NBSIR 88-3091

GROUP INDEX AND

TIME DELAY MEASUREMENTS

OF A STANDARD REFERENCE FIBER

B. L. Danielson

C. D. Whittenberg

FU EOT

BE NET H

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303-3328

July 1988

Stimulating America's Progress 1913-1988

NBSIR 88-3091

GROUP INDEX AND

TIME DELAY MEASUREMENTS

OF A STANDARD REFERENCE FIBER

B. L. Danielson

C. D. Whittenberg

Electromagnetic Technology Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303-3328

July 1988

Sponsored in part by

Department of the Navy

Naval Weapons Station/Seal Beach

Corona, California 91720-5000

U.S. DEPARTMENT OF COMMERCE, C. William Verity, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Contents

Page

1 . Introduction 1

2 . Group Index Measurements 3

2.1 Theory of the Scanning Interferometer 4

3. Time Delay Measurements 5

4. Error Analysis 5

4.1 Group Index Errors 6

4.2 Pulse Time-of-Flight Errors 8

4.3 Total Length Uncertainty for Long Fibers 9

5. OTDR Calibration 9

6. Conclusion 10

7. References 10

iii

Group Index and Time Delay Measurements of a Standard Reference Fiber

B. L. Danielson and C. D. Whittenberg

National Bureau of Standards

Boulder, Colorado 80303-3328

We describe measurement techniques for establishing a standard reference fiber with well characterized group index and

time 01 group delay. Evaluation of an interferometric method

indicates that fiber group index can be determined with a total

estimated uncertainty of about 0.03 percent in small samples.

Group delay of the reference fiber was measured with an overall

uncertainty less than 0.004 percent in a 7 km waveguide. We

discuss the application of a standard reference fiber to

calibration of the distance measurement accuracy of an optical

time-domain reflectometer (OTDR)

.

Key words: calibration procedures; optical delay line; optical

fiber group index; optical fiber group velocity; optical timedomain reflectometer ; OTDR; standard reference fiber; standard

test fiber

1 . Introduction

A standard reference fiber (SRF) is a commercially available

lightguide which has been well characterized for selected

transmission properties at certain wavelengths [1]. Such a fiber can

be used as an interim standard reference material for application in

calibrating test instruments such as the optical time-domain

ref lectometer (OTDR) and also for evaluation of the accuracy of

different measurement techniques through inter laboratory comparisons

1
This report is primarily concerned with the development of

techniques for precision length determinations of single-mode optical

fibers at a wavelength of 1300 nm. We also discuss the application

of these techniques to the calibration of distance measurement

accuracy for the optical time-domain ref lectometer

.

Two methods can be used to measure fibers that are several

kilometers in length. Winding machines used for wrapping fiber on

spools usually have provisions for distance readout. Also, length

can be inferred from transmitted time of flight of an optical pulse.

The latter approach requires a knowledge of fiber group index and

delay time of an optical pulse of short duration. Of the two

methods, we think that the optical means are not only more versatile

and controllable, but more accurate as well. We will, therefore,

only consider optical length determinations here.

Fiber length L can be calculated from the relation,

c Td (A)

L =

N(A)

( 1 )

where Td (A) is the time delay or group delay of an optical pulse

transmitted one way through the test fiber at the wavelength A, and

c/N(A) the group velocity. Here c is the velocity of light and N(A)

is the effective group index of refraction of the fiber defined as a ratio of the speed of light in a vacuum to the speed of an optical

pulse in the lightguide, when the pulse has a spectral content spread

over a finite wavelength interval [2]. Independent optical

measurements of N(A) and Td (A) at a common wavelength are necessary

and sufficient for determining a unique value of the physical length

of the fiber.

2
2 . Group Index Measurements

The group index (or group velocity) of a fiber is not only a function of wavelength but will also vary from fiber to fiber

depending on the specific profile design as well as manufacturing

details. For the most accurate length determinations, the group

index of the individual fiber or cable under test must be known. The

effective group velocity of a cable may be different from the

constituent fibers due to an excess fiber path designed for stress

relief in the cable. Group index data may sometimes be available

from the manufacturer [3,4]. Experimentally, the effective group

index may be obtained from eq (1) by an inverse process where

propagation delay information is available on a fiber of known

length. In principle, any of the techniques for measuring dispersion

can be used for this purpose [5]. A key problem in this connection

involves establishing accurate values for length.

