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EVANESCENT WAVE SPECTROSCOPY USING
MULTIMODE OPTICAL FIBRES
BY
JOSEPH ANTHONY MURPHY
A THESIS PRESENTED
TO
DUBLIN CITY UNIVERSITY
FOR THE DEGREE OF M.SC.
AUGUST 1990
PHYSICS DEPARTMENT,
DUBLIN CITY UNIVERSITY,
IRELAND.
ACKNOWLEDGEMENTS
A
project
completion
of
without
this
the
nature
help
cannot
be
of many people,
brought
and
to
I would
like to thank all who have helped me in any way.
The author wishes to express sincere
hours
all
thanks for the
of dedication, untiring encouragement
possible
MacCraith
and
help
Dr.
offered
Vincent
by
my
and extending
supervisors
Ruddy, of
the
Dr.
Optical
Brian
Sensors
Group, Dublin City University.
To the Physics technicans, Alan, Al, Joe, John, Susan
and Mike for their co-operation and assistance while I have
been
at the University.
To Tommy
(Mechanical
Engineering)
for his endless efforts and advice.
To
the
Physics
Department,
Trinity
College, Dublin
for the use of their scanning electron microscope.
To Joan
(British Gas pic) for the excellent work on
the diagrams and Mr. D. Pinchbeck for his advice.
Finally, but certainly not in order of importance,
I
would like to thank my parents for their continued support
and
understanding
patience
and
to
Orla
for
her
during the course of this study.
encouragement
and
DEDICATION
This thesis would not be possible without the
support
and
encouragement
from my
parents
and
love, understanding and patience of Orla "Pud".
the
ABSTRACT
The
use
of multimode
optical fibre as an intrinsic
chemical sensor, with application in on-line analysis in
the process
industry,
is described.
The technique of
attenuated total reflection spectroscopy is applied to the
unclad section of the fibre which is in contact with the
chemical being detected. A model based on selective mode
propagation
is
developed
to
relate
the
evanescent
absorption coefficient of the fibre probe to the bulk
absorption coefficient of the absorbing species.
An experimental system was constructed to verify
the
theoretical model. Evanescent wave absorption in an aqueous
dye solution was performed using multimode fused silica
fibre which was unclad at the sensing region. In order to
produce modes close to cutoff in the sensing region,
tunnelling modes were launched into the clad lead-in fibre.
The measured evanescent absorbance of the dye solution was
found to vary linearly with the exposed core length and to
exhibit a square root dependence on concentration. The
former effect is predicted from theory while the latter is
attributed to adsorption on the core surface which obeys a
Debye-Huckel-type concentration dependence. In adddition, a
concentration enhancement of two orders of magnitude was
observed due to this adsorption.
Because the adsorption process
is of an irreversible
nature, the potential for evanescent wave spectroscopy on
fused silica fibre is severly limited for ionic solutions.
The effect may be exploited, however, in disposable probes
to give increased sensitivity due to the enhanced surface
concentrations.
TABLE OF CONTENTS
CHAPTER 1
CHAPTER 2
INTRODUCTION
1.1
Historical Introduction............. 1
1.2
Optical Fibre Sensors............... 2
1.3
Remote Spectroscopy..................4
1.4
Evanescent Wave Spectroscopy........5
THEORETICAL BACKGROUND
2.1
Introduction......................... 7
2.2
Internal Reflection Spectroscopy... 9
2.3
Optical Fibre Considerations........16
2.3.1 Optical Fibre Modes..................16
2.3.2 Total Number of Modes............... 23
2.3.3 Power Flow in the Cladding.......... 25
2.4
Evanescent Wave Spectroscopy using
Multimode Fibres.................... 28
2.5
CHAPTER 3
Summary............................... 33
EXPERIMENTAL SYSTEM
3.1
Measurement System...................35
3.2
Calibration and System Response.... 41
3.3
Sensing Fibre and Preparation.......47
3.4
Mask and Sample Chamber............. 57
3.5
Electronics
and Software
Development.......................... 61
3.5.1 Electronics.......................... 61
3.5.2 Software Development.................63
CHAPTER 4
RESULTS AND ANALYSIS
4.1
Methodology.......................... 69
4.2
Results............................... 73
4.2.1 Evanescent Absorbance vs Sensing
Length............................... 73
4.2.2 Evanescent Absorbance
vs Concentration.................... 76
4.2.3 Evanescent Absorbance dependence
on V-Number.......................... 81
4.3
Analysis.............................. 83
4.4
Summary............................... 86
CONCLUSION................................................... 87
REFERENCES................................................... 89
APPENDICES.
APPENDIX A.
Internal Reflection Spectroscopy............ A. 1
APPENDIX B.
Total Number of Modes........................ B.l
APPENDIX C.
Evanescent Wave Spectroscopy using
Multimode Optical Fibres..................... C.l
APPENDIX D.
Specification of Monochromator.............. D.l
APPENDIX E.
Specification of PCS Optical Fibres........... E.l
APPENDIX F.
Circuit Diagrams of Electronics...............F.l
APPENDIX G.
Software Programs............................. G.l
APPENDIX H.
Debye-Hiickel Model....................
H.l
CHAPTER 1
INTRODUCTION
1.1 Historical Introduction.
The field of fibre optics is based on the guidance of light
by multiple reflections along channels formed from glass or
plastic. The reflection process
reflection
(TIR)
is that of total internal
at a dielectric
interface,
and the first
recorded observation of this principle was by
Tyndall
(1)
in 1854.
It
was
not
practical
1927,
until
early
twentieth
century
that
application of this phenomenon was proposed.
Baird
applied
the
(2)
for
in
the
UK,
and
Hansel
(3)
patents
for
image-transferring
in
the
devices
a
In
USA
using
fibres of silica.
However,
was
since
uncoated
low and applications were
that
Van Heel
(4)
however,
from
came
STL
in
demonstrating
thin,
in
few.
when
Harlow,
light
Kao
has
communications
has
the
efficiency
It was not until
and
England,
may
be
flexible glass fibre guides.
industry
used,
1954
The major milestone in fibre optics,
1966
that
were
announced the invention of the cladded
dielectric waveguide.
the
fibres
become
become
Hockham
published
guided
with
a
low
loss
in
of
the
and
lightwave
most
important
cornerstones of the telecommunications industry.
1
paper
Over two decades later,
established
one
(5) , working
1.2 Optical Fibre Sensors.
The
future
of
communications
particularly
there
is
optical
channel
is
long
distance
for
a
great
development
industrial
the
of
deal
rate,
as
a
firmly
practical
established,
communications.
interest
fibre
applications
such as displacement,
now
of
optical
fibre
in
sensors
the
for
design
and
scientific
and
for the measurement
acceleration,
strain,
However,
of parameters
pressure,
flow
fluid level, temperature, current, magnetic field and
chemical composition (6).
An optical
optical
field,
sensor may be defined as a device
signal
is
such that
modulated
signal.
frequency,
phase,
This
extrinsic or
may
colour,
of these properties)
fibre
response
the measurand may be
modulated
Optical
in
mean
in which an
to
a
measurand
recovered
modulation
polarisation
in
from the
intensity,
(or any combination
of the guided light.
sensors
may
be
generally
classified
as
intrinsic and each of these categories may be
subdivided further into coherent and incoherent devices.
Extrinsic sensors merely use the
medium
to
optical
transport
sensors
light
which,
to
in
fibre as a light-guiding
and
from
response
more
to
conventional
an
external
parameter, modify the coupling between the input and output
fibre(s).
They
may,
however,
be
affected
by
small
environmental changes in cable properties unless particular
care
is
taken
in
their
design.
2
Intrinsic
sensors,
in
contrast,
rely on the optical
fibre itself as the sensing
A very wide range of optical
fibre sensors based on both
element.
coherent
and
undergoing
incoherent
optical
development.
techniques
Incoherent
devices
are
currently
are
based
multimode fibres in which the coherence of the guided
is
not
phase
maintained
and
and
the
polarization
consequence,
is
rapidly
information
measurand
restricted to
beam
induced
phase
is
maintained,
modulation
greater
sensitivity
modulated
and
devices;
interferometrically,
primarily
(7).
allowed
In
general,
versatility
since
In
A detailed discussion of
has
sensors.
lost.
is
The availability of monomode optical fibres,
coherence
beam
depolarized;
hence
modulation
intensity changes.
these sensors is given by Jones
is
on
the
they
the
development
these
than
phase
are
in which beam
exhibit
of
much
the
intensity
is
recovered
generally
termed
interferometric (8).
Many
of
sensors
the
rely
initial
on
engineering
their
inherent
applications
advantages
of
over
optical
the
conventional electrically based sensors:
(i)
Freedom from Electromagnetic Interference
(ii)
Intrinsic safety in hazardous environments
(iii) Passive operation
(iv)
High electrical isolation
(v)
Geometric versatility
3
(EMI)
more
The
main
thrust
of
this
project
is
the
application
of
optical fibres to chemical sensing.
1.3 Remote Spectroscopy.
Recently there has been considerable interest in the use of
Remote
have
Fibre
been
Spectroscopy
devised
for
(RFS)
and
probing
a
number
hostile
of
or
schemes
otherwise
inaccessible environments by using optical fibres to link a
centralized spectrometer and excitation source to a remote
location
(9,10,11,12).
techniques
with
measurements
Moreover,
Systems
fibre
of
combining
optics
composition
can
and
spectroscopic
yield
other
quantitative
fluid
properties.
the approach permits use of multiple probes,
necessarily all sensitive to the same variable,
not
to provide
multiple on-stream measurements, nearly in real time.
David et al
(13)
have reported the use of colour-changing
reagents
coated on glass rods acting as optical wave-guide
sensors.
Lubbers
and
Opitz
(optical + electrode)
concept
at
an
the
distal
end
of
presented
their
"Optrode"
(14) : an optical
transducer
optical
fibre
specificity in an RFS environment.
provides
The transducer
chemical
in this
case consists of chemical reagents whose optical properties
(absorbance
or
fluorescence)
respond
to
a
particular
analyte.
An
alternative
optical
fibres
to
the
Optrode
as
"light
pipes"
information from a remote cell
4
approach
to
is
obtain
to
use
the
spectroscopic
(15). The simplicity of this
technique is demonstrated in a series of papers
et
al
(16,17,18,19,20).
A
remote
by
detection
Inaba
system
for
methane, propane and other explosive gases was demonstrated
over a 2-km silica
A
similar
optical fibre link.
system
has
been
mid-infrared absorption.
mid-infrared
used
to
monitor
ammonia
using
This is the first reported use of
transmitting
fibres
for
spectroscopic
monitoring (21) .
The
main
disadvantage
of
the
Optrode
and
"light
pipe"
techniques is that a structure (either optical or chemical)
be
fixed
to
alternative
the
fibre
approach
is
end
to
in-situ spectroscopic sensor.
for
use
the
point
of
total
applications.
fibre
itself
An
as
an
This technique relies on the
interaction of the evanescent wave,
each
RFS
internal
that is established at
reflection
within
the
waveguide, with the surrounding medium.
1.4
Evanescent Wave Spectroscopy.
An all fibre remote spectroscopic sensor overcomes many of
the disadvantages of the two approaches outlined in section
1.3.
It is potentially more reliable and sensitive and is
particularly attractive for distributed sensing.
Evanescent
internal
wave
sensing
reflection
is
a
generalization
spectroscopy,
with
the
of
guided
total
wave
continuously probing the optical properties of an external
medium.
The
totally
non-propagating
reflected
evanescent
wave.
5
light
This
beam
generates
evanescent
a
wave
penetrates the surrounding medium to a depth of the order
of one wavelength and decays exponentially with distance in
the
lower
light
index
falls
medium,
amount
then
of
region.
within
an
If
absorption
evanescent
wave
absorption will
in
the
cladding
band
of
of
absorption
the
the
will
depend on the
the species to be measured.
tail
the wavelength
guided
external
occur.
