Light‐Induced Virtual Electrodes for Microfluidic Droplet Electro‐Coalescence

Electro‐coalescence is the fusion phenomenon between a pair or more microfluidic droplets that are immersed in an immiscible medium under an electric field. This technique is frequently used to merge confined droplets in surfactant‐stabilized microfluidic emulsions using local electric fields. Despite the necessity of miniaturized electrodes, this method has proven highly successful in microfluidics and lab‐on‐a‐chip applications. Miniaturized electrodes severely curtail the spatial and temporal flexibility of the electric potential, thus hindering real‐time and flexible operation and leading to high production costs. The current study addresses this problem with reconfigurable electric field potential by light‐driven functional virtual electrodes. These electrodes are light‐induced on a non‐centrosymmetric ferroelectric photovoltaic crystal placed below a microfluidic droplet channel. The photovoltaic effect in the crystal is responsible for the space charge distributions that act as virtual electrodes, whose evanescent field is screened by free charges into the two liquids inside the channel. A numerical model is developed to describe the evolution of the evanescent electric field causing electro‐coalescence. Based on this prediction, two coalescence processes occur at two different timescales and with different numbers of droplets involved. Controlled exposure time modulation allows either rapid on‐demand coalescence of droplet pairs or breakup of the entire emulsion.


Introduction
The phenomenon of droplet coalescence is the fusion between a pair or more isolated liquid volumes immersed in an DOI: 10.1002/adfm.202305286immiscible medium.This phenomenon occurs due to the destabilization of the interface layer between droplets caused by external forces.The electric field is the most commonly used external stimulus for the coalescence of water in insulating oil droplets. [1]This method has enabled numerous applications, ranging from water extraction [2] to materials synthesis. [3]ith the advent of microfluidics, electrocoalescence has been also widely used in droplet-based lab-on-a-chip for chemical reactions, [4,5] as well as for manipulation of biological cells [6,7] or performing miniaturized diagnostic tests. [8]The application of strong electric fields was especially necessary for surfactant-stabilized emulsions, [9] which are frequently employed to maintain the stability of each droplet over prolonged periods of time. [10]he electro-coalescence of microfluidic droplets revealed unexpected behaviors, such as collective coalescence waves [11] and upstream coalescence. [12]The discovery of these phenomena provided access to tailoring an entire emulsion of droplets, such as by breaking the emulsion [13] or by merging individual pairs of droplets. [14]The standard technique for the electro-coalescence of microfluidic droplets is based on physical electrodes, [15] which represent an insurmountable physical limit for system reconfigurability.On the one hand, a single electrode corresponds to only one specific electrical potential configuration within the device.On the other hand, each electrode must be miniaturized and aligned within micrometer devices, which requires considerable fabrication effort.Inevitably, the number of electrodes inside a microfluidic device is limited, even with the use of advanced fabrication techniques, and so is the spatial control of the phenomenon.This feature is incompatible with the high demand for real-time, flexible, and powerful tools to ensure decision-making and efficient operation in microfluidic devices. [16]Therefore, an electrodeless solution that can guarantee spatial and temporal customization of the electrical potential is highly demanded.
In this context, optical tools are a promising solution [17,18] due to the unique nature of light to be optically structured. [19]However, optical forces alone are not suitable for droplet manipulation due to the mesoscale nature of the droplets and the low contrast in refractive indices between the two liquid phases.Therefore, light is alternately used as a trigger for other forces and The coalescence process of water droplets (blue) in an oil phase (orange) is triggered only by light-induced virtual electrodes generated by photovoltaic current j PV .This current is the consequence of the photoexcitation of charges from Fe 2+ sites in Fe:LiNbO 3 , as shown by the schematic band structure in the inset.c) Example of coalescence caused by a light stripe with a width of w = 234 μm and a homogeneous light intensity I = 2.5•10 5 W m −2 .d) The schematic shows the working mechanism of the screening effect in the presence of charged micelles (blue/red) in the oil.This reduces the evanescent field compared to the case with an insulating medium with negligible free charges.
effects [17] to maintain the advantage of optical shaping.For example, droplets were controlled by the surrounding photosensitive materials, either the droplet-dispersing liquid or the rigid material constituting the microfluidic device.Functional materials were introduced into microfluidic devices to change their shape or mechanical properties when stimulated by light. [20,21]26] Light-induced electric field generation methods are still the most demanded due to the wide range of electric fieldbased techniques and applications in microfluidics, such as dielectrophoresis. [27]Among the materials suitable for this purpose, those with photovoltaic (PV) [18] or photothermal [28,29] properties have been shown to efficiently generate local electric fields for droplet manipulation at moderate light intensities.[32][33] In particular, the PV effect enables the generation of space charge distributions inside the material shaped by structured light. [34]45][46] The use of virtual electrodes on this material for droplet manipulation has recently been extended to surfactant-stabilized droplets, revealing different behaviors for concentrations below or slightly above the critical micellar concentration (CMC). [47]urfactants have extensive applications in droplet microfluidic devices with concentrations above CMC, especially in stabilizing droplet emulsions. [10]Emulsions with concentrations above the CMC exhibit extended stability due to the inhibition of spontaneous coalescence. [10]Thus, they are essential for almost all practical applications of microfluidic emulsions for droplet isolation.Despite their advantage in stabilization, coalescence processes present a particular challenge with the presence of surfactant concentrations exceeding the CMC.Achieving coalescence operations in these emulsions is crucial for merging specific droplets in a controlled manner.
The electro-coalescence of confined and surfactant-stabilized droplets in microfluidic devices has never been observed using light-induced virtual electrodes.This work investigates the electro-coalescence of surfactant-stabilized microfluidic droplet emulsions through light-induced virtual electrodes by PV effect upon structured light illumination of a ferroelectric crystal.The latter replaces the solid substrate (typically glass) in standard soft microfluidic devices [48] (see Figure 1a).A microfluidic circuit based on a T-junction is used to generate the water-in-oil emulsion flowing on the top of the crystal.The evanescent part of the electric field outside the crystal interacts with the flowing confined droplets inside the channel, causing electrocoalescence.[51][52] This screening effect has been observed for particles and is attributed to the presence of charged micelles. [49,51]To model this phenomenon, we employ a Maxwell-Wagner two-layer model [53] for an estimation of the timescale.Additionally, we validate our results through numerical analysis, specifically by examining the changes in the evanescent field between droplets.The experimental results consist of the observation of two regimes of coalescence: one after a few milliseconds of illumination between pairs of droplets, and the other after longer illumination times characterized by collective behavior.The first coalescence occurs before the electric field is screened, while the second has an abrupt behavior and depends on the illumination times.Based on the screening time, customized light pulses allow the selection of coalescing droplet pairs within a large emulsion using the first regime, as well as sequential and reproducible coalescence.The frequency of successive coalescence processes is compatible with standard microfluidic operations, demonstrating the feasibility of such a real-time approach in microfluidic devices.