We have chosen here to evaluate a new interferometric technique

[6] which is simpler and uses shorter samples than those reported in

other interferometric methods. The technique is illustrated in

figure 1. The procedure is as follows:

(1) The physical length of the fiber Lp is measured by placing a fiber sample in a vacuum chuck mounted on a translation

stage, and noting the distance on the translation micrometer

required to align either end of the fiber with crosshairs in

the microscope eye piece. The length of the sample in these

experiments was limited by the maximum travel of the

micrometer to about 50 mm.

(2) The optical length Lopt is measured from observations of the

change in air path in the reference arm between visibility

maxima in the interferograms reflected from the two ends of

the fiber. Typical signatures are illustrated in figure 2.

(3) The group index is then calculated from the relation

3
( 2 )

L,'opt

N

Lp

2.1 Theory of the Scanning Interferometer

The complete theory of the asymmetric scanning Michelson

interferometer is given in standard references by Bell [7] and

Chamberlain [8]. Chapter 8 of [7] shows that the shift in the peak

of the interferogram (the grand maximum) occasioned by insertion of a sample with index of refraction n (A) in an otherwise balanced

interferometer is given by

where n is some suitable average index of refraction. However, the

location of the maximum is given by the stationary phase condition,

D = (n-l)Lp , (3)

d 2tx — ( — [ n-1 ] Lp - D) = 0 . (4)

dA A

This is just the condition which defines the group index [1],

dn

N(A) = n - A (5)

We conclude that the excess optical path due to the sample is

D = (N - 1) , ( 6 )

which is equivalent to eq (2) .

4
3. Time Delay Measurements

Lightguides can be used as precise optical delay lines [9], In

some signal processing systems the value of this delay is critical

[10]. In order to minimize wavelength dependence, we have measured

Td at the zero-dispersion wavelength AQ (around 1300 nm for

dispersion unshifted fibers) . The pulse time-of-flight was obtained

with a conventional digital delay generator as illustrated in

figure 3. The full width at half maximum of the optical pulse,

convolved with the oscilloscope response, is about 600 ns (fig. 4).

The pulse transit time in the SRF was obtained by adjusting the

electronic delay of the digital delay generator to equal the optical

delay in the test fiber. The equality of delays was established by

aligning the pulse with a fiducial point on the oscilloscope set from

a short jumper fiber.

4. Error Analysis

Ve use Gauss's law of propagation of error to estimate the

standard deviation of the total uncertainty in the quantities we wish

to measure (group index, time delay, and length). In this case the

total uncertainty, aN , is a function of the errors in several

observables, a- , and we can write

where aL is the standard deviation of each uncorrelated observable

xi

. Similar expressions are assumed to hold for the time delav i total SRF length. For simplicity we will not distinguish between

systematic and random errors in this analysis.

5
4.1 Group Index Errors

Systematic errors inherent in the measurement of fiber sample

length Lp include those arising from end wedge angles and

uncertainties in determining the optical features which indicate the

fiber end. Random errors occur since the microscope crosshairs can

not be precisely aligned with the ends. The end angle, as determined

from an interference microscope [11], was kept less than 1°. This

insured that uncertainties due to this source (considering both ends) were less than 2 fim. The precision of repeated measurements was about 7 /j.m. The total uncertainty in was estimated to have a one- sigma value of about 1.8 x 1CT 4

.

There are similar uncertainties in determining the optical length

Lopt . The stepping motor translation stage was compared directly

with the micrometer by moving the micrometer screw in one direction

and the stepping motor a nominally equal amount in the opposite

direction and noting any discrepancies in fringe location. The

stepping motor drive did not completely agree with the micrometer,

and a small correction was added to the reading indicated on the

motor drive unit (1.9 x 10~ 4 ). Again, the micrometer was assumed to

have no systematic errors. A small hystersis in the stepping motor

drive could be eliminated by maintaining a consistent direction of

travel for all observations. The precision of location of the peak

fringe was obtained from repeated measurements and was about 3 /z

m

(one way) due to a combination of temperature drift in the

interferometer and errors associated with resetting the micrometer.

Alignment errors were judged to be negligible, since no changes could

be observed on realignment of the optical components.

A major concern with our method of measuring group index has to

do with variations of transmission properties along the length of the

reference fiber. As a practical matter, we can only sample

6
the properties of the fiber at either end, and make the assumption

that the average value of N is representative of the entire length.

The assumption of fiber uniformity has been examined in some detail

for production fibers of the same type as used for the present

standard reference fibers [4] . The authors find that the properties

are indeed uniform within 0.02 percent. This sampling error

constitutes the largest uncertainty in the group index.

