2.1.

Catapulting Particles with Generalized Phase Contrast

Our setup for catapulting microspheres benefits from an extended working distance made possible by using low numerical aperture (NA) objectives.^49–51 Using counter-propagating catapulting beams, it has also been demonstrated that such low NA setups can actuate microstructures by transversely translating and adjusting the relative intensities of the beam pairs.^49–51 Low NA objectives allow the light to interact with the sample environment in a wider, 3-D manner, which will allow us in the future to perform advanced studies using different microtools.^45,48 Furthermore, this extended geometry facilitates the extraction of $z$-depth information through direct side-view imaging. These features come at the price of typically having a smaller back aperture in the low NA objective lenses used. In commonly used holographic optical tweezers,⁵² a wider back aperture (higher NA) is necessary to get a wider conjugate image of the spatial light modulator (SLM) through the aperture. The generalized phase contrast (GPC) method circumvents these NA constraints through the use of a “$4f$” imaging geometry. This means that a localized focused light distribution is situated at the objective lens’s back aperture, and hence, potential losses from aperture truncation are minimized. Similar to diffractive holography, GPC is also an efficient “phase-only” laser beam-shaping technique.^53,54 However, unlike in diffractive holography, GPC-shaped beams have a well-defined extended region where the beam intensity is more uniform, speckle-free, and with well-defined boundaries. The uniform lateral beam profile of GPC-shaped beams results in a relatively extended axial profile as the beam propagates, which improves the optical catapulting of microspheres over long distances.

The GPC method works by transforming an incident Gaussian beam into desired output shapes, such as a top-hat, through a direct mapping of the input phase mask patterns.⁵⁵ To produce a desired output intensity shape, an input phase mask is visualized at the output plane as an intensity distribution through common path interference with a synthesized reference wave (SRW). The SRW is brought about by a phase-contrast filter (PCF) that usually applies a 180-deg phase shift to the beam’s lower spatial frequency components. Unlike in the case of using a Gaussian beam, a microsphere being catapulted by a GPC-shaped beam receives a uniformly intense radiation flux over its cross section. A schematic of the GPC light-shaping method is illustrated in Fig. 1.

Fig. 1

Schematic diagram of the GPC light shaping method.

When optically catapulting microspheres over an extended distance, it is desirable to have a beam distribution that remains relatively localized as it propagates. A well-known example of a beam with extended propagation is a Bessel beam.⁵⁶ However, in order to efficiently generate a Bessel beam, an axicon phase distribution must be generated using a freeform refractive optical element or an extra SLM, which would increase the cost of the optical setup. Furthermore, the energy in the intense area of the Bessel beam is only half of the energy available, as the other half is spread throughout the periphery and accounts for the “reconstructed light” in subsequent planes. Despite having a relatively shorter propagation distance where the beam is localized, compared to a Bessel beam, GPC is more effective in utilizing the available light, with an energy efficiency of about 84%.⁵⁵ Furthermore, instead of a freeform refractive optical element or an additional SLM, GPC requires simple binary phase masks, which are easier to fabricate.

Figure 2 illustrates different scenarios for how a microsphere and beam can overlap. The distributions in Figs. 2(a) and 2(b) represent different magnifications of a typical Gaussian, Airy-disk or other focal spot distribution characterized by a gradual intensity roll-off. Figure 2(c) represents a sharply bounded top-hat that can be generated by GPC. In Fig. 2(c), the light incident at the microsphere is more evenly distributed compared to that in Fig. 2(a), while also being more confined to the microsphere compared to the case in Fig. 2(b). As the beam gets narrower in Fig. 2(a), this configuration also approaches that of an optical tweezer that has a shorter manipulation range and will rather attract instead of catapulting the microsphere. When using GPC to generate a top-hat as in Fig. 2(c), the setup requires about a third of the power, compared to the case in Fig. 2(b), for generating the same intensity level.⁵⁵ Combined with the relatively uniform light intensity distribution on the microsphere, this efficiency advantage is why GPC was selected as a light-shaping method in this study.

