S.R.Taplin, A. Gh.Podoleanu, D.J.Webb, D.A.Jackson AB STRACT. Keywords: fibre optic sensors, white light, channeled spectra, ccd, signal processing.

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1 White-light displacement sensor incorporating signal analysis of channeled spectra S.R.Taplin, A. Gh.Podoleanu, D.J.Webb, D.A.Jackson Applied Optics Group, Physics Department, University of Kent, Canterbury, Kent, ENGLAND. CT2 7NR AB STRACT We have developed a technique for distance measurement in which the spectrum from a sensing interferometer is monitored directly with the aid of a diffraction grating and a linear charge-coupled device (CCD) array. The method described is a form of white light interferometry whereby a diffraction grating disperses the composite frequencies which are then examined by a CCD array. This paper presents the experimental results obtained for a fibre Fabry-Pérot version of the sensing interferometer, using a powerful pigtailed super luminescent diode (SLD). Presented also are the processing techniques used to recover the displacement. The techniques are based upon a software package designed to derive the signal frequency of the channeled spectra. The results are compared with those obtained using previously described signal processing methods. Methods of calibration are explored using reference cavities of sub-micron accuracy to allow absolute measurement. Keywords: fibre optic sensors, white light, channeled spectra, ccd, signal processing. 1 INTRODUCTION White light interferometry provides methods for the absolute determination of interferometric measurements requiring no initialisation. Different systems have been devised based on the modulation of the spectrum of a broad band source by a sensing interferometer.17 The spectrum obtained is known as a channeled spectrum and its periodicity is directly proportional to the path imbalance of the sensing interferometer. In principle, despite the large bandwidth of the system, it is possible to deduce the path imbalance with similar accuracies to that of coherent light interferometric methods. In order to achieve precisions of the order of a wavelength, different processing techniques have been proposed. They involve correlation, averaging and fitting procedures as a method of obtaining the sensing information.7'1 The aim of this paper is to present our results obtained by taking the Fast Fourier Transform (FFT) followed by a Gaussian fit of the signal delivered by a linear CCD array used to convert the channeled spectrum into an electrical signal. This yields greater accuracies than previously determined. The arrangement has now been constructed using fibre. 94 ISPIE Vol Fiber Optic and Laser Sensors XII (1994) O /94/$6.OO

2 SLD SOURCE (:EE:;) FIBRE MIRROR ON TRANSLATION STAGE INDEX MATCHING GEL GRATING SIGNAL PROCESSING Figure 1: Experimental arrangement 2 EXPERIMENTAL DETAIL The experimental configuration is depicted in figure 1. A powerful SLD (Superlum-361, 820nm, 3mW, l8nm bandwidth), pigtailed to single-moded fibre, is used as a broad band optical source. A single-mode fibre coupler is used to carry the source to the sensing interferometer (Fabry-Pérot) set up between the cleaved fibre end and a mirror placed on a stepping motor translation stage of micron resolution. The light returned from the sensor is collimated by a lens and directed onto a diffraction grating blazed at 800nm with 1200 lines per mm. The first order diffracted light is then focussed by another lens onto the linear CCD array (Thomson - CSF TH 8711 with TH7931D drive module, 1728 pixels) whose output is read in by a computer (PC). The computer also controls the translation stage via an RS232 interface. 3.1 Data acquisition and preparation 3 SIGNAL PROCESSING The voltage output from the CCD containing the pixel information is stored digitally using an Analogue to Digital converter board in the PC computer triggered by the read-out synchronisation signal of the CCD driver. The signal is over sampled by approximately twice the pixel sample rate since aliasing may occur if the sample rate is close to the pixel frequency introducing low frequency noise which can not be filtered. The pixel frequency is a source of noise and is filtered using a 1MHz low-pass filter. The data prepared for post-processing may be seen in figure 2. The signal may be represented as a multiplication of the Gaussian source profile with the transfer function of the interferometer (eqn. 1) where C is a constant, \ is wavelength, A0 is the peak wavelength of the source, F is a function of the finesse of the Fabry-Pérot and 6 is a function of the wavelength and cavity width. I(,6) = CExp (_(Ao)2) ( (1) SPIE Vol Fiber Optic and Laser Sensors XI! (1994)1 95

3 2 Time (s).3 x 10 Figure 2: Channeled spectrum output from CCD 3.2 Post-processing of data Once the data is taken, the frequency characteristics of the signal are derived by performing a 4096 point FFT (figure 3). Due to the low bandwidth of the frequency components of the channeled spectrum, the peak corresponding to any one frequency of the channeled spectrum for a given cavity width is relatively low in number of samples (maybe ten points) limited by the number of points used in the FFT. In order to minimise the error in determining the centre frequency of the peak, a simplex least mean squares fit is made to the FFT of the data using a Fourier transform of the Gaussian source profile approximated by the theoretical model (figure 4). The frequency at the peak of the fitting envelope is taken and may be used to deduce the cavity width. 3.3 Calibration Calibration is currently performed by plotting a line of best fit through a series of data points indexed to the motor translation stage controller. The procedure is limited by errors introduced by the translation stage. This is acceptable as the device is quoted as having micron resolution over a 1OOtm range. One method of calibration that would give better accuracy would be to linearly interpolate between the frequency of the channeled spectrum yielded by a reference cavity of known spacing to O.lpm, and 0/Am corresponding to 0Hz (or another reference cavity of a different spacing) since the frequency dependence is linear as a function of cavity width. The interpolation would describe a range of frequencies that may be compared with experimentally taken data in order to determine the cavity width. These may be used before the system is installed or optically switched either in the sensing arm of the coupler or the dummy arm. Theoretically, the accuracy would then be limited by the precision of the reference cavity. 96 / SPIE Vol Fiber Optic and Laser Sensors XII (1994)

