Reduction of semiconductor laser diode phase and amplitudenoise in interferometric fiber optic sensors
T. P. Newson, F. Farahi, J. D. C. Jones, and D. A. Jackson
An optical configuration employing two conventional Michelson interferometers and a fiber Fabry-Perotinterferometer connected in parallel is used to demonstrate the principle of common mode rejection of boththe amplitude and frequency noise of a semiconductor laser. Common mode noise rejection is maximizedwhen the outputs of the two interferometers with matched path imbalance, fringe visibility and amplitude aredifferentially combined. One interferometer is used as a reference, and the other as a sensing interferometer.The fiber Fabry-Perot interferometer is used as the sensing interferometer and is demonstrated as aminiature acoustic sensing element.
1. Introduction
Semiconductor laser diodes offer considerable ad-vantages over gas lasers for illuminating fiber opticinterferometric sensors. Compared to gas lasers theyare much smaller, more robust and cheaper. In addi-tion they also have the major advantage that theirfrequency is dependent on the injection current' andtherefore electronic processing systems can be basedon frequency modulation.
To process an interferometric signal, it is necessaryto be able to control the phase between the referencearm and signal arm of the interferometer. This can beachieved either by varying the optical path length ofeither arm, e.g., by stretching the fiber, or by varyingthe frequency of the source.
For remote point sensing an all fiber Fabry-Perotinterferometer has been demonstrated.2'3 To fullyutilize the point sensing capability of such a sensor, it isgenerally inappropriate to incorporate a fiber stretch-er owing to the associated increase in the size of thesensing element and the requirement for an activeelement in the measurement region. Instead it is moreadvantageous to rely on frequency modulation of thelaser source for the signal processing. This generallynecessitates the use of a semiconductor laser.
When this work was done all the authors were with University ofKent, Physics Laboratory, Canterbury, Kent CT2 7NR, U.K.; J. D.C. Jones is now with Heriot-Watt University, Edinburgh, U.K.
An alternative technique based on white light inter-ferometry has been demonstrated which permits theuse of a passive sensing element and therefore truepoint sensing capability while using a fixed frequencysource.4 The output of one sensing interferometer isused to illuminate a second interferometer of matchedpath imbalance. Processing is performed by control-ling a PZT mounted mirror in the second interferome-ter so that the overall path imbalance of the two inter-ferometers is held at the first quadrature point.5 Thepresent major limitation of white light interferometryis the difficulty of coupling sufficient power into asingle mode fiber and therefore the signal to noise ratiois at present limited by photodetector noise.
Using semiconductor laser diodes provides us withthe opportunity of dispensing with active elementsrequired for varying the optical path length and per-mits the extremely small remote sensors to be manu-factured. However, semiconductor laser diodes ex-hibit both frequency and amplitude fluctuationswhich both contribute to the overall noise in the inte-ferometric sensor. In conjunction with an unbalancedinterferometer, frequency noise is transduced to phasenoise.
The principal method for reducing either amplitudeor frequency fluctuation noise is to stabilize the laser.68
In the case of amplitude noise a signal derived from aphotodetector monitoring the optical power is fed backto the laser injection current so that the optical poweris maintained constant. As an alternative to currentmodulation, the temperature of the laser can be con-trolled.9 To stabilize the frequency of the laser asecond cavity (for example, a Fabry-Perot etalon) isused to obtain an interferometric output dependent onthe fluctuation of the mean lasing frequency. This
signal is then used to control the injection current sothat frequency fluctuations are minimized. Althougheither the intensity or frequency of the laser can becontrolled by varying either the injection current ortemperature of the laser, these are not independentvariables and in practice it proves difficult to stabilizeboth the intensity and frequency of the laser simulta-neously. Generally the frequency of the laser is stabi-lized by locking to an external cavity and the ampli-tude noise is compensated in the receiver by using asignal from a photodetector measuring only the ampli-tude of the source.