Fig. 2

Typical configurations at which a microsphere and beam can overlap. In (a), the majority of the light’s intensity is incident at the particle, but is significantly lower toward the edges of the particle. The incident light distribution in (b) is more uniform; however, energy outside the particle’s boundaries is wasted. In (c), the incident light intensity is more uniform, while also preventing energy waste. GPC light shaping (c) provides $3\times$ higher intensity on the particle compared to (b) for the same beam input power.

A typical GPC-generated output beam has a characteristic top-hat field profile characterized by a sharp change in intensity at its boundaries. However, as the beam propagates, this profile changes due to diffraction as shown in Fig. 3.⁵⁷ Despite this change in radiation profile, the beam intensity remains relatively localized when compared to a typical Gaussian or Airy-disk focal spot generated from a similar optical setup. Hence, a more consistent amount of scattering force pushes the microsphere as it traverses in the axial direction. This makes it ideal for catapulting microspheres over a longer distance.^47,55,57,58 Although it is also possible to extend the propagation of Gaussian or Airy-disk beams by modifying the setup’s magnification, such an expanded beam would lead to a less efficient system, having more energy falling outside the microsphere’s cross-sectional area.

Fig. 3

Pseudocolor plot of the $xz$-plane intensity distribution appearing at $z>0$ (arbitrary units) for a typical focused Gaussian and GPC-generated beam directed toward the positive $z$-axis.⁵⁷ The Gaussian and GPC profiles were set in the simulation so that their energy falls within the same microsphere region. Due to the subsequent focusing with GPC, the color bars are scaled differently to keep the features visible.

Simulated propagations of a GPC-generated top-hat and a similarly confined Gaussian beam are shown in Fig. 3. The simulation emulates practical scenarios wherein all the optical energy overlaps with the microsphere [as in Figs. 2(a) and 2(a)] and scaled to match the parameters used in our experiment. Hence, we chose a GPC disk radius that matches the microsphere’s radius and a Gaussian waist that is one-third of the microsphere radius (and also one-third of the GPC disk radius). It can be seen that the GPC beam diverges more slowly than the narrow Gaussian and therefore provides more consistent force to a microsphere moving along the axial direction.

The effective force components acting on a spherical particle, which are typically in the order of piconewtons, were investigated by Rodrigo et al.⁵⁷ These forces depend on the light intensity distribution, the refractive indices of the host medium and the particle, and on the fact that the refraction angle is higher at the edges of the particle than at its center. We are expecting that the densest light intensity distribution will take place at the beginning of the microspheres’ movement, where the spatial distribution is closer to the ideal top-hat. As a microsphere is moving upward inside the chamber, the light intensity incident to it is gradually decreasing, which should lead to a deceleration of the microsphere due to opposing forces, such as gravity and drag forces.

2.2.

Optical Catapulting Experimental Setup

In order to investigate the movement of the microspheres inside the mucin solutions, the setup in Fig. 4 was constructed. A 1070-nm laser (IPG Photonics, Massachusetts) shaped by a GPC system was used to catapult the microspheres. An LCoS type SLM (Hamamatsu Photonics, Japan) with $800\times 600$ pixels with a pixel pitch of $20\mu \mathrm{m}$ was used to actuate the shaped GPC output via a “Holo-GPC” configuration.⁵⁹ Holo-GPC works by multiplexing speckle-free GPC top-hats into holographically distributed 3-D locations in the sample volume by utilizing the convolution principle.^53,60 Hence, having Holo-GPC available is convenient for addressing multiple microspheres over a wide-working volume. The measurements in this paper, however, were performed on individual microspheres, which means that the method is equally applicable if standard GPC, without the holographic multiplexing, is used. Hence, despite having an SLM in the setup, the catapulting experiments reported herein did not take advantage of this.

Fig. 4

Schematic diagram of the setup for catapulting experiments. Illumination for side-view imaging was achieved with the aid of a portable light source placed near the sample (not included in the diagram).

