimator waveguide 221, such that tapered optical
collimator waveguide 221 includes: optical collimator entry
wall 209 that receives diverging light 202 and communicates
diverging light 202 into an interior of tapered optical colli-
mator waveguide 221; collimating sidewalls 207 disposed
obliquely to optical collimator entry wall 209 and including
a first collimating sidewall 207 and a second collimating,
sidewall 207 that obliquely opposes the first collimating
sidewall 207, such that the first collimating sidewall 207 and
the second collimating sidewall 207 internally reflect the



US 2024/0027680 Al

diverging light 202 inside of tapered optical collimator
waveguide 221 and convert diverging light 202 to interme-
diate light 203; and an optical collimator exit wall 208
obliquely disposed to collimating sidewall 207 and opposing
optical collimator entry wall 209 and that receives interme-
diate light 203 from the interior of tapered optical collimator
waveguide 221, and communicates intermediate light 203 as
collimated light 204, such that collimated light 204 is
collimated; fluid channel 218 in optical communication with
tapered optical collimator waveguide 221 and including:
fluid channel entry 214 that receives fluid 219 including
microparticles 225 and communicates microparticles 225
into an interior of fluid channel 218; fluid channel sidewalls
211 disposed along a length of fluid channel 218 and that
constrain flow of fluid 219 to the interior of fluid channel
218; and fluid channel exit 216 that communicates fluid 219
out of fluid channel 218; and light-fluid interaction volume
201 disposed in fluid channel 218 and provided by an
overlap within fluid channel 218 of collimated light 204
from tapered optical collimator waveguide 221 and fluid
219; and light-fluid interaction volume boundary 206 that
bounds light-fluid interaction volume 201 at a periphery of
collimated light 204 that propagates in fluid channel 218,
such that fluid channel 218 receives fluid 219 with micropar-
ticles 225 and collimated light 204 in light-fluid interaction
volume 201, produces product light 205 from collimated
light 204 in response to microparticles 225 interacting with
collimated light 204 in light-fluid interaction volume 201,
and communicates product light 205 out of fluid channel
218.

[0043] In an embodiment, spatio-temporal profilometer
200 includes optical fiber channel 220 disposed on substrate
210 in optical communication with tapered optical collima-
tor waveguide 221 and that receives diverging light 202 and
communicates diverging light 202 to tapered optical colli-
mator waveguide 221. In an embodiment, spatio-temporal
profilometer 200 includes optical fiber 212 disposed in
optical fiber channel 220 in optical communication with
tapered optical collimator waveguide 221 and that receives
diverging light 202 and communicates diverging light 202 to
tapered optical collimator waveguide 221.

[0044] In an embodiment, spatio-temporal profilometer
200 includes forward light detection waveguide 230 dis-
posed on substrate 210 in optical communication with fluid
channel 218 and that receives product light 205 that propa-
gates in a forward direction from fluid channel 218 with
respect to collimated light 204. In an embodiment, forward
light detection waveguide 230 is a straight waveguide or
tapered waveguide. In an embodiment, optical fiber 212 is
disposed in forward light detection waveguide 230, receives
product light 205, and communicates product light 205 to
optical detector 251.

[0045] In an embodiment, spatio-temporal profilometer
200 includes back light detection waveguide 234 disposed
on substrate 210 in optical communication with fluid chan-
nel 218 and that receives product light 205 that propagates
in a forward direction from fluid channel 218 with respect to
collimated light 204. In an embodiment, light blocking
member 270 is disposed on substrate 210 in optical com-
munication with tapered optical collimator waveguide 221,
is optically interposed between back light detection wave-
guide 234 and tapered optical collimator waveguide 221,
and blocks the light from being communicated between
tapered optical collimator waveguide 221 and back light

Jan. 25, 2024

detection waveguide 234. In an embodiment, optical fiber
212 is disposed in back light detection waveguide 234,
receives product light 205, and communicates product light
205 to optical detector 251

[0046] In an embodiment, spatio-temporal profilometer
200 includes light source 250 disposed on substrate 210 in
optical communication with tapered optical collimator
waveguide 221 and that produces diverging light 202 and
communicates diverging light 202 to tapered optical colli-
mator waveguide 221.

[0047] In an embodiment, spatio-temporal profilometer
200 includes flow controller 260 in fluid communication
with fluid channel 218 and that provides the fluid 219 to fluid
channel 218.

[0048] In an embodiment, spatio-temporal profilometer
200 includes optical detector 251 in optical communication
with forward light detection waveguide 230 and that
receives product light 205 from forward light detection
waveguide 230.

[0049] In an embodiment, spatio-temporal profilometer
200 includes out-of-plane light collector 237 in optical
communication with forward light detection waveguide 230
and that receives product light 205 from fluid channel 218.
[0050] In an embodiment, spatio-temporal profilometer
200 includes a lens disposed between optical collimator exit
wall 208 of tapered optical collimator waveguide 221 and
fluid channel 218 and that receives collimated light 204 from
tapered optical collimator waveguide 221 and communi-
cates collimated light 204 to fluid channel 218.

[0051] In an embodiment, flow controller 260 is in fluid
communication with fluid channel 218 and provides fluid
219 to fluid channel 218.

[0052] In an embodiment, spatio-temporal profilometer
200 includes: a substrate; a microchannel that accepts an
optical fiber and contains a tapered waveguide structure; a
microchannel that accepts flow of a fluid; and a fluid in a
microchannel that can include molecules such as fluorescein
or particles such as cells. In an embodiment, spatio-temporal
profilometer 200 includes: a light source that communicates
input light to a tapered waveguide structure or to an optical
fiber that is inserted into optical fiber insertion channel in
tapered waveguide structure; an aperture at the end of the
tapered waveguide structure that communicates light to the
flow channel; an optical interrogation region where light
communicated from the light source and modified by the
tapered waveguide channel to form patterned light that
interacts with chemical or particles within a fluid; a trans-
mission light collecting structure that receives light from the
optical interrogation region and communicates light to an
optical detector for transmitted light, such that communica-
tion of transmission light also can occur through an optical
fiber intermedi and a fluorescence or scatter collecting
waveguide that receives fluorescence or scattered light from
the optical interrogation region and communicates that light
to an optical detector for said light. It is contemplated that
additional fluorescence or scatter collecting waveguides can
be arranged in other orientations that can be different than or
the same as the first such waveguide.

