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NATL INST. OF STAND & TECH

AlllDS Tfl5fl75

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z NBS TECHNICAL NOTE 1050

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

Backscatter

Signature

Simulations
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Backscatter Signature Simulations

NatfonH Sur««u of standards

Ubrary. £^j Atfjnin. B(dg.

MAR 1 1982

ClUoo

\\h^ ^cJa^xO.c,'x<J- \noi c^

B.L. Danielson

Electromagnetic Technology Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

Issued December 1981

Sponsored by:

Communications Systems Center

U.S. Army Communications R&D Command

Fort Monmouth, New Jersey 07703

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Director
National Bureau of Standards Technical Note 1050

Nat. Bur. Stand. (U.S.), Tech. Note 1050, 100 pages (December 1981)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1981
CONTENTS

Page

1. Introduction 1

2. OTDR Signatures: A Modeling of the Backscatter Process 2 2.1 Theoretical Background 2 2.2 Di screte Model 3 2.3 Display Techniques 3

3. Signature Examples 4

3.1 Point Defects: Effect of Probe Pulse Width and Shape 5 3.1.1 Scatter-Like Point Defects 5 3.1.2 Absorption-Like Point Defects 6

3.1.3 Composite Point Defects 7 3.1.4 Discussion of Point Defect Signatures 9

3 .

2

Extended Defects 10

3.3 Symmetry and Length-Dependent Effects 11

3.4 DiVita Technique 13

3.5 Wavelength Dependence 14

3.6 Noise Considerations 14

3.7 Point Defects in Close Proximity: The Resolution Question 15

3.7.1 Resolution of Scatter-Like Defects 16

3.7.2 Resolution of Absorption-Like Defects 18

3.7.3 Resolution of Composite Defects 19

3.7.4 Conclusions and Recomnendations 20

4. Deconvolution 20

5. References 22
Table 1. List of Symbols, Nomenclature, and Units

Symbol Nomenclature Units

A Rayleigh scattering coefficient m"^ijni'*'^ B Absorption coefficient m"-'- C(X) Wavelength dependent absorption m"^

D Smallest resolvable defect

separation in time s ERW Equivalent rectangular width s

F Capture fraction

FWHM Full width half maximum s

G]^ Actual splice loss in

forward direction dB

Go Actual splice loss in

backward direction d6

i Detector current A

J /^

k Number of points in model

L Smallest resolvable defect

separation in distance m

log Logarithm to base 10

Mj^ Measured backscatter loss

in forward direction db

M2 Measured backscatter loss

in backward direction dB

<M> Mean measured splice loss dB

n Summation index

NA Numerical aperture

P(N) Probability of occurrence of

amplitude N SNR Signal-to-noise ratio

t Time s

V Group velocity ms"-*-

W. Pulse width s X Distance along a fiber m

a^ Rayleigh scattering loss

coefficient m"

aj Total loss coefficient m"-"- AT Time delay s

9 Half vertex angle of fiber

output radiation

X Wavelength um

a RMS width of a Gaussian pulse s * Power W « Angular frequency s"^
Backscatter Signature Simulations

B. L. Danielson*

National Bureau of Standards

Boulder, Colorado 80303

This report presents a collection of computer-generated backscatter signatures which represent realistic replicas of signals that can be encountered in

optical time-domain reflectometer (OTDR) systems. Emphasis is placed on illustrating the appearance of backscatter signatures originating from localized and

distributed imperfections which are superimposed on an otherwise uniform optical

fiber. The details of these signatures are shown to be a function of the particular type of fiber perturbation, experimental parameters, and data reduction

methods. This compilation of simulated responses is intended to facilitate the

correct interpretation of OTDR signals as well as to point out sources of error which can arise in the characterization of optical fibers using backscatter

techniques.

Key words: backscattering; backscatter signatures; optical fiber scattering;

optical time-domain reflectometer; OTDR.

1. Introduction

As early as 1972, Kapron, Maurer, and Teter [1] pointed out the possibilities of using

the Rayleigh backscattering in optical fibers for fiber characterization purposes. It remained to Barnoski and Jensen [2], in 1976, to implement these ideas in a practical

device. The result is the optical time-domain reflectometer which has gained acceptance as one of the most versatile instruments used in optical fiber metrology. Here a short pulse

of optical radiation is launched into the fiber and, as the pulse propagates along the

length of the waveguide, light is continuously scattered from variations in the index of

refraction as well as flaws and other perturbations. A small amount of this light is

trapped as guided radiation in the backward direction. This light signal, as a function of

time, is characteristic of the fiber under test and is referred to as the backscatter

signature, from which much useful information may be extracted. In a recent review article,

Rourke [3] has enumerated some of the many applications areas in which the backscatter

method has demonstrated its utility. The most important applications are in fiber parameter

estimation, principally with regard to length, defect location and identification,

attenuation, core diameter fluctuations, splice loss, and, to a lesser extent, pulse

broadening. Probably the most significant advantages of this measurement technique are that

it is nondestructive and can be used with only one end of the fiber accessible. However,

OTDR methods are not without their limitations. Occasionally, the interpretation of the

structure observed on the signatures is not completely straightforward, or even unambiguous. In addition, the accuracy and reliabilty of backscatter data often suffers in

comparison with other measurement techniques.

Electromagnetic Technology Division, National Engineering Laboratory.
This report presents a number of simulated signatures which have been generated on a digital computer. They are intended to represent the backscatter response of a number of

types of defects and irregularities which can occur in fiber waveguides. There are two main

motivations for presenting these detailed simulations. The first arises from a hope that

the examples will aid in interpreting signatures from fiber anomalies. A second reason has

to do with the fact that OTDR methods are an attractive candidate for use in standard test

procedures, acceptance testing, and quality control applications. Since the qualitative as well as quantitative nature of the signature depends on the details of the experimental

conditions and display techniques, these examples may help minimize parameter measurement

errors and possibly promote a consensus concerning the most desirable format for OTDR data

in specific applications areas.

2. OTDR Signatures: A Modeling of the Backscatter Process

2.1 Theoretical Background

Consider a fiber whose transmission properties, for a given set of launch conditions,

are constant (i.e., not a function of length) and the same in both forward and reverse

directions. Under these conditions, the OTDR signal *(t) at the detector, and as a function

of time, can be shown to be [4,5]

$(t) *' = 0.5 $ogstg W V a F exp [-a.v t], (2-1)

where * is the peak power injected into the fiber, W is the time duration of that probe

pulse, V its group velocity, a^ the Rayleigh scattering coefficient, F the capture fraction, and o^ the total attenuation coefficient. This backscatter response is due largely to

Rayleigh scattering^ which has an angular dependence of (1+cos^e), with 9 the angle of

scattering relative to the fiber axis, and a wavelength dependence of X"^. This type of

scattering originates in dopant-concentration fluctuations and index of refraction variations which occur on a scale small compared to a wavelength. For most fibers encountered in

practice, in addition to the background signal given in eq (2-1), there will be backscatter

contributions due to reflection, scattering and/or absorption arising from imperfections in our assumed uniform fiber. In the following text, many examples will be seen of the influence of these defects and nonuniformities on the backscatter response. The specific nature

of the signatures due to non-Rayleigh components is a function of many variables involving

fiber parameters and experimental conditions. These include the type of fiber perturbation

and its location, wavelength of operation, probe pulse shape and duration, and output

graphics, among others.

^Brillouin scattering has the same angular and wavelength dependence as Rayleigh scattering,

but ony about 13 percent of its magnitude in optical fibers [6]. Raman scattering is

negligible. Nonlinear processes [7] can be a concern, especially in single-mode fibers, but

will not be considered here.
Some of the signatures included in this report are nothing more than the convolution of

the impulse response of the fiber h(t) with the probe pulse shape f(t). The backscatter

response in this case is

oo *(t) = / f(t-T)h(T)dT). (2-2)

In writing this equation, we assume that the fiber-defect system is linear, shift-invariant,

and causal [8].

2.2 Discrete Model

Computer codes have been developed for this work which generate a simulated backscatter

signal for sample fibers possessing many different types of perturbations. The phenomenological model on which these codes are based is applicable to multimode fibers, and has been

described in detail elsewhere [9]. For the present application, we have divided the fiber

into 512 elements, each of which is characterized by six bulk parameters: forward and reverse absorption loss, forward and reverse scattering loss, and forward and reverse capture fractions. Kor a discrete model such as this, the appropriate approximation to a delta

function probe pulse is the "delta sequence" which is one point in time duration and of unit

amplitude. The corresponding analogy to the backscatter impulse response is referred to as the delta response. In this report we will, however, make no distinction between impulse

response and delta response since the signatures will differ in an obvious way.

In all of the cases considered here, we have ignored pulse broadening due to fiber

dispersion. This is a good approximation for graded-index fibers and the pulse durations

encountered in most OTDR systems.

The discrete analogy to the convolution integral given in eq (2-2) is

$(n) =

I f(n-k) h(k), (2-3)

k=0

where n and k refer to points in the range to 511.

2.3 Display Techniques

There are three main types of graphic displays used in signature analysis. The ordinate of the X-Y plot can be a variable proportional to the (1) direct detector output, (2)

logarithm of the detector output, or (3) differential logarithm of the detector output. The

abscissa can be either time or distance along the fiber axis. In this report we will choose

time as the appropriate variable as this is the experimental observable. The linear display, $(t) versus t, requires the least signal analysis and may be observed directly on an oscilloscope. Semi logarithmic plots, 10 log [*(t)/${0)] simplify the estimation of fiber

attenuation and make obvious losses which are length dependent. This technique does require

additional experimental equipment which, in the analog case at least, must be calibrated.

The differential method, also referred to as the "two-point" or "two-channel" technique, was originated by Conduit et al . [10,11,12]. This approach can yield the local attenuation
directly and, when used in data acquisition, has several experimental advantages, including

insensitivity to pulse-to-pulse laser power variations and long term drifts. It also

requires a minicomputer for data analysis. The quantity which is plotted as a function of

time, 10 log['l'(t-|^)/$(tj^-AT)] is proportional to the differential loss between points corresponding to times t-|^ and t-j^-AT, where AT is an adjustable, but constant, time delay. In a digital sense, this reduces to the derivative of the logarithm if the delay AT is taken to

be small compared with system resolution. In the differential signals to follow we have

taken the delay AT to be positive so that increasing loss appears as a negative-going

signal. This convention was adopted to facilitate comparisons with the semi logarithmic

display. It should be noted that this differs slightly from the definitions given by

Conduit et al . Also, those authors chose AT to maximize the signal-to-noise ratio (SNR) in

their data acquisition system. However, in systems where the data are processed by a digital computer, the final display may be chosen independently of the format of the input

data. It may be desirable here to select AT for the most convenient and edifying output

graphics. We will examine some of these possibilities later.

3. Signature Examples

In this section we will illustrate the dependence of some backscatter signatures on various fiber properties as well as experimental conditions and graphic displays. The fiber

properties include length-dependent Rayleigh scattering, and the presence of fiber defects

both localized and distributed over lengths comparable to the physical length of the probe

pulse. Among the experimental parameters we will give examples of the effect of probe pulse

width and shape, wavelength, and noise.

For purposes of illustration we will consider three types of probe pulse shape. The

first is the impulse response (delta response) mentioned earlier. The second is the rec- tangular probe pulse of unit height and duration W. This type of pulse demonstrates the

effect of a fast leading edge on the backscatter response. The third type of pulse is

Gaussian shaped, also with unity maximum amplitude and a duration specified in terms of an equivalent rectangular width (ERW). The ERW of any pulse g(t) is defined by the equation

""7 g(t) dt ^ max

where [g(t)]j^g^ is the maximum value of g(t) and is presumed to be single-valued. If the

pulse is normalized so that its maximum amplitude is one, then ERW=W, and the energy (area)

is the same as the corresponding rectangular pulse of unit amplitude. This convention was chosen since, from eq (2-1), the magnitude of the backscatter signal is, to a first approximation, proportional to W. If g(t) is assumed to be Gaussian, then W is approximately a factor of 2.5 times the rms value (sigma). This is illustrated in figure 3-1. The Gaussian

pulse has an ERW of W=51 time units, and a sigma of 51/2.5 time units. The energy is the

same for both pulses.
3.1 Point Defects: Effect of Probe Pulse Width and Shape

We will now consider the evolution of some point-defect signatures for the probe pulses

enumerated above.

