We demonstrate an optical micro-particle size detection technique based on phase sensing by a fiber interferometer through phase-generated carrier (PGC) modulation/demodulation. Particle diameters were resolved from phase shift due to particle-induced optical scattering. Polystyrene nanoparticles, air bubbles and yeast cells in a microfluidic channel were tested using this technique, and particle diameters ranging from 0.7 to 5.5 μm can be resolved in real-time. In comparison with existing amplitude-sensing techniques which require tens of milliwatts of laser irradiance, phase-sensing through PGC can successfully utilize probe laser powers as low as 220 μW to measure the test particle sizes. We further constructed a theoretical model based on phase scattering and PGC demodulation, which obtained good agreement between experimental data and calculated phase shift as a function of particle time-of-flight. This technique may be applied to a wide range of potential applications, ranging from real-time analysis of clinically relevant cell samples, to contamination control of processing fluids used in the semiconductor industry.
© 2016 Optical Society of America
Rapid micrometer-sized particle measurement and detection is of great importance in many modern industries including water treatment, biosensors, public health and pharmaceuticals [1,2]. For example, pharmaceutical testing critically relies upon the ability to accurately quantify bacteria sizes to study the effects of drug therapy in patients, and to study bacterial fitness, replication, and inhibition. There are several bacterial quantification techniques available to pharmaceutical engineering, such as quantitative polymerase chain reaction (qPCR) , plaque titers , and image enhanced microscopy (IEM) . However, these quantification techniques require time-consuming procedures, which may take up to several hours to analyze a single sample [3–5]. Quantification techniques for mammalian cell types are also in demand in medicine, for purposes such as the diagnosis of breast cancer  and prenatal screening . A real-time measurement method is highly desirable for cell sorting these applications, as it would allow for rapid size quantification in a continuous flow of particles, in contrast to sample-by-sample traditional sorting methods based on fluorescence  and immunomagnetic separation .
While some optical scattering methods for particle detection and size measurement exist, they often rely on amplitude sensing wave scattering from focused, relatively high-intensity laser beams. Examples include electrokinetically driven micro flow cytometers incorporating buried fiber optics for on-line cell/particle detection , and background-free interferometric schemes to detect the field amplitude scattered from a laser-irradiated particle . These techniques all require laser powers ranging from 20 to 200 mW. For biological particles, these laser intensity may become so high as to cause overheating or changes to cellular properties, as cells have different tolerance degree of laser power and the same cell has different absorptivity of laser light at different wavelength [12,13], resulting in potentially errors in the analysis.
Phase sensing is an attractive alternative to amplitude sensing techniques that can significantly reduce the required probing laser intensity. Optical phase generated carrier (PGC)-based techniques can be capable of sensing extremely small phase shifts as low as 10−8 rad, which have previously been used as a high-resolution phase detection techniques in other applications including homodyne demodulation schemes for fiber-optic sensors, picometer displacement measurements, and multiplexing of extrinsic Fabry-Perot interferometer sensors [14–17]. The combination of optical fibers and PGC opens new possibilities for the real-time rapid monitoring of particle sizes low laser intensities
In this article, we present a method to measure the diameters of micrometer-size particles in continuous fluid flow in real time, by using a fiber optic probe to transmit a phase-modulated laser beam onto the particles in a micro-fluidic channel, and analyze reflected signals from both the particles and a background reflector. Phase-modulated interference signals were resolved to obtain particle sizes by implementing PGC modulation/demodulation and scattering theory. Actual particle sizes measured in real time for air bubbles, yeast cells, and polystyrene nanospheres were in good agreement with theoretical model calculations. This fiber-based PGC particle size detection system allows for real-time filtering, classifying of particles with high throughput speed and micro-watt power detection, with an energy density of 0.39 J/cm2, well below the photo-damage threshold of 0.5-5 J/cm2 for red blood cells, e.g , which can be a promising technology in biological applications including cellular detection of flowing serum, cerebrospinal fluid, and antigen-antibody complexes in microfluidic samples.
