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NASA-CR-165624 19810002770 KSC TR 32-3

December 1979

NASA Contract Report 165624

Optical Fiber Dispersion Characterization Study

Final Report

fJ3Rf~RY COpy NOV 241980

Lf.! ~C.L[( R~SE';"lCH CErnER

L,3R;RY, r~ASA

HAMPTON, VIRGIl'!IA

National Aeronautics and Space Administration 1111111111111 1/1/ 111111111111111 111/111111111 NI\S/\ John F. Kennedy Space Center

NF01837

KSC FORM 16-12 (REV 8/76)

https://ntrs.nasa.gov/search.jsp?R=19810002770 2020-06-13T18:47:26+00:00Z

OPTICAL FIBER DISPERSION

CHARACTERIZATION STUDY

CONTRACT #NAS10-9455

FINAL REPORT

DECEMBER 1979

N r /- II L 7i .J-

f'-,

ABSTRACT

"Optical Fiber Dispersion Characterization Study"

NASIO-9455 FINAL REPORT

This report presents the theory, design, and results of

optical fiber pulse dispersion measurements. Detailed de-

scriptions of both the hardware and software required to

perform this type of measurement are presented. Hardware

includes a thermoelectrically cooled ILD (Injection Laser

Diode) source, an 800 GHz gain-bandwidth produce APD

(Avalanche Photo Diode) and an input mode scrambler. Soft­

ware for a HP 9825 computer includes fast fouirer transform,

inverse fouirer transform, and optimal compensation de-

convolution. Test set construction details are also included.

Test results include data collected on a I Km fiber, a 4 ~

fiber, a fused spliced, eight 600-meter length fibers con-

catenated to form 4.8 Km, and up to nine optical connectors.

This work was performed at Kennedy Space Center with the aid

of University of Central Florida, Orlando, Florida, under

contract NASIO-9455.

OPTICAL ~IBER DISPE~SION CHARACTERIZATION STUDY AT KENNEDY SPACE CENTER~ ;PART II

by

Sedki M. Riad, Michael E. Padgett Alan Geeslin, Achia AR Riad

An optical fiber dispersion characterization test set

was developed at Kennedy Space Center with the aid of the

University of Central Florida, Orlando, Florida. This

development included the test algorithin development, hardware

design and signal processing software implementation for HP

9825 computer. Part I, presented at FOC 79, reported the

characterization of fibers up to 2ft Km in length. Test set

and software modifications include the thermoelectrically

~ cooled ILD source, 800 GHz gain bandwidth product APD,

addition of a modescrambler and development of a frequency

domain optimal compensation deconvolution routine. Test data

was collected on 4 Km lengths of fiber, a fused splice, eight

600 meter lengths of fiber concatenated to form 4.8 Km, and up

to nine optical connectors. Results showed the 4 Km fiber

to have a bandwidth of 290 MHz, which relates to a 1.16 GHz

Km capacity and a dispersion of 1.10 ns full duration at half

maximum FDHM or 0.275 ns/Km. The fused splice showed a

bandwidth of greater than 2 GHz,as did a total of nine

connectors.

FOREWORD

The work reported herein was accomplished by Drs. Sedki,

M. Riad and Aicha A. R. Riad, formerly Assistant Professors of

Electrical Engineering, University of Central Florida, Orlando,

Florida, and currently with the Electrical Engineering

Department, Virginia Polytechnic Institute and State University.

ment:

The following students participated in the work accomplish-

1 - Alan E. Geeslin, M.S.

2 - Robert B. Stafford, M.S.

3 - Seward T. Salvage

4 - Glenn A. Birket

Mr. Geeslin and Mr. Stafford used their work for their

Master's degrees in Electrical Engineering, University of

Central Florida, December 1979.

The authors would like to asknowledge the invaluable

cooperation of Mr. Michael E. Padgett, Design Engineer,

Electro-Optic Laboratory, Kennedy Space Center, throughout

the course of this work.

i

OVERVIEW

Kennedy Space Center's requirements for high data rate

and wideband transmission led to the development of an optical

fiber communication evaluation program in 1973. This program

has involved the development and evaluation of optical fiber

components and systems. In June 1977 an optical fiber cable

was installed in KSC's harsh, underground ducts for evaluation.

This 2Km, fiber cable has been used to test fiber systems up

to 16 Km in length. In addition to testing major system

components, the optical parameters of the fiber are being

closely monitored.

The pulse dispersion characteristics/frequency transfer

function of the optical flber is considered to be one of the

key parameters of the cable. KSC required technical assistance

in developing a method to measure and analyze this parameter.

This wa~ the subject of the first portion of the study perform­

ed by the Optical Communications and Signal Processing Group

at UCF in cooperation with the Electro-Optic Laboratory at

KSC. The basic objective of this study effort is to design

an algorithm for optical fiber dispersion analysis to be

used by the KSC Electro-Optics Laboratory on a regular basis

to detect possible changes in optical fiber transmission

links with age. It will also establish a basis for evaluating,

specifying, and acceptance testing future fiber cables.

Dispersion information about an installed fiber system is

ii

essential to obtain maximum bandwidth capability.

As a result of the first portion of the study, an

algorithm for determining the fiber's optical dispersion

was developed, an experimental set up for measuring the

optical dispersion was built, and the associated signal ac­

quisition and processing software was written and debugged.

The following is an outline for the optical dispersion test

algorithm:

1. Launch a short duration optical pulse into a reference

fiber.

2. Measure and record the detected fiber output. This

signal is considered the reference waveform.

3. The response waveform is to be recorded by repeating

the above procedure while inserting the fiber under

test in the optical path.

4. Apply the Fast Fourier Transform to both the refer­

ence and the response waveforms to obtain their

frequency domain forms.

5. Apply frequency domain deconvolution to both fre­

quency domain transforms to obtain the fibers transfer

function and impulse response.

6. The frequency domain resolution of the resulting

transfer function can be increased by using a

resolution enhancement procedure developed for

this study.

7. Display the magnitude and phase components of the

inverse of the transfer function in the form of

iii

attenuation in dB and phase in degrees vs frequency

on a logarithmic scale.

8. Fiber bandwidth is the frequency at which the

attenuation is 3 dB higher than its low frequency

value. And fiber dispersion can be indicated by the

full duration at half the maximum (FDHM) of the im­

pulse response.

The short duration optical pulse used in steps 1 and 3

above was generated using an Injection Laser Diode (ILD), and

an Avalanche Photo-Diode (APD) was used for the optical

detection in steps 2 and 3. Signal acquisition and processing

were performed using a Digital Processing Oscilloscope

(Tektronix DPO) interfaced with an HP9825 desk-top minicomputer.

Optical dispersion data were collected for I and 2.4 km

fiber pieces. The results of these measurements indicated

that several test set modifications could improve the measure­

ment capability. Such modification would allow the measurement

of KSC's 8 krn link used for lab work and component and system

evaluation.

As an extension to the above mentioned study, KSC requested

the design of modifications to the existing pulse dispersion

test set to increase its measurement capabilities. The target

for the measurement dynamic range was 45 dB, and for the band­

width was 100 MHz to 3 GHz with 10 MHz resolution. KSC also

requested the collection and analysis of dispersion data for

various fiber lengths as well as various types of fiber

connectors and splices. This information is to be used to

iv

.,

predict the total dispersion properties of a fiber link composed

of various fiber lengths, connectors and splices.

As a result of the study extension, the following modifi­

cations to the pulse dispersion test set (POTS) were designed

and implemented:

1. The design and construction of a highly stable, long

life, ILD impulse generator/trigger source. The

impulse generator is operating at a higher repetition

rate (- 15 kHz) and is thermoelectrically cooled.

2. The design and construction of a new APO biasing/

coupling circuit which reduces the transient over­

loading of the DPOls sampling unit (Tek. 7Sl2/S6).

3. The use of a high gain-bandwidth product APD,

(Spec. 800 GHz). The maximum bandwidth of this APD

is 2 GHz, at gain values up to 100.

4. The use of reliable, wideband, low attenuation

connectors for inserting the fiber under test in the

optical path. In this method the reference fiber

is to be included in the response measurement and

therefore maintaining the same launch and coupling

conditions in both reference and response measurements.

5. The development of the optimal compensation frequency

domain deconvolution technique which proved to yield

good results with very low noise content.

The computer software was modified to accommodate the

above mentioned modification. And the modified POTS was used

v

for testing a 4 km fiber length. The current dynamic range

of the modified PDTs is sufficient for testing fibers up to

8 km in length.

The modified PDTS was used to study dispersion proper­

ties of a fuse splice and one type of connectors. The study

showed that both the splice and the connector have frequency

bandwidths greater than 2 GHz, (the PDTS' current bandwidth

measurement limitation). Also, measurements were made to

determine the dispersion properties of concatenated fibers.

The results of this test displayed some irregularity. How­

ever, an average relation for the fiber's bandwidth vs.

length is graphed in the report.

In the conclusion of this study, KSC has the capability

to evaluate optical dispersion properties of fibers and

fiber components, and to determine their useful bandwidths.

The test set and software may require future modifications

to allow the evaluation of single mode fibers and corres­

ponding components, as well as the operation at longer

wavelengths.

The ability to evaluate optical fiber dispersion para­

meters will play an important role in KSC's specifications,

procurement, and operation of future f1ber communication

systems.

Principle Investigator: Sedki M. Riad .fdA; t1. Kia.l

Co-Investigator Aicha A. R. Riad

vi

i

.,

CON TEN T S

Page

FOREWORD i

OVERVIEW ii

CONTENTS iii

1. INTRODUCTION 1

II. APPROACH 2

III. EXPERIMENT 4

IV. DEVICES 6

V. SIGNAL PROCESSING 9

VI. SOFTWARE 14

VII. DISPERSION MEASUREMENTS AND RESULTS 14

VIII. DISCUSSION 19

IX. REFERENCES 22

FIGURES 23

APPENDICES

A. FREQUENCY DOMAIN OPTIMAL COMPENSATION

DECONVOLUTION 76

B. COMPUTER SOFTWARE 99

C. DISPERSION TEST RESULTS ON CONCATENATED

FIBERS 117

vii

OPTICAL FIBER DISPERSION CHARACTERIZATION STUDY

CONTRACT # NAS 10-9455 FINAL REPORT

DECEMBER 1979

I. INTRODUCTION

Kennedy Space Center's requirements for high data rate

and wideband transmission led to the development of an

optical fiber communication evaluation program in 1973.

This program has involved the development and evaluation of

optical fiber components and systems. In June 1977 an

optical fiber cable was installed in KSC's harsh, underground

ducts for evaluation. This 2Km, fiber cable has been used

to test fiber systems up to 16 Km in length. In addition

to testing major system components, the optical parameters of

the fiber are be1ng closely monitored.

The pulse dispers10n characteristics/frequency transfer

function of the optical fiber is considered to be one of

the key parameters of the cable. KSC required technical

assistance in developing a method to measure and analyze

this parameter. This was the subject of the first half

of the study performed by the Opt1cal Communications and

Signal Processing Group at UCF in cooperation with the

Electro-Optic Laboratory at KSC. The basic objective of

th1s study effort is to design an algorithm for optical

fiber dispersion analysis to be used by the KSC Electro-

2

Opt1CS Laboratory on a regular basis to detect poss1ble

changes in optical fiber transmission links with age.

It will also establish a basis for evaluating, specifying,

and acceptance testing future fiber cables. Dispersion

information about an installed fiber system is essential

to obtain maX1mum bandwidth capability.

As an extension to the above mentioned study, KSC

requested the design of modifications to the existing pulse

dispersion test set to increase its measurement capabilities.

The target for the measurement dynamic range was 45 dB, and

for the bandwidth was 100 MHz to 3 GHz w1th 10 MHz resolution.

KSC also requested the collection and analysis of dispersion ry data for various fiber lengths as well as various types

of fiber connectors and splices. This 1nformation is

to be used to predict the total dispersion properties of

a fiber link composed of various fiber lengths, connections,

and splices. This final report is a complete overview

of the work done in the above mentioned optical dispersion

study. The report presents the approach, the experiment,

the analysis, as well as the results of the study.

