$\mathscr{P}_{0}$ is defined in such a way that $\Pi_{0}$ is its disjoint
union, and for every (not necessarily induced) copy of $F$ in $G$ there is a
copy in $\mathscr{P}_{0}$ projecting to it. When for some $i\in[N]$ the system
$\mathscr{P}_{i-1}$ has just been determined, we let $\mathscr{P}_{i}$ be the
union of all copies of $\mathscr{P}_{i-1}$ corresponding to the standard
copies of $\Pi_{i-1}$ in $\Pi_{i}$. Roughly speaking, the final system
$\mathscr{P}_{N}\subseteq\binom{\Pi_{N}}{F}$ consists of all copies of $F$
which are ‘relevant’ for the verification of
$\Pi_{N}\longrightarrow(F)^{e}_{r}$, so that in an obvious sense we have
$\mathscr{P}_{N}\longrightarrow(F)^{e}_{r}$. An easy induction along the
partite construction reveals that any two distinct copies in $\mathscr{P}_{N}$
are either disjoint, or they intersect in a single vertex, or they intersect
in two vertices joined by an edge. Summarising the discussion so far, we have
shown the following.

######  Proposition 4.5.

For every graph $F$ and every number of colours $r$, there exists a graph $H$
together with a system $\mathscr{H}\subseteq\binom{H}{F}$ such that

  1. ( )

$\mathscr{H}\longrightarrow(F)^{e}_{r}$;

  2. ( )

$\omega(H)=\omega(F)$;

  3. ( )

and any two distinct copies in $\mathscr{H}$ are either disjoint, or they
intersect in a vertex, or they intersect in an edge. ∎

This raises several questions. In view of the topic of this survey, the
perhaps most immediate one is whether in ( ) ‣ 4.5 the clique number can be
replaced by girth (provided that $F$ is not a forest). Such an assertion would
certainly require a different construction, because even for $F=C_{5}$ the
graph $H$ we produced contains lots of four-cycles. For more than a decade,
this was a common problem of all known proofs of the induced Ramsey theorem.
Erdős [Erd75] asked whether a graph $H$ with $H\longrightarrow(C_{5})^{e}_{2}$
and $\mathrm{girth}(H)=5$ exists, and expected a negative answer. This was due
to the fact that, at that time, he believed in some kind of meta-conjecture
that edge-colourings of finite graphs display phenomena similar to vertex-
colourings of uncountable graphs. Thus he took the fact that no $C_{4}$-free
graphs of uncountable chromatic number exist as an indication that at least
some graph of girth $5$ should have no Ramsey graph of girth $5$. Jarik and
Rödl [NR87] refuted this suspicion. Their argument is capable of controlling
cycles of lengths $5$, $6$, and $7$ as well. However, it was always clear that
excluding $8$-cycles is horrendously difficult. The problem remained a central
goal of Rödl’s research programme for almost forty years, until it was
recently solved in [girth].

######  Theorem 4.6 (Girth Ramsey theorem, first version).

For every graph $F$ which is not a forest and every number of colours $r$
there exists a graph $H$ such that $H\longrightarrow(F)^{e}_{r}$ and
$\mathrm{girth}(H)=\mathrm{girth}(F)$. ∎

Let us next point to another question suggested by Proposition 4.5. Its clause
( ) ‣ 4.5 gives complete control over the possible intersections of two copies
in $\mathscr{H}$. In the nontrivial case $e(F),r\geq 2$ it certainly needs to
happen from time to time that two copies in $\mathscr{H}$ share an
edge—otherwise we could colour the copies in $\mathscr{H}$ one by one without
making any of them monochromatic. In the spirit of Theorem 3.14 it would be
even more satisfactory to control the possible intersection patterns of more
than two copies. The best one could hope for is that locally the Ramsey system
of copies has a forest-like structure in the following sense.

######  Definition 4.7.

Given a graph $F$ we call a set $\mathscr{N}$ of graphs isomorphic to $F$ a
forest of copies of $F$ if there exists an enumeration
$\mathscr{N}=\bigl{\\{}F_{1},\ldots,F_{|\mathscr{N}|}\bigr{\\}}$ such that for
every $j\in[2,|\mathscr{N}|]$ the set
$z_{j}=\bigl{(}\bigcup_{i<j}V(F_{i})\bigr{)}\cap V(F_{j})$ satisfies

  1. ( )

either $|z_{j}|\leq 1$

  2. ( )

or $z_{j}\in\bigl{(}\bigcup_{i<j}E(F_{i})\bigr{)}\cap E(F_{j})$.

We denote the union of a forest of copies $\mathscr{N}$ by
$\bigcup\mathscr{N}$; explicitly, this is the graph with vertex set
$\bigcup_{F_{\star}\in\mathscr{N}}V(F_{\star})$ and edge set
$\bigcup_{F_{\star}\in\mathscr{N}}E(F_{\star})$. A graph $G$ is said to be a
partial $F$-forest if it is an induced subgraph of $\bigcup\mathscr{N}$ for
some forest $\mathscr{N}$ of copies of $F$.

The following result from [girth] analyses the local structure of Ramsey
graphs completely.

######  Theorem 4.8 (Girth Ramsey theorem, second version).

For every graph $F$ and all $r,n\in{\mathds{N}}$ there exists a graph $H$ with
$H\longrightarrow(F)^{e}_{r}$ such that every set $X\subseteq V(H)$ whose size
it at most $n$ induces a partial $F$-forest in $H$. ∎

The proof of Theorem 4.8 constructs $H$ together with a distinguished system
of copies $\mathscr{H}\subseteq\binom{H}{F}$, which satisfies, in particular,
the partition relation $\mathscr{H}\longrightarrow(F)^{e}_{r}$. A further
interesting claim can be made about this system $\mathscr{H}$, which seems to
be stronger than the conclusion that $H$ is locally a partial $F$-forest.
Namely, $\mathscr{H}$ itself has a comparable property. But before making this
precise we should emphasise a bizarre difference between ordinary forests and
$F$-forests. Everybody knows that the former are closed under taking
subgraphs. Subsets of $F$-forest, on the other hand, can fail to be
$F$-forests themselves (see Figure 4.2).

$F$$F_{0}$$F_{1}$$F_{2}$$x_{2}$$x_{1}$$x_{0}$ Figure 4.2. The subforest
$\\{F_{0},F_{1},F_{2}\\}$ fails to be a forest.

In the example we have chosen $F$ is any graph containing a triangle
$x_{0}x_{1}x_{2}$. For every index $i\in{\mathds{Z}}/3{\mathds{Z}}$ the copy
$F_{i}$ of $F$ has the edge $x_{i+1}x_{i+2}$ but nothing else in common with
$F$. Except for these intersections the copies in
$\mathscr{N}=\\{F,F_{0},F_{1},F_{2}\\}$ are mutually disjoint. This
enumeration exemplifies that $\mathscr{N}$ is a forest of copies. However its
subset $\mathscr{N}^{-}=\mathscr{N}\smallsetminus\\{F\\}$ fails to be such a
forest. For instance, for the enumeration
$\mathscr{N}^{-}=\\{F_{0},F_{1},F_{2}\\}$ the set $z_{2}=\bigl{(}V(F_{0})\cup
V(F_{1})\bigr{)}\cap V(F_{2})=\\{x_{0},x_{1}\\}$ is certainly not in case ( )
‣ 4.7 of Definition 4.7 and, as it fails to be an edge of $F_{0}$ or $F_{1}$,
it does not satisfy ( ) ‣ 4.7 either. By symmetry a similar problem arises
when one enumerates $\mathscr{N}^{-}$ in any other way.

