Laser Doppler Vibrometry System using the Synthetic-Heterodyne ...

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CSNDSP08 - 134 - Proceedingsand analysis are presented and in section IV someconclusions are presented.II. LDV SYSTEMA schematic diagram of the LDV system isschematically shown in Fig. 1 and the experimental setupis shown in Fig. 2. The light from a laser diode iscollimated and illuminates a reflection holographic opticalelement (RHOE) and a transmissive HOE. The RHOEreconstructs the beam of light originally scattered from adiffusely reflecting surface, to act as a reference beam.The RHOE efficiency of 50% allows the transmission ofthe remaining incident light. The reflected light from thevibrating object is efficiently transmitted through the twoHOEs and interferes with the reference beam at theCMOS camera. More details on the HOEs can be found in[9]. The detected light signal is then processed by thecamera DSP to retrieve the vibration signal.III.SYNTHETIC-HETERODYNE INTERFEROMETRICDEMODULATION THEORYThe detected photocurrent from a two-beaminterferometer can be written asI() t A[ 1 + V cosθ( t)]= (1)The constant A is proportional to the optical power of thedetected light beams and the mixing efficiency of thedetector and V is the interferometer visibility. θ (t)isthe phase difference between the arms of theinterferometer. A typical plot of (1) is shown in Fig. 3.The sensitivity of the interferometer is maximized whenthe mean phase difference between the detected lightbeams is an odd integer multiple of π/2. When this is thecase the interferometer is said to be operating inquadrature.drive current. The resulting laser frequency modulation isconverted to phase modulation by the non-zero cavity pathdifference of the interferometer. It can then be shown that[10]I( t) A{ 1 + V cos[ C cos( ω0t)+ φ(t)]}= (2)where φ(t)contains the signal of interest and slowenvironmental effects. The most important effect istemperature variations that cause refractive index changesin the interferometer, which leads to the interferometerdrifting in and out of quadrature. If the single-mode laserdiode is modulated with a small-signal sinusoidal currentof amplitude I mthendνC ≈ 2πImτdI(3)dν dI and τ are the differential of the laserwhereoptical frequency with respect to the applied current andthe average time difference between the interferometerarms respectively. Typical values of dν dI are in therange of a 100s of MHz/mA for conventional Fabry-Perotlaser diodes [11] . (2) can be expanded into a series ofsidebands at integer multiples of ω 0that contain thesignal of interest φ (t). In synthetic-heterodynedemodulation, the first two sidebands of (2) are mixedwith in-phase local oscillators at ω0and 2ω0and lowpassfiltered to giveSS12= AVJ1(C)sinφ(t)= AVJ ( C)cosφ(t)2(4)where J1and J2are Bessel functions of the first kind oforder one and two respectively. Taking the timederivatives of S1and S2givesSS34= AVJ1(C)& φ(t)cosφ(t)= −AVJ( C)& φ(t)sinφ(t)2(5)Figure 3. Typical two-beam interferometer transfer function.Multiplying S1by S4and S2by S3givesSS5622( AV ) J1(C)J2( C)& φ(t)sinφ(t22( AV ) J ( C)J ( C)& φ(t)cosφ(t)= −=12)(6)In the synthetic-heterodyne technique a sinusoidalmodulation with frequency ω0and amplitude C isimposed on the interferometer. In this work themodulation is carried out by modulating the laser diodefrequency via sinusoidal amplitude modulation of the laserSubtracting S5from S6givesS o2( AV ) J C)J ( C)dφdt= (7)1 ( 2
Proceedings - 135 - CSNDSP08dφ dt is proportional to the object velocity and isessentially immune to slow environmental fluctuations.Sodepends on the product J1( C)J2(C), which has itsmaximum value of 0.22 when C = 2.37. This conditiondictates the magnitude of the modulation current used fora given laser and cavity length.IV. VIBRATION RETRIEVAL AND ANALYSISIn the experiment, the current driving a 650 nm Fabry-Perot laser diode was sinusoidally modulated at 1 kHz.The modulation amplitude was chosen such that C is inthe range of its optimum value of 2.37 for the choseninterferometer path difference of 10 cm. A block diagramof the synthetic-heterodyne demodulation technique asimplemented on the camera DSP is shown in Fig. 4. Thesignal processing was implemented on the camera usingthe camera development software, which allows thealgorithm to be created in C before compiling anddownloading to the camera DSP. The camera was alsointerfaced to a PC running customised software forsubsequent analysis and display of the retrieved vibrationsignal.ADC limits can be optimised to cover the incoming lightrange for a maximum visibility over the 255 grey digitallevels available.The ADC output is linearised by taking its exponentialbefore being processed using the synthetic-heterodynedemodulation. The sampling rate of the ADC and thevibration spectrum of the object under test are such thataliasing is not present. For test purposes the vibratingobject used was a metal plate mounted on a piezoelectrictransducer (PZT) driven by a signal generator. The camerawas focused on to the object to obtain a sharp imagewhich was monitored on a computer screen. Individualcamera pixels with good amplitude modulation wereFigure 6. Customised PC software showing the demodulationalgorithm settings and the retrieved 100 Hz vibration spectrum at asingle pixel corresponding to a particular point on the vibratingobject. Because of the limited frequency resolution of the signalprocessing the detected frequency is 97.7 Hz.Figure 4.Block diagram of the synthetic-heterodyne demodulationscheme as implemented on the DSP cameraFigure 5. 100 Hz retrieved vibration signal (upper trace) and thedrive signal applied to the plate (lower trace).In the camera the detected light signal from the chosenpixel is amplified by a logarithmic CMOS circuit and thendigitised by the ADC. The amplifier gain parameters andselected and analysed.A typical example of a successfully retrieved syntheticheterodynedemodulated 100 Hz vibration signal is shownin Fig. 5. Previous work we have carried out on syntheticheterodynedemodulation indicates that the noise presentin the detected signal is primarily due to quantizationnoise caused by the ADC. The noise also possiblycontains subharmonics of signal of interest. This occursdue to the non-linear nature of the demodulation algorithmand is especially prevalent when the vibration signal islarge.The power spectrum, obtained using a fast Fouriertransform, of the retrieved vibration signal is shown inFig. 6. Some instability was experienced because the sidemoderejection ratio of the Fabry-Perot laser was onlyapproximately 7 dB. In addition, although the lasertemperature was carefully controlled, the laser was stillprone to mode-hopping. It was not possible to determinethe minimum magnitude of vibration that can be detected.This will be the subject of future work. It will depend onthe laser linewidth, the pixel noise and in particularquantization noise due to the ADC [10].A much improved performance would be expectedfrom a single-wavelength laser such as a distributedfeedback laser although such lasers are difficult to sourcein the 650 nm region. Our current work involvesextending the wavelength range of the HOEs to the 730nm region, where DFB lasers are readily available.
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