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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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x (t) ... 1 h ( t )
y(t)= h(t) * x(t)
Y (e iw ) = H (e iw ). X (e iUJ )
FIGURE 1: TIME DOMAIN INPUT-OUTPUT
RELATION AND THE CORRESPONDING
FREQUENCY DOMAIN TRANSFORMATION.
.. y (t) -
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N W
~
x (t)
y ( t)
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7 -1
F = FOURIER TRANSFORM ;--1 = INVERSE FOURIER
TRANSFORM
FIGURE 2: THE OPTIMAL COMPENSATION FREQUENCY DOMAIN DECONVOLUTION PROCESS
,)
h ( t)
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llLD APDr IlO 7, FIBER - APO SAMPLING TRIGGER ---. IMPULSE ··UH BIAS a a-SCOPE GENERATOR COUPLER
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PROCESSING SYSTEM
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FIGURE 4:
J
MODE SCRAMBLER CD SHORT FIBER OUTPUT
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\ \
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J OUTPUT (RESPONSE)
FIBER INSERTION MEASUREMENT USING FIBER CONNECTORS.
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(REFERENCE' LAUNCH m 0 ' , 0 CD OUTPUT
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CONNECTOR 0 (RESPONSE) UNDER TEST
FIGURE 5: CONNECTOR(S) OR SPLICE INSERTION MEASUREMENT
N -..J
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AT = TIN
FREQUENCY DOMAIN TRANSFORM
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N FREQUENCY DOMAIN 6fM = I/TM = FM/N
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ENHANCEMENT WITH INTERPOLATION
USING THE FFT PROPERTIES.
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FIGURE 17: DISPERSION TEST SIGNAL
PROCESSING FLOW CHART
39
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MAGNITUDE S PHASE OF IIH
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FIGURE 20b: ATTENUATION AND PHASE FUNCTIONS OF LOOP #1 600m FIBER.
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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
x(t)----)~ h(t) I-----t) y(t)
Figure 1. Time Domain Representation of a Linear System.
,-----Figure 2. Frequency Domain Representation of Figure 1.
Figure 3. Frequency Domain Optimal Compensator Design.
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I.D I-'
5 I I 8 , I 5 & J I ! I ) I I • ! I
~., ---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