[0053] _ It should be appreciated that spatio-temporal refers
to both space and time. Spatio-temporal profilometer 200 is
a device that acquires data for microparticle 225 that is
localized at a discrete set of locations in both space and time
within light-fluid interaction volume 201. Each data point
represents the time and location of an interaction event



Patent Application Publication Jan. 25,2024 Sheet 27 of 35 US 2024/0027680 Al

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US 2024/0027680 Al

from the laser spot. In addition, making a well-defined and
uniform laser profile with a well-defined border between
illuminated and non-illuminated zones provides advantages
for cytometry that include measurement of the size and
velocity of objects in flow, wherein, with reference to FIG.
15, velocity is determined deduced as time between entrance
to decay of signal and width being the time from entrance to
peak of signal.

[0101] The articles and processes herein are illustrated
further by the following Example, which is non-limiting.

EXAMPLE

[0102] Uniform beam shaping using all-polymer inte-
grated waveguides for optofluidic particle analyzers

[0103] Optical measurements are widely useful for ana-
lyzing microparticles such as cells, microplastics, mineral
aerosols in clinical, environmental, and geological fields.
Optofluidic instruments, such as flow cytometers, velocime-
s, or fluid spectrometers, comprise a major category of
optical devices that rely on shining beams of light to sense
and/or effect particles within fluids. For maximum perfor-
mance, the microfluidics at the heart of such instruments
require carefully designed beam interfaces to precisely
transmit light to and from analysis regions. However, precise
micro control of beam shape and uniformity is a technical
challenge and practical options available for instruments are
limited. Despite advances in advanced micro-optics, tradi-
tional, bulky, and alignment-prone lenses are still common
choices for beam shaping. Furthermore, interfaces to micro-
fluidics lack versatility for beam shaping, with a majority
using single-mode fiber optics that impose a Gaussian-
shaped profile to transmitted beams. Limitations in crafting
appropriate sensing interfaces can be a reason that micro-
fluidic chips have not achieved parity with electronic chips
in terms of ubiquity or commercial success, despite the large
promise of MEMs devices.

[0104] A highly desirable—but challenging to realize
beam shape for optofluidics particle analyzers is a uniform
rectangular prism, or “cube of light” (CoL). Optically, an
idealized CoL can be described as a collimated light field
with 1) rectangular boundaries, 2) excellent uniformity in all
dimensions, and 3) low dispersion side lobes. CoLs promise
high coupling efficiency with optofluidics, since the recti-
linear shape of a CoL matches the rectilinear shape of many
microfluidic channels. The uniformity and collimation of a
Col. would simplify measurements by eliminating angular
and spatial factors from measurements of particles passing
the beam. CoL could provide tight spatial control over
measurements because their low dispersion allows the for-
mation of a sharp boundary between the illuminated and
non-illuminated region of microfluidics.

[0105] Several approaches exist that make real-world
approximations for CoLs, but substantial tradeoffs exist
between beam uniformity, geometry, and of coupling to
microfluidics. In the near-field, multimode optical wave-
guides (MMOWs) with low numerical aperture can appear
as a quasi-flat-top spot, but this mode quickly dissipates
away from the fiber, making it impractical for uniform
excitation of a broad region of interest in a microfluidic
channel. Recent work has enabled shaping outputs of
MMOWs in the far-field, but relies on complex, adaptive
shaping of the input field wavefront using spatial light
modulators or binary optical elements. These involve many
prisms and lens elements, which cannot fit on-chip, and can

Jan. 25, 2024

introduce speckle patterns that substantially reduce the beam
uniformity, sharpness, and rectangularity. Chip-scale beam
shaping using transformation optics with solid dielectric
materials or liquid waveguides is a promising new research
area. However, work remains to be done to fully resolve
issues such as instability in the cross-section profile of the
beam. Previously, we demonstrated an alignment-free
method to interface fiber optics with planar waveguides for
facile coupling to microfluidic flowmeters and flow cytom-
eters. This method used micromolding to create 3D wave-
guides, which marked a substantial simplification over past
methods requiring multiple lithography, oxidation, and
chemical or plasma etching steps. However, these wave-
guides produced either dispersed beam profiles or pseudo-
Gaussian profiles with low transmission efficiency. Overall,
new strategies are needed to create chip-scale, uniform CoLs
using integrated optics.

[0106] We overcame complex beam shaping processes by
designing a delivery waveguide that produces a desirable
rectangular beam profile without lenses. A novel single-
layer, planar waveguide with 2D-taper-based geometry is
proposed for efficiently collimating spatially uniform beams
originating from fiber optics. Using analytical models,
numerical simulation, and experimental testing, waveguide
geometries for facile, chip-scale microfluidic integration are
characterized. Lastly, the diverging waveguide was inte-
grated into a microfluidic device to create a microparticle
analysis instrument. The rectangular light profile enabled
automated digital processing of the instrument’s optical
signals and a new metrology technique is demonstrated for
measuring absolute size and velocity of microparticles.
[0107] Design Approach