Photoinduction of Virtual Electrodes in Microfluidic Platforms
The electro-coalescence presented in this work relies on virtual electrodes induced by light on photovoltaic crystals.Among the photovoltaic crystals, iron-doped lithium niobate (Fe:LiNbO 3 ) is the most widely used for droplet manipulation due to the high electric fields achievable (on the order of kV mm −1 ) at moderate light intensities [34][35][36][37][38][39][40]47] (i.e., I<10 6 W m −2 ). We ave integrated a crystal of Fe:LiNbO 3 as the underlying surface of a droplet microfluidic circuit embedded in a substrate of Polydimethylsiloxane (PDMS).Figure 1a depicts the double-layer device, where droplets flow on the top of the crystal.During the illumination of Fe:LiNbO 3 with a light pattern, photoexcited carriers are separated along the polar axis of the crystal (c-axis) by the PV effects within the crystal, as shown in Figure 1b.The accumulation of charges leads to a space charge distribution that depends on the orientation of the c-axis and the light structures. Te local distribution of space charges on the crystal surfaces acts as virtual electrodes, applying an electric field whose evanescent part extends into the microfluidic channel (purple lines in Figure 1b). Te interaction between the evanescent electric field and the flowing droplets in the channel causes the formation of liquid bridges between droplets, and thus, electro-coalescence.Stripe-shaped light patterns with widths w similar to the droplet sizes and constant length l s = 891 μm induce coalescence due to this electric field, as shown in Figure 1c.

Electro-Coalescence Mechanism
Electro-coalescence occurs when the oil layer separating the droplets is disrupted by the formation of liquid bridges con-necting two droplets.According to the Taylor-Melcher leaky dielectric model, an electric field causes an accumulation of free charges at the interface between the droplet and the surrounding medium, thus creating a Maxwell stress that acts against the capillary pressure. [12]This stress leads to a droplet deformation and a net body force on the droplets.In the presence of nonuniform electric fields, dielectrophoretic forces can drag droplets into close contact, destabilizing the oil layer and causing coalescence.In the case of a single droplet, disintegration occurs, [11] when the Maxwell stress overcomes the capillarity.For multiple droplets, the oil layer separating the droplets is destabilized at a critical value of the electric field, which is below the dielectric breakdown due to the dynamic destabilization of this liquid dielectric layer. [54,55]An exemplary threshold value of ≈1.5 MV m −1 has been measured for IsoparM oil with SPAN80 as a surfactant.This value is ten times lower than the oil's voltage breakdown threshold. [54]The electric field in the gap between two droplets is also enhanced by the reaction of electrical polarization of the two droplets due to the presence of the field, and the consequential interaction between droplets.In addition, the presence of surfactant adds further interaction with the electric field.Recent research using virtual electrodes has shown that droplet surfactant layers can act as insulating barriers, preventing charge transfer. [47]Furthermore, the introduction of an electric field can cause surfactant molecules to displace and reorient themselves, resulting in concentration gradients and surface tension variations within a channel. [56,57]Such gradients can lead to the emergence of Marangoni forces, which can potentially destabilize the oil layer between droplets.
In the proposed system, these phenomena depend on the evolution of the evanescent electric field inside the channel.This field emerges due to the accumulation of surface charge density C inside the crystal by the PV effect, which depends on the exposure time t and the light intensity I.For simplicity, we used homogeneous intensities I between 10 5 W m −2 and 10 6 W m −2 and illumination times t up to 100 s.The light consists of a continuous wave laser beam with a wavelength  = 532 nm structured by a light shaping technique.In this range of intensity I and illumination time t, the optothermal effect and pyroelectric effect of the crystal have a minor contribution to the electrical field at the virtual electrodes (see section B of the Supporting Information).

Photovoltaic Virtual Electrodes in Fe:LiNbO 3
38][39][40]47,58,59] The bulk PV effect in non-centrosymmetric ferroelectric crystals occurs due to the photoexcitation of charges with a preferential momentum along the polar c-axis, leading to a photocurrent directed along this axis.In Fe:LiNbO 3 , the effect is enhanced by the presence of iron doping, which acts as both electron donors and acceptors (see inset in Figure 1b).This is attributed to two valence states of the iron sites in LiNbO 3 that have two valence states: Fe 2+ and Fe 3+ . [60]Photoexcitation in Fe:LiNbO 3 requires light within a spectral range in the visible with a peak at 477 nm.The charge transport in doped Fe:LiNbO 3 during illumination within this spectral range can be described by the one-center model, [61,62] which considers iron sites as the only donor and acceptor centers.One result of this model is the estimation of the photovoltaic current as: where q is the electron charge and s = 4.55•10 −22 m 2 is the photoionization cross-section, [33] [Fe 2+ ] is the donor concentration, L PV = 5 Å is the PV transport length, ϕ = I (h v) −1 is the photon flux with Planck's constant h, the light frequency v = c  −1 , and light intensity I.
The value of the light intensity I in the manuscript considers the losses due to reflection and the absorption of the crystal. [34]he versor u z is due to the preferential momentum of carriers along the c-axis, corresponding to the crystal's z-axis (see Figure 1).Another significant result of the one-center model is the prediction of the photoconductivity (i.e., the conductivity of the illuminated crystal) as: where μ = −5•10 −7 m 2 V −1 s −1 is the electron mobility,  0 = 2.58•10 −10 F m −1 is the permittivity along the c-axis of the crystal,  = 10 −15 m 3 s −1 is the recombination constant of electrical carriers, and  PV is the dielectric relaxation time.The time constant  PV ranges from 0.3 s to 1.6 s for the crystal and light intensities used in this work.The photoconductivity, therefore, depends on the light intensity, and for the range used it varies between 8•10 −10 S m −1 and 1.6•10 −10 S m −1 .These conductivities are much larger than the crystal's dark conductivity, which is ≈10 −15 S m −1 . [63]In our experimental case, the crystal is always subjected to the white light of the microscope for imaging purposes.The conductivity in this low white light regime is measured as 5•10 −12 S m −1 , which corresponds to a dielectric relaxation time  WL ≈150 s (see section D of Supporting Information).Net charges accumulate on the opposite sides of the c-axis due to the charge transport through the current J LN of Equation 1. Charge accumulation only occurs in the illuminated region, as long as transverse currents to the c-axis such as diffusion are negligible.Therefore, the final surface charge density C has the same shape as the light field, allowing the light to directly shape the virtual electrode.In open circuit conditions, the temporal evolution of space charge density C can be approximated as a capacitor charging curve with a time constant equal to the dielectric relaxation time  PV .However, in the case of water droplets in hexadecane, the conductivity of the liquids affects the charge accumulation due to screening effects in the microchannel (see Figure 1d).

