Multiplexed demodulation of quasi-static measurands without a receiving interferometer C. M c G a r r i t y and D.A. Jackson Indexing ternis: Optical scnsocr, Fibre optic sensors The classical technique of dual wavelength interferometry is used to detennine the absolute OPD of very short cavities using a paramel ric plot of the relative interferometric intensifies. A network of eight :jensors is demonstrated with phase resolution of 1Smratl corresponding to 0.2nm with an unambiguous range of 114pm Measuring the absolute optical path difference (OPD) of an interferometric sensor is a key goal of optical fibre sensing. Early work used dual-wavelength interferometry with pseudo-heterodyne processing for passive sensors. This requires the sensor to have a path imbalance of -1 cm [I]. Problems were experienced with laser amplitude modulation and high tcmpcrature cross-sensitivity caused by the path imbalance. White light interferometry (WLI) has received attention as it overcomes this difficulty and produces subnanometre resolution [2]. WLI reduces wavelength stability requirements but does require a stable receiving interferometer or a stable reference cavity. We present an application of the classical technique of dual-wavelength interferometry for measuring very short cavities. \Ne demonstrate that one representation of the data allows demodulation of quasi-static measurands from zero OPD to the effective wavelength using the relative intensity of the two interferograms. The short cavity length reduces temperature sensitivity. This technique does not require a receiving interferometer, but does require the sensor to be perturbed, and it provides comparable resolution and range to conventional dual-wavelength WLI. 0 0 . 2 0 . L 0.6 0.8 1 12 1.L 1.6 intensity of second interferograrn,a.u 18 2 1136311 points are points of ambiguity. An extension of this concept to three dimensions can eliminate these crossing points. Using a third wavelength to produce a 3-D LF, crossing points need not occur as the 2-D data occupies a volume of space. The third wavelength only provides this third degree of freedom. The concept was experimentally verified using a Mach-Zehnder (MZ) combined with simple electronics to distinguish the interferograms. A computer sampled the resulty. To distinguish the interferograms the lasers were amplitude modulated at 5 and 7kHz. The output was mixed with these frequencies and lowpass filtered to produce the interferograms. The resoltuioii of the A/D is 12bits. The least significant bit (LSB) accuracy is 1 part in 4096. Samples therefore have a resolution of 0.2nm or 1.5mrad at 827 nin. Sufficient optical power and careful electronic design ensure the noise is <0.5 LSB. Fig. 2 Network multiplexing eight interjhrometer sensors 7 c x 5:opped: 7367 Acquisitions ; 1- I Fig. 1 Lissujous representing intcrfefcronwter OPD using two wavelengths Two laser sources with specific wavelength differences illuminate the sensor. The separate interferograms can be combined in a parametric plot to generate a Lissajous figure (LF) as shown in Fig. 1. The X axis is the intensity of the smaller wavelength and the Y axis is the intensity of the larger wavelength. Displaying the interferograms as a LF represents their relative phase in two dimensions. The trace represents the OPD from zero to the effective wavelength. Zero OPD occurs at the top right hand corner. The solid tract: begins there and extends to half of the effective wavelength. The dotted trace represents the OPD from this point to the full effective wavelength. Although not every point in this figure is unique, any finite length of the trace is unique. Performance is optiinised by making a careful choice of wavelengths. Fig. 1 was produced for demonstration using wavelengths of 800 and 870nm. Clearly any finite part of the trace is unique rather than any individual point, so the technique requires the phase to be subject to constant ch,ange. Most single measurements of the intensities provide the relative phase and the absolute OPD, but the crossing ELECTRONICS LETTERS 20th June 1996 Vol. 32 No. 13 1225 Multiplexing using this technique is straight forward. The network illustrated in Fig. 2 uses a combination of frequency and time division multiplexing successfully demonstrated with interferometric sensors 131. Acousto-optic modulators are used as both switches and isolators. Simultaneous pulses of light from each pair of lasers are launched into the network. The 50m length of fibre delays the signal from the second sensor of each pair by 0 . 5 p . The detector receives signals from two pairs separated in the frequency domain. Fig. 3a shows a sample of the signal. The ‘dead space’ in the timing is deliberate as the AOM is on at this time. The AOM is off when pulses are returning. Fig. 3b indicates the time demultiplexing of one pulse. This pulse contains frequency multiplexed signals from two sensors. The sampling frequency is filtered out and the signal is processed using the scheme described above. Modulation frequencies of 3 , 5 , 7 and 9kHz were applied to the four lasers. The wavelengths of the laser pairs were 827nm. 833nm (effective wavelength 1 1 4 . 8 ~ and ) 823nm, 8301x11 (effective wavelength 97.58pi).Eight low finesse Fabry-Perot sensors were fully demodulated for quasi-static signals up to -100Hz. Seven of these sensors consisted of a cleaved fibre end and a mirror. One sensor (No.5) consisted of a GRIN lens partially coated with aluminium and a mirror. lised. A reference sensor would provide a fixed point on the LF against which to check wavelength calibration. In conclusion we have reported the use of a novel representation of the classical dual-wavelength technique which allows the unambiguous demodulation of quasi-static measurands for very short cavities with comparable resolution to WLI, but without the requirement of a stabilised receiving interferometer. 