Parallel self-mixing imaging system based on an array of vertical-cavity surface-emitting lasers

Parallel self-mixing imaging system based on an array ofvertical-cavity surface-emitting lasers

John R. Tucker,1 Johnathon L. Baque,2 Yah Leng Lim,1 Andrei V. Zvyagin,1,3

and Aleksandar D. Rakic1,*1School of Information Technology and Electrical Engineering, The University of Queensland, St. Lucia, Queensland 4072,

Brisbane, Australia2Department of Mechanical Engineering, School of Engineering, The University of Queensland, St. Lucia, Queensland

4072, Brisbane, Australia3Centre for Biophotonics and Laser Science, School of Physical Sciences, The University of Queensland, St. Lucia,

Queensland 4072, Brisbane, Australia

*Corresponding author: [email protected]

Received 20 February 2007; revised 20 June 2007; accepted 22 June 2007;posted 28 June 2007 (Doc. ID 80251); published 22 August 2007

In this paper we investigate the feasibility of a massively parallel self-mixing imaging system basedon an array of vertical-cavity surface-emitting lasers (VCSELs) to measure surface profiles of dis-placement, distance, velocity, and liquid flow rate. The concept of the system is demonstrated usinga prototype to measure the velocity at different radial points on a rotating disk, and the velocity profileof diluted milk in a custom built diverging-converging planar flow channel. It is envisaged that ascaled up version of the parallel self-mixing imaging system will enable real-time surface profiling,vibrometry, and flowmetry. © 2007 Optical Society of America

OCIS codes: 120.3180, 120.7250, 250.7260, 280.2490, 280.3340, 280.7250.

1. Introduction

The behavior of a semiconductor laser diode withexternal optical feedback is a complex but well re-searched phenomenon [1,2]. It is often seen as a hin-drance in many applications since it can increase theintensity noise of the laser [3], but it is also the en-abling process behind many applications [4,5].

The optical feedback is a result of the laser beambeing partially reflected from an object back into thelaser cavity. The reflected light interferes or “mixes”with the light inside the laser cavity, and producesvariations to the operating frequency and outputpower of the laser. This process is commonly referredto as the “self-mixing” effect, and the resulting outputpower variations can be monitored as photocurrentfluctuations of the photodiode (PD) integrated withthe laser package or by the change in the junctionvoltage across the laser diode [6]. This phenomenon

allows the laser to be used as both a source anddetector, and significantly reduces the cost andcomplexity of the interferometric sensing system.The self-mixing phenomenon has been used formany constructive purposes that include linewidthreduction [7], measurement of target displacement[8], distance [9], velocity [10], angle [11], and liquidflow rate [12,13]. It has also recently found applica-tions in measurements of the laser linewidth [14] andthe laser linewidth enhancement factor [15]. The self-mixing effect has also been used to create three-dimensional (3D) surface profiles of an object. Most ofthese demonstrations have employed scanning tech-niques where the laser beam is mechanically shiftedacross the surface of the object [16–18].

However, there are surprisingly few reports on par-allel imaging systems using the self-mixing effect. Theadvantages of parallel detection over scanning meth-ods are well known: higher frame rates and a highersignal to noise ratio (SNR). So far, only a rudimentaryparallel self-mixing imaging system has been con-structed with three commercial semiconductor lasers

0003-6935/07/256237-10$15.00/0© 2007 Optical Society of America

1 September 2007 � Vol. 46, No. 25 � APPLIED OPTICS 6237

to measure the speed and distance to different pointson a rotating disk [19]. While the number of points inthe image can be increased by using an array of lasersand detectors, preceding infrared laser technology hashampered the development of a massively parallel self-mixing imaging system.

With the advent of vertical-cavity surface-emittinglasers (VCSELs) it is now possible to cost effectivelymanufacture a two-dimensional monolithic array oflasers. In this paper, we consider a massively parallelself-mixing imaging system based on an array ofVCSELs. We demonstrate, for what we believe to bethe first time, the feasibility and advantages of thissystem by the successful operation of a small scaleprototype consisting of eight individual VCSELswith integrated PDs to measure the velocity profilesof a rotating disk and a custom built diverging-converging flow channel. A massive implementa-tion of the system will be useful in many industrialand biomedical applications requiring real-timesurface profiling and velocimetry.