Screening Effect
The evolution of the evanescent field has been related in the literature to the charge accumulation neglecting eventual external contribution. [30,34]This is a valid approximation as long as the outer material is poorly conducting, such as air or highly insulating liquids.This condition leads to a screening effect that alters the evolution of the evanescent electric field in the microflu-idic channel.This is the case for water droplets and high surfactant concentration oil, whose free charge carriers interact with the evanescent field generated by the accumulation of charges in the crystal.During the photoexcitation and the charge accumulation of the +c surface of the crystal, the evanescent field is the result of the charges inside the crystal and the channel, as shown in Figure 1d.
The screening effect is due to the accumulation of free charges in the liquid medium at the interface between the channel and the Fe:LiNbO 3 during the generation of virtual electrodes.The presence of free carriers in nonpolar dielectric liquid like hexadecane is due to the presence of charged micelle for surfactant concentration above the critical micellar concentration (CMC).This phenomenon has been observed by the increase of the conductivity of the oil-surfactant mixture, [51,52,64] by the formation of a double layer, [50] and by the screening effect on charged particles. [49]or the mixture of SPAN80 and hexadecane used in this work, the conductivity has been measured by impedance spectroscopy (see section C of the Supporting Information) and agrees with the literature value of  hex = 4•10 −8 S m −1 . [64]This high value compared to one of pure hexadecane (typically <10 −14 S m −1 ) shows the presence of charged micelles.Despite the introduction of surfactant showing a strong variation in the conductivity, it has been reported to have a minor contribution to the dielectric constant, [50,65] and thus, the dielectric constant of pure hexadecane is a good approximation.This leads to a dielectric relaxation time of the oil phase of 454 μs.The screening effect for the electric field between droplets occurs mainly in the oil since it is in direct contact with the Fe:LiNbO 3 .Conversely, the electric field within the water droplets is screened by free charges in the water moving at the droplet surface.This effect is faster compared to the accumulation of charges in the crystal due to the faster dielectric relaxation time of MilliQ water of 126 μs (conductivity  w = 5.5•10 −6 S m −1 ) than the crystal's one,  PV .Therefore, the droplets develop immediately an electrical polarization according to the charge accumulation in the crystal and this polarization screens the electric field inside the droplets.The electrical polarization of droplets is also responsible for the interaction between the droplets.In the simplest case, this interaction would be dipole-dipole interaction, but higher order terms may occur (for simplicity we will call this interaction dipole-dipole).
The screening effect in the oil layer between the droplet and the virtual electrode can be modeled by the Maxwell-Wagner relaxation effect. [53]This effect has been recently used to simulate the conductivity of a similar system, [53] and it describes the accumulation of charges across the interface of composite materials in an external electric field.The charge accumulation is characterized by a time constant which depends on the electrical conductivity  1,2 , the dielectric constant  1,2 , and the thickness d 1,2 of the two materials, respectively.In the presented configuration, the two layers are the Fe:LiNbO 3 photo-inducing an internal charge distribution and the oil layer underneath the droplet compensating the photocarriers in the crystal.Compared to conventional models, [53] there is no external voltage and the  MW gives an estimation of the response time of the screening effect.The oil phase parameters are the measured conductivity  hex , the thickness of the lubrication oil layer around the droplet, which we consider as 5 μm (typically it is between 1-10 μm [66,67] ), and the dielectric constant of hexadecane (i.e., 2.05).The parameters considered for the crystal are listed in Table 2S (Supporting Information) for the thickness and dielectric constant.The conductivity of the crystal depends on the light conditions and, thus, the Maxwell-Wagner time constant depends on the illumination conditions.In dark conditions, the crystal behaves as a dielectric and the screening time constant is  MW,dark = 33 ms (see section D of the Supporting Information).The photoconductivity is estimated by Equation 2 and depends on the light intensity, thus resulting in  MW,light between 27 ms and 16 ms.

