Optical step frequency reflectometerK. Iizuka, Y. Imai, A. P. Freundorfer, R. James, R. Wong, and S. Fujii Citation: Journal of Applied Physics 68, 932 (1990); doi: 10.1063/1.347179 View online: http://dx.doi.org/10.1063/1.347179 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/68/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in V -band frequency hopping microwave reflectometer in LHDa) Rev. Sci. Instrum. 79, 10F109 (2008); 10.1063/1.2969036 Frequency hopping millimeter wave reflectometer Rev. Sci. Instrum. 75, 3865 (2004); 10.1063/1.1788834 Design and performance of a reflectometer to measure optical properties of multilayer optical thin films AIP Conf. Proc. 378, 667 (1996); 10.1063/1.51176 ATF twofrequency correlation reflectometer Rev. Sci. Instrum. 61, 3049 (1990); 10.1063/1.1141723 Differential reflectometer for studies of adsorption on stepped crystal surfaces Rev. Sci. Instrum. 53, 1058 (1982); 10.1063/1.1137087

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Optical step frequency reflectometer K. lizukaa )

ATR, Seika-cho Soraku-gun, Kyoto-Fu, Japan

Y. Imai,b) A. P. Freundorfer, R. James, and R. Wong University of Toronto, Department of Electrical Engineering, Toronto, Ontario, Canada M5S lA4

S. Fujii ATR, Seika-cho Soraku-gun, Kyoto-Fu, Japan

(Received 27 November 1989; accepted for publication 8 February 1990)

The carrier generated by a solid-state laser can be frequency shifted by a significant amount. This fact was exploited to implement a high-resolution optical-fiber fault locator. A resolution of 4 mm was achieved. Compared to the resolution of a frequency-domain refiectometer that shifts the frequency of the AM modulation of the light, the proposed fault locator has a resolution about 1000 times better. The potential of developing the proposed refiectometer into an ultrahigh-resolution integrated optics fault locator is also discussed.

I. INTRODUCTION

With an increasingly large number of installations of fiber-optical communication lines, the need for fiber-optical fault locators will continue to increase. Optical time-domain reflectometers 1 (OTDR) have been most widely used for locating the positions of breaks in the fiber. The time for a light pulse to make a round trip determines the locations of the faults in the fiber. One of the drawbacks of the OTDR is its inability to locate faults within 12 m of the source of the fault locator. This is because the front end amplifier has to be short circuited while the strong intensity transmitted light is launched. Another drawback is that to attain a longer range, the light pulse width has to be increased for larger energy, yet for better resolution the light pulse width has to be short­ened. These are the mutually conflicting requirements of a fault locator. The commercially available OTDR can nor­mally switch between longer range with less resolution and shorter range with higher resolution. It is not possible to maintain higher resolution for a longer range. In order to amplify the shortest pulse width, a wide-frequency.band am­plifier is needed. In fact the ultimate resolution of the OTDR is determined by the frequency bandwidth of the receiver.

Frequency-domain refiectometers have been proposed. They are equivalent to the time-domain refiectometers be­cause time and frequency domains are related by Fourier transform. The instrumentation makes the difference. The reflected complex (both amplitude and phase) signals are measured as a function offrequency and the result is Fourier transformed to obtain a time-domain pulse for display. The frequency is either swept continuously or stepwise.

Both continuous and step frequency sweeps have advan­tages over the time-domain refiectometer i.n that both meth-

oj On leave of absence from University of Toronto, Toronto, Ontario, Can­ada.

b) On leave of absence from Kyushu Institute of Technology , Department of Computer Science and Electronics, Iizuka, 820 Fukuoka, Japan.

ods use the continuous wave and there is neither a blind spot nor the mutually conflicting requirements of resolution and range.