The laser was demagnified to have a 1-mm diameter, which matches a prefabricated GPC light shaper.⁶¹ The GPC light shaper used two Fourier lenses ($f=50\mathrm{mm}$) to form a $4f$ configuration, and had a circular phase mask with a diameter of 0.39 mm, and a PCF with a $38\text{-}\mu \mathrm{m}$ phase-shifting radius. The Fourier transform of the illuminated phase mask was expanded onto the SLM by $5\times$ by placing a lens ($f=250\mathrm{mm}$) after the light shaper. The distribution at the SLM was subsequently demagnified onto the back aperture of the objective lens by $1/3\times$ using a pair of lenses ($f_1=300\mathrm{mm}$ and $f_2=100\mathrm{mm}$).

Two objective lenses ($f=3.6\mathrm{mm}$, $\mathrm{NA}=0.55$) were used to image the GPC disks onto the sample and for the top view and a third objective lens ($f=45\mathrm{mm}$, $\mathrm{NA}=0.1$) for the side camera. The resulting disk after the $f=3.6\mathrm{mm}$ objective lens had a calculated diameter of $\sim 17\mu \mathrm{m}$, which closely matches the $15\text{-}\mu \mathrm{m}$ diameter of the microspheres. The longer focal length and the working distance of the side-view objective leave enough clearance from the measurement cuvette and the top and bottom objectives. Although the relevant data were obtained through side-view imaging, the top view was necessary for alignment of the system and ensuring that the beam was aimed at the microspheres to be catapulted.

2.3.

Mucin Preparation

The microspheres to be optically catapulted were suspended in varying concentrations of PGM (type II, Sigma Aldrich cat. no. M2378) prepared in HEPES (Sigma-Aldrich Denmark A/S, cat. no. H0887, pH 7.0-7.6) containing Tween 80 (MP Biomedicals, California, cat. no. 02103170). A 10-mM HEPES buffer was prepared by diluting the 1 M HEPES stock in millipore water ($18.2\mathrm{M}\mathrm{\Omega }·\mathrm{cm}$ at 25°C). For all experiments, the mucin solutions were prepared by adding mucin to the 10-mM HEPES buffer and allowing it to rehydrate for 20 min at room temperature under mixing at 300 rpm using an IKA RH basic two magnetic stirrer. About 0.1% Tween 80 was added to the samples used in rheology measurements. About 0.1% Tween 80 and 1.5% of $15\mu \mathrm{m}$ polybead polystyrene microspheres (Polysciences Inc., Pennsylvania) were added to the mucin dispersions for optical catapulting experiments. The refractive index of the solutions was measured and can be considered constant, as the difference between millipore water and the 5% mucin concentration medium is below 1%.

2.4.

Rheology Measurements

The effect of mucin concentration on viscosity was evaluated using an ARES-G2 rheometer (TA Instruments, New Castle, Delaware), equipped with a peltier plate and truncated cone (1 deg, 40 mm from TA Instruments, New Castle, Delaware), and the temperature was set to 21°C. To prevent evaporation during measurements, a solvent trap cover was used (TA Instruments, New Castle, Delaware). Test samples were carefully pipetted to the center of the peltier plate, and proper sample distribution and subsequent equilibration were ensured by a conditioning step with pre-shear set to 10 Pa followed by an equilibrium step of 5 min at 21°C. Subsequently, a steady state flow step was carried out by applying a shear rate of 10 to $5000{\mathrm{s}}^{-1}$, conducting three consecutive measurements of 10 s each, allowing a maximum of 5% variance, collecting four points per decade. All samples were measured in triplicate ($n=3$). Statistical analysis of the rheological data was done via a one-way analysis of variance using GraphPad Prism version 7.0b (GraphPad Software, San Diego, California).

The viscoelastic behavior of the 5% mucin samples was not characterized. These concentrated samples precipitated during the conditioning step, leading to an obvious phase separation.

2.5.