II. APPROACH

To fully characterize a device (a f1ber or connector,

etc.) in terms of its pulse dispers10n, 1t 1S needed to

define either: ~ I 1

( 3

1. The impulse response waveform h(t); which is the device output due to an ideal impulsive input (Dirac delta impulse) •

2. The complex transfer functlon H(e jw ); WhlCh is the ,ratio between the device harmonic outp~t Y(e Jw ) and the exciting harmonic input X(e JW ).

Presenting the device response in the time domain form

h(t) displays its dispersion properties and therefore the

limit on signaling speed (rate) of the transmitted information.

However, h(t) will not give a direct measure for frequency

or phase-shift distortion at high transmission rates. This

information, as well as a direct determination of the useful

frequency bandwidth of the fiber, is directly obtainable

from the frequency domain presentation H(e jw).

Since a true Dirac delta time impulse cannot be

generated,a duration-limited input impulse x(t) wlll be

used. The output waveform yet) due to x(t) can be written

as

yet) = h(t) * x(t)

where (*) denotes the convolution operation, Figure 1.

Appendix A* describes in detail the deconvolution procedure

to obtain H(e jw ) and h(t). In the following a brief

summary of the procedure is presented.

*Appendix A is a copy of a paper submitted for publication

to the IEEE Trans. on Acoust., Speach & Signal Processing.

4

First, apply the Fourier transform to the time domain

waveforms x(t) and yet) to obtain X(e Jw ) and Y(e jw ),

respectively, for which

Y (e jw ) = H (e jw ) • X (e jw ) .

Second, calculate H(e jw ), the complex transfer function as given by

H(e jw ) =Y(e jw ) • x*(ejw)/[Ix(e jw)12 + A]

where x*(e jw ) is the complex conjugate of x(e Jw ), and

A is an optimization parameter. The optimum value for

the parameter A yields the lowest noise content in the

deconvolution result. Finally, apply the 1nverse Fourier

transform on H(e jw ) to obtain h(t). This is the optimal

compensation frequency domain approach to deconvolve

x(t) from yet) to yield h(t), Figure 2. In this approach

both H(e jw ) and h(t) are available.

III. EXPERIMENT

Figure 3 shows the experimental set-up and devices to

be used in the dispersion characterization test. For cost,

size, and convenience considerations, an injection laser

diode (ILD) is to be used for optical impulse generation,

and an avalanche photodiode (APD) for optical detection.

To insure uniform mode loading in the fiber/connector under

test, a mode scrambler is used at the ILD (launch) side.

The faster the temporal (impulse) response of the ILD/mode

scrarnbler/APD combinat1on, the better the accuracy of the

oS , I

"

5

results will be. For picosecond time resolution, a

sampl~ng osc~lloscope is needed to observe the detected

waveforms. Also, to compensate for the signal time delay

in various devices, as well as in the fiber length, a

variable time delay unit is needed. Delay variations

should correspond to various fiber lengths used in the

test set. Finally, for signal processing, a digitizing,

acquisition and computation system is needed, e.g. a digital

processing oscilloscope (DPO) / minicomputer combination.

The dispersion test is designed to be an insertion

type measurement. For fiber testing, a typical arrangement

is shown in Figure 4, and the corresponding procedure

would be as follows: A reference waveform x(t) is recorded

as the detected APD output while a short piece of fiber

(~2 m length) is Joining the optical path between the

mode scrambler and the APD. The short fiber is used to

account for the input and output launch conditions such

that the resulting transfer function becomes more independent

of alignment and interface geometry. The response waveform,

y(t), is then recorded by inserting the fiber to be

characterized between the mode scrambler and the short

fiber and acquiring the output of the APD. The insertion

is performed by the help of fiber connectors. The connectors

used were tested to show repeatability within ±O.S dB.

The connector's response has to be accounted for in the

6

signal processing to determine the fiber's response.

However, for the fiber connector dispersion test, long

fiber pieces are needed on both sides of the connector (s)

to simulate real applications. The arrangement for this

test is shown in Figure 5 to consist of the same mode

scrambler and short fiber pieces, two 600 m (long) pieces,

and a 6 m piece fuse-spliced to the two 600 m fibers.

The reference waveform x(t} is recorded and then the

6 m piece is broken at a point where the connector under

test is installed and the response waveform y(t} is then

acquired.

IV. DEVICES

This section of the report discusses the choice of

devices to be used in the test, Figure 3, and the electronic

circuitry associated with them.

A. The Optical Source

The SG 2002 semiconductor injection laser diode (ILD)

was chosen because it 1S one of the commercially available

pulsed ILD's with low current threshold and capable of

generating 2 watts of optical power in the form of approximately

100 ps pulses [1].

This ILD requires a current pulse generator that can

deliver 3.5 Amps for time durations less than 1 ns (100 ps

to 1 ns). An 1mpulse generator having these specifications,

<t t I

7

with repetition rates suitable for sampling oscilloscope

monitoring, was designed by Dr. James R. Andrews of the

National Bureau of Standards, Boulder Laboratories [1].

The impulse generator schematic is given in Figure 6.

This impulse generator requires a triggering pulse of

approximately 2 volts amplitude and 2 ns duration. A

trigger circuit designed to meet these requirements is

given in Figure 7. This circuit also provides two additional

features:

a) variable delay control for the trigger output

with respect to the pretrigger which triggers the

DPO, and,

b) variable repetition rate control.

The repetition rate has to be kept low (~5 KHz) for long

life operation of the impulse generator's avalanche

transistor. However, for better signal acquisition,

the repetition rate has to be increased. This problem

was resolved by increasing the repetition rate while

cooling the avalanche transistor.

The impulse generator circuit/ILD were built on a

thermoelectrically cooled copper block. Cooling both the

avalanche transistor and the ILD help increase their life­

times as well as reduce the jitter noise in the generated

optical pulse. Both the avalanche transistor and the ILD

were thermally in contact with the cooled block. The

, ..

8

construction details of the lmpulse generator circult/ILD

are given in Figure 8, and the thermoelectric cooling element

and regulating circuit are shown in Flgure 9.

B. The Mode Scrambler

The mode scrambler used is shown in Figure 10. It

consists of joining three 1 m fiber pleces ln series,

a step-index fiber, a graded-index, and a step-index fiber

[ 2 ]. The joints are made by fuse splicing the fibers

together. This mode scrambler significantly reduced

the dispersion measurement variations due to source

launch-condition changes.

c. The Optical Detector t),

The PD 1002 semiconductor avalanche photodiode (APD)

was chosen as the optical detector because it is the best

commercially available APD. This APD is specified by the

manufacturer to have an 800 GHz gain-bandwidth product.

Figure 11 shows the circuit used to bias the APD and couple

the detected output to the sampling oscilloscope.

D. Sampling Oscilloscope / Signal Processing Systems

The sampling oscilloscope used in this set-up for

acquiring the detected waveforms is a Tektronix S6-7Sl2

sampling unit installed in a digital processing oscilloscope

(DPO). This DPO was interfaced and controlled by an HP 9825

computer. Software was wrltten to acquire, process, and

display data taken using this equipment configuration.

r

9

One important finding to report at this point is that

the test set-up as described here displayed about 20 ps

of jitter noise in detected waveforms. This jitter noise

was reduced considerably by software signal averaging.

However, due to the long time involved in this process

(approximately 4 minutes for 50 averages), other sources

of noise and errors such as thermal fluctuations and drifts

are introduced in the averaged waveform.

V. SIGNAL PROCESSING

The dispersion test as described before requires

the acquisition of two time domain waveforms. These

waveforms will then be transformed to the frequency domain

using the fast Fourier transform (FFT). The FFT's frequency

domain resolution is related to both the time domain

resolution and the number of processed points (samples)

by the relation: [3]

~T • ~f = 1 / N

where ~T is the time duration between two samples in the

time domain waveform, and ~f is the frequency spacing

between two samples in the frequency domain transform,

Figure 12.

To increase the signal processing accuracy and resolution,

N must be taken as large as possible. The DPO can give

up to 512 time domain samples for a waveform. However,

for a duration limited signal, it is possible to increase

the number of processed points by adding new points (samples)

10

of zero magn1tude, thereby extending the time window.

N can be increased using this "add zeros" technique up

to 1024 points, a limit imposed by the KSC's HP 9825

capacity and the amount of signal processing involved

in the dispersion test. It is important to realize

that the "add zeros" technique can be used only to enhance

the frequency domain resolution since AT, and hence the

time domain resolution, is limited by the 512 samples

11mit imposed by the DPO, and also by the acquisition

time window.

Having these limits in m1nd, the choice of the

acquis1tion time window 1S critical and is the only

controllable variable in setting the time and frequency

domain resolutions. The following example illustrates

this point:

Example: Let T denote the fastest transition duration

in the acquired time domain waveform. The correspond1ng

bandwidth in the frequency domain can be estimated as:

[4]

BW '" 0.35/T

T1me and frequency domain resolutions can be expressed

in terms of Nt and Nf : the number of samples within T

and BW, respectively, Figure 13.

BW = N • f

td

f"-I

11

Using these relations, it follows that:

Nt • Nf • AT • Af = •. BW = 0.35

but

AT • Af = liN = 1/1024

therefore,

Nt • Nf ~ 360

For equal degrees of resolution in both time and frequency

domains, take

Therefore,

AT = ./Nt

~ ./20

and the corresponding DPO acquisition time window is

given by

512 AT ~ 25., or • ~ T/25.

As will be seen later in this section, it is possible to

increase the frequency domain resolution, i.e. increase

Nf , with interpolation using the FFT properties. Hence

it might be advisable to favor Nt over Nf rather than

equating them.

In the dispersion test, both reference and response

waveforms must be acquired with the same ~T in order to

have point to point correspondence in both time and frequency

domains. In this case it is preferable to choose T based

on the impulse response information. A preliminary run

can be used to estimate • for the impulse response waveform,

from which T can be chosen.

12

Once the waveforms are acquired, the FFT is used to

obtain the corresponding frequency domain transforms.

The complex transfer function H{e jw ) is then obtained

as described in Appendix A. The impulse response h{t)

can be obtained by applying the ~nverse fast Fourier

transform (IFFT) to the obtained H{e jw ).

As mentioned earlier in this section, the transfer

function's frequency domain resolution can be increased

with an interpolation technique using the FFT properties.

The process is shown in a block diagram form in Figure

14. The idea is to apply IFFT on M sample points out of

the total N sample points (M < N) , provided the transfer

function's bandwidth is included in the processed band

(M/2 > Nf ). The obtained time domain transform (impulse

response) will contain M sample points equally spaced

by

t.T = l/{M • t.f) M

Using the lIadd zeros ll technique to increase the number of

processed points back to N, the resulting frequency domain

transfer function will contain N sample points with frequency

spacing:

= M flf N

which is less than flf; i.e. the frequency domain resolution

was increased by a factor of N/M.

~ )

')

13

Finally, the complex transfer function H(e jw )

can be presented in magnitude and phase functions of

frequency. An alternative is to present the information

in the l/H(e jw ) magnitude of phase (attenuation and

phase) functions of frequency. The attenuation function

expressed in DB is given by:

ATTEN = -10 loglO H{e Jw )

and the phase function is given by:

PHASE = - arg [H(e jw )]

where arg [ ] is the continuous argument function. This

argument function is to be formed by reconstructing the

computed argument defined between -~ and +~, to make it

a continuous one by adding (or subtracting) integer

multiples of 2~, Figure 15. The continuous argument

function will contain a linear phase component, which

needs to be removed in order to reveal the details of

the phase function. This linear phase component is due to

the difference between the fiber-length delay and the compensating

delay-unit delay times. Eliminating this linear component

does not affect the information content of the phase function

regarding the dispersion characteristics, and therefore the

amount of linear phase to be eliminated is arbitrary, Figure

16.

14

VI. SOFTWARE

The required computer software for performing the

dispersion characterization test as described earlier was

written for the DPO/HP9825 system. This software is given

here in three forms: block diagram in Figure 17, flow

charts, and HP9825 listings in Appendix B.

