The advent of two-dimensional arrays of Vertical-Cavity Surface-Emitting Lasers (VCSELs) opened a range of potential sensing applications for nanotechnology and life-sciences. With each laser independently addressable, there is scope for the development of high-resolution full-field imaging systems with electronic scanning. We report on the first implementation of a self-mixing imaging system with parallel readout based on a monolithic VCSEL array. A self-mixing Doppler signal was acquired from the variation in VCSEL junction voltage rather than from a conventional variation in laser power, thus markedly reducing the system complexity. The sensor was validated by imaging the velocity distribution on the surface of a rotating disc. The results obtained demonstrate that monolithic arrays of Vertical-Cavity lasers present a powerful tool for the advancement of self-mixing sensors into parallel imaging paradigms and provide a stepping stone to the implementation of a full-field self-mixing sensor systems.
© 2009 Optical Society of America
Self-mixing interferometry is a sensing technique used to detect small displacements, velocity, change in the refractive index of materials, and flow [1, 2, 3]. The self-mixing phenomenon occurs when the laser beam is partially reflected from an external target and injected back into the laser cavity. The reflected light interferes or ‘mixes’ with the light inside the laser cavity and produces variations to the threshold gain, emitted power, lasing spectrum and the laser junction voltage. The reflected light can be frequency shifted, by means of Doppler effect, before being mixed with the original laser emission. The resulting output power variations are usually monitored by the photodiode integrated within the laser package. This phenomenon allows the laser to be used as an interferometric sensor incorporating the light source and the interferometer in one device thus significantly reducing the cost and the complexity of the sensing system. The coherent detection nature of this sensing scheme inherently provides very high sensitivity, frequently at the quantum noise limit.
Self-mixing sensors based on semiconductor lasers have long been regarded as a low cost, compact and robust solution for velocity  and displacement measurement [4, 5]. The self-mixing systems reported so far in the literature are essentially single beam systems where spatial variations in a measured quantity are obtained by mechanically scanning the laser beam over the area to be imaged in a raster fashion. The raster scanning technique has one serious limitation: the time required to complete a full scan. This effectively limits the applicability of the technique to sensing stationary phenomena. Studies on hybrid parallel sensing systems are scarce [6, 7] and to the best of the authors’ knowledge, there has been no report on multichannel velocity measurements using a monolithic laser array.
Vertical-Cavity Surface-Emitting Lasers (VCSELs) have become commercially available in the last ten years. Surface-normal emission of these devices allows the VCSELs to be monolithically integrated into densely packed matrix-addressable 2D arrays. Mass production of VCSELs for optical communications resulted in significant cost reductions - VCSELs are nowadays arguably the most affordable lasers on the market. This makes them a perfect choice for array-based sensors to detect spatial distribution of displacement, velocity and a range of related quantities including the change in the refractive index of biological tissue or microvascular perfusion.
This article reports, for the first time to our knowledge, a full-field self-mixing interferometer with monolithic VCSEL array. It thereby proposes a sensing system incorporating a simultaneous readout from multiple sensors by using a monolithic VCSEL array as the sensor and the emitter array. A Self mixing signal was acquired by detecting the change in VCSEL junction voltage caused by the light scattered from the target and injected back into the laser, rather than using the signal from an associated photodetector array . Removing the need for the photodetector array integrated with the VCSEL array significantly reduces the complexity and the cost of the system.
This article is organised as follows: Sec. 2 provides a brief overview of the self-mixing effect in VCSELs and application to velocity measurement. Section 3 describes in detail the experimental setup used to validate the sensor, followed by the results obtained. Finally, conclusions are drawn in Sec. 4 where advantages and limitations of the technique in characterising velocity distributions are discussed.
To demonstrate the performance of the system we used a target with a known distribution of velocity on its surface — a rotating disc. Light back scattered from the target moving with velocity ν⃗ experiences a Doppler frequency shift fD given by 
where k⃗inc and k⃗sc are the wave vectors of the incident and scattered light respectively, and λ is wavelength of light in the medium surrounding the target. In the self-mixing interferometer configuration used here, the scattered signal is collected by the same lens used to focus the beam on the target and (1) becomes
where θ is the angle between the axis of the incident beam and the velocity vector. For light reflected from a rough moving surface the Doppler signal is amplitude modulated by a random speckle effect, since the illuminated part of the target is changing continuously.