Optical Catapulting Experiments

For each set of measurements, $15\text{-}\mu \mathrm{m}$ diameter polystyrene microspheres were placed along with a mucin solution inside the $250\times 250{\mu \mathrm{m}}^2$ square channel (Fig. 5) from a quartz cuvette (Hellma GmbH, Germany). The microspheres rapidly sedimented on the bottom of the microchannel. The system was then aligned to focus on one randomly selected microsphere for catapulting. The height of the measurement channel was chosen to match the thickness of the mucus layer in the human digestive tract.⁶ The videos were recorded using laser powers (as set on the laser source) of 0.20, 0.50, 1, 1.50, and 1.80 W and mucin concentrations of 0.1%, 0.25%, 0.5%, 1%, 3%, and 5%. This allowed us to investigate the effect on increasing laser powers on catapulting the microspheres in relation to the different mucin concentrations.

Fig. 5

Bright field image of a microsphere being catapulted inside millipore water taken with the side-view camera. a: Measurement cuvette containing microspheres mixed in mucin dispersion; b: lower cuvette wall; c: upper cuvette wall; d: microsphere being catapulted; e: other microspheres lying on the bottom of the measurement cuvette. The microspheres have a diameter of $15\mu \mathrm{m}$. The visible top (c) and bottom (b) inner walls of the cuvette are $250\text{-}\mu \mathrm{m}$ apart.

2.6.

Microsphere Tracking and Data Analysis

The motion of the microspheres was captured with a point gray camera at 10 fps. The Manual Tracking plugin designed by Fabrice P. Cordelières for the ImageJ software⁶² was used for tracking the microspheres for all the experiments. The accuracy of the tracking is limited by the pixel size of the recorded videos to $\sim 0.1\mu \mathrm{m}$. The microspheres were tracked from the first frame in which they rise above the lower cuvette wall until the last frame just before reaching the upper cuvette wall (a distance corresponding to $\sim 250\mu \mathrm{m}$, as defined by the chamber height). The “instantaneous” velocities of the microspheres (for the shortest observable time intervals of 0.1 s, as determined by the frame rate) were computed in the software and either used as such (denoted as instant velocities) or averaged for the entire trajectory (denoted as average velocities). Recordings where a second microsphere interfered with the catapulting were excluded from the analysis. The trajectories of 10 microspheres from five different samples were analyzed for every mucin concentration and catapulting laser power.

The motion of microspheres in 3% mucin using 0.2 W input laser power was extremely slow, which would cause significant errors in tracking due to subpixel size displacements in between consecutive frames, and thus it was excluded from the data analysis. In 5% mucin, an input laser power of 0.2 W was not sufficient to push the microspheres upward.

The sensitivity of the system in terms of its ability to respond to perturbations caused by the presence of mucin is given by the slope of the linear fit passing through the origin in the velocity versus laser power plots. This parameter was calculated from both the average and maximum instant velocities and is given in $\mu \mathrm{m}·{\mathrm{s}}^{-1}·{\mathrm{W}}^{-1}$).

3.1.

Viscoelastic Behavior of Mucin Samples

As it can be seen in Fig. 6, the viscoelastic behavior of samples containing low concentrations of mucin (up to 0.25%) is very similar to that of buffer (no statistical differences). This indicates that in these samples, the glycoprotein chains do not form a detectable network of secondary interactions, most likely due to the too large distances between the mucin fragments.

Fig. 6

Rheological characterization of samples ($n=3$) containing different mucin concentrations.

The samples with mucin concentrations between 0.5% and 3% behave in similar manner and are characterized by increased viscosity and a changed viscoelastic behavior (shear thinning) compared to buffer. This indicates the formation of a viscoelastic network. Based on these results, the critical concentration for the formation of a viscoelastic network in our experimental conditions should be between 0.25% and 0.5% mucin.

3.2.

Catapulting in Water

In order to ensure that our setup allows reproducible measurements, we initially conducted a series of experiments using a “blank” sample without mucin, which contained millipore water, 0.1% Tween 80 and 1.5% of $15\mu \mathrm{m}$ polystyrene microspheres.