The paper is organized as follows: Section 2 de-scribes how the self-mixing effect can be utilized tomeasure velocity and liquid flow rate; in Section 3 wedescribe in detail the proposed massively parallel im-aging system; the feasibility of the system is demon-strated with the experimental setup described inSection 4 and the results are presented and discussedin Section 5 along with a description of the plans fora massive implementation of the system; conclusionsare drawn in Section 6.

2. Self-Mixing Applications

A. Velocity

The self-mixing effect occurs when the light emittedfrom a laser reflects from a target, and is injectedback into the laser. To measure the velocity of a tar-get, the output power waveform can be considered tobe the result of coherent mixing inside the laser cav-ity of the lasing field and the Doppler-shifted lightbackscattered from the target. For the self-mixingconfiguration, the frequency shift of the incident lightdue to the Doppler effect is given by [12]

fDoppler �2�targetn cos �

�, (1)

where �target is the magnitude of the target velocity, nis the refractive index of the surrounding medium, �is the angle between the target velocity vector andthe longitudinal axis of the laser, and � is the wave-length of the laser.

The superposition of the laser light and the fre-quency shifted backscattered light leads to an inten-sity modulation of the laser at a frequency that isequal to the Doppler frequency calculated with Eq.(1). However, the Doppler signal from a rotating tar-get is randomly amplitude modulated by speckle ef-fects, since the part of the target that is illuminated

by the laser light continuously changes [20]. Thismakes it difficult to employ peak counting techniquesto determine the Doppler frequency. However, thebeat frequency of the output power waveform can beeasily determined by detecting the peak frequency inthe fast Fourier transform (FFT) spectrum of the out-put power, which is linearly proportional to the ve-locity of the target, as it will be shown later in thispaper.

B. Liquid Flow Rate

Light scattered from a moving particle is shifted infrequency by an amount determined by the Dopplereffect as indicated by Eq. (1). For a laminar flow ofliquid, the velocity profile in a circular glass tube isparabolic, with the velocity increasing from zero atthe boundary of the tube wall to a maximum value atthe center [21]. The optical system collects lightscattered from a number of different particles withdifferent velocities, which leads to a distribution ofDoppler shifts in the output power spectrum.

For weakly concentrated scattering solutions and asuitable optical setup, a well defined peak appears inthe FFT spectrum corresponding to the Doppler fre-quency of the moving particle. This information canthen be used along with the velocity profile of the flowchannel to determine the flow rate of the liquid. How-ever, there is only one report of a well defined Dopplerpeak in the frequency spectra of the output power forthe measurement of the liquid flow rate using theself-mixing effect [22].

In general, a broad distribution of Doppler shifts isobtained in the frequency spectrum of the outputpower, and peak detection algorithms can no longerbe used to accurately measure the flow rate of theliquid. The shape of the distribution is also compli-cated by the fact that, in highly concentrated scatter-ing solutions, such as blood or milk, there is a stronglikelihood that a photon will be scattered by morethan one moving particle before it travels back to-wards the laser [23]. If a large number of these eventsoccur, then there is an increased number of higherorder scattering events or multiply convoluted Dopp-ler shifts. As a consequence, there is no longer asingle peak above zero frequency in the frequencyspectrum of the output power, and it is difficult todetermine the velocity distribution [23]. However,the spectrum displays a decay with a half width thatis proportional to the scattering particle size and themean speed of the liquid [13,23].

In this case, the flow rate of the liquid can be de-termined by calculating the weighted moment �� ofthe spectrum, which is given by [12]

��

�0

�

�S��d�

�0

�

S��d�

, (2)

6238 APPLIED OPTICS � Vol. 46, No. 25 � 1 September 2007

where w is the frequency of the output power spec-trum S. In practical situations, the integration limitsin Eq. (2) are reduced to a finite bandwidth, to elim-inate errors from low frequency motion artifacts andhigh frequency white noise. The calculation of theweighted moment then gives a result that is a pro-portional to the mean speed of the liquid, which canthen be used to determine the flow rate of the liquid.