The result of coherent mixing within the VCSEL resonant cavity between the lasing field and the Doppler-shifted light backscattered by a moving target is a fluctuation of photon density and consequently the output power. Doppler frequency is usually obtained by observing the laser power spectrum obtained from the time domain signal through the fast Fourier transform (FFT). In this study, fluctuations in VCSEL terminal voltage were used as the source of the self-mixing signal instead of the usual current signal from the external photodiode.
The model commonly used to describe the dynamics of the self mixing effect is based on the Lang and Kobayashi equations, a set of rate equations with time-delayed feedback terms [10, 11] linking the carrier density with the photon density. If the photon density in the laser cavity is disturbed by the injection of the back-scattered (and possibly Doppler shifted light) its forced variations will cause corresponding fluctuations in the carrier density. The solution to Lang and Kobayashi system links the optical feedback to the variation in the carrier density, which in turn, translates to the variation in the laser heterojunction voltage through several mechanisms, as suggested by Mitsuhashi et al. . The terminal voltage in a multiple quantum well (MQW) laser close to threshold can be interpreted as the difference in the Fermi levels in the separate confinement heterostructure regions between which the MQW structure is located . The variation in the junction voltage is mainly caused by the reduction in the quasi-Fermi level separation due to the carrier depletion by stimulated emission in the quantum well region. Simplified expressions linking the carrier density to the junction voltage proposed so far suggest a logarithmic relationship between the junction voltage and the carrier density [14, 12, 15]. However, instead of the total junction voltage (in the case of a GaAs VCSEL close to 2.2 V) we observe its fluctuations (in the μV range) at the self-mixing signal frequency. In small signal approximation, the variation in the VCSEL terminal voltage is a linear function of the carrier density, and therefore can be used as a source of the self-mixing signal instead of the usual photodetector current obtained form the monitoring photodetector. This approach becomes increasingly attractive when the number of lasers used in a parallel sensing system is large. In such cases, integration and alignment between the photodetector array and the laser array becomes more complicated and the alternative voltage sensing approach significantly reduces the complexity of the optoelectronic system.
3. Experimental setup and results
To investigate the performance of the proposed architecture we designed a system schematically shown in Fig. 1, based on a commercial 1×12 monolithic VCSEL array (EMCORE Corporation, Gigalase 8185-1100 ). The EMCORE VCSELs are AlGaAs planar, top-surface emitting devices with 15 μm circular apertures in the top mirror contact, and have a pitch of 250 μm. This particular VCSEL array can operate in both single mode and multimode regimes, depending on the laser driving current. The average threshold current of the VCSELs is about 6 mA and each laser has a peak wavelength at around 850 nm. A single Thorlabs C240 as-pheric lens with a clear aperture of 8 mm and NA of 0.5 was employed to image all 12 laser beams onto a rotating disc. The aluminium disc, 10 cm in diameter, was sandblasted to provide a moving diffuse target. The disc was driven by a DC servo motor with a 43:1 gear reduction controlled by an Elmo Whistle motor controller. The stability of the disc’s angular velocity for the duration of the experiments was better than 1%, as established by monitoring the frequency of the motor’s rotary encoder. A custom built 12-channel laser driver was used to individually bias each laser to 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 accoupled, single stage, low noise preamplifier with gain G = 100 located in the proximity of the laser array. 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 applied to bring the signal to a level suitable for processing by a 16-bit Data Acquisition card and the total bandwidth of the 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 an effective measuring bandwidth of 400 kHz. Even though the measuring bandwidth is smaller than the amplifier bandwidth, aliasing was not a problem as there is not much signal above 200 kHz. The acquisition time for each laser channel was 41 ms. The Fast Fourier Transform (FFT) of the time domain signal was performed in the LabVIEW programming environment to obtain the self-mixing signal spectrum and 8 consecutive spectra were averaged before extracting the Doppler frequency. Considering that the maximum Doppler frequency in this experiment was expected at fD = 27 kHz, the bandwidth of the system was more than adequate for the task.