VII. DISPERSION MEASUREMENTS AND RESULTS

In this section, four dispersion tests will be presented

along with the corresponding results. The four tests

were performed to study long fiber length dispersion

properties, the effect of concatenating fiber lengths

on dispersion, dispersion properties

of a fused-splice and finally dispersion properties of a

single-connector and multi-connectors in optical fiber

links.

A. Dispersion due to long fiber lengths

The optical fiber dispersion characterization test

was performed on fiber lengths up to 4 km. The various

test waveforms and related processing signals for the

4 km length fiber are demonstrated in Figure 18. As seen

from the figure for the computed fiber's impulse response

h(t), the 4 km fiber has a 1.10 ns full duration at half

the maximum value (FDHM), which corresponds to an FDHM

15

dispersion of 0.275 nS/km. Also, from the figure for the

fiberrs attenuation function, the 3 DB bandwidth of the

4 km fiber is 290 MHz, which corresponds to a 1.16 GHz.km

fiber bandwidth capacity (bandwidth-length product). These

values are in close agreement with the 2.4 km results

previously given in Progress report III. The 2.4 km

values are 0.28 ns/km for dispersion and 1.34 GHz.km

for bandwidth-length product.

b. Concatenation of Fibers and Dispersion

In this experiment, eleven 600 m fiber loops were

used to study the effect of concatenation on dispersion.

The dispersion test was performed on the individual 600

m. loops, the results are given in AppendixC. A sample

result(loop #1) is given in Figures 19 and 20. Ten of

the eleven 600 m. loops were then used to form five 1.2

km loops by fuse splicing. The dispersion test was run

on the individual 1.2 km loops. The test results are

also given in Appendix C, and a sample result is given

in Figure 21 and 22. This time, four of the five 1.2

km loops were used to form two 2.4 km loops. Again, the

dispersion results on the individual 2.4 km loops are given

in Appendix C, and a sample is given in Figure 23. Finally,

the two 2.4 km loops were concatenated to form one 4.8 km

loop. The dispersion test was performed on the 4.8 km loop

and the result is given in Appendix C as well as in Figures

24 and 25.

16

TABLE 1

600 m 1.2 km 2.4 km 4.8 km

LOOP BW LOOP BW LOOP BW LOOP BW # MHz # MHz # MHz # MHz

1 1300

2 1400 2,3 870 2-5 455 2-9 110

3 1260

4 1380 4,5 1580

5 1600

6 1105 6,7 915 6-9 440

7 1740

8 1145 8,9 905

9 1490

10 1600 10,11 1420

11 1405

»

17

The 3 dB frequency bandwidths as computed from the

fiber loops transfer functions are listed in Table 1.

These data are also plotted in Figure 26 in an attempt

to fit them to the power relation

1(BW)m = constant

where t is the length of the fiber loop and BW is at

3 dB frequency bandwidth. Taking the log of the above

relation, it can be written that,

log (BW) = I log (t) + constant m

Plotting log BW vs. log t in Figure 26 did not display

the straight line relation suggested by the above equation.

However, local fitting of the power relation for various

ranges of t yields the following values of m:

m ~ 1. 63 0.6 km < t < 1.2 km

m ~ 1. 04 1.2 km < 1 < 2.4 km

m ~ 0.5 2.4 km < t < 4.8 km

c. Optical dispersion of a fuse-splice

The test arrangement for the fuse-splice was described

earlier in this report and is shown in Figure 5. The

reference waveform was acquired using a 6 m piece fuse-

spliced to two 600 m fiber loops. The 6 m piece was then

broken then fuse-spliced and the response waveform was

acquired. Reference and response waveforms are shown in

18

Figures 27 and 28a, respectively. Figure 28b shows

the fuse-splice attenuation and phase as functions of

frequency. As seen from the Figure, the 3 dB frequency

bandwidth of the fuse-splice is >2 GHz.

d. Optical dispersion of connectors

The same arrangement and procedure used to test the

fuse-splice was used to test a single connector. The

reference waveform in this test is the same one aquired

in the fuse-splice test, given in F1gure 27. The single

connector response waveform as well as the attenuation

and phase functions are given in Figures 29a and 29b,

respectively. Figure 29b shows a 3 dB bandwidth of the

single connector to be >2 GHz.

The dispersion test was repeated while inserting

more connectors within the 6 m piece. This experiment

was performed to study the effect of closely spaced connectors

on dispers1on. The results for the cases of 3, 6, and 9

connectors are given in Figures 30, 31, and 32, respectively.

The 3 dB bandwidth for these 3 cases was also >2 GHz.

19

VIII. DISCUSSION

Dispersion measurement performed on the 4.8 km concatenat­

ed fibers revealed that the current dynamic range of the KSC

pulse dispersion test set (POTS) is approximately 25 dB. With

the addition of a 20 dB gain wideband amplifier on the detected

signal line, the dynamic range can be increased to the requested

45 dB value. One of such wideband amplifiers has been ordered

by KSC and was not available for use until the present time.

On the other hand, dispersion measurements on splices and

connectors showed that the POTS' bandwidth is in the neighbour­

hood of 2 GHz with 6.25 MHz resolution. Although all the pro­

posed techniques for improving the system's bandwidth was not

obtained. The current limiting factors are:

I-Limited number of waveforms acquired for averaging because of

the long averaging time.

2-Limited bandwidth of optical detection, although the manu­

facturer's specifications for the APD used is 800 GHz gain­

bandwidth product, the bandwidth of the APO was found to be

about 2 GHz.

In the following, the results of the dispersion test pre­

sented in the previous section will be discussed, and their

implications will be analyzed.

a-The results of the 4 kID fiber test were in close agree­

ment with those of the 2.4 km fiber. This shows con­

sistency of the KSC POTS performance. It also increas-

20

es the confidence level in the test results.

b-Although the test on an 8 km fiber length was not per-

formed because of time limitations, it is felt that the

PDTS is capable of performing such measurement. The

reasons are: first, the 8 km fiber requires less band-

width limitations than the 4 km fiber. And second, the

4 km fiber displayed low frequency attenuation of 10 dB,

i.e. the 8 km fiber is expected to have about 20 dB low

frequency attenuation, which is within the PDTS current

dynamic range.

c-Test results on concatenated fibers showed some tendency

to be inconsistent. As seen from Table 1, joining two

600m fiber pieces, loop #4 with 1380 MHz bandwidth, and

loop #5 with 1600 MHz bandwidth, resulted in a 1580 MHz

bandwidth for the concatenated 1.2 km loop. While join-

ing loops #10 and #11 with bandwidths 1600 MHz and 1405

MHz, respectively, yielded a 1420 MHz bandwidth for the

combination. Also, in concatenating 1.2 km fibers to

form 2.4 km lengths, bandwidths of 870 MHz and 1580 MHz

resulted in a 455 MHz, while 915 MHz and 905 MHz Ylelded

440 MHz. This inconsistency is due to the differences

between the varlOUS fiber pieces in their graded-index

of refraction profile (dispersion compensation). An

overcompensated fiber piece concatenated with an under-

compensated one may result in an overall performance

close to that of a correctly compensated fiber.

, I I

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21

d-The dispersion test was performed on only one type of

splices and only one type of connectors because other

types were not available for testing in time. The

test showed that the fuse splice as well as the con-

nector have fai1y wide bandwidths (greater than 2 GHz).

The test also showed that the POTS is unable to yield an

accurate value for bandwidths greater than 2 GHz.

Finally, two points need to be discussed concerning the

current KSC's POTS limitations mentioned earlier in this

section:

l. Limited signal averaging capability can be improved

only by high speed hardware signal Averaging.

2. Limited optical detection bandwidth can be improved

by using faster optical detectors.

Neither the high speed hardware signal Averager or the faster

optical detector are commercially available. But, it is be-

lieved that the speed of the currently used APO can be improved

by removing it from its commercial packaging and mount it on

a high frequency strip line built on a substrate using the

Thick-Film technique. The biasing and coupling circuit can

be also built on the same substrate.

22 -

IX. REFERENCES

[1] J. R. Andrews, "Inexpensive Laser Diode Pulse

Generator for Optical Waveguide Studies," Rev.

Sci. Instrum., Vol. 45, No.1, pp. 22-24, January

1974.

[2] W. F. Love, "Novel Mode Scrambler for Use in Optical­

Fiber Bandwidth Measurements," Topical Meeting on

Optical Fiber Communication Digest, Washington, D.C.,

pp. 118-120, March 6-8, 1979.

[3] W. D. Stanley, Digital Signal Processing, Reston

Publishing Company, Inc., a Prentice-Hall Company,

Reston,Virginia, 1975, Ch. 9.

[4] H. Wallman, and G. E. Valley, Vacuum Tube Amplifiers,

New York: McGraw-Hill, 1948.

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FIGURE 2: THE OPTIMAL COMPENSATION FREQUENCY DOMAIN DECONVOLUTION PROCESS

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ENHANCEMENT WITH INTERPOLATION

USING THE FFT PROPERTIES.

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PROCESSING FLOW CHART

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APPENDIX A

FREQUENCY DOMAIN OPTIMAL COMPENSATION DECONVOLUTION

by Sedki M. Riad

Department of Electrical Engineering Virginia Polytechnic Institute and State University

Blacksburg, Virginia 24061

ABSTRACT

76

A new approach for deconvolution in the presence of

noise is presented. The approach involves a frequency

domain optimization of a single variable to design an

optimum frequency domain compensating function. An

illustrative application on optical fiber impulse response

characterization is shown with very low noise in the

deconvolution results.

77

I. Introduction

The present paper introduces a new approach for

solving the deconvolution problem in the presence of noise.

The new approach involves the design of a frequency domain

optimal compensating functions. This compensator is to be

applied to the convolution product to yield the required

deconvolution result. The design of the optimal compensator

involves a frequency domain optimization of a single variable.

Using the Fast Fourier Transform, FFT, the deconvolution

computation time is considerably short and the programing

is simple.

In the next section, the deconvolution proble~ will

be defined and noise source will be identified. Previous

approaches to deconvolution are surveyed and discussed.

In section III, the development of the optimal compensator

design is presented. And finally, in section IV, an

illustrative application is shown to yield successful low

noise deconvolution.

78

II. THE DECONVOLUTION PROBLEM

Deconvolution is the process of separating a convolution

component from a known convolution product. In time domain

representation, if x(t) and h(t) and the convolution

components, y(t), the convolution product is

y(t) = f X(T) h(T - t) dT (1)

or

y(t) = f h(T) X(T - t) dT (2)

The symbolic representation of either of the above convolution

integrals is

y(t) = x(t) * h(t) (3)

where * denotes the convolution operation. Hence, deconvolu-

tion is the process of determining x(t) knowing both y(t) and

h(t), or determining h(t) knowing both y(t) and x(t).

The deconvolution process is often encountered in linear

system analysis and characterization. In time domain measure­

ments of a linear system, Figure l,y(t) represents the output

signal of a system due to an exciting input signal x(t), while

the system's impulse response is h(t).

In frequency domain representation, Figure 2/ the convolution

process converts into a product one

(4)

79

where Y(ejw), X(ejw) and H(ejw) are the frequency domain

representations (Fourier transforms) of y(t), x(t) and

h(t), respectively. Based on equation (4), deconvolution

takes the simple form of division, i.e.

or

(6)

From equations (4), (5), and (6) it is clear that the same

deconvolution process may be used to obtain either of X(ejW )

or H(ejW). Therefore, without loss of generality, only

equation (6), the deconvolution to obtain H(ejW ) will be

considered in the rest of this paper.

It can be concluded from equation (4) that the zeros of

X(ejw) are also zeros of Y(ejW ). The same is also true for

poles. At these points, (zeros and poles), equations (6)

will become indeterminate. Consequently, the result of the

division operation will be erronious unless the poles and

the zeros of X(ejw) are exactly cancelled out by those of

Y(ejw). Any errors in the data representing X(ejW ) and

Y(ejW ) degrade the cancellation and introduce errors (noise)

in the resultant H(ejW). These noise like errors in the

H(ejw ) will be clustered around the poles and zeros of X(ejW ).