What this shows is that given a graph $F$ we cannot ask for Ramsey systems
$\mathscr{H}$ such that all ‘small’ subsets of $\mathscr{H}$ are forests of
copies. We can still demand, however, that every ‘small’ subset
$\mathscr{N}\subseteq\mathscr{H}$ is contained in a forest of copies that is
not much larger than $\mathscr{N}$. The following result from [girth] makes
this precise.

######  Theorem 4.9 (Girth Ramsey theorem, third version).

Given a graph $F$ and $r,n\in{\mathds{N}}$ there exists a graph $H$ together
with a system of copies $\mathscr{H}\subseteq\binom{H}{F}$ satisfying not only
$\mathscr{H}\longrightarrow(F)^{e}_{r}$ but also the following statement: For
every $\mathscr{N}\subseteq\mathscr{H}$ with $|\mathscr{N}|\in[2,n]$ there
exists a set $\mathscr{X}\subseteq\mathscr{H}$ such that
$|\mathscr{X}|\leq|\mathscr{N}|-2$ and $\mathscr{N}\cup\mathscr{X}$ is a
forest of copies. ∎

It deserves to be pointed out that the upper bound
$|\mathscr{X}|\leq|\mathscr{N}|-2$ is best possible. Roughly this is because
it requires $|\mathscr{N}|-2$ triangles to triangulate an $|\mathscr{N}|$-gon.
If $F=K_{3}$ and there is some $C_{|\mathscr{N}|}$ in $H$ such that every copy
in $\mathscr{N}$ contains a unique edge of this cycle, then the copies in
$\mathscr{X}$ need to triangulate the cycle (see Figure 4.3).

(a) A cycle of triangles

(b) Adding further triangles creates a forest

Figure 4.3. The necessity of $\mathscr{X}$ in Theorem 4.9

###  4.3. Ideas.

There is not much we can say about the proof of any version of the girth
Ramsey theorem in a few pages. A general theme is that it is difficult to
isolate special cases, which are simpler than the general result. It is rather
the other way around: One has to develop several further concepts, such as
trains, Roman $\mathrm{Girth}$, and German $\mathfrak{Girth}$, which allow the
formulation of even more general Ramsey theoretic statements (see, e.g.,
[girth]*§4.4 and §10.3), which can then be proved by an induction scheme
resembling a transfinite induction up to $\omega^{\omega}$.

As in §3.3 the proof cannot be understood if one just wants to focus on the
graph case. In fact, each of our three versions of the girth Ramsey theorem
holds for linear hypergraphs instead of graphs as well, and the proof requires
this level of generality for roughly the same reason we have already seen.

Jarik and Rödl [NR87] discovered that the proof of Theorem 4.3 we have
outlined in §4.1 can be used for maintaining linearity.

######  Theorem 4.10.

Given a linear, $k$-uniform hypergraph $F$ and a number of colours $r$ there
exists a linear, $k$-uniform hypergraph $H$ such that
$H\longrightarrow(F)^{e}_{r}$.

There is no problem with the partite lemma, because for every linear,
$k$-partite, $k$-uniform hypergraph $B$ all Hales-Jewett powers $B^{n}$ are
linear as well. What requires some thought when proving Theorem 4.10 is that
no $2$-cycles are introduced in the amalgamation steps (see Figure 4.1). In
[NR87] Jarik and Rödl accomplish this by studying the possible intersection
patterns of partite copies of $B$ corresponding to combinatorial lines very
carefully. More recently (see e.g. [BNRR, girth]) a different approach to this
issue became popular. One first runs the partite construction under the
additional assumption that $H$ is a $k$-partite, $k$-uniform hypergraph as
well. This has the advantage that vertically we do not have to use Ramsey’s
theorem. Instead, it is preferable to use the Hales-Jewett partite lemma not
only horizontally, but also vertically. Accordingly we end up getting a
$k$-partite Ramsey hypergraph again, and in this case it is much easier to
check that linearity is preserved. So the result is that we have a new partite
lemma for linear, $k$-partite, $k$-uniform hypergraphs, called the clean
partite lemma. In comparison to the Hales-Jewett partite lemma, its main
advantage is that it generates systems of partite copies satisfying clause ( )
‣ 4.5 of Proposition 4.5. This renders it rather obvious that linearity is
preserved when we want to prove Theorem 4.10 by a partite construction using
Ramsey’s theorem vertically and the clean partite lemma horizontally.

The reason why we have spent so much time on this somewhat subtle point in a
proof variant of Theorem 4.10 is that such usages of the partite construction
method as a ‘cleaning device’ occur all over the place in the proof of the
girth Ramsey theorem. Whenever we obtain a Ramsey theoretic result with
‘complicated possible intersections’ of copies, we try to clean it by running
the partite construction once more. Of course this plan also imposes some
restrictions on the proof strategy: concepts we introduce and additional
properties we acquire can be considered useful only when they are
‘indestructible by partite constructions’. For instance, the extension lemma
(cf. [girth]*Lemma 9.1) and the German $\mathfrak{Girth}$ iterability lemma
(cf. [girth]*Proposition 9.14) implement this theme.

Besides Ramsey’s theorem, the Hales-Jewett partite lemma, and constructions
derivable from them by means of the partite construction method, the proof of
the girth Ramsey theorem also involves a different procedure for obtaining new
constructions from known ones, called the extension process. The basic idea
was again pioneered by Jarik and Rödl, who used it in their work on
$C_{4}$-free Ramsey graphs [NR87] mentioned in the previous subsection. A
major step in their argument is the following $C_{4}$-free partite lemma.

######  Lemma 4.11 (Jarik and Rödl).

For every $C_{4}$-free bipartite graph $B$ and every number colours $r$ there
exists a $C_{4}$-free bipartite graph $H$ such that for every $r$-colouring of
$E(H)$ there exists a monochromatic, induced, partite copy of $B$.

The proof of this lemma has certain similarities with the proof of Lemma 4.2
we sketched in §4.1. Attempting to emphasise the common features of both
proofs we define for every bipartite graph $B=(X,Y,E)$ with the properties
that

  1. $\bullet$

all vertices in $X$ have the same degree $t\geq 2$

  2. $\bullet$

and no two vertices in $X$ have the same neighbourhood

the $t$-uniform neighbourhood hypergraph $F=\mathrm{NH}(B)$ by setting

$V(F)=Y\quad\text{ and }\quad E(F)=\\{N(x)\colon x\in X\\}\,.$

For instance, the neighbourhood hypergraph of the bipartite graph $B(m,t)$
defined in the proof of Lemma 4.2 is the $t$-uniform clique $K_{m}^{(t)}$.
Roughly speaking the proof of Lemma 4.2 consists of the four steps

$B(m,t)\overset{\mathrm{NH}}{\xrightarrow{\hskip
28.45274pt}}K_{m}^{(t)}\overset{\mathrm{extension}}{\xrightarrow{\hskip
56.9055pt}}K_{|Z|}^{(t_{\star})}\overset{\mathrm{Ramsey}}{\xrightarrow{\hskip
56.9055pt}}K_{m_{\star}}^{(t_{\star})}\overset{\mathrm{NH}^{-1}}{\xrightarrow{\hskip
28.45274pt}}B(m_{\star},t_{\star})\,,$

where the first and last arrow indicate the formation of the neighbourhood
hypergraph and its inverse operation, respectively; the second ‘extension’
arrow yields a $t_{\star}$-uniform hypergraph, where our choice
$t_{\star}=(t-1)r+1$ prepares an application of the box principle; finally,
the third arrow indicates an application of Ramsey’s theorem with
$r^{t_{\star}}$ colours.