[0108] The optical interrogation of particles in flow ana-
lyzers is an inherently complex measurement system involv-
ing the interplay of fluidic, optical, and kinematic phenom-
ena. Yet, we identified an idealized light obscuration
scenario (FIG. 24A) that offers a straightforward mechanism
for measuring particle size and velocity. A sphere passing
perpendicularly to a perfectly collimated, uniform, and
sharp-edged beam would obscure the light with a distinct
“pulse-shaped” temporal profile. The duration of the pulse
plateau relates to the particle velocity; the rise and fall time
of the pulse relates to the particle diameter. Real-world fiber
optics for light delivery, however, are unideal for this
purpose because they disperse rays and output non-uniform
(ie., Gaussian) beam profiles. Here, a tapered waveguide
redirects rays emanating from multimode fiber optics. It may
be possible to use a tapered waveguide as a microscale
approximation of a traditional parabolic mirror and project
collimated beams from a disperse light source (FIG. 24B).
[0109] Theoretical Principles of Collimation by a Diverg-
ing Waveguide

[0110] From the ray optics point of view, a planar guided
ray exiting a fiber optic will propagate through a butt-
coupled straight-walled waveguide through total internal
reflection with a constant reflection angle. In contrast, rays
propagated in waveguides constructed with angled sidewalls
undergo variable reflection angles. Given a diverging wave-
guide geometry (a,<a,, where a, and a, are the widths of the
waveguide entrance and exit apertures, respectively), guided
rays proceed down the waveguide with ever-decreasing
reflection angles (FIG. 24B). The successive reflections in a
diverging waveguide cause the ray’s propagation angle to
progressively align with the axis of the waveguide. The



US 2024/0027680 Al

200 including: a substrate 210; the tapered optical collimator
waveguide 221 disposed on the substrate 210 and including:
the optical collimator entry wall 209; collimating sidewalls
207 disposed obliquely to the optical collimator entry wall
209 and comprising a first collimating sidewall 207 and a
second collimating sidewall 207 that obliquely opposes the
first collimating sidewall 207; and an optical collimator exit
wall 208 obliquely disposed to the collimating sidewall 207
and opposing the optical collimator entry wall 209: a fluid
channel 218 in optical communication with the tapered
optical collimator waveguide 221 and including: a fluid
channel entry 214; fluid channel sidewalls 211 in fluid
communication with the fluid channel entry 214 and dis-
posed along a length of the fluid channel 218; and a fluid
channel exit 216 that communicates the fluid 219 out of the
fluid channel 218; and a light-fluid interaction volume 201
disposed in the fluid channel 218 and provided by an overlap
within the fluid channel 218 of the collimated light 204 from
the tapered optical collimator waveguide 221 and the fluid
219; and a light-fluid interaction volume boundary 206 that
bounds the light-fluid interaction volume 201 at a periphery
of the collimated light 204 that propagates in the fluid
channel 218; communicating the diverging light 202 from
the optical collimator entry wall 209, into an interior of the
tapered optical collimator waveguide 221; internally reflect-
ing the diverging light 202 between the first collimating
sidewall 207 and the second collimating sidewall 207 inside
of the tapered optical collimator waveguide 221 and colli-
mating the diverging light 202 in response to the internal
reflections on the collimating sidewalls 207; producing
intermediate light 203 from the diverging light 202 due to
the internal reflections; receiving, by the optical collimator
exit wall 208, the intermediate light 203 from the interior of
the tapered optical collimator waveguide 221; communicat-
ing the intermediate light 203 as collimated light 204 from
the optical collimator exit wall 208, such that the collimated
light 204 is collimated and has a uniform light profile;
receiving, by the fluid channel entry 214 of the fluid channel
218, a fluid 219 comprising microparticles 225 and com-
municating the microparticles 225 into an interior of the
fluid channel 218; receiving, by the fluid channel entry 214,
the collimated light 204 from the tapered optical collimator
waveguide 221; subjecting the microparticles 225 to the
collimated light 204 in the light-fluid interaction volume
201; producing product light 205 from the collimated light
204 in response to the microparticles 225 interacting with
the collimated light 204 in the light-fluid interaction volume
201; communicating the product light 205 out of the fluid
channel 218; detecting the product light 205 from the fluid
channel 218; and determining a spatial profile and a tem-
poral profile of the microparticles 225 flowing in the light-
fluid interaction volume 201 from the product light 205
[0086] In an embodiment, performing time-resolved spa-
tial profilometry includes receiving diverging light 202 by
the optical collimator entry wall 209 of a tapered optical
collimator waveguide 221; constraining, by the fluid channel
sidewalls 211, flow of the fluid 219 to the interior of the fluid
channel 218; and communicating, by the fluid channel exit
216, the fluid 219 out of the fluid channel 218.

[0087] Accordingly, spatio-temporal profilometer 200
converts diverging light into a uniform or patterned intensity
and collimated beam projected within a roughly rectangular
cross section of fluid channel 218 and has the unexpected
advantage of making measurements of light-matter interac-