3.1.1 Scatter-Like Point Defects

A scatter-like defect is defined here to be a perturbation whose impulse response shows

an increase in backscatter signal, due to scattering or a reflection, which is greater than

the subsequent signal decrease [13]. Changes in the fibers' capture fraction (numerical

aperture or index of refraction) can also produce a scatter-like response. Since scatter is

a form of loss, there will always be an absorption component, however small, associated with

this type of defect. An air line in the fiber, due to a bubble in the preform, may give

rise to this type of signature. Occasionally, splices, connectors, and couplers may exhibit

this type of response also. Figures 3-2 to 3-16 illustrate a uniform fiber possessing a single scattering defect whose signature is determined by various combinations of probe

pulse width and shape. In all cases, the ordinate gives a realistic indication of the

magnitude of the backscatter response relative to the impulse response. Variations in the

signature are given as follows:

1. Figure 3-2. The impulse response for a scatter-like imperfection. Logarithmic display. This signature is the archetype for the entire sequence in this section.

2. Figure 3-3. Scatter-like imperfection; Gaussian probe pulse; equivalent rectangular

width 5 time units. Logarithmic display.

3. Figure 3-4. Scatter-like imperfection; Gaussian probe pulse; equivalent rectangular

width 10 time units. Logarithmic display.

4. Figure 3-5. Scatter-like imperfection; Gaussian probe pulse; equivalent rectangular

width 20 time units. Logarithmic display.

5. Figure 3-6. Scatter-like imperfection; Gaussian probe pulse; equivalent rectangular

width 30 time units. Logarithmic display.

6. Figure 3-7. Scatter-like imperfection; Gaussian probe pulse; equivalent rectangular

width 40 time units. Logarithmic display.

7. Figure 3-8. Scatter-like imperfection; Gaussian probe pulse; equivalent rectangular

width 50 time units. Logarithmic display.

8. Figure 3-9. Scatter-like imperfection; Gaussian probe pulse; equivalent rectangular

width 100 time units. Logarithmic display.

9. Figure 3-10. Scatter-like imperfection; rectangular probe pulse of width 5 time

units. Logarithmic display.

10. Figure 3-11. Scatter-like imperfection; rectangular probe pulse of width 10 time

units. Logarithmic display.

11. Figure 3-12. Scatter-like imperfection; rectangular probe pulse of width 20 time

units. Logarithmic display.

12. Figure 3-13. Scatter-like imperfection; rectangular probe pulse of width 30 time

units. Logarithmic display.
13. Figure 3-14. Scatter-like imperfection; rectangular probe pulse of width 40 time

units. Logarithmic display.

14. Figure 3-15. Scatter-like imperfection; rectangular probe pulse of width 50 time

units. Logarithmic display.

15. Figure 3-16. Scatter-like imperfection; rectangular probe pulse of width 100 time

units. Logarithmic display.

3.1.2 Absorption-Like Point Defects

An absorption-like defect is defined for our purposes to be a perturbation whose

impulse response shows a decrease in backscatter signal which is greater in absolute magnitude than any preceding associated scattering feature [13]. Most imperfections fall under

this classification. Included particles, splices, couplers, microbends, macrobends, and

various scattering processes which scatter radiation largely in the forward direction can produce absorption-like signatures. Figures 3-17 to 3-31 illustrate a uniform fiber possessing a single absorption defect whose signature is determined by various combinations of

probe pulse width and shape. As before, the ordinate gives a realistic indication of the

magnitude of the backscatter response relative to the impulse response. Variations in the

signature are given as follows:

Figure 3-17. The impulse response for an absorption-like imperfection. Logarithmic

display. This signature is the archetype for the entire sequence in this section.

Figure 3-18. Absorption-like imperfection

tangular width 5 time units. Logarithmic display

3. Figure 3-19. Absorption-like imperfection

tangular width 10 time units. Logarithmic

4. Figure 3-20. Absorption-like imperfection

tangular width 20 time units. Logarithmic

5. Figure 3-21. Absorption-like imperfection

tangular width 30 time units. Logarithmic

6. Figure 3-22. Absorption-like imperfection

tangular width 40 time units. Logarithmic

7. Figure 3-23. Absorption-like imperfection

tangular width 50 time units. Logarithmic

8. Figure 3-24. Absorption-like imperfection

tangular width 100 time units. Logarithmic display

9. Figure 3-25. Absorption-like imperfection

units.

10. Figure 3-26. Absorption-like imperfection

units. Logarithmic display.

11. Figure 3-27. Absorption-like imperfection

units. Logarithmic display.

Gaussian probe pulse; equivalent recGaussian probe pulse; equivalent rec- display.

Gaussian probe pulse; equivalent rec- display.

Gaussian probe pulse; equivalent rec- display.

Gaussian probe pulse; equivalent rec- display.

Gaussian probe pulse; equivalent rec- display.

Gaussian probe pulse; equivalent recrectangular probe pulse of width 5 time

rectangular probe pulse of width 10 time

rectangular probe pulse of width 20 time
12. Figure 3-28. Absorption-like imperfection; rectangular probe pulse of width 30 time

units. Logarithmic display.

13. Figure 3-29. Absorption-like imperfection; rectangular probe pulse of width 40 time

units. Logarithmic display.

14. Figure 3-30. Absorption-like imperfection; rectangular probe pulse of width 50 time

units. Logarithmic display.

15. Figure 3-31. Absorption-like imperfection; rectangular probe pulse of width 100 time

units. Logarithmic display.

3.1.3 Composite Point Defects

A composite defect is defined as a perturbation whose impulse response .shows features

which are both scatter-like and absorption-like in nature, that is, they exhibit a pronounced increase in backscatter signal followed by a pronounced decrease in signal level.

As long as the defects produce small power losses, the resulting signature will be, to a good approximation in our model, an additive superposition of the features due to the individual scatter and absorption components. The composite-type defect therefore produces a signature whose features can be inferred from the examples detailed in the previous two

sections. We will give an example of such an imperfection in the following series. Here we simulate a fault which has a rather large scatter cross section, but associated with this is

a much smaller capture fraction than shown in section 3.1.1. This could happen, for

example, at a flaw which scatters radiation largely in the forward direction. Variations in

the composite signature are given as follows:

1. Figure 3-32. The impulse response for a composite imperfection. Logarithmic display.

This signature is the archetype for the entire sequence in this section.

2. Figure 3-33. Composite imperfection; Gaussian probe pulse; equivalent rectangular

width 5 time units. Logarithmic display.

3. Figure 3-34. Composite imperfection; Gaussian probe pulse; equivalent rectangular

width 10 time units. Logarithmic display.

4. Figure 3-35. Composite imperfection; Gaussian probe pulse; equivalent rectangular

width 20 time units. Logarithmic display.

5. Figure 3-36. Composite imperfection; Gaussian probe pulse; equivalent rectangular

width 30 time units. Logarithmic display.

6. Figure 3-37. Composite imperfection; Gaussian probe pulse; equivalent rectangular

width 40 time units. Logarithmic display.

7. Figure 3-38. Composite imperfection; Gaussian probe pulse; equivalent rectangular

width 50 time units. Logarithmic display.

8. Figure 3-39. Composite imperfection; Gaussian probe pulse; equivalent rectangular

width 100 time units. Logarithmic display.

9. Figure 3-40. Composite imperfection; rectangular probe pulse of width 5 time units.

10. Figure 3-41. Composite imperfection; rectangular probe pulse of width 10 time units.

Logarithmic display.
11. Figure 3-42. Composite imperfection; rectangular probe pulse of width 20 time units.

Logarithmic display.

12. Figure 3-43. Composite imperfection; rectangular probe pulse of width 30 time units.

Logarithmic display.

13. Figure 3-44. Composite imperfection; rectangular probe pulse of width 40 time units.

Logarithmic display.

14. Figure 3-45. Composite imperfection; rectangular probe pulse of width 50 time units.

Logarithmic display.

15. Figure 3-46. Composite imperfection; rectangular probe pulse of width 100 time units.

Logarithmic display.

Figures 3-47 to 3-48 illustrate the effect of varying the delay AT in the differential

display 10 log [*(t2^)/0(t-]^-AT)]. We have chosen the response of figure 3-10 as the archetype for this series (Gaussian probe pulse of equivalent rectangular width 10 time units).

Changing the time delay AT from one time unit to 100 time units generates the following

sequence:

1. Figure 3-47. Composite imperfection; Gaussian probe pulse; equivalent rectangular

width 10 time units; delay 1 time unit. Differential display.

2. Figure 3-48. Composite imperfection; Gaussian probe pulse; equivalent rectangular

width 10 time units; delay 2 time units. Differential display.

3. Figure 3-49. Composite imperfection; Gaussian probe pulse; equivalent rectangular

width 10 time units; delay 5 time units. Differential display.

4. Figure 3-50. Composite imperfection; Gaussian probe pulse; equivalent rectangular

width 10 time units; delay 10 time units. Differential display.

5. Figure 3-51. Composite imperfection; Gaussian probe pulse; equivalent rectangular

width 10 time units; delay 15 time units. Differential display.

6. Figure 3-52. Composite imperfection; Gaussian probe pulse; equivalent rectangular

width 10 time units; delay 20 time units. Differential display.

7. Figure 3-53. Composite imperfection; Gaussian probe pulse; equivalent rectangular

width 10 time units; delay 25 time units. Differential display.

8. Figure 3-54. Composite imperfection; Gaussian probe pulse; equivalent rectangular

width 10 time units; delay 30 time units. Differential display.

9. Figure 3-55. Composite imperfection; Gaussian probe pulse; equivalent rectangular

width 10 time units; delay 35 time units. Differential display.

10. Figure 3-56. Composite imperfection; Gaussian probe pulse equivalent rectangular width

10 time units; delay 40 time units. Differential display.

11. Figure 3-57. Composite imperfection; Gaussian probe pulse equivalent rectangular width

20 time units; delay 50 time units. Differential display.

12. Figure 3-58. Composite imperfection; Gaussian probe pulse equivalent rectangular width

30 time units; delay 60 time units. Differential display.
13. Figure 3-59. Composite imperfection; Gaussian probe pulse equivalent rectangular width

40 time units; delay 100 time units. Differential display.

3.1.4 Discussion of Point Defect Signatures

From a perusal of the foregoing signature examples we may draw the following conclusions:

1. The magnitude of the distributed Rayleigh component is approximately proportional to

the energy in the probe pulse. This may also be seen from eq (2-1). In our examples

the probe pulse always had a maximum amplitude of one, so that the backscatter signal

is approximately proportional to the ERW.

2. The magnitudes of the scatter-like signatures do not increase with probe pulse duration

the way the Rayleigh signature does; rather, this defect structure tends to broaden out

and the contrast becomes washed-out. This wash-out phenomenon is due to the fundamentally different reflection properties of discrete and distributed systems when irradiated with finite-width optical pulses. Reflection from localized regions returns a basically unaltered pulse in the backward direction. Reflection from extended regions

involves a convolution process of the probe pulse with the scattering medium. Therefore, scatter-like signatures will have a strong functional dependence on the probe

pulse ERW.

3. Absorption-like defects provide a signature from which the loss (determined from the

step signal decrease) can always be inferred even at probe pulse widths that completely

wash-out a scatter-like signature under similar conditions. The main effect of increasing the probe pulse width in this case is to cause a relative decrease in the

higher frequency components of the signature.