The
concentration
of
Attenuation of the evanescent
region
causes
a
reduction
in
the
guided wave power in the core which, when detected, permits
the analyte concentration to be quantified.
Evanescent
wave
"attenuated
Fourier
measurements
total
internal
transform
infrared
have
been
reflection"
(FTIR)
reported
cells
(22)
spectrometers
in
and
(23) .
Total internal reflection devices have relied primarily on
evanescent
optic
interaction by prism coupling to
evanescent
wave
demonstrated by Simhony
absorption
et al.(24)
cells
using
IR
fluids.
Fibre
have
been
fibre and by
Tanaka et a l . (25) using silica fibre.
This work describes the characteristics of evanescent wave
spectroscopy
of
absorbing
dyes
optical fibres.
6
using
multimode
silica
CHAPTER 2
THEORETICAL BACKGROUND.
2.1 Introduction,
When a light beam is incident on
transparent
media,
refractive index
occurs
(26)
travelling
the interface between two
from the medium
of
higher
(ni > ng) , total internal reflection
(TIR)
when the angle of reflection o is larger than
the critical angle ©C .
eC
= sin- 1 (n¿2 / n 1 )
(1)
Closely related to this phenomenon is the existence of an
electromagnetic
wave
form
which
is
generated
in
the
optically rarer medium near to the reflecting surface. This
evanescent wave
penetrates
the
lower
refractive
medium and can interact optically with compounds
index
close to
or at the surface.
It was Fahrenfort
spectroscopic
Internal
Harrick
(27)
tool
and
Reflection
(29)
is
and Harrick
the
developed
denser
dependence
measured
by
of
but
what
is
Spectroscopy (IRS).
technique
spectrum of a sample material
optically
(2 8) who used TIR as a
of
light
shown in figure 1.
7
into
known
as
according to
the
optical
is in contact with an
medium;
the reflectivity of
introducing
IRS
recording
that
transparent
today
this
the
the
wavelength
interface is
denser
medium,
as
Fig.1
\
I n t e r n a l Reflection S p e c tr o s c o py
The Sample M a te ria l Absorbs Energy via
Interaction with the Evanescent Wave
8
2.2 Internal Reflection Spectroscopy.
Although geometric optics provides the condition for total
internal
the
reflection to occur,
phenomenon
or
any
it offers no explanation of
information
distribution at reflection.
about
the
energy
To gain further insight in to
this phenomenon, the results of electromagnetic theory must
be applied to the case.
The following discussion,
detailed
in Appendix A, is partially based on the treatment outlined
by
Hecht and Zajac (26) .
Suppose that the incident monochromatic light wave is plane
polarized so that it has the form
E i = EQi exp [i (i^.r
- w it)
]
(2)
The reflected and transmitted waves can be written as
Er = EQr exp [i
(kr .r- o>rt)
]
(3)
Et = Eot exp t;L
(^t*r" CJtt ^ ]
(4*
It is shown in appendix A that when TIR occurs
IE
I = IE -I
i or1
1 oi1
Since
lEo r |
=
|Eo i |,
all
the
reflected, which implies that
Therefore,
cannot, on
although
the
(for e. > © )
i
c'
energy
in
(5)
the
wave
is
exist,
it
|Eo t | = 0 •
transmitted
wave
does
average, carry energy across the interface.
However,
in order to satisfy the boundary conditions, there
must
a
be
disturbance
in
the
second
medium
and
this
shown to be
E
t
= E „ e-6zei(V
ot
9
sinV
nti ' wt)
(6)
is
i.e.
the disturbance
in the less dense medium is periodic
in x but exponentially decaying in the z direction. This is
the evanescent wave. In the denser medium a stationary wave
pattern
is
set
up
owing
to
the
interference
between
the
incident and reflected beams and in the less dense medium
the
amplitude
falls
off
exponentially,
although
the
amplitudes are equal at the interface.
The spatial rate of decay of the field in the second medium
is
determined
by
the
attenuation
constant
5.
Related
to
this constant 6 is a very important characteristic of the
evanescent
This
wave
known
as
the
depth
of
penetration
(dp ).
is defined as the distance required for the electric
field amplitude to fall to exp
(-1) or 37% of its value at
the surface and is given by
d
p
= 1/5 =
( V n )
(7)
2tt [sin2e
where
n
t i
is
the
ratio
of the
- n
refractive
indices
of
the
incident and transmitting media. Illustrated in figure 2 is
a
standing-wave
evanescent
wave
therefore
the
determined
by
Consequently,
absorbing
near
a
totally
couples
to
properties
the
if
medium,
the
the
of
environment
the
reflecting
evanescent
net
reflected
the
just
beyond
is
the
and
wave
are
interface.
penetrates
that
The
wave,
reflected
wave
effect
interface.
into
some
of
an
the
previously totally internally reflected energy is absorbed.
The
penetration
depth
divided
10
by
the
wavelength
A.
is
F ig.2
: S ta n d in g -Wave A m p litu d e s Established n e a r a
T o ta liy R e f le c t in g In te rfa ce
There is a S in u so id a l Dependence of the
Electric Field Amplitude on the Distance from
t h e S u rfa c e in th e D e n s e r Medium 1 and an
Ex ponentially Decreasing Am plitude in the
R a re r Medium 2 (29)
11
is plotted versus angle of incidence,
in figure 3, for a
number of interfaces (29). Harrick (29) points out that the
penetration is about one-tenth the wavelength in the denser
medium
near
materials,
grazing
incidence
(e
-
90°)
et
microscopic
al
(30)
level
investigated
the
interaction
index
to the transmitted
illustrates
angle
evanescent
of
at
the
of evanescent waves with atomic dipoles
and showed that the evanescent absorption
with
high
but becomes infinitely large as e approaches e .
Carniglia
which
for
intensity.
the
molecular
incidence
field
This
for
©,
is proportional
is shown
in
absorption
figure
probability,
for a molecule located
different ratios
of
4,
in
an
a
of
distance
molecule from interface to wavelength. One can observe from
this
plot
being
that
probability of
by
the
the
angle
absorbed
dramatically
critical
rate
the
as
angle
depending
and
on
falls
the
an
surrounding
of
off
evanescent
medium
incidence
with
distance
the
increases
approaches
increasing
of
photon
angle
molecule
the
at
from
a
the
interface.
Equation
(6)
also
shows
that
the
larger with closer index matching
increases
appropriate
with
choice
increasing
of
of
the
wavelength
optical interaction
(i.e as n/n.
wavelength.
the refractive
internal reflecting element
and
penetration
X,
depth
-- > 1)
Thus,
index
n
is
and
by
an
of
the
(IRE), of the incident angle e
one
mainly
can
with
12
select
compounds
a
d^to
close
promote
to
or
•
0O0
I
2
3 4
5
6 7
8
9 10 II 12 13 14 IS IB
f e n 10* 15* 20« 25* 30» 35*
40* 45» 50* 55* 60* 65* 70* 73*
83*
f'2i 1/4 .239 342 4 2 3 .500 .574 6 4 3 707 .766 .819 666 .906 .940 966 985 996
ANGLE OF INCIDENCE
6
Fig.3 ! Fractional Penetration Depth of Electromagnetic Field in
R a re r Bulk Medium for Total Internal Reflection i/5 Angle
of Incidence for a Number of Interfaces. The Penetration
Depth is Infinitely Large at the Critical Angle (2 9]
13
0°
15°
30°
45°
A n g l e of In c i d e n c e
F ig .4
60°
0C
75°
9
; The M o l e c u l a r Absorption P r o b a b i li t y, with Angle of
icidence 6 ,f o r i
le c u le Local
in an Evanescent Field, fo r Several
D i f f e r e n t Ratios of Distance a, of Molecule
fro m Interface to Wavelength i 30)
14
90°
affixed at the interface and minimise interaction with bulk
solution.
The depth of penetration
determine
the
is
attenuation
one
of
caused
four
by
factors
absorbing
which
films
in
internal reflection. The other factors are the polarization
dependent
electric
field
intensity,
the
interaction
area
which increases with number of reflections N and matching
of the refractive index of the two media.
Of
the
various
significant
factors
is the
which
internal
influence
1RS,
reflection element
the
most
(IRE). The
geometry of the IRE is a function of both the nature of the
sample
( usually a small
quantity of liquid)
and the
1RS
technique employed.
A
large
variety
of
IRE's
have
been
developed
(29),
simplest of which is the single reflection prism,
the
shown in
Fig.1.
The number of reflections
(L) ,
the
incidence
thickness
(e)
of
(N)
the
is a function of the length
waveguide
(T)
and
angle
and is given by
N = (L/T)cote
The
of
longer and thinner
the waveguide,
(8)
the larger is N and
the more frequently the evanescent wave interacts with the
surrounding medium.
It
is shown by Sutherland
et al
(31)
that the reflection loss R after N reflections is:
RN = 1 - Na
for
small a,where
a is the absorption
15
(9)
coefficient.
A very promising multiple reflection
element
IRE
is the
optical fibre. Here light is introduced at angles exceeding
the critical angle and propagates
through
the
fibre
by
total internal reflection. Fibres are used as IRE's because
of their small diameter and
so
that
the
effective
(potentially)
number
of
unlimited length
reflections
can
be
very
large.
The
remainder
multimode
of
this
optical
chapter
fibre
as
is
the
devoted
sensing
to
IRS
element
using
and
the
development of a model relating evanescent wave absorption
in
a
liquid
to
the
corresponding
reduction
of
light
intensity in the fibre.
2.3 Optical Fibre Considerations.
The picture of light propagation in optical fibres that has
been used so far,
and
forth
from
that is of rays of light reflected back
the
core
- cladding
boundary
travelling zig-zag fashion along the fibre,
most
purposes.
phenomenon
and
But
modes
light
of
is
guided
an
and
thereby
is adequate for
electromagnetic
wave
propagation,
wave
rather
than rays, provide a more comprehensive representation.
2.3.1 Optical Fibre Modes.
An optical fibre is a dielectric waveguide that operates at
optical
frequencies.
waveguide
can
propagating,
be
The
propagation
described
in
of
terms
light
of
a
along
the
set
of
electromagnetic field distributions called the
modes of the waveguide. These guided modes are referred
16
to
as the bound or trapped inodes of the waveguide. Each guided
mode is a pattern of electric and magnetic field lines that
is repeated along the
fibre
operating
The
wavelength.
at
most
intervals
widely
equal
accepted
to
the
waveguide
structure is the single solid dielectric cylinder of radius
a
and
index
cylinder
of
refraction
is known
surrounded
by
as the
a
material
2
shown
in
core of the
solid
refractive index n
ni
figure
fibre.
dielectric
5.
The
cladding
The
core
is
having
a
that is less than n . Variations in the
1
composition
of
the
commonly used fibre types,
core
give
rise
to
the
two
step-index and graded-index,
as
shown in figure 6. Both the step-index and the graded-index
fibres
can
multimode
fibre
be
further
classes.
sustains
As
divided
into
name
implies,
mode
of
the
only
one
single
a
mode
single
propagation,
and
mode
whereas
multimode fibres may contain many hundreds of modes.
A mode traveling in the positive z-direction (that is along
the fibre axis) has a time and z dependence given by (32)
e 1 *“
The
factor
vector
/3 is
k whose
the
z component
magnitude
space wavelength)
discrete
requirement
that
equations and the
is
of
2IT/A.
the wave
(where
A
propagation
is
the
free
and is the main parameter of interest in
describing fibre modes.
certain
(10)
For guided modes (3 can only assume
values,
the
which
mode
field
electric
and
17
are
determined
must
satisfy
magnetic
field
from
the
Maxwell's
boundary
F ig.5
■
Schem atic of □ Single Fibre S tr u c tu re
A Circular Solid Core of Refractive Index ni is
Surrounded by a Cladding having a Refractive
Index n 2 < n ,.A Plastic Buffer
Encapsulates the Fibre
18
>
Fiber Cross Section and Ray Paths
Index Profile
»,
|*i,
Typicul Dimensions
L
125 yin
(cladding)
■
1
8-12 yin
_________
I (corei
T
_
r
M ononiode slep-index fiber
"Jl
1 2 5 -4 0 0 /ini
(cladding)
_T‘
la
5 0 -2 0 0 /ini
(core)
_1.
