1. Introduction

Flow cytometry is a powerful method to optically analyze biological materials in fluids [1]. In part because of its success, producing a microfabricated flow cytometer has become one of the major goals of microfluidic technology [2]. Flow cytometers obtain quantitative analysis by precisely controlling the intersection of a fluid borne sample stream with a laser focal spot. Commercial table-top systems are capable of extremely high throughput detection by collecting fluorescence and scattering data on tens of thousands of cells or beads per second.

Building on recent progress in microfluidics, there have been several successful implementations of microfabricated flow cytometers using lithographically patterned fluidic structures [3, 4]. Although microfabricated flow cytometers frequently rely on traditional microscopes for optical detection, there are clear advantages in integrating the optical components as well. Microoptical components have dimensions on the same order as microfluidic structures. Consequently, arrays of both systems can be implemented on the same chip to realize higher speed through parallelization [5, 6]. Another advantage of integrating optical and fluidic systems onto the same chip is that their alignment is defined lithographically and then fixed during fabrication. Alignment of the sample stream to the laser spot is critical in flow cytometry, and as future devices continue to shrink and parallelize these intersections, off chip alignment will become increasingly more challenging.

The primary method to integrate optical detection into microfluidic devices has been to use optical waveguides. Optical fibers can be easily integrated into planar microfluidic devices and are very effective at delivering light from lasers and coupling collected light to photodetectors [7–9]. One major drawback of waveguide optical excitation, however, is that there is limited control of the excitation field distribution. The field emitted by fibers lying outside the fluidic channel diverges before it intersects the detection region and frequently exceeds a width greater than 50 μm, which severely limits spatial resolution. To help decrease spot sizes and increase local intensity, planar lenses patterned into the channel walls have been used to focus excitation fields from both fibers [10] and LEDs [11]. Although these planar lenses have resulted in greater signal strength, they have not demonstrated focusing tighter than 50 μm. In addition to limited excitation field control, in-plane lenses are inefficient light collectors. For collecting Rayleigh scatter, efficiency is not crucial, but for collecting weaker fluorescence signals, high numerical aperture (NA) two-dimensional lenses have much higher collection efficiency.

Instead of in plane integration of optical elements, we demonstrate the use of an array of diffractive microlenses that operate through the top wall of a channel. The device is operated in an epi-illumination mode, where both the excitation and emission pass through the same diffractive microlens on the same side of the sample, as shown in Fig. 1 . Each microlens has an NA of 0.73, which produces a tightly focused excitation spot and efficiently collects fluorescence emission. In addition to large focusing power, astigmatism is added to the microlens design so that the excitation focal spot is formed into a line that runs perpendicular to the channel direction. Line excitation is used in table-top flow cytometers [1] and also has been used in single molecule detection [12], so that analyte traveling through the flow focused stream intersects the same intensity at different cross-sections. Reducing the coefficient of variation for homogenous samples is extremely important in order to quantitatively compare the fluorescence amplitude from each particle.

 

Fig. 1 Schematic of the optofluidic fluorescence measurement system. The microfluidic channel and microlens array are integrated onto the same substrate. The microlens array is illuminated by a broad fluorescence excitation laser beam and imaged onto a high speed CMOS camera by off chip relay optics that have unity magnification. The fast CMOS camera is a Phantom V7.1 from Vision Research. Image stacks are collected by the camera and later analyzed to quantify the fluorescence signal collected from each detection region.

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The organization of this paper is as follows. In section 2, we first introduce a mathematical description of the astigmatic microlens and definitions of the desired focal spot distribution. The microlenses are then experimentally characterized both in a bulk fluid reservoir and aligned to a single microfluidic channel. Section 3 shows the results for counting homogenous solutions of fluorescent beads at low and then high throughput. The coefficient of variation is also discussed for this homogenous sample. Section 4 demonstrates the resolution of bead size for a heterogeneous sample and compares the results for each of two detection regions. Finally, section 5 presents a multiple field of view velocimetry technique using the astigmatic microlens array.