If one compares the continuous and step frequency sweeps, it is evident that even though the continuous sweep renders a real time display, the step frequency sweep renders not only higher measurement accuracy but also the possibil­ity of switching among the large number ofIasers for a wider range of frequency sweep. MacDonald2 continuously swept over a range of 89.10 MHz. Krotky 3 stepped the frequency over a range of 2.0 MHz. Nielsen4 used a signal processing unit similar to that used by the step frequency radar for gen­erating the ultrahigh frequency (UHF) image of under­ground targets. S

•b The frequency was stepped over a 5-MHz

range. Ghafoori-Shiraz and Okoshi/ Nakayama, Iizuka, and Nielsen, g and Shadaram9 all stepped the frequency over ranges of 2 MHz, 4 MHz, and unspecified, respectively.

In each case, it has been the frequency of the sinusoidal amplitude modulation that was swept or stepped. The fre­quency of the optical carrier has never been swept or stepped. In the present paper, a step frequency fault locator that stepped the frequency of the carrier rather than the fre­quency of the amplitUde modulation of the light will be pre­sented. The frequency was stepped over a 20-GHz range. This resulted in resolution 103 times better than that of the fault locator reported earlier.

II. PRINCIPLE OF OPERATiON

The principle of the optical step frequency refiectometer is quite similar to that in the UHF region. 5 For complete­ness, a brief outline will be presented here.

The light wave with carrier frequency J,

(1)

is launched toward a single reflector located at distance z. The returned signal is then expressed by

(2)

932 J. Appl. Phys. 68 (3), 1 August 1990 0021-8979/90/150932-05$03.00 @ 1990 American Institute of Physics 932

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where v is the velocity of the light in the medium. The phase of the returned signal is delayed from that of the incident wave by

2z ¢=217'-/ (3)

v If the phase delay if> of the reflected signal Es is measured as a function of light frequency f, the distance z to the target is found from Eq. (3). This, however, is possible only when there is one reflector. Ifthere is more than one reflector, the returned signal E is a superposition of the signals reflected from each reflector with reflection coefficient Sk:

(4)

There are N terms if there are N reflectors. If lis changed, the real (imaginary) part of each term changes sinusoidally with respect to f, with amplitude Sk and frequency 2Zklv. The phasor associated with the longer distance rotates faster than that of the shorter distance, and the sinusoidal change of the real (imaginary) part with respect to I is at a higher frequency. In other words, the real (imaginary) part of E is the superposition of sinusoidal waves with amplitude Sk and frequency 2Zklv with respect to / Recall that the Fourier transform can determine the amplitude Sk of each compo­nent sinusoidal function from the sum of sinusoidai func­tions of various frequencies, 2zk lv.

In reality, however, E is not measured continuously but is measured at a discrete step of frequency. The reflected complex signal is measured by cw light one carrier frequency at a time and the same measurements are repeated at N dif­ferent frequencies. Next, the expressions for the step fre­quency case will be derived. Let the frequency of the light carrier at the nth step be

In = /0 + nil/, (5)

where n = 0,1,2,'" ,N - 1,/0 is the frequency at the initial step, and I::!fis a step offrequency. Similarly, let the distance be expressed by

(6)

where Zo is the reference distance. t::.z is an increment of the distance.

The returned signal Etl for the transmitting frequency In can be obtained by summi.ng the returned signals from all reflectors. Rearrangement ofEq. (4) after inserting Eqs. (5) and (6) gives

N- I En = E

re j2(3,,zo L Skej2fJol'.zkei(47rAZAl/t')tlk, (7)

k~O

where

130 = (21Tlv)lo,

f3n = (21Tlv) (fo + nAf)·

If one imposes the condition

2NI::!IIlzlv = 1,

Eg. (1) can be further simplified, and it becomes lV-I

h" = L Sk ej(21r/Nlnk,

k=O

where

933 J. Appl. Phys., Vol. 68, No.3. 1 August 1990

(8)

(9)

(0)

TABLE I. Relationship between sweep range and quantized distance at A = 1.5 jJxn in medium of n = 3.