Numerical Investigation of Screened Virtual Electrodes
Light-induced virtual electrodes in Fe:LiNbO 3 crystal can be screened by free charges in the liquids.To demonstrate the consequence of the screening effect on the evanescent field, we performed a 2D numerical simulation of the charge transport inside the crystal considering only the PV contribution (more details are given in section E of the Supporting Information).For this purpose, we have used the Finite Element Method implemented by COMSOL Multiphysics.The three different layers (i.e., Fe:LiNbO 3 , channel, and PDMS) are considered to be immersed in a larger area of air (see Figure 2a).The thickness of the c-cut Fe:LiNbO 3 crystal was 0.5 mm, as in the experiments.The droplets are approximated as squeezed rectangles with circular caps on the two sides.The droplets have a length of 400 μm and a height of 90 μm and they are arranged in an array of 10 consecutive droplets with a minimum gap distance of 5 μm.The height of the microfluidic channel and the PDMS layer on top are 100 μm and 3 mm, respectively.For simplicity, the droplet flow has been neglected in the simulation, and droplets are in a fixed position during the time evolution.Different positions are tested to understand the role of the positioning (see section E of Supporting Information).
The screening effect in the channel has been considered proportional to the evanescent electric field (more detail of the simulation can be found in section E of Supporting Information).Different numerical simulations have been performed with stripes with constant width w = 234 μm and for several values of intensity.An example of the result is reported in Figure 2 for I = 2.5•10 5 W m −2 .To observe the screening behavior, the time evolution of the electric field in this geometry is calculated in a range of 10 s.The two examples at t = 27 ms and t = 10 s in Figure 2b,c, respectively, show the two components of the electric field.
Consistent with the charge accumulation due to the PV effect, Figure 2b shows an electric field inside the crystal ≈100 times smaller than Figure 2c.Although charges accumulate similarly on both surfaces of the crystals under ideal open-circuit conditions (see section E of the Supporting Information), the screening effect in the microchannel is responsible for the asymmetry of the electric field.It is important to note that the simulation does not consider any charge accumulation in the air at the bottom.While this could have potentially lessened the asymmetry, the low conductivity of air (≈10 −14 S m −1 ) would have limited its impact.For example, the simulation considers the charge accumulation in PDMS (conductivity of 2.5·10 −14 S m −1 ), which does not provide any significant contribution.Similarly, the air contribution can be neglected.
Both electric field components have similar asymmetric shapes within the crystal at t = 27 ms and t = 10 s.The only substantial difference between the electric fields is in the gaps between the droplets, which is highlighted by the insets of both Figure 2b,c.Notably, the electric field in this region is the highest in the entire microchannel.This result shows the relevant role of the dipole-dipole interaction between the droplets and the screening effect taking place in this region between 27 ms and 10 s.The graph in Figure 2d reveals an exponential decrease of the xelectric field component in the central part of the gap between the droplets close to the virtual electrode due to the screening effect.|E x (gap)| reaches the maximum at the instant t max of 8 kV cm −1 at 27 ms before screening occurs, which in contrast leads to a decrease to 0.06 kV cm −1 after 10 s, although the electric field within the crystal is increased by 100 times in the same temporal interval.This behavior agrees with the screening effect description and the timescales agree with  MW,light (I = 2.5•10 5 W m −2 ) = 0.19 s, despite the simple approximation.
The screening effect and the dipole-dipole interaction between the droplets drastically affect the evanescent electric field, which is not directly proportional to the electric field evolution in the crystal.The dipole-dipole interactions enhance not only the evanescent field in the gap between droplets close to the stripe but also for other droplets in the array, as shown in Figure 2e,f by the intensity profile of the x-component of the electric field along the cut line in Figure 2a.In both graphs, the shape of the field is similar and decreases as the droplets move away from the virtual electrodes.Nevertheless, the electric field in Figure 2f is ≈100 times lower than that in Figure 2e due to screening.
Notably, varying the position of the droplet array with respect to the virtual electrodes slightly changes the value of |E x (gap)|.The latter depends on the screening effect over time, and also on the position relative to the light field (see section E of the Supporting Information).At a distance of 23 μm from the edge of the virtual electrode, the maximum value of |E x (gap)| reaches 8 kV cm −1 .This value is comparable with an exemplary threshold observed in the literature. [54]The field values above the coalescence threshold are achieved only during a limited time interval before the screening effect.Additionally, this occurs in a limited spatial region around the stripe's edge.Therefore, coalescence is predicted to occur before the screening effect and within a region proximate to the virtual electrodes.The flow of the droplets during the generation of virtual electrodes makes it complex to predict exactly the temporal evolution of the region where |E x (gap)| is above the coalescence threshold.Nevertheless, we will make an experimental analysis and discussion in Section 3.3.1 considering the flow of droplets.

Coalescence Regimes During Continuous Illumination
The first experiments use virtual electrodes induced by continuous illumination for an interval of 100 s.Two different coalescence regimes are observed during this interval.In Figure 3a,b, six frames show both regimes, distinguished by the timescales and the number of droplets involved.
The first coalescence, hereafter called local coalescence, in Figure 3a, occurs between two droplets located near the position of the electrodes and a few milliseconds after the start of illumination.The resulting merged droplet then flows along the channel like the other droplets.After the initial coalescence phenomenon, the droplets continue to flow undisturbed in the channel for a few seconds.Then, another coalescence process takes place (see Figure 3b), hereafter called breaking coalescence, which involves the entire emulsion of droplets in the channel.The timescales of both processes are shown in the graph of Figure 3c for each droplet flow rate fq (it depends on the flow rates of the two liquid phases Q w and Q o ) and for each channel configuration tested (i.e., the ratio between the channel section on the funnel part l 2 /l 1 ).The data does not evidence a significant variation of the timescale t of the two coalescence regimes (the time after the start of the illumination) due to different microfluidic parameters (i.e., fq and l 2 /l 1 ).The local coalescence shows a timescale that varies between a few milliseconds and seconds, and it occurs only for I≥1.25·10 5 W m −2 .Breaking coalescence has a timescale of several seconds and has been observed over the entire range of light intensity.
It is worth mentioning that devices with glass and undoped LiNbO 3 as bottom substrates did not show any coalescences despite the same microfluidic configurations, and illumination parameters.Video SV4, SV5, and SV6 (Supporting Information) are examples of these tests with different materials.In these videos, the evidence of the illumination is the fluorescence response of the fluorescent dyes added to the oil phase.The absence of coalescence in the glass device shows an irrelevant contribution of optical heating within the channel.Therefore, any Marangoni forces due to light-induced heating are negligible.Furthermore, the absence of coalescence for the undoped crystal indicates the relevant role of iron doping.