When H(ejw ) is transformed to the time domain to obtain h(t),

the noise like errors will cover the entire transform time

window, swamping the useful information content.

Typical sources of errors in X(ejW ) and Y(ejw) are

80

sampling errors and noise in signal acquisition, leakage

and aliasing errors in the Fourier transformation, and

rounding and computational errors in the computing machine.

The latter two sources can be greatly reduced and neglected

in most cases. While the first source, signal acquisition

errors and noise, is the major one and cannot be overcome

in most practical applications.

Various techniques were developed to reduce the noise

in the deconvolution result, H(ejw). In the following, four

primary approaches will be briefly examined. The first

approach, acquisition averaging is aimed to reduce signal

acquisition errors and noise by averaging several acquisit­

ions taken within a short period of time. This technique is

known to help reduce the noise greatly, but it introduces

another class of errors to the signal due to time drift~l]A second approach is aimed at suppressing the noise in the

deconvolution result by applying a filter~2]The filter will

modify the result H(e jW ) as it eliminates the noise, thereby

introducing its own errors. The third approach in this [3 ]

survey is the iterative technique, in which successive

approximations to an estimated H(ejw), (or h(t)), are made

in order to minimize the error between the computed output

(based on the estimate) and the actual output Y(ejW ), (or

y(t)). The main difficulties in this technique lie in

having a close estimate for H(ejW ) to start with, and also

in formulating a correction function for error minimization.

( f

r

81

Moreover, repeating the iteration process for each decon­

volution operation presents complications since the iteration

is dependent on the form of Y(ejW ). The fourth and final

h · h . I . h' [4] . I approac ~s t e opt~ma compensat~on tec n~que. It ~nvo ves

the design of a compensator (deconvolution) function that

operates on a convolution output to yield one of its inputs.

The design of the compensator involves an iteration process

on a single variable. The iteration process need not be

repeated for various deconvolution operations involving the

same input signal x(t), since the compensator is a function

of X(e jW ) only as will be shown in the next section. Decon-

volution using optimum compensation was developed in the

time domain by previous workers. The process in the time

domain is very inconvenient since it requires inversion of

1 . . [ 4 ] Al h . k' d 1 arge SLze matr~ces. so, t e prev~ous wor ers eve opment

did not include an optimization argument for the interation

process other than getting 'stationary results'.

In the following section, optimal compensation in the

frequency domain will be presented taking advantage of the

convenience and speed of the FFT computations over matrix

inversion.

82

III. OPTIMAL COMPENSATION DECONVOLUTION

The compensation principle in deconvolution is to design

a transfer function C(ejw ) to be applied to Y(ejW) to yield

He(ejW ), an estimate to H(ejW), Figure 3; i.e.,

(7)

The main design criteria is to minimize Ee' the error energy

in the estimate given by n . . 2

Ee = f 1He(eJW) - H(eJw ) I dw (8) o

where n is the frequency band of interest. This minimization

condition yields

which results in an unbounded value for C(e jW), which in turn

yields a noisy form for He(ejW). To limit the noise, another

design criteria will be imposed, C(ejW) will be constrained

to be a bounded function. Since H(ejw ) is a bounded function,

(a physical one), for convenience, the second design criteria

will be to keep the energy Ec finite, where Ec is defined as

n . . 2 Ec = fIH(eJW ) C(eJW )I dw (9)

o

So, the problem is to minimize Ee while keeping Ec

finite. These two requirements can be grouped into one, to

minimize the energy E defined as

83

(10)

where A is an optimization parameter whose significance can

be demonstrated by considering the two extreme cases:

a: A = 0, which results in a minimization of Ee

with no constraints on C(ejw).

b: A = 00, which results in a minimization of C(ejW );

an extreme of keeping it finite.

Both extremes of A are undesirable, and an optimum value

Aopt is expected to yield an optimum compensator Copt(ejW),

for which He,opt(ejW ) is the best estimate for the unknown

input function H(ejw).

Substituting equations(B)and(9)in(10),E takes the form

S1 • • 2 •• 2 E = J{ 1He(eJW) - H(eJw ) I + A IH(eJw)C(eJw ) I }dw (11)

o

using equations (4) and (7), He(ejW ) takes the form:

(12)

which when substituted in (11) yields

E = ~{IH(ejW) X(ejw) C(ejw ) _ H(ejW )1 2

o

S1 • 2 • • 2 = fIH(eJW ) I {IX(eJw ) C(eJw ) - 11

o

84

(13)

where

To make the compensator design a general one, the error

energy E should be minimized for all possible forms of H(ejw),

which implies the minimization of Q(ejw), as can be seen from

equation (13). Using the complex forms

X(ejW ) a XR(ejW ) + jXr(ejW ),

where the subscripts Rand r indicate real and imaginary

parts, respectively, equation (14) yields

To minimize Q, the partial derivatives are set to zero;

and

Using equations (15, (16) and (17), it can be shown that

(15)

~ I

85

(18)

where the superscript (*) denotes the complex conjugate.

Equation (18) above, shows the form for the compensating

transfer function C(ejW ) for a given input X(ejW). Combining

equations (7) and (18), the compensation deconvolution

process yields:

(19)

The value of A in this relation has to be optimized as dis-

cussed earlier. An iterative process is required to find Aopt '

the optimum A, for which an optimization criteria has to be

decided. In the next section, an example is given where

visual inspection of the noise in IH (ejw)1 was used to select e

Aopt ' which yielded good results for He,opt(ejW ) and its

corresponding time form h t(t). e,op

86

IV. AN ILLUSTRATIVE APPLICATION

In this section, the impulse response characterization

of a 4-km optical fiber link will be considered as an illus-

trative application of the optimal compensation deconvolution

technique. The reference waveform (input), x(t),and response

waveform (output), yet), are shown in Figures 4 and 5,

respectively. The fibers complex transfer function H(ejw),

as computed using equation (6), (or equation~9)with A = 0),

is given in Figures 6 and 7 in the form of magnitude and phase

functions. The corresponding impulse response h(t) is given

in Figure 8; while its integration, the step response, is

given in Figure 9. In Figures 6 and 7, the frequency domain

division resulted in noise in the high frequency range above

1400 MHz due to the small values (zeros) of X(ejw ) in that range. ~ This noise resulted in the noise observed in Figure 8 obscuring

the impulse response information.

In order to find Aopt in the optimal compensation decon­

volution technique, equation (19) was used with various values

for A, for which the resulting IH(e jW ) I are shown in Figure 10.

From the figure, it is noticed that in the variation of A

between a and 100 did not introduce any significant changes

in the low noise portion of the response. While a A = 1000

value introduced a noticable change. Based on the above dis­

cussion, Aopt = 100 was chosen for optimal compensation. The

corresponding He,opt(ejW ) as resulting from equation (19) is

given in Figures 11 and 12. The corresponding optimum impulse

87

response h 0 t(t) is given in Figure 13, while its integra­e, p

tion, the step response is given in Figure 14.

Comparing Figures 8 and 13, also 9 and 14, it can be

concluded that optimal compensation eliminated the noise in

the deconvolution operation without any noticeable distortion of

the information content.

V. CONCLUSION

The frequency domain optimal compensation deconvolution

presented here was successful in eliminating deconvolution

noise. Although visual inspection of the deconvolution

result was used to select the optimum valve for A in the

example presented here, other selection criteria can be

developed to suit various application. For example, one

good criterion is to minimize the rms error between the step

responses of the cases A = 0 and A = Aopt ' e.g., to minimize

the rms error between Figures 9 and 14.

It is important to mention in the conclusion that the

iteration in the frequency domain optimal compensation to

find the optimum deconvolution involved only one variable A

and was performed in the frequency domain, thus greatly

reducing the computation time as well as the simple formulation

(programming) required by equation (19).

VI . ACKNOWLEDGEMENT

This work was done as a part of the NASA contract,

NAS 10-9455, "Optical Fiber Dispersion Characterization

Study", for Kennedy Space Center.

VII. REFERENCES

88

1. W. L. Gans and J. R. Andrews, "Time Domain Automatic Network Analyzer for Measurement of RF and Microwave Components," NBS Tech. Note 672, Ch. 9, September 1975.

2. S. M. Riad, "Optical Fiber Dispension Characterization Study," Progress Report III, NAS 10-9455, NASA, Kennedy Space Center, Florida, April 1979.

3. See as an example H.F. Silverman and A. E. Pearson, "On Deconvolution Using the Discrete Fourier Transform," IEEE Trans. Audio Electroacoust., vol. AU-2l, pp. 112-118, April 1973.

4. M. P. Ekstrom, "An Iterative, Time Domain Method of System REsponse Correction," WESCON Technical Papers, Part 14, August 19-22, 1969.

89

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~., ---i-iTTr-- . -- -r- - I ! r-i--I- -- - - --1 ,- --;- --- --- -~ T -or -fl I I I. I I.: ~ '; I 'I 'I fIBl- - --, - r- i- - --- , ~ - - --- i I ---!!' I I

;. ~----- I : : ---' --- - --~-' if- :--------- +------j---- ---I I : t- - 1- j i ~--I-----~----f-- --~-~I-- - - - ,----- -- -- ri - ! -- --- -j- - ; : I ! I I Il:~ 1 i' : • I I I i I I I I -~YD I : i I I 1 I i I . 1 ,: I - I I r - -- f--:- - 1-----, -- -i - - -, - ,-. I - --

~ --- i : -- --1 -1 - -- - ,I - J---' !: - --- ,I - ! i ! i I I \' >I I ,! I I , I ' I' I I _-3~!~; dj~ T[~-t~~- I~I--t~ _m __ !. i di-. i !, IT

I ! I I I, I " I ' I : --T- - I--t-- -1-- --1- --- - - - -- ---;--- -- - - r- j : ---- I Ii' I I I i ~2L-1 I Iii I '_ ,UIIA' ~ - ,-,_--'-1_- -: 1 J 1'- -)- I

,1'vi~l ~i,! I, : I I I : -2~ ~ '-;. '-;-'~' , , , " , ; , : ' 1 I ff I r . i I : Iii' I - , I I I! I.-----l--:-I---I----W I I I I , I I v~l~I-- ----I - - -:- '~ : 1, I 'I

f-- ---:j-----1- ~-I- -l---I-~"- -1-- -- r-- _.- -- /- Vir -- 1,- -- ·1- - -;, I , : i I

r-~~ --: - ! '~~- i p~r-L r;----I -~ 1 I: l\ I L 1-· --+ ----- - --1- --I -- -- --~ 1- -- i ! - - T' :' II 111 I

~L-t 'I ; -I - - -·t'~I---- I--I--!·--e-----+-~;, I, :I'~ --' :t I - - - ,. .. I --- r- - , _.".5,_ : ----~- I 11 -1- ~, - -- -1--: ' -Lt- ---- r- - - : ---+-I~ i J! t I' .

'. I' I I' I II --- ,-t- -I-~r-l: ----!~ L-- -', --- ~'_-T - - \I ----- -- -- - : I! l ! I

L-~ ______ L..l.lL __ ~ __ .__ __ ~L ____ ~_~_ _L 1-1..." . ____ .1.. __ 11 t1 H~, .L__ L J J : i . .1

~)

. . . • I I ! I I I J • , I \ " • • !

Figure 6. IH(ejw ),; Magnitude of Fiber Transfer Function in dB vs. Frequency, as computed using Equation (6) (direct frequency

domain division)

~ )

\0

'"

: I 93

- ------- ," ----- - ----, -------

r _, ___ ~ ________ I ____ _ --------.-

, .. !------T-----, ----1""- -- - ._-___ - --- -- ___ ~ ___________ w

I ------ ---------,------ -------- ----- ---------. -- ", --!. ---- - --, <---

~ ,1-...-.------

~~I ___ '_I'_,~--.-+---~-----+i----~-----------i~'------_-_-__ r .~ ___ ~ ___ ~_

I ---l---"~T~~~'~---~ ...... ~~! ----~~ -f---- I

-i ! - :6:' J-=l J-Hi'll

,--'-l--~-L--~-----; _______ .t--_i --t---~---- - - : S~! _______ J

- I ' I: :: , I \'

! I I ' 11: \ 'I I: I \

i I I I! \ til I

'\

t - I ; I t i \ I

94

Figure 8. Fiber Impulse Response h(t)j The Inverse Fourier Transform of H(ejw) of Figures 6 and 7. (2ns per horiz. div.)