Jan. 25, 2024

tions independent of their position within the flow channel,
which permits calculation of optical properties of the fluid,
such as photobleaching, absorbance, fluorescence efliciency,
optical scatter, size, shape, and refractive index. collimated
light 204 From tapered optical collimator waveguide 221
can be used to determine the concentration, position, or
abundance of microparticle 225 or flow profile of fluid 219
in fluid channel 218. Beneficially, spatio-temporal profi-
lometer 200 can be used in flow meters, microfluidic spec-
trometers, cytometers, fluorimeters and the like. Spatio-
temporal profilometer 200 can include optical elements such
as lenses, reflectors, and filters.
[0088] In making collimated light 204 with a uniform
illumination profile by tapered optical collimator waveguide
221, diverging light 202 can be provided by another wave-
guide (e.g. an optical fiber) or free-space light source. The
input light source does not need to be coherent or collimated,
and collimated light 204 is collimated and of uniform
intensity in a desired area or volume neglecting absorption.
Collimation and uniformity of collimated light 204 is pro-
duced by interaction of diverging light 202 into intermediate
light 203 as it propagates in tapered optical collimator
waveguide 221 and intemally reflects from collimating
sidewalls 207 of tapered optical collimator waveguide 221
as shown in FIG. 13, wherein a flat-top rectangular light
profile for collimated light 204 is made by tapered optical
collimator waveguide 221 having collimating sidewalls 207
that diverge at a specific angle. Other geometries and
configurations can be used, including have sidewalls 207
that diverge in a parabolic profile or by inducing gradients
in refractive index at the edges of waveguide 221.
[0089] Optical rays contained in a multimode optical
waveguide (MMOW) with a certain numerical aperture
(NA) leave the waveguide within the range of angles deter-
mined by the differences in refractive indices between the
core of the waveguide and the medium into which the light
is propagating (O,,., in FIG. 13). Inserting a selectively
designed MMOW into a device propagates and shapes light
from an optical fiber to project into fluid channel 218.
[0090] With reference to FIG. 14, a straight-walled wave-
guide propagates light via diffractive Gaussian profile (left
panel A). When diverging light 202 is focused into a
MMOW with selected properties of various parameters
(sidewall shape, refractive index, and length), a well-defined
ize and shape with uniform intensity of collimated light 204
is made from diverging light 202 as shown in the right panel
of FIG, 14.
[0091] Diverging light 202 entering tapered optical colli-
mator waveguide 221 cab have orientation in any direction.
The rectangular cross-section of tapered optical collimator
waveguide 221 determines two orthogonal planes that are
collimated and homogenized. Because of the random orien-
tation of diverging light 202 in in tapered optical collimator
waveguide 221, having structure (e.g. divergent) sidewalls
207 in one plane can collimate and uniformly distribute
collimated light 204 in both planes of tapered optical colli-
mator waveguide 221. It should be appreciated that a pair
(e.g. top and bottom) walls of the waveguide can be parallel
instead of diverging, while the other pair of walls diverge.
Additional features of tapered optical collimator waveguide
221 can be included to effect the intensity profile of colli-
mated light 204. The width of the flat-top rectangular profile
can be controlled by changing optical collimator exit wall
208 (e.g. fiber core diameter), by varying the length of



Patent Application Publication Jan. 25,2024 Sheet 14 of 35. US 2024/0027680 Al

Laser beam Laser beam

Waveguide 1 ===> Waveguide 2 ==> )
eed

ee

Beare q Se q

Diffractive Gauss! i
profile =p

FIG. 14


Patent Application Publication

Jan. 25, 2024 Sheet 16 of 35

US 2024/0027680 Al

ap ay

Flow --~ 4

Microfluidic channel



Patent Application Publication Jan. 25, 2024 Sheet 2 of 35

200

> A

US 2024/0027680 Al

.~211

~s

r~210



US 2024/0027680 Al

tion of the disclosed subject matter when considered in
connection with the following drawings, in which like
reference numerals identify like elements.

[0006] FIG. 1 shows, according to some embodiments, a
perspective view of a spatio-temporal profilometer.

[0007] FIG. 2 shows, according to some embodiments, a
plan view of the spatio-temporal profilometer shown in FIG.

1.

[0008] FIG. 3 shows, according to some embodiments:
(A) a cross-section along line A-A of the spatio-temporal
profilometer shown in FIG. 2, A) a cross-section along line
B-B of the spatio-temporal profilometer shown in FIG. 2,
and A) a cross-section along line C-C of the spatio-temporal
profilometer shown in FIG. 2.

[0009] FIG. 4 shows, according to some embodiments, a
spatio-temporal profilometer.

[0010] FIG. 5 shows, according to some embodiments, a
spatio-temporal profilometer.

[0011] FIG. 6 shows, according to some embodiments, a
spatio-temporal profilometer.

[0012] FIG. 7 shows, according to some embodiments, a
spatio-temporal profilometer.

[0013] FIG. 8 shows, according to some embodiments, a
spatio-temporal profilometer.

[0014] FIG. 9 shows, according to some embodiments, a
spatio-temporal profilometer.

[0015] FIG. 10 shows a spatio-temporal profilometer.
[0016] FIG. 11 shows, according to some embodiments, a
spatio-temporal profilometer.

[0017] FIG. 12 shows, according to some embodiments, a
spatio-temporal profilometer.

[0018] FIG. 13 shows, according to some embodiments,
ray tracings of light exiting an optical fiber in free space (top
panel) or into a diverging optical waveguide (bottom panel)
that both collimates and uniformly distributes light rays
exiting the fiber.

[0019] FIG. 14 shows, according to some embodiments,
fluorescent images of light exiting waveguides and exciting
fluorescent molecules in a flow of fluid through a microflu-
idic channel having edges indicated with horizontal lines. A
location of waveguide structure is also indicated. (Left
panel) Straight-walled waveguide showing diverging Gauss-
ian intensity profile. (Right panel) Diverging waveguide
showing collimated uniform (flat-top) intensity profile. Bot-
tom traces are an intensity profile horizontally through the
center of each beam.

[0020] FIG. 15 shows, according to some embodiments,
an Image of a flat-top laser profile and how a flat-top laser
profile is used simultaneously to determine the velocity (v)
and diameter (d) of particles moving through the laser of
length (1). I(x) indicates the laser profile (along a horizontal
line) when the channel is filled with a fluorescent material.
1(0 is measured fluorescence intensity in time as a fluores-
cent particle moves through the laser profile. Uniformity of
the laser profile in the x-dimension permits continuous
determination of the integrated intensity of the whole par-
ticle over the width of the laser profile, which greatly
enhances the signal-to-noise ratio of the intensity measure-
ment over noise in I(t)

[0021] FIG. 16 shows, according to some embodiments,
ray manipulation by a tapered waveguide (left). Modifica-
tions to projected beam profiles occur by changing the
waveguide wall taper angle. wherein three microscope
images of different light beams 271 are made by a wave-

Jan. 25, 2024

guide channel with no taper (left), a taper linearly diverging
towards the fluid channel (middle), and a taper linearly
converging towards a fluid channel (right).