The target was located 26.7 cm away from the laser array in-order to obtain a series of beam spots with a pitch of 0.8 cm on the target. The laser array was oriented vertically (in the y-direction), with the VCSEL designated LD1 located at the bottom of the array. After imaging the array on the disc, LD1 forms the highest spot due to the image inversion characteristic of the single element lens used. The vertical positioning of the array was set to locate five beam spots on each half of the disc surface with the central beam (LD6) located on the centre of the disc. Figure 2(a) shows the self-mixing signal obtained from one of the VCSELs. The multiple harmonics in the Doppler spectrum of the self-mixing signal indicate strong feedback. Based on the measured reflectivity of the target and the geometry used we estimated the value for the feedback parameter C ≈ 6, which is commensurate with the signal shape obtained. We determined the optimal operating condition for each of the VCSELs by maximising the signal to noise ratio while the lasers are positioned along the vertical axis of the disc. This was obtained by fitting, in real time, the fundamental spectral feature of the signal to a combination of the Gaussian profile and the parabolic noise floor and by varying the driving current to maximise the Signal-to-noise ratio (SNR) [see Fig. 2(a)]. SNR obtained for all VCSELs was between 25 and 30 dB over the range of measured Doppler frequencies (approx. 5 – 27 kHz). To estimate the accuracy of the system we first measured the velocity on the vertical diameter of the disc. The magnitude of the velocity ν at a distance r from the centre of the disc is given by
where ω is the angular velocity of the disc. This provides a linear distribution of velocity as a function of distance from the centre of the disc, a perfect test bed to quantify the quality of the system. Clearly, substitution of (3) into (2), suggests a linear distribution of fD as a function of distance from the centre of the disc.
Figure 3(a) compares the measured and calculated values for the velocity distribution on the vertical diameter of the disc. A photograph of the setup with the VCSEL beams on the disk surface is shown in Fig. 3(b). In order to test the linearity of the system, two sets of signals were acquired; for the second measurement the VCSEL array was translated vertically up by 12 μm, (half the array pitch) effectively providing interlaced spatial resolution of 4 mm. The results show that the measured distribution agrees closely to the calculated velocity profile of the rotating disc with error below 3 % for all pixels. Most importantly, the even frequency spacing between the adjacent channels suggests that there were no noticeable alignment problems even in the interlaced measurement mode. When compared with the earlier raster-scan and hybrid-integrated parallel systems , this implementation shows the superiority of the lithographic alignment of VCSELs in a monolithic array. Most of the problems encountered with using the hybrid array were related to relative misalignment between individual VCSELs comprising the array; this problem is inherently absent in case of the monolithic array and will enable the realisation of full field imaging systems based on 2D VCSEL arrays.
To investigate the spatial resolution and imaging characteristics of the system the spatial distribution of velocity was mapped across the surface of the disc. We utilised an interlaced broom sweep with mechanical scanning in a horizontal direction. This provided a 47 × 23 square grid of pixels on the rotating disc from which an image was generated. Unlike raster scan systems, vertical mechanical scanning was replaced by parallel acquisition. It should be noted that each laser beam corresponds to one spatial pixel in the target plane.