When proving Lemma 4.11 we start with some $C_{4}$-free bipartite graph
$B=(X,Y,E)$ instead of $B(m,t)$. Without loss of generality we can assume that
all vertices in $X$ have the same degree $t\geq 2$. Thus $B$ has a $t$-uniform
neighbourhood hypergraph $F=\mathrm{NH}(B)$. The assumption
$C_{4}\not\subseteq B$ implies that $F$ is linear. Without going into a lot of
detail here, one then forms a linear, $t_{\star}$-uniform ‘extension’ $M$ of
$F$. Instead of Ramsey’s theorem we employ Theorem 4.10, thus getting a
linear, $t_{\star}$-uniform hypergraph $N$ such that
$N\longrightarrow(M)^{e}_{r^{t_{\star}}}$. Finally, the linearity of $N$
implies that the bipartite graph $H=\mathrm{NH}^{-1}(N)$ is again
$C_{4}$-free.

Based on the plan

$B\overset{\mathrm{NH}}{\xrightarrow{\hskip
28.45274pt}}F\overset{\mathrm{extension}}{\xrightarrow{\hskip
56.9055pt}}M\overset{\mathrm{Thm}\leavevmode\nobreak\
\ref{thm:631}}{\xrightarrow{\hskip
56.9055pt}}N\overset{\mathrm{NH}^{-1}}{\xrightarrow{\hskip 28.45274pt}}H$

it is not too difficult to work out how one needs to define the ‘extension’
$M$ in such a way that $H$ will be as required by Lemma 4.11. In any case, the
curious reader can find full details in [NR87].

The abstract version of the extension process defined and studied in the proof
of the girth Ramsey theorem deals with structures called pretrains: these are
pairs $(H,\equiv)$ consisting of a hypergraph $H$ and an equivalence relation
$\equiv$ on $E(H)$. The wagons of a pretrain $(H,\equiv)$ are the equivalence
classes of $\equiv$. For instance, with every bipartite graph $B=(X,Y,E)$ we
can associate a pretrain by declaring two edges to be equivalent if and only
if they intersect on $X$. The wagons of this pretrain are stars whose centres
are in $X$. In the proofs of Lemma 4.2 and Lemma 4.11 we used the box
principle in order to find Ramsey objects for the wagons and we applied
Ramsey’s theorem or Theorem 4.10 to the hypergraphs describing how the wagons
intersect each other. More generally, when we have two constructions $\Phi$,
$\Psi$ applicable to hypergraphs we can similarly define a construction
$\mathrm{Ext}(\Phi,\Psi)$ applicable to (certain) pretrains (see
[girth]*Section 6).

The way in which the extension process enters the proof of the girth Ramsey
theorem is quite unrelated to Lemma 4.11. Suppose that we want to perform any
partite construction over a linear hypergraph $G$. Now any two constituents of
our pictures will either be vertex-disjoint, or they share a unique music
line. Suppose further that in each step of the construction the partite lemma
we use delivers a system of partite copies satisfying Proposition 4.5( ) ‣
4.5. These mild assumptions already cause severe limitations as to how the
constituents can ‘develop’ in the course of the construction. In picture zero,
every constituent is a perfect matching (augmented by some isolated vertices).
The constituents of the next picture are either disjoint unions of such
matchings or they arise from such unions by identifying some vertices on a
common music line, so that they look like Figure 4.4(a). Similarly, the most
general constituent of the next picture is shown in Figure 4.4(b).

(a)

(b)

Figure 4.4. Two 3-uniform trains

In general, hypergraphs of this form are called trains. Officially a train is
a hypergraph equipped with a nested sequence of equivalence relations
satisfying some rules on intersections of edges. Since the constituents of
pictures are trains, it suffices to study partite lemmata applicable to
trains. These can be obtained by iterative applications of the extension
process. For further ideas and details we refer to [girth].

###  4.4. Infinite structural Ramsey theory

We would finally like to talk about some results on the question whether the
induced Ramsey theorem generalises to the transfinite setting. Given a (finite
or infinite) graph $F$ and a cardinal $\mu$ one would like to have a graph $H$
such that $H\longrightarrow(F)^{e}_{\mu}$. An early result of Hajnal and
Komjáth [HK88, HK92] shows that, consistently, such a graph $H$ does not
always exist. Notably, they showed that adding a Cohen real also adds a
bipartite graph $F$ on $\aleph_{1}$ vertices such that $H\mathrel{\mkern
5.5mu\arrownot\mkern-5.5mu}\longrightarrow(F)^{e}_{2}$ holds for all graphs
$H$ in the generic extension. Later Komjáth [kom94] found a surprisingly
simple proof that any non-trivial forcing whose conditions form a set adds an
uncountable graph $F$ such that for some cardinal $\mu$ there is no graph $H$
with $H\longrightarrow(F)^{e}_{\mu}$. This is complemented by a deep result of
Shelah [Sh289], which is proved by means of a difficult proper class forcing.

######  Theorem 4.12 (Shelah).

It is consistent with $\mathrm{ZFC}$ that for every graph $F$ and every
cardinal $\mu$ there exists a graph $H$ such that
$H\longrightarrow(F)^{e}_{\mu}$. ∎

Careful readers will have observed that the aforementioned negative
consistency results involve uncountable graphs $F$ only. This leaves some room
for $\mathrm{ZFC}$ theorems addressing ‘small graphs’. Building on the ideas
in [EHP75] and transferring them into a partite setting, Hajnal [Hajnal]
clarified the situation for finite graphs.

######  Theorem 4.13 (Hajnal).

For every finite graph $F$ and every cardinal $\mu$ there exists a graph $H$
such that $H\longrightarrow(F)^{e}_{\mu}$. ∎

But what about countable graphs? Here the case of finitely many colours was
already addressed in [EHP75].

######  Theorem 4.14 (Erdős, Hajnal & Pósa).

For every countable graph $F$ and every natural number $r$ there is a graph
$H$ such that $H\longrightarrow(F)^{e}_{r}$. ∎

For infinitely many colours the problem is open and Shelah [Sh666]*Question
8.12 calls it a “mystery”.

######  Question 4.15.

Is it provable, in $\mathrm{ZFC}$, that for every countable graph $F$ there
exists a graph $H$ such that $H\longrightarrow(F)^{e}_{\omega}$?

We conclude with an old problem of Erdős related to Proposition 4.5( ) ‣ 4.5,
whose original source we have forgotten. But it is restated in
[Sh666]*Question 8.11.

######  Question 4.16 (Erdős).

Does there provably exist a $K_{4}$-free graph $H$ such that
$H\longrightarrow(K_{3})^{e}_{\omega}$?

By Shelah [Sh289] the existence of such graphs is consistent (even for
arbitrarily many colours). It would also be interesting to derive a positive
answer from $\mathrm{GCH}$ or from $V=L$.

