The self-mixing sensing technique is a compact, interferometric sensing technique that can be used for measuring fluid flows. In this work, we demonstrate a parallel readout self-mixing flow velocity sensing system based on a monolithic Vertical-Cavity Surface-Emitting Laser (VCSEL) array. The parallel sensing scheme enables high-resolution full-field imaging systems employing electronic scanning with faster acquisition rates than mechanical scanning systems. The self-mixing signal is acquired from the variation in VCSEL junction voltage, thus markedly reducing the system complexity. The system was validated by measuring velocity distribution of fluid in a custom built diverging-converging planar flow channel. The results obtained agree well with simulation and demonstrate the feasibility of high frame-rate and resolution parallel self-mixing sensors.
© 2010 Optical Society of America
The laser self-mixing sensing technique is a simple interferometric sensing technique where a portion of the light emitted from the laser reflects from a target and re-enters the laser cavity where it causes measurable changes in emitted power  and junction voltage . The resulting output power variations are usually monitored by an integrated photodiode within the laser package but it is also possible to measure the junction voltage variations which removes the need for a photodiode . This phenomenon allows the laser itself to function as both the light source and the detector making possible low-cost and compact sensors. The laser self-mixing sensing technique has been used for a wide variety of measurements including absolute distance , vibrations , velocity  and fluid flow rate .
Most self-mixing sensors are single-point systems and acquiring measurements over an area is typically achieved by mechanical scanning . An obvious extension to single-point acquisition is to use multiple individual lasers in a single sensor package, however, parallel sensing systems using individually packaged lasers suffer from misalignment which directly contributes to measurement inaccuracies of flow velocity, as was observed in previous work conducted by Tucker et. al . The Vertical -Cavity Vertical-Cavity Surface-Emitting Laser (VCSEL) construction offers advantages compared to in-plane lasers because VCSELs emit light normal to the surface of the wafer. VCSELs can therefore be operated without dicing of the substrate, allowing the lasers to maintain their precise lithographic alignment. We have previously demonstrated such an array for velocity measurements . In this work, we present, to the best of the authors’ knowledge, the first self-mixing flow mapping system utilizing a monolithic VCSEL array with parallel readout.
The multi-channel sensor makes use of a 1×12 VCSEL array for measuring fluid motion to demonstrate the feasibility of a self-mixing array-based flow-imaging system. The self-mixing signals are obtained directly via feedback-caused variation in the VCSEL junction voltage. This key solution offers significant technological advantage as it avoids optical monitoring of laser power fluctuations, removing the need for VCSEL-photodiode array hybrid integration and the complexities associated with this process . Moreover, the feedback occurs in the high-finesse laser cavities and is coherent in nature, thus the problem of optical crosstalk is avoided.
The paper is structured to provide the Doppler theory necessary for the flow velocity measurements in Sec. 2. A detailed description of the experimental setup is presented in Sec. 3. In Sec. 4 we report on the simulated results for the velocity distribution of fluid within the flow-channel. These simulation results are then compared against the experimental results presented in Sec. 5. Finally conclusions are drawn in Sec. 6.
For a moving target with velocity v⃗, the back scattered light experiences a Doppler frequency shift f D given by 
where k⃗inc and k⃗sc are the wave vectors of the incident and scattered light respectively. In the self-mixing interferometer configuration, the scattered signal is collected by the same lens used to focus the beam on the target and Eq. (1) becomes
where k̂ is the unit vector in the direction of the laser emission, λ 0 is wavelength of light in vacuum and n corresponds to the refractive index of the medium surrounding the target. The result of coherent mixing within the laser cavity between the lasing field and the Doppler-shifted light backscattered by a moving target leads to a fluctuation of photon density and consequently the output power and junction voltage.
In fluid flow, the moving target consist of moving particles suspended in the fluid. The light scattered from a moving particle is frequency shifted by an amount determined by the Doppler effect as indicated by Eq. (2). The optical system collects light scattered from a number of different particles with different velocities, which leads to a distribution of Doppler shifts in the output power spectrum and its shape is dependent on the level of particle concentration in the solution . For a solution where particle concentration is low enough that multiple scattering can be ignored, a well defined peak appears in the frequency spectrum corresponding to the Doppler frequency of the moving particle . This information can then be used to determine the flow rate of the liquid.