2. Diffractive optic design and fabrication

Diffractive elements rely on the geometry of a grating pattern to modify the phase of diffracted waves. We use electron beam lithography to pattern microlens masters, and consequently we have extremely precise control over the local grating geometry [13]. By contrast, it is much more difficult to control the geometry of refractive microlenses that require the three-dimensional fabrication of curved surfaces. Consequently, the focal length of diffractive microlenses can be defined with much higher precision than refractive microlenses [14], which is critical for microlens arrays that are lithographically aligned. In addition, using techniques from computer generated holography; diffractive microlenses can be designed that produce almost arbitrary intensity distributions in their focal plane.

The diffractive microlenses are designed by first calculating the complex field distribution of the desired focusing wave at the cross section of the microlens, which is spaced by the focal length from the microfluidic channel. In this case, we want the focusing wave to form a line excitation across the channel. This can be produced by the multiplication of a spherical wave with a cylindrical wave,

After the desired phase profile of the focusing wave has been calculated using Eq. (1), we apply a thresholding function that transforms the continuous valued complex field into two discrete phase values. The threshold function in this case sets any phase value from [0,π) to 0, and [π,2π) to 1 [15]. Two level phase diffractive elements have a maximum diffraction efficiency of 40.5% when the relative path length between the two levels has a difference of π [16]. The refractive index contrast in our microlenses is between PDMS and air and has a value of 0.45. We are interested in optimizing the diffraction efficiency for fluorescence emission with a wavelength of 575 nm, so the ideal thickness of the diffractive elements is 640 nm.

The designs are patterned into SU8 using electron beam lithography to form microlens masters that can then be molded into PDMS. While it is possible to pattern thin films of SU8 with features as small as 30 nm using electron beam lithography [17], thicker films are more challenging. For a film of SU8 that has a thickness of 450 nm, we have found that we can reliably produce gratings that have a line width of less than 500 nm and a pitch of 900 nm. First, SU8 2000.5 is spun onto an Indium Tin Oxide coated microscope slide at 3000 RPM. We use an Elionix ELS-7000 100 kV electron beam lithography system for the exposure. The pattern is written at 20 pA and with a dosage of 4.4 μC/cm². SU8 has a much lower exposure threshold than other electron beam resists, so consequently larger patterns can be written in smaller time.

Using an atomic force microscope, we measure that the resulting SU8 pattern has reasonably straight sidewalls and a depth of 400 nm. Due to electron scattering in the relatively thick resist, it is difficult to obtain deeper features. However, a thickness of 400 nm is enough to produce good diffraction efficiency. Using a home built beam propagation algorithm, we estimate that the diffraction efficiency for the fluorescence excitation with a wavelength of 532 nm is 0.34 and the diffraction efficiency for the fluorescence emission with a wavelength of 575 nm is 0.31. These values are somewhat lower than the ideal diffraction efficiency of a π-phase grating of 0.41, but are still more than three times larger than the diffraction efficiency of an amplitude grating, which is 0.10.

Fig. 2(a) shows an SU8 diffractive microlens master that has f_o = 210 μm, f₁ = 1050 μm, and 2R = 195 μm. The resulting f_f is 175 μm, which is chosen because the microlenses are designed to focus through a No. 1 coverslip that is 170 μm thick. From Fig. 2(a), we can see that the normally circular Fresnel zones are slightly elongated in the vertical direction as a result of the added astigmatism. After the microlens masters have been fabricated, the surfaces are treated with a salinization layer. Then PDMS is poured onto the SU8 masters and baked at 65°C overnight.

 

Fig. 2 Astigmatic diffractive microlens. a) Microscope image of SU8 lens master. b, c) Experimentally-observed focal spot intensity distribution at front and back focal planes, respectively, taken with a 50× objective lens.