Coalescence Mechanism
Local and breaking coalescence are both characterized by the formation of liquid bridges between droplets due to the disruption of the oil layer separating droplets.The bridge formation can be observed, for example, as the opaque region between the merging droplets in the center frame in Figure 3a,b, for both regimes.The main difference between the two regimes is the timescale and the number of droplets involved.The accumulation of free charges inside the water droplet is simultaneous with the accumulation in the crystal since the relaxation time of water can be considered infinitesimally small (relaxation time of 126 μs).For this reason, the dipole-dipole interaction enhances in both regimes the electric field between droplets as highlighted in Figure 2d,e.In contrast, the role of oil is not the same for both processes.Local coalescence exhibits timescales t< MW,light (see Figure 3c) in agreement with the low screening regime described by the simulation in  For illumination times below  MW,light , the charges at the virtual electrodes have still to be screened.At these timescales, the charge density C is not yet completely screened, and the field between two droplets reaches the highest value.The numerical simulation indicates that the electric field reaches its peak at t max , increasing the chances of coalescence.The timescale for local coalescence in Figure 3c agrees with t max in the entire range of intensities.
It is important to note that an evanescent field above the coalescence threshold can be achieved with exposure times shorter than t max .Indeed, the spatial region with an electric field above the coalescence threshold the largest at t max , but it is not negligible for a time shorter than t max .To estimate the instant t th when the maximum of |E x (gap)| is above the coalescence threshold, we used the method described in section F of Supporting Information.The method relies on the evolution of |E x (gap)|, like the one shown in Figure 2d, for 7 different values of I and considering the experimental timescale t for local coalescence at I = 1.25·10 5 W m −2 as the threshold time t th at this intensity.The values of t th at other intensities are obtained by this method and are shown for the entire intensity range in Figure 2c.Despite the rough approximation of the threshold, the majority of the dataset of experimental values for local coalescence present a larger timescale than t th (only one point is close to the expected, but it has large dispersion).In conclusion, the comparison between t th , t max ,  MW,light , and the experimental timescale for local coalescence confirms that the local coalescence is driven by the PV effect and occurs in a temporal window before the screening effect.The entire dynamics considering droplet flow and charge accumulation is hard to predict since the position of droplets at the start of electrode induction instant is challenging to precisely control.This is particularly in-teresting for modulated illumination which is discussed further in Section 3.3.Notably, the typical threshold behavior observed for local coalescence in Figure 3c agrees with conventional electrode experiments, [11][12][13][14][15] where a threshold field is observed.It is also worth mentioning that the screening effect has usually not been considered in conventional electrode configurations due to the high frequency of the applied voltage, i.e., the frequency is higher than the typical inverse response time of the oil phase.
Different from local coalescence, breaking coalescence presents a timescale that is way above  MW,light .In this case, the field generated by charge accumulation is screened in the channel and any droplet deformation or dragging processes are strongly depleted.In this work, we do not want to develop a comprehensive model that accounts for every detail to fully comprehend the specific mechanism of breaking coalescence.Instead, we propose several potential factors that may contribute to the phenomenon of breaking coalescence, based on experimental results.First, screening charged micelles in the oil must compensate for both the increasing charge density C at the crystal surface and the free charges at the droplet interfaces.While in the crystal photoexcited charges are continuously supplied at this timescale, the screening charge is limited by the concentration in the oil.For example, in a rough approximation of open circuit conditions, the crystal saturates after 10 times  PV .The continuous increase of C over time due to PV current can lead to a sudden lack of screening charges to compensate for both the droplets and C. Despite the continuous flow of the oil in the channel, the density of screening charges is limited, [34][35][36][37][38][39][40]47] and there is a continuous exchange between the screening layer and the flowing liquid. Thisdeficiency leaves uncompensated the high density of charges accumulated in the droplets, causing instantaneous instabilities and rupture of the oil layer between several droplets.This is consistent with the absence of a threshold behavior since the same charge density C can be achieved with any kind of intensity but longer exposure times, as long as the conditions for Equation 1 are met.In addition, the trend of breaking coalescence timescale is inversely proportional to I similar to  PV .The decrease in the timescales for I>3·10 5 W m −2 is probably due to an inaccurate description of the PV effect by Equation 1.At such an intensity range the contribution of centers other than iron becomes significant and the pyroelectric contribution is contributing significantly to charge transport.
Second, the realignment and displacement of the adsorbed surfactants at both the droplet interfaces and the crystal interfaces may be no longer negligible on this timescale and can provide a significant contribution.It is well-known that the surfactant may realign in an electric field. [56,57]In addition, the large displacement of surfactant towards the virtual electrodes may cause gradients of surfactant concentration, and thus it can lead to the emergence of Marangoni forces.
Lastly, the crystal exhibits a strong asymmetry of electric field and charges along the c-axis due to the screening on the surface of the crystal in contact with the microchannel.This behavior is also evident in the electric field in Figure 2b.This is due to the uncompensated charges on the opposite side of the crystal, which is not in contact with the microfluidic channel, but with air that has negligible screening effect.It is worth noting that this behavior is due to both liquids.The numerical simulation results for a crystal with both faces (+ and -c) in contact with oil reveal that the effect is lowered, but it does not disappear completely.Surely, this asymmetric behavior due to the screening effect also plays a relevant role in the breaking coalescence.The virtual electrode is larger than the original light pattern, in this case, and the field to be compensated is larger at a longer timescale, as shown in Figure 2b,c.An abrupt loss of the screening leads to a virtual electrode, which is not localized anymore and is larger than the original one.This effect explains the larger number of droplets involved in the breaking coalescence compared to the local coalescence.Furthermore, the larger is the area of the virtual elec-trode, the larger the amount of screening charges required for a screening effect.At some critical value of the size of the electrodes, the layer might become unstable.In this condition, the generation of instability at some critical point, [55] such as an incoming new droplet in the channel, can disrupt the screening layer.
In conclusion the screening effect is a valid explanation for the large difference in the timescale and the number of droplets involved between the two processes.Other possible explanations of these differences, such as the contribution of the pyroelectric effect are neglected due to the minor contribution of this effect at this timescale (see section B of the Supporting Information).