This paper describes a novel configuration in whichboth the amplitude and phase noise can be compensat-ed by matching the measuring interferometer to a ref-erence interferometer. The signal from each interfer-ometer is then simultaneously affected by both phaseand amplitude noise and the differential intensity out-put of the two interferometers demonstrates a signifi-cant improvement in the signal-to-noise ratio. Theadvantages and disadvantages of this method com-pared to frequency locking of the laser are discussed.
11. Theory
The irradiance of the output from a two beam inter-ferometer illuminated by a noise-free source can bewritten as
I = A 1 [1 + k cos, 1],
where I, is the phase difference between the interfer-ometer arms, k is the visibility, and A1 is a constant.It is instructive to consider the situation in which theinterferometer is nominally held at quadrature, butwith a time dependent phase signal, 01(t), superim-posed so that i, = q1 (t) + 2m7r - (r/2), where m is aninteger. We may hence write
I = A 1 [1 + k sinqkl(t)]. (1)
In the presence of both amplitude and frequency noiseof the semiconductor laser source
A2) and visibility (k1 and k2) of each interferometer aremade equal, we can then subtract the photodetectoroutputs of the signal and reference interferometersgiving
I,-I, = Ak[1 + A(t)]
X sin[01(t) + Ao(t)] - sin[AO(t)]), (6)
where
A01(t) = A02 (t) = A04),
Al = A2 = A.
(7)
(8)
Since Ak(t) is generally <<1 and we are interested inmethods to detect signal levels of a similar magnitudeto the phase noise
sin(0 1(t) + Ap(t)) = ,l(t) + Atk(t),
sin[A^ (t)] = Ao(t).
(9)
(10)
Hence Eq. (6) becomes 1 1 -12 = Ak(1 + AA(t))0 1 (t) sothat the signal-to-noise ratio arising from amplitudenoise is simply 1/AA(t), and is independent of themagnitude of the signal. Because AA(t) is small, wemay approximate the result by
I - 2 = Akol(t). (11)
That is the phase and amplitude noise can both besubtracted from a signal interferometer by using amatched reference interferometer.
This approximation does not simply neglect ampli-tude noise; instead the product of amplitude noise andthe signal i.e. A(t)0 1(t) in comparison to the signal01(t) is neglected. In view of the fact that we areprincipally interested in detecting small signals this isnot a restricting assumption. Amplitude noise is nor-mally a problem with a single interferometer becauseof the D.C. term in the transfer function of a two beaminterferometer. Using our subtraction technique thisterm is cancelled as well as the phase noise arising fromlaser frequency jitter.
where AA(t) expresses the amplitude fluctuations andA&01(t) is the phase noise arising from the frequencyfluctuations of the laser which is given by
2vrln iv(t)A01(t) = cn ' (3)
where Av(t) is the fluctuation in laser frequency, 11 isthe path imbalance of the interferometer, n the re-fractive index, and c is the speed of light in vacuo.
Similarly for the reference interferometer
I2 = A1 + AA(t)]{1 + k2 sin[A0 2(t)]j, (4)
where A0 2(t) is given by
A()27rl2n22\v(t)
Provided each interferometer is held at quadrature,the path imbalance (n111 and n212), amplitude (A1 and
111. Experimental
The optical configuration used in these experimentsis shown in Fig. 1. It consists of three interferometers;two conventional bulk optic Michelson interferome-ters and a fiber Fabry-Perot interferometer. Onlytwo interferometers are actually required for stabiliza-tion, but it is convenient to use three to make inter-comparisons. The fiber Fabry-Perot was manufac-tured in the laboratory by cleaving a single-mode fiberinside a close fitting capillary tube.2 The two portionsof fiber are secured with adhesive to the capillary tubeto provide a stable reflective splice. The interferome-ters are illuminated by a 5-mW semiconductor laser,with a nominal wavelength of 780 nm (Hitachi HL7801). The beam is first amplitude divided by a beamsplitter. One portion is used to illuminate the fiberFabry-Perot interferometer and the remaining light isdivided by a second beam splitter to illuminate each ofthe Michelson interferometers.