Although the group index of dispersion-unshifted silica-based

fibers undergoes a minimum in the wavelength interval around 1300 nm,

the wavelength dependence of the optical sources on measurements in

this region is not entirely negligible. We account for this

dependence by measuring the group index and time delay as close to

the zero-dispersion wavelength as possible. Next we estimate the

magnitude of the error which accrues if comparisons are made at

wavelengths slightly different from A 0

.

The group index of the fiber can be expanded in a Taylor series

about A 0 as

dN

' N(A) = N(A 0 ) + —

dA

(A - A 0 ) +

> A 0

1 d

2 N

2 dA2 (A - A 0 ) 2 + ....

Aq

( 8 )

where A 0 is assumed to be known. Equation (8) can be written as

1 N(A) - N(A 0 ) - - C

2

dD

'

dA J*o

(A - A 0 ) 2 (9)

since (dN/dA) A0 is proportional to the dispersion D (A) and is zero by definition. The constant (d2 N/dA2

) A0 is proportional to dD/dA . !

7
can be estimated from the fact that the Electronic Industries

Association (EIA) recommendations restrict the value of the

dispersion to less than ± 3.5 ps (km-nm) in the interval 1285 to

1350 nm. This implies that dD/dA < 2.4 x 10' 2 ps (km-nm2 ).

Equation (9) then predicts that N(A) - N(A 0 ) should be less

than 1.0 x 10' 5 within 20 nm of A 0.

4.2 Pulse Time-of-Flight Errors

Some of the uncertainties which can be identified with Td include

repeatability problems and inaccuracies in the digital delay

generator. Most of the uncertainty in the time interval measurement

comes from the limitations of the digital delay generator, and these

are specific to the particular commercial instrument used in these

investigations. An estimate of the magnitude of these errors may be

obtained from the manufacturer's specifications and is approximately

0.9 ns for a 7 km fiber, i.e. a fractional uncertainty of 4.0 x 10' 5

. This figure includes inherent instrumental error and jitter, along

with effects due to aging and temperature stability.

Since we determine delay by visual alignment of an oscilloscope

trace with a marker, there will be some error associated with the

precise location of the pulse maximum. Because the pulse shape is

approximately Gaussian, we can take this uncertainty to be 2 times

the one sigma pulse duration (considering the two ends) , or about

0.4 ns

.

Pulse distortion due to dispersion effects is totally negligible

under these experimental conditions. The combined fractional

uncertainty is about 4.2 x 10" 5

.

8
4.3 Total Length Uncertainty for Long Fibers

Using eq (1) and the propagation of error formula, we can

estimate the total uncertainty in the length determination of a long

fiber. For the 7 km SRF used in the present work we have

AL = 2.0 m, and AL/L = 2.8 x 10" 4

. These figures are dominated by

group index uncertainties

.

5. OTDR Calibration

One of the reasons for developing a standard reference fiber is

to aid in the characterization and calibration of OTDRs . Along with

attenuation, distance measurement accuracy is one of the principal

quantities which is susceptible to accurate calibration in these

devices [1]. The SRFs provided to contractors are also characterized

for spectral attenuation; although, we do not discuss these

measurements here.

An SRF can be combined with a fiber directional coupler to

generate an infinite series of markers located precisely at L/2 on

the OTDR display. These recirculating delay line calibrators have

been described in the literature [12,13].

For calibration purposes only the time interval Td at the

calibration wavelength need be specified accurately, since the OTDR

does not measure length directly, only time interval. The

ref lectometer calculates length according to eq (1). Specifying the

correct value for Td , along with any group index N, is sufficient to

establish the accuracy of the inferred values of length given by the

OTDR. Therefore, the actual physical length of the SRF is

immaterial. The correct value of N is required in determination by

the OTDR of the actual physical length of another fiber. This point

is important when establishing the errors associated with distance

9
measurement accuracy. Since Td can be measured much more accurately

than N, the group delay uncertainties determine calibration accuracy

for OTDR distance measuring capabilities.

6. Conclusion

We have described techniques for measuring two transmission

properties of interest in standard reference fibers: group index of

refraction and group delay. The asymmetric scanning Michelson

interferometer has been demonstrated to be a simple, reliable, and

accurate instrument for determining group index in small fiber

samples. The estimated accuracy of these measurements, primarily

limited by sampling errors, is about 0.03 percent. The group delay

in a 7 km fiber was about 1.4 ns or 0.004 percent. This implies that

the length of 7 km fiber can be determined with an overall

uncertainty of about 2.0 m. However, the only important quantity for

calibrations of OTDR distance measurement accuracy is the time delay

of the SRF, so these calibrations can be performed with an accuracy

of about 0.004 percent. Using the same experimental techniques with

better equipment, the group delay accuracy can probably be improved

at least an order of magnitude.