4. There are always transient effects at t=0, at the end of the fiber and at discontinuities, which are apparent signatures from finite width pulses. These transients appear

over time intervals approximately equal to the probe pulse duration. Problems in

signature interpretation can occur if the defect response occurs in this nonequilibrium

region.

5. Another transient effect which appears with increasing probe pulse duration is the

apparent time-shift in the appearance of the most prominant defect signature features.

This is due to the fact that the time scale in our examples is "triggered" at the 10

percent amplitude of the probe pulse. With the rectangular input pulse the location of

the defect is still given correctly by the leading edge of the defect signature.

6. The precision associated with the visual location of a defect is determined more by the

rise time of the probe pulse than its duration.

7. Signatures arising from point defects will have recognizable time durations approximately the same as the input pulse.

8. When the log differential display is used, a convenient criterion for maximizing the

signal while avoiding signature ambiguities is to set the probe pulse ERW = Delay.
That is, W = AT. This produces a signature which closely resembles the derivative of

the semi logarithmic plots.

3.2 Extended Defects

If a fiber possesses regions of anomalous properties which occur on a length scale less

than or comparable to the physical length of the probe pulse in the fiber, the resulting

backscatter response will differ in a qualitative way from that due to point defects. Here,

the time dependence of the returned signal is determined by a convolution integral involving

the probe pulse and the scattering region. In general, the backscatter signature will be

broadened when compared with the input probe pulse duration. As an example of this, we consider a distributed scattering region centered at x^ in the fiber, and extending over a length surrounding x^ in a roll -off characteristic of a Gaussian function with an rms width

(sigma) equal to a^. That is, the backscatter response from a delta function input pulse is

h(t) = exp[-(t-tQ)^/2a^2], (3-2)

where

o^ = 2a^/Vg (3-3)

and

to = 2x„/Vg, (3-4)

with V the group velocity of a pulse in the fiber. If now the probe pulse is changed to a Gaussian pulse itself, or

f(t) = exp[-t^/2a2^], (3-5)

then the resulting backscatter response can be shown to be yet another Gaussian-shaped pulse

proportional to

$(t) = exp [-(t-tQ)2/2a32], (3-6)

whose width is determined from the relation

/ 2 ^ 2A/2 ,

7X 03 = (cJj^ + 0^ }

. 3-7)

As a further example, consider a region Ax of a fiber with a high, but constant, scattering loss, the fiber itself having negligible loss. The impulse response from this type

of imperfection will appear as in figure 3-60, where 2AX/v = 100 time units. If now the

probe pulse is rectangular in shape, the signature will resemble a truncated pyramid, as in

10
figure 3-61, with increased amplitude as expected. Note that the backscattered pulse width

measured at the full width half maximim (FWHM) will be the same as that of the impulse

response. This is true for all proDe pulse widths W < 2AX/v . In figure 3-62 the probe

pulse is equal in duration to the impulse response (100 time units). For probe pulses of

duration greater than the impulse response we again get the truncated-pyramid shape as in

figure 3-63. Here W = 150 time units. The measured FWHM of the signature for W < 2 AX/vg

will be equal to W.

3.3 Symmetry and Length-Dependent Effects

It has been shown elsewhere [9] that errors are introduced in backscatter-derived

attenuation determinations, and signature interpretations can become troublesome, if either

of two types of fiber anomalies occur. One source of error originates in distributed fiber

properties (scattering, absorption, numerical aperture, diameter) which are a function of

length; the second relates to the lack of fiber symmetry with respect to the forward and reverse directions of propagation of radiation. We will refer to a fiber as uniform if its

loss and/or transmission properties denoted by a^(jt) (appropriate to the mode volume under

consideration) are invariant to a displacement along the fiber axis t + t' ; i.e., aj(jt) = a^()t + ^'). In a similar vein, reciprocity is used in the sense of invariance to reversal

of the propagation direction, i.e., a^(jt) = a^(-)t). These properties may be intrinsic to

the fiber, such as numerical aperture changes, or may be due to mode coupling effects occuring in multimode fibers in either the probe pulse or the backscattered radiation. Mode

conversion in conjunction with differential modal attenuation causes the radiation to propagate in an environment which is length dependent and possibly nonreciprocal as well. Figure

3-64 illustrates several types of nonuniform and nonreciprocal behavior which can occur in

fibers either on a local (at splices or couplers) or distributed basis. Figures 3-64 (a),

(b), and (c) represent splices between dissimilar fibers. Figure 3-64 (d) illustrates

schematically the case where the forward travelling probe pulse is launched into a set of

low order modes. These modes can, and often do, have lower average losses than the higher

order modes. The Rayleigh backscatter, on the other hand, is approximately isotropic, and

this excites a different set of modes including the higher order, more lossy, modes represented by the ray B in the figure. The average loss in the two directions can be significantly different, as much as 1 dB/km with some fibers. We will now give several examples of

signature distortion when nonuniform and nonreciprocal fiber properties are encountered.

The series of figures 3-65 to 3-67 illustrate the condition where the capture fraction

F increases toward the remote end by 50 percent (this is equivalent to a 22 percent increase

in numerical aperture). Figure 3-65 shows the capture fraction dependence on fiber length

(in arbitrary units). The resulting signature appears in figure 3-66. A slight negative

curvature^ can be detected in the logarithmic plot. This curvature is more apparent in the

plot of residuals in figure 3-66. The residuals are taken to be

^The usual definition of positive curvature implies that as one moves along the curve toward

larger times, the path tends to move generally in a counterclockwise direction.

11
Residual (dB) = Actual Attenuation (dB) - Predicted Attenuation (dB) (3-8)

where the predicted attenuation is given by a linear least-squares fit. When the same fiber

is reversed end for end, the resulting signature and residuals are illustrated in figures

3-68 and 3-69, respectively. Rather surprisingly, the curvature of both figures is the

same. The (neasured attenuation is different, as expected [9].

A similar series for scattering loss is given in figures 3-70 to 3-74. Figure 3-70

shows the functional dependence of scattering loss in the forward direction; the scattering

loss increases 20 percent from one end to the other. Figure 3-71 shows the resulting signature and figure 3-72 the corresponding residuals. Figures 3-73 and 3-74 illustrate the

changes observed when the fiber is reversed end for end. The curvature undergoes a sign

change in contrast to the previous example (figures 3-68 and 3-69).

The final series represents the case for absorption loss, figures 3-75 to 3-79. Figure

3-75 shows the functional dependence of absorption loss in the forward direction; the absorption loss increases 50 percent from one end to the other. Figure 3-76 shows the resulting signature and figure 3-77 the residuals. Figures 3-78 and 3-79 illustrate the changes

observed when the fiber is reversed end for end.

It can be seen that, in all cases, the sign of the curvature of the semilog plot and

the residuals is the same. However, the interpretation of this curvature is ambiguous. A

negative curvature may be due to either scattering loss or absorption loss increasing toward

the remote end, or to numerical aperture changes. The positive curvature may be identified

with either absorption loss or scattering loss decreasing toward the far end.

Splices and couplers in fiber links are probably the most important examples of situations which can exhibit symmetry and length-dependent anomalies. An extreme example of an unsymmetric splice is displayed in figures 3-80 and 3-81, representing the signature from

opposite ends of the fiber. In figure 3-80, the near-end fiber (#1, represented by t < 200)

has 50 percent greater scattering loss than the far-end fiber (#2, t > 200). In this case,

there is zero loss at the splice but nevertheless the signature exhibits the normal type

step response indicating a loss. On reversing the fiber end-for-end the signature in figure

3-81 results. There is apparent "gain" at the splice. Several authors have analyzed problems of this sort [9,14-17], and also effects of this nature have been observed experimentally [17,18]. It can be shown that the measured splice loss Mi (determined from the magnitude of the step in the backscatter signature) in the forward direction is

M^ = -^-^ + 5 log (^^) (dB) , (3-9)

2 a^2''2

where Gi and Go are the actual splice losses (in dB) in the forward and reverse directions

respectively, and a^ represents the scattering loss and F the capture fractions of the two

fibers 1 and 2, as before. The corresponding measured splice loss M2 from the opposite end

Is

12
M2 = -^—^ - 5 log(-^^) (dB), (3-10)

It can be seen that the mean measured splice loss from both ends <M> is

<M> = _-L_£_ = _J_£_ (dB), (3-11)

2 2

i.e., the correct value of the splice loss averaged in both directions. Only round-trip

splice loss can be determined exactly using the backscatter technique. In almost all cases,

what is really desired is an estimate of the one-way splice loss. In this case, we can say

with certainty only that the one-way splice loss G-j^ lies in the region < G]^ < 2 <M>.

Estimating Gi by identifying its value with <M> therefore can involve a potential error of

magnitude ± <M> (100 percent error). It is not possible to obtain bounded estimates of G-j^ from backscatter measurements made from one end of the fiber only, unless the quantity

^°'sl'^l''°'s2'^2^ is known. However, if necessary, this quantity may be determined from independent measurements on both fibers prior to the splicing operation [17]. With

5^og{a^l'F^/a^2'^2) ^ known quantity, we may then estimate Gj^ when only one end of the spliced

fiber is available. This can be done by using eq (3-9) and assuming Q-^=G2- The maximum

error involved in estimating Fj^ in this way will be ±l^i-S}oq{a^-^?-^/a^2^2)^-

3.4 DiVita Technique

In the previous section it was shown that making backscatter measurements from both

ends of the fiber can eliminate certain types of errors in signature interpretation. DiVita

and Rossi [19] have generalized this approach to provide a means for separating the distributed loss of the fiber from the backscatter contributions due to any imperfections. We

will give an example of the power of this approach. The backscatter signals from either end

of the fiber are taken to be w^(x) and W|j(x). In both cases, the distance x is measured

from the same end face. The separation of the distributed loss from local perturbations can

be made by defining the following two quantities:

I(x) = (w^(x) Wjj(x))^/2 = const. F(x) a^(x) (3-12)

D(x) = (w^(x)/Wjj(x))^^^ = const. exp{-2 / a^(x')dx'}. (3-13)

Here the capture fraction F(x) and scattering coefficient a5(x) are functions of the distance from the fiber end. The power decay, from which the attenuation is obtained, is given

by D(x) and local perturbations, as a function of distance, by I(x). Ambiguities in signature interpretation are thus removed at the expense of requiring measurements from both ends

of the fiber.

As an example of this technique, we apply eqs (3-12) and (3-13) to the situation demonstrated previously in figures 3-80 and 3-81. The resulting log power loss D(t) is shown in

13
figure 3-82. This shows clearly that there is no loss at the splice and that the attenuation of both fibers is different. The attenuation value of each segment may be inferred

from the log scale though this has not been expressed in dB here. The perturbation parameter I(t) in figure 3-83 also shows the dependence of the (in this case) scattering coefficients ttg, but the vertical scale is arbitrary.

3.5 Wavelength Dependence

A convenient expression for resolving the total background loss of a fiber into its

component parts is given by [20]

a(x) =-|+ B + Ic.(X). (3-14)

A

In this expression, a(X) is the total loss at wavelength X, A is the Rayleigh scattering

coefficient, B is the excess loss term having no wavelength dependence, and C^(X) is the

i'th contribution to a wavelength dependent absorption. Absorption due to OH radicals is

usually the most important of these. Curve fitting the attenuation of many sample fibers to

eq (3-14) has demonstrated that Rayleigh scattering is the dominant loss term at 850 nm, even in fairly high loss fibers. On the other hand, many localized imperfections will have

defect signatures that are largely independent of wavelength. Also, backscatter structure

due to diameter fluctuations appears to be nearly constant [10]. From eqs (2-1) and (3-14)

it is apparent that the magnitude of the background Rayleigh signature will vary as the

inverse fourth power of the wavelength.^ For this reason, the qualitative nature of most

backscatter signatures containing localized defects will change with wavelength in a predictable way. Two examples are shown in figures 3-84 and 3-85. These correspond to fibers

whose loss consists entirely of Rayleigh scattering and whose composite defect is wavelength

independent. The ordinate in both cases indicates relative scattering levels for wavelengths of 800 and 900 nm. It can be seen that the t=0 scattering level is higher in the

800 nm case by a factor of (800/900)"^ or about 2 dB, but the slope at t = is greater.