Figure 9. Fiber Step Responsej The Integral of h(t) of Figure 8. (2ns per horiz. div.)

-)

dB - 4S

-'ii"l

-3S

-33

- 2S

-:;m

-IS

-HI

-5:

OJ ') It

Ii ill' (1\ \, ill":t:I!lltI ~ /' . \11 d ,I 1\ 1 I .1. I 1\ \ '} , 'h!\1 I I I, I, II,~ I 1 •

~ 111"1111 ii, '\1 ~, \ 11 "'~;' I' I r \ II, I I II ~ I II, \ ,jl

fl 1111 1 i li11j' (1\'\ !\I :I~rl~ \ /\"\ \.0°

ill I , , 'I tf I I, t l,l '\' r.!/ I f\ '\1

1 ,1 ,: I i III ( I I ,\1 \1 ,It! ~ ~ ,~ I, II ~I ~ I I I, I 1/\ ' , ''', 1\1 ' , I , ,,= '000 ~I 1\ 11/:' \1 ~ II '''/'\ \1\,1 ;: \i li!1 \ I'l,ll'~ I , r\ I"'h h, I,' 'Ill I JI \qlll

t,1 ': .:\ II 1\ lil\' \ : \11\1 rl\: :1' :\~r ;1\1 I'!

)

1 I \1 '.i~I:~f It,' I ,II ; ,II n h ' 1,11/.'[,;1 ,I,~ '\ '\ I) \1 Ii 1 I} M.A ,~.I \ 'J,- I; ,'1:,,\ \Y

"I \ I"

- -------------- I i 1\ i ..

Figure 10.

m ~ I1H~

Choosing A t' IH(ejW)1 vs. Frequency for various values of A. op

1\

I 1.0 V1

:L __ -L _____ ~ ____ ~ ______ 1_=_ t_==-_~ __ =--~-~----~: --- L ee~az i I: I,' , I

---------- -1-- - - - -- ----- ----- - - ------ ---'-----T----'----4-I ===- ___ ~ __ ~ ____________ 1 ___ _ ~~ ___ ,

~ i , c __ - ____ ' _---=:.- -- -- -- -- ---- -- - ----- - - -- ----- - --t---~: ---I~

I 1 , -1- - -I 22

, , --= .::s ------------ - ---~------------- -------.~

l _ _ i I ! i : -C: ----1---1_

-.,..--

I I --:-=======--=- -- -- -- --,

::s~ I

-I

I I I

I ,

1-,

- ...---- I

I I ,

I ==- I ,

~ ! ,

i I I

:~ ,

! I

....s;; "

-~ I I

,

~

~-! I

--, 1

1-1 ----1-1-------1-- ----i --- -f------- ------ ---\- -- t------t---r-

1--~+-, -t-----1--, : -- --~; --t-----.,-:~-!--~-l i I

~ ! ' ; - : i - -+-! --1- : I \' -1 : - ' j

I ; -+-.1--1; --+--~i --I----+:----+---'--~ _+-__ f - r--!--r' - - I--~ -+----:--,-: --1 r ; I' , l i it: ,I

:. I' I' I Iii I ' : : I I :

1 I

: I

.-r I , - r - I ! I - .~ ~ I ! I ! : 1 Ii,

r----...L---~--t---;- : 1--+---0---1 -t--- 1-

! I I 'L I , f---;-------l--- --:- --_-I---r-i--- ---1-_ -i--- ---i--lit : I iii

t----t i --- r ---r-----i - -r-- 1-- t l- -- ---i-, , ,

1

1-­i

!

, 'I . -- -L --- --~ - --,

i I I I ! I I i

Iii I Iii i

~-~ ! I-'~'_-'-I: --~r-- -'11-- ----ill -~- --+1---~- --II' !; --I! -- J--<-!j----l

.::::-: -ti\:-~-~-- - _! ~~ , _, ~ • ~ f- -··rY- - ~4 ----,-:..,.. L' • ,~ I I I -t:_+-·l'I-l_4:r-:-_.I._ , I I I: I : I I 'I I

, 96

til

> -.

3 . .., Q,) '-"

oW Po o Q,)

::t:

~ I

~) o Q,)

"0 ::3 oW 'M ~ CO cO ~

) -) --)

I "! _ __ f- I I ,----- -i-- - 4 ~ II t I, 1h I r _ ~ ITT-I--i 1 __ '_ 9 1 _ : I H~t~. i-I Ii, 1 a 9 1 2 1

J • S I •

i~l:, M-~_f--pEP:mrl ,"'~" ; 1 r ,,----....

I : ! Iii' I I I '-1- -_ -'- - I r4- I; I ,--- - ----- " :

I' ': ~.;; - ~... - r" ... I' - -''-;- ----- ---l-- --: -- -~ _' :; i! I ... ~. .- .. ... I I --11=-[l~L~' l I T-~'- -~ ',' ,'~- , I' I - -- -'l~~ .~~~ - _. 1 ' I , ~ ~I ----1-- ~f-- __ 1 ____ ~~ _ _ -. T ~ - -! , i: T~-- - ~ ~I~~- ~~--, I ! I'l - - II--+--

f-~~-----I----I--I-l' _I"~' -+- _+_.1, ..1 i<\1 . I"~ .-~- ... I' ,1 • I . I," 3 j'.~ ~ r~ -; ~~: I JI! I I

~i

I --r--I ~rr --y- : I I - NI[ l'-r-ll!r ~---~j --- - ~il-:-' --;- ~~-r'-~ i i ~ ftI' llll f--'f-~--- I 1.- --- --- 1 , -_:.-1---- -:- -~11111--

I I I I ~: I I " I 'I I , '

-- r---: --i I I

I • __ I !

1

I I

I

-,

I I I

I

I

I -- -~I---- --T- --1--1- --- - ---- -- - -~--': ---- -1- i I ~~~lrJ ~ -- -r- I -I I I ' . I l-,-~t \

: I, I,

I

I"

l 1

, I -.l -; r-'-I i I

CDI I I I .--L ' ; L1 ~I ',i j 1 ,J --1-" , I ,; - I '-7--- _:! --,

, -- --I - -- - - - -- - ---! /1: - - I 1- - - -- --- I

_--\-I-~~_- --l ... -~ -. -._~.o/r~//'v -; I' nTr-LI----- J __ ~ _L :il: I I /- t

I---'~r- I _~ __ --, , , " , if--t-l--I-' I I I ~

----- -~':: - - i -- --- -- ~ - - - -;~, ,-- I - : ; 1 1 1--1 1 - H 11-- --. L-. ___ l_ J ___ ~ ____ --L ___ __ _ _ _ _ ____ J~_, ______ I: _______ ~ ____ LL

, I I 9 1 ~ I 1 I 9 1

Figure 12. Phase part of H t(e jW) vs. Frequency. e,op

I

~Ir; I; 111\ !

I

I 1 ,

I I : i 1

:1 I -11

.-1--, ! , ,

: I I ._ t-- - I-

I I ,

- j -,

~ -...J

Figure 13. Fiber's Optimum Impulse Response

he,opt(t).

(2ns per horiz. div.)

Figure 14. Fiber's Optimum Step Response,

the Integration of he,opt(t). (2ns per horiz. div.)

98

r

APPENDIX B

COMPUTER SOFTWARE

99

') --"

START

01101 X 0024] , Y [1024]

DIM CSl6]

CALL "T"F"

I"pl

CALL "T-F"

2-pl

SET DEGREE

MODE

GET ·DECON I"

FROM DISK

STOP

-T "F M

pi

INITALIZE ARRAYS II AND Y

TO ZERO

.J

ASIGN CS FILE CooE TO DISK

READ II FROIol DISK

~IZ TIME POINTS

CALL "FFT" IOZ4-pl 1Il- pZ

MODIFY

FILE CODE

OPEN

DISK FILE

CS

FIRST 20 VALUES

X,Y

RETURN

A

PULSE DISPERSION TEST

I j

~ o o

)

DECON

DIMENSION A [~131 • B [~131 C [~131 • 0 [~131

DIMENSION

RS[6] .0 S[6]

ASSIGN OISK CODES

RS TO I OS TO 2

I -I

r A [I]·+B[I]· ... L .. D

(A[IJIEC(I] + B[I)*D[I)I/D- R I (D[l)*A[l] -C(lJIIBU1/0-J R "AU] J-BIO

)

MODIFY

FILE CODE

OPEN DISK FILE

34 RECORDS

OS

F ASSIGN DISK

CODE

OS

GET FROM DISK

"RESO 2"

B

)

~ o ~

OECONVOLUTJOK PROGRAM

..

~

I'm / START DISK X ,Y FOR

"RESO 2" I' I TO 513 NO 1.2 M

YES

["" / DIMENSION OS (6), RS[6] "POINTS = M"

X [1024), Y [1024]

fl-Y! ..... I)

r'O' j j""''' / NUMBER Of REAL

POINTS WAVEFORM I= 2M + I

1+ I-I 1~1024

r~' / 102 FILE CODE I

I REAL RS

IMAGINARY OS 1+ I-I 1'::: M II-XIII-YII)

INITALIZE K[Il-X(2M-H2]

X, Y TO ZERO -Y U)-Y [2M-1+2] I~1024

I YES

-) ~

I

~

j''''''' / REAL AND

IMAGINARY WAVEfORMS

CALL ·FFT"

2M- pi 1- p2UFFTI

/""" / TIME DOMAIN

WAVEFORM

ZERO Y ARRAY

LOCATE MAK

NO AND MIN OF TIME WAVEFORM

X

~

ROTATE TIME

WAVEfORM TO INSURE CONTINUITY

/'"'''' / TIME

WAVEfORM

CALL "FFT"

1024- pi fl-p2lffTl

j''''''' / REAL AND IMAGINARY WAVEfORM

BEGIN

MAGNATUDE

AND PHASE

1 C

RESOLUTION ENHANCEMENT PROGRAM

)

...... o IV

')

J' I

J+ I-J I J .2:~13

JX[J]I+ y[J]I- M ..

SIGN OF Y[J]-S

lon-I (Y[J]/X[J] I

- Y[J]

-y

M-X [J]

NO Y(J) +11' *S.Y[J]

YES

OPEN OS

34 RECOROS

D

RESOLUTION ENHANCEMENT PROGRAM

-)

I-' o w

..

DIMENSION

X 1024

V 1024

INITIALIZE VARIABlES .OF POINTS

N = 2" WHERE

( LN(NI

M:INT LN(21+!I

I-J

J: = I

1 t 1+1 120

)

P-K

J + K-J

NO

X [JJ -a X1D- X IJI a"XtIl

V (JJ -C V DI-V IJ)

C-VIJJ

J- K-J

K/2-K

L. I

L~M

2L

_ R

R/2-Q

J = I

J~Q

1 = J

It R =I 12N

,)

I-U r8-v Q-O

COS I"./ol .. w -SIN (1T/ol-x

E

-0-0

FFT AND INVERSE FFT (IFFT)

)

f-' o ~

J

-- , -,

NO

It-O ... S

X[S]- B Y [S] .. C

x [1]- B. x [S] Y [I] - C. Y [5] X[l]+ B· XII] Y[I]+ C .. Y [I]

YES

NO I BftU-C*V"A ----;~~. BftV+Cft U"C

A-B

NO UftW-VlEX"'A UftX+V*W--V

A+U

')

YES

STOP

I c I

I ~ N

NO

X [I]tH "XU]

Y [1]tH .Y[l]

F

- ~)

...... o 111

FFT AND INVERSE FFT (tFFT)

__ J __ _

LOG AMPLITUDE AND

CONTINUOUS PHASE

DIM IoIS(61

A (512)

B [512]

SET RADIAN

MODE

4II.,2+C

1 c I

1.1-1 1~512

10 LOG (A[I] I-A[I] ,2-,1

180K BU]/" ... , 2

,2-,1-,3

C-2-C

C+2-C

,2+CKI80-BIII

NO

-,j

G

I-' o O't

LOG AMPLITUDE AND CONTINUOUS PHASE

-,

.X

.,>

')

NO

. -)

M II 180/lUl -,3

X. I

It I-I I 1>512

B 00-11-1,*,3

-8[0

NO

PLOT AMPLITUDE AND PHASE WAVEFORMS

STOP

-j

H

I-' o -..]