JL
125 pm
(cladding)
50 it m
(core)
M ultim ode groded-index fiber
F ig.6
: Comparison of Sinale - M o d e and Multimode Step-Index
and Graded - Index Optical Fibres ( 32)
19
conditions at the core-cladding interface.
Figure
7 represents
a cross-sectional
view
fibre cut along its axis. It shows the
several
low order modes.
of
field
mode
is
also
The order of a mode
related
to
the
optical
patterns
the number of field maxima across the guide.
the
an
angle
of
is equal
to
The order of
that
the
ray
corresponding to this mode makes with the axis of a fibre;
that is, the steeper the angle, the higher the order of the
mode.
The
figure
shows
that
the
electric
fields
of
guided modes are not completely confined to the core
the
(that
is, they do not go to zero at the core-cladding boundary) ,
but,
instead,
they extend partially into the cladding.
The
fields vary harmonically in the guided region of refractive
index
For
n
low
and
exponentially
order modes,
near the
the
decay
centre
cladding
the
of the
region.
fields
outside
are
core with
On the
of
tightly
this
region.
concentrated
little penetration
other hand,
for higher
into
order
modes the fields are distributed more toward the edges of
the core and penetrate further into the cladding region.
Solving
Maxwell's
supporting
a
equations
finite
number
fibre
waveguide
modes
that are not trapped
fibre
but
problem.
are
The
has
still
shows
an
of
guided
infinite
in
modes,
continuum
addition
the
of
to
optical
radiation
in the core and guided by the
solutions
radiation
that,
field
of
same
basically
optical power that is outside the
20
the
fibre
boundary-value
results
from
acceptance
the
angle
TE0
te
1
te
2
Fig.7 : Cro ss-Sectional View of an 0 p tic a l Fibre Cut Alonq its Axis,
Showing the Field Patterns of Several Low Order Modes
i
being
refracted
out
of
the
core.
Because
of
the
finite
radius of the cladding, some of this radiation gets trapped
in the cladding, thereby causing cladding modes to
appear.
As the core and cladding modes propagate along the fibre,
mode
coupling
higher
occurs
order
between
modes.
of
This
cladding
coupling
occurs
because
cladding.
A diffusion of power back and forth between the
core and cladding modes occurs,
not
the
to
extend
are
the
confined
but
modes
and
fields
core
guided
modes
electric
the
the
the
completely
partially
into
the
which generally results in
a loss of power from the core modes.
In addition to bound and refracted modes,
of modes
optical
called
fibres.
tunneling modes
These
are
a third category
(33,34,35)
called
is present
tunneling modes
as
in
they
appear to tunnel a finite distance into the cladding.
The
modes are attenuated by continuously radiating their power
from the
modes
core
are
as
they propagate.
collectively
known
Refracted
as
leaky
and
modes
tunneling
as
both
experience power loss.
It can be shown that a mode remains guided as long as
(3
satisfies the condition
n k < /3 < n k
2 0
10
(11)
where kQ is the free space propagation constant = 2tt/A q and
is the free space wavelength.
The boundary between truly guided modes and leaky modes is
defined by the cutoff condition 0
-*
22
=
n k . As
2
0
soon
as
/3
becomes smaller than n2k Q , power leaks out of the core into
the cladding.
Leaky modes can carry significant amounts of
power in short fibres (3 6).
2.3.2 Total Number of Modes.
A mode is
referred to as being cutoff when its field in the
cladding
guide,
ceases to be evanescent and is detached from the
that
is,
the field in the cladding does not go to
zero.
As
stated in section 2.2,
field
in
the
constant
cladding
<5. For
is
the rate of decay of the
determined by
large values
of
<5, the
the
value of the
field
is tightly
concentrated inside and close to the core. With decreasing
values
of
5,
the
cladding.
Finally,
from
guide.
the
called
the
connected
field
for
The
cutoff
with
the
reaches
6 = 0 ,
the
frequency
at
frequency.
cutoff
farther
field
which
An
frequency V (also called the V-number)
where
n
and
n
are
core
and
into
detaches
this
is
itself
the
respectively and a is the core radius.
is
parameter
normalized
defined by
(n2 - n2)1/2
cladding
the
happens
important
condition
V = (2na/\)
out
refractive
(12)
indices
The modes that can
exist in a waveguide as a function of V may be expressed in
terms of a normalized propagation constant b defined by
b = (0/k) 2 - n2
n
2
1
- n
2
—
2
A plot of b as a function of V is shown in figure
23
(13)
8.
V— ►
Fig.8 \ Normalized Prop agation Constant as □ Function of V
The Fig ure Shows th a t Each Mode can only Exist
for V -V a lu e s that Exceed a Certain Limiting Value Vc
This is Called the Cut Off V a l u e (371
iw
This figure shows that each mode can exist only for values
of V that exceed a certain limiting value.
The modes are
cut off when |S/k = n g .
The
parameter V can also be related to the number of modes
M in a multimode fibre when M is large
(32) . In appendix B
it is shown that the total number of modes M which can be
guided in a fibre is given by
M ~ V2/2
(14)
2 . 3 . 3 Power Flow In The Cladding.
As is illustrated in figure 7, the electromagnetic field for
a
given
mode
does
not
go
to
zero
at
the
core-cladding
interface, but changes from an oscillating form in the core
to an exponential decay in the cladding. The further a mode
is
from
energy
flowing
its
is
cutoff
in
in
the
the
frequency,
core.
core
and
The
the
the more
relative
cladding
concentrated
amounts
can
be
of
its
power
obtained by
integrating the Poynting vector in the axial direction
Sz
= 1/2 Re(E X H*).ez
(15)
over the fibre cross section.
By assuming that there
is a very small
difference
refractive indices of the core and cladding
= weakly guided mode approximation), Gloge
(n
-
in the
«
1
(38) has derived
the fractional power flow in the cladding of a step-index
fibre as a function of V,
as
addition,
the average total power in the
far from cutoff,
illustrated
cladding has been derived for fibres in
25
in figure
which
many
9.
In
modes
F ig.9 \ FrpctionQL Power Flow in the Clcddinq ofg Step-Index
Qpticcil Fibre
qs
q
Function
26
of
V-Number 138)
can propagate. Because of this large number of modes, those
few modes
ignored
The
that are
to
a
reasonable
derivation
tungsten
appreciably close
assumes
filament lamp,
to
(38)
that
the
can
be
approximation.
an
incoherent
which,
source,
in general,
fibre mode with the same amount of power.
Gloge
cutoff
total
average
such
excites
as
a
every
It is shown by
cladding
power
can
be
obtained from the expression
r=
Pci ad
=
p ^r
where
Pciad
is
the
cladding and Ptot
evanescent
4
A
i"
—
2
,,,,
(16)
field
intensity
in
the
is the total light intensity in the core
and cladding. The power flow in the cladding decreases as V
increases.
For
example,
a
600
fibre
of
numerical
aperture
0.4
operating at a wavelength of 500nm, has a V-number of 1508.
From
equation
(16),
approximately
0.125%
of
the
power
propagates in the cladding. For a typical single mode fibre
of V-number 1 and same operating wavelength,
the total power flows in the cladding.
27
about 70% of
2.4 Evanescent Wave Spectroscopy Using Multimode Fibres.
If
the
cladding
absorbing
index n
fibre
fluid,
=
fluid
is
n
2
of
a
fibre
is
characterised
- ik , then
2'
attenuated
by
replaced
by
the
a
locally
complex
propagated
evanescent
by
an
refractive
power
in the
absorption.
The
transmitted power is predicted to be (39)
P(L) = P(o)e_yL
where
the
L
is
power
the
distance
transmitted
along
in
the
the
(17)
unclad
absence
length,
of
an
P(o>
absorbing
species and y is an evanescent absorption coefficient.
above
equation
(an equivalent
Beer-Lambert
is
The
relationship)
takes into account the power distribution within the fibre.
The evanescent absorption coefficient may be related to the
bulk absorption coefficient a for two cases:
(i) where all
bound modes are launched and (ii) where selected modes only
are launched.
(i) All M o d e s :
Tanaka et al
(39) have shown that,
using equation
(16) and
equation (17), the transmitted power becomes
P (l )
Therefore,
unclad
the
fibre
of
=
P (0 ) e -r<XL
(18)
evanescent
absorbance
L°gi0 (P(o)/Ptu ) of
length
surrounded
by
L
a
fluid
of
an
bulk
absorption coefficient a is given by
A
=
vL =
2.303
raL
2.303
(19)
This equation predicts that the evanescent absorbance in an
28
optical fibre depends linearly on both exposed fibre length
L
and
fluid
concentration
and
inversely
on
the
fibre
V-number from equation (16), for any fluid which obeys the
Beer-Lambert law.
Analysis
of
decreasing
the
the
above
V-number
discussion
[=
2na/X
illustrates
(n^
-
that
n ^ ) 1/2],
by
r
increases and more light becomes available for interaction
with
the
surrounding
index of the
fluid n
fluid.
Therefore,
as
the
approaches that of the
light energy in the external medium
refractive
core nithe
increases.
(ii) Selected M o d e s :
This
analysis
is based upon the
expression
of Snyder and
Love (36)
y = NT
(20)
where N is the number of reflections
per unit length of
fibre and T is the Fresnel transmission coefficient at the
interface of a lossless core and
In
the
case
waveguide
of
meridional
and absorbing cladding.
raysa
in
a
weakly
guiding
(ni~ n ) of normalized frequency parameter V ,
the
relationship between the evanescent absorption coefficient
■jr and bulk absorption coefficient a
shown to be
for a lossy cladding
is
(Appendix C)
a) Meridional Rays are those which cross the fibre axis
between reflections as distinct from skew rays which spiral
around the fibre without crossing the axis.
29
where ®zis the angle the ray makes with the core axis and
©c
is
the
complementary
illustrated
in
figure
critical
10.
The
angle
result
(cos
n2/ n!)
is accurate
as
for all
bound meridional rays whose direction is not close to the
critical
angle.
However,
this
expression
needs
to
be
modified to cater for non—weakly guiding modes which occur
when
the
cladding
based
liquid)
core
index
of
of
refractive
index
approximately
1.46
for
(in this
1.33
silica
is
case
not
glass.
close
a water
to
Removing
the
this
i
condition,
and allowing all values of o
< ec the value for
T can be shown (appendix C) to be
T
-
“ * n2 COSS
n
Using
equation
(n
v 1
(20)
- n
)
2
and
(22)
! 2
. 7T *3
J sin © - (n2/nx)
equation
(22)
the
evanescent
absorption coefficient then reduces to
K
—
=
a
where
©
is
interface
A n cos2©
----- ~—
-----------------------2 n
a sin© (n
- n ) "I .
.
2
.
2.
1 1
2'sin © - (n / n x)
the
(©
=
angle
tt/
2
between
-
© )
the
and
ray
©
Z
critical angle for the two media
3
is
and
normal
the
(23)
to
the
conventional
C
(©
' c
= sin-1 n /n ) .
2'
1
For fluids obeying the Beer-Lambert law the bulk absorption
coefficient
(a)
is proportional to fluid concentration.
Propagation along a straight line between interfaces in the core
o f a step-profile planar waveguide.
F ig .10 i The Incident Ray a t Q is Totally Internally Reflected
If Os<0z < 0 ' c ( 36)
31
From
equation
(23),
coefficient
is
therefore,
predicted
the
evanescent
be
proportional
to
absorption
also
to
concentration.