Also, the features of the defect signature are altered somewhat even though the defect

parameters are unchanged.

3.6 Noise Considerations

Up to this point we have considered the effect that various fiber perturbations can have on the backscatter response of a uniform fiber. Experimental influences incidental to

the data acquisition process may also cause distortions in the backscatter signature. We

will consider one example of this.

The major limitation of OTDR techniques is the limited dynamic range over which adequate SNR may be obtained. The fact that backscatter signals are inherently very small**

"^he backscatte'r levels will also depend on the capture fraction F which is proportional to

the square of the fiber's numerical aperture. This quantity is, however, not strongly

dependent on wavelength. See, for example, reference [21].

"A fairly representative backscatter power level is about -50 dB down from the peak power of

the forward propagating probe pulse at the same point in the fiber [13].

14
means that system noise is almost always a concern. Thermal noise, background radiation,

fluctuations in the carrier multiplication process in the avalanche photodiode, and laser

diode power fluctuations can contribute significant amounts of noise in OTDR systems. As an illustration of signature distortion caused by noise, we have modeled a backscatter response

which contains additive Gaussian detector noise. The noise in this case has a dc average

value of zero and the probability P(N) that the amplitude will have a value between N and N+

AN is given by

N+AN 2 P{N) = YT? ^ exp(--^)dn, (3-15)

o {2ti) ' N 2a

n n where Op is the rms noise current amplitude. The amplitudes in eq (3-15) are determined by

Monte-Carlo methods. For our purposes, the electrical SNR can be defined to be

1 SNR = 20 log (—) (dB)

.

(3-16)

o

n

Here i'^ is the detector signal current equal in magnitude to the optical backscatter power.

Figure 3-86 indicates the appearance of a segment of the noisy backscatter signal with a SNR

of 10 at the midpoint of the scan. The same data are presented in figure 3-87 on a semilogarithmic plot. It is clear from the display that the log scale tends to skew the average

values toward higher loss values. That is, logarithmic scales are nonlinear, and positivegoing noise excursions do not affect the signature to the same extent as corresponding

negative-going excursions. A least-squares fit or other type of averaging in the log space

will therefore contain a bias when low SNRs are encountered. The remedy is simple: Averaging noisy signals in the logarithmic domain should be avoided.

3.7 Point Defects in Close Proximity: The Resolution Question

Backscatter signatures of localized defects in close association present special problems. One is the uncertainty in interpretation of the resultant structure which is often

observed in the signature. Another question which arises is related to the probe pulse

characteristics which are required to completely resolve and identify the defects. As we shall see, the signatures can be rather complex under certain conditions, being a function

of the properties of the defect in question, the magnitude of the backscatter signal generated, as well as the probe pulse width, shape, and type of graphic display.

Although in principle the distributed Rayleigh signature can be separated out from the

contribution of the imperfections, we have usually not pursued that approach here. The

rationale is that, experimentally, one always observes the background and perturbations

together and interpretations must always be made in this type of nexus.

We assume that the resolution is determined exclusively by the probe pulse. That is,

that fiber dispersion is negligible, and the response of the APD and data-processing electronics does not contribute appreciably to the shape of the defect signatures.

15
By resolution we mean the ability of the OTDR system to distinguish between defects

which are in close proximity in the fiber. The smallest spacing between point scatterers,

L, that can just be resolved is usually taken to be [22]

V W

L = -^, (3-17)

2

where, as before, v_ is the group velocity and W the pulse duration of the assumed rectangular probe pulse. ^ More correctly, this is referred to as the "limit of spatial resolution"

rather than "resolution", although often these terms are used interchangeably. In the

following sections we will illustrate the appearance of some signatures from closely spaced

imperfections under excitation by various types of probe pulses. Since the signatures are plotted as a function of time rather than distance, the resolution criterion corresponding

to eq (3-17) is

D = W, (3-18)

where is the temporal spacing of the defects in the impulse response.

3.7.1 Resolution of Scatter-Like Defects

The signatures in figures 3-88 to 3-120 are based on two adjacent point scatterers

separated by ten (arbitrary) time units. These defects occur at t=200 and t=210. Variations in the signature are given as follows:

1. Figure 3-88. The impulse response for two scatter-like imperfections. Logarithmic

display. This signature is the archetype for the entire sequence in this section.

2. Figure 3-89. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 5 time units. Logarithmic display.

3. Figure 3-90. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 9 time units. Logarithmic display.

4. Figure 3-91. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 10 time units. Logarithmic display. This pulse width corresponds to the resolution criterion given in eq (3-17). Comparison with figure 3-90 shows that small

changes in probe pulse width are quite significant in distinguishing these defects.

5. Figure 3-92. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 15 time units. Logarithmic display. The two defects are now completely unresolved. Also there is an apparent shift in location.

6. Figure 3-93. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 20 time units. Logarithmic display.

'^This criterion is also used in radar applications where it is called the "radar resolution

cell" [23].

16
7. Figure 3-94, Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 25 time units. Logarithmic display.

8. Figure 3-95. The impulse response for two scatter-like imperfections. Linear display. Compare with figure 3-98.

9. Figure 3-96. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 5 time units. Linear display. It can be seen in this and the following figures

that there is no great difference in the linear and logarithmic displays, at least for

this demonstration.

10. Figure 3-97. Scatter-like imperfections; Gaussian probe pulse of width 9 time units.

Linear display.

11. Figure 3-98. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 10 time units. Linear display.

12. Figure 3-99. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 15 time units. Linear display.

13. Figure 3-100. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 20 time units. Linear display.

14. Figure 3-101. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 25 time units. Linear display.

15. Figure 3-102. Scatter-like imperfections; rectangular probe pulse of width 5 time

units. Logarithmic display.

16. Figure 3-103. Scatter-like imperfections; rectangular probe pulse of width 9 time

units. Logarithmic display. The defects are still completely resolved.

17. Figure 3-104. Scatter-like imperfections; rectangular probe pulse of width 10 time

units. Logarithmic display. The presence of two defects is observed only with difficulty.

18. Figure 3-105. Scatter-like imperfections; rectangular probe pulse of width 15 time

units. Logarithmic display. Note the structure due to pulse overlap.

19. Figure 3-106. Scatter-like imperfections; rectangular probe pulse of width 20 time

units. Logarithmic display.

20. Figure 3-107. Scatter-like imperfections; rectangular probe pulse of width 25 time

units. Logarithmic display.

21. Figure 3-108. Scatter-like imperfections; rectangular probe pulse of width 5 time

units. Linear display.

22. Figure 3-109. Scatter-like imperfections; rectangular probe pulse of width 9 time

units. Linear display.

23. Figure 3-110. Scatter-like imperfections; rectangular probe pulse of width 10 time

units. Linear display.

24. Figure 3-111. Scatter-like imperfections; rectangular probe pulse of width 15 time

units. Linear display.

25. Figure 3-112. Scatter-like imperfections; rectangular probe pulse of width 20 time

units. Linear display.

17
26. Figure 3-113. Scatter-like imperfections; rectangular probe pulse of width 25 time

units. Linear display.

Figures 3-114 to 3-120 represent a few selected signatures plotted according to the

differential technique. All are logarithmic displays.

1. Figure 3-114. The impulse response for two scatter-like imperfections. Differential

display. This signature is the archetype for the sequence in following examples.

2. Figure 3-115. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 5 time units; delay 5 time units. Differential display. Note the transient at

t=0; this is characteristic of all differential displays.

3. Figure 3-116. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width; delay 5 time units. Differential display. The interpretation here is ambiguous.

4. Figure 3-117. Scatter-like imperfections; equivalent rectangular width 10 time units;

delay 10 time units. Differential display. The two defects are completely unresolved

here.

5. Figure 3-118. Scatter-like imperfections; rectangular probe pulse of width 5 time

units; delay 5 time units. Differential display.

6. Figure 3-119. Scatter-like imperfections; rectangular probe pulse of width 10 time

units; delay 5 time units. Differential display.

7. Figure 3-120. Scatter-like imperfections; rectangular probe pulse of width 10 time

units; delay 10 time units. Differential display. The two defects are again completely unresolved.

3.7.2 Resolution of Absorption-Like Defects

The signatures in figures 3-121 to 3-139 are based on two adjacent absorbing defects

separated by ten (arbitrary) time units. These defects occur at t=200 and t=210. Variations in the signature are given as follows:

1. Figure 3-121. The impulse response for two absorption-like imperfections. Logarithmic

display. This signature is the archetype for the entire sequence in this section.

2. Figure 3-122. Absorption-like imperfections; Gaussian probe pulse; equivalent rec- tangular width 5 time units. Logarithmic display.

3. Figure 3-123. Absorption-like imperfections; Gaussian probe pulse; equivalent rec- tangular width 10 time units. Logarithmic display. The two defects are completely

unresolved.

4. Figure 3-124. The impulse response for the two absorption-like imperfections. Linear

display.

5. Figure 3-125. Absorption-like imperfections; Gaussian probe pulse; equivalent rec- tangular width 5 time units. Linear display.

18
6. Figure 3-126. Absorption-! ike imperfections; Gaussian probe pulse; equivalent rec- tangular width 10 time units. Linear display.

7. Figure 3-127. The impulse response for two absorption-like imperfections; delay 1 time

unit. Differential display.

8. Figure 3-128. Absorption-like imperfections; Gaussian probe pulse; equivalent rec- tangular width 5 time units; delay 1 time unit. Differential display.

9. Figure 3-129. Absorption-like imperfections; Gaussian probe pulse; equivalent rec- tangular width 5 time units; delay 10 time units. Differential display. The defects

are now completely unresolved.

10. Figure 3-130. Absorption-like imperfections; Gaussian probe pulse; equivalent rec- tangular width 10 time units; delay 5 time units. Differential display.

11. Figure 3-131. Absorption-like imperfections; Gaussian probe pulse; equivalent rec- tangular width 10 time units; delay 10 time units. Differential display.

12. Figure 3-132. Absorption-like imperfections; rectangular probe pulse of width 5 time

units; delay 5 time units. Differential display.

13. Figure 3-133. Absorption-like imperfections; rectangular probe pulse of width 5 time

units; delay 10 time units. Differential display.

14. Figure 3-134. Absorption-like imperfections; rectangular probe pulse of width 10 time

units; delay 5 time units. Not only are the defects unresolved, but confusing structure arises with these parameters.

15. Figure 3-135. Absorption-like imperfections; rectangular probe pulse of width 10 time

units; delay 10 time units. Differential display. The defects are completely unre- solved in this case.

16. Figure 3-136. Absorption-like imperfections; rectangular probe pulse of width 5 time

units. Logarithmic display.

17. Figure 3-137. Absorption-like imperfections; rectangular probe pulse of width 10 time

units. Logarithmic display. The defects are completely unresolved in this case.

18. Figure 3-138. Absorption-like imperfections; rectangular probe pulse of width 5 time

units. Linear display.

19. Figure 3-139. Absorption-like imperfections; rectangular probe pulse of width 10 time

units. Linear display.

3.7.3 Resolution of Composite Defects

As mentioned in section 3.1.3, the scatter-like and absorption-like features of a composite -type defect will approximately add in the resultant signature. The effects of

this type of imperfection can therefore be inferred from the foregoing material. Only one example will be given here. Figure 3-140 is the impulse response of two composite defects

separated by 100 time units. The corresponding differential display for a Gaussian probe

pulse having an equivalent rectangular width of 5 time units and delay of 5 time units is

given in figure 3-141. It is seen that the defects are completely resolved in this case.