2. Measurement principle
The underlying principle for phase-based optical size detection of micrometer-sized particles is PGC modulation/demodulation through a fiber interferometer. As shown in Fig. 1, a distributed feed back (DFB) laser diode (LP1550-SAD2, Thorlabs, US) emitting a 1550 nm wavelength beam was used as a probe signal, split by a 2 × 1 fiber power splitter. One taper output of the splitter, used for particle sample beam delivery, is mounted on a piezoelectric ceramic vibrator driven by a sinusoidal reference signal generator (33250A, Agilent, US), to produce a beam with a PGC modulation signal. This probe beam is delivered to a microfluidic channel fabricated from a glass capillary , where the probe beam scatters and subsequently was partially reflected back using a micro-reflector. The other portion of the split probe signal forms the reference beam, which serves to interfere with the incoming reflected signal. A photodiode connected to the other port of the 2 × 1 fiber power splitter collects the returned, post-interference signal, which was then amplified and stored in a digital oscilloscope (Picoscope 4262, Pico Technology, UK). The total output power transmitted from the taper fiber was measured at 220 μW.
A detailed view of the beam interference setup is shown in Fig. 2. As the taper fiber vibrated back and forth from the piezoelectric vibrator, the optical pathlength is altered, forming a probe beam with a PGC modulation signal, which was emitted into the microfluidic channel. After passing through the sample, the probe beam was reflected by the gold-plated micro reflector, and was partially re-collected by the same taper fiber for interference. The post-interference signal was recorded by a digital oscilloscope, and the phase information of the reflected interference beam was obtained by waveform fitting. When a small particle passed through, its scattered light collected by the taper fiber can perturb the interference, leading to a slight phase change in the interference signal. By comparing the phase of a perturbed interference signal with an unperturbed, no-particle baseline measurement, the phase shift can be modeled to deduce the size of the passing particle.
We denote the field of the reference beam, the light reflected by the taper fiber end face, as Eref, and the field of the signal beam, the light through the microfluidic channel reflected by the gold-plated micro reflector, as Esig. Then Eref = E0 ·ej(ωt + φ) and Esig = E0 ·ej[ωt + M·sin(ω0t+φ0)]. When there is no particle in the beam path, the intensity distribution I1 collected by the detector is calculated as
When there a particle passes through the beam, its scattered light, denoted as Es, introduces a new amplitude and phase to the interference signal. For an amplitude scattering coefficient r1 of the particle, then Es = r1·E0 ·ej[ωt + ψ + M·sin(ω0t+φ0)] and the intensity distribution I2 collected by the detector is calculated asEq. (1) and Eq. (2), which has a positive correlation with the size of the particle in a certain range expounded below.
The value of I2 is related to the diameter of the particle as following: when the particle is at the center line of the signal beam, its diameter introduces a phase shift, denoted as σ:
Due to the intensity distribution of the signal light, the final measured phase difference, denoted as θ, is different from σ. θ is calculated asEquation (4) describes the relationship between the phase difference and the particle size in a 2π phase range dependent on wavelength of the laser diode, we demonstrate in the following that by solving the phase difference between Eq. (1) and Eq. (2), the particle size can be obtained from Eq. (4).
To experimentally verify the measurement principle, we started with air bubbles as test particles. The experimental system layout is displayed in both Figs. 1 and 2, where the diameter of the taper fiber is 60 μm, and a surfactant, water and piezoelectric ultrasonic vibrator are used to produce air bubbles in the flowing test sample. Using an injection syringe connected to a segment of rubber tube, air bubbles were moved smoothly into the field of view of the taper fiber and the gold-plated micro reflector via a stretched capillary, while the particle size and velocity were manually controlled under a microscope.
The phase shift of an air bubble with a diameter of 3.23 μm passing through the signal beam is illustrated in Fig. 3 (left), which indicates a clear phase perturbance of the original PGC modulation interference signal. The corresponding positions of the particle are demonstrated as screen grabs in Fig. 3 (right, inset a to f), which indicates that the phase shift is at a maximum when the particle is located at the center of the signal beam, which is the point best used for calculating particle size by its relationship to the phase change between waveforms.