Of course the real question is whether Theorem 4.13 remains valid when we add
the demand $\omega(H)=\omega(F)$. It is certainly impossible to achieve such a
result for girth instead of the clique number. For instance, if $F$ fails to
be bipartite, then every every $C_{4}$-free graph $H$ satisfies
$H\mathrel{\mkern 5.5mu\arrownot\mkern-5.5mu}\longrightarrow(F)^{e}_{\omega}$;
this is because Theorem 3.17 yields $\chi(H)\leq\aleph_{0}$, wherefore $H$ is
a union of countably many bipartite graphs. However, it still seems
conceivable that for every cardinal $\mu$ there could be a graph $H$ such that
$H\longrightarrow(F)^{e}_{\mu}$ and the shortest odd cycles in $F$ and $H$
have the same length.

More generally, one would hope to find a transfinite analogue of Theorem 4.9.
So given a finite graph $F$ the question is which finite configurations of
copies of $F$ need to be present in systems $\mathscr{H}$ with
$\mathscr{H}\longrightarrow(F)^{e}_{\mu}$, when $\mu$ gets arbitrarily large.
This kind of ‘transfinite girth Ramsey theory’ is certainly a very challenging
subject. Nevertheless, there are no convincing reasons to believe that it is
more difficult than finite girth Ramsey theory.

### Acknowledgements

It is a great pleasure to thank Joanna Polcyn for the wonderful graphical
illustrations, and guest editor Vojtěch Rödl for the invitation to contribute
to this volume. Furthermore, we would like to thank Sevda Guliyeva [Sevda],
Max Pitz, and Vojtěch Rödl for interesting discussions.

## References


Article title
Low-cost fluorescence microscope with microfluidic device fabrication for
optofluidic applications

Authors
Nagaraj Nagalingama,∗, Aswin Raghunathana,∗, Vikram Koredea, Edwin F. J.
Overmarsa, Shih-Te Hungb, Remco Hartkampa, Johan T. Paddinga, Carlas S. Smithb
and Huseyin Burak Erala

∗denotes equal contribution

Affiliations
aProcess & Energy Department, Delft University of Technology, Leeghwaterstraat
39, 2628 CB Delft, The Netherlands.

bDelft Center for Systems and Control, Delft University of Technology,
Mekelweg 2, 2628 CD Delft, The Netherlands

Corresponding author’s email address and Twitter handle
<EMAIL_ADDRESS>(Nagaraj Nagalingam)

Abstract

Optofluidic devices have revolutionized the manipulation and transportation of
fluid at smaller length scales ranging from micrometers to millimeters. We
describe a dedicated optical setup for studying laser-induced cavitation
inside a microchannel. In a typical experiment, we use a tightly focused laser
beam to locally evaporate the solution laced with a dye resulting in the
formation of a microbubble. The evolving bubble interface is tracked using
high-speed microscopy and digital image analysis. Furthermore, we extend this
system to analyze fluid flow through fluorescence$-$Particle Image Velocimetry
(PIV) technique with minimal adaptations. In addition, we demonstrate the
protocols for the in-house fabrication of a microchannel tailored to function
as a sample holder in this optical setup. In essence, we present a complete
guide for constructing a fluorescence microscope from scratch using standard
optical components with flexibility in the design and at a lower cost compared
to its commercial analogues.

Keywords
Microfluidics, experiments, laser-induced cavitation, fluorescence microscopy
and high-speed imaging.

Specifications table
o —X—X[3,l]— Hardware name Low-cost Microscope - for laser assisted studies
with in-house microfluidic device fabrication Subject area • Engineering and
material science • Chemistry and biochemistry • Flexible and modular open
source microscope • Educational method for microfluidic device fabrication
Hardware type • Mechanical engineering and materials science • Protocol to
chemical sample handling and preparation • Imaging tools • Laser assisted
microscopy Closest commercial analog Nikon’s ECLIPSE Ti inverted microscope
($\approx\textup{\texteuro}\,100,000-150,000$) Open source license CC BY 4.0
Cost of hardware € 46,429.05 (excluding laser and high-speed camera but
including additional accessories such as optical breadboard, flow control
device and 3D printer).
Refer Bill of Materials for the split-up of the costs. Source file repository
Mendeley data: http://dx.doi.org/10.17632/fy86gxm4mp.1

##  1\. Hardware in context

The evolution of optical microscopy has been sparked by the recent
advancements in digital image processing and machine vision that have led to
improved mobility and flexibility with microscopes through the use of open
hardware and software [1]. A fluorescence microscope is a non-invasive,
visualization and optical measurement tool widely employed in the field of
life sciences over the past several decades [2]. In recent times, a microscope
combined with an excitation laser has gained traction in the optofluidics
domain with an increasing number of applications that include cell sorting
[3], micro-robotics [4], microparticle synthesis [5, 6], droplet drying [7],
optical micromanupulation [8], fluid microfilms and nanofilms [9] and other
microfluidic systems [10, 11]. Commercially available microscopes often entail
huge costs ($\textup{\texteuro}\,100,000-150,000$ depending on the options and
manufacturer) and offer limited flexibility with the design. With rapid
technological advancements, microscopes have come with sophistications that
require technical expertise for operation and maintenance [12]. Moreover,
optofluidic applications generally require frequent modifications in the
optical setup which makes the use of conventional microscopes difficult.

Several microscope designs have been developed specifically to perform laser-
induced cavitation studies in microfluidic systems [13]. Rau et al. studied
the hydrodynamic effects of cell lysis using a pulsed Nd:YAG laser beam [14].
In this setup, the source beam is bisected using a beamsplitter to both lyse
the cell and illuminate the sample. Zwaan et al. performed controlled
cavitation experiments by focusing an expanding Nd:YAG laser beam with a 40x
objective to study the resulting planar bubble dynamics within different lab-
on-a-chip device geometries fabricated using Polydimethylsiloxane (PDMS) [15].
Similar experiments were carried out by Quinto-Su et al. and Sun et al. by
focusing the Nd:YAG laser beam in microfluidic gaps of variable height created
with coverslips and spacers [16] and a microtube with two different diameters
[17], respectively. Cavitation-based micropump was devised with a pulsed laser
for its application in valve-less pumping [18]. For the micropump, in addition
to recording the bubble evolution with the high-speed camera, the effect of
PDMS compliance was investigated together with the visualization of flow
fields using the conventional PIV technique. Besides single component systems
(e.g., aqueous dye), laser-induced cavitation of supersaturated aqueous
solutions inside microwells have revealed crystal nucleation surrounding an
evolving bubble [19]. Techniques such as fluorescence-based thermometry [20],
high-speed micro-PIV [21] and microparticle tracking velocimetry [22] when
combined with cavitation experiments have proven to help with the
characterization of the phenomena with the measurement of the associated
parameters such as temperature and flow fields. Although many distinct
microscopy configurations have been reported in the literature to perform
laser-induced cavitation and PIV experiments, very limited emphasis is given
to the design details, assembly of the experimental setup and the fabrication
protocols for the microfluidic devices used.

In the present work, we delineate the construction of a low-cost customizable
microscope using optomechanical components in conjunction with a pulsed laser
to primarily study laser-induced microbubble dynamics within an in-house
fabricated microchannel. In order to emphasize the flexibility of the devised
setup, we conduct an experiment using the fluorescence-PIV technique achieved
with a minor modification in the optics assembly. Furthermore, we demonstrate
the fabrication procedure of PDMS microchannels used in the experiments. We
limit our hardware design to the basic models of commercially available
counterparts. However, with dedicated customization, its applications can be
extended beyond the addressed laser-induced cavitation and PIV analyses.