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To visualize the focal spot distribution, the microlenses are aligned to a fluorescent dye (Resorufin) filled reservoir. The microlenses are placed face down on a No. 1 coverslip which acts as the roof of the reservoir. A single microlens is then illuminated by the fluorescence excitation laser. From the opposite side of the reservoir, we image the fluorescence emission using a 50× microscope objective and a fluorescence bandpass filter centered at 575 nm. Images of the emission at the front and back focal planes of the astigmatic microlenses are shown in Fig. 2(b), and (c), respectively. The front focal plane lies very close to the coverslip-fluid interface. This is the focal volume that we will use to define our detection region as, by contrast, the back focal plane lies beyond the microfluidic channel.

Fig. 3(a) shows the completed device, where three astigmatic microlenses are aligned and reversibly bonded to a microfluidic channel downstream from a flow focus junction. The sample enters the middle inlet channel on the left and is hydrodynamically focused by two sheath flow channels on the top and bottom. The main interrogation channel is 30 μm wide and 6 μm deep. Eq. (2) predicts that the excitation spot is 32 μm wide in the vertical direction of Fig. 3(a) and consequently slightly overfills the width of the main channel.

 

Fig. 3 Optofludic device. a) Brightfield microscope image, taken with a 10× objective lens, of the flow focus microfluidic device aligned to the diffractive microlens array. The diffractive microlenses are separated from the microfluidic channel by the coverslip thickness of 170 μm, so they appear slightly out of focus. b) Fluorescent emission resulting from the diffractive lenses focusing the excitation laser into the dye-filled channel, showing the focal spot distributions of all three detection regions.

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Fig. 3(b) shows an image of the induced fluorescence after flooding the device with Resorufin and illuminating all three diffractive microlenses with the fluorescence excitation laser. The three microlenses produce three excitation lines separated by 200 μm that traverse the channel cross section. From the fluorescence images, the full width at half maximum (FWHM) spot size of each focal region is found to be 7 μm along the channel direction. Due to diffraction of the excitation beam through the finite depth of the channel, the width of the excitation spot is significantly larger than the diffraction-limited size of the focal spot, but still less than one quarter of the channel width.

3. Bead counting

Fluorescent beads are commonly used as calibration standards in flow cytometry because, among other reasons, they can be made relatively monodisperse. We use polystyrene beads from Invitrogen that have a diameter coefficient of variation (COV) of 4.5%. The beads have Nile Red fluorescent dye mixed into their volume, so assuming that all the beads have the same dye concentration, we expect that the COV of the fluorescence signal from each bead to be 14%. Fig. 4(a) shows a one second trace, collected at 4,000 frames per second (fps), of the signals from each of the three different diffractive lenses along the microfluidic channel. The plotted signals are obtained by integrating the fluorescence intensities over the pixels corresponding to each diffractive microlens in the CMOS camera image. In this experiment the sample consists of a suspension of 2 μm beads at a concentration of 0.1% by weight in de-ionized water, while the sheath fluid is de-ionized water. The sample stream is driven by a syringe pump at a rate of 20 μL/hour and the sheath fluid is driven at a rate of 50 μL/hour.

 

Fig. 4 Bead counting at multiple detection regions. a) Time trace sampled at 4,000 frames per second (fps) of signals produced at each of three detection regions (DR), corresponding to each of three diffractive microlenses. Inset shows a higher resolution time trace of seven beads as they flow by the three detection regions. b) Histograms of the peak heights for each of the three different detection regions.