Coalescence Regimes during Modulated Illumination
Pulsed illumination introduces a non-continuous evolution of the space charge distribution compared to the continuous case.The charge accumulation in the crystal and consequently the screening effect depends on the time duration of each pulse t on , on the possible residual carriers generated by previous pulses, and thus, on the time duration between two consecutive pulses t off .During each pulse, the charges accumulate as in the continuous case, and during the time between two pulses t off , the charge can recombine or be fully screened.Despite the difference in the evolution of the virtual electrodes, the two regimes still occur for pulsed illumination depending on the two intervals t on , t off (see Figure 4a).Two scenarios arise with two different periodic modulations described in Table 1.
Both sets refer to a stripe electrode of w = 234 μm in the same channel configuration and flow rates as in the continuous illumination cases.A comparison between the two modulations can be seen in the examples shown in Figure 4a,b.For the first set (1 in Table 1), local coalescence is observed in correspondence of the pulses (see Figure 4c,d).For the second set (2 in Table 1), no local coalescence is observed, while a delayed breaking coalescence occurs (see Figure 4e,f).Thus, the introduction of the modulation changes the behavior of the virtual electrodes.For both modulations, during a single interval t off , the recombination of charges within the crystal is negligible, since the dielectric relaxation time constant of the crystal  WL ≈150 s is much longer than t off (see section D of the Supporting Information).
Local coalescence is strongly suppressed for the second set, because the electric field between droplets does not achieve a value above the coalescence threshold during each pulse.This is due to t on «t max and t on close to the threshold time t th (i.e., 3 ms at I = 2.5•10 5 W m −2 ).Below t th , the electric field in the gap between droplet |E x (gap)| does not reach the coalescence threshold in any position.For time t on close to t th , the spatial region with |E x (gap)| above the coalescence threshold is expected to be negligible, and thus local coalescence is strongly suppressed.In addition, t off is much shorter than the typical screening timescales (i.e.,  MW,light ), and, after the first pulse, the local coalescence is strongly depleted due to screening.However, t off is shorter than  WL and the recombination of accumulated charges is negligible.Therefore, the buildup of the PV charge accumulation occurs in each pulse undisturbed by each t off .We observed that each breaking coalescence process observed for the second set occurs at a delayed time, which corresponds to the timescale of the continuous case delayed by the sum of each t off (see section G of the Supporting Information).This is also valid varying the t off and different I (see section G of the Supporting Information).This confirms the dependence between breaking coalescence and accumulated PV charges.Possible mechanisms explaining the effect have to consider the role of the PV accumulated charges.
Conversely, the first set presents t on in the same order of magnitude of t max and always larger than t th (i.e., 3 ms at this intensity).The screening effect at this timescale is negligible and the spatial region of the electric field above the coalescence is the largest.Therefore, local coalescence is not suppressed anymore.The breaking coalescence is, instead, strongly delayed by the slow buildup of the PV charges.For example, a t off = 0.5 s and t on = 0.05 s results in an expected delay of 120 s, during which the laser does not illuminate the crystal (calculated considering a total amount of illumination time equal to the equivalent timescale for continuous illumination at this I).Such a delay is of the same order of magnitude as  WL and recombination may play a role in delaying the breaking coalescence even more.We did not observe breaking coalescence in any condition for the first set, despite 100 s of recording.The local coalescence during each pulse depends on the positioning of the droplet interface with respect to the maximum of the field achieved during each t on .A local coalescence process occurs in each pulse if the droplet interface flows in a region of |E x (gap)| above the critical field for coalescence.This behavior depends on the speed of the droplets, t on , and I. Since the droplets are randomly distributed in the channel at the beginning of each t on , the behavior of local coalescence is studied by 40 consecutive pulses.For each t on , t off combination, the efficiency is estimated by the ratio r c between the number of coalescences and the number of light pulses.
From the discussion about the spatial features of the electric field coalescence threshold made in Section 3.2, it is expected a high r c for exposure time close to t max , and low r c for t on approaching t th , since the size of the region of the electric field above the coalescence threshold depends on the exposure time (see section E of Supporting Information).Similarly, the speed of droplets influences the r c , since it increases the chances of having an interface between two droplets in the region of the electric field above the coalescence threshold during t on .In addition, we expect a higher ratio r c at greater I due to the faster charge accumulation.For this reason, we carried out the same experiments of pulsed illuminations with different values of I, as shown in the graph of Figure 5a.We observe a ratio r c = 1 for I = 2.5•10 5 W m −2 and, since t on = 0.1 s>t max = 27 ms (see Figure 3c).It is noteworthy that r c drops to zero for I approaching the threshold of the intensity I th (see section F of Supporting Information).This value is defined as the intensity at which the |E x (gap)| max achieves the critical field for coalescence.Also, the result in Figure 5a shows that for t on ≈t max the r c decreases differently for different speeds of droplets (i.e., lower droplet rates fq).Not all the different droplet rates fq exhibit the same behavior, showing the importance of positioning the droplets during t on .Despite being t on >t th , the results in Figure 5a show a relevant role of fq in this light intensity range, as described in the following section.

Comparison of Droplet Rate and t on
The number of droplets flowing during the interval t on depends on the injection rate or the production frequency fq.At constant intensity I = 2.5•10 5 W m −2 and t off = 1 s, the efficiency shown in Figure 5b depends on both the time t on and the rate fq.The reason is the low average number of droplets N dr = fq t on flowing in the region of the evanescent field above the coalescence threshold during the interval t on .Since the spatial region of the electric field above the coalescence threshold is limited in space (see section E of the Supporting Information) and time by the screening effect, faster droplets have higher chances to flow in the region, and, thus, higher chance of coalescing.This effect can be expressed quantitatively by the number N dr .The same efficiency results plotted against N dr do indeed reveal a univocal trend as shown in Figure 5c.The graph shows a clear linear trend for N dr >1, and it reaches a fixed plateau at r c = 1 for N dr <1.A number N dr = 1 corresponds to the flow of at least one interface between a droplet pair across the stripe pattern during the pulse duration, t on .Consequently, the probability of electrocoalescence, reflected by the efficiency ratio r c , increases when the interval t on is longer than the time required for at least one droplet pair to flow through the virtual electrode inside the channel.As long as t on >fq −1 , the efficiency of the electro-coalescence approaches 100%.Therefore, the process is not directly limited by the droplet rate.Even droplets with rates of kHz can be processed with a t on of tens of milliseconds, allowing the use of the method in high throughput systems. [68]It is worth mentioning that droplet generation with microfluidic devices integrating Fe:LiNbO 3 is well-known.Monodispersed droplets can be generated with either T-junction or co-flow configurations following the literature droplet scaling laws. [45,46,69]The droplet frequency fq is, indeed, proportional to the flow rates Q w , Q o . [40]For simplicity, the ratio Φ = Q w Q o −1 is kept constant at 1 throughout our work.The ratio Φ is proportional to the ratio between the volumes of the two phases in the channel and, thus, determines the density of the droplet emulsion in the channel.No differences are observed in the local coalescence regime for the less dense droplet arrays, especially in the funnel-shaped part of the channel, for more details see section H of the Supporting Information.In addition, the position and the number of droplets involved in a local coalescence can be customized by the position of the virtual electrode and, thus, by the light pattern (for more details and results see sections I and J of the Supporting Information).