Another signal processing method commonly usedby many self-mixing researchers to ascertain the flowrate of a liquid involves the determination of a cutofffrequency in the frequency spectrum where the self-mixing signal spectrum intersects the spectral noisefloor [12,22,24,25]. This frequency is assumed to beequal to the maximum Doppler frequency in the dis-tribution, which can then be used to determine theflow rate of the liquid.

The flow rate can also be determined by fitting thefrequency spectrum of the output power to an ana-lytical function. In this case, one of the fitting param-eters for the analytical function is proportional to theflow rate of the liquid. Different types of analyticalfunctions have been used in different experimentalsetups based on the laser Doppler effect including theuse of Lorentzian [26] and exponential fitting func-tions [27] to successfully measure the flow rate of theliquid. So far, only an exponential fitting function hasbeen used by Zakian et al. to determine the flow rateof a liquid using the self-mixing effect [13].

3. Proposed Imaging System

Section 2 illustrates how the self-mixing effect can beused to take a measurement from a single point on anobject. This measurement principle can be extendedto acquire an image of the surface profile by mechan-ically scanning the laser beam across different pointsof the object [16–18]. However, the acquisition timefor each pixel in the image must be long enough toachieve the desired SNR, which is directly propor-tional to the acquisition time for a shot-noise limiteddetection scheme. If a large number of pixels arerequired for the image, then the scanning operationprecludes real-time image acquisition and a measure-ment of rapid variations in the surface profile of theobject.

This limitation can be overcome with the use of“full-field” or “parallel” imaging techniques. In thesesystems, the whole measurement area is illuminatedby a light source, and scattered light is detected withan array of PDs. This allows for the simultaneousacquisition of data from every point on the measure-ment area, and drastically reduces the image acqui-sition time compared to the scanning operation.Parallel imaging systems also have a higher SNR fora fixed image acquisition time since the acquisitiontime for a single pixel can be much longer comparedto scanning type imaging systems.

In many parallel imaging systems, a single sourceof light is used to illuminate the whole measurementarea [28–30]. However, larger source powers areneeded to adequately illuminate larger measurementareas, which can lead to safety concerns. This can be

countered by using a low power laser beam for eachmeasurement point, but this approach suffers froman increase in the complexity of the alignment of theoptical system, which can make the size of the systemlarge and expensive.

In this paper, we investigate the feasibility of amassively parallel self-mixing imaging system basedon an array of VCSELs. A drawing of a scaled downversion of the proposed system is shown in Fig. 1.This system is more compact and robust compared toother parallel imaging systems since each VCSEL isused as both a source and a detector. Therefore, thistype of imaging system will be extremely useful in theobtrusive and remote environments that are com-monly encountered in many industrial and biomedi-cal applications.

It is also possible that different embodiments of thesystem proposed in Fig. 1 can be employed. On onehand, it may be possible to use a different opticalconfiguration such as a single macro-lens to focus thelight from each VCSEL in the array onto the target.This would reduce the size and complexity of theoptical system and would also make the system morecompact and robust.

Another possibility is to discard the PD array en-tirely and monitor the self-mixing signals by thechange in the junction voltage across each element ofthe VCSEL array [6]. This would not only reduce thecost and size of the system, but would also eliminateany misalignment or back reflections from the PDarray. This makes a voltage based self-mixing systemextremely attractive.

4. Experimental Setup

To demonstrate the feasibility of the imaging sys-tem proposed in Section 3 we constructed a smallscale prototype using eight individual TO-46 pack-aged single-mode Lasermate VCT-F85A32-OS VCSELswith integrated PDs arranged in a linear arrayshown in Figs. 2(a) and 2(b). The VCSELs weremounted in a custom made aluminum block with apitch of 5.8 mm. A separate block was constructed to

Fig. 1. (Color online) Illustration of a scaled down version of theproposed parallel self-mixing imaging system.


mount eight plastic aspheric Konica T544C lenses(N.A. � 0.47, clear aperture 3.17 mm, and focallength f � 3.38 mm), with the same pitch as that ofthe VCSELs [shown in Fig. 2(b)]. The lens block wasattached to the VCSEL block so that the lenses werealigned with the VCSELs. The VCSEL block wasattached to a translation stage to facilitate the align-ment of the VCSEL beams in the longitudinal andlateral directions.