[0022] FIG. 17 shows, according to some embodiments,
geometric factors for modifying projected beam profiles
[0023] FIG. 18 shows, according to some embodiments, a
spatio-temporal profilometer with lens elements that narrow
and focus uniform beams into light-sheets with high ray
density.

[0024] FIG. 19 shows, according to some embodiments,
light sheet beam uniformity, particle fluorimetry, uncertainty
quantification, and sizing enabled by light-sheet-modified
tapered waveguide to a serial cytometer.

[0025] FIG. 20 shows, according to some embodiments,
fluorescence calibration for measurement of concentration.
[0026] FIG. 21 shows, according to some embodiments, a
tapered waveguide that projects a uniform, collimated, wide
beam of light to a flow channel, wherein spatial resolution
sensitivity to flow in the device was ~50 wL min7.

[0027] FIG. 22 shows, according to some embodiments,
analysis of particles interrogated by a uniform light beam
within a microfluidic channel, including interrogating light
intensity profile and a resultant pulse signal produced by
obscuration of the light beam during the passage of one
microsphere.

[0028] FIG. 23 shows, according to some embodiments,
(A) two filtered trapezoidal signals as a microparticle bead
travels through two measurement regions excited by colli-
mated, uniform light beams produced by diverging wave-
guides (DWs). (B) Recorded beads at a region and each
bead’s measured size and velocity. For comparison, the
velocity as determined by region-to-region time-of-flight is
indicated.

[0029] FIG. 24 shows, according to some embodiments,
uniform collimated beams for microparticle analysis in
optofluidies: (A) 3D/2D for particle sizing and velocimetry
with an idealized cube of light(CoL) excitation beam. (B) A
micromolded diverging waveguide for CoL beamshaping.
[0030] FIG. 25 shows, according to some embodiments,
characterization of ray densities within taper waveguides
and emitted light beams. (A) 2D heatmaps from a represen-
tative tracing simulation converging with increasing total
ray count of 10' rays, 10° rays, and 10° rays, from left to
right. (B) Oscillating patterns of light density, visualized by
a simulated 2D ray heatmap (i) and fluorescence microscopy
image of a rhodamine-B-doped tapered waveguide (ii). Red,
black, and blue arrows mark points with high, flat, and low
ray density along the waveguide axis. Both images are
normalized by flat-field corrections. (C) Variation of spatial
profiles of emitted beams depending on waveguide length.
Left: cartoon schematic illustrating fiber over-insertion
method to vary effective waveguide lengths. Right: com-
parison of microscopy images of a fluorescently labeled
microdevice, 2D ray heatmaps, and 1D beam profiles. (=0.
O11 rad, NA=0.115, L=5 mm).

[0031] FIG. 26 shows, according to some embodiments,
quantitative characterization of simulated beams exiting
diverging tapered waveguides. (A) Simulated beam (L=8.4
mm, @=15 mrad), projected profile, and strategy for mea-
suring waveguide performance metrics. (B), (C), (D), (E).
and (F) Heatmaps of five waveguide performance metrics
screened over waveguide taper (2.5 mrad resolution) and
length (100 um resolution). Each heatmap pixel represents
‘one beam simulated as 10° rays.



Patent Application Publication Jan. 25,2024 Sheet 25 of 35 US 2024/0027680 Al

Y
« ,
' _ y
7 Efectve
. Waveguide
| Length

Lo

y

on on on

py

FIG. 25A FIG, 25B FIG. 25C


Patent Application Publication Jan. 25,2024 Sheet 1 of 35 US 2024/0027680 Al

200

FIG. 1


US 2024/0027680 Al

guides prior to photopolymerization curing with UV light,
first for | h under a UV lamp (100 W longwave 365 nm), and
next for 4 min of UV light directed through the waveguide
(375 nm diode laser at 30 mW nominal power).

[0129] Optofluidic Instrumentation

[0130] |The optofluidic chip for microparticle analysis con-
sisted of a straight flow channel (square cross-section, 100
ymx100 um) flanked both on the left and on the right with
a series of 8 diverging waveguides spaced apart along the
flow direction. Each set of 8 waveguides consisted of a
duplicated set of 4 different waveguides geometries. Wave-
guides on one side were designated for excitation and were
coupled to blue lasers (488 nm diode laser, 200 mW nominal
power, 0.5% stability over 8 h, 0.2% RMS noise) using
either 1:1 or 1:4 splitter patch cables (patch cable specs). The
opposing waveguides were designated for transmission
detection and were coupled to silicon photomuttipliers (42%
uniformity, +0.5% linearity, 100 KHz bandwidth). Fluidic
lines were connected to syringe pumps (30 um min-1
minimum pulse-free actuation speed) via either fluorinated-
ethylene-propylene or flexible polymer tubing.

[0131] Digital Signal Processing

[0132] Raw signals from photodetectors were digitized to
a workstation computer by a streaming data acquisition card
(8 analog inputs, 16-bit resolution, sampling rate 2x10°
Automated MATLAB software was used to: 1) filter win-
dows containing peaks from the background of the signal
stream in real-time, 2) annotate peaks with approximate
signal boundaries, background level, integrated area, height,
and width, 3) match signals corresponding to each micropar-
ticle, and 4) log compressed files with copies of this data.
Next, the peak metrics of background level, integrated area,
height, and width were refined using a new strategy. The
signal boundary points were iteratively expanded to the first
and last samples at which the smoothed peak (centered
moving average, window size of 4% peak duration)
exceeded the background level. After each expansion the
mean background level was re-evaluated, and the expansion
continued until the relative decreases in mean background
level fell below a tolerance of 1%. Finally, the integrated
area, height, and width annotations were recalculated using
the refined signal boundaries and background level.