Sweep range

in frequency

Nb/(GHz) 1000

10000 30000

in wavelength

NllA (nm) 7.5

75 225

h = (E IE )e -1211"z" n n r ,

Quantized distance

b.z (ttm) 50

5 1.6

01 )

(12)

Equation (10) is exactly in the form of an inverse discrete Fourier transform. h n are the measured quantities and skare the desired quantities. The Fourier transform of Eg. (10) produces Sk from hn :

, N- I

S . = ~ "C' 1. e - j(21l'/N)kn K ~ nn .

lif n '_ 0

(13)

The side lobes due to the finite number N can be reduced using a window function 10 W:

N I

S =.!. ~ W h e' j(271/N)kn k ~ n 11 •

IV n=()

(14)

The quantized distance liz, which is approximately the resolution, is

t:.z = u/2Nb..f, (15)

and the maximum distance range Nt:.z is

d max = v/21::!J (16)

Table I shows the relationship between total frequency shift, wavelength shift, and quantized distance at A = 1.5 j.tm in a medium ofn = 3. 11

III. IMPLEMENTATION

The probing light beam was coherently detected using the carrier frequency shifted reference beam. Figure 1 shows a block diagram of the optical step-frequency refiectometer (OSFR). The source light is first divided into probing and reference beams by means of a nonpolarizing beam splitter NBS]. The probing beam passes through NBS2 and then is focused into the test object with the aid oflens LI . The probe beam returned from the target goes back through NBS2

again and reaches the mixer. The reference beam, on the other hand, goes through the acousto-optic modulator AOM, and the carrier frequency of the light is shifted by a constant amount j~ = 40 MHz for simple detection of the phase of the probe beam later. The output from the AOM passes through NBS2 and reaches the same mixer. The beat between the signal beam and the frequency-shifted reference beam creates a beat signal of frequency 1M that contains in­formation about both the phase and amplitude of the re­turned signal En' The phase referred to the reference beam is obtained by using a phase comparator. As the carrier fre­quency of the laser is stepped, the measurement of the re­turned signal is repeated. The output from the comparator is fed into the fast-Fourier-transform (FFT) processor. Final-

lizuka et al. 933

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40 MHz Oscillator

40 MHz Reference

Timing Signal

Jy, the output of the FFT, Sk, is displayed as a function of distance.

One of the major advantages of the present system is that no matter how much the range of the frequency steps Nl1fis increased for higher resolution, the frequency band­width requirement of the amplifier remains the same. It is also practically independent of the choice of the carrier fre­quency of the source.

IV. PARAMETERS USED

A Nd-YAG laser of wavelength 1.3 ;1m and output power 25 m W, was used as a source. The carrier frequency of the laser was stepped by stepping the temperature of the laser cavity. The range of frequency of the laser that could be changed in this manner was approximately 20 GHz, which gave from Eq. (15) a quantized distance of I1z = 4.8 mm in glass with n = 1.55. The number of frequency steps was N = 128 and hence the frequency step was I1f = 156 MHz, which gave the maximum distance of 0.62 m from Eq. (16).

Phase jitter that may have been present in the reference beam due to nonideal operation of the AOM could have been eliminated if necessary. The 40-MHz signal that would con­tain the same phase jitter as that in the reference beam could have been generated by beating the zero- and first-order beams from the AOM on the photodetector D 1 • The 40-MHz output from D\ would contain the same phase jitter as the reference light beam. If this 40-MHz signal was to have been fed to the comparator through Sl , both the reference and signal channels would have the same jitter and the jitter would be cancelled in the comparator. It was found, how­ever, that such a precaution was not necessary. The 40-MHz

934 J. AppL Phys., Vol. 68, No.3, 1 August 1990

Target

FIG. L Block diagram of optical step­frequency refiectometer.

AOM driver voltage was directly fed to the reference chan­nel of the phase comparator through switch S2 .

A pinhole was placed in front of the mixer input window to minimize the background light.