##  2\. Hardware description

A schematic of the optical architecture is provided in Figure 1. Micro-sized
vapor bubble is generated by heating the solution locally using a 532 nm,
frequency-doubled, pulsed Nd:YAG laser having a beam diameter of 8 mm and a
pulse duration of 4 ns. The beam path is guided from the laser source using a
fully reflecting mirror and a partially reflecting beamsplitter. An energy
meter connected to an oscilloscope is used to measure the pulse energy
transmitted by the beamsplitter. The reflected laser pulse from the dichroic
filter is directed towards a 3-axis translation stage where the microfluidic
device is positioned. Depending on the desired laser beam diameter, a Galilean
telescope arrangement (a set of convex and concave lenses separated by the sum
of their focal lengths) can be constructed to either increase or decrease the
laser beam diameter as indicated in Figure 1. Alternatively, a beam expander
with the required magnification range can be used for this purpose but is
relatively more expensive. The flexibility of the design allows the placement
of the telescope at any position between the source laser and the dichroic
filter.

Figure 1: Architecture of the experimental setup. The sketch was made using a
free vector graphics library for optics
(http://www.gwoptics.org/ComponentLibrary/).

An inverted microscope arrangement consisting of an infinity-corrected 20x
objective with a numerical aperture (NA) of 0.5 is used to focus the laser and
form a microbubble. The energy intensity of the laser at the focal spot is
estimated to be in the order of GW/cm2. In this case, the same objective is
also used to image the sample. A red LED light of 625 nm wavelength is used to
illuminate the sample. In contrast to conventionally used white light, red
light offers some advantages. Firstly, the entire light can pass through the
dichroic filter, thereby providing better illumination at a lower intensity.
Furthermore, the spectral response of the camera is found to be the highest
for this particular wavelength. A notch filter provided beneath the dichroic
filter protects the camera by completely blocking the reflected or scattered
laser light. The sample using the objective is imaged over the camera’s sensor
with a tube lens. The high-speed camera operating at 264,000 frames per second
(fps) is used to record the events that occur at microsecond timescales.

The laboratory view of the experimental setup is depicted in Figure 2. The
3-axis translation stage (13 mm range with a least count of 10 $\upmu$m) that
holds the sample is mounted over a linear translation stage (50 mm range and
with a least count of 10 $\upmu$m) to have a larger travel range along the
microchannel axis. The microchannels are fabricated using PDMS and offer
several advantages over commercially available plastic microfluidic chips
[23]. For instance, the permeability of PDMS to gases can be exploited to
remove residual gas bubbles and improve the functionality of the device in
view of the cavitation experiments [24]. Furthermore, the elastomeric nature
of PDMS can mimic vascular pressure-driven flows which can also aid in
providing a real-time flow representation [25].

With the existing system, laser-induced cavitation is implemented in the
microchannels using a solution of aqueous red dye (DR81, Sigma-Aldrich). The
addition of a doublet lens in the laser path before the dichroic filter
enables us to perform fluorescence-PIV as a second application. PIV is carried
out in a pressure-driven flow using fluorescent tracer particles (0.955
$\upmu$m, Rhodamine B). The cavitation and PIV experiments performed in this
work are independent of each other and only highlight the adaptability in the
design of the optical setup. However, these can also be combined together into
a single experiment depending on the nature of the study [20, 18].

Figure 2: Annotation of components in the experimental setup. 1. Mounted LED,
2. Slide holder, 3. Energy sensor, 4. 20x objective, 5. Right-angle kinematic
mirror mount with round beamsplitter, 6. Right-angle kinematic mirror mount
with laser mirror, 7. Camera, 8. 3-axis travel stage, 9. Damped post, 10. Lab
jack, 11. Linear translation stage 12. Kinematic fluorescence filter cube with
dichroic and notch filters, 13. Tube lens with cage plates (tube lens) and
threading adapters, 14. Cage cube with rectangular mirror, 15. Cage plate
(objective) with threading adapter, 16. Cage system iris diaphragm, 17. Cage
plates (lens), 18. Optical post, 19. Pedestal post holder, 20. Clamping fork,
21. Cap screw. The green track indicates the laser path.

##  3\. Design files summary

The design files summary contains the required CAD and STL files that are
necessary for 3D printing the mold of microchannels.

Design filename |  File type |  Open source license |  Location of the file
---|---|---|---
Microchannels mold (for 3D printer) |  SLDPRT, STEP and STL |  CC BY 4.0 |  repository link

##  4\. Bill of materials summary

The spreadsheet containing the bill of materials (Bill of materials.xlsx) can
be found in the repository: http://dx.doi.org/10.17632/fy86gxm4mp.1. The
materials are mentioned in the same order as presented in the following
section. An additional spreadsheet containing the description of the materials
(Description of materials.xlsx) used is also provided in the repository.
Please note that the material costs furnished might vary with different
suppliers, time period and the location of purchase.

##  5\. Build instructions

This section provides the complete procedure for the assembly of the
experimental setup using discrete optomechanical components. The main emphasis
is laid on the ease of alignment and the quality of imaging. The optical train
is constructed predominantly using 30 mm cage components. The details of
mountings for each of the components are given in the respective links
provided in the bill of materials. The setup is built starting with the
dichroic filter and subsequently branched in three directions namely the
objective branch, tube lens branch and the laser guidance and telescope branch
as depicted in Figure 3. Additionally, some laser mirrors are used to guide
the laser path from the source and this might vary in each case.

###  5.1 Microscope construction

Figure 3: Sketches of a) dichroic filter in a cage system. b) sub-assembly of
the objective branch. c) sub-assembly of the tube lens branch. d) sub-assembly
of laser guidance and telescope branch. e) complete assembly of the
microscope.

  1. 1.

At first, mount the laser (Part #1) on the optical breadboard (Part #2) with
the help of Allen keys (Part #3) while allocating sufficient space for the
remaining components of the setup.

  2. 2.

Place the dichroic filter (Part #4) inside the kinematic fluorescence filter
cube (Part #5) and position it accordingly such that it is inclined at 45∘ to
the incident laser beam while the coated side faces the incoming laser light
as shown in Figure 3a.

  3. 3.

Using the help of cage assembly rods (Part #6), assemble the cage system iris
diaphragm (Part #7) followed by the cage plate (Part #8) for the objective on
the side of the reflected laser light as depicted in Figure 3b.

  4. 4.

Screw the 20x objective (Part #9) to its cage plate while making use of the
threading adapter (Part #10) in order to match the screw threads. In the
current setup, the objective has a NA = 0.5 and focal length,
$f_{\mathrm{objective}}$ = 10 mm. The calculated pupil diameter of the
objective is, $2\,(\textup{NA})\,f_{\mathrm{objective}}=10\,\textup{mm}$.

  5. 5.

On the opposite side of the kinematic fluorescence filter cube, secure the
notch filter (Part #11) in the emission filter port with the engraved
transmission arrow pointing away from the dichroic filter.

  6. 6.