In the next section we will propose the values shown here as a preferred resolution criterion.

19
3.7.4 Conclusions and Recoinmendations

The foregoing signature examples demonstrate the complexity of the backscatter response

when defect responses appear with time separations comparable to the probe pulse width. The

situation is complicated by the number of types of possible defect signatures, relative magnitude of the backscatter signals, launched pulse characteristics and graphic display techniques. For example, a comparison of the results of sections 3.7.1 and 3.7.2 indicate that

scatter-like defects are often easier to resolve visually than absorption-like defects under

similar experimental conditions. Also, it appears that the conventional definition of resolution given in eqs (3-17) and (3-18) is not really an adequate measure of the ability of

the OTOR system to distinguish between all types of defects in close proximity. In some

cases, e.g., figure 3-123, adjacent imperfections are completely unresolved using this

criterion. We suggest a more conservative working definition of resolution might be more appropriate in backscatter applications. For example, in all examples considered here, the

defects are distinct and the interpretation unambiguous if the resolution is defined to be

different by a factor of two from eqs (3-17) and (3-18), or

L = VgW, (3-19)

and

D = 2W. (3-20)

The criterion for the differential display, AT=W, which is discussed previously seems to be

satisfactory in this connection also.

4. Deconvolution

In this report we have emphasized that the only unique backscatter signature in the

time domain, for a given fiber, is represented by that fiber's impulse response h(t). This,

as has been noted, is the backscatter return due to a delta function probe pulse. If OTDR

methods are to be used in fiber and cable inspection, acceptance testing, defect analysis or specifications, it is desirable to have signature displays which are independent of the

details of the particular experimental apparatus generating the backscatter data. One

approach is to adopt standard test conditions such as probe pulse shape and duration.^

However, there are engineering tradeoffs between resolution and SNR, and special requirements may dictate the use of a particular probe pulse characteristic. Another possible

stratagem for the production of uniform displays makes use of the method of deconvolution.

Review articles by Jones [24] and Nahman [25] examine some of the difficulties and errors

inherent in this approach. We will briefly review some of the salient points as they apply

to backscatter signatures.

As noted previously, if h(t) represents the backscatter impulse response of a fiber,

and the finite experimental input probe pulse is f(t), then the resulting distorted output

^An examinatTon" of the specifications of some eleven commercial OTDR systems indicated

working probe pulse durations in the range of 4 to 130 ns.

20
backscatter response is given by the convolution integral in eq (2-2). Written in the usual

simplified notation this becomes

$(t) = f(t) * h(t). (4-1)

For this relation to be valid we must have a linear, causal system where

h(t) =0 t < 0. (4-2)

The desired impulse response may be recovered from *(t) in eq (4-2) in either the time

domain or the frequency domain using conventional techniques [24-29]. The main problem

which arises in attempts to implement these convolution processes is the adverse, sometimes

disastrous, effect of extraneous noise and mathematical approximations which occur in the

analysis of real-world data. For example, the most straightforward deconvolution calculations are done in the frequency domain using discrete fast Fourier transformation (FFT)

techniques. In the transform representation, eq (4-1) is given by the product relation

H^oi) = F(ja)) . H(ja)), (4-3)

where $(j(i)), F(joj) and H(ju)) are the discrete Fourier transforms of 4(t), f(t) and h(t),

also considered as discrete functions of k points. In this application, H(ju)) is sometimes

referred to as the system function. Then, by a simple point-by-point division,

HO) = |[M. (4-4)

The desired impulse response h(t) is obtained by a discrete inverse FFT. However, the zeros

of *(ja)) and F(jw) must occur at exactly the same points in the complex plane in order to

avoid indeterminate results. Small amounts of noise, sampling errors, and errors in analogto-digital conversion in the region of the zeros of *(ja)) and F(ja)) can result in yery large

discrepancies in the resulting value of H(ju)). In certain extreme cases the calculated

values of impulse response can be quite meaningless. There are a number of strategies for

minimizing these errors which involve filtering in the frequency domain [25]. This data

processing must, of course, be done with a digital computer. Nevertheless, with care, the

desired impulse response may be approximated adequately using these deconvolution methods.

Backscatter signatures presented in this manner will be unambiguous and will also eliminate

the time shift errors observed in many of the examples shown in this report. Although

somewhat elaborate data processing is required, this is definitely the preferred display

technique.

This work was supported by the Communications Systems Center, U.S. Army Communications

Command, Fort Monmouth, New Jersey 07703.

21
5. References

[1

[2

[3

[4

[5

[6

[7

[8

[9

[10

[11

[12

[13

[14

[15

[16

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Barnoski, M. K. ; Jensen, S. M. Fiber waveguides: a novel technique for investigating

attenuation characteristics. Appl. Opt. 15(9) :2112-2115; 1976 September.

Rourke, M. D. An overview of optical time domain reflectometry. Proceedings American

Ceramic Society Meeting on Physics of Fiber Optics; 1980 April 28-30; Chicago, IL. Personik, S. D. Photon probe—an optical time domain reflectometer. Bell Syst. Tech.

J. 56(3):355-366; 1977 March.

Neumann, E. G. Analysis of the backscattering method for testing optical fiber

cables. AEU, Electron, and Commun. 34(4) :157-160; 1980.

Lin, Shih-Chun; Giallovenzi, T. G. Sensitivity analysis of the Sagnac effect optical

fiber ring interferometer. Appl. Opt. 18(6) :915-931; 1979 March 15.

Stolen, R. H. Nonlinear properties of optical fibers. Chapter 5 in Optical fiber

telecommunications. Miller, S. E.; Chynoweth, A. G., eds. New York, NY: Academic

Press; 1979. 125-150.

Papoulis, A. Signal analysis. New York: McGraw-Hill Book Co.; 1977. 431 p. Daniel son, B. L. An assessment of the backscatter technique as a means for estimating

loss in optical waveguides. Nat. Bur. Stand. (U.S.) Tech. Note 1018; 1980 February.

76 p. Conduit, A. J.; Payne, D. N. ; Hartog, A. H. Optical fiber backscatter-loss

signatures: identification of features and correlation with known defects using the

two-channel technique. Proceedings 6th European Conference on Optical Communications;

1980 September 16-19; University of York, United Kingdom. 152-155.

Conduit, A. J.; Hartog, A. H.; Payne, D. N. Spectral- and length-dependent losses in

optical fibers investigated by a two-channel backscatter technique. Electron. Lett.

16(3):77-78; 1980 January 31.

Conduit, A. J.; Hullett, J. L. ; Hartog, A. H.; Payne, D. N. An optimised technique

for backscatter attenuation measurements in optical fibers. Opt. and Quant. Electron.

12(2): 169-178; 1980 March.

Danielson, B. L. Backscatter measurements on optical fibers. Nat. Bur. Stand. (U.S.)

Tech. Note 1034; 1981 February. 44 p. Costa, B.; Esposto, F.; D'Orio, C; Morra, P. Splice loss evaluation by means of the

backscattering technique. Electron. Lett. 15(18) :550-551; 1979 August 30.

Matthijsse, P.; DeBlok, C. M. Measurement of splice insertion loss using the

backscattering method. Proceedings 5th European Conference on Optical Communications;

1979 September 17-19; /Vnsterdam, Netherlands. 9.5.1-9.5.4.

LeBoutet, A. Contribution to splice loss evaluation by the backscattering

technique: a statistical comparison with insertion loss data. Nat. Bur. Stand.

(U.S.) Spec. Publ. 597; Technical Digest--SymposiLin on Optical Fiber Measurements;

1980 October. 77-84.

22
[17] Matthijsse, P.; DeBlok, C. M. Field measurement of splice loss applying the

backscattering method. Electron. Lett. 15(24) :795-797; 1979 November 22.

[18] Hillerich, B. On site location of optical fiber defects and evaluation of

transmission loss. Proceedings 26th International Wire and Cable Symposium; 1977

November 15-17; Cherry Hill, NJ. 373-379.

[19] DiVita, P.; Rossi, U. Backscatter measurements in optical fibers: separation of

power decay from imperfection contribution. Electron. Lett. 15(15) :467-469; 1979

July 19.

[20] Inada, K. A new graphical method relating to optical fiber attenuation. Opt. Commun.

19(3): 437-439; 1976 December.

[21] Sladen, F. M. E.; Payne, D. N.; Adams, M. J. Definitive profile-dispersion data for

germania-doped silica fibres over an extended wavelength range; Electron. Lett.

15(15) :469-470; 1979 July 19.

[22] Marcuse, Dietrich. Principles of optical fiber measurements. New York: Academic

Press; 1981. 360 p. [23] Bird, G. J. A. Radar precision and resolution. New York: John Wiley & Sons; 1974.

151 p. [24] Jones, A. F.; Missel, D. L. The problem of error in deconvolution. J. Phys. A: Gen.

Phys. 3:462-472; 1970.

[25] Nahman, N. S.; Guillaume, M. E. Deconvolution of time domain waveforms in the

presence of noise. Nat. Bur. Stand. (U.S.) Tech. Note (to be published). 115 p.

[26] Silverman, H. F.; Pearson, A. E. On deconvolution using the discrete Fourier

transform. IEEE Trans. Audio Electroacoust. 2(12) :112-118; 1973 April.

[27] Hunt, B. R. Deconvolution of linear systems by constrained regression and its

relationship to the Wiener theory. IEEE Trans, on Auto. Control 17(5) :703-705; 1972

October.

[28] Riad, S. M. Optical fiber dispersion characterization study. NASA Contract #NAS

10-9455, Final Report; 1979 December.

[29] Riad, S. M. Optical fiber impulse response using frequency domain optimal

compensation deconvolution. Proceedings Third International Fiber Optics and

Communications Exposition; 1980 September 16-18; San Francisco, CA. 210-213.

23
1 . t-Kf

1 .ee

— 1 1 —

1

2.62

/"\

u / \ Q / \ U / \

1- / \ H / \

-I / \

E 0.60 / < / \\

UJ / \

(0 / \

-1 / \ 3 / \

"^ 0.40 / \

0.20

- / \

0.00 1 1 .^---,

25 50 75 TIME Carbllrory unite)

100 125

Figure 3-1. Illustration of the concept of equivalent rectangular width,

9.0

6.0

1 1 1 1 1 1 1 1 1 1

r\CD

TJ\J

OL

liJ 3 3.0 - _ £

ocu

tt-<o 0.0 ^ ^^-'^^-^.^.^^^^ o ^'*^'*.*^^,^ < ^^^^^^^__^ ta '^^^,^

(9 ^^^^^.^^ o ^^"^^^.^.^^ _i ^^^^^ -3.0 ^^^-^-^^

-6.0

^^^^-.^

100 200 300 TIME Copbilrary unil«>

400 500

Figure 3-2. The impulse response for a scatter-like imperfection. Logarithmic display.

24
15.8

12.0 -

CD

u

g 9.0

0.

a:kJ

II-m 6.0 u

<

ffl (9O

3.0

0.0

—r 1 1 r- 1 1 1 1 1 —1

100 200 300 TIME Carbilrary units?

400 500

Figure 3-3. Scatter-like imperfection; Gaussian probe pulse; equivalent rectangular

width 5 time units. Logarithmic display.

15.0

200 300

TIME Carbilrary unite?

400 500

Figure 3-4. Scatter-like imperfection; Gaussian probe pulse; equivalent rectangular

width 10 time units. Logarithmic display.

25
15.8

2ee see

TIME Carbilrary unils^

Figure 3*5. Scatter-like imperfection; Gaussian probe pulse; equivalent rectangular

width 20 time units. Logarithmic display.

16.

lee 2ee see

TIME Carbilrary unils^

422 see

Figure 3-6. Scatter-like imperfection; Gaussian probe pulse; equivalent rectangular

width 30 time units. Logarithmic display.

26
18.

e

tee 2ee 3ee TIME Carbilrary unite)

4ee see

Figure 3-7. Scatter-like imperfection; Gaussian probe pulse; equivalent rectangular

width 40 time units. Logarithmic display.