A
typical
fibre
used
in
this
work
has
diameter and a numerical aperture (NA) of
•
Since
*
N.A.
maximum
= 0.4 = sm<6
launch
angle
2
=
max
<b
max
(n
2
co
=
23.6°
- n
a
for
core
0.4.
•
1/ 2
cl
600iim
)
,
this yields
bound
a
meridional
rays. This maximum launch angle gives rise to the critical
angle ©^, at the core-cladding interface.
©C for clad fibre = 90° - sin"1 (0.4/1.457)
©
However,
is
= 74°.
c
in the sensing region, where the removed cladding
replaced
with
an
aqueous
solution,
whose
refractive
index n CI^ 1.33, the local critical angle is given by
. -1(1.33/1.457)
© = sin v
'
C
s C = 66°
Accordingly,
the
clad
it
is not possible to
fibre
which
will
be
launch bound modes
incident
at
the
in
core-fluid
interface at angles closer than 8°to the critical angle.
As outlined
in section 2.3.1,
cylindrical
geometry,
modes
which
are
numerical
propagate
for
mode
at
aperture
substantial
(40)
condition
sustain
launched
meridional
attenuation
will
and
on
the fibre,
non-bound
greater
than
the
permits.
These
modes
can
with
negligible
some of them will
32
or tunneling
angles
distances
reaching the
by virtue of its
sensing
satisfy the bound
region.
Low
order
inodes,
which
have
little
power
blocked
using
an
optics
(41).
Alternatively,
generated
at the
annular
in
the
beam mask
cladding,
placed
higher
at
order
can
the
launch
modes
may
sensing region by tapering the
be
be
fibre at
this location (42) or by bending (15).
As in the case of all bound modes,
predict
both
that
unclad
evanescent
fibre
equations
absorption
sensing
length
varies
and
(19) and (23)
linearly
with
concentration
for
fluids obeying the Lambert-Beer law in bulk absorption.
The sensitivity per unit length of the fibre optical sensor
can be determined from equation
multimode optical
ratio,
r,
is
fibre,
dependent
the value of the
on
the
propagation modes of the sensor,
energy
of this,
(18). When the sensor is a
evanescent wave
excitation
state
of
the
i.e. with electromagnetic
distribution amongst the fibre modes.
As a result
reproducibility of the sensitivity of the sensor
will not necessarily be obtained.
2.5 Summary.
The theoretical model predicts the relationship between the
evanescent
coefficient
absorption
a
for
two
coefficient
separate
r
and
bulk
situations
absorption
when
using
an
optical fibre with part of its cladding removed.
When all bound modes are launched,
that
the
exposed
evanescent
fibre
absorbance
length
L
and
inversely on the fibre V-number,
33
equation
depends
fluid
(19)
linearly
predicts
on both
concentration
for any fluid
that
and
obeys
the Beer-Lambert law.
When selected inodes only are launched,
is
corrected
evanescent
for
non-weakly
absorption
guiding
coefficient
proportional to concentration.
34
equation
modes,
to
(23) which
predicts
be
the
linearly
CHAPTER 3
EXPERIMENTAL SYSTEM
3.1 Measurement System.
The experimental system is shown in figure 11 and consists
of
a
light
source,
monochromator,
sample
chamber,
electronics with data acquisition and a microcomputer.
Optical radiation is supplied by a quartz tungsten halogen
source
(12V,
50W)
(PTR
Optics,
and
focused onto an
USA,
photomultiplier
Model
(model
R1546)
f/4
monochromator
MC1-02).
tube
A
monitors
the
intensity from the terminated optical fibre.
output
from
recording
the
detector
and/or
sent
can
to
be
a
used
12
to
bit
Hamamatsu
light
The analogue
obtain
a
chart
analogue-digital
converter. The digital output is then averaged and analysed
by the BBC microcomputer.
The monochromator is a Fastie-Ebert design and consists of
a
spherical
parallel
collimating/focusing
light
diffraction
onto
grating
a
plane
and
mirror
that
reflective
converges
a
directs
holographic
segment
of
the
dispersed light on to the exit slits as shown in figure 12.
Two
diagonal
mirrors
fold
the
beam
configuration. The full specification
in
to
an
in-line
of the monochromator
is given in appendix D.
The
monochromator
is
stepper
motor
microprocessor based controller/driver.
driven
by
a
This unit contains
a 2 00 byte internal memory and is programmable by any ASCII
35
50W
Lens
L a r g e NA
O bj e ct iv e
Sample
Ch ambe r
Unclad
Fibre
A
O
o
Source
— Mask
Cl ad Fi b re
Mas k
Fig. 11 I Schematic of Exper im en tal System and Optical Mask
Collimating
M irro r
Folding
irrors
Entrance S lit
Fig, 12 \ Schematic □¡□gram of the F a s t i e - E b e r t Monochromator
37
keyboard
allow
or
computer.
the
user
velocity",
"ramp
operation
the
to
3 0 ASCII
program
slope
together
particular,
Over
and
with
"move
length",
a
"search
high
distance",
"half
for
or
commands
"initial
full
zero
step"
order".
In
a routine is stored within the unit to return
monochromator
to
zero
order
wavelength.
controller has such a small memory capacity,
to
level
interface
it to
the
Because
the
it was decided
BBC microcomputer via
the RS
2 32
port. In this way all the software was written in BASIC and
stored on floppy disk.
A silicon photodetector or photomultiplier tube is mounted
at
the
response
figures
response
exit
port
curves
13
of
and
of
of
14,
silicon
the
sample
these
photodetectors
respectively.
is
chamber.
wider,
a
Although
The
are
the
spectral
shown
in
spectral
photomultiplier
has
a
greater sensitivity in the visible region. It was therefore
decided to use this detector for all experimental work.
38
(A/W )
Responsivity
W a v e l e n g t h ( nm )
Fig. 13
: Sp e d r a l Resp onse of □ S i lic o n P h o f o d e t e c t o r (^3)
39
MA / W
W a ve l e n g t h ( n m )
Fig. 14
!
Sp e c t r a l Response of a P h o to m u I f ip l i e r Tub e ( 43)
40
3,2 Calibration and System Response.
The grating mount has
protect
it
from
defined
by
the
an upper and
being
damaged.
separation
lower limit
The
between
switch to
wavelength
these
range
two
is
limits.
Calibration may be performed at any wavelength of interest
provided
a
wavelength.
reference
source
is
available
at
that
It was decided to calibrate at zero order for
two reasons:
(i)
as
all
wavelengths
monochromator,
are
transmitted
through
the
the output energy is large relative to the
diffracted wavelength output and is easier to detect as a
definite
peak
in
output
energy.
Therefore,
no
special
spectral sources are required.
(ii)
the
manufacturers
(PTR
Optics,
USA)
calibrate
the
diffracted wavelengths relative to zero order.
The calibration consisted of the determination of the low
and
high
location
limits
of
relative
zero order
other wavelengths
to
zero
is always
are measured.
order.
known and
A
Therefore,
the
from this all
program was
written
perform this procedure automatically and is listed
to
in the
software section.
The calibration was then checked using a Mercury arc lamp
and the spectral output is shown in figure 15.
The system spectral response from lOOnm to 800nm is shown
in figure 16. This indicates the spectral range over which
useful data can be obtained. In investigating the response
41
(a r b. uni t s)
Intensity
W a v e l e n g t h ( nm )
Fig. 15
!
C a l i b r a t io n of Sy stem U s i n g M e r c u r y Arc L a m p
( arb.units )
Intensity
100
BOO
500
W a v e l e n g t h ( nm)
Fig. 16 ; System S p e c t r a l Response
7Q0
two
problems
were
encountered
which
were
of
significant
importance in the setting up of the experimental system. As
seen in figure 16 there is a peculiar feature or "kink" at
460nm
of
full
dirty optics,
width
half
maximum
misalignments
grating
occurring
Having
out
one
it was discovered to be
anomaly.
It
is
in
E
polarization efficiency
the
ruled
or other obvious reasons by a
process of systematic elimination,
a
20nm.
of
three major
anomalies
of
the
holographic grating used in this monochromator. The feature
can
be
relative
seen
in
the
throughput
efficiency
curve
in
curve
of the
grating
and
figure
17 and
figure
18,
respectively. While these anomalies are undesirable they do
not indicate a grating defect.
44
Ef f i c i e n c y
W a v e l e n g t h ( nm )
Fig. 17
:
Efficiency Curve of the H o l o g r a phic G r a tin g
as a Function of W a v e l e n g th (43)
W a v e l e n g t h ( nm)
Fig. 18
!
R e la tiv e T h r o u g h p u t Curve of the M o n o c h r o m a t o r ( 4 3 )
3.3 Sensing Fibre and Preparation.
The
optical
fibre
selected
as
the
experiments was plastic clad silica
sensor
(PCS)
in
fibre
these
(TSL,UK).
The core is made of high purity fused silica to allow low
attenuation across a wide spectral range. As illustrated in
figure 19, the attenuation of the fibre in the range 400nm
to 700nm is less than 30 dB/km. The cladding is a silicone
resin and surrounding this
is a protective plastic Tefzel
(ETFE) outer coating to provide mechanical protection. This
multimode step index fibre was originally chosen because of
the
ease
in which
the
cladding
can be
core to provide the sensing element.
stripped
from the
Another advantage of
this fibre is the high transmission characteristics in the
near
UV
and
visible
range.
The
fibre
is
also
readily
available in either 200jum or 600jim core diameter,
both of
numerical aperture 0.4.
This enables efficient coupling of
light
in to
and
also
volume
to
with
the
the
fibre
interact
specification
for
2 00jLim and
provides
a
absorbing
600/im
fibres
large
sensing
species.
is
outlined
The
in
appendix E.
The
length
of
fibre
used
in the
experimental
set-up
was
approximately lm. For efficient coupling of radiation into
the fibre it is necessary that the end-faces are flat
perpendicular
to
the
optical
axis
of
the
fibre.
and
Several
commercially available fibre cleaving tools provide smooth
mirror-like end-faces
for fibres of core diameter
47
between
Guaranteed Values
of A t t e nu a t i on
A/im
0.50
0.60
0.70
0.85
PCS 6 00
dB/km
30
20
14
12
120
110
100
90
80
70
60
50
40
30
20
10
0
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Wa v e length /jm
Fig.19
;
A t t é n u a t i o n Curve of Plastic Clad
Silica Core Optical Fibre ( 4 4 )
48
1.1
3um and
50/iiti and cladding diameter
view
the
of
there
is no
large
core diameter
cleaving tool
satisfactory
quality
(figure
of
125/^m.
the
However,
fibre
in
used here,
available that would produce a
endface.
machine (Logitech Ltd,U.K.)
end-faces
of
A
polishing
and
lapping
is used to produce good quality
20) . The
fibres
are
placed
in
a
mild
steel barrel and waxed in position, being slightly proud of
the end. When the wax has solidified, the barrel is secured
in a polishing jig and this is then placed on the polishing
plate.
The polishing occurs first on the wax,
then the fibres and
finally on the base of the
Assuming the barrel
is
perpendicular
fibre
end-face
observed that
the
more
macro-cracks
to
is
the
cylinder.
plate,
one
perpendicular
is
to
assured
its
the more packed the barrel
stable
and
secure
will
develop
a
they
few mm
obtain a satisfactory quality end-face,
used at first. Thereafter,
the
It
was
axis.
is with
are.
from
that
the
Otherwise,
endface.
9/im grit
for greater quality,
fibres,
To
(A1203) is
3/im grit is
used.
An
important
choosing
aspect
an
interaction
in developing the
adequate
region.
procedure
First
the
to
the
remaining
different
cladding
etchants
were
is
removed
examined
obtain
Tefzel
removed using a mechanical stripping
in-line
a
outer
sensor was
clean
coating
core
is
tool. Following this,
by
such
etching.
as
boiling
Several
chromic
acid, sodium hydroxide in ethanol and a proprietary solvent.