LOG AMPLITUDE AND CONTINUOUS PHASE

~

------- - - - --------- -- ----------- ------------------------

~~LSE LlS~~h~10N 1~S1 4-16-79

0: "~uLb~ ~lS~hRbI0~ TEST": 1: 01nl X lllJi.4 1, y llu24) ~: d 1fil l.~ l b j J: ell "1+1:'" (1) 4: e 11 ' 'I + r' ' (2) ~: deg b: ent "lb 'HllS ~l\'1l\ 'l'0 BE IJECONVOLVLlJ?",L;if L=O:stp 7: get "J:JLCOtd" 8: "'1'+ r " : Y: 1na x,'r lU: if J:-l=l;ent "EN'1'ER I{Er'ERI:.i'<CI:. FILE CODE" ,C$ 11: 1f r;,1=2ient "El'l'l'ER OU'l'PUT FILE CODE" ,C$ 12: asgn C$,l 13: rread 1,1 14: for 1=1 to 51~ 15: sread 1,XLI) 16: next 1 17: ell 'rr'l' (lU~4,U) lb: ".Pr"&C~l3,6J+C~ 1~: ent "IS TRANSfORM FIL~ Nb~?",rliif rliopen C$,34 LU: asgn C$,2 2.1: r read i.,1 ~~: for 1=1 to 513 i.J: sprt 2,Xll),Yl1j L4: next 1 ~~: ent "~AN'l 'IRE FIRST 20 VALUES??",r2iif r2=O;jmp 4 26: for 1=1 to 20 L. 7: p r t 1, X [ I) , Y [ 1 ) i s pc 2 2b: next 1 2Y: ret 30: "FFT": 31: "~RITTI:.N BY klKE PADGC'lT 10-21-78": 3i.: "pl=N0. OF POINTS IN FFT": 33: "p2=0++FF'I, p2=1++1FFT": 34: 1t p2.=OiQSP "FF'l NOW BEING PERFORHED" 35: 1f p2=1idsp "IFFT IS NOw BEING PERFORHED" 36: "1nit": 37: rad 30: esv 39: u+P 40: p1+h 41: 1nt(1n(N)/ln(2)+.5)+M 42: N/2+PiN-l+0:1+J 43: "proe" :beeJ:; 44: for 1=1 to 0 45: 1f l>=Ji)mp 3 46: X[J)+biX[I)+XLJ]ib+X[l) 47: YlJ]+CiYll]+ylJ]iC+Y[I] 4b: P+K 4Y: if K>=Ji)rnp 2 ~U: J-K+JiK/2+Ki)mp -1 51: J+l\+J 52: next 1

108

r

53: for L=l to N 54: 2" L+h, 55: 1<./2+l,J 5 b: if CJ::: 1 ; ) m~ 4 ';)7: 1+{J; U+V; Q+D 58: if F#Ui-L+lJ ':J9: cOG(n/~)+h;-5in{n/D)+X aU: for J=l to c.. 01: for I=J to N by R 62: l+C+S;Xlbj+B;Y[Sj+C b3: if J=li]rnp 4 64: B*{J-C*V+A 65: B*V+C*U+C bb: A+B 67: X ll]-b+ Xl S] ; Y [I] -C + Y [S j 68: X[1]+B+Xl1];Yl1]+C+YlI] 69: next 1 70: if Q=li)rnE- 3 71: U*W-V*X+A;U*X+V*W+V "'2: A+U 73: next J 74: next L 75: if p2=Uiprt "FF,!' COMPLE'rED";beepiret 76: for 1=1 to N 77: X L I ] /N + X [ 1 j 78: Yll]/N+Y[I] 79: next 1 80: prt ilIFF''!' COMPLETED"iret

109

1.JLCt,,(~VU LU'I' 10L~

U: "uLCLN1": 1: "'HllS l'IWGkAl-l i-lL:lUo'ORMS DECONvOLUTION Of' O/R": 2: dlm Al51jj,B[513j,Cl513],O[513) J: dim H $ [6 ) ,0$ [6 ) 4: ent "LAMPDA EQUALS", L ~: ent "L~1~k RhFL:RENCE ~ILE C00E",R~ 6: ent "~N1ER OUTPU1 FILE CODE",O$ 7: prt "h.t..i:"t..hhNCl:..",R$,lourl'PU'l·",o~ b: asgn ~~,lia&gn 0$,2 ~: rread 1,1 10: for 1=1 to 513 11: sread 1,Allj,b[1] 12: next 1 13: rreaa 2,1 14: for 1=1 to 513 15: sreaa ~,ClI],DlI1 16: next I 17: for 1=1 to 513 1~: All] .... 2+B [1] .... 2 +L-+-D

19: (A[1]C[11+BlI]D[I) )/IJ+R Lv: (DlljA[I]-C[I]b(I1)/D+J 21: R+AlI);J+U[I] 22: next 1 23: "~R"&R$l3,6]+R$;"PI"&0$[3,61+0$ 24: l-'rt "DLCON SAVE.L ON",R$,O;, 25: enl "IS DECON FILE NEW??",r3;lf r3iopen R$, 17 io pen 0$,17 Lo: asgn R$,3iasgn 0$,4 27: r re ao 3,1 2H: sprt 3,A[*] 29: rreaa 4,1 3U: sprt 4,B[*j 31: prt "DECU~ FINISHED" 32: get "KES02"

• I

110

" ,

•

.,,-....

hbS~Lu11U~ LNhA~CENEN1

U: "hLSULlJ'1'1U('-l LNl1Al'JCEfliILlo,j'l' PHOGHAM ": 1: d 1m 0$ [6 ] , £-.$ [6 ] L: alm xl1024] ,Y[1024] ,T[1001 J: ent "wAt~ll '1\) 'IiA'l'CH PROCESS??", r13 4: ent II E~1ER ~0. of PO IN'l'5" ,M 5: ent "l:.N'lER rILl:. CODE FOR REAL",R$,"IMAGINARY",O$ 6: "star t" : 7: ina x,Y b: asgn h~,l;rread 1,1 9: for 1=1 to 513 1u: sread 1,X[I] 11: next I 12: asgn O~,2;rread 2,1 13: for 1=1 to 513 14: sread 2,Y[I] 15: next I 16: spe 3 17: prt "===:==","********", "======"ispe 2 18: prt "POIN'l'~=" ,l>1 lSi: ell 'look'(O) 2 U: ell 'look' (1) L.l: for 1=2 to M ~~:

23: 24: L.5: ~6 : 27: 28: 29: 30: 31 : 32: 33: 34: 35: 3b: 37: 38: 3~: 40: 41: 42: 43: 44: 45 : 46 : 4./: 4b: 4SJ: ~u : ~l: 5~:

~3:

X[I]+X[2M-I+2] - Y II ] + Y [ 2f.'l-1 + 2] next I U+Y It-1+1] for 1=2M+l to 1024 O+X[l]+Y[I] next I ell 'look' (1) dsp "READY 1'0 SHOW ylI; stp ell 'lock' (O) ell 'FF1" (2M,1) ell 'look' (l) dsp "ready"istp ell ' 1 00 k' (O) ina Y ent "l:.N'lEH RUTA110N VALUE",Tiell 'rotate' (T) ell ' tau' ina Y ell 'loCJk' (1) ell 'FF'l"(1024,O) c 11 ' 1 co k' (I) ell 'look' (0) stp IINandF": asp "handP" tor ..1=1 to 513 " (X l J ] ... 2 + Y [J ] ... 2) +M sgn(YlJ] )+5 atn(Y[J]/x[J)+Y[J) 1f X[Jj<OiY[J]+n*S+YlJ] M+X[Jj next J

III

~4: ell 'look' (1) iprt "MAG~I'rUDE" 55: ell 'leok' (0) iprt "PHASE" 56: ent "WAN1 TO SAVE Mandp RESO?",r10i1£ r10=Oi9to "more" f:J 7: "save": 58: "~M"&0$[3,61+0$iprt "MandP RESO on",O$ 5~: ent "IS fv'landP FILE NEW?",r1i1f r1iopen 0$,34 ou: asgn CJ$,5 01: rread 5,1 62: for 1=1 to 513 63: sprt 5,XLl],YLlj l>4: next 1 05: get "LandCl" uo: "more" :ent "l:.N'l'E.H NU. Of P()lN'lS LJESIHI:.D" ,Mi9to "start" b7: "t'fo1''': bb: "W~lTTI:.~ BY MIKE ~AUGLTT 1U-21-7e": 6~: "pl=NU. uF t'Ul~'l'S IN 1"1:"1''': 70: "p2=U++r'f'1', p2=1++IFr'I''': 71: 1t pL=Uidsp "Flo''!' NOW 131:.1NG t'ERFORMEI.;" 7~: 1f p2=lidsp "IFFT IS ~O~ BEING PEhfORMED" 73: "ln1t": 7 4: r ad 75: p1+N 76: 1nt(ln(N)/ln(2)+.5)+H 77: N/2+PiN-1+0il+J 78: "proc":beep 79: for 1=1 to 0 bO: 1f I>=Ji]mp 3 b1: XLJ]+BiX[I]+X[J] iB+X[I] b2: YLJ]+Ci Y LI]+Y[J)i C+Y[1) 83: P+K b4: if K>=JiJmp 2 b~: J-K+J;K/2+K;]mr- -1 ti6: J+t\+J e7: next I 88: for L=l to H b~: 2 ..... L+R ~ll: h/~+\t

~1: 1f ("'=li JmfJ 4 ~2: l+UiU+ViU+U ~ 3: 1 f f- L.Jt U i - D+ I.; ~4: eos(n/D)+Wi-sin(n/D)+X 9~: for J=l to Q ~ 6 : for 1 =J tON by R ~7: I+Q+SiXlS)+BiYlSj+C ~ 8: 1 f J = 1 i J rot.- 4 99: b*U-C*V+A 100: B*V+C*U+C 101: A+B 102: X[I]-B+XlS]iY[I]-C+Y[S] 1u3: XLI]+B+XlI] iYl1J+C+Y[I) 1u4: next I lu5: if ~=liJrop 3 106: U*w-V*X+AiU*X+V*W+V lu 7: A+U lOti: next J 1U9: next L

1 I

112

110: 111: 11~ : 113: 114: 11~: 116: 117: lIS: 11~: 1i-0: 121: 122: 123: 124: 125: 126: 127: 128: 129: 130: 131: 132: 133: 134 : 135 : 136 : 137: 138 : 139: 140: 141: 142 : 143: 144: 145: 146 : 147: 148: 149: 150 : 151: 1:'2: 153: 154: 155: 156: 157: 15b: 159: 16U: 161: 162: 163: 164:

if ~2=O;prt "Ff'll COMPLE'lIED"ibeepiret for 1=1 to N X[l)/N+X[l] Yll]/N+Ylll next 1 ort "H'F'l' CUMPLI:.'1'E:lJ" i ret t'look" : if r13-0iret fIt 3 "~1=0 b~N~S ARRAY S,pl=l SENDS ARRAY A": frnt 8,x,f.0,z dsp "SELEC'I' W/F ""13"" Ot~ DPO"istp rnax(x[*1)-rnin(X[*])+A if max(Y[*] )imin(Y[*]) ;rnax(Y[*]) -min(Y[*] )+8;)rnp 2 l+B 802/A+F;71-rnin(X[*1)*F+G;802/B+E;71-rnin(Y[*])*E+S wtb 701, "DPB " for 1=1 to 512 if pl=l;wrt 701.8,X[1]*F+G 1f pl=O;wrt 701.8,Y[1]*E+S next 1 wtb 701,13,lU