2e.e

2ee see TIME Carbilrary uniis)

Figure 3-8. Scatter-like imperfection; Gaussian probe pulse; equivalent rectangular

width 50 time units. Logarithmic display.

27
28. e

108 208 300

TIME Carbilrary unils)

400 588

Figure 3-9. Scatter-like imperfection; Gaussian probe pulse; equivalent rectangular

width 100 time units. Logarithmic display.

15.8

188 288 388 TIME Carbilrary unil<s5

488 588

Figure 3-10. Scatter-like imperfection; rectangular probe pulse of width 5 time units,

Logarithmic display.

28
15.0

12.0 -

01

UJg 9.0

a.

oe. UJ

II-« 6.0 u

<

(0O

3.0 .

0.0

100 200 300 TIME Carbllrary units)400 500

Figure 3-11. Scatter-like imperfection; rectangular probe pulse of width 10 time

units. Logarithmic display.

15.0

100 200 300 TIME Carbllrary unll«3

400 500

Figure 3-12. Scatter-like imperfection; rectangular probe pulse of width 20 time

units. Logarithmic display.

29
18.0

208 300 TIME Carbitrary units5400 500

Figure 3-13. Scatter-like imperfection; rectangular probe pulse of width 30 time

units. Logarithmic display.

18.0

200 300

TIME Carbitrary unitsJ

400 see

Figure 3-14. Scatter-like imperfection; rectangular probe pulse of width 40 time

units. Logarithmic display.

30
21 .0

I 00 200 300 TIME Carbilrary unilsJ400 500

Figure 3-15. Scatter-like imperfection; rectangular probe pulse of width 50 time

units. Logarithmic display.

21 .0

100 200 300 TIME Carbilrary unils5

400 500

Figure 3-16. Scatter-like imperfection; rectangular probe pulse of width 100 time

units. Logarithmic display.

31
2.0

-13.0

100 200 300 TIME Carbilrary unils5

400 500

Figure 3-17. The impulse response for an absorption-like imperfection. Logarithmic

display.

9.0

7.0

^ 5.0

3.0 -

1 .0 .

1 .0

-3.0 .

-5.0

200 300 TIME Carbilrary units)

Figure 3-18. Absorption-like imperfection; Gaussian probe pulse; equivalent rectangular

width 5 time units. Logarithmic display.

32
12.8

lee 200 300 TIME Carbilrory unils5

400 500

Figure 3-19. Absorption-like imperfection; Gaussian probe pulse; equivalent rectangular

width 10 time units. Logarithmic display.

15.0

200 300 TIME Carbilrory unils!)

Figure 3-20. Absorption-like imperfection; Gaussian probe pulse; equivalent rectangular

width 20 time units. Logarithmic display.

33
17.0

lee 288 300 TIME Carbilrary unils^400 500

Figure 3-21. Absorption-like imperfection; Gaussian probe pulse; equivalent rectangular

width 30 time units. Logarithmic display.

18.0

100 200 300 TIME Carbi Irary unils)

400 500

Figure 3-22. Absorption-like imperfection; Gaussian probe pulse; equivalent rectangular

width 40 time units. Logarithmic display.

34
18.

lee 280 300 TIME Carbilrary unils^

400 508

Figure 3-23. Absorption-like imperfection; Gaussian probe pulse; equivalent rectangular

width 50 time units. Logarithmic display.

21 .0

200 300 TIME Carbitrary units)

Figure 3-24. Absorption-like imperfection; Gaussian probe pulse; equivalent rectangular

width 100 time units. Logarithmic display.

35
9.8

lee 2ee see TIME Carbilrary uniis^4ee see

Figure 3-25. Absorption-like imperfection; rectangular probe pulse of width 5 time

units.

12.0

2ee see TIME Carbilrary un I l«5

Figure 3-26. Absorption-like imperfection; rectangular probe pulse of width 10 time

units. Logarithmic display.

36
15.8

I 00 200 300 TIME Carbilrary uniis^

400 500

Figure 3-27. Absorption-like imperfection; rectangular probe pulse of width 20 time

units. Logarithmic display.

17.0

200 300 TIME Carbllrary unllsJ

Figure 3-28. Absorption-like imperfection; rectangular probe pulse of width 30 time

units. Logarithmic display.

37
17.0

100 200 300 TIME Carbilrary unilsJ

400 500

Figure 3-29. Absorption-like imperfection; rectangular probe pulse of width 40 time

units. Logarithmic display.

19.0

16.0

-I r- -1 r- -1 T"

100 200 300 TIME Carbilrary units!)400 500

Figure 3-30. Absorption-like imperfection; rectangular probe pulse of width 50 time

units. Logarithmic display.

38
21 .0

lee 200 see

TIME Carbilrary unilsJ

490 see

Figure 3-31. Absorption-like imperfection; rectangular probe pulse of width 100 time

units. Logarithmic display.

12.

e

tee 2ee see TIME Carbilrary units)

4ee see

Figure 3-32. The impulse response for a composite imperfection. Logarithmic display.

39
12.0

108 200 300

TIME Carbitrary unils3

400 see

Figure 3-33. Composite imperfection; Gaussian probe pulse; equivalent rectangular width

5 time units. Logarithmic display.

200 300 TIME Carbilrary units3

Figure 3-34. Composite imperfection, Gaussian probe pulse, equivalent rectangular width

10 time units. Logarithmic display.

40
15.0

12.0

-9.0

100 200 300 TIME Carbitrary unilsD

400 500

Figure 3-35. Composite imperfection; Gaussian probe pulse; equivalent rectangular width

20 time units. Logarithmic display.

24.0

200 300 TIME Carbitrary units?

Figure 3-36. Composite imperfection; Gaussian probe pulse; equivalent rectangular width

30 time units. Logarithmic display.

41
24.0

21 .0

100 200 300 TIME Carbiirary onits5

400 500

Figure 3-37. Composite imperfection; Gaussian probe pulse; equivalent rectangular width

40 time units. Logarithmic display.

24.0

100 200 300 TIME Carbiirary unltsD

400 500

Figure 3-38. Composite imperfection; Gaussian proDe pulse; equivalent rectangular width

50 time units. Logarithmic display.

42
24.0

100 200 300 TIME Carbilrary unils!)

400 500

Figure 3-39. Composite imperfection; Gaussian probe pulse; equivalent rectangular width

100 time units. Logarithmic display.

12.0

•12.0 100 200 300 TIME Carbitrary units?

400 500

Figure 3-40. Composite imperfection; rectangular probe pulse of width 5 time units,

Logarithmic display.

43
15.0

-9.0

100 200 300 TTMF r<nr-K i f.r ar V units!)

400 500

Figure 3-41. Composite imperfection; rectangular probe pulse of width 10 time units

Logarithmic display.

15.0

12.0 .

'^ 9.0 _

6.0 .

3.0 .

0.0 .

-3.0 .

-6.0 .

-9.0

100 200 300

TIME Carbltrarv units)

400 500

Figure 3-42. Composite imperfection; rectangular probe pulse of width 20 time units

Logarithmic display.

44
24.

Q

21. e

1 1 1 1 1 1 r 1 1 1—

r\ 18.0 m

M

«-»

a.

Ui 15.

e

3

• O /***^**'**'*--.^ a. /

"^'"**"—*"*'-**-^ \

UJ 12.0 / ^^ ^\

1- / \ 1- / A < / o / <0 9.

a

/ o f < f ax

1 (0o 6.0 1 ' "~'"^-~---_

_i ^~'"~'~"^^--—

^,_._^__^

3.0^

0.0

100 200 300

TIME Corbllrary units)

400 see

Figure 3-43. Composite imperfection; rectangular probe pulse of width 30 time units.

Logarithmic display.

24.0

180 200 300

TIME Carbllrary unlls)

400 see

Figure 3-44. Composite imperfection; rectangular probe pulse of width 40 time units

Logarithmic display.

45
24.

tee 222 300 TIME Carbilrory unftsD

4ee see

Figure 3-45. Composite imperfection; rectangular probe pulse of width 50 time units

Logarithmic display.

24.0

100 400 500

Figure 3-46

200 300

TIME Carbilrory unitsD

Composite imperfection; rectangular probe pulse of width 100 time units

Logarithmic display.

46
ffi 0

\^

UJ3

O

a.

Oiu

<o

(0u

<

01

6.0

3.0

e.Q .

< -3.8 . Z

UJ

Oi. UJ

u.

u.M

a

(0o

-6.0 .

-9.0

100 200 300 TIME Carbitrory units)

400 500

Figure 3-47. Composite imperfection; Gaussian probe pulse; equivalent rectangular width

10 time units; delay one time unit. Differential display.

6.0

100 200 300 TIME Carbitrory units)

400 500

Figure 3-48. Composite imperfection; Gaussian probe pulse; equivalent rectangular width

10 time units; delay 2 time units. Differential display.

47
6.8

ffi D

UJ3

O

a.

a.

hi<o

(0<

h-Z

UJ

QL

UJ

U.

u.H

(0o

-I

-6.0

-9.0

200 300 TIME Carbilrory unils>

400 500

Figure 3-49. Composite imperfection; Gaussian probe pulse; equivalent rectangular width

10 time units; delay 5 time units. Differential display.

6.0

100 200 300 TIME Corbilrory unil*>400 see

Figure 3-50. Composite imperfection, Gaussian probe pulse; equivalent rectangular width

10 time units; delay 10 time units. Differential display.

48
6.8

tee 2Qe see

TIME Carbitrory units)

4m see

Figure 3-51. Composite imperfection, Gaussian probe pulse, equivalent rectangular width

10 time units; delay 15 time units. Differential display.

6.8

lee 2ee see TIME Carbitrory units)

4ee see

Figure 3-52, Composite imperfection; Gaussian probe pulse; equivalent rectangular width

10 time units; delay 20 time units. Differential display.

49
m

TJ

a.bJ3

o

a.a

hi

I1-<

O

(0ao

<

ffi <

H

I-Z

hJ

Of

UJ

u.

u.Ho

o

-I

3.0

1 1 1 r—

e.e 1

-3.

/

-6.8 -

-9.0

V

1 . _i r ] 1 1 1 1 1 1— 100 200 300 TIME Carbilrory units)

400 508

Figure 3-53.

ffi 0

UJO

Q.

o:kl

I1-<u

(0u

<

ffi

-1<Hz

bJm

UJu.

u.H

(Z)

(3O

Composite imperfection; Gaussian probe pulse; equivalent rectangular width

10 time units; delay 25 time units. Differential display.

6.0

3.0 .

0.0

-3.0

-6.0 _

-9.0

108 200 300 TIME Corbitrary units)400 500

Figure 3-54, Composite imperfection; Gaussian probe pulse; equivalent rectangular wiath

10 time units; delay 30 time units. Differential display.

50
6.Q

"0^ 3.0

a:UJ3

O

Q.

q: 8.8

UJ<

o

0)o -3.8 <

CO

z -6.8 .

UJo:ui

u.

u.H^ -9.8 I

(9O

-12.8

188 288 388 TIME Carbilrory uniis^

488 588

Figure 3-55. Composite imperfection; Gaussian probe pulse; equivalent rectangular width

10 time units; delay 35 time units. Diipferential display.

6.8

188 288 388 TIME Carbilrory unils)

488 588

Figure 3-56. Composite imperfection; Gaussian probe pulse; equivalent rectangular width

10 time units; delay 40 time units. Differential display.

51
6.e

108 288 388 TIME Carbilrory units)488 588

Figure 3-57. Composite imperfection; Gaussian probe pulse; equivalent rectangular width

10 time units; delay 50 time units. Differential display.

6.8

188 288 388

TIME CarbiLrory unil«>

488 588

Figure 3-58, Composite imperfection; Gaussian probe pulse; equivalent rectangular width

10 time units; delay 60 time units. Differential display.