49
F ig .20 \ A Polishing and Lapping Machine Used to Produce
Good Quality End-Faces
50
Newby
(45)
subjected
similar
fibres
to
a
combination
of
processes: hot chromic acid, autoclave, and radio frequency
glow
analysis.
photoelectron
microscopy
consists
The
cores
were
spectroscopy
then
examined
by
and
scanning
electron
(XPS),
Xray
(SEM). The reason XPS was used is that the core
primarily
of
silicon
and
oxygen,
while
the
cladding contains a high percentage of carbon atoms.
Very
high Si/C and 0/C ratios indicate a cladding free surface.
Although
this
technique was
not
available
to
us,
Newby's
results did indicate that chromic acid might be a suitable
etchant.
The
fibre was
Tefzel
laid
on
a
flat
surface
and
the
protective
coating
removed
from
a
central
location
being
careful
not
to
scratch
the
scalpel,
important
that
all
the
cladding
be
using
core.
removed
It
since
a
is
any
particles on the surface would produce a scattering effect
which would
sensor.
was
To ensure a clean sensor area,
immersed
8 5 °C,
impair the surface sensitive qualities
in
a
container
the stripped fibre
containing
chromic
for 40 minutes to remove the residual
sensor was then cleaned thoroughly
of the
acid
cladding.
in ethanol
and
at
The
finally
wiped using an acetone soaked tissue.
This
procedure
durations of 10,
to
determine
the
was
40,
repeated
70,
amount
for
acid
bath
treatment
and 100 minutes and SEM was used
of
residual
cladding.
shows a series of micrographs of 600/xm fibre for
51
Figure
21
70 and
F ig .21 I Two Microg r a p hs of 600/um Fibre for 70 and IQOminute
Treatments in Chromic Acid a t8 5 ° C
52
and
100
minute
apparent
treatments
in
chromic
from these photographs,
acid
there
at
85 °C.
appears to be no
reproducibility or improvement with treatment time
quality of the fibre sample.
As
in the
In view of the unsatisfactory
quality of the sensor surface and because of the hazards of
the chemicals required this technique was not pursued.
The next technique consisted of placing the stripped fibre
in a solution of sodium hydroxide in ethanol.
However,
the
fibre had to be left in the bath for a period of between 1 2
and 14 hours. From the
micrograph shown in figure 22 it is
evident that an irregular contour of the surface is formed
with
this
method
and
in
no
case
was
all
the
cladding
removed.
The
etching procedure
adopted as
a standard
in this work
used a solvent which was less hazardous than the previous
two methods
The
and
removed
proprietary
solvent,
France)
the
cladding
Optical
relatively
Fibre
quickly.
Stripper,
developed to remove silicone coatings,
(Lumer,
was placed
in the evanescent sample chamber with the fibre as shown in
figure
23.
Several
scalpel and placed
of
between
then
24
with
samples
were
in a Lumer solution
5 minutes
cleaned
Figure
short
and
one
ethanol
illustrates
hour.
followed
SEM
prepared
using
a
for time durations
The
by
micrographs
etched
fibre was
distilled
of
water.
samples
for
different etching times and it can be clearly seen that for
etching
times
greater
than
53
20
minutes,
a
clean
glass
F ig .2 2
;
Microg ra ph of 600Ajm Fibre After Been L e t t i n □
Solution of Sodium Hydroxide in E th a n o l for
a Period of Between 12 and 14h o u rs
Sk
Fig. 2 3
!
Evanescent
Sample C h a m b e r
with Fibre I n - L i n e
55
2 20 / jm P C S F i b r e in
E t c h a n t f o r 5mins
600 yum PCS Fibre in
Etch ant for 30mins
2 0 0 / j m PCS Fibre in
E t ch an t f o r 5mins
Showing Core/Cladding
In t e r f a c e
Fig. 2 k \ I l lu s t r a t e s SEM Microg r a phs of Samples for
D if f e r e n t Etching Times in Lumer Solution
56
surface with no visible residual particles is obtained.
A
comparison
Lumer
of
etchant
residual
the
is
above
the
cladding
three
most
methods
suitable
relatively
shows
as
it
easily,
in
that
the
removes
the
the
shortest
possible time, and minimizes hazards in a laboratory.
3.4 Mask and Sample Chamber.
As
illustrated
includes
a
in
figure
cylindrical
placed within
it.
11,
flow
the
cell
The bare core
experimental
with
the
a
1 mm
diameter
collimated by a 1 0
into
the
fibre
exit
sensing
fibre
is exposed to the sample
solution along a maximum length of 22cm.
from
set-up
port
of
The emerging beam
the
monochromator
is
cm focal length lens and then launched
using
a
x40
microscope
objective
of
numerical aperture 0.65. Assuming that the collimated beam
completely
fills
the
entrance
microscope
light
is 40.5°,
calculated
from NA = n sin<p . where n is the refractive
0
max
0
However,
air,
and
exiting
the
the half
of
of the
of
objective,
index
angle
plane
d>
max is the maximum
angle
of
emission.
the fibre has a numerical aperture of 0.4 and an
acceptance
angle e
of
23.5°,where
© is
the
maximum
angle
between an incident ray and the fibre axis that will allow
propagation by total
internal
reflection
(neglecting
skew
rays that will not pass through the fibre axis). Therefore,
by using
high numerical
aperture
well as non - bound modes will
57
be
launch optics
populated.
bound
as
Some
of
quickly
the
light
decays
propagates
away
due
to
in
the
the
cladding
high
where
attenuation
of
it
the
cladding.
However,
as
tunnelling
angles
stated
modes
greater
in
section
which
than
are
the
permits are sustained.
2.4,
launched
meridional
some
non-bound
into
the
fibre
numerical
or
at
aperture
It is these modes that are used to
enhance the evanescent absorption in this work. An annular
mask
was
fabricated
to
tunnelling modes only.
of the mask
launch
high
order
modes
and
The outer non transparent section
prevented the
launching
of
leaky refracting
modes in the cladding.
An
x-y
micropositioner
at
the launch
end
was
used
to
optimise the coupling between the source and optical fibre.
The opposite end of the fibre was terminated in a modified
SMA connector and was connected to the adapted mount at the
entrance port of the photomultiplier.
As
explained
in
chapter
two,
in
order
sensitivity of an evanescent wave sensor,
to
enhance
the
it is desirable
to have the highest possible ratio of
P c 1ad
~~P
core
where the parameters are as defined in section 2.3.3.
Experimentally,
various
sized
this
theory
annular
was
masks
investigated
in
the
microscope objective to preferentially
58
by
backplane
excite
the
placing
of
the
higher
order modes only.
making
a
The mask shown in figure 11 was made by
large
scale
drawing
photographically reducing
first
and
then
to the appropriate size.
It was
then photocopied onto
an acetate sheet and cut out using a
scalpel. A
masks
series
of
were
made
of
constant
outer
diameter and inner core ranging from 1.4 mm to 5.5 mm.
series of
measurements of evanescent wave absorption with
the various masks revealed the optimum mask
mm.
A
size to be 4
This was a compromise between the mask size that gave
maximum
evanescent
wave
absorption
and
maximum
optical
throughput of the system.
Figure
25
function
is
of
a graph
wavelength
of
evanescent wave
for
different
absorption
mask
as a
diameters.
The
absorbing fluid is EosinrTetrabromofluorescein with a peak
absorption
at
larger
inner
P
the
52 0nm.
mask
It
can
diameter
clearly
the
be
greater
seen
the
that
ratio
the
of
cl ad /P core , a greater fraction of higher order modes were
excited and therefore the greater the sensitivity.
It is important to note that the same Eosin concentration
was
used
for
all
measurements
cleaned thoroughly after each
and
the
sensing
fibre
was
measurement by flushing the
cell with ethanol and wiping the bare core with an acetone
soaked tissue followed by de-ionized water.
59
590
W a v e l e n g t h ( nm)
Fig. 25
i
Evanescent Absorption as a Function of Wavelength for
Different Inner Mask Diameters and Constant Outer Diameter
The Absorber, Eosin; Tetrabromoflourescei^was of
Constant Concentration for a l l Mea su rements
740
3.5 Electronics and Software Development.
3.5.1 Electronics.
A schematic diagram of the hardware electronics is shown in
figure 26. A 12 bit analog to digital converter
(ADC)
digital
to
in
supply
unit
analog
was
converter
made
to
to the photomultiplier.
analog to digital
(DAC)
interface
with
the
built
BBC
and
power
microcomputer
This entailed signal conditioning,
conversion,
and
interfacing electronics
to computer buses.
The ADC accepted any
unipolar analog input in the range 0
to
use
10V.
In
order
to
the
full
range
of
the
non-inverting variable gain amplifier of gain XI,
and
X10
was
digitising.
used
to
condition
the
ADC,
a
X 2 , X5,
signal
before
This amplifier also protects the ADC from high
voltage inputs. The 351 operational amplifier from Motorola
was
also
used
to
drive
an
analog
meter
which
allowed
monitoring of the signal strength.
The
ADC
AD574A,
signal
chip
used
obtained
is
from
conditioning
accuracy of 0.025%
and
a
successive
Analog
Devices.
sufficient
approximation
Using
signal
the
type
above
averaging,
an
was obtained.
The electronics interface consisted of decoding the address
lines and buffering of the data lines to the 1 MHz bus of
the BBC microcomputer.
The power supply was filtered,
high
frequency
noise.
Use
61
well-regulated,
of
noisy
and free from
supplies
may
cause
A n alog
In pu f
In te rfa c e
to
BBC
Fig.2 6
: Schematic Diagram of the Electro nics H a r d w a r e
unstable
output
codes
to
be
capacitors were placed on all
generated.
the power
Decoupling
supply
lines
and
the signal lines were well screened.
The corresponding circuit diagrams
of the above electronics
are shown in appendix F.
3.5.2 Software Development.
The
signal
processing
software was written
in
BASIC
such
that memory space was conserved at all times. The structure
was
as
shown
sections;
in
figure
27
(i) acquisition,
and display of data.
i.e.
divided
into
(ii) processing,
three
(iii)
main
analysis
The software is included in appendix
G for reference.
(i) Data acquisition.
This program interfaces the BBC microcomputer with external
peripherals via the ADC,
control
specific
the
stepping
time
thereby enabling the operator to
motor
intervals
and
over
sample
the
the
detector
desired
at
wavelength
range.
The monochromator
data points
are
is
incremented by
sampled,
then
one
averaged
nanometre
and
the
and
60
resulting
value stored in an array. The process is repeated following
the next increment.
The flow chart of the program is illustrated in figure 28.
63
FLOW CHART OF PROGRAM STRUCTURES
Figure 27: Flow Chart of Program Structure.
64
FLOW CHART OF DATA ACQUISITION
Figure 28: Flow chart of data acquisition.
65
(ii) Data processing.
This
program
corrects
spectra
by
dividing
the
recorded
spectra by the overall system spectral response in order to
give a true transmission spectrum of the analyte.
The true
absorption spectrum is obtained by dividing spectrum A
sample)
by
spectrum B
moving
point
(in water) . It will
average
to
measurement of interest.
before
and
after
each
reduce
noise
(in
also perform a
content
in
the
This entails summing three points
point
and
storing
the
result
in
memory.
The structure of the program is shown in figure 29.
(iii) Data analysis and display.
This
program
wavelength
calculates
using
the
absorbance
[ I 0 (*)/I (*) ]
Lo<? 1 0
at
a
where
transmitted intensity of the sensor in water,
transmitted
The
intensity
maximum
displayed and
in the
absorbance
a
plot
for
presence
a
particular
IQ
particular
the
and I is the
of Methylene
of absorbance versus
Blue.
wavelength
wavelength
then obtained on a plotter.
The structure of the program is shown in figure 30.
66
is
is
is
FLOW CHART OF DATA PROCESSING.