Fig. 1. Optical configuration used to demonstrate common mode noise reduction of both amplitude and frequency noise of a semiconductorlaser diode.
In the case of the fiber Fabry-Perot the light isfurther amplitude divided at a fusion type bi-direc-tional coupler. One output of the directional couplerleads to the fiber Fabry-Perot. The second output isterminated by a nonreflective cleave and coated withindex matching gel to avoid unwanted reflections.The interferogram of the fiber Fabry-Perot is detectedat the fourth port of the bi-directional coupler.
One mirror of each of the Michelson interferometersis mounted on a PZT transducer to permit the opticalpath imbalance to be varied by a few microns andhence locked at the quadrature position using a lowfrequency servo. The second mirror of each interfer-ometer is mounted on a mechanical translation stage toallow the two Michelsons to be adjusted to the sameoptical path imbalance as the fiber Fabry-Perot inter-ferometers.
To accurately match the path imbalance of all threeinterferometers, the injection current of the semicon-ductor is modulated with a sawtooth waveform, fre-quency 2 kHz, of sufficient amplitude to drive the fiberFabry-Perot interferometer over precisely one fringeas judged by inspecting and maximizing the funda-mental 2-kHz frequency while simultaneously mini-mizing the 4-kHz harmonic. The Michelson interfer-ometers are also adjusted until they too are each beingdriven over one fringe. The accuracy of this adjust-ment is better than 100 Am, or 0.05% of the overalloptical path imbalance of 203 mm.
Having thus ensured all three interferometers wereof similar optical path imbalance, the principle of com-mon mode rejection of both amplitude and phase noisewas first demonstrated using the two Michelson inter-ferometers, for two situations. In the first case, bothMichelsons are locked at quadrature by controlling theposition of their PZTs to maintain the intensity outputfrom each interferometer at a value equal to the meanof the maximum and minimum value of the corre-sponding interferogram. The frequency bandwidth ofeach servo is -5Hz. As the output intensity of theinterferometer at quadrature is dependent on thesource intensity, a reference intensity is derived direct-ly from the source using an additional photodiode (notshown).
The optical receivers are reverse biased photodiodeoperated in a transimpedance mode so that the voltageoutput is linear with optical power.
In the second case one Michelson is locked again bycontrolling the position of its PZT mounted mirror andthe laser frequency is locked to the second Michelsonto give a quadrature output by using a low frequencyservo (5-Hz bandwidth) to control its injection current.
Prior to recording the frequency spectra of eachinterferogram, each interferometer is adjusted usingneutral density filters and polarization analysers sothat both their visibilities and amplitudes arematched. Frequency spectra are then obtained foreach interferometer and for the differential output of
the two interferometers using a differential amplifierwith common mode rejection of 55 dB.
The principle of common mode rejection of bothamplitude and phase noise was then demonstratedusing one Michelson interferometer and the fiberFabry-Perot interferometer. The visibility of the fi-ber Fabry-Perot interferometer is found to be 87%which is greater than that achieved with the conven-tional Michelson. In order for both amplitude andphase noise to be simultaneously rejected, it is impor-tant that each interferometer has the same visibility.A portion of light is therefore launched into a fiber anddirected via a delay line, to avoid unwanted interfer-ence, onto the photodetector recording the fiberFabry-Perot interferogram, thus reducing the visibili-ty. By varying the efficiency of the launch into thedelay line, the visibility of the fiber Fabry-Perot ismatched to the value obtained with the Michelsoninterferometer, which is 43%.
Although the initial visibility of the fiber Fabry-Perot is high the amplitude of the signal is of an orderof magnitude lower than that of the Michelson. Theoutput of the photodetector used to measure the fiberFabry-Perot interferogram is therefore amplified by afactor of 10. With this additional amplification thevoltage ouput representing the fringe amplitude of thetwo interferometers can be accurately matched usingneutral density filters.
The laser is then locked by controlling its inputcurrent thus maintaining the Fabry-Perot interfero-metric output at quadrature; the Michelson is lockedby controlling the PZT mounted mirror and the fre-quency spectra are recorded for each interferometerand also the differential output.