52
6.8

01

"0^ 3.8

u.

bJ3

O

a

bJ

»-

I-<o

(0O

<

<

H

»-Z

Uibl

b.

U.H

(9O

8.8

-3.8 .

-6.8 .

-9.8 .

-12.8

188 288 388

TIME Carbilrory uniis^

488 588

Figure 3-59. Composite imperfection; Gaussian probe pulse; equivalent rectangular width

10 time units; delay 100 time units. Differential display.

1.8

1 1 1 1 1 1 1 1 1 r—

8.9 .

8.8 - -

2

8-7

S 8.6

- -

Of

iij t= 8.5

1-§ 8.4

o

ffi 8.3

-

8.2 - -

8.1 - -

8.8

-8.1 1 1 1 1 58 188 158 288 258 388 TIME

358 488 458 588

Figure 3-60. The impulse response for an extended scattering imperfection. Linear

display.

53
55

45 .

a. 35

Id3O

o.

at

111 25 <u

n

V.u

A 15 .

5 .

-5

258 388

TIME

Figure 3-61. Extended scatter-like imperfection; rectangular probe pulse of width 50

time units. Linear display.

58 188 158 288 258 388 TIME

358 488 458 588

Figure 3-62, Extended scatter-like imperfection; rectangular probe pulse of width 100

time units. Linear display.

54
I to

100

90

1 1 1 1 1 1 1 r———^-1 r—

.

80 - /r\

Qi. 70 \

UJ // \\ 3 / \ O / \

Q. 60 . / \

OL if \

hi I \ •-

1- 50

J

\ < t \ U

(0 40 1

\

vc i V u 1

\ ^ 30 / \

20 / \

t0 / \

-10

/ \

1 1 1 1 1 1 1 1 1 L_ 50 100 150 200 250 TIME

300 350 400 450 500

Figure 3-63. Extended scatter-like imperfection; rectangular probe pulse of width 150

time units. Linear display.

Qsi as2

(a) (c)

> •-F

(b) (d)

Figure 3-64. Examples of conditions in optical fibers which exhibit nonuniform and/or

nonreciprocal transmission properties: (a) Splice between fibers of

different diameter, (b) splice between fibers of different numerical

aperture, (c) splice between fibers having different scattering loss, and

(d) fiber with a different mode volume excited in the backward direction.

55
2.e

zo

H1—o 1 .5 < ^^_...—-** a: ^^^.-^"""^ u.UJ3

Q£

_^^,^—^^^"^ ^^^,^-—*—^''^ ^ h- ^^^..*-*^''^ 0.o

< ^—-^"^

^^^^*-^''**''^ ^ UJ ^—'—

' > ^^^^^^^-"^"""^ H 1 .0 ,_——'''' <

_lUJ

oc

a.

5

1 1 1 1 1_ tee 2ee see

FIBER LENGTH

4ee see

Figure 3-65. Variation of capture fraction with length in the forward direction,

1 .e

-14.

e

2ee 300

TIME Carbllrary unll«3

Figure 3-66. Impulse response signature of fiber with perturbation shown in figure 3- 65. Logarithmic display.

56
0.04

a. 02 .

0.00

<Q -0.02 M

inkJ

Oi.

-0.04

-0.06

-0.08

100 200 300

TIME Carbllrarv unllsJ

400 500

Figure 3-67. Residuals for signature in figure 3-66

1 .0

-14.0

100 200 300 TIME Carbllrarv units)

400 500

Figure 3-68. Impulse response signature for fiber shown in figure 3-66 when fiber is

reversed end-for-end.

57
0.04

-0.08

100 200 300

TIME Carbllrory unite)

400 see

Figure 3-69. Residuals for signature of fiber shown inn figure 3-68.

1 .3 1 , — 1 — -r 1

1 .2

v> ^^^^

CO ^

o ^^^-^^"^ -1 ^^^^-^''^

CO ^^^•""^^'^ z ^_^.^--''"''''^ M ^^.^-'^''''"^ q: ^^^.^"''''^ UJ ^^^..^-"^'^^ 1- ^^.^.^'-''''''^ l-o

<

1 . 1 ^^.-"^"'^

^^.^^-""^ ^ to ^^^^^-^-"^ UJ> ^^^^^^""^"^ ^

M ^^..^-^''''''^ t- ^^^---''''''^ < ^—^'^ -1 ^

UJ

en. 1 .2 ^

0.9

100 200 300 FIBER LENGTH

400 500

Figure 3-70. Variation of scattering loss with length in the forward direction,

58
1 .0

14.0

200 300

TIME Carbilrary units)

400 500

Figure 3-71. Impulse response signature for fiber with perturbation shown in figure

3-70. Logarithmic display.

0. 1

0.0 .

-0.1 .

-0.2

100 200 300 TIME Carbltrary unilc5

400 500

Figure 3-72. Residuals for signature of fiber shown in figure 3-71.

59
1 .0

14.0

200 300 TIME Carbltrary units)

400 500

Figure 3-73. Impulse response signature for fiber shown in figure 3-71 when fiber is

reversed end-for-end.

0.2

ca0

(0

-I<a

hi

<0

UJ 0.0 .

-0. 1 100 200 300 TIME Carbltrary unite)

400 500

Figure 3-74. Residuals for signature of fiber shown in figure 3-73.

60
2.0

100 200 300 FIBER LENGTH

400 500

Figure 3-75. Variation of absorption loss with length in the forward direction

1 .0

-2.0 .

liJ g -5.0

0.

iX. UJ

tI-<^ -8.0 o<

(DO

-I -11.0 .

-14.0

-| r- -T r- -1 r100 200 300

TIME Carbilrary units)

400 500

Figure 3-76. Impulse response signature for fiber with perturbation shown in figure 3- 75. Logarithmic display.

61
e. 15

0.05 .

<a -0.05

H

<n

IjJ

-0.15 _

-0.25

200 300 TIME Carbltrary units)

500

Figure 3-77. Residuals for signature of fiber shown in figure 3-76.

1 .0

14.0

200 300 TIME Carbltrary units)

Figure 3-78. Impulse response signature for fiber shown in figure 3-75 when fiber is

reversed end-for-end.

62
0.20

0. 15

0. 10

(0

_l 0.05 .

0.00 .

-0.05

-0.10

200 300 TIME Carbltrary units:)

500

Figure 3-79. Residuals for signature of fiber shown in figure 3-78.

2.e

-12.0

tee 2ee see

TIME Carbllrary units)

4ee see

Figure 3-80. Impulse response signature of a splice in the forward direction,

Logarithmic display.

63
2.0

tae 288 388 TIME Carbllrary units)

488 588

Figure 3-81. Impulse response signature of the spliced fiber in figure 3-80 when the

fiber is reversed end-for-end.

ex

u>o

8.4

1 1 1 1 T 1 1

1 1 r8.2 ^>v -

8.8 - ^\

-8.2 - ^\^

-8.4 1 1 1 1 J 1 1 1 1 1- 188 288 388 TIME Carbllrary unll«)

488 588

Figure 3-82. Logarithm of the power loss of fiber shown in figures 3-80 and 3-81.

64
e.8

lae 288 388 TIME Corbllrory units)

488 588

Figure 3-83. Variation of the scattering parameter with length for fiber shown in

figures 3-80 and 3-81.

6

u. 3

UJ3

o

0.2 8

H

1-<U

CO

•a. o

-3 <

<DO

J -6

-9

-12

188 288 388 TIME Corbltrory unllsD

488 588

Figure 3-84. Signature of a fiber with composite defect; measurement at 800 nm. Logarithmic display.

65
6 .

Oi 3

Ul3

o

0.

UJ 8

^-t-<o

to^ -3

o

<

(D

tDO

-I -6

-9

-12

280 388 TIME Corbltrory unil«3

488 500

Figure 3-85. Signature of fiber in figure 3-93; measurement at 900 nm,

3.0

•I .0 100 200 300

TIME Carbilrary units)

400 500

Figure 3-86. Signature with noise; SNR = 10 dB. Linear display.

66
5.0

-20.0

100 200 300 TIME Carbitrary units)

400 500

Figure 3-87, Signature of fiber in figure 3-95. Logarithmic display.

3.0

0.0

ca

-a\^

u.g -3.0

0.

(H. UJ

Il-<

)^ -6.0 <m

o

-9.0 .

-12.0

Ml

100 200 300

TIME Carbilrary unite)

400 500

Figure 3-88. The impulse response for two scatter-like imperfections. Logarithmic

display.

67
9.0

108 ?00 300

TIME Carbilrary units)

400 500

Figure 3-89. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 5 time units. Logarithmic display.

12.0

9.0

6.0

3.0

0.0 .

-3.0 100 200 300

TIME Carbilrary units)

400 500

Figure 3-90. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 9 time units. Logarithmic display.

68
12.0

tee 200 300

TIME Carbitrary units?

400 500

Figure 3-91. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 10 time units. Logarithmic display.

15.0

12.0

u

g 9.0

cn. UJ

»-

I-<

(O 6.0 o<

too

3.0

0.0

-I r- -T r- -I 1—

100 200 300 TTMF Carbitrary units?

400 500

Figure 3-92. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 15 time units. Logarithmic display.

69
<o

in

V.o

<

CDo

15.0

12.0

9.0

6.0

0.0

200 300 TIME Carbitrary units)

400 500

Figure 3-93. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 20 time units. Logarithmic display.

15.0

100 200 300 TIME Carbitrary units)

400 500

Figure 3-94, Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 25 time units. Logarithmic display.

70
1 .5

100 200 300

TIME Carbllrary unite?

480 see

Figure 3-95. The impulse response for two scatter-like imperfections. Linear display.

6.0

100 200 300 TIME Carbllrary unltsJ

400 see

Figure 3-96. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 5 time units. Linear display.

71
9.e

200 300 TIME Carbilrary units)

400 500

Figure 3-97. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 9 time units. Linear display.

12.0

9.0 -

a:O

a.

t= 6.0

I-<o

o

<

3.0

0.0

-I r 1 1— "T 1 r r-

_i L- 100 200 300 TIME Carbilrary units)

400 500

Figure 3-98. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 10 time units. Linear display.

72
15.0

I 00 200 300 TIME Carbllrary units)

480 500

Figure 3-99. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 15 time units. Linear display.

25.0

100 200 300

TIME Carbitrary units)

400 500

Figure 3-100. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 20 time units. Linear display.

73
25. e

100 208 300

TIME Carbilrary unilc5

400 500

Figure 3-101. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 25 time units. Linear display.

9.0

200 300 TIME Carbilrary un i ts5

Figure 3-102. Scatter-like imperfections; rectangular probe pulse of width 5 time

units. Logarithmic display.

74
12.0

100 200 300 TIME Carbilrary units!)400 500

Figure 3-103. Scatter-like imperfections; rectangular probe pulse of width 9 time

units. Logarithmic display.

12.0

100 200 300

TIME Carbitrary units)

400 500

Figure 3-104. Scatter-like imperfections; rectangular probe pulse of width 10 time

units. Logarithmic display.

75
15.

100 200 300 TIME Carbitrary unils5400 500

Figure 3-105. Scatter-like imperfections; rectangular probe pulse of width 15 time

units. Logarithmic display.

15.0

100 200 300

TIME Carbitrary united

400 500

Figure 3-106. Scatter-like imperfections; rectangular probe pulse of width 20 time

units. Logarithmic display.

76
15.0

12.0

LiJ

UJ

6.0

3.0

0.0

100 200 300

TIME Carbilrary units)

400 500

Figure 3-107. Scatter-like imperfections; rectangular probe pulse of width 25 time

units. Logarithmic display.

6.0

5.0

a 4 .

o

CO

m 2.0 .

0.0

-I r100

—

1

r-

_i I 1 1- 200 300 TIME Carbitrary units)

-1 r400 500

Figure 3-108, Scatter-like imperfections; rectangular probe pulse of width 5 time

units. Linear display.

