Improved phase generated carrier demodulationalgorithm for eliminating light intensitydisturbance and phase modulationamplitude variationYouwan Tong,* Hualin Zeng, Liyan Li, and Yan ZhouOptoelectronics System Laboratory, Institute of Semiconductors, Chinese Academy of Science, Beijing, China*Corresponding author: youwantongsemi.ac.cnReceived 26 June 2012; revised 4 September 2012; accepted 4 September 2012;posted 5 September 2012 (Doc. ID 171123); published 5 October 2012In this paper we propose a novel, improved, phase generated carrier (PGC) demodulation algorithmbased on the PGC-differential-cross-multiplying approach (PGC-DCM). The influence of phase modula-tion amplitude variation and light intensity disturbance (LID) on traditional PGC demodulation algo-rithms is analyzed theoretically and experimentally. An experimental system for remote no-contactmicrovibration measurement is set up to confirm the stability of the improved PGC algorithm withLID. In the experiment, when the LID with a frequency of 50 Hz and the depth of 0.3 is applied, thesignal-to-noise and distortion ratio (SINAD) of the improved PGC algorithm is 19 dB, higher thanthe SINAD of the PGC-DCM algorithm, which is 8.7 dB. 2012 Optical Society of AmericaOCIS codes: 060.2370, 120.3180, 120.5050.1. IntroductionRemote no-contact microvibration measurement isanimportantsubjectinscientificresearchandindus-trial manufacture. Using a laser interferometer isone of the most effective and accurate techniques1. To recover the phase-shift signal from the inter-ferometer, several phase demodulation algorithmsare available now. Among them, the phase generatedcarrier (PGC) is the most widely used for modulatingand demodulating because it has many advantagessuch as a wide dynamic range, high sensitivity,and good linearity.In the PGC demodulation scheme, a high-frequency sinusoidally modulated optical carrier isapplied to the reference beam to up-convert the de-sired vibration signal shift onto its sidebands. A pairof quadrature components are acquired by detectingone oddandone evenharmonic ofthesignalfrom theinterferometer to overcome the bias-induced signalfading 2. There have been some traditional ways torecover the vibration-induced phase shift from thetwo quadrature components such as the differential-cross-multiplying approach (PGC-DCM) and arctan-gent approach (PGC-arctangent).The linearity of the demodulation algorithm andthe ability of eliminating the light-intensity distur-bance are of great importance. The demodulationresult of the PGC-DCM approach is related to thelight intensity 35, and the linearity of the PGC-arctangent approach depends on the phase modula-tion amplitude. 58 Consequently, the method thatis not influenced by light intensity and phase modu-lation amplitude is still needed.2. Principles and analysisA. PrinciplesFigure 1 shows the schematic of the improved demo-dulation algorithm. The phase carrier can be appliedto the reference beam by an acoustic modulator or a1559-128X/12/296962-06$15.00/0 2012 Optical Society of America6962 APPLIED OPTICS / Vol. 51, No. 29 / 10 October 2012piezoelectric transducer (PZT). The interferencesignal received by the photodiode is given byI.0133t.0134.0136A .0135 B cos.0137C cos.01330t.0134.0135.0133t.0134.0138; (1)where A and B are the dc and ac components respec-tively, A and B depend on the light intensity of thesignal beam and the reference beam. C is the PGCphase modulation amplitude, 0is the PGC modula-tion frequency, and .0133t.0134 is the desired phase-shiftsignal which is related with the vibration of the ob-ject we are concerned about and the low-frequencyenvironmental noise mainly introduced by the varia-tion of the refractive index of air. So we assume thatthe vibration signal is a single-frequency signal and.0133t.0134 can be written as follows:.0133t.0134.0136D cos.0133st.0134.0135.0133t.0134; .01332.0134whereDistheamplitudeofthevibrationsignal,sisthe frequency of the vibration, and .0133t.0134 is the lowfrequency environmental noise.Firstly, the interference signal is separately multi-plied with the fundamental carrier, the second-harmonic carrier, and the third-harmonic carrier.The carriers have already been synchronized withthe interference signal 9. After the high-frequencycomponents are filtered out by three low-pass filters,and L1.0133t.0134, L2.0133t.0134, and L3.0133t.0134 are obtained:L1.0133t.0134.0136BJ1.0133C.0134sin .0133t.0134; (3)L2.0133t.0134.0136BJ2.0133C.0134cos .0133t.0134; (4)L3.0133t.0134.0136BJ3.0133C.0134sin .0133t.0134; .01335.0134where J1.0133C.0134, J2.0133C.0134, and J3.0133C.0134 are respectively thefirst-order, second-order, and the third-order Besselfunctions with C. Subtracting L3.0133t.0134 and L1.0133t.0134 yieldsE.0133t.0134.0136L3.0133t.0134L1.0133t.0134.0136 BJ3.0133C.0134sin .0133t.0134.0135BJ1.0133C.0134sin .0133t.0134.0136 B.0137J3.0133C.0134.0135J1.0133C.0134.0138sin .0133t.0134: (6)According to the recurr