This setup was then used to measure the veloc-ity profiles of a rotating disk and a custom madediverging-converging planar flow channel. A mechan-ical drawing and photograph of the constructed flowchannel is shown in Figs. 3(a) and 3(b). Fittings wereattached to both ends of the flow channel to allowthe connection of silastic tubing. A Watson–Marlow101U�R peristaltic pump then forces diluted milkthrough the silastic tubing and flow channel at apredetermined flow rate. The liquid passes throughthe cross section of the flow channel, as we show inFig. 3, which was milled out of an aluminium block,and a microscope slide is clamped on top to allow theVCSEL beams to illuminate different points in thedevice. The channel has a constant depth of 2.5 mm

and a varying width profile, which is inversely pro-portional to the average velocity. The width of thechannel changes from the entrance to form a diverging-converging section so that the average velocity de-creases after the entrance, followed by an increaseback to the initial velocity at the exit.

A block diagram of a single channel of the imagingsystem is shown in Fig. 4. Each VCSEL has an indi-vidual driver circuit so that the current injected intoeach laser can be individually controlled. The back-scattered light from the target is collected by thecollimating lenses and mixed with the light inside thecorresponding VCSEL cavities. The resultant fluctu-ations in the output power are detected by the inte-grated PDs, followed by a transimpedance amplifierand ac-coupler circuit for each channel to produce thehigh contrast self-mixing signals for the measure-ment points. The output of each channel is sampledsimultaneously by a National Instruments 16-bitdata acquisition card, and sent to a personal com-puter (PC) for processing and display in LABVIEW.

LABVIEW was also used to perform additional signalconditioning to the frequency domain signals, includ-

Fig. 2. (Color online) Small scale prototype using eight individualsingle-mode VCSELs with integrated PD arranged in a lineararray. Pitch of the array is 5.8 mm. A separate block holds eightaspheric lenses (N.A. � 0.47, clear aperture 3.17 mm, and focallength f � 3.38 mm). (a) Angled view of the constructed imagingsystem; (b) front view of the constructed imaging system.

Fig. 3. (Color online) (a) Mechanical drawing of the top view of thecustom made diverging-converging planar flow channel; (b) photo-graph of the constructed flow channel.

Fig. 4. Block diagram for a single channel of the experimentalsetup.


ing the use of a seven-term Blackmann–Harris win-dow. The frequency spectrum for each channel wasaveraged 50 times and subsequently saved. A totalof 50 averaged frequency spectra were recorded forfurther processing in MATLAB to calculate the velocitymeasured at different points on the rotating disk or inthe flow channel. The velocities for the rotating diskwere calculated using the peak frequency of the sig-nal in the FFT spectrum, and Eq. (1) and the meanspeed of the liquid were calculated by the weightedmoment of the spectrum in Eq. (2).

The actual velocity of the spinning disk was mea-sured by a stroboscope. The velocity distribution inthe flow channel was determined by a numerical sim-ulation in the software package FLUENT [31]. The sim-ulation was performed with water as the flowingliquid, so only a weakly concentrated scattering so-lution was used in the experiment, consisting of onepart homogenized full cream milk to 50 parts water.

5. Experimental Results and Discussion

A. Rotating Disk

In the first experiment, we measured the velocity atdifferent radial distances on the surface of a rotatingdisk. Each VCSEL is operated at the same bias cur-rent of 3.5 mA with the disk 60 mm away, and thesurface tilted at an angle of 79° with respect to theoptical axes of the VCSELs. The FFT spectra ob-tained from a single point on the disk rotating atdifferent speeds is shown in Fig. 5. Ignoring thestrong peak at zero due to the dc offset of the signal,the peak frequency in the spectrum increases as thespeed of the disk increases. By blocking the light fromdifferent channels we also observed that there was nochange in the FFT spectrum, which indicates thatthere was no noticeable crosstalk.