3. Experimental setup
Figure 1 shows the schematic diagram of the experimental setup used to measure the fluid flow profile in a custom made flow channel. The source used was a commercial 1×12 monolithic VCSEL array (EMCORE Corporation, Gigalase 8185–1100) which are AlGaAs planar, top surface emitting devices with 15 μm apertures in the top mirror contact and laser pitch of 250 μm. The average threshold current of the VCSELs is about 6 mA and each laser has a peak wavelength at around 850 nm. C-mount camera objective lenses were selected to image the laser beams on the flow channel to minimize field distortion. The imaging system was designed to provide a non-inverted image with 2× magnification and made use of a 25 mm focal length lens (lens 1) and a 50 mm focal length lens (lens 2). The pitch between the spots on the flow channel is 500 μm.
Figure 2(a) shows the dimensions of the custom made diverging-converging planar flow-channel. It is 3 mm deep and a microscope cover slip of 160 μm thickness is employed as the top window sealing cover allowing the VCSEL beams to illuminate different points in the channel. The channel was mounted onto a translation stage that has 50 mm travel in the scanning direction and the stage movement was driven by a DC servo motor that was controlled by an Elmo Whistle  motor controller. The scanning was carried out with a step size of 1 mm in all experiments.
A custom built 12-channel laser driver was used to individually bias each laser just above its threshold in order to obtain maximum sensitivity to the self-mixing effect. The self-mixing signals were obtained through terminal voltage variations across individual VCSELs. Terminal voltage fluctuations were first amplified individually using an ac-coupled, low noise preamplifier with a voltage gain of 100. The pre-amplified voltage signals were then fed to a computer controlled analog multiplexing module for addressing and switching of the laser signals. Additional amplification (G = 100) was subsequently applied to the multiplexed voltage signal, bringing it to a level suitable for processing by a 16-bit data acquisition card. The total bandwidth of this multi-stage amplification system is 600 kHz. A sampling rate of 800k samples per second was used to acquire the self-mixing signals which gives a effective measuring bandwidth of 400 kHz. Fast-Fourier Transform (FFT) was applied to the time-domain signals to obtain frequency spectra consisting of 32k points. The frequency spectrum for each channels was subsequently averaged 32 times and saved. A customized LabVIEW application was developed to carry out the signal acquisition, in conjunction with automating the channel scanning.
4. Flow-channel simulations
The fluid flow distributions in the flow channel depicted in Fig. 2(a) were simulated in order to provide a comparison to the experimental results obtained with the experimental results from the self-mixing sensor. The fluid parameters used for the simulations were those of water at room temperature. The simulations were performed using the commercial computational fluid dynamics package, CFD-ACE+ from ESI-Group. The results provide 3-D distribution of the velocity vectors for points within the flow channel on a fine hexahedron structured grid containing 30, 292 and 31 points in the x, y and z directions respectively [see Fig. 2(a)].
5. Measurement results
The experiment was carried out with the angle, θ, between the flow channel and the laser axis set to 80°. The fluid used was a dilute solution of one part homogenised full cream milk to 50 parts water to obtain a single scattering regime. The total image height of the 12-channel array projected onto the flow channel is 5.5 mm. Laser LD6 of the VCSEL array was set along the center-line of the channel while the last channel (LD12) was omitted in experiments to achieve geometrical symmetry as shown in Fig. 2(a). The entire channel was scanned by performing three horizontal broom sweeps starting from the top portion of the channel, resulting in a total of 33 vertical points that are swept across the channel. The area of the channel that was scanned is shaded in Fig. 2(a).