\/0 STABILITY REQUIREMENT OF THE SOURCE

The range over which the OSFR can be used strongly depends upon the narrowness of the linewidth of the source. The OSFR measures the interference between the reference and probe light beams. The signal returned from a distant reflector at z = Zk has left the laser 2Zk/V seconds ago. This

, light interferes with a reference light beam that has just left the laser. In order to measure the phase of the returned sig­nal, the laser has to be stable for at least 2zk lu seconds. The degree of stability required of the laser source will be briefly calculated. 1 J Since the probe and reference beams take the same path from the laser to NBS l , the path difference is measured starting at NBS!. The field En of the probe light beam first enters the target and then comes back to NBS2

and finally goes to the mixer, and the field Er of the reference beam goes to the mixer by way of the AOM that shifts the frequency. These light beams are expressed by

En =SkCOS[21Tfnt+2!3nZk +e(t- 2:k)] +n.,(t), (17)

Er = cos [ 2rrifn + IM)t + B (t -~)

+ BM(t -~)] + ns(t), (18)

where r is the path difference of the reference beam from NBS\ to NBSz by way of AOM and the probe beam from

lizuka et al. 934

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NBS! to NBSz, O( t) and OM (t) are phase jitters originating in the light source and AOM, respectively. ns (t) is the am­plitude noise, which includes both shot and thermal noises. The output current from the mixer is

(19)

where A is the detector area, Zo is the impedance of free space, h is Planck's constant, 1] is the quantum efficiency of the mixer and e is the electron charge.

Insertion of Eqs. (17) and (18) into Eq. (19) gives

( 2Zk) (r)] - () t - -t-) + eM t - ; (20)

where the higher-frequency and de components were filtered out. Also the amplitude noise was assumed to be negligible. The output current i" is fed to the signal port of the phase comparator. If a portion of the drive current to the AOM is directly fed to the reference port of the comparator, the ref­erence current can be represented by

i,. = cos 2rrjut. (21)

The comparator generates the product of Eqs. (20) and (21). The output of the comparator is

i = !Zo ~ ASk cos [2f3nZk + I) (t _ 2Zk) h/ 11

after the high-frequency component has been fUtered out. The output from the comparator, Eg. (22), contains the

phase jitter () M caused by the AOM, but this can be removed by switching onto Sj from S2 to use the beat signal from detector DI . The output current from V] is

i;= h;mcos[2rr.t:lft+BM(t-~)], (23)

where m represents the light power into the diode. If i; in Eg. (23) rather than iF in Eq. (21) was used as the reference signal to the comparator, the phase jitter 8M would have been removed from the output current i in Eq. (22).

If ()M(t) is removed, the phase jitter term in Eq. (22) becomes

(24)

tte is the phase jitter of the source during the time difference in which the probe and reference beams make the round trip:

ttt = 2zJv - rlv. . (25)

Suppose we can tolerate a change of, let us say,

MJ= 17'/2 (26)

during !l.t. This means that we tolerate 217' radians phase jitter in 4!l.t seconds, or the tolerated phase jitter in terms of frequency is

11/= v/4(2zk - r). (27)

935 J. Appl. Phys., Vol. 68. No.3, 1 August 1990

-50 \I 5 10 20 25

ie) Dislance in cm

[+12 !+2(

(b) Frequency in GHz

FIG. 2. OSFR display and its input to FFT processor. The reflector was a mirror. (,,) OSFR display. The object is a front surf"cc mirror. (b) Com­plex input to FFT processor.

It should be noted that III is not exactly the frequency Iinewidth of the laser source, unless the frequency shift of Ilj takes place slowly. The frequency spectrum depends not only on how much the frequency shifts, but also how fast the frequency shifts. For simplicity we assume that the frequen­cy shift takes place slowly. Using Eq. (27), with the present laser whose spectral width is 1 kHz, the fault locator has a range of 25 km. Needless to say, the linewidth requirement relaxes as r is made close to 2z k •

5

0

.CJ ...,

.S -0

'" '" -10 ~ ';:: .. '" -15

:>Ii

i

-20

~, -25 l

0 25 50

Distance in em

FIG. 3. OSFR display when break in optical fiber was 8 em from the feed point.

lizuka et al. 935

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2

0

~~ "" -2 "" .S

"" ] -4

a "" -6 " ::I!

· r h i. -to 0 5 10

Distance in em

FIG. 4. OSFR display; the object was a 4-mm-thick lens.