Conclusion
This work demonstrates the electro-coalescence of confined droplet emulsions flowing in a microchannel using light-induced virtual electrodes in ferroelectric crystals.The virtual electrodes consist of photoexcited spatial charge distributions in Fe:LiNbO 3 crystal due to PV current.For the first time, controlled electrocoalescence is achieved with this optical method for surfactantstabilized emulsion flowing in a microfluidic channel.The evanescent field arising from the virtual electrodes is responsible for electro-coalescence.Light structures can functionally define the accumulation of charges in the crystal, both in density and shape.The electric field configurations are thus unlimited in terms of shape, position, and intensity by light structuring.We have shown that simple stripe patterns act as virtual electrodes with light intensities between 10 4 -10 6 W m −2 and exposure times between milliseconds to seconds.Two regimes of coalescences are observed considering for the first time the screening effect due to charge carriers in both liquid phases.The local coalescence regime occurs between droplets located close to the electrode after a few milliseconds of illumination.The breaking coalescence regime is a collective coalescence and it takes place when the electrodes are exposed for tens of seconds.A screening effect has been numerically studied and proposed as the origin of the differences between the two regimes, considering the presence of the charged micelles in the hexadecane with surfactant concentration above the CMC.So far, similar regimes (local and collective) have only been observed with metallic electrode configuration, [11,12] which does not allow any reconfigurable configuration.Both coalescence processes are fundamental operations in standard droplet microfluidic protocols.On the one hand, fast and selective coalescence is essential for real-time operation at high throughput. [68]On the other hand, emulsion breaking is necessary for cleaning and resetting the microfluidic circuit state. [12]Achieving this process with a reconfigurable electrode paves the way to customize emulsions and gain new insights into coalescence behaviors.
We adapted pulsed illuminations to achieve one of the two regimes based on the discharge time of the surface charge densities from the two contributions.The local coalescence is achieved for each pulse of duration >5 ms with remarkable efficiency and reproducibility.The optical nature of the electrode allows the se- ) both substrates are treated with air-plasma, to activate the surfaces (2.), and then, covalent bonds are formed by contact (3.).c) Scheme showing the microfluidic circuit.d) The experimental setup: the syringe pumps and the microfluidic droplet generation device, the microscope consisting of a white light source (WT), a condenser lens (CL), a filter (F), a tube lens (TL) and a camera (CAM).The photo-inducing source for the virtual electrodes consists of a continuous wave laser (CW laser), whose polarization is controlled by a polarizing beam splitter (PBS) and a half-wave plate (/2).The illumination intervals are controlled by a mechanical shutter (SH), and a photodiode (PD) connected to an analog-to-digital DAQ module measures these intervals for the residual light part from the PBS.An amplitude spatial light modulator (ASLM) in a 4f lens configuration (L3, L4) shapes the beam, which is previously cleaned by a beam cleaner (L1, PH, L2).Finally, the structured light is coupled into the microscope via an external tube lens (L5) and a dichroic mirror (DM).lection of the location and the coalescing droplet pair for each pulse.The proposed method meets the high demand for the reconfigurability of lab-on-a-chip, which benefits from real-time control of microfluidic droplets. [16]In addition, virtual electrodes do not present the tedious and costly requirements of electrode miniaturization and wiring, since the device is fabricated with conventional methods without the need for cleanrooms.Embedding ferroelectric crystals in microfluidic devices is indeed straightforward due to the excellent microfluidic properties of these crystals, such as optimal wettability, [69] biocompatibility, [70] and chemical resistance.After proper cleaning procedures of the microchannel, the same device could be used for different purposes at the same time and for complex operations.For example, in lab-on-a-chip applications that require multiple operations based on real-time decision making an electrode that can be turned on and off, positioned, and reshaped on demand is essential.Such a method could find profound lab-on-a-chip applications for chemical or biological operations, such as using fused droplets as microreactors. [4,5]Finally, the virtual electrodes are not limited to droplets but can also handle biological samples [71] or optically active media, such as liquid crystals. [44]In conclusion, this optical method of the virtual electrode represents an optimal solution for real-time reconfigurable electro-coalescence for microfluidic droplet emulsion applications.PDMS Microfluidic Channels: The microfluidic channel was realized by standard soft lithography in PDMS as shown in Figure 6a.The microfluidic structures were replicated in PDMS from molds consisting of Si wafer and SU8-2075 photoresist (Microchem).A 100 μm thick layer of SU8 was spin-coated onto a Si wafer, followed by a UV exposure performed at 33 mW cm −2 for 7 s, and the wafer was developed in SU8-developer (Microchem) for 5 min.The SU8-Si mold was replicated in a PDMS substrate, which was cured at 80 °C for two hours.Bonding between the PDMS and one of the three substrates (i.e., Fe:LiNbO 3 , LiNbO 3 , and a standard glass slide) was achieved by OH-bonds after an air plasma treatment for 2 min.The schematic in Figure 6b shows the principle and the procedure used.The microfluidic circuit consists of a T-junction droplet generator that forms droplets and injects them into a large channel (see Figure 6c).Two channel configurations were used: the first one has channel widths of l 1 = 100 μm and l 2 = 600 μm (l 2 /l 1 = 6), and the second one has two channel combinations of l 1 = 200 μm with l 2 = 800 μm and l 1 = 100 μm with l 2 = 400 μm (l 2 /l 1 = 4).In each configuration, the height of the channels was equal to 100 μm, the distance from the T-junction to the l 2 channel was 7 mm, and the length of the l 2 section was 2.5 mm.

Experimental Section
Microfluidic System: The two liquid phases were MilliQ water (resistivity 18.6 MΩ cm −1 ) and hexadecane (CH3(CH2)14CH3, 99%, Sigma Aldrich) with a non-ionic surfactant concentration of 3% (w/w) of SPAN80 (C24H44O6, Sigma Aldrich).The surface tension between the two phases was 4.76±0.26mN m −1 measured by the pendant drop method. [72]A syringe pump (Nemesis S, Cetoni) injects the two liquids into the device at controlled flow rates, Q w and Q o , respectively.Rhodamine 6G (Sigma Aldrich) was included in the oil solution with a concentration of 41 μM to indicate the location of illumination for the experiments with glass and LiNbO 3 .
Experimental Setup for Light-Induced Droplet Coalescence: The setup shown in Figure 6d was based on an inverted microscope (Ti-series, Nikon) with a 4x/0.10 objective used for simultaneous imaging and induction of the virtual electrodes.A high-speed camera (MV2-D1280, Photonfocus) mounted on the microscope body captures the flow and coalescence of the droplets.A dichroic mirror directs the photoinduction beam through the microscope objective.The light source for the photoinduction was a continuous wave laser (wavelength  = 532 nm maximum power P = 1.5 W, Samba, Cobolt) polarized by a half-wave plate and a polarizing beam splitter, expanded by a telescope and shaped by an amplitude spatial light modulator (ASLM, HED6001 Holoeye).The shaped beam was coupled inside the microscope using a 4f lens configuration.A mechanical shutter (LS6 6 mm and driver VMM-D1, Uniblitz) modulates the illumination.A photodiode monitors the time evolution of exposure by collecting the residual light output from the polarizing beam splitter.The intensity signal from the photodiode was amplified by a photodiode amplifier (PDA200C, Thorlabs) and digitized by a DAQ (USB-6009, National Instruments).