The frequency spectra of self-mixing signals acquired at two points in the channel for a 15 mL/min inlet flow rate are plotted in Fig. 2(c) where the color of the spectra corresponds to the same colored dots as indicated in Fig. 2(a). It was observed that the width of the Doppler frequency peak increases with increasing velocity, and it’s amplitude decreases. These spectral trends were consistent to the work by Post et. al . The spectral width of the Doppler frequency should be proportional to the velocity and the spot size of the laser beam. Since the spot-size remains constant throughout the experiments, the broadening of the spectral width will depend solely on the velocity. This observation was used in formulating the following behavioral function which was fitted to the measured spectra in order to extract the frequency peak corresponding to f D:
where a and b in the first term are parameters used for fitting the 1/ f-noise as suggested by Serkland et. al. . The second term, c, is used for fitting the spontaneous emission of the laser. The last term is a Lorentzian function where d corresponds to the strength of the Doppler peak. The half-width at half-maximum of the Doppler spectra is represented by the denominator term, f/n, which is scaled by factor n and is directly proportional to frequency. The inclusion of noise in our fitting routine is required to ensure an accurate value of f D is extracted as the noise has a significant influence on the acquired spectra, particularly at low frequencies as can be seen in Fig. 2(c). Subsequently, the component of velocity in the direction of the laser beams can be inferred from f D at each spatial position on the flow channel Eq. (2), taking into consideration the refractive-index of the fluid (n ≈ 1.333) that will refract the laser emission.
Simulation showed that there is a small component of velocity in the z-axis which will have the effect of introducing errors in the inferred x-axis flow velocities. However, these velocity components were only significant around the inlet and outlet regions of the channel. As a result, flow distributions were measured in the center region of the channel approximately 10 mm from the left and right edges of the flow channel where there is no significant flow in the z-axis direction. It would be possible to add additional lasers with different emission angles in order to extract the individual flow velocity components . In many applications this is not necessary as the fluid flow direction is well known. For example, flow direction in peripheral tissues is well guided by the blood vessels .
Figure 3 shows the laminar flow profile along the center-line of the flow channel at 3 different inlet flow-speeds of 10, 15 and 20 mL/min respectively. The red-lines in Fig. 3(a), 3(b) and 3(c) represent the fluid velocity in the direction of the laser beam at different channel depths, obtained from simulations. The depth spacing between adjacent red lines is 100 μm. The optical arrangement employed in this system ensures a shallow depth-of-focus when compared to single lens systems employing a collimated beam. Using the Gaussian beam approximation, we calculated the depth-of-focus of the laser beams to be 254 μm. This suggests that the measured results correspond only to a limited section of the entire channel. The green-line in each graph represents the average fluid velocity calculated across a selected section 300 μm deep (within the range of red-lines) that best fits the measurement results. The results show close correlation with similar trend between simulated and measured results. However, there are minor discrepancies in the measurements which are likely caused by micro bubbles present in the channel while laser scanning was performed. Figure 3(d) illustrates the effect of a tiny trapped air bubble on the back face of the glass window, which was encountered while laser scanning was performed. These air bubbles alter beam parameters such as depth-of-focus and spot-size, and can significantly alter the beam angle which leads to erroneous reading of f D.
All the measured data were subsequently combined to form a two-dimensional map of the fluid flow distribution as depicted in Fig. 4. A good agreement can be seen between the simulated and measured results confirming the ability of the system to accurately create a 2-D flow map. A minor difference between the measured and simulated results is the stronger central jet in the measured results. This may be due to the high sensitivity of the flow profile on the inlet geometry and surface properties that are difficult to reproduce accurately in the simulation.
In this paper, we demonstrated a full-field self-mixing sensor system with simultaneous readout from an array of VCSELs for measuring fluid-flow velocities. A small scale prototype of the system, based on the 1×12 VCSEL array has been implemented. The performance of the system has been validated by imaging the distribution of fluid flow velocity in a custom made channel. The results obtained match closely the simulated velocity distributions of the channel and suggest that the image quality improvement due to lithographic alignment of lasers constituting the monolithic array is essential for expanding this concept in the creation of a massively parallel Doppler imaging systems based on two-dimensional VCSEL arrays. The VCSELs in this system are used as both the light source array and the sensor array by sensing the change in junction voltage across each VCSEL. This sensing technique removes the need for the hybrid integrated photodetector array with the VCSEL array, which significantly reduces the complexity the proposed system. Furthermore, this coherent detection scheme efficiently suppresses the optical crosstalk from the neighboring lasers. In comparison with a single spot-raster scan system, the acquisition time is significantly shortened as the mechanical scanning process in one axis is replaced by concurrent acquisition at all channels/pixels. Further to this, the use of a 2-D VCSEL array will remove the need for mechanical scanning completely, thus improving acquisition time, temporal resolution and reducing mechanical complexity.
This research was supported under Australian Research Council’s Discovery Projects funding scheme (DP0988072).
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