113

1f p 1 iprt "r<lAX At-1P",rnax(Xl*]),"MIN",rnin(X[*]),"S'l'EP",A/8i spe 2 1f ~1=Oiprt ill-lAX l-'HASE II ,max(Y[*1),lIr'HN",rnin(Y[*]),"STEP",B/8;spe 2 fxd 2 ret IIrotate": for 1=1 to M X [1 J + Y [ 1 +M] next 1 for l=H+l to 2M X[l]+Y[l-H] next 1 ara Y+X ret "tau ll

:

O+T for 1=1 to 2lJl 'l'+X 1 I J +'I'+Y [I J next I ell 'look' (0) O+rl~

for 1=1 to 20 YlIJ+r15+r15 next 1ir15/20+r16 0+r15 for 1=2M-20 to 2M Y[I]+r15+r15 next 1ir15/20+r17 (r17-r16)/200+T r 16-'1'+r IS i r 16+T+r 19 ell 'h1st'(r18,rlY,1,M/2,r2l,r22) r 17-'1+r Ib ; r 17+T+r 19 ell 'hi5t'(r18,rl~,3M/2,2M,r25,r26) r24+(r26-r24)/10+Ti r 26-(r26-r24)/10+Z

1b~: 10+r 18+r 19 Ib6: for 1=1 to 2M 167: if Y[11-T<r18~YlII-T+r18~I+r16 lQb: 1f Yll1-Z<r19~Yll]-Z+r19il+r17 109: next 1 1 7 U: r 17 - r 16 +'£ 171: prt "POIN1S =",Tiret 172: "hist": 1 'j 3: 1 na '1' 174: for 1=~3 to p4 175: int lY ll]Y9/{r19-r18) +1-9~r18/(r19-r18) )+r20 176: 1f K<l or K)lUUi]rnp 2 177: 'r [K 1 + 1 +'1' l K 1 178: next I 17~: for 1=1 to luU Ibu: it 'll1}=max('rl*]) il+p5 181: next 1 182: (p5-(1-~9pl/{p2-pl)))/99/(p2-pl)+p6 183: ret

, :

114

.,-.... I

LUG Ar-u-L 1 'l'U1JJ:. AND CON'lINOUS PllA~E

0: "LuG At'J,tiL1'l'UUt:: AlW CON'l'lNUlJS PHASE": 1: dlIn t.~ l6J ,A[512],B l~12] 2: ent "~NTLR MandP FILE CODE",M$ j: asgn N$,l 4: "star t" : ~: rreaa 1,1 b: [or 1=1 to 512 I: s r eae 1, l\ [I] , B L 1 ] 8: next 1 9: ell 'look'(O) lU: ent "ENTbR eont. ANGLE 1n DEG.",D 11: rad 12: O+C 13: U+r2 14 : 15: 16: 17: Ib: 1~: 2U: 21: 22: :2 j: 24 : ~~:

for 1=1 to 512 lu10g(A[I])+AL1] r2+r1 180*B [IJ /n+r2 r"::-r1+r3 1f r3)uiC-2+C if rJ<-uiC+2+C rL.+C* Ib U+IJ [1] next 1 c 11 ' 1 00 k' (1) dsp "RLALJY 'lU SHUW PHASl:." i s tl:-' ell 'leok' (0)

115

2b: 27: 28:

ent "~'IAN'I' '10 ChANGE 'I'HE cont. ANGLE.?" ,Qiif Qigto "start" prt "PHASE.=",Bl512],"at p01nt#",512,"jr of n's added",C ent "WAN'1 TO MODIFY THE PHASE?",Liif L=Oi]mp 8 ent "l:.NTbR n's to be removed",Miprt In's",M 29:

30 : 31 : 32 : 33: 34: 35: 36: 37: 31:3: J ~: 40: 41: 4~:

43: 44: Ll5 : 46 : 47: 4b: 4~:

M* 180/511+r3 [or 1=1 to 512 B[1]-(1-1)*r3+Bll] next 1 ell 'look' (0) ent "~AN'1 '10 MOLJ1FY PHASE. M0RE?",r7iif r7=li]rnp -6 "plotFF'I'" : prt "I-lAX At-'pI,rnax(A[*]),"MIN At-'lP",rnin(A[*]),"HAX PHASE",rnax(B[*]) prt "MIN ~HASE",min(IJ[*l) deg asp II Hl:.Al.JY '1'0 f'LO'l: t-IAGN1'l'UUE II i stp ent "l:.ntcr IIIIUI:.L'l'A F""I1,1l "axes" : ent "~ant AXIS Urawn?",Xi1f X=Oigto " sea le1n" scI u,150,U,100 for 1=1 to 3 for J=10"(1-1) to 10"1 by 10"(1-1) plt 1~+120/3*lo9(J) ,10 ip1t U,80,-1 next Jinext liiplt 0,80ipen

~U: for 1=1 to 4 ~ 1: for J = 1 U'" ( 1- 1 ) tolD'" 1 by 1 0 ,. 1 5L:: 15.~+120/3*log(J)+K;lf K)65i1f K(84igto +2 53: plt K,.7,liCS1Z 1.1,2,11/l5,9UifXd Oilbl 2*J 54: next Jinext 1 ~::>: pIt 15,lUiiplt 120,O,-1;r,lt 15,10 ~b: fer 1=1 to fj

':J7: 1plt 0,10 58: 1plt .5,Ui1plt -1,Ui1plt .5,0 ~9: next liiplt 12U,O,-lipen bU: "scale1n":ent "EN~LR ~U. Of VER~ DIVlbl0NS",V bl: ent "LN1hR VLk~ SCL ~ER UIVlSI0N",S 6L;: it ~=Uigto "scale" oj: CS1Z 1.1,~,11/1~,O b4: tor 1=1 to V 65: pIt 6,lu+lu1,1 bb: Ibl 81 67: next I 6b: "scale": b9: ent "~ant lW~~k1 Data?",Yiif Y=lismpy -lA+Aismpy -lB+B 70: scI -1.5*3/12+10g(2e6) ,13.5*3/12+1og(2e6) ,-VS/8,9*VS/8 11: for 1=L; to 512

116

7 L;: 1 flog ( ( 1 -1 ) * H) ) 1 og (2 e~) i pIt log (2 e 9) , A [ 1 -1) i 512 + 1 i J mp 2 73: pI t log ( ( 1-1) * H) , A l I ] 74: next lipen 75: stp 7b: "phase": )7: ent "ENTER NO. PHASE VER1. DIVISIONS",V 7 8: ent "LN'!'l:.R VER'l'. PHASE PER uIV", S 79: scI -1. 5* 3/12+1 eg (2e6) ,13.5* 3/12+1 cg (2e6) , - 5VS/8 ,5VS/8 8u: for 1=2 to 512 bl: if log«1-1)*H»log(2e9) iplt log(2e9),BL1-1) i512+IiJmp 2 ti2: 1f Ull)4VS/8i4VS/8+Bllli~12+IiJmp 2 b 3: pI t log ( (1-1) * H) , b [1 ] e4: next 1 oS: pen 86: stp ti 7: "100 k" : 88: "f:Jl=O bE.Nl;S ARHAY B, pl= 1 SENDS ARhAY A": 09: fmt 8,x,f.O,z ~ u: as£- "ShL hC1' Y~/f "" b"" ON LJPO" i stp Yl: rnax(Al*] )-min(Al*])+A;max(b[*] )-min(Bl*) )+B 9~: 802/A+r;71-m1n(Al*)*F+G;8U2/U+L;71-m1n(Bl*)*l:.+8 ~3: wtb 701,"U~u " ~4: for 1=1 to Sl~ ~5: 1f pl=liwrt 701.8,A[lj*r+G Y 6 : i f .i:' 1 = 0 i .... r t 7 U 1 • 8 , 13 L 1 ] * L +8 97: next 1 98: wtb 701,13,10 99: if p1i[-rt "HAX AMl:'II,max(Al*]),IIMIN",min(A[*),"8TEP",A/8iSPC 2 100: 1f p1=Oiprt "['IAX ~IlA8E" ,rnax(Bl*) ,"HIN",rnin(B[*]) ,"STEp lI ,B/8;spc 101: ret

2...----.,

.--... I

t

APPENDIX C

DISPERSION TEST RESULTS ON CONCATENATED FIBERS

117

PI>226A VOLTS

I.SE BI

l.lfE BI

1.2f: BI

I.BE BI

B.BE BB

6.BE ElB

'i.BE BB

2.ElE BB

E1.BE ElB

-)

16 m Id id . r:g N

FIGURE D1:

ELECTRO-OPTICS LRB KENNEDY SPACE CENTER 8-ILJ-79

m i m m HI SECONDS lB IS HI id id Iii ~

, , I lti !t! ~ &f . . I-'

:r Ul m - '" I-' co

REFERENCE WAVEFORM FOR TESTING 600 m FIBER LOOPS.

"

-> )

-)

PD22613 VOLTS

B.CE: ""

7.BE: "e

6.BE: ae

i.BE: Be

'i.BE: aB

3.ee: ae

2.ee: 00

r • BE: im

e.BE: BB

I

I

! 1

if m ki i!! . cg 1'1

FIGURE D2a:

--)

ELECTRO-OPT KENNEDY SPACE CENTER

liQ m liQ SECONDS ld ld i!!

:r t.D m

cs LRB 8-t~-79

!B i if ~ ~ !2J

RESPONSE WAVEFORM OF LOOP #1 600 m FIBER.

-)

m m ~ ld

I-' - 1'1 I-' \0

dB DEG

IS 231

16 21 I

Itt ISS

.. 12 IS8

I- iiI 132

8 IB6

I- 6 19

I- Y 53

I- 2 26

-)

PM ~26E

Wi ~~

V V ~ I I V

V V

V V V

V ATTEN. V f-' -- r-... ~

I- I.r::

~ !.-... ---.r-., ~ I~ I~

r---_ ~ ..... "" PHASE _ L--- I-

FREQUENCY in MHz

FIGURE D2b: ATTENUATION AND PHASE FUNCTIONS OF LOOP #1 600rn FIBER.

~ )

I-'

'" o

v

121

ElEi1'Z

EIIi1-JB"

til 111-39',

~ r.l

IT: III H

.J m

rx.

111-311" 5 r- 0 I \0 :r

Ln'l N

ED =It:

V p.. Ba-3Z" §

f- rx. 1I1 0

[Lei 0

~ (' z

oE Cl 0 v rx. W ~ I

v U1

w :3:

o~ r.l SEE'B Ul

Ir~ 5 p..

f-~ Ul

gJ

V~ 1iIiJ-31'g .,

W III M CI

.J gJ

W ::J 1iIiJ-3B'h (.!)

H rx.

HB 31'S

v LD 151 151 til 151 til 151 til 151 151

f'\J 151 til til til til til til til til

I~ f'\J w w w w w w w w w C til til 151 151 til 151 151 til 151 , , a. m I" UI '" ;r PI N til

18 237 PM ~26( ..,

~ 16 211

Il.i 185

~ 12 158

iii 132

8 IEl6

6 79

I- l.i 53

2 26

)

~

~ ~

V V

~ V V V rt

/ V I..r"" ~ 1--- ",.....r 1"'-0-.. r-- -~ J"

V I~ I~ l---""' .--

FREQUENCY IN ~mz

FIGURE D3b: ATTENUATION AND PHASE FUNCTIONS OF LOOP #2 600m FIBER.

~

~

~

I~

J

..... N N

'.

,

-)

PD'2'26D

B.I'£ I'Er

7.1'£ 1'1'

6.1'£ EIEI

S.EI£ Ell!!

Y.I!!£ I!!I!!

3.1'£ I!!EI

2.1'£ Ell'

I .1'£ £lEI

£1.1'£ aa

-j

ELECTRO-OPT KENNEDY SPACE CENTER

C5 LRB 8-14-79

+-----+-==::;T~--_+_I - +--~ I I , 1====-=-t II ltl a;z

m ki N

m ki :r

~ m m m m m ~ ~ SECONDS ~ ~ ~ iii UJ a2

FIGURE D4a: RESPONSE WAVEFORM OF LOOP #3 600m FIBER.

m Id N

)

I-' I'U W

"

~ 18 237 PM 226[

IS 211

.. Itf 185

12 158

~ 15 132

~ 8 IBS

6 79

~ tf 53

2 2S

)

~ .