In addition, the fiber Fabry-Perot interferometerwas demonstrated as a miniature acoustic sensing ele-ment. The frequency spectrum at the differentialoutput of the two interferometers is obtained with thefiber sensing element exposed to an acoustic soundfield of 95 dB(A) in an acoustically shielded enclosure.
IV. Results
The results of the first series of experiments, inwhich both Michelson interferometers are locked attheir quadrature positions by actively controlling thetwo PZT mounted mirrors, are shown in Figs. 2(a) and(b). Figure 2(a) is of the frequency spectrum of justone interferometer and Fig. 2(b) is of the frequencyspectrum of the differential outputs of each interfer-ometer. The servo bandwidth is so low that the region*of the spectrum within the bandwidth is unobservablein all the spectra shown.
The visibility and fringe amplitude (difference be-tween maximum and minimum) of each Michelsoninterferometer equalled 43% and 4.2 volts. The meanoptical power corresponding to 4.9 volts is estimated tobe approximately 9.8 W, taking the photodetectorsensitivity to be 0.5 A/W.
For a single inteferometer of several centimeterspath imbalance, the predominant noise source is due toa laser frequency jitter seen as phase noise in the
a)
b)
Fig. 2. (a) Frequency spectrum of a single Michelson interferome-ter locked at quadrature by active path length tuning. Fringeamplitude = 3 dB(V). (b) Differential frequency spectrum of twomatched Michelson interferometers both locked at quadrature byactive path length tuning. Resonant peak of one PZT is discernable.
interferometer output. The phase noise is propor-tional to the path imbalance of the interferometer; forcomparison it is appropriate to normalize our noisefigures by dividing by the path imbalance. The ampli-tude of one fringe equals 3 dB(V), [OdB(V) = 1 volt], sotaking 5 kHz as our observation frequency, and a band-width of 95 Hz, we obtain a reduction in noise floorfrom -56 db(V) to -83 db(V) or normalized and interms of radians and, 570 n radians/mm -+/Hz (rms) to25 n radians/mm Hz.
One PZT has a resonance at approximately 3 kHz.It is discernable only in the differential output with thelower noise floor, demonstrating the increased sensi-tivity of the system.
Similarly, with one Michelson locked to the quadra-ture position by controlling the laser inspection cur-rent, the noise floor equals -56 dB(V) compared to thedifferential output of the two interferometers whichequals-79 dB(V), see Figure 3. The output of the twoMichelson interferometers increases slightly; the visi-bility remains at 43%, but the fringe amplitude equals4.3V or 4 dB(V). The noise floors correspond to 505 nRadians/mm /Hz for the output of single interferom-eter and 36 n Radians/mm /Hz for the differentialoutput of the two interferometers respectively. Theoptical power is approximately equal to 10.1 W (seeFig. 3).
Fig. 3. (a) Frequency spectrum of a single Michelson interferome-ter locked at quadrature by active wavelength tuning. Fringe am-plitude = 4 dB(V). (b) Differential frequency spectrum of two
matched Michelson interferometers one locked using active wave-length tuning, the other locked using active phase tracking.
Finally, the spectrum of the fiber Fabry-Perot andMichelson interferometer are shown in Figs. 4(a) and(b). The visibility of the Fabry-Perot interferometeris initially 87% but is reduced to equal the Michelsoninterferometer value of 43%; the mean optical power ofthe fiber Fabry-Perot equals 0.2 MW. The noise floorof the sensing fiber Fabry-Perot is reduced from -67dB(V) to -83 dB(V). The fringe amplitude equals-10 dB(V) and so these figures correspond to noiselevels of 714 n Radians/mmV\Hz and 113 n Radians/mm-\Hz respectively.
Figure 4(b) also shows the signal obtained when thefiber is exposed to the acoustic sound field of 95 dB (V)just below the noise floor of the fiber Fabry-Perotinterferometer and is therefore only visible when thenoise floor was reduced, by taking the differential out-put of the two interferometers.