In this study we found no evidence of optical crosstalk between the channels. While some of the self-mixing papers dismiss the possibility of crosstalk between the channels due to the coherent nature of the self-mixing scheme [17, 18] there is evidence that injection locking in VCSELs can occur even for injection levels as low as 10-3 of the slave VCSEL power [19, 20]. The frequency detuning under which locking has been observed is limited and depends on the injected signal level. Locking typically happens only for a small range of phase differences and requires mode matching conditions[22, 23]. Further study is required to make any predictions related to the immunity of this sensing scheme to inter-channel crosstalk and the feedback levels at which it may occur. In self-mixing laser-Doppler systems the direction of the scattered beam is colinear with the incident beam, therefore, according to Eq.(1), the quantity measured is the projection of the velocity vector on the laser beam direction. Figure 4(a) shows the calculated contour plot of the velocity distribution on the disc — a set of perfect concentric circles of equal velocity. If we had used an optical system with all the laser beams parallel to each other and horizontal, the Doppler signal acquired would have resulted in a distribution as shown in Fig.4(b) - parallel horizontal bands. When changing the pitch of array image in the measurement plane, two design choices are available, either to maintain the individual gaussian beams parallel to each other, or to use an imaging system with the required magnification in which the individual beams diverge from each other. Both designs allow for simple recovery of the signal. In this study we opted for the second system to demonstrate that even with an extremely simple and compact lens, and using a magnification factor of M = 35 it was possible to image a 10 cm diameter disc on a 3 mm long laser array with virtually no distortion. This claim was substantiated by simulating the square distribution grid projected onto the disc using a Code V simulation package (Optical Research Associates). The correction for the fact that each beam arrives at the target at a different angle αi is quite trivial and is contained in the dot-product of Eq. (1). When expanded for the geometry used here, the velocity component detected by the laser beam with coordinates (x,y) on the target is given by
where θ is the tilt angle of the disc [see Fig. 2(b)], α is the angle the individual beam makes with the optic axes of the system [see Fig. 2(c)], and x and y are the horizonal and vertical axes respectively. The calculated distribution of the velocity component parallel to the laser beam incident on the target is shown in Fig. 4(c). Agreement with the measured distribution shown in Fig. 4(d) is excellent. Along the horizontal diameter of the circle, the velocity vector has only the vertical (νy) component, and the detected signal should be zero (projection of the velocity vector on the laser beam is zero). Apart from this line, the recovery of the velocity distribution is simple; the distributions recovered from the calculated and experimental values are shown in Fig. 4(e) and (f) respectively. The agreement is strikingly good — both images represent a series of concentric circles. This demonstrates clearly that even with the ultimately simple and compact optical system, comprised of a single aspheric lens, less than three times the size of the laser array used, we could produce a virtually distortion free velocity distribution. Image distortion created by the lens system can be further corrected simply by pre-calculating the positions of the laser beams in the target plane in a lens design tool and by storing the beam positions in a lookup table. This would enable the use of a wide angle imaging lens and provide potentially a very short working distance. The said correction was implemented for the system used here but the improvement in the shape of the equi-velocity circles was not visually noticeable. The quality of the laser alignment on a monolithic array is evident from the perfect circular shape of the equal-velocity lines. All the problems usually encountered with raster scanning and hybrid arrays are completely absent in this implementation. This suggests that the lithographic alignment of lasers constituting the monolithic array is essential for expanding this concept to massively parallel Doppler imaging systems based on two-dimensional VCSEL arrays.
In this article we proposed a full-field self-mixing sensor system for simultaneous readout from a plurality of lasers by using an array of VCSELs as both the light source array and the sensor array. The light emitted from one laser in the matrix illuminates one spot on the target, and is reflected back into the same laser to create the self-mixing signal. The s elf mixing signal is detected by sensing the change in VCSEL junction voltage caused by the light dynamically scattered from the target and injected back into the laser, rather than using the signal from a photodetector array. Removing the need for the photodetector array hybrid integrated with the VCSEL array significantly reduces the complexity and the cost of the proposed system. This coherent detection scheme provides not only for the high sensitivity and dynamic range usually associated with of the heterodyne detection, but also efficiently suppresses the optical crosstalk from the neighbouring lasers. In comparison with the spot-raster laser, the acquisition time is significantly shortened — the mechanical scanning process is replaced by concurrent acquisition at all channels/pixels. We have implemented a small scale prototype of the system, based on the 1×12 VCSEL array and validated the performance of the system by imaging the distribution of velocity on a rotating target. The results obtained resemble closely the calculated velocity distribution with error below 3% for the entire imaged surface. Results obtained suggest that the image quality improvement due to lithographic alignment of lasers constituting the monolithic array is essential for expanding this concept to massively parallel Doppler imaging systems based on two-dimensional VCSEL arrays.
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