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From Fig. 4(a), we observe that each bead produces a pulse as it passes by a detection region because the short focal length diffractive microlenses have well-defined collection volumes analogous to those of confocal microscopes [18]. The relative delay between consecutive detection regions is approximately 1.5 ms, corresponding to an average velocity of 130 mm/s. Using an algorithm that counts peaks from the signal traces, we find that over a five second time span, detection regions 1-3 counted 447, 441, and 440 beads respectively. Fig. 4(b) shows histograms of the peak heights for each detection region, from which COVs of 0.27, 0.21, and 0.22 can be found. We estimate that a COV of 0.14 can be attributed to bead volume dispersion as estimated from the manufacturer. We believe the remaining variation to be attributed to the detection system, primarily caused by the intensity gradient along the depth of the channel. More sophisticated microfluidic designs are capable of flow focusing in the depth direction as well [2], and this could further reduce the measured COV. At this flow rate and bead concentration, counting occurs at 90 beads per second. However, the bead concentration can be considerably increased before coincidence rates become detrimental. For the data shown in Fig. 4, camera frames are captured every 250 μs, over which time the beads travel an average of 32 μm.

In addition to excitation uniformity, the line focus of the astigmatic lenses enables high time resolution because the excitation spot is narrow in the flow direction. To explore the temporal resolution, we need to increase the sampling speed of the camera. Fig. 5 shows the time trace for 1.1 μm beads traveling past two consecutive astigmatic microlenses, where the camera capture rate has been increased to 40,000 fps, or a frame every 25 μs. The sample stream is driven at 20 μL/hour and the sheath fluid is driven at a rate of 40 μL/hour, resulting in an average velocity of 90 mm/s. With the faster camera sampling rate, we can see in the inset of Fig. 5(a) that the signal pulses now consist of multiple samples.

 

Fig. 5 Time resolution characterization. a) Time trace sampled at 40,000 fps of signals produced at two detection regions. Inset shows a higher resolution time trace of the signal from two beads. b) Autocorrelation of each detection region, yielding a half width at half maximum of 23 and 31 μs, respectively. For a velocity of 90 mm/s, beads travel an average of 2.3 μm in between frames.

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The autocorrelation of the signal from each detection region shows the average time that a bead spends in the excitation region of each lens. The half width half maximum for the two autocorrelation peaks, shown in Fig. 5(b), are 23 and 31 μs, resulting in full widths of 46 and 62 μs. By multiplying the bead velocity by the full width of the autocorrelation peaks, we experimentally determine the width of the excitation regions to be 4.1 and 5.6 μm, respectively. These values are similar, but slightly lower than the width of the excitation spot (7 μm), measured by flooding the channel with fluorescent dye. We estimate that the smaller width is due to the fact that micron sized beads probe the intensity distribution closer to the center of the channel where the excitation is more tightly focused. In comparison, the much smaller Resorufin molecules from the previous characterization probe the entire channel depth, which include regions close to the channel walls that are further away from the focal plane.

4. High throughput sizing

The real power of flow cytometry lies in its ability to quantitatively measure optical signals of heterogeneous samples at high speeds. To demonstrate this functionality, we load a mixture of 500 nm and 1.1 μm diameter beads into the device, at a concentration by mass of 3*10⁻⁵ and 2*10⁻⁴, respectively. To obtain high throughput, we drive the sample and sheath flow at a rate of 100 and 300 μL/h and operate the camera at close to its maximum speed at 100,000 fps. Fig. 6(a) shows the time trace for two consecutive detection regions. We can observe two distinct peak heights in the trace, corresponding to the difference in brightness of the 500 nm and 1.1 μm beads. The histograms in Fig. 6(b) and (c) show clearly the resolvability of the two sizes of beads at each detection region. The distributions in the histograms are plotted as a function of the cube root of intensity because the numbers of fluorescence molecules approximately scale with the volume of the bead. The histogram peak value for the 1.1 μm beads is slightly greater than twice the peak value for the 500 nm beads, which is consistent with the expectation that the fluorophore concentration is the same for each bead size.

 

Fig. 6 High speed size discrimination. (a) Time trace sampled at 100,000 fps of signals produced at two detection regions for a mixture of 500 nm and 1.1 μm beads. (b) and (c) Histograms of the peak heights at the first and second detection region, respectively, plotted as a function of the cube root of peak intensity.