Figure 29: Flow chart of data processing routine.
67
FLOW CHART OF DATA ANALYSIS.
Figure 30: Flow chart of the data analysis program.
68
CHAPTER 4
RESULTS and ANALYSIS
4.1 Methodology.
In figure 11,
the optical
system used to launch tunneling
modes in either 2 0 0 /nm or 600jm fibre of numerical aperture
0.4 is shown. Light from a 50W tungsten halogen source was
dispersed in an f/4 monochromator which had a 1mm diameter
exit aperture and the emerging beam was collimated and then
focused by a 0.65 NA objective
the clad fibre.
lens
into the end-face of
The objective lens contained the annular
beam mask to restrict the launched light into higher order
modes
and
tunneling modes
only,
as described
in section
3.4. The intensity profile emerging from the objective lens
was
consistent
with
a
range
of
incident
angles
at
the
core-cladding interface of 70° to 72.5°; these angles being
greater
fused
than the
critical
silica/water
angle
interface
of
(= sin-1(n /n ))
6 6 °.
As
for
the variation
a
in
refractive index of the Methylene Blue was not greater than
1
part
assumed
in
105
that
over
the
there was
concentration
negligible
range
change
used,
in the
it was
critical
angle as a function of concentration.
At approximately the centre of the length of fibre used the
cladding
was
removed
by
etching
and
then
cleaned
with
ethanol as previously described in section 3.3.
In
order
to
investigate
the
dependence
absorbance on absorber concentration,
69
of
evanescent
it was decided to use
a
fluid
whose
concentration
bulk
(i.e.
absorption
obeyed
the
varied
linearly
Beer-Lambert
with
Law).
The
following fluids were examined for Beer-Lambert behaviour:
Acid
Yellow,
Potassium
Permanganate,
Potassium
Chromate,
Phenol Red, Bromocresol Purple, Eosin:Tetrabromofluorescein
and Methylene Blue.
The Methylene Blue,
of molecular weight 319g, was the only
fluid that obeyed the Beer-Lambert law,
over a large range
of concentrations.
A 1 x 10 ~ 3 molar solution was prepared by dissolving 0.319g
of Methylene Blue
used
as
the
in 1 litre of deionised water.
standard
concentration
and
This was
subsequent
concentrations were obtained by appropriate dilutions, e.g.
diluting
lOOmls
in 900mls
of deionised water was used to
give a 1 x 10 - 4 molar solution. This procedure was repeated
to produce solutions down to 1
x 1 0 - 9 molar concentration.
A Hewlett Packard diode array spectrophotometer was used to
measure
bulk
Methylene
absorbance
Blue
in
absorbance
the
range
spectrum,
10 " 6 molar dye in a 1cm cuvette,
400nm
to
obtained
800nm.
with
a
A
1 x
is shown in figure 31. The
spectrum shows a cle a r peak at 664nm corresponding to the
monomer
595nm
form
due
throughout
bulk
to
of
the
dimer
were
absorbance
Methylene Blue,
molecule
formation.
based
as
on
a
and
The
a
shoulder
absorbance
the monomer
function
of
is shown in figure 32,
70
peak
at
emerging
values
664nm.
concentration,
at
used
The
for
from which the Beer
Absor banc e
W avelength
F ig.31
!
(nm)
M e th y lene Blue Bulk Absorbance Spectrum,Obtained with
a 1x
1Q~6
M olar Dye in a 1cm Cu v e t t e
71
Absor b o n c e
Bu Ik
Co n c e n t r a t i o n ( M )
Fig. 32
!
B u lk A b s o r b a n c e as a Function of Concentration
for M e t h y lene B l u e
( X 1E - 6 )
from which the Beer-Lambert bnehaviour is shown.
Using
the
section
unclad
3.1,
obtained
and
the
transmittance
in
Methylene
fibre
the
Blue
case
by
of
apparatus
and
described
absorbance
the
same
aqueous
referencing
each
spectrum
values
were
solutions
against
in
of
the
spectrum obtained with deionised water alone in the sample
chamber.
To
minimise
problems
associated
with
surface
contamination the sensor region was cleaned carefully (with
ethanol)
before
evanescent
solution
a
spectrum
is
shown
spectrum
was
recorded.
of
10 - 6
molar
1
x
in figure
33.
This
A
typical
Methylene
spectrum
Blue
is similar
to the bulk absorbance spectrum in figure 31.
4.2 Results.
In
order
to
characterise
the
evanescent
wave
sensor
the
following parameters were investigated:
(i)
Evanescent absorbance
vs length
(ii)
Evanescent absorbance
vs concentration
(iii)
Evanescent absorbance
vs fibre V - number
4.2.1
Evanescent Absorbance
vs Sensing Length.
To
measure
the
unclad length
dependence
of
evanescent
absorbance
with
(for a fixed dye concentration), a series of
sensing lengths were prepared as discussed in section 3.3.
600)iim PCS
fibre
was
used
in
•
an
aqueous
.
solution
absorbing dye Eosin at a concentration of 1 x 10
- 3
of
the
M. The
dependence of the evanescent absorbance on sensor length is
shown in figure 34.
73
W a v e l e n g t h (nm)
F ig.33
\ M e t h y le n e Blue Evanescent A b s o r b a n c e S p e c t r u m ,
Obtained w ith a 1 x 10 6 M
Solution
Absorbance
Evanescent
Interaction
L e n g t h (cm)
Fig. 3k I Variation of Ev ane sc ent A b s o rb an c e with Unclad Fibre Length for
Absorber Eosin:Tetrabromofluor es ce in of Constant Concentration
The
observed
predicted
linear
functional
behaviour
forms
of
is
consistent
equations
18
with
and
19.
the
From
these equations the slope of the evanescent absorbance vs
length plot
is given by ra/2.303
where r is the cladding
power ratio and a is the absorption coefficient.
slope
of
this
graph
and
the
measured
bulk
Using the
absorbance,
a
cladding power ratio, r, of approximately 0.7% is obtained.
This is considerably larger than the value of 0.1% reported
by DeGrandpre and Burgess
the mask used
(15). However, the value of r for
in our work
(corresponding to a e range of
70° - 72.5°) can be calculated from an expression developed
by
Ruddy
(46)
to
be
0.8 7%.
Thus
an
enhanced
absorbance
which is mask dependent is observed.
4.2.2 Evanescent Absorbance vs Concentration.
Evanescent absorbance values
range
of
3 x
10~8M - 5 x
at
664nm for a concentration
10-6M
of
aqueous Methylene
Blue
were measured using both PCS 2 00jLtm and 600fim fibres.
The interaction lengths were 22cm and 20.5cm, respectively.
The results are shown in figure
35.
The non-linear nature
of the evanescent data is evident.
Using
equation
23,
the
theoretical
evanescent
absorption
coefficient values for 1 x 10-6M aqueous Methylene Blue in
contact
with
600/Lim
diameter
core
silica
calculated as a function of incident angle
figure
664nm,
36.
The
model
uses
n
=
1.457,
n2
fibre
can
be
(e) as shown in
=
1.335,
X =
a = 3 00jnm. For the launch optics used in this work,
76
Concentratio n ( M )
F ig.35
i
Evanesc ent Absorbance as a Function of Concentration for
200AJm and 600/jm PCS Unclad Fibre.
The Interaction Lengths were 22cm and 20.5cm, Respectively
and the Absorber was Methylene Blue
6 5. 0
67.5
70.0
72.5
75.0
77.5
8 0. 0
82.5
85.0
Incident A n g l e
Fig. 36
'•
Ratio of Evane sc ent A b s o r ption and Bulk Absorption C o e ffic ie n t for
6 0 0 ;um PCS Fibre in M ethylene Blue as a Function of Incident Angle s
maximum absorbance will occur at e = 70° at which value if/a
is predicted to be
This
yields
absorbance
(via
for
approximately
equation
1 x
x
8
19)
a
10 4
(see Fig.
theoretical
10_6M Methylene
Blue
of
36) .
evanescent
1 x
10 3. The
experimental value of 0.2 is observed in figure 35. Thus an
enhanced absorption which is non linear with concentration
is observed.
A ln-ln plot of evanescent absorbance vs
shown
in
linear
0.52
37
relationship
and
square
this
figure
0.519
root
for
is
were
the
root
fibre
obtained
measured
dependence.
square
two
A
in
concentration
diameters
each
case.
indicating
least-square
dependence
yielded
an
fit
the
is
used.
Slopes
A
of
approximate
analysis
of
correlation
coefficients shown below;
Coefficient of
Correlation
Coefficient of
Determination
Fibre Diameter
(m)
200
0. 925
0.962
600
0.989
0 .994
This square root dependence on concentration is in contrast
to the expected linear dependence given by equation (19) in
chapter
2.
In
addition,
predictions
of
both
cladding,
and
Stewart
chemical sensor.
it
Snyder
et
al
is
and
(47)
in
Love
for
conflict
(36)
an
In both cases absorbance
increase linearly with concentration.
79
for
with
a
evanescent
the
lossy
wave
is predicted to
)
absorbance
( Evanescent
Log
Log ( C o n c e n t r a t i o n )
Fig.37
\ I n (A bsorba nce ) / s i n (Concentration) for Ev an escent Absorption
on 2 0 0 / j m and 6 0 0 j u m PCS F i b r e
However,
the
non
linear
concentration
has
been
dependence
observed
of
for
absorbance
attenuated
on
total
reflection by other workers.
Using 200jum PCS fibre and Oxazine 4 perchlorate dye as the
absorbing
species,
absorbances
DeGrandpre
for both
clad
and
Burgess
and unclad
(15)
measured
The
cladding
fibre.
was permeable to the non polar solvents used.
of
the
clad
fibre
concentration
fibre,
from
absorbance
a
dependence
In
the
root
Beer-Lambert
is
shown
in
figure
(evanescent
dependence
for
an
law.
of
of
using
of
et
38.
This
core
linear
and
bulk
is equivalent
absorbance
(48)
on
obeying
reported
absorbance
Silver
unclad
The
material
al
on
Data extracted
evanescent
evanescent
900jim
the
absorbance ) 2
absorbing
Schnitzer
dependence
concentration
absorbance
non linearity was reported.
between
concentration
of
case
is evident from this graph.
square
parabolic
linear
observed.
work
relationship
to
was
however,
their
a
In the case
on
Halide
a
fluid
fibre
operating at A = 5.8^m.
4.2.3 Evanescent Absorbance dependence on V-Number.
Although
the
evanescent
absorbance
values
for
the
2 00/im
fibre are greater at all concentrations than those obtained
with the 600/Ltm fibre,
the enhancement
factor is less than
the threefold increase predicted by the
equations
(16)
and
(19) . This
may
be
1/V dependence
due
to
the
of
smaller
mask diameter used with the 200jum fibre. This gives rise to
81
)
ce
Absorban
( Fi bre
B u l k Ab so r ba n ce
Fig.38
;
1 Evanescent Absorbance)2 vs Bulk Absorbance for Oxazine Perchlorate
on Unc la d 2 0 0 ;um PCS Fibre.
D ata of De Grand pre and B u r g ess (15)
a different
different
range
modal
of
launching angles © and therefore a
propagation
in
the sensor.
propagation state of the sensor determines
power
flow,
decrease
r,
the
sufficient
in
the
mask
optical
absorbance
for
consistent
with
cladding.
inner
diameter
throughput
the
in
smaller
the
It
the
theory
fractional
necessary
order
sensor.
V-number
general
the
was
in
The modal
to
to
have
The
larger
is
however
fibre
of
sections
parabolic
dependence
2.3.3 and 2.4.
4.3 Analysis.
The
enhanced
concentration
dye
molecules
absorbance
is
on
and
consistent
the
with
polar
adsorption
surface
of
the
of
the
fused
on
ionic
silica
core. The high density of OH ions on the glass is expected
to give an enhanced concentration of dye molecules at the
surface.