0 IEE 1996 I M a y I996 Electroiiics Lerrers Online No: I9960771 C. McGarrity and D.A. Jackson (Applied Optics Gvoup, Physics Luhorcilorj., Ciiiwrsilj of Kent, Cunterbury, Kent CT2 7 N R , United Kingdoin) References KERSEY. A.D., CORKE, M., and JONES, J.D.c.: ’Pseudoheterodyne detection scheme for optical interferometers’, Elerrion. Lerr., 1982. 18, (25), pp. 1081-1083 2 PATTEN. R A : ’Michelson interferometer as a remote gauge’, Appl. Opr., 1971. 10. (12), pp. 2717-2721 3 McGARRITY. C., CHL. B.C.B., and JACKSON, D.A.: ‘Multiplexing Of Michclson intcrfcromctcr scnsors in a matrix array topology’, Appl. Opt., 1995. 34. (7); pp. 1262-1268 4 DAUDRIDGE. . A . TVETEN. A.B , and GIALLORENZI, T : ‘Homodyne demodulation scheme for fiber optic sensors using phase generated carrier‘. IEEE Trciris. Microii,. Theory Tech., 1982, MTT-30, (IO), pp. 1635-1641 1 J.ACKSOX D A.. Simple technique for apodising chirped and unchirped fibre Bragg gratings R. Kashyap, A. Swanton and D.J. Armes Fig. 4 Results j i k m sensor No.5 ond sensor No.1 U No.5. b No.] Electronic noise from the time demultiplexing contributes to the total noise. The noise level approaches 0.5 LSB. Fig. 4 shows two partial LFs of the experimental results from sensor No.5 (left hand side) and sensor No.1. Three samples are displayed. The small traces in each plot are two separate samples of a signal of IOOmrad at IOOHz applied to the mirror. The long traces are samples of several minutes of natural drift. The traces represent drifts of 915.6nin (No.5) and 909.2nm (No.1). The software controlling data acquisition easily determines the size of periodic signals and their mean OPD, or the absolute OPD of single samples. The visibility of sensor No.5 is constant over the full range. The resolution of this sensor is constant and is the same as the MZ (0.2nm). Divergence from the bare fibre means the visibility is maximised about the central third of the range. About this OPD the conversion resolution is < 0.5 LSB. The drop in visibility near zero OPD and near 1 0 0 p causes the noise to increase to 0.68 LSB, which halves the resolution. The simple scheme used to separate the interferograms is limited to short cavities to ensure no phase modulation occurs. The mixing and filtering process produces the same output as the phase generated carrier technique [4] for larger OPDs. This problem can be minimised by ensuring the modulation is minimal and optimising the mixing electronics. Alternatively it can be eliminated using a diffraction grating to separate the interferograms. The technique requires wavelength stability and amplitude stability. Small changes can be compensated in the processing if detected. An adjustment is required if the power of one laser changes. The LF then has a different aspect ratio. The spacing between traces is also scaled so the relative phase is still unambiguous. The range is maintained but the resolution is compromised. Wavelength drift of either laser changes the position of the trace. This effects the range but not the resolution. The first half of the LF is always unique. Careful choice of the wavelengths ensures a large ‘window’ to maintain the uniqueness of the second half. At least one of the lasers of each pair should be temperature stabi- 1226 For the first time, a simple technique is reported for apodising chirped or unchirped gratings of arbitrary length. Also reported for the first time is the fabrication and measurement of unapodised and apodised l O O m m long, step-chirped fibre gratings with a dispersion parameter of -1.6ns-n1n-’ and a bandwidth of up to 0.75nm. It is shown that long chirped gratings may be fabricated at predetermined wavelengths in standard telecommunications fibre for dispersion compensation. Introduction: The step chirped grating (SCG) has been demonstrated to be highly effective for producing fibre Brdgg gratings of arbitrary dispersion and reflection profile [I]. In particular, the Bragg wavelength and chirp can be pre-programmed into the phase mask for easy replication into a fibre by either scanning [l, 21. or by the use of an interferometer. Apodisation, i.e. the gradual change in the refractive index modulation, of chirped fibre gratings is necessary when the coherence length of a signal determined by the bandwidth of the chirp is a few per-cent of the length of the chirped gating. Thus, apodisdtion has been implemented by several workers [3, 41, but these methods use either active variable control during the writing of the grating [4], or some post-processing to tailor the amplitude of the refractive index profile of the grating along its length. These methods, while producing good results, need careful calibration of the response of the fibre [3], or active control of the amount of dither applied to the fibre as a function of scan-position [4]. This Letter demonstrates an extremely simple method of apodisation of fibre gratings of arbitrary chirp and profile, usable for all types of gratings, and it is shown that step-chirped phase masks of l00mm length with 0.75nm bandwidth may be written with a constant dispersion parameter. Phase inaslcs: Previously, the only report of the SCG has been for low dispersion over a broad bandwidth 151. These gratings have been shown to completely compensate for dispersion of ultra-high bit-rate transmission (100Gbit/s) over -4km 161. However, narrow band, highly dispersive SCGs have not so far been reported. In the ELECTRONICS LETTERS 20th June 1996 Vol. 32 No. 13
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