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The data shown in Fig. 6 is collected for one second, during which 8359 beads are counted in the first detection region and 8248 beads are counted in the second detection region. By gating the histogram in between the two peak values, we determine that the first detection region counts 6790 beads with diameter 500 nm, and 1569 beads with diameter 1.1 μm. The second detection region counts 6698 beads with diameter 500 nm, and 1550 beads with diameter 1.1 μm. For the 10 μs exposure used here, we measure a signal to noise ratio of 8 for the smaller 500 nm beads. A threshold of one half the mean signal from a 500 nm bead is used to discriminate beads from background noise, which corresponds to 4 times the background noise standard deviation.

5. Cross correlation velocimetry

In addition to characterizing the measurement system’s performance, simultaneous detection at multiple locations enables velocimetry by analyzing the transit time between detection regions. Particle image velocimetry [19] and fluorescence correlation spectroscopy [20,21] both use correlation techniques to obtain velocity information, and have frequently been used in microfluidic devices. A major advantage of using our system over previous systems is that we are not limited to the single field of view of a microscope objective. By using arrays of high NA astigmatic lenses, we can obtain high time resolution, because the detection regions are small, and a large effective field of view, because the detection regions are spaced far apart from each other. This large effective field of view enables a much larger dynamic range in transit time measurements.

Fig. 7(a) shows the cross correlation of two consecutive detection regions found from the data set that is also plotted as Fig. 6. The curve shows a sharp spike occurring at a time delay of 360 μs. Consecutive detection regions are spaced by 200 μm, so this rising edge of the correlation curve corresponds to a maximum velocity of 560 mm/s. The correlation peak has a finite width, which implies that beads in the channel have a distribution of velocities. Beads traveling down the center of a microfluidic channel have the fastest velocity, while beads closer to the channel walls travel slower. From Fig. 7(a), we also observe that the correlation curve has a secondary peak at a time delay of 680 μs, almost twice as long as the rising edge.

 

Fig. 7 Size resolved velocity dispersion. (a) Cross correlation of the total signal of a heterogeneous sample of 0.5 and 1.1 μm beads from two consecutive detection regions. (b) Cross correlation of the intensity gated signals from the same two detection regions, showing that the 1.1 μm beads have greater velocity dispersion.

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As is common in flow cytometry, we are able to gate the time signals by intensity [1], and consequently analyze separately the signals from the 500 nm and the 1.1 μm beads. Unlike flow cytometry, however, we have access to data at multiple detection regions which enables velocity measurements. Fig. 7(b) shows the cross correlation of the 500 nm and 1.1 μm beads separately. We observe that the maximum velocity of each bead size occurs at the same time delay, but that a larger fraction of the 1.1 μm beads arrive at larger time delays. We believe that this is caused by the fact that more 1.1 μm beads are farther from the center of the channel. Although a complete investigation is outside the scope of this paper, this is consistent with recent studies on inertial focusing of particles in microfluidic channels [22]. Inertial forces push particles away from the channel center and have been found to act stronger on particles that fill a greater fraction of the channel width.

6. Conclusions

We have demonstrated a fluorescence detection system based on the integration of an astigmatic diffractive microlens array with microfluidics. By shaping the focal spot distribution of the diffractive microlenses into a line, we obtain high time resolution and reduce the coefficient of variation of the measured signal for homogenous samples. Arrays of high numerical aperture microlenses enable efficient light collection over much larger regions than would be possible using a single microscope objective. Due to the efficient fluorescence collection, we have demonstrated high throughput counting and sizing of beads at 8,300 per second at multiple regions along the channel. We have also exploited the multiple detection regions to demonstrate a new velocimetry technique based on a cross correlation analysis of fluorescence signals occurring at two different detection regions along the channel. The combination of velocimetry and flow cytometry enables characterization of the interaction between complex flow distributions and heterogeneous distributions of particles.