The instantaneous, average, and maximum velocities of the microspheres in water are shown in Fig. 7. The system is optimized such that the GPC disks are formed at the lower wall of the measurement chamber, where the microspheres are also lying, and thus provides an optimal overlap with the GPC disks in the beginning of the microsphere trajectories. However, due to the axially changing intensity distribution of GPC-shaped beams (Fig. 3), there is an initial “slowness” in the microsphere motion and the highest velocities are achieved a fraction of a second after the microspheres start being pushed by the laser beam, after the microsphere goes past the more intense region of the beam. The local intensity maxima before the broad intense region (Fig. 3) could also be causing weak gradient forces that initially attract the microsphere. As the microspheres move vertically through the measurement chamber, their speed is decreasing sensibly, which is to be expected, as described in Sec. 2.1. This decrease as the microspheres are catapulted further from the image plane of the GPC beam is more obvious at high laser powers (1.5 and 1.8 W), as it can be observed in Fig. 7(a). At low laser powers (0.2 and 0.5 W), the frame-to-frame displacement of the microspheres is of only several pixels, which causes the calculated instant velocity signal to be noisy and makes the velocity decrease less observable.

Fig. 7

Tracking results in water samples containing Tween 80 ($n=10$): (a) instant velocities as a function of time for different laser powers and (b) maximum and average velocities as a function of laser power.

A comparison between different input powers for catapulting in water is shown in Video 1. The microsphere displacement 0.5 s after turning on the laser beam can be seen in Fig. 8(a).

Fig. 8

Comparison of optical catapulting of polystyrene microspheres using different input laser powers in (a) water (Video 1) and (b) 1% mucin (Video 2). The frames shown correspond to (a) 0.5 s and (b) 1 s after turning on the laser beam for catapulting. (Video 1, MP4, 0.5 MB[URL: https://doi.org/10.1117/1.JBO.24.3.035001.1].; Video 2, MP4, 2.3 MB[URL: https://doi.org/10.1117/1.JBO.24.3.035001.2].).

3.3.

Catapulting in Mucin

In order to understand how the presence of short mucin glycoprotein chains affects the ability to catapult microspheres in our system, we investigated aqueous dispersions containing 0.1% to 5% mucin. Among these, the 3% and 5% aqueous mucin dispersions can be considered simple mucus models due to the similarity with the 2% to 5% mucin content of native mucus.

A comparison between different input powers for catapulting in 1% mucin is shown in Video 2. The microsphere displacement 1 s after turning on the laser beam can be seen in Fig. 8(b).

The experimental results obtained using different laser powers in aqueous mucin dispersions with concentrations up to 5% are presented in Fig. 9. Each experimental data point was calculated by averaging the velocity of 10 microspheres. The average values, including standard deviations, are given in Sec. 5.

Fig. 9

Average velocities ($n=10$) at different laser powers and different mucin concentrations. “B” is a blank sample containing 0.1% Tween 80 in millipore water.

As it can be seen in Fig. 9, increasing the laser power leads to a velocity increase for all tested samples. On the other hand, the average velocities of the microspheres decrease as the mucin concentration increases. This is an anticipated behavior due to the biobarrier properties of mucus, which the mucin dispersions replicate to some extent. The velocity decrease can be attributed to a combined effect of altered light propagation in mucin dispersions and to physicochemical interactions between the polystyrene microspheres and the simple mucus model. Polystyrene surfaces are slightly charged and hydrophobic,⁶³ with loose polymer chains present at the interface.⁶⁴ Thus, it is to be expected that the polystyrene microspheres employed in our study can lead to hydrophobic interactions⁶⁵ with the mucin fragments.

The sensitivity of the system (calculated from both instant and average velocities) decreases exponentially as the mucin concentration increases, as shown in Fig. 10. This shows that the addition of mucin glycoprotein chains in low concentrations (0.1% to 1%) significantly changes the behavior of the microspheres, which can be partly attributed to the physicochemical interactions between the polystyrene microspheres and the mucin fragments. The addition of low amounts of mucin does not change the viscoelastic behavior, but it can already lead to hydrophobic interactions between the microspheres and the sample. Beyond 0.5% mucin, the glycoprotein fragments assemble in a viscoelastic network. This can explain why further increasing the mucin concentration has a lower effect on the sensitivity.

Fig. 10

Sensitivity decrease of the system at increasing mucin concentrations. The sensitivity values were calculated from both the average and maximum velocities versus laser power plots.