These ions will tend to reduce the electric field
experienced by other ions in solution.
This
electrostatic
shielding
was
treated
by
Debye
and
Hiickel (49) as a modified Coulomb potential
exp (-r/Ao)
(24)
r
where the shielding length
X
D
where n
e
is given by
=
A
kTs
2
e n
e
is the ion density
c is the electrical permittivity
83
-„ .
(25)
k is Boltzmann's constant
T is the temperature in Kelvin
e is the electronic charge
For the concentration range
here,
the
value
analytical
Of
X
wavelength
D
(3 X 10 " 8 to 5 X 10 6 M)
varies
(664
nm)
from
and
12%
is
to
1%
used
of
substantially
the
less
than the penetration depth of the evanescent field in the
solution.
Although the Debye - Hiickel theory was derived to determine
how
far
an
electric
three dimensions,
functional
field
penetrates
within
a plasma
in
it is shown in appendix H that the same
solution
is
obtained
using
cylindrical
polar
coordinates. The only difference is a numerical constant in
equation (25), which does not affect the ion density
Application
of the
above model
to this
case
ng.
requires the
fibre to be considered as the electrode with the ion cloud
as
the
about
large
it.
remain
ionic
Because
exactly
dye
of
static
molecules
thermal
at the
in
thermal
agitation,
fibre;
the
ions
cannot
instead,
they
form a
Only
inside
restless
cloud
in the vicinity
of the
fibre.
the
cloud
does
shield
the
ion
outside
the
cloud,
the
the
fibre
absorbing
equilibrium
dye
is
ion
solution;
unaffected.
The
thickness of the cloud is called the shielding distance, or
the
Debye distance
and depends
dye in the vicinity of the fibre.
84
on the
temperature
of the
There is general agreement that the Debye - Hiickel theory
gives the correct description of the
ion-ion
interactions
at the limit of extremely weak solutions
(49). Because the
shielding
root
length
density,
it
derivative
molar
is
depends
observed
functions
volume
on
square
Gibbs
a
Energy
square
dependence,
based
on
ion
as partial
dependence
on
(< 1 x 10~3M) . A cube
a disordered
lattice model
predicted to occur for concentrations of 0.1M is a substantially higher range
the
(50) that
such
root
concentration for low concentrations
root
of
in electrochemistry
of the
exhibit
the
than
that
4M,
used
is
which
in
this
work.
Freundlich
(51)
concentration
expressed
in
the
the
form
of
adsorption
an
dependence
empirical
power
on
law
isotherm
X = Kc1/n
where
X
is
the
concentration
of
quantity
the
(26)
of solute
equilibrium
adsorbed,
solution
c
and
is
K
the
is
a
constant, n is a parameter with a value greater than unity.
A value of n = 2 is consistent with our observations.
Two
groups
between
(42,52)
evanescent
have
observed
absorbance
Villaruel et al (42) used
and
a
linear
fluid
relationship
concentration.
Methylene Blue in water on lOOjim
diameter core silica fibre tapered to 3 0/im minimum diameter
on a
37mm
length.
Their
absorbance value was
linear with
concentration with n/a value of 0.015. The maximum value of
85
the cladding power ratio
(r)
at the neck of the taper
is
calculated to be approximately 0.02. Thus no adsorption is
indicated. This may be due to passivation of the surface by
the etchant used in tapering.
Rhodamine
6G
dye
Paul and Kychaoff
in nonpolar organic solvents.
(52)
used
Their data
is consistent with the total mode analysis of section 2.4
with no enhanced absorption due to dye adsorption.
4.4 Summary.
Enhanced
absorbance was
observed
in evanescent
absorption
of Methylene Blue on unclad silica multimode optical fibre.
The absorbance was found to scale as the square root of dye
concentration,
law
for
i.e.
evanescent
the dye
does
absorption
not
when
obey
the
a Beer-Lambert
solvent
used
is
water and the fibre is of silica. This non linearity can be
explained
by
ionic
shielding
known
as
the
Debye-Hiickel
effect.
The
measured
linear
dependence
of
evanescent
absorbance
with unclad sensing length is consistent with the predicted
functional forms of equations
(18) and (19).
The relationship between evanescent absorbance and V-number
showed
an
threefold
equations
enhancement
increase
factor
predicted
(18) and (19).
86
which
by
the
was
1/V
less
than
dependence
the
of
CONCLUSION.
Evanescent
optical
wave
absorption
spectroscopy
fibres has been demonstrated.
using
It
is
multimode
shown that a
length of silica fibre with an unclad central length may be
used as an ATR absorbance probe for aqueous solutions which
absorb visible radiation.
A theoretical
model
followed by
experimental verification was used to evaluate
600 /im PCS
and 200 11m PCS fibre probes.
The launching of tunnelling modes which reach the sensing
region at angles close to the critical angle significantly
enhance
the
sensitivity
evanescent
absorbances
significantly
greater,
of
using
however,
standard evanescent wave models.
dependence
of
the
evanescent
technique.
Methlene
than
Blue
values
on
are
predicted
In addition,
absorbance
Measured
by
the observed
concentration
deviates considerably from the predicted Beer-Lambert type
linear
relationship.
attributed
to
Both
surface
of
these
adsorption
effects
due
to
have
been
electrostatic
interactions between the polar silica surface and the ionic
solution.
The
observed
evanescent
absorbance
square
root
on concentration
dependence
of
is consistent with
the Debye-Huckel model for ion-ion interactions.
The
measured
linear
relationship
between
evanescent
absorbance and unclad sensing length is consistent with the
predictions of the theoretical model.
87
Because
of
the
irreversible
nature
of
the
adsorption
process,
the potential for evanescent wave spectroscopy on
fused silica fibre is severly limited for ionic solutions.
The effect may be exploited,
however,
in disposable probes
to give increased sensitivity due to the enhanced surface
concentrations. Adsorption may be minimized by treatment of
the
silica
material
film,
of
surface
such
as
thickness
with
a
thin
film
of
dichlorodimethylsilane
of
several
a
hydrophobic
(DDS).
nanometres,
Such
would
a
not
significantly attenuate the evanescent intensity available
for absorption.
88
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I.
Sensing
by
Evanescent Field Absorption: the Sensitivity of Optical
Waveguides" , SPIE. Vol. 0990, Boston (1988).
48
I. Schnitzer,
Tacke,
A. Katzir, U. Schiessl,
"Fibre-Optic-based
Evanescent
Spectroscopy using Tunable Diode
1048, Los Angeles,
49
J.D. Jackson,
New York,
50
SPIE,
"Introduction
Shaw,
to
Liquid State
Chemistry",
(1977).
"Introduction
to
P.H. Paul and G. Kychakoff,
Colloid
and
R.M.
Gagliardi and S. Karp,
Wiley, New York
(1976).
94
Surface
(1986).
"Fiber-Optic Evanescent Field
Absorption Sensor", Appl. Phys. Lett., 51(1), 12,
53
Vol.
"Classical Electrodynamics", Wiley & Sons,
Chemistry" , Butterworths, London,
52
Lasers",
Infrared
(1962).
Y. Marcus,
D.J.
Field
and M.
(1989).
Wiley & Sons, New York,
51
W. Riedel,
"Optical
(1987).
Communications",
APPENDIX A
Internal Reflection Spectroscopy
Although geometric optics provides the condition for total
internal reflection to occur,
the
phenomenon
distribution
at
or
any
it offers no explanation of
information
reflection.
To
gain
about
the
further
energy
insight
into
this phenomenon, the results of electromagnetic theory must
be
applied
partially
to
the
based
on
case.
the
The
following
treatment
discussion
outlined
by
Hecht
is
and
Zajac (26) .
Suppose that the incident monochromatic light wave is plane
polarized so that it has the form
E i = Eoi exp
(A. 1)
~ Wjt)]
The reflected and transmitted waves can be written as
For TE modes,
Er = EQt exp [i(kt .r - wtt ) ]
(A.2)
Et = EQt exp [i(kt .r - u>tt) ]
(A.3)
where the electric
to the boundary interface,
field vector
is parallel
it is shown by Hecht and Zajac
(26) that the amplitude of the reflected wave, EQ r , relative
to the incident ray, Eq^
is given by the Fresnel amplitude
reflection formulae
E
or
cose. - (n,/n.) cose,
l
v t'
t
By manipulating Snell's law
Al
(A.4)
sine^ = n^. sino^.
(A. 5)
it can be shown that
cose = [1 - (n^/nt ) 2 sin 2e ^ ] 1 / 2
(A. 6 )
Thus, replacing ©t with e^ gives
„
E
t r
, , .2
.2
4/2
cose. - —
[ 1 - (n./n. ) sin e.]
i n .
' 1 ' t'
iJ
or _ ___________ 1 __________________________
Eoi
cose. + —
[1
1
n±
(A.7)
- (n./n . ) 2 sin2 e .]1 / 2
1
For e^ > e , it is possible for the terms within the square
root to produce negative values.
Therefore,
equation (A.5) becomes
cos©t = -
i.e.
when total
[1 - (n^/nt ) 2 sin 2 e ^ ] 1 / 2
(A. 8 )
internal
reflection occurs,
equation
cose. +
[sin2ei - ( n ^ n ^ 2] 1 / 2
(A. 5)
becomes
°r EQi
cosei +
Because
the
numerator
(A.9)
[sin 0
is
the
. -
(r^/n^
complex
conjugate
denominator the moduli of both are equal,
Since
which
E .= E
01
or
implies
all
that
the
E .
i Eo r i -
i Eo i i
energy
in
=
0
the
(for
Hecht
and
e^=
the
incident
and
the
reflected
Therefore,
it cannot, on the
It is shown by
reflected waves
not have a phase difference of n and therefore
A2
is
©r ) .
carry energy across the boundary.
Zajac that
of
i.e.
wave
although the transmitted wave does exist,
average,
]
do
destructive
interference cannot occur.
In order to satisfy the boundary conditions,
a disturbance
in the
there must be
second medium and we will
therefore
examine the transmitted wave function.
The wave
function for the transmitted electric field is
Et = EQt exp i (k^.r - wt)
From
(A.3)
the propagation vectors of figure A.l, we have
V *
= ktx * + kty 5
(A'11)
But k,
= k. sin©, and k.
= k. cos©,
tx
t
t
ty
t
t
Using Snell's law (equation A.5), we have
kfcy = ± ikfc [1 - (sinsjr / n ^ ) ] 172
(A. 12)
where nfc^ = n^/n^.
But since sin©. > n . . for total internal reflection
l
ti
kty = ±i kt [ (sin2©i / n 2^
- 1] 1/2 = ± i 6
(A. 13)
Also,
kt
= kt sin©t = kt sin©^
(A. 14)
Therefore,
Et = Eot expi (ktx x + kty y ■ ut)
= E t exp^ (iöy) exp(kt sin©^ x - wt)
nti
A3
(A-15)
ce
Fig. A1 : P l a n e Waves Incident on the B o u n d a r y between Two
Homoqeneous , Isotropic. Lossless Dielectric Media
( 26)
E
t
E
(A.16)
ot
i.e. the disturbance in the less dense medium is therefore
periodic in x but exponentially decaying in z . This is the
evanescent wave.
In
the
denser
medium
owing to constructive
reflected beams
and
falls exponentially,
a
stationary
wave
pattern
interference between the
in the
less dense medium
is
set
up
incident and
the
amplitude
although the amplitudes are equal
at the
The spatial rate of
decay of the field in the second
medium
is determined by the
attenuation constant <5.
interface.
From equation
_
(13)
,
, ,
. 2
.
2 .
_ n 1/2
5 = kt [ (sin e±/ nt i ) - 1]
1/2
The penetration depth d
so we have
p
is defined as
1/S,
APPENDIX B
Total Number of Guided Modes
The V-number can be related to the number of modes M in a
multimode fibre when the total number of modes M is large.
