## 3 Microfluidic Flowmetry Measurements  
Here, a series of flow rate measurements inside a 192 \(\times\) 192 \(\upmu\)m DF micro-channel were applied to investigate the sensing performance of two OFI systems. First, we tested a standard VCSEL chip in TO46 package mounted onto a laser mount (224 TEC TO-Can Laser Mount, Arroyo Instruments) without microlens on the laser and no lens on the channel. This basic setup served as a reference, and it is shown in Figure 7a, where the inset indicates the bulk glass lens pair. In the secondary measurements, we used the new miniaturized system proposed above as the sensor scheme. The entire setup is sketched in Figure 7b. In both cases, the incident angle between the laser axis and the normal to the channel was around 10 degrees. This value was selected because, for the integrated lens system, it is a good trade-off between the Doppler frequency shift and the minimum possible distance from the PCB to the channel chip. In this configuration, the distance from the integrated sensor to the channel top surface was around 1 mm, and the collimation beam diameter was approximately 40 \(\upmu\)m. The focusing lens could efficiently collect this on the channel surface. Of course, because of the  
Figure 5: Photograph of the microfluidic chip: (**a**) View of the entire serpentine channel chip and size comparison with a coin of 0.7 inches in diameter (**b**) Zoom on the central part of the microchannel with focusing microlenses deposited on the surface. The lenses are positioned at the center of the channel in the X direction and spaced 500 \(\upmu\)m apart in the Y direction. Figure 6: Modeling of laser incidence irradiation profile in the cross-section of the microchannel (X-Z plane) (ZEMAX). (**a**) Via bulk glass optical setup, (**b**) via miniaturized microlens set-up, (**c**) laser beam waist radius profile through the microchannel along the Z direction in both cases. bulk optics, the operating distance for the basic setup is much higher (around 8 mm). In both optical configurations, the sensor position was controlled by micrometric translation stages. It was set so that the acquired signal spectrum showed the highest amplitude in the frequency domain of interest. The tracing object, 4.89 \(\upmu\)m Polystyrene Spheres (PS) aqueous solution with a concentration of 0.1% w/v was pumped into the channel using a syringe pump (PHD 22/2000 Harvard Apparatus). By precisely varying the pumping flow rate, we could verify the system sensing performance robustness over a flow rate ranging from 5 to 30 \(\upmu\)L/min. The OFI signal was acquired through the junction voltage of the VCSEL. The signal was amplified using a custom made amplifier and using a National Instrument acquisition card (NI USB 6251) at a sampling frequency of 400 kHz. Processing of the signal consisted of 30 averagings of the fast Fourier transform (FFT) of \(2^{15}\) samples length. Thus, the total acquisition window length was 983040 (\(30\times 2^{15}\)). A dedicated LabVIEW program automates all the data acquisition procedures and processing. We evaluated the signal visibility over the available laser biasing current range to find the optimal current value at which the OFI sensors could lead to the maximal signal. The OFI flowmetry measurements were repeated within applied laser operation currents ranging from 1.5 mA (threshold current value) to 3.5 mA at a 10 \(\upmu\)L/min flow rate. The resulting OFI signal frequency spectra are depicted in Figure 8. It should be noted that when the current was set to be 1.5 mA, the OFI modulation was too weak. The OFI frequency spectral signal was overwhelmed by the system noise floor and it could hardly be observed. Moreover, all over the considerable current range, the spectrum presented a well-defined Gaussian-shaped peak. The Doppler frequency and the signal level can be calculated automatically by fitting a Gaussian function [16].