4 E 6000 Frequency (Hz) Figure 3: FFT of channeled spectrum Frequency (Hz) Figure 4: Gaussian fit to FFT data SPIE Vol Fiber Optic and Laser Sensors Xl! (1994)! 97

5 Figure 5: Frequency dependence of channeled spectrum as a function of cavity width 4 RESULTS The signal processing is applied to cavity widths spanning the entire range of the system. Indexing these frequencies to the motor translation stage controller we obtain figure 5. A line of best fit is performed in order to give a slope value which may be used for conversion between frequency and cavity width. The accuracy over the full l500pm range is seen to be 2.2pm (calculated from the root mean square deviation from the line of best fit) but if we look at the residuals obtained by subtracting the experimental values from the line (figure 6), we see that there appears to be a systematic error when the cavity width is below 250pm due to the translation stage and a random error after 750pm. The accuracy over the range between these distances can be calculated as 0.26pm root mean square deviation from linearity. 5 DISCUSSION Processing method Full range (pm) Accuracy (pm) Accuracy (%) Spectrum Analyser (Taplin et al) Cross-Correlation (Montgomery-Smith et al) Gaussian Fit to FFT (Taplin et al) Table 1: Comparison between spectral analysis techniques Our system compares favourably over previous techniques described. Table 1 shows the accuracies over the full range of previously described systems and our current system. These methods29 do not perform any spectral linearisation to account for the small non-linear effect of the grating equation. As has been shown,4 performing a de-chirp procedure, can compensate in part for the systematic errors encountered. 98 / SPIE Vol Fiber Optic and Laser Sensors XII (1994)

6 4 Cl) 2 E >. l) :O E 0.Q Co Cavity Width (microns) Figure 6: Deviation of data points from linearity 6 CONCLUSIONS The channeled spectrum of a single mode pigtailed SLD driven interferometric system is interrogated by a diffraction grating and a linear CCD array in order to determine the path imbalance in a fibre sensing interferometer. One sample of the CCD signal is processed by an FFT for a given cavity width and a numerical approximation procedure is used to determine the position of the Gaussian peak in the FFT spectrum. Comparison of this technique with the results obtained using time averaging methods shows an immediate improvement of almost triple the accuracy over the full range and an order of magnitude improvement in the most accurate region. Further accuracy may be obtained by performing a spectral linearisation upon the channeled spectrum to take into account the slight chirping effect of the diffraction grating since there is a slight non-linear effect described by the sinusoidal nature of the grating equation. Also, the use of a more accurate translation stage will remove the systematic error. 7 ACKNOWLEDGMENTS Adrian Podoleanu participated in this activity with the support of the Commission of the European Communities within the framework of the TEMPUS scheme. Stephen Taplin acknowledges the support of Shell U.K. and recognises the technical assistance of Mr. Lance Walton and Dr. Mark Calleja (University of Kent). 8 REFERENCES {1J S. Chen, B. T. Meggitt, and A. J. Rogers. Electrically-scanned white light interferometry with enhanced dynamic range. Electronics Letters, 26(20):1663, SPIE Vol Fiber Optic and Laser Sensors Xl! (1994) / 99

7 [2] S. R. Taplin, A. Gh. Podoleanu, D. J. Webb, and D. A. Jackson. Displacement sensor using channeled spectrum dispersed on a linear ccd array. Electronics LeUers, 18(1):78, [3] A. Gh. Podoleanu, S. R. Taplin, D. J. Webb, and D. A. Jackson. White light interferometric spectral analysis for displacement sensing. In Fiber Optic and Laser Sensors XI, page Technical conference 2070, Boston, [4] D. A. Norton. System for absolute measurements by interferometric sensors. In Fiber Opiic and Laser Sensors X, page 371, [5] A. Gh. Podoleanu, S. R. Taplin, D. J. Webb, and D. A. Jackson. Channeled spectrum display using a ccd array as an experimental setup for student lab demonstrations. European journal ofphysics, Accepted for publication. [6] A. Gh. Podoleanu, S. R. Taplin, D. J. Webb, and D. A. Jackson. Channeled spectrum liquid refractometer. Review of Scientific Insirumenis, 64(1O):3028, [7] S. Chen and A. J. Rogers. Electrically scanned optical-fibre young's white-light interferometer. Optics Leflers, 16(1O):761, May [8] 5. Chen, A. W. Palmer, K. T. V. Grattan, and B. T. Meggitt. Digital signal processing techniques for electronically scanned optical fibre white light interferometry. Applied Opiics, 31(28):6003, [9] L. Montgomery-Smith and C. C. Dobson. Absolute displacement measurements using modulation of the spectrum of white light in a michelson interferometer. Applied Opiics, 28(15):3339, [10] C. Blanchet, J. M. Maillard, and M. Lequime. A new optical demodulation board for white light interferometric fibre sensors. In 9th Optical Fibre Sensors Conference, page 171, Firenze, Italy, [11] R. Dändliker, E. Zimmermann, and G. Frosio. Noise resistant signal processing for electronically scanned white light interferometry. In 8th Optical Fibre Sensors Conference, page 53, Monterey, / SPIE Vol Fiber Optic and Laser Sensors XII (1994)