The beams were aligned so that there were fourbeams on each half of the surface of the disk. How-ever, the system could not be perfectly aligned sincethe individual VCSEL chips were not perfectly cen-

tered in the TO-46 packages. This fact was confirmedby a change of the spot position on the target whenthe corresponding TO-46 package was rotated in theoptical mount. To counter this problem, the VCSELpackages were fixed in one position and aligned ap-proximately in a horizontal line. An infrared camerawas then used to determine the spot positions on atransparent target for a wide range of target dis-tances, which was then used to calculate the anglethat each beam makes with the target velocity vector.With this information, we calculated the target ve-locity measured by each channel using the averageVCSEL wavelength of 850 nm.

The results in Fig. 6 show the actual velocity versusthe measured velocity and the accuracy of the mea-surement for different radial points of the disk spin-ning at 26 rpm. In these diagrams the negative signfor the radial distance indicates that the laser beamis from one half of the disk, while a positive sign

Fig. 5. Frequency spectra for a single channel at disk speeds of30 rpm (squares), 54.1 rpm (open circles), and 74.8 rpm (trian-gles).

Fig. 6. (a) Actual (square) versus measured velocity profile forrotating disk for multiple channel operation (open circle) and sin-gle channel operation (triangle) at a disk speed of 26 rpm; (b)accuracy of velocity for different channels for rotating disk formultiple channel operation (squares) and single channel operation(open circles) at a disk speed of 26 rpm.


indicates the velocity that is measured on the otherhalf of the disk. The velocity at the center of the diskwas not measured, but the theoretical value of zerohas been included to illustrate the correct velocityprofile of the disk. From this we can see that themeasured profile corresponds closely to the calcu-lated velocity profile of the rotating disk, and a highlevel of accuracy is obtained. We also include theresults obtained for the individual operation of eachchannel in these diagrams, which show that there isno noticeable change due to crosstalk. This suggeststhat the main source of error is from the alignment ofthe individual VCSELs within the package.

B. Flow Channel

The system was then used to measure the velocityprofile of the custom made flow channel described inSection 4. Each VCSEL was operated at a bias cur-rent of 5 mA with the flow channel 70 mm away, andat an angle of approximately 87°. The beams werealigned along the centerline of the flow channel start-ing from the entrance of the diverging section to theexit of the converging section. The dimensions of thechannel allowed for six beams to be aligned alongthe centerline of the flow channel.

Figure 7(a) shows the spectra of the output powerfor a single channel at four different inlet flow ratesranging from 3.9 to 10 mL�min. The width of thespectra is increasing with the velocity of the liquid.We noticed the change in the width of the spectrumwhen all channels are operated at the same time, aswe show in Fig. 7(b). This indicates the presence ofoptical crosstalk in the experimental setup, an issuethat needs to be addressed if the system is to beoperated with all the VCSELs operating concur-rently. In some of the earlier self-mixing papers thepossibility of interference between the channels isdismissed outright due to the coherent nature of thedetection scheme [19,32]. However, there is a weightof evidence that suggests that injection locking inVCSELs can occur even for injection levels as low as10�3 of the affected (slave) VCSEL power [33–35].This issue could not be thoroughly investigated usingthe current experimental setup, since any generationof optical crosstalk in the system is compounded bythe fact that the monitoring PDs have an area that islarger than that of the VCSELs. The commercialVCSEL hybrid, integrated with the monitoring PD, isshown in Fig. 8(a). The output light intensity is mon-itored by a reflection off the glass window of the pack-age, instead of the rear-facet of the VCSEL as weshow in Fig. 8(b). The susceptibility of the PD toenvironmental light was also confirmed by the pres-ence of a strong 100 Hz signal when the fluorescentlights in the lab were turned on. To the best of ourknowledge, at the time of this writing, there are nodetailed theoretical nor experimental accounts ofthe effect of optical crosstalk in self-mixing sensorspresent in the open literature. An investigation intothe causes and effects of the optical crosstalk encoun-tered in this study would require a system with a