[0133] Several approaches were used to estimate the
change points K,, K3. Ks, and K,, marking, respectively, the
signal onset, plateau initiation, end of plateau, and disap-
pearance of signal. For all methods, initial guesses for K,
and K,, were the refined signal boundaries described above:
guesses for K, and K, were

 — ) — FWHM (8)

aft:

0! = 0) — FWHM
— aT

O)

aft nage

where FWHM (full width half max) is the width annotation
described above. The tested methods were the Kneedle
algorithm, free-knot spline approximation, L-method knee-
points, statistical changepoints, and a custom fit. The custom
fit was a constrained minimization

Jan. 25, 2024

0)

¥y <p <¥3 <4
app Sy <5

min
pester

You-»*{
[0134] where y is the original data and y,, is the data fitted
by a piecewise discontinuous linear fit with segment bound-
aries at X,, X,, X;, and x,. The intersections between the
linear fit lines were chosen as K,, K>, K3, and K,. Regard-
less of changepoint detection method, equations (6-7) were
used to calculate particle size and velocity.

[0135] For validation purposes, a previously reported
technique using spectral analysis was applied to measure
relative particle size and velocity. Briefly, the spectral
method seeks to reverse the effects of particle size and
velocity on the shape of the signal. The result of the method
is a mapping of signals onto a reference curve and per-
particle estimates of relative size and velocity.

[0136] Geometric Optics Derivation

[0137] FIG. 30 shows a geometric optics model for propa-
gating rays in a diverging waveguide. Given the geometry of
a total internal reflected ray propagating through a tapered
waveguide in FIG. 30, trigonometric relationships can be
derived to describe the propagation angle 8, of rays entering
the waveguide at initial angle 8, prior to the m” successive
internal reflection. The waveguide geometry is described by
a total length L, entrance aperture half-width a,, and exit
aperture half-width a. The waveguide wall taper angle @ is
thus

sla)

[0138] Observing the two right triangles with acute angles
6, and B,. and 8, and By. respectively,

x s
=(2-a)+¢ (1b)

0, = 5 - Bi +9) = 4-29. (slo)

[0139] Extending this to arbitrary numbers of reflections,

(sid)

(sl)

where m,,,, is the maximum possible number of reflections
the ray can undergo before becoming “effectively colli-
mated.” Effective collimation is defined when

P20 oy 2P {s2a)

9218 )1-2m, 92-9 (s2b)
(0140] Thus,

(s2)

mot = {la wed) Wize
0, al<e



US 2024/0027680 Al

Jan. 25, 2024 Sheet 33 of 35

Patent Application Publication

g0€ ‘Sls

V0e ‘SIs



US 2024/0027680 Al

230 or optical fiber 240 and can be wider than tapered
optical collimator waveguide 221 to capture more light from
light-fluid interaction volume 201.

[0070] Product light 205 can be fluorescence, scattered
light, or a change in transmission of collimated light 204
resulting from interaction of collimated light 204 with
microparticle 225 in light-fluid interaction volume 201. In
an embodiment product light 205 is emitted light from a
fluorescent microparticle 225. In an embodiment, product
light 205 can include loss of fluorescence due to photo-
bleaching of microparticle 225. Transmission of product
light 205 to forward light detection waveguide 230 or back
light detection waveguide 234 can be modified by optical
components. Product light 205 can have a wavelength from
240 nm to 1000 nm, specifically from 350 nm to 750 nm.

[0071] Optical detector 251 receives product light 205 and
can record properties of product light 205. In an embodi-
ment, product light 205 is in optical communication with
forward light detection waveguide 230 other optical detector
251 can be connected back light detection waveguide 234 or
out-of-plane light collector 237 when present. Optical fiber
240 can be interposed between forward light detection
waveguide 230, back light detection waveguide 234, or
out-of-plane light collector 237 and its optical detector 251.
In an embodiment, optical fiber 240 is a 125-micrometer
diameter multimode fiber that carries a visible wavelength of
light. In an embodiment, optical detector 251 is a broadband
photodiode connected to a power meter. In an embodiment,
the photodiode has a spectral range from 200 nm to 1100
nm. In an embodiment, the photodiode is preceded by an
optical filter that reduces the effective power of the light
transmitted to optical detector 251. In an embodiment, the
photodiode is preceded by a spectral filter to reduce the
spectral bandwidth of the transmitted light reaching optical
detector 251. In an embodiment, the combined photodiode
and power meter has a sensitivity in a power range from 10
pW to 200 mW. In an embodiment, optical detector 251 is
a spectrometer that measures a spectrum of product light
205. The photodetector can be a photodiode, photomultiplier
tube, avalanche photodiode or the like. In an embodiment,
optical detector 251 can be an optical component disposed
‘on substrate 210. In. an embodiment, measurements provided
by optical detector 251 provide an estimated power of
collimated light 204 incident on microparticle 225 and
measures time-dependent changes in the interaction between
collimated light 204 and microparticle 225 through process-
ing of product light 205. In an embodiment, power and
spatial uniformity of collimated light 204 or product light
205 in light-fluid interaction volume 201 is measured by a
wide-field fluorescence microscope that can be in optical
communication with light-fluid interaction volume 201, e.g.,
via out-of-plane light collector 237. In an embodiment, a
light propagation path can be visualized with fluorescein as
a component of fluid 219, wherein collimated light 204 has
a wavelength of 488 nm, and the microscope is viewing fluid
channel 218 (particularly light-fluid interaction volume 201)
from above the plane of substrate 210 as indicated by
out-of-plane light collector 237 shown in FIG. 9. In an
embodiment, the spatial uniformity of collimated light 204
observed from optical collimator exit wall 208 on the optical
axis of tapered optical collimator waveguide 221 is visual-
ized by acquiring collimated light 204 in a microscope in the
position of optical detector 251. In an embodiment, the filter
blocks wavelengths outside the range from 500 nm to 540

Jan. 25, 2024

nm, allowing only fluorescence emitted from fluorescein to
reach the detector. The photodetector can be a photodiode,
photomultiplier tube, avalanche photodiode, or the like.