V. Discussion
The principle of noise cancellation of semiconductorlaser diode phase and amplitude noise is demonstratedby electronically subtracting the photo-detector cur-rent from two interferometers each held at their quad-rature points. This is demonstrated first using twoconventional Michelson interferometers with both in-terferometers locked at quadrature by controlling thePZT mounted mirrors in one arm of each interferome-
a)
b) _
Fig. 4. (a) Frequency spectrum of fiber Fabry-Perot interferome-ter, when subject to an acoustic signal of 95 dB(A), locked by activewavelength tuning. The signal induced by the acoustic wave is notdetectable. Fringe amplitude equalled = 10 dB(V). (b) Differen-tial frequency spectrum of the fiber Fabry-Perot interferometerlocked by active wavelength tuning and matched Michelson inter-ferometer locked using active phase tracking. Presence of same
acoustic signal is clearly discernable.
ter, and then by locking one of the interferometers bycontrolling the laser injection current. Both methodslead to similar noise reductions of 27 and 23 dB(V) atan observation frequency of 5 kHz. The degree towhich the noise floor can be reduced is critically depen-dent on matching the amplitude, visibility and pathlength of each interferometer as well as locking bothinterferometers at precisely their respective quadra-ture points. For improved noise reduction each ofthese parameters would therefore have to be moreclosely controlled. In our final demonstration usingthe Fabry-Perot interferometer as an acoustic sensor,the noise floor is limited by the photodetector noisefloor.
Although our noise cancellation is demonstrated byelectronic subtraction it is feasible to perform thissubtraction optically by locking the second interfer-ometer to the quadrature point 1800 out of phase to thefirst measuring interferometer, and then adding theiroutputs on to the face of a photodetector. A delaygreater than the coherence length of the source is re-quired to avoid unwanted interference of the two sig-nals. The advantage of this refinement lies in dispens-
ing with the differential amplifier which can be alimiting factor in maximizing the common mode noisereduction as a result of introducing its own noise andcan also limit the frequency response of the system.
The performance realized in our experiments is lim-ited by the relatively low optical power coupled intothe fiber interferometer. The launched power is limit-ed by the onset of optical feedback into the laser cavity.We use a simple optical isolator between the laser andfiber, comprising a polarizer and quarterwave plate.However, the isolator has limited efficiency, so it isnecessary to misalign the launching optics to reducethe feedback to an acceptable level, but with a concom-itant reduction in launched power. Suitable use of aFaraday isolator would be more effective, and wouldallow higher powers to be coupled into the fibers.
VI. Conclusions
The widespread use of semiconductor lasers for fiberoptic sensors is limited by their inherent problem ofamplitude and frequency fluctuations leading to noiseon the interferometric output. The phase noise aris-ing from frequency fluctuations is less easily compen-sated for than amplitude noise and is also proportionalto the path imbalance of the interferometer. Thislimits the use of laser diodes to interferometers withpath imbalances of a few centimeters for micro radianresolution.
Successful stabilization of a laser using an externalcavity is governed by the electronics of the lockingservo. In practice the amplifier, photodetector, andlaser all contribute to the overall phase delay of thelocking servo and therefore limit the overall gain thatcan be achieved while avoiding the instability of thecontrol loop. Since the gain determines the reductionof phase noise, this limits the noise level that can beachieved. Even when the laser is locked, the phasenoise is still proportional to the path imbalance of theinterferometer, thus setting an upper limit to the pathimbalance which can be employed usefully.
In theory our differential technique overcomes thisproblem, provided a second reference interferometercan always be built to match the sensing interferome-ter. We have demonstrated the reduction of phaseand amplitude noise using a second reference interfer-ometer using two conventional interferometers andhybrid system incorporating a fiber Fabry-Perot and aconventional Michelson. The theoretical limitation isonly that of the stability of the reference cavity andphotodetector shot noise.
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This work was partially supported by the Paul Instrument Fund.