.

~ ~

V V

V it1

V V

It V

V ~ V ...-""'--~ "- ~ ~ IJ

~ ~ ...... t'-~ I~ -- 1-7 -v--

FREQUENCY IN MHz

FIGURE D4b: ATTENUATION AND PHASE FUNCTIONS OF LOOP #3 600m FIBER.

~

"

~

I~

)

I-' tv .".

-;

P!>226E

B.EI£ EIEI

7.EI£ EIEI

6.EI£ EIEI

S.EI£ EIEI

Lt.ElE EIEI

3.EI£ EIEI

2.EI£ EIEI

I . EI£ ElEi

EI.EI£ EIEI IB m ~ ~ lSI C'I

-)

ELECTRO-OPT KENNEDY SPRCE CENTER

lil lD II! ~ Id ~ SECONI>S :s- In m

CS LRE3 8-1~-79

Hi IS Iii ~

I

tlJ ~ -

FIGURE DSa: RESPONSE WAVEFORM OF LOOP #4 600m FIBER.

)

•

IS i ~ id

C'I f-' tv U1

126

~ tlWlc. 0I!IIIi.. ')

;:5- ~ N

~ .7 ~ ,

"" "- Z H

~ \ >< U . Z P:

~ \ ~~ ~

\f -~

h

[il [il ::J p:j 01 H

~ Ii..

Ii.. 5 0 \0

<0:1' =#:

p..

8 H

~ f' > mx. til

;> "" Z 0

'" <.. H E-I , L

( )

U Z ::J Ii..

1 ) \ \ \

( I \

[il

~ p..

Q ') ~ z 0 H E-I ~ D Z [il E-I E-I ~

.. ..Q

tltJ l/) Q

~ ::J t9 H Ii..

UJ ~ ~ Q..

r- - lit ED N Ul PI - ED 111 PI 151 D1 PI to N N - - - - r- ILl N

aJ Ul :r N 151 - - - - - CD to :r N

I- I I I

)

PD2266

B.l!!E l!!l!!

7.ErE: ErE!

S.l!!E ErEl

S:.ErE l!!EI

Lf.l!!E l!!EI

J.ElE l!!EI

2.ElE: Ell!!

I.ElE iUI

Er.ErE ErEi i IB It! ld lSI N

-)

ELECTRO-OPT KENNEDY SPACE CENTER

IB IB m SECONDS kI Id ld

:r IJ:I til

CS LRB 8-14-79

i iB ~ ~ ~ -

FIGURE D6a: RESPONSE WAVEFORM OF LOOP #5 600m FIBER.

--------

-j

..

IB Ii ~ iii

N I-' N .....,J

IB 237 PM 2~6~ .

16 21 I

14 IBS

,... 12 IS8

HI 132

8 le6

I- 6 79

y S3

1-

I- l! 26

-)

---......... ~ ~ r"- r... V f./ ~ '"' V r--V' ~ ~ I~ V- V ~ ~

U V

V V V ~ r\ ~ ~

~

~ ~

"" ~

V

WI

I

~ I-' IV

FREQUENCY IN MHz 00

FIGURE D6b: ATTENUATION AND PHASE FUNCTIONS OF LOOP #5 600m FIBER.

,) )

~.

-I 1

I

)

PD226F

B.ElE: EIEI

7.ElE: nEl

Ei.ElE: nn

S:.ElE Eln

Lf.E!!E: ElE!!

3.aE: £lEI

2.nE: Eli:!

I .£IE nB

11I.£IE: E!B • I ,. II fa Id It! ISZ N

-;

ELECTRO-OPT KENNEDY SPRCE CENTER

I I +---il lil fa SECONDS Id Id ld :r UI aI

CS LRB 8-IY-79

IB IB IB ftf ~ Iii

FIGURE D7a: RESPONSE WAVEFORM OF LOOP #6 600m FIBER.

m m !i! It!

N

)

I-' r-J \0

r- 18 237 PM ~26F

r- 16 211

r- 14 185

r- 12 158

r- 18 132

r- 8 186

-

r- 6 79

4 53

'2 26

-.J

~ N' V

I V ~ / :J'-\

/ V V V r"" ~ fI r-.. V-

~ ~ ~ ~ ~ V' f....' j\.. ~ -:~

----~

FREQUENCY IN MHz

FIGURE D7b: ATTENUATION AND PHASE FUNCTIONS OF LOOP #6 600m FIBER.

-.J

j

~

~~

eli eli eli r

)

r-' LV o

.'

)

PI>226H

B.BE: EIEI

7.ElE: EIEI

Ei.BE: EIEI

S:.BE: EIEI

if.BE: EIEI

:i.BE: El2J

2.BE: EIEI

r • BE: 2J2J

B.BE: DEI (I ID Itt ~ Ell N

-)

ELECTRO-OPT KENNEDY SPACE CENTER

~ m ~ SECDNDS lit :r UJ CD

CS LRB B-I'i-79

~ is III ~ tli - - -

FIGURE DBa: RESPONSE WAVEFORM OF LOOP #7 60DIn FIBER.

_OJ •

•

i ~ ~ - N f-' W I-'

132

-- ~ rJrn:Jr. ~ ~

~ ~ ~ --....... r' p<:

~ ~ F .~ ~ t> z

~ =>

~

P:: ~ III H ~

~ ( ~

\ j

\~ 1 l

6 0 1.0

r--=11=

p.. 0 0 H

~ 0

~~ "'\l ~

«

(f) z 0 H 8 U

5 () ~

~

J) \

~ I

1 1-J

/

(f) f':t!

~ ::r: p..

0

~ 6 H 8 :3 z ~ E-I f':t!

.. .0 co

_Dr. 0

~ ::> t!J H ~

ffi ~ :i: C.

,... - 111 III N Ul 1"'1 - III 111 1"'1 tg C1 1"'1 Ul N N - - - - ,... Lt1 N

III Ul :r N tg - - - - - [D I.D :r N

I i i i i

-) ) ) •

..

PD2261 ELECTRO-OPTICS LR~ KENNEDY SPACE CENTER 8-t~-79

B.BE ElB

7.BE EIEI

S.ElE EIEI

~.IE EIEI

!.f.ElE ElB

3.BE EIEI

2.ElE eEl

I.BE ElEI

B.BE EIEI I

~ ~ il i m SECONDS ~ ~ IB i ~ iii iii ~ ~ ltd

:r . . . . !:II N La III - N ....

W w

FIGURE D9a: RESPONSE WAVEFORM OF LOOP #8 600m FIBER.

134

~ ~ ~kl"

~ ~ '--.... ~

N :r: ;:;::

~ ~ z H

~ '" >< U Z ~

~ \ ~

iii iii ::J ~ 01 H

~ rx. ~ 6

0 \0

00 =#I

ill

( 8 ..:I

~ \. ~" Ul

"" / Z

0 \ H

8

\. \ \ J

U

5 ~

} ~ Ul ~

\ :r: ill

Q

\ \

~ Z 0 H 8

:3 z iii 8 8 ~

.. .0

Dt. cr'I Q

~ ::J l!l H ~

Ln

~ ::E: 0-

r-- - 111 CD N LD ~ - CD ~ ~ lSI 01 ~ LD N N - - - - r-- 111 N ,

~ I

m LD :r N lSI - - - - - [D lD :r N

I I I I I I I I I

-')

P[}i!26L1

B.BE: BB

7.BE: BB

&.BE: BB

S:.BE: BB

"I.BE: BB

3.BE: BB

2.BE: BB

I .BE: BB

B.BE: BB I m Itt ~ lSI N

')

ELECTRO-OPT KENNEDY SPACE CENTER

il HI iii Id ~ SECDNDS :r UJ m

cs LRB 8-ILi-79

~ ~ ~ -FIGURE DlOa: RESPONSE WAVEFORM OF LOOP #9 600m FIBER.

-J ..

..

~ ~ . - .... ...... W lJ1

18 237 PM ~26l

16 211

_ I Li 185

12 158

IE! 132

_ 8 IS6

6 79

Lf 53

'2 26 1-

)

~ -~ ~ "-~ /' ~ f...I ~ r-V-~ r--'

~ V' ...../ i'..I ,.....,

I~ --

/ V

V V V ~

V ~ -

~ ~

V II ~

"V

)

~

1- ...... w

FREQUENCY IN MHz 0"1

FIGURE DIOb: ATTENUATION AND PHASE FUNCTIONS OF LOOP #9 600m FIBER.

-_., .-- ----- .J. -. --." -_. )

....

.,

")

PD!!£!6K

B.ElE EIEI

7.ElE EIEI

Ei.ElE EIEI

i.ElE ElEI

"'.ElE ElEI

3 • .,E EIEI

2.ElE EIEI

r .ElE Ell!!

EI.Ot ElEI I ~ It! . a;a 1'1

)

ELECTRO-OPT KENNEDY SPACE CENTER

~ ~ Rl SECONDS ~ :z- IG m

CS LRE3 B-llf-79

Hi ~ =

N . - - -

FIGURE Dlla: RESPONSE WAVEFORM OF LOOP #10 600m FIBER.

-)

..

~ m ki - N

I-' W -..J

~ 18 237 PM ;J26~ .

16 211

ILJ 18S

~ 12 IS8

HI 132

~ 8 IB6

6 79

LJ S3

2 26

~ _____________________ ~ L--..

)

V V

V V

~v l/V[\ - _ ~f-/t'-r-..Vf...'t'-r. ~hr' Vt-'r..V~~ I~ .... --~

- -- --

/ ~

V ~

I

~

IS IS IS I"

I-' w

FREQUENCY IN MHz co

FIGURE Dllb: ATTENUATION AND PHASE FUNCTIONS OF LOOP #10 600m FIBER.

-.. -- - - - - ~-.-, )

."

"

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STANDARD TITLE PAGE

1. Report No \2

Government AcceSllon No 3 RecIpIent's Catalog N ...

CR-165624 4. TItle and Subtotle 5 Report Date

Optical Fiber Dispersion Characterization Study, Final Report 6. PerformIng OrgGnlZatoon Code

7. Authar{s) Alan Gees11n, kh1a AR Riad, sedK1 M. Riad, 8 PerformIng OrganIzatIon Report No

Michael E. Padgett 'IR 32-3 9. PerformIng Orgonlzatlon Name and Address 10. Work Unit No

Kennedy Space Center, Florida - 32899 and 11. Contract or Grant No.

university of Central Florida NI\S 10-9455 P.o. Box 25000, Orlando, Florida 13. Type of Report and Period Covered

12 Sponsoring :.iency Name and Address Optical Fiber Dispersion Nation Ae~nautics and Space lldministra tion Dec. 78 - Dec. 79~ Washington, D. C. - 20546

14 SponsorIng Agency Cod.

DL-DED-32 15 Abstract

'!his report presents the theory, design, and results of optical fiber pulse dispersion measurements. Detailed descriptions of both the mrdware cnd software required to perform this type of measurement are presented. Hardware includes a thermoelectrically cooled lID (Injection Laser Diode) source, an 800 GHz gain-bandwidth produce APD (Avalanche Photo Dime) and an input mme scrambler. Software for a HP 9825 canputer inc1trles fast fouirer transform, inverse fouirer transform, and optimal compensation deconvolution. 'lest set construction details are also incltrled.

Test resul ts include data collected on a 1 KID fiber, a 4 KID fiber, a fused spliced, eight 600-rneter length fibers concatenated to form 4.8 KID, am up to nine optical connectors.

'!his ~rk was performed at Kennedy Space Center with the Aid of the University of Central Florida, Orlando Florida under contract NAS 10-9455.

16. Key Words

Optical fiber, fiber dispersion, pulse dispersion, fiber bandwidth, optical connectors and splicers.

17. B,bloograph,c Control 18 Distrobutlon

STAR Ca tegory 51 Unlimited

",-..... ,

19 Security ClaSSlf (of thIS report) 20 Security ClaSSlf (of thl' pag,,) 21 No of Page. 22 Proce

Unclassified N:>ne KSC FORM 111-272NS (REV 7/781

End of Document