[0072] In an embodiment, spatio-temporal profilometer
200 is connected to flow controller 260 that provides a flow
of fluid 219 into fluid channel 218. In an embodiment, flow
controller 260 is a syringe pump that delivers volumetric
flow from 100 picoliter per minute (pL/min) to 100 micro-
liters/min. In an embodiment, flow controller 260 is a vessel
filled with fluid 219 at a fixed height above the outflow of
flow controller 260. Gravity or externally applied pressure
can control pressure on fluid 219 and provide a flow rate of
fluid 219 as a function of fluidic resistance through fluid
channel 218. In an embodiment, external pressure is applied
to the vessel to provide a greater pressure drop than achieved
by gravity. Other flow controllers can be attached to fluid
channel 218 and modified with or without feedback based on
analysis of product light 205. Exemplary flow controllers
206 include peristaltic pumps, rotary pumps, piston pumps,
diaphragm pumps, and the like.

[0073] In an embodiment, fluid channel 218 is orthogonal
to tapered optical collimator waveguide 221. In some
embodiments, fluid channel 218 in whole or in part is
oblique to fluid channel 218 as shown in FIG. 12. collimated
light 204 can propagate across multiple fluid channel 218
disposed on substrate 210.

[0074] Light source 250 can include a light-emitting
diode, laser, and the like that produces collimated light 204
at a selected wavelength. The properties of collimated light
204 and type can be selected based on packaging of substrate
210, level of interaction with fluid 219 and microparticle
225, and transmission of product light 205 by forward light
detection waveguide 230.

[0075] Collimated light 204 can imprint a contrast to fluid
219 or microparticle 225. In an embodiment, microparticle
225 is a caged fluorophore. In an embodiment, microparticle
225 is fluorescein. Collimated light 204 can be selected
based on whether collimated light 204 interacts with fluid
219 or microparticle 225. A wavelength of collimated light
204 and diverging light 202 can be from 240 nm to 1000 nm,
specifically from 350 nm to 750 nm, and more specifically
375 nm. In an embodiment, the wavelength of collimated
light 204, intermediate light 203 diverging light 202 are the
same. The intensity of collimated light 204 can be selected
based on optical properties for modifying fluid 219 or
microparticle 225, the nature of flow of fluid 219, and
selected characteristics of product light 205. Intensity of
collimated light 204 can be from 1 nW to 200 mW.

[0076] Tapered optical collimator waveguide 221 converts
diverging light 202 received from light source 250 to col-
limated light 204 and communicates collimated light 204 to
light-fluid interaction volume 201. Filters or bifurcations can
be included along the propagation of diverging light 202 or
collimated light 204 to reduce the intensity of light or direct
part of the light to a light intensity meter. In an embodiment,
tapered optical collimator waveguide 221 is filled with
optical material that permits total internal refection of light.
Tn an embodiment, the optical material is a photocurable
adhesive that has a higher index of refraction than substrate
210. In an embodiment, optical collimator exit wall 208 can
have a curved surface or lens to shape collimated light 204
received in light-fluid interaction volume 201. In an embodi-
ment, collimated light 204 has a substantially uniform



US 2024/0027680 Al

Jan. 25, 2024 Sheet 28 of 35

Patent Application Publication

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Patent Application Publication Jan. 25,2024 Sheet 12 of 35. US 2024/0027680 Al

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US 2024/0027680 Al

[0141] Next, the reflection distances L,, of complete inter-
nal reflections are modeled. “Complete internal reflections,”
as illustrated in FIG. 30B, are defined as rays that travel to
the waveguide wall, reflect, and finally cross the waveguide
centerline. For the first reflection, the distance L, required
for the ray at initial position hg to reflect against the wall and
return to the waveguide axis is the sum of the distances L,
and Ly, including, respectively, the first and second leg of
the reflection path. Trigonometrically:

(s3a)

(s3b)

where 6, is the extension of the waveguide width at the point
of reflection. Solving for 8,:

ae tang (so)
61 = (a-ha ang
[0142] | Trigonometrically:
(a= ho +6) (3d)
nn tand)
(a +6) (s3e)
ta ands

[0143] Thus, after expanding and rearranging,

(en)

tand;
hat he=h=(0-h(o~)
1 ( }o “0 1
tand; tand; tan

[0144] Similarly, for an arbitrary number of reflections
after the first, i.e., for m>1,

3)
3m)
(si)
(s3))
a1 +5y (3k)
ft ali

Jan. 25, 2024

-continued
(s31)

(=: “+ tangtant
by = | ————

tit
Tandy, — tang {andy tanBmst)

[0145]

Accordingly,

Tan (83)

candy
o-oo)

a = tang } 1

‘and ‘ant, [

tL
— ond
| ——__—"4

vl ay

1 1
re
Tan, — tang le maa) *

[0146] Equation (s3) assumes a positive entrance angles,
6,>0. By symmetry, however, the reflection distances for
negatively angled rays L; can be expressed as

Lge Lyf Oy ho) (4)

(0147] It is useful to also define the total distance @,, at
which a given reflection point occurs

Eels, (653)

[0148] The exit position of the rays h, with M complete
internal reflections achieved prior to reaching the exit aper-
ture is given by

Tio + Dandi, s

(-¥

ay +81

M=0

u
1)! x Es)tanb yest, >L

be

(LC yeeitandyeeas yer <L

[0149] Equation (s5) includes three cases. The first case
accounts for rays that have not reflected in the waveguide.
The second case accounts for rays having a final segment
(i.e., after the last complete internal reflection) that does not
intersect the wall before reaching the end of the waveguide.
The third case accounts for rays whose final segment have
a partial reflection (rays reach another reflection point ¢ 4,,,
but cannot complete the second reflection leg before reach-
ing the end of the waveguide; see Figure S1A with .
The multiplicative pre-factor recognizes that ray positions
will be on opposite sides of the waveguide with each
reflection. Again, although equation (s5) assumes positive
entrance angles, 0,>0, by symmetry arguments, the exit
position of the rays h; with el <0 is

y= ig)

(36)

[0150] The above model assumes that the angle 8, of rays
entering the waveguide do not surpass the waveguide effec-
tive critical angle 8..¢9:

8p BAPZUIMonid waveguide) ) 49 (87)


US 2024/0027680 Al

elements should not be limited by these terms. For example,
a first current could be termed a second current, and,
similarly, a second current could be termed a first current,
without departing from the scope of the various described
embodiments. The first current and the second current are
both currents, but they are not the same condition unless
explicitly stated as such.