7 . References

[1] Danielson, B. L. , "Calibration and standardization issues

for the optical time-domain ref lectometer . " Nat. Bur.

Stand. (U.S.) NBSIR 87-3078; 1987 December.

[2] Cohen, L. G. and Stone, J., "Interferometric measurements of

minimum dispersion spectra in short lengths of single-mode

fiber." Electron. Lett. 18(13): 564-566; 1982 June 24.

[3] Product information PI-115, Effective group index of

refraction for SMF-21 Optical Fiber. Corning Glass Works.

Corning, New York 14831.

10
[4] Saunders, M. J. and Gardner, W. B., "Interferometric

determination of dispersion variations in singie-mode

fibers." J. Lightwave Technol. LT-5 (12): 1701-1705; 1987

December

.

[5] Gardner, W. B., "Dispersion measurements of single-mode and

multimode optical fibers." Proc . of SPIE, Vol. 559: 18-23;

1985 August.

[6] Danielson, B. L. and Whittenberg, C. D., "Guided-wave

reflectometry with micrometer resolution." Appl. Opt.

26(14); 2836-2842: 1987 July 15.

[7] Bell, R. , Introductory Fourier transform spectroscopy. New

York, NY: Academic Press; 1972. 382 p.

[8] Chamberlain, J. E., The principles of interferometric

spectroscopy

.

New York, NY: John Wiley; 1979.

[9] Wilner, K.and van den Heuvel, A. P., "Fiber optic delay

lines for microwave signal processing." Proc. IEEE 64(5):

805-807; 1976 May.

[10] Jackson, K. P., Newton, S. A., Moslehi, B., Tur , M. , and

Cutler, C. C., IEEE Microwave Theory Tech. MTT-33: 193-210;

1985 March.

[11] Newport Research Corporation Model F-IM1. This commercial

product is mentioned in order to completely describe the

experimental procedures, and does not imply endorsement.

Other products may be equally suitable.

[12] Danielson, B. L. , "Optical time-domain reflectometer

specifications and performance testing." Appl. Opt. 24(15):

2313-2322; 1985 August 1.

[13] Newton, S. A., Nazarathy, M. , and Trutna, W. R., " Measured

backscatter signature of a fiber recirculating delay line."

Appl. Opt. 25(12): 1879-1881; 1986 June 15.

11
TEST

Figure 1. Experimental setup for measurement of group index with the

asymmetric scanning Michelson interferometer. The cat's

eye reflector is used in the test arm only to facilitate

alignment of the test fiber in the vacuum chuck.

12
TEST

FIBER

\

Figure 2. Typical interf erograms (B) and (C) are generated from

Fresnel reflections at the two ends of the fiber sample.

The interf erogram at (A) is due to the reflection from the

launch fiber and is not important in the present context.

13
Figure 3. Experimental setup for measurement of time delay in the

SRF. The electronic delay in the digital delay generator

is made equal to the optical delay in the fiber.

14
Figure 4. Profile of the optical pulse as displayed on the

oscilloscope shown in figure 3.

15
NBS-1 1 4 A ihe V. 2-801 U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO. NBSIR 88-3091

2. Performing Organ. Report No. 3. Publication Date

July 1988

4 . TITLE AND SUBTITLE

Group Index and Time Delay Measurements of a Standard Reference Fiber

5. AUTHOR(S)

B. L. Danielson and C. D. Whittenberg

6. PERFORMING ORGANIZATION (If joint or other than NBS, see in struction s)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9.

SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

Department of the Navy

Naval Weapons Station/Seal Beach

Corona, California 91720-5000

10.

SUPPLEMENTARY NOTES

Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bi bliography or literature survey, mention it here)

We describe measurement techniques for establishing a standard reference fiber

with well characterized group index and time or group delay. Evaluation of an interferometric method indicates that fiber group index can be determined with

a total estimated uncertainty of about 0.03 percent in small samples. Group delay

of the reference fiber was measured with an overall uncertainty less than

0.004 percent in a 7 km waveguide. We discuss the application of a standard

reference fiber to calibration of the distance measurement accuracy of an optical

time-domain reflectometer (0TDR).

12.

KEY WORDS (Six to twelve entries; a Iph abeti cal order; capitalize only proper names; and separate key words by semicolon s) calibration procedures; optical delay line; optical fiber group index; optical fiber

group velocity; optical time-domain reflectometer; OTDR; standard reference fiber;

standard test fiber

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