Vi. EXPERIMENTAL RESULTS

The first measurement was made using a plane surface mirror as a target. Figure 2 shows the output display of the OSFR and the amplitude and phase with respect to the light carrier frequency. The frequency sweep range is 20 GHz, and the total number of steps is IV = 128. The figure demon­strates a good constancy of amplitude in the upper panel of Fig. 2(b) and good linearity with respect to frequency in the lower panel of Fig. 2 (b). This verifies a successful sweep in the carrier frequency of light. The Fourier transform of the returned signal is the display shown in Fig. 2(a). The verti­cal axis is the scattering coefficient skin dB and the horizon­tal axis is the distance z. The first side lobe level is 14 dB below the main lobe. The symmetry of not only the main lobe but also that of the side lobe is excellent.

Next, a break in the fiber occurring just outside the fer­rule of an optical-fiber holder was investigated. Figure 3 shows the OSFR display when the break is 8 em from the feed point of the fiber. The same frequency range, frequency steps, and window function as used in Fig. 2 were used. The first peak in the figure corresponds to the entrance to the optical fiber and shows that the OSFR can measure from exactly zero distance, thus eliminating the blind spot present in a time-domain refiectometer. The second peak corre­sponds to the break only 8 cm away from the input point. The display shows two peaks clearly separated.

Next, the finest resolution that the OSFR can resolve was determined. The target was a 4-mm-thick lens. The thickness of the target was 20% thinner than the quantized distance!1z = 4.8 mm. Figure 4 shows the results. The front and back surfaces are still resolvable with a deep null be-

936 J. Appl. Phys., Vol. 68, No.3, 1 August 1990

tween the peaks. The reason that the OSFR is able to resolve below the quantized distance is that the interface at the back surface of the lens is from glass to air while the interface at the front surface of the lens is from air to glass hence the reflection coefficients at the back and front surfaces are op­posite in sign.

VII, CONCLUSIONS

An optical step-frequency refiectometer that steps the carrier frequency rather than the frequency of the sinusoidal amplitude modulation was realized. The resolution of such an optical refiectometer is phenomenally high, and a resolu­tion of 4 mm was demonstrated. The OSFR showed that faults, including those located at zero, can be detected.

Recently, a semiconductor laser with a tuning range of 50 nm (6.45 THz) at A = 1.5 pm including mechanical tun­ing has become available. 12 With such a source, the obtaina­ble resolution ofOSFR is on the order of micrometers. Such an OSFR can locate faults even inside integrated optics wa­fers or can see through integrated-circuit chips from any direction from outside· because both Si and GaAs wafers are transparent at A = 1.5 /lm,

ACKNOWLEDGMENTS

We wish to thank Dr. Y. Furuhama for a fruitful discus­sion. This research was financially supported by the Ontario Laser and Lightwave Research Center of Canada.

1 B. L. Danielson, App!. Opt. 24, 2313 (1985). 2R.I. MacDonald, App!. Opt. 20.1840 (1981). 3 P. Krotky, Bachelor's Degree Thesis, University of Toronto, Toronto

(1981). 4 J. Nielsen, Master's Degree Thesis, University of Toronto, Toronto

(1984). 5 K. Iizuka. A. P. Freundorfer, K. H. Wu, H. Mori, H. Ogura, and V. K. Nguyen, J. AppJ. Phys. 56, 2573 (191\4).

6 K. Iizuka, in Proceedings of the 1984 International Symposium on Noise and Clutter Rejection in Radars and Electro-magnetic Sensors, edited by X. Musha, IS NCR, pp. 15-24.

7 H. Ghafoori-Shiraz and T. Okoshi, J. Lightwave Techno!' LT-4, 316 ( 1986).

"J. Nakayama, K. Iizuka, and John Nielsen, App!. Opt. 26, 440 (1987). "M. Shadaram, in Digest of the 14th Congress of the International Com-

mission for Optics. Quebec, Canada, August, 1987. \OF. J. Harris, Proc. IEEE 66,51 (1971). 11 K. Iizuka, Advanced Technol. Res. J. (to be published). 11 J. Mellis, S. A. Al-Ghalabi, K. H. Cameron, R. Wyatt, J. G Regnault,

W. J. Devlin, and M. C. Brain, Electron. Lett. 24, 988 (1988).

lizuka et al. 936

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