Figure 1 .
Figure 1.a) Photo of the microfluidic device during the induction of the virtual electrodes with green light.The 3D schematic shows the double-layer configuration: the transparent PDMS layer on the top and the brown Fe:LiNbO 3 crystal on the bottom.A light pattern propagating along the c-axis defines the space charge distribution in the crystal, as shown in the schematic of the side xz-view in b).The coalescence process of water droplets (blue) in an oil phase (orange) is triggered only by light-induced virtual electrodes generated by photovoltaic current j PV .This current is the consequence of the photoexcitation of charges from Fe 2+ sites in Fe:LiNbO 3 , as shown by the schematic band structure in the inset.c) Example of coalescence caused by a light stripe with a width of w = 234 μm and a homogeneous light intensity I = 2.5•10 5 W m −2 .d) The schematic shows the working mechanism of the screening effect in the presence of charged micelles (blue/red) in the oil.This reduces the evanescent field compared to the case with an insulating medium with negligible free charges.

Figure 2 .
Figure 2. a) Schematic diagram of the 2D geometry used for the numerical simulations of the PV electric field created by a c-cut Fe:LiNbO 3 crystal with a microfluidic channel on top.The light stripe has a width of 234 μm and the intensity is 2.5•10 5 W m −2 .b), c) Spatial distribution of the PV field for exposure times of 27 ms and 10 s, respectively.In b) and c), the upper graphs correspond to the z-component of the field (E z ), while the bottom graphs correspond to the x-component (E x ).The insets show a magnified view of E x in the gap between two water droplets.d) Time evolution of |E x | in the gap between two droplets, located 140 μm away from the center of the illumination.e), f) Representation of |E x | along the cut line that passes through the center of the droplets in the microfluidic channel, as shown in a).

Figure 3 .
Figure 3. Two different coalescence regimes occur during the photoinduction of the virtual electrode.a), b) Three consecutive frames show an example of local and breaking coalescence processes (from the video SV1 in section A of the Supporting Information), respectively, with a stripe pattern illumination of w = 468 μm and I = 1.75•10 5 W m −2 , highlighted by the green rectangles.c) The graph shows the results obtained for the timescales of the two regimes in the intensity range used for different configurations: flow rates in μL min −1 , stripe pattern in μm, and channel configuration.The error bars are smaller than the size of the markers when not visible.

Figure 2 .
Figure2.For illumination times below  MW,light , the charges at the virtual electrodes have still to be screened.At these timescales, the charge density C is not yet completely screened, and the field between two droplets reaches the highest value.The numerical simulation indicates that the electric field reaches its peak at t max , increasing the chances of coalescence.The timescale for local coalescence in Figure3cagrees with t max in the entire range of intensities.It is important to note that an evanescent field above the coalescence threshold can be achieved with exposure times shorter than t max .Indeed, the spatial region with an electric field above the coalescence threshold the largest at t max , but it is not negligible for a time shorter than t max .To estimate the instant t th when the maximum of |E x (gap)| is above the coalescence threshold, we used the method described in section F of Supporting Information.The method relies on the evolution of |E x (gap)|, like the one shown in Figure2d, for 7 different values of I and considering the experimental timescale t for local coalescence at I = 1.25·10 5 W m −2 as the threshold time t th at this intensity.The values of t th at other intensities are obtained by this method and are shown for the entire intensity range in Figure2c.Despite the rough approximation of the threshold, the majority of the dataset of experimental values for local coalescence present a larger timescale than t th (only one point is close to the expected, but it has large dispersion).In conclusion, the comparison between t th , t max ,  MW,light , and the experimental timescale for local coalescence confirms that the local coalescence is driven by the PV effect and occurs in a temporal window before the screening effect.The entire dynamics considering droplet flow and charge accumulation is hard to predict since the position of droplets at the start of electrode induction instant is challenging to precisely control.This is particularly in-

Figure 4 .
Figure 4. a), b) Light intensities collected by the photodiode for modulations with t on = 0.1 s t off = 2.5 s, and with t on = 5 ms and t off = 40 ms, respectively.c), d) Examples of local coalescence for droplets with Q w = Q o = 1 μL min −1 , and Q w = Q o = 20 μL min −1 after a single pulse of t on = 0.1 s and 0.03 s , respectively.e), f) Examples of breaking coalescence for periodically modulated illumination with t on = t off = 5 ms after a time of 99.4 s and 36 s from the first pulse, respectively.The Video SV7, SV8, and SV9 (Supporting Information) refer to f), c), and d), respectively.

Figure 5 .
Figure 5. a) Efficiency ratio r c is plotted against I for modulated illumination with t off = 1 s and w = 234 μm for five different values of t on and droplet flow rate fq.The corresponding flow rates of the two phases are Q w = Q o = 1, 2, 4, 5, 10 μL min −1 .The purple dashed line is the threshold intensity I th estimated in Section F of Supporting Information.b) Efficiency ratio r c versus the pulse duration t on for modulated illumination with t off = 1 s, I = 2.5•10 5 W m −2 , and a stripe shape with w = 234 μm.The purple and gray dashed lines indicate the t th and t max , respectively.c) Same results plotted against the number of droplets flowing during t on on the virtual electrode N dr .The legend used in b) is also valid for c).

Figure 6 .
Figure 6.a) Schematic of the mold replication technique: (1.) a mold made by standard lithography is replicated by pouring PDMS (2.), which is cured and cut accordingly (3.).b) Scheme of the air-plasma bonding technique: (1.) both substrates are treated with air-plasma, to activate the surfaces (2.), and then, covalent bonds are formed by contact (3.).c) Scheme showing the microfluidic circuit.d) The experimental setup: the syringe pumps and the microfluidic droplet generation device, the microscope consisting of a white light source (WT), a condenser lens (CL), a filter (F), a tube lens (TL) and a camera (CAM).The photo-inducing source for the virtual electrodes consists of a continuous wave laser (CW laser), whose polarization is controlled by a polarizing beam splitter (PBS) and a half-wave plate (/2).The illumination intervals are controlled by a mechanical shutter (SH), and a photodiode (PD) connected to an analog-to-digital DAQ module measures these intervals for the residual light part from the PBS.An amplitude spatial light modulator (ASLM) in a 4f lens configuration (L3, L4) shapes the beam, which is previously cleaned by a beam cleaner (L1, PH, L2).Finally, the structured light is coupled into the microscope via an external tube lens (L5) and a dichroic mirror (DM).