[0162] The modifier about used in connection with a
quantity is inclusive of the stated value and has the meaning
dictated by the context (e.g., it includes the degree of error
associated with measurement of the particular quantity). The
conjunction or is used to link objects of a list or alternatives
and is not disjunctive; rather the elements can be used
separately or can be combined together under appropriate
circumstances.

1. A spatio-temporal profilometer for performing time-
resolved spatial profilometry with a uniform light profile, the
spatio-temporal profilometer comprising:
a substrate;
a tapered optical collimator waveguide disposed on the
substrate and that receives diverging light, internally
reflects the diverging light by internal reflections on
collimating sidewalls of tapered optical collimator
waveguide, collimates the diverging light in response
to the internal reflections on collimating sidewall, pro-
duces intermediate light from the diverging light due to
the internal reflections, produces collimated light from
the intermediate light that is communicated from the
tapered optical collimator waveguide, such that the
tapered optical collimator waveguide comprises:
an optical collimator entry wall that receives diverging
light and communicates diverging light into an inte-
rior of the tapered optical collimator waveguide;

the collimating sidewalls disposed obliquely to the
optical collimator entry wall and comprising a first
collimating sidewall and a second collimating side-
wall that obliquely opposes the first collimating
sidewall, such that the first collimating sidewall and
the second collimating sidewall internally reflect the
diverging light inside of the tapered optical collima-
tor waveguide and convert the diverging light to the
intermediate light; and

an optical collimator exit wall obliquely disposed to the
collimating sidewall and opposing the optical colli-
mator entry wall and that receives the intermediate
light from’ the interior of the tapered optical colli-
mator waveguide, and communicates the intermedi-
ate light as collimated light, such that the collimated
light is collimated and has a uniform light profile;

a fluid channel in optical communication with the tapered
optical collimator waveguide and comprising:

a fluid channel entry that receives a fluid comprising
microparticles and communicates the microparticles
into an interior of the fluid channel;

fluid channel sidewalls disposed along a length of the
fluid channel and that constrain flow of the fluid to
the interior of the fluid channel; and

a fluid channel exit that communicates the fluid out of

»

light-fluid interaction volume disposed in the fluid
channel and provided by an overlap within the fluid
channel of the collimated light from the tapered optical
collimator waveguide and the fluid: and

17

Jan. 25, 2024

a light-fluid interaction volume boundary that bounds the
light-fluid interaction volume at a periphery of the
collimated light that propagates in the fluid channel,

such that the fluid channel receives the fluid with the
microparticles and the collimated light in the light-fluid
interaction volume, produces product light from the
collimated light in response to the microparticles inter-
acting with the collimated light in the light-fluid inter-
action volume, and communicates the product light out
of the fluid channel.

2. The spatio-temporal profilometer of claim 1, further
comprising an optical fiber channel disposed on the substrate
in optical communication with the tapered optical collimator
waveguide and that receives the diverging light and com-
municates the diverging light to the tapered optical collima-
tor waveguide.

3. The spatio-temporal profilometer of claim 2, further
comprising an optical fiber disposed in the optical fiber
channel in optical communication with the tapered optical
collimator waveguide and that receives the diverging light
and communicates the diverging light to the tapered optical
collimator waveguide.

4. The spatio-temporal profilometer of claim 1, further
comprising a forward light detection waveguide disposed on
the substrate in optical communication with the fluid chan-
nel and that receives product light that propagates in a
forward direction from the fluid channel with respect to the
collimated light.

5. The spatio-temporal profilometer of claim 4, wherein
the forward light detection waveguide is a straight wave-
guide or tapered waveguide.

6. The spatio-temporal profilometer of claim 4, further
comprising an optical fiber disposed in the forward light
detection waveguide and that receives the product light and
communicates the product light to an optical detector.

7. The spatio-temporal profilometer of claim 1, further
comprising an back light detection waveguide disposed on
the substrate in optical communication with the fluid chan-
nel and that receives the product light that propagates in a
forward direction from the fluid channel with respect to the
collimated light.

8. The spatio-temporal profilometer of claim 7, further
comprising an light blocking member disposed on the sub-
strate in optical communication with the tapered optical
collimator waveguide and optically interposed between the
back light detection waveguide and the tapered optical
collimator waveguide and that blocks the light from being
communicated between the tapered optical collimator wave-
guide and the back light detection waveguide.

9. The spatio-temporal profilometer of claim 7, further
comprising an optical fiber disposed in the back light
detection waveguide and that receives the product light and
communicates the product light to an optical detector.

10. The spatio-temporal profilometer of claim 1, further
comprising a light source disposed on the substrate in optical
communication with the tapered optical collimator wave-
guide and that produces the diverging light and communi-
cates the diverging light to the tapered optical collimator
waveguide.

11. The spatio-temporal profilometer of claim 1, further
comprising a flow controller in fluid communication with
the fluid channel and that provides the fluid to the fluid
channel.


Patent Application Publication Jan. 25,2024 Sheet 15 of 35 US 2024/0027680 Al

FIG. 15