Figure 4 shows measured phase shift of the PGC modulated waveforms and collected signal intensity as a function of particle moving position, recorded as time of flight in the digital oscilloscope. The maximum of the phase shift occurs when the test particle is located at in the center of the signal beam, which is set to be zero on time axis in Fig. 4. With the known diameter of the test particle, theoretical values of the phase shift as a function of particle position are also calculated according to the aforementioned measurement principle by using Eqs. (1)-(4), indicated as a dotted red curve in Fig. 4. The results fit well with the experimental data. The collected signal variation is also recorded as a blue solid curve in Fig. 4. It shows that passing through of the particle causes a sharp drop in received interference signal. The change in intensity is compared with theoretical calculations (blue dotted line). A reasonably good fit is obtained except for two spikes in the beginning and end of the particle passing process, which is due to the reflection off particle side surface that is not taken into account in theoretical analysis.
With the experimental methods described above, air bubbles of different sizes were tested and the relation between their diameters and phase shifts is shown in Fig. 5 (black triangles). To produce bubbles of different sizes, the ratios of surfactant–to-water as well as injection syringe needle gauges were adjusted. It is noticed that the phase shift is monotonically proportional to the particle diameter, which agrees with that of calculated from theoretical modeling.
To explore the applicability of this technique for various particle sizes, polystyrene standard nanospheres (Duke 3000, Thermo Fisher Scientific, US) and yeast cells are then tested in the same experimental setup; the experimental and theoretical results are shown in Fig. 5 (red and blue curves respectively). Since their sizes are either much smaller or bigger than air bubbles, taper fiber with different diameters were used: 16 μm and 125 μm respectively. In theoretical models, the amplitude coefficient a in Eq. (4) was adjusted to fit both refraction indices of the two types of particles and the distance between taper fiber and microfluidic channel. In both cases, calibrated theoretical calculation agrees with experimental data very well, further confirming the validity of this size detection method based on phase sensing using PGC modulation.
As shown in Fig. 5, particle diameters ranging from 0.7 to 5.5 μm can be measured in real-time even at laser powers as low as 220 μW. Figure 5 also shows that a measurement error between 5 and 7% was found in the experiments. These errors can be attributed to the vibration noise disturbance, measurement of the size of particles using pixel estimation, and fluctuation in laser wavelength. As PGC-based fiber interferometers are sensitive to external vibration, the whole setup was placed on a shock absorbing platform to stabilize the interference waveforms. In addition, the tested particle’s speed is limited by the sampling frequency of the digital oscilloscope and the signal generator’s frequency. To get an accurate measurement, 10 cycles of the PGC waveforms were be included in the process of the tested particle passing through. In this experiment, the signal generator frequency is set to be 3.4445 kHz to acquire a PGC waveform of 6.889 kHz, which allows the particle to pass through the fiber optical mode field in 1.45 ms. Assuming the mode field diameter is 9 μm, the fastest speed of the test particle is 6.2 mm/s, while the speed of the tested particles in this experiment is around 30 μm/s, which is far below the limit. If the test particles speed up, the frequency of signal generator can increase accordingly to meet the measurement.
The experiment verifies the measurement principle that the phase shifts detected by PGC modulation waveforms has a good correspondence with the diameter of the particles. Further experiment is in progress to detect nanoparticles by adjusting laser power, diameter of taper fiber, and microfluidic channel properties.
We have demonstrated that a fiber interferometer based on PGC modulation detection is capable of detecting the size of micrometer-range particles in a continuously flowing fluid sample. With a laser power as low as 220 μW, particle diameters ranging from 0.7 to 5.5 μm were measured real-time. The method presented allows for size monitoring of a collection of particles, which is an advantage when it comes to in-vivo measurements. By further improving signal-to-noise ratio of the system, it is expected to extend detection limit beyond sub 100 nm. This fiber-based PGC modulation size detection technique may be applied in many areas such as biosensors and microfluidic chips with a low-cost, low power, high sensitivity and high detection rate, and has the potential to improve pharmaceutical research and water treatment. It will also be possible to utilize a slightly high optical power for optical tweezer applications to trap the particle simultaneously, thereby acquire the size information for subsequent classification or transportation. Further work include development of detection systems with probe lasers of two different wavelengths, where each probe may have a unique beam size and phase shift characteristics to improve measurement accuracy and expand the measurement range.
This work was supported by the National Natural Science Foundation of China (NSFC) under grant 61378086.
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