Following this, sandwich the tube lens (Part #12) between the two cage plates
(Part #13) with the aid of threading adapters (Part #15) and then attach this
sub-assembly to the cage assembly rods (as indicated in Figure 3c) beneath the
notch filter making sure that the transmission arrow points away from the
notch filter. The required magnification ($m$) can be achieved by choosing the
tube lens with the right focal length ($f_{\mathrm{tubelens}}$),

$m=f_{\mathrm{tubelens}}/f_{\mathrm{objective}}.$ (1)

In order to achieve a magnification of 20x, the tube lens with
$f_{\mathrm{tubelens}}=200\,\textup{mm}$ is chosen.

  7. 7.

At the bottom, connect the cage cube (Part #16) containing the rectangular
mirror (Part #17) inclined at 45∘ to the incident light with the cage assembly
rods.

  8. 8.

On the laser incident side of the kinematic filter cube, fasten the cage
assembly rods (Part #18) and attach two cage plates (Part #19) for lenses as
in Figure 3d. The use of lens is required only if there is a need for varying
the laser source beam diameter as shown in Figure 1. One of the cage plates is
secured whereas the other is left free to slide so that adjustments can be
made depending on the focal length of the lenses used. Additionally, a drop-in
cage mount (Part #20) holding the achromatic doublet lens (Part #21) is
mounted as shown in Figure 3e only while performing the PIV experiments.

  9. 9.

Take a couple of right-angle kinematic mirror mounts (Part #22) each
encompassing a round beamsplitter (Part #23) and a round laser mirror (Part
#24) respectively and connect them using the cage assembly rods. Insert this
sub-assembly to the other end of the cage assembly rods extending from the
kinematic filter cube as represented in Figure 3d. The distance between the
two mirror mounts can be adjusted for varying the height based on the laser
source position by adding or removing the cage assembly rods.

  10. 10.

In order to erect the setup upright, secure the right angle kinematic mirror
mount to the optical breadboard with the help of optical posts (Part #26),
right angle post clamp (Part #27), pedestal post holder (Part #28), clamping
fork (Part #29) and cap screw (Part #30). Place the lab jack (Part #31)
beneath the cage cube for support as portrayed in Figure 2.

  11. 11.

Alongside the setup, clamp the linear translation stage (Part #32) to the
breadboard and mount the damped post (Part #33) on top of it (refer Figure 2
\- side view). Insert the post mounting clamp (Part #34) through the damped
post and tighten it. By making use of the optical posts and right angle post
clamp, set up the 3-axis travel stage (Part #35). Connect the slide holder
(Part #36) to the travel stage using an optical post and ensure that it
remains on top of the objective by adjusting the height. The linear travel
stage facilitates a larger translation in the horizontal direction whereas the
3-axis travel stage helps with smaller translations in all three directions.
In addition, the post mounting clamp provides a rotational degree of freedom
to the slide holder.

  12. 12.

With the support of an optical post, post holder, clamping fork and cap screw,
place the mounted LED (Part #37) on top of the slide holder (refer Figure 2 \-
side view). Connect the cable from the LED light to the LED driver (Part #38)
and power the LED driver using the power source. The LED driver controls the
light intensity.

  13. 13.

Similarly, align the energy sensor (Part #39) above the beamsplitter to
measure the energy of each laser pulse. The output of the sensor is connected
to the oscilloscope (Part #40) which reads the measured output voltage. The
energy can be calculated from the voltage using the calibration curve of the
energy sensor provided by the manufacturer for the laser wavelength used.

  14. 14.

Finally, position the camera (Part #41) in-line with the cage cube as shown in
Figure 3e. Link the camera and laser by means of a BNC cable (Part #42) to the
digital delay generator (Part #43). The camera is triggered to record starting
with 5 image frames before pulsing the laser so as to image the initial
condition of the sample just before laser irradiation.

###  5.2 Alignment of the optical components

During the construction of the microscope, the objective, tube lens and camera
are initially positioned based on the design specifications provided by the
manufacturer. The working distance of the tube lens is used as the distance
between the tube lens and the camera. While, the distance between the
objective and tube lens, $L$, is calculated using [26],

$L=f_{\mathrm{tubelens}}(\phi_{2}-\phi_{1})/\phi,$ (2)

where $\phi_{1}$ is the objective exit pupil diameter, $\phi_{2}$ is the tube
lens entrance pupil diameter and $\phi$ is the camera’s sensor size.

However, in practice, an alignment laser (Part #44) is used for the purpose of
aligning these components precisely [27]. This laser is first passed through
the tube lens towards the objective as shown in Figure 4a. During this
process, the dichroic and notch filters are removed temporarily so as to allow
the transmission of the laser. The position of either the objective or the
tube lens is varied such that the alignment laser exiting the objective’s
front lens remains collimated at any distance further from the objective. This
is ensured with the help of a detector card (Part #47). The above procedure
allows us to determine the exact position of the tube lens relative to the
objective or vice versa. The same alignment procedure can also be followed for
non-infinity corrected objectives. However, a very precise positioning of the
objective relative to the tube lens is required to overcome the drawbacks due
to potential loss in image quality. On the other hand, infinity-corrected
objectives allow the positioning of additional optical components such as
dichroic and notch filters between the objective and camera without causing
any aberrations or distortions.

Figure 4: Illustrations of a) the alignment of objective and tube lens. b) the
alignment of camera. c) the alignment of lenses. d) the alignment of doublet
lens for PIV.

In a similar manner, the precise position of the camera is determined to
obtain a sharp image. First, the objective is unscrewed from the cage plate
temporarily and the alignment laser is placed such that it passes through the
kinematic fluorescence filter cube (without the dichroic filter) towards the
direction of tube lens. The point where the tube lens focuses the alignment
laser is found using the detector card as depicted in Figure 4b. The camera
sensor is mounted exactly at this marked position. In this configuration, an
additional mirror is used in between the tube lens and the camera to guide the
light - allowing us to position the camera horizontally (stable orientation).

In the case of using a pair of lenses (as a Galilean telescope) to vary the
source beam diameter, the lenses are initially placed at a distance equal to
the sum of their focal lengths. In order to fix this distance accurately and
ensure whether the beam remains collimated in the far field, the lenses are
positioned in between the alignment laser and the shearing interferometer
(Part #48) as shown in Figure 4c. The laser light passing through the lenses
forms an interference fringe pattern on the diffuser plate (or shear plate) of
the shearing interferometer. When the fringes are parallel to the ruled
reference line marked in the diffuser plate, the beam is collimated, and hence
this distance between the lenses can be maintained while performing the
experiments.

###  5.3 Alignment for PIV experiment

For performing the PIV experiment, a doublet lens is placed in between the
right-angle kinematic mirror mount with the beamsplitter and the kinematic
fluorescence filter cube containing the dichroic filter. The focal length of
the doublet lens is chosen such that:

demagnification = diameter of laser beam / field number,

where the desired field number is the diameter of the view field. The position
of the doublet lens is determined such that the beam from the alignment laser
passing through the doublet lens remains collimated when it leaves the
objective as represented in Figure 4d.

###  5.4 Microfluidic device fabrication

Microfluidic devices allow us to both process and analyze samples with small
volume handling. In this work, PDMS (Part #49) is used to fabricate the
microchannels [28], for which a 3D printed mold is used. The microchannels
with a rectangular cross-section ($100\,\upmu$m× $250\,\upmu$m) are employed.
Since the dimensions of the channels described are in the order of hundreds of
microns, a higher precision is required for preparing the mold. The mold is
fabricated using Form 3+ resin printer (Part #50) with a layer resolution of
$25\,\upmu$m using Formlab’s clear V4 resin. Alternatively, the molds can also
be prepared using silicon wafers employing the photolithographic technique.
Although silicon wafers offer very high layer resolution ($\sim 2-5\,\upmu$m),
they are quite expensive ($\sim$ €1000).