77
9.0

a 6.0

LlJ

100 200 300

riME Carbitrary units)

400 500

Figure 3-109, Scatter-like imperfections; rectangular probe pulse of width 9 time

units. Linear display.

12.0

9.0

6.0

3.0

0.0

100 200 300

TIME Carbitrary units)

400 500

Figure 3-110. Scatter-like imperfections; rectangular probe pulse of width 10 time

units. Linear display.

78
15.8

100 200 300 TIME Carbilrary unitsj400 500

Figure 3-111. Scatter-like imperfections; rectangular probe pulse of width 15 time

units. Linear display.

25.0

20.0 _

UJ

2 10.0 <

5.0

0.0

100 200 300 TIME Carbilrary unitsi

400 500

Figure 3-112. Scatter-like imperfections; rectangular probe pulse of width 20 time

units. Linear display.

79
kJO

25.0

20.0 _

15.0

10.0

5.0

0.0

100 200 300 TIME Carbitrary units!)

400 500

Figure 3-113.

01

DC

UIO

Q.OL

kJ

Il-<

o

<

(D

CDO

Scatter-like imperfections; rectangular probe pulse of width 25 time

units. Linear display.

8.0

5.0 .

2.0 .

-1.0 .

-4.0 .

-7.0

100 200 300 TIME (.arbitrary unitsD400 500

Figure 3-114. Impulse response for two scatter-like imperfections; delay one time unit

Differential display.

80
5.

a

m0 4.8

V

tt. bl3 3.8 O

a.

tt

III 1- 2.U

1-<

u

«

V

o 1.8 <m

J

<

8.8

1-Z

lU

<KU

li. -1.8

b.H

O

O -2.8

-3.8

1 1 1 1 1 1 1 1 1 r—

' -

\ 1

II

188 288 388 TIME Carbilrary unils^

488 588

Figure 3-115

atV«-»

a.

kJo

q:bJ

t-<u

(0

a.u

<

CDCDO

Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 5 time units; delay 5 time units. Differential display.

18.8

8.8

6.8 .

4.8 .

2.8 .

8.8 J

-2.8

8 188 488 588

Figure 3-116

288 388 TIME Carbilrary unilsD

Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width; delay 5 time units. Differential display.

81
6.8

188 288 388 TIME Corbllrary unilsD

488 588

Figure 3-117. Scatter-like imperfections; Gaussian probe pulse; equivalent rectangular

width 10 time units; delay 10 time units. Differential display.

5.8

188 288 388 TIME Corbilrary unilti

488 588

Figure 3-118. Scatter-liKe imperfections; rectangular probe pulse of width 5 time units;

delay 5 time units. Differential display.

82
bJO

Q.

q:

111

I-<

U

(0

y.o

<m

o

o

3.8

2.0 .

1.0 .

0.0

-t.0 .

-2.0

200 300 TIME Corbilrary unllsD

400 500

Figure 3-119. Scatter-like imperfections; rectangular probe pulse of width 10 time units;

delay 5 time units. Differential display.

2.0

-3.0

100 200 300

TIME Corbilrary unil«D

400 500

Figure 3-120. Scatter-like imperfections; rectangular probe pulse of width 10 time units;

delay 10 time units. Differential display.

83
-3.0

s;— 1 1 —1 1 1 1 1 1 1 1—

/^ ^S.

<D ^v^ -0 ^Sw^

<-» ^ on

1 Id ^. 2 -6.8 J o 1 a. s.

a. ^\.

\xi ^*w^

1- ^*^^^ H ^s. < ^s.

'^ -9.0 ^V.

^ ^Ss^ o ^Sy^^ < ^S,^

OD ^S^

(0 ^V.

O ^*^s. _l ^*s^ -12.0 \^

-15.0 1 1 1 1 1 1 1 " i »— 100 200 300

TIME Corbllrory unll«3

400 500

Figure 3-121. The impulse response for two absoption-like imperfections. Logarithmic

display.

8.0

5.0

1 1 1 1 1 1 1 1 1 —1—

r» ^>v

at ^^. 0 ^s.

\ji ^v.

tt ^v,^^^

Ul ^^^ 2

2.0 A

y

tt \

hi Y

1- x^. 1- ^^^ < ^^w ^ -1.0 ^s. ^ ^\^^ O ^N^ < ^^w n ^V^^

o

^*»^

o ^^^

-1 ^^^^ -4.0 ^\^

-7.8''''

i_

180 488 588

Figure 3-122,

288

TIHE Corbilrory unfUi)

Absorption-like imperfections; Gaussian probe pulse; equivalent rectangular

width 5 time units. Logarithmic display.

84
12.8

188 200 300

TIME Corbllrorv unlUi

400 500

Figure 3-123. Absorption-like imperfections; Gaussian probe pulse; equivalent rectangular

width 10 time units. Logarithmic display.

100 200 300 TIME Corbllrorv unllcD

400 500

Figure 3-124. The impulse response for the two absorption-like imperfections. Liner

display.

85
6.0

5.8

a. 4.Q

tu

0.

a.Id

1- 3.8

»-<oM

^O

<

ffi 2.8

1.8 .

8.8 i

-I 1 I r

I I I I -I I I I 8 188 288 388

TIME Carb I Ir arv unll«3

588

Figure 3-125. Absorption-like imperfections; Gaussian probe pulse; equivalent rectangular

width 5 time units. Linear display.

12.8

188 288 388

TIME Corbllrorv unll«)

488 588

Figure 3-126. Absorption-like imperfections; Gaussian probe pulse; equivalent rectangular

width 10 time units. Linear display.

86
0.5

01

TJ

v./

a.UJ3

O

o.

q:

ui

II-<

u

(0<

<H

»-Z

Id

UJ

U.

U.H

COO

0.2

1 1 —

T 1 --I—- - —

-1 1 1

-0.1 -

-0.4 - -

-0.7 -

-1.0 1 1 1 1 1 1 1 1 1 »— 100 200 300 TIME Carbllrary unlU^

400 500

Figure 3-127. The impulse response for the two absorption-like imperfections; delay 1 time unit. Differential display.

5.8

100 400 500

Figure 3-128,

200 300

TIME Carbllrary untlsD

Absorption-like imperfections; Gaussian probe pulse; equivalent rectangular

width 5 time units, delay 5 time units. Differential display.

87
I.

180 288 388

TIME Corbllrory unll«3

488 588

Figure 3-129, Absorption-like imperfections; Gaussian probe pulse; equivalent rectangular

width 5 time units, delay 10 time units. Differential display.

9.8

188 288 388

TIME Carbllrorv unll«5

488 588

Figure 3-130. Absorption-like imperfections; Gaussian probe pulse; equivalent rectangular

width 10 time units, delay 5 time units. Differential display.

88
S.0

IQQ 200 300

TIME Corbllrory unlUJ

400 500

Figure 3-131. Absorption-like imperfections; Gaussian probe pulse; equivalent rectangular

width 10 time units, delay 10 time units. Differential display.

m

kl3

O

a

a.klH

I-<U

(0

i£. O

<

<H

I-Z

kJU

ki

k.

k.M

(DO

5.0

4.0 .

3.0 .

2.0 .

1.0 .

0.0

-1.0

100 200 300

TIME Corbllrory unlU)

400 500

Figure 3-132. Absorption-like imperfections; rectangular probe pulse of width 5 time

units; delay 5 time units. Differential display.

89
5.0

100 200 300

TIME Carbllrary units)

400 500

Figure 3-133. Absorption-like imperfections; rectangular probe pulse of width 5 time

units; delay 10 time units. Differential display.

9.0

100 200 300 TIME Corbllrory unllsD

400 500

Figure 3-134. Absorption-like imperfections; rectangular probe pulse of width 10 time

units; delay 5 time units. Differential display.

90
5.

a

m

u

3

O

OL

liJ tt-<

o

(0

V.o

-I<H

I-z

UJ

bJ

h.

Ii. H

Q

(9O

4.8

3.8 -

2.8 -

1.8 -

0.8

1

-!.8 [ U

-2.8

188 288 388

TIME Corbllrory unll«i

488 588

Figure 3-135. Absorption-like imperfections; rectangular probe pulse of width 10 time

units; delay 10 time units. Differential display.

5.8 \^^\^

a. 2.8 ^Nv

•-

1-<

o -1.8

^^ -

(9O

-i -4.8 ^\ -

-7.8 \

8 188 488 588

Figure 3-136.

288 388

TIME Corbllrory unlU3

Absorption-like imperfections; rectangular probe pulse of width 5 time

units. Logarithmic display.

91
12.0

idd 280 388 TIME Corbllrary unllsD480 500

Figure 3-137. Absorption-like imperfections; rectangular probe pulse of width 10 time

units. Logarithmic display.

6.0

5.0

1

1 1 1 1 1 1 1

1 r—

UJ

(t 4.0 \\\ Q ^^

A. \

tt \

ki ^^

1- 3.0 \^

(- ^^ < ^V_ O ^V

(0 X^

V. ^V o X^ <

ffi 2.0

A

1.0 ^-^^.^^^^

8.8 1 188 288 388

TIME Corbllrory unIl«D

480 588

Figure 3-138. Absorption-like imperfections; rectangular probe pulse of width 5 time

units. Linear display.

92
12.8

18.8

1— 1

1 1 1 1 1 1 1 1—

hi

a, 8.8 \\ 3 \

O \

a. \

oc \

UJ ^^

1- 6.8 \. t- ^V^ < ^^ u ^V

CO x^ a ^v o ^v^ s 4.8 \

2.8 v^^^

8.8

188 288 388

TIME Carbllrary unll«5

488 588

Figure 3-139. Absorption-like imperfections; rectangular probe pulse of width 10 time

units. Linear display.

2.8

-1.8 .

a.s

II-§ -7.8 u

O

""-18.8

-13.8

1 1 1 1

_ I . 1

1 1 r 1 1 1

188 280 388

TIME Carbllrary unll«3

488 588

Figure 3-140. Impulse response of two composite imperfections separated by 100 time

units. Logarithmic display.

93
m

TJ

<H

I-Z

biQ£

bJ

b.

b.Ha

5.0

4.0 .

3.0 .

2.0 .

1 .0 .

0.0

-1.0

-2.0

(0o -3.0

-4.0

200 300 TIME Corbilrory unitsJ

400 500

Figure 3-141. Composite imperfections; Gaussian probe pulse; equivalent rectangular width

5 time units, delay 5 time units. Differential display.

94
NBS-n4A (REV. 2-ec) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBS TN-1050

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

December 1981

4. TITLE AND SUBTITLE

Backscatter Signature Simulations

5. AUTHOR(S)

B. L. Daniel son

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

10/1/80 - 10/1/81

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

Communications Systems Center

U.S. Army Communications R&D Command

Fort Monmouth, New Jersey 07703

10. SUPPLEMENTARY NOTES

1^21 Document describes a computer program; SF-185, FlPS Software Summary, is attached.

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

bibliography or literature survey, mention it here)

This report presents a collection of computer-generated backscatter

signatures which represent realistic replicas of signals that can be encountered

in optical time-domain reflectometer (OTDR) systems. Emphasis is placed on illustrating the appearance of backscatter signatures originating from localized

and distributed imperfections which are superimposed on an otherwise uniform

optical fiber. The details of these signatures are shown to be a function of

the particular type of fiber perturbation, experimental parameters, and data

reduction methods. This compilation of simulated responses is intended to

facilitate the correct interpretation of OTDR signals as well as to point out sources of error which can arise in the characterization of optical fibers

using backscatter techniques.

12. KEY WORDS (S/x to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

backscclttering; backscatter signatures*, optical fiber scattering;

optical time-domain reflectometer; OTDR

13. AVAILABILITY

[X] Unlimited

I I For Official Distribution. Do Not Release to NTIS

[^ Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

|X_5 Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

100

15. Price

$9.50

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U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

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