sensing architecture where the PDs are insensitive toenvironmental light. This can be achieved by flip chipbonding a VCSEL to a PD and removing the sub-strate of the VCSEL [36] so that the PD is insensitiveto light from other channels. However, it represents atechnologically challenging solution to the problem,with only one fabricated array device reported re-cently [36]. Instead, the PD array can be discardedcompletely by monitoring the self-mixing signal withthe change in junction voltage of each element in theVCSEL array. This makes a voltage based VCSELarray self-mixing imaging system very attractive as itreduces the component size and cost, and eliminatesany misalignment or back reflections from a PDarray. However, further work is still needed to in-vestigate the immunity of this sensing scheme to in-terchannel crosstalk and the feedback levels at whichit may occur. On the other hand, the potential ef-fects of optical crosstalk with the monolithically

Fig. 7. (a) Frequency spectra for a single channel at inlet flowrates of 3.9 mL�min (solid curve), 5.9 mL�min (dashed curve),7.9 mL�min (dotted curve) and 10 mL�min (dashed dotted curve);(b) frequency spectra for a single channel at an inlet flow rate of3.9 mL�min with other VCSELs not operating (solid curve), andwith all VCSELs operating concurrently (dashed curve).


integrated VCSEL array can be minimized by anoptimized design of the optical system using anarray of microlenses. A similar approach has al-ready been successfully implemented for minimiz-ing the crosstalk between channels in VCSEL basedfree-space optical-interconnects [37,38], and the au-thors believe that this will lend the proposed systemto a wide variety of sensing applications.

To correctly measure the velocity profile of the flowchannel, each VCSEL in the array was operated in-termittently. A calibration was first performed with asingle channel to relate the weighted moment of theoutput power spectrum to the velocity of the flow. Theweighted moments for different inlet flow rates from3.9 to 10 mL�min for a single channel were calcu-lated using Eq. (2) over a fixed frequency intervalconsisting of a low cutoff frequency of 75 Hz, whichwas above the low frequency noise in the measuredspectra, and an upper cutoff frequency of 1.45 kHz,

which is the point where the spectrum decays to 3 dBabove the noise floor for the smallest measured ve-locity. These results are shown in Fig. 9(a), and dem-onstrate that the weighted moment of the spectrumcan be fitted to a quadratic function of the inlet flowrate.

The local velocities at different points in the flowchannel were computed by a two-dimensional (2D)simulation of the flow channel using the softwarepackage FLUENT, and deemed as the calibration ve-locities. For inlet flow rates ranging from 3.9 to10 mL�min, simulations show that the velocities ofthe measured points are linear functions of the inletflow rate. Using the velocity of the calibration pointfrom the simulation and the fitted quadratic functionin Fig. 9(a), an expression was developed to relate theweighted moment of the spectrum to the actual ve-locity of the measurement point.

In another experiment performed by the authors,the spectrum of the self-mixing signal at this concen-tration of the scattering solution was found to behighly dependent on the target angle. Therefore, the

Fig. 8. (Color online) (a) Microscope image of VCSEL and PDinside the TO-46 package; (b) component layout of the TO-46package.

Fig. 9. (a) Weighted moment (squares) for a single channel atdifferent inlet flow rates fitted to a quadratic function (dashes); (b)actual (solid curve) versus measured (squares) centerline velocityprofile for flow channel.


weighted moment was also assumed to be propor-tional to the longitudinal component of velocity or�target cos � in Eq. (1) to compensate for the misalign-ment, and to correctly calculate the velocities mea-sured by each measurement channel. The measuredvelocities and the calibration velocities from the sim-ulation along the centerline of the flow channel for aninlet flow rate of 3.9 mL�min are compared in Fig.9(b). The measured profile and the simulated velocityprofile exhibit a similar trend with discrepancies no-ticeable in the middle of the flow channel. Figure 10compares the measured and the simulated 2D veloc-ity profile of the flow channel. The vertical (y) positionof the flow channel was shifted with a translationstage to five equidistant points to simulate a linescanning operation. The experimental velocity distri-bution displays a reasonable agreement with the sim-ulated data. The difference between the two contourplots in the middle of the flow channel, which wasconsistent with the measurements of the centerlineprofile of the channel in Fig. 9(b), can be explained bya number of factors. First, the simulation used here isonly 2D in nature and does not take into account the3D structure of the flow. A 3D simulation on a similarstructure compared to the fabricated device showsthat the average velocity decreases after the entrancefollowed by an increase leading back to the initialvelocity at the exit, as it was observed in the experi-ments and the 2D simulation. It should also be notedthat the total range of velocities measured in theexperimental setup were close to the resolution ob-tained by other authors for this measuring technique[12,13]. Another source of the difference between themeasured and simulated velocity profiles stems from