The microchannels preparation process is illustrated in Figure 5. During the
fabrication, a cover glass is attached to the PDMS cast to cover the open side
of the channels. For this purpose, the PDMS mixture is applied over a #1 cover
glass (Part #51) using a spin coater (Part #52), which is then bonded to the
cast. The inlet and outlet ports for the microchannels are created by piercing
the PDMS cast with a precision tip (Part #53) before attaching the cover
glass. A detailed preparation protocol can be found in the Microchannel
preparation.docx document.

Figure 5: Visual demonstration of the fabrication procedure of microchannels.
a) PDMS mixture is prepared. b) 3D printed mold is placed inside the
petridish. c) The centrifuged PDMS mixture is poured into the petridish
containing the mold. d) Vacuum is applied to remove the air bubbles present.
e) PDMS is cured together with the mold and the required portion of PDMS along
with the mold is cut carefully after curing. f) PDMS cast is separated from
the mold. g) Inlet and outlet ports are created using the precision tip. h) A
layer of PDMS is spin-coated over the cover glass. i) Coated cover glass is
bonded with the PDMS cast to obtain the final device.

During the experiment operation, the laser passes through both the cover glass
and a thin layer of PDMS within the microchannel. The PDMS coating over the
cover glass in the microchannel preparation is not only used to bond the PDMS
cast to the cover glass, but also ensures that the fluid experiences uniform
friction across all the surfaces that it is in contact with.

##  6\. Operation instructions

Safety: Always remember to wear the laser safety glasses (Part #54) to protect
your eye during the operation of the laser.

###  6.1 Laser-induced cavitation in microchannels

Transient micro-vapor bubbles are produced by focusing the laser within
aqueous solutions containing a red dye. Since water is transparent to 532 nm
wavelength, a dye is used to facilitate the solution’s absorbance to produce
thermo-cavitation [10]. The red dye (Part #55) with a concentration of 0.5 wt%
and an absorption coefficient of 173.47 cm-1 is used in this study.

The laser (Nano L 50-50 PIV, Litron) is operated in a pulsed mode using the
delay generator to produce single laser pulses on demand. The flash lamp and
Q-switch are triggered externally using two TTL pulses (4V) with $96\,\upmu$s
time delay. This delay between the flash lamp and Q-switch can vary based on
the laser model and the oscillator (for twin-headed lasers). The digital delay
generator is set to externally trigger the camera at least 5 image frames
before the Q-switch is triggered. Before pulsing the laser, the settings for
the camera which include the field of view in pixels, frame rate and trigger
options for recording are assigned accordingly using the Photron FASTCAM
Viewer (PFV) 4 software (https://photron.com/photron-support/). After the
laser pulse is shot, the created vapor bubble exists for tens of microseconds
depending on the energy supplied. The recorded images are saved in ‘.MRAW’
file format as it can then be converted to any desired format using the same
software. Further details regarding the absorbance measurements, calibration
of the camera and experiment protocols for sample preparation and setup
operation can be found in Raghunathan [29].

###  6.2 Visualization of the flow field in microchannels

Fluid flow inside microchannels is visualized by performing fluorescence-PIV.
Tracer particles (fluorescent indicators) are prepared with 2.5% w/v aqueous
dispersion of Rhodamine B (0.955 $\upmu$m with COOH=80 $\upmu$mol g-1, Part
#56) by diluting in water to 0.09 v/v%. The closest alternative to the
Rhodamine B particles (with a diameter of 0.955 $\upmu$m) currently available
in the market is the red-fluorescent particles (Part #57).

The operation procedure for the laser and camera similar to the cavitation
experiment is adopted with a few modifications as follows. During these
experiments, the laser is triggered externally with the triggering rate set to
50 Hz - the maximum allowable frequency for the laser. In coordination with
the laser, the camera’s recording frequency is also set to 50 fps. The
recording time in the camera is set to 2 s. Pressure is applied to one end of
a channel to induce flow and is regulated using a flow control system (Part
#58). Real-time control and automation of pressure is achieved using the
software interface OxyGEN (https://www.fluigent.com/research/software-
solutions/oxygen/). The top and bottom walls of the microchannel are
determined by identifying the stationary particles.

##  7\. Validation and characterization

Following the instructions for constructing the microscope and fabricating the
optofluidic device, we demonstrate the working and validation of the setup.
Here, we exploit two different implementations of the hardware: laser-induced
cavitation and fluorescence-PIV, achieved with minimal modifications to the
microscope assembly. The validation of this working setup along with the
customizations can prove to be beneficial for a multitude of research
applications [30].

###  7.1 Bubble dynamics

The microchannel filled with aqueous red dye solution is placed on the slide
holder and the laser pulse at an energy of 118.1 $\upmu$J is focussed at the
channel centre to produce a vapor bubble. The images of the vapor bubble
captured using the high-speed camera are represented in Figure 6a. Only the
central part of the bubble is imaged due to lower number of pixels available
for recording at the operated high frame rate.

The time evolution of the vapor bubble after processing the images is
presented in Figure 6b. The size of the bubble ($L$) and the time ($t$) are
non-dimensionalized with respect to the channel hydraulic diameter
($d_{\mathrm{h}}$) and collapse time of the bubble ($\tau$), defined as the
time taken by the bubble to collapse from maximum size to zero, respectively.
This non-dimensionalization allows us to compare our results with the existing
literature. The observed time scale associated with the length scale of the
bubble is in good agreement with the experiments reported by Hellman et al.
[31] and Quinto-Su et al. [32] as shown in Figure 6c. The values of the
parameters used to plot Figure 6c are provided in Table 1 below.

Table 1: Parameter values used in the analysis of laser-induced cavitation experiments. Author |  Marker |  Channel Dimensions [$\upmu$m] |  $\mathbf{d_{\mathrm{h}}}$ [$\upmu$m] |  $\mathbf{\tau}$ [$\upmu$s]
---|---|---|---|---
This work |  $\square$ |  $100\times 250$ |  143 |  30
Hellman et al. [31] |  $\bigcirc$ |  $50\times 100$ |  66.7 |  25
Hellman et al. [31] |  $\Diamond$ |  $50\times 200$ |  80 |  15
Quinto-Su et al. [32] |  $\triangle$ |  $30\times 50$ |  37.5 |  17
Figure 6: Laser-induced cavitation experiments. (a) Experimentally obtained
bubble images recorded using the high-speed camera operated at 264,000 fps and
supplied laser pulse energy of 118.1 $\upmu$J. (b) Bubble evolution obtained
from the post-processed experimental images. The error bars represent the
standard error of 5 trials performed. (c) The non-dimensionalized parameter
values compared against experiments from literature [31, 32].
$L_{\mathrm{max}}$ represents the maximum size of the bubble.

###  7.2 Flow field detection

A $100_{-25}^{+0}\,\upmu$m × $250_{-30}^{+0}\,\upmu$m microchannel is used to
perform the PIV experiments. The flow of the fluorescent particles is imaged
at different planes along the depth of the channel ($100\,\upmu$m) starting
from the channel bottom in steps of 10 $\upmu$m. Since the frequency of the
laser source is 50 Hz, the camera is also operated at 50 fps. An example image
acquired for the flow field measurement through PIV within the microchannel is
shown in Figure 7a.

Figure 7: PIV measurements. (a) Typical example image from the PIV experiments
performed. The white dots represent the fluorescent particles, the yellow
lines indicate the channel boundaries (250 $\upmu$m apart) and the white arrow
points to the direction of the flow. (b) Normalized flow velocity along the x
direction. $z=0$ is the mid-plane of the channel having a depth of 80
$\upmu$m.

The data acquired from the PIV measurements is processed with the OpenPIV
package (http://www.openpiv.net/openpiv-python/) using the Python script PIV
analyzer.ipynb. The velocity of the flow along the depth ($z$-direction) of
the channel can be expressed using the following equation [33]:

$u=u_{\mathrm{max}}\left(1-\frac{4z^{2}}{H^{2}}\right)$ (3)

where $H$ is the channel depth, $z\in[-H/2,H/2]$ is the distance from the mid-
plane and $u_{\mathrm{max}}$ the magnitude of the velocity at $z=0$.

The normalized velocities measured at different distances from the
microchannel’s mid-plane are plotted in Figure 7(b). It can be seen that the
results obtained from the experiments are in very good agreement with the
theory for shallow laminar flows (Hele-Shaw flows).

To conclude, we have provided a guide for building a low-cost microscope from
scratch dedicated to laser-assisted optofluidic studies with fully customized
optics. Two different experimental techniques were carried out using the
working setup with minimal changes in the optical architecture. Furthermore,
the in-house fabrication procedure for the microfluidic device that is used to
analyze the sample solutions is also demonstrated. Finally, we have validated
the experiments against the theory and empirical data to exhibit the full
working functionality of the system. With dedicated adaptations, this proposed
design can be utilized for a vast range of applications, e.g., in
microfluidics [34, 35] and laser-induced crystallization research [36].

Ethics statements Animal and human rights: Not applicable.

Credit author statement Nagaraj Nagalingam: Conceptualization, Methodology,
Validation, Investigation, Writing - Original Draft. Aswin Raghunathan:
Methodology, Visualization, Writing - Original Draft. Vikram Korede:
Methodology, Resources. Edwin F. J. Overmars: Resources. Shih-Te Hung:
Methodology. Remco Hartkamp: Writing - Review & Editing, Supervision. Johan T.
Padding: Writing - Review & Editing, Supervision. Carlas S. Smith:
Methodology, Writing - Review & Editing. Huseyin Burak Eral: Writing - Review
& Editing, Supervision, Funding acquisition.

Declaration of Competing Interest The authors declare that they have no known
competing financial interests or personal relationships that could have
appeared to influence the work reported in this paper.

Acknowledgements The authors thank Rumen Georgiev for the training in
microfluidic device preparation. We also thank Dr. Daniel Irimia for guiding
us with the optics. This work was funded by the Netherlands Science Foundation
(NWO) through the Open Technology Programme, project number 16714 (LightX).

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Ir. Nagaraj Nagalingam is a PhD researcher in the Process & Energy department
at the Delft University of Technology, where he investigates the physico-
chemical phenomenon of “Non-Photochemical Laser Induced Nucleation” through
experiments and numerical simulations. Nagaraj received his M.Sc. degree in
Mechanical Engineering – specializing in Energy, Flows and Process Technology
from TU Delft. His previous work during the masters was on “Shape dependent
motion of particles subjected to Stokes/creeping flow in a microfluidic
channel having a Hele-Shaw geometry”. He is also a qualified Application
Engineer in the field of turbochargers with 2 years of experience. He has a
strong determination to contribute to the field of transport phenomena.

Ir. Aswin Raghunathan is a master graduate from the Process & Energy
department at the Delft University of Technology, where he investigated the
mechanism behind laser-induced crystallization through microfluidic
experiments. Previously, he received his bachelors degree in Mechanical
Engineering from SASTRA University, India in 2016. His research interest
includes fluid mechanics applied to industrial processes. He also has over 2
years of work experience as a Design Engineer in the automotive sector.

Ir. Vikram Korede is a PhD researcher at the Process & Energy department in
the Delft University of Technology. He is working on non-photochemical laser
induced nucleation and anti-solvent crystallization. Vikram received his M.Sc.
degree from the Department of Chemical Engineering at TU Delft and bachelors
degree from the National Institute of Technology, Tiruchirappalli, India.
During his masters, he worked on the topic titled “Controlling crystal size in
solvent exchange process”. He combines the knowledge of microfluidics,
crystallization, optics, multiphase phenomena and aims to understand the
interplay happening between light and matter in producing highly crystalline
materials that has direct applications to fine speciality chemicals
industries, pharmaceutical industries, catalyst industries, etc.

Ing. Edwin F. J. Overmars is an expert in optical measurement techniques in
the Laboratory for Aero and Hydrodynamics at Process & Energy department at
the Delft University of Technology.

Shih-Te Hung is a PhD student at Delft University of Technology. He received
his Physics degree from NANU Taiwan, and a master’s degree in Photonics from
Friedrich Schiller University, Jena, Germany. His research focuses on super-
resolution microscopy and adaptive optics.

Dr. Remco Hartkamp is an assistant professor in the Process & Energy
department at the Delft University of Technology, where he investigates
molecular and macroscopic phenomena at the solid-fluid interface, with a
special interest in the formation of electric double layers. Before starting
his position at TU Delft in 2017, Dr. Hartkamp obtained a PhD (2013) in
mechanical engineering from the University of Twente and Swinburne University
of Technology and held postdoctoral positions at the Massachusetts Institute
of Technology and Vanderbilt University. Website:
https://rmhartkamp.github.io/

Dr. Johan T. Padding is a full professor and chair of Complex Fluid Processing
in the Department of Process and Energy (P&E) at Delft University of
Technology. He has an MSc in applied physics and a PhD in chemical physics
from University of Twente, focusing on microscale and mesoscale simulations of
soft matter. After several postdocs in Cambridge (UK), Twente (NL) and
Louvain-la-Neuve (BE), Johan got a tenured position at Eindhoven University of
Technology in 2011 where he shifted his attention to larger scale multiphase
flows. He moved to Delft University of Technology in 2016. Website:
http://padding.freecluster.eu

Dr. Carlas S. Smith is an assistant professor in the Delft Center for Systems
and Control at Delft University of Technology. His research transcends the
classic boundaries between biology and engineering to visualize single
molecules in living cells. For this purpose, he combines advanced control
strategies, algorithm development, and computational microscopy technology.

Dr. Huseyin Burak Eral is an assistant professor in the Process & Energy
department at the Delft University of Technology, where he investigates
crystal engineering, colloidal physics and hydrodynamics/microfluidics. After
receiving his bachelor and master degrees in chemical engineering at Boğaziçi
University and University of California Santa Barbara respectively, H. Burak
Eral obtained his PhD degree in applied physics at the University of Twente in
2012. He went to the Massachusetts Institute of Technology to work as postdoc
at MIT-Novartis center for continuous manufacturing. He then moved to Delft
University of Technology in October 2016. He also holds a guest faculty
position in Van’t Hoff labs in Utrecht University. Website:
https://erallab.com/

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