the fact that the laser beams are not all focused in thesame plane, resulting in a slight depth offset whenmapping the measurements. We expect that the useof a monolithic VCSEL array and a well aligned op-tical system will lead to an accurate measurement ofthe velocity profile for velocities that are within theresolution of a single channel of the measuring sys-tem. Finally, the measurement error of the Dopplerfrequency increases significantly for very small veloc-ities [39].

Although we have demonstrated the potential per-formance of the proposed imaging system with a smallscale prototype, there are a number of issues thatshould be considered for the construction of a massivescaled up version of the system. First, the diameters ofthe TO-46 packages used in the experimental setupwere 5.4 mm, which precludes a miniaturization ofthe system. A monolithically integrated VCSEL ar-ray with pitch spacing of 250 �m between deviceswill represent an attractive alternative for the designof the miniaturized VCSEL system.

The scaled up version of the parallel VCSEL basedimaging system also poses a problem of real-timeindividual channel signal processing, since the num-ber of operations required per second is hardly pos-sible with a single central processor unit. To counterthis problem, a number of parallel processors can beimplemented with electronic circuits, such as thefield-programmable gate array platform described byZhu et al. for a 256 256 laser Doppler blood flowcamera [40], although this would come at the expenseof an increased circuit size and complex layout. How-ever, the physical size of the circuit and layout can bereduced with the use of very large scale integration(VLSI) or ultralarge scale integration (ULSI) tech-nology.

The circuit size can also be reduced by employingmultiplexing in the system so that only a smallnumber of channels are read in at the same time.However, this method is another form of scanning.Instead of the laser beam being mechanicallyguided towards different parts of the object, it iselectrically guided by the switching circuit or mul-tiplexing operation. The maximum frame rate andSNR will also be reduced compared to a completelyparallel system, but will still be greater than thatachievable with single point scanning. Therefore, itis desirable to have individual driving, receiving,and processing circuits for each channel to obtainthe maximum frame rate and SNR for the proposedimaging system.

6. Conclusions

In this paper, we have proposed and analyzed a par-allel imaging system using the self-mixing effect in aVCSEL array. The system can be used to accuratelymonitor rapid variations in the surface profiles ofdisplacement, distance, velocity, and liquid flow rate.We demonstrated, for the first time, the feasibilityand potential of the proposed system by measuringthe velocity profiles of a rotating disk and a custombuilt flow channel using a small scale prototype. Po-

Fig. 10. (Color online) Velocity distribution in the flow channel;(a) width of flow channel versus entrance length; (b) simulatedvelocity profile of flow channel; and (c) measured velocity profileof flow channel. The numbers on the contour map in (b) corre-spond to the velocities of the liquid at each contour level with theunits of mm�s. Both (b) and (c) have ten contour levels with a0.42 mm�s change in velocity between neighboring contour lev-els as indicated in (b).


tential issues related to the construction and perfor-mance of a massive scaled up version of the systemhave also been discussed. The proposed imaging sys-tem demonstrated in this paper is envisaged to beuseful in many industrial and biomedical applica-tions, where remote real-time surface profiling, vibro-metry, and velocimetry�flowmetry are required.

The authors thank P. Jacobs (Department of Me-chanical Engineering, The University of Queensland)for advice on the design of the flow channel and K.Lane (School of Information Technology and Electri-cal Engineering, The University of Queensland) forthe construction of the flow channel.

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Parallel self-mixing imaging system based on an array of vertical-cavity surface-emitting lasers

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