An
approximate
relationship
derived from ray theory.
for
step-index
be
fibre if it lies within an
angle © defined by the numerical aperture
(NA)
as given by
(B.l)
/
2
2
.
1/2
NA = sin© = (n
' 1 - n 2')
For
can
A ray incident on the end of a
fibre will be accepted by the
equation
fibres
practical
numerical
apertures
(B.l)
sins
=
©.
The
solid
acceptance angle for the fibre is therefore
^
Q
For
=
tt©
electromagnetic
2
=
.2
2.
- n)
' 1
2'
(B.2)
7T (n
radiation
of
wavelength
A
emanating
from a laser or a waveguide the number of modes per unit
solid angle
is given by 2A / A2, where A
mode is entering or leaving
is the
the
core
fact
cross
that
orientations.
the
The
is the area the
(50) . The area
section na2. The
plane
wave
can
total
numberof
A in this case
factor two
have
two
modes
M
comes
from
polarization
entering
fibre is given by
2
M
l
B1
.2
2
(B.3)
the
APPENDIX C
Evanescent Wave Spectroscopy using Multimode Optical
Fibres.
The
power
loss
due
to
an
absorbing
described directly by geometric
occurs
beyond
effect,
In
the
the
ray
path
cladding
optics,
and
is,
cannot
because this
therefore,
a
be
loss
wave
dependent on the wavelength of light in the core.
limit
of
classical
geometric
optics,
X =
0,
the
fields are zero beyond the ray path.
For
the
values
of
X
greater
than
zero
for
light,
the
evanescent fields lose some of their power to the absorbing
cladding.
This in turns leads to a loss of power from the
ray path.
The
following
analysis
is
based
upon
the
expression
of
Snyder and Love (3 6 )
7 = NT
(C.l)
where 7 is the evanescent absorption coefficient,
N is the
number of reflections per unit length and T is the Fresnel
transmission
core
and
a
coefficient
lossy
at
the
interface
cladding.
The
refractive
of
a
index
lossless
of
the
latter is given by n 2 - ik, where
a = 47ik/ X
(C .2)
is the bulk absorption coefficient of the cladding material
at an analytical wavelength. The approach adopted by Snyder
and Love
weakly
(36) was modified by Ruddy (46) to cater for non
guiding
modes
which
Cl
occur
when
the
cladding
refractive
index
(in this
case
a water
based
liquid)
of
refractive index of approximately 1.335 is not close to the
core index of 1.457 for silica glass.
The number of reflections N is a function of the length L,
the thickness of the waveguide T, and angle of incidence e
(C.3)
N = L/T. cots
The above equation assumes there are no skew rays.
The Fresnel transmission coefficient is given by (26)
4 sine
T
z
(sin2e
z
(C.4)
- sin2© )
c
(sine + (sin2e - sin2e } 1 / 2 ) 2
'
z
1
z
C J
'
In the case where the refractive index of the cladding is
complex
then equation
T = 4 sine
(C.4) becomes
Re [ (n2, / n 2 ) - cos2e ] 1 / 2
L' c l /
co'
zJ
z
I
.
,
/
2
.
2
.
2
,
sinen + { (n , / n ) - cos e }
1
z
' cl
co
z
If we write
r
.
1
n .. = n t - in -,
cl
cl
cl
then
C2
1 / 2
I 2
1
and because n ^
is very small, we can ignore n ^ 2 , so that
ncl = tn; x ] 2 + 2i n;x n l
cl
(C.6 )
If z is a complex number = r e i 0 then
z
,, ,
1/2
_
/—
ie
= v r e
1 /2
= r
/2
1 /2
so that
Re z
cose/2.
Since
sin 2ec = 1- n ^
2
nco
then
n2
= 1 - sin2© = cos2 ©
c
c
2
(C.7)
nco
Using
©z as illustrated in figure 10
equation (C.7) becomes
(C. 8 }
•I (n2 ,/n2 ) - cos2©
' cl/ co'
z
Because ©
c
> ©
"1 cos © 2 - cos © 2
z
c
z
cos 2 © - cos2 © is negative and so the
c
z
Re \ (n2 ,/n 2 ) - cos2© = r 1 / 2 sine/2
' cl' CO
z
= -Jcos2©
.
where tan£ = 2
r
i
.
,
z
- cos2©
2
(nci n c l } / nco
. 2 . 2 .
2
(nol/nc o ) ■ cos ®z
Because n ^
is so small, /3 is small
therefore tan/3 = ¡3 = sin/3 implies that
C3
c
[sin tan 1 /3]
r
i
i
n cl" cl
Re -J (n2 ,/n2 ) - cos ©
' cl 7 co'
2
COS
2
0
Z
2
COS
©
2
“
COS ©
-
2
COS
Ä
©
C
C
therefore,
r
i
ncl
% 1
- n2
4 sin ©
T =
.2
sin
CO
*| c o s 2 ©
, ,
2
+ (cos©
©_
z
c
cos2 ©
-
z
c
-
z
r
i
ncl
% 1
4 sin©
r
'
L
2
cos ©
n.
I
sin© z
• /
(C.9 )
2 . 1/2 II2
cos e )
COS
2
2
.
2
+ l cos © Z - cos ©C )
Q
l/2 -i
J
4 S l n e 2 "Cl " ‘cl
2
cos ©
n
2
z
- cos ©
* 2
2
( s m © + cos © - cos2©c )
v
z
z
c
4 sin©z n c' n ^
(C.10)
n
substituting
2
f
co
2
sin e
2
.cos ©
c A
2
- cos o
n ^ = otA
47r
we get
T -
aA n ,
cl
n n_s m
CO
sin©
©_
C
A
C4
COS
2
©
Z
z
-
(C.ll)
2
COS ©
C
or using equation (C.l) j = NT = tan© 2 T
2a
where a is the core radius.
K =
ocX n ,
cl
2
2 na n
co
If we use Harrick's
d
p
v
=
sin©„ tan©„
z
z
.2
s m ©c -4cos 2 0„
„„2
- cos
s
c
z
(29) expression
n
_
I
2
2 n A cos ©
CO
we get
for the penetration depth
2
- cos ©,
*
e
^3
p
sin© tan©
a fn c] 1 — —
z
z
.
2
n
y “ "a
CO
sm ©
c
for any ©
Z
(C.12)
< ©
C •
Because the penetration depth rises rapidly near the critical
angle, y will increase dramatically, accordingly.
In the small angle approximation
sin©
sin©
z
— 0
c
= ©
c
so that equation (C.12)
z
reduces to
©
y = a ncl
----a n
CO
n
cl
= a
a n
co
X
© —
c n
---- ---1-------------J 2
2
^ ©
0
c
z
2
CO
(®z/ec )
A_
2n
0C
C5
a)
1
2
-
©
,2
/©
Z/ c
(C.13)
If n , = n
, then
cl
co'
(e /©
' z' c'
I---------^ l - e2/e
z7 c
a
ak 0
K = n
°
00
where k=27T/X.
"0
a
0
V
which
is
the
final
2
z
1
(C.14)
«11 -,1 — ©2 /, 2©
z'
c
ec
expression
derived
by
Snyder
and
Love
(equation 6-21, page 127)
a
, 2 , 2.
V
1
- < V ec>
This result is accurate for bound rays, with the exception of
those few rays whose directions are close to ©
In the
case
solution
valid;
all
of
the
a silica
weakly
core
guiding
in contact
with
approximation
is
= © .
an aqueous
no
longer
i.e. nc -L< nc Q . Removing this condition and allowing
values
of
© <
z
© ,
c
Ruddy
(46)
shows
that
the
transmission coefficient becomes
aX
T =
cos©
n ,
___________ c l __________
, 2
7T (n
2
(C.15)
.
- n ,)
v co
cl'
C6
sin2© - (n ,/n , ) 2
' cl
CO
and the attenuation coefficient r(©) of that ray
?(©) = aA ncl f(e)
2na (n2
- n 2, )
'
w h ere
Using
-, .
f(o)
v '
2
=
equations
relating
the
CO
(C.16)
c l 7
|---------------------------------
COS 0
—r
.
sm e n
2
s i n
(C.15)
evanescent
©
-
and
.
2 . 2 .
(n , / n )
' cl' co
(C.16),
absorption
the
final
coefficient
expression
r( 0 )
and
bulk absorption coefficient a is
y
~a
X n ,
cl
2 îra sin©
(n
c o s 2q
co - ncl> i s i n2® - (ncl/n co)
C7
(C.17)
APPENDIX D
Specification of the Monochromator.
f number............................ 3.9
Focal length.......................74mm
Grating.......... 18 OOg/mm, holographic
Resolution (600/um slits)........ 4.3nm
Wavelength Accuracy............. ± 0.2%
Spectral Range.............300 - 800nm
D1
APPENDIX E
Specification of PCS Optical Fibre.
PCS fibre consists of:
silica core
silicone resin optical cladding
ETFE protective coating
PCS 2 0 0
Characteristics
600
± 24
380 ± 30
750
± 60
600 ± 48
1060 ± 85
Core diameter
jum
200
Cladding diameter
Aim
Coating diameter
¿im
± 8
0 .4
Numerical aperture
El
PCS 600
0 .4
APPENDIX F
Electronic Circuit Diagrams.
This
appendix contains
supply,
analog/digital
converter.
Their
the
circuit
converter
operation
is
3.5.1.
FI
as
diagrams
and
of
digital
described
the power
to
in
analog
section
Fig. F1 '< Power Supply Unit
7 3 9
C onn.4
Analogue<
Input
Conn.3
Fig. F2 : 12 Bit A /D Convertor
Analogue
Out
M1
A/D
Board
Connector
APPENDIX G
Software Programs.
The
following pages
contain
this project in BASIC.
all
the
software
written
for
The structure of the programs are
explained in section 3.5.2.
Gl
I\jJ
20
30
40
50
60
f yj
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
«X- sX» vV il> \L>
vi> vL> <J/ «Ir tl> >1/
P\p.[*] <
p ^ ^ ^ >X/X*- O*' ^^«X^- ^^vV^O»^ \1>
'T'* ^'Y' si>
^ <TKvt>'Tv>X*- a>/p»ir ^
íj^*^v^^ /y\
REM
**
**
REM
** PROGRAM TO CONTROL THE **
REM **
MINICHROM
**
REM **
MODEL 02
**
REM
**
**
n P.P|
^ <7** ^ ^ ^ ^ * <T>'T'^ M
''T''T'‘T''T'* * * 'T' 'T' ■
’T'-^ * iT‘
M0DE4
DIM Y( 1 0 0 0 )
VDU15
YMAX=0: F=0
PRINT : PRINT
PROCMENU
END
DEF PROCMENU
CLS
PRINT"SELECT FUNCTION:-"
PRINT:PRINT
PRINT
TAB(1 2 ) "SET PARAMETERS
1
PRINT
TAB( 1 2 ) "SET WAVELENGTH
2
PRINT
TAB( 1 2 ) "SINGLE SCAN
3
PRINT
TAB( 1 2 ) "MANUAL SCAN
4
PRINT TAB( 1 2 ) "SAVE DATA ON FILE 5
INPUT "SELECT OPTION";d
IF d = l GOTO 410
IF d=2 GOTO 810
I F d = 3 GOTO 1190
IF d=4 GOTO 1430
I F d=5 GOTO 2020
IF d o l GOTO 130
REM * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
REM *
*
REM
* THE FOLLOWING PROGRAM
*
REM
* INTERFACES WITH THE CB1 *
REM
* CONTROLLER AND CHANGESANY*
REM
* OF THE PARAMETERS
*
REM*
*
f ] TI W
tX
*^ v
X
^^ ^ ^ vi*^ sL
»^ ^ ^L
»
O Q fjk
Q YJ
n T7 L i
iX’ vX/- <1/ 'X/’ \L \is
iX tl* >X »I/ >x vl' ■«X'>X »X vl< >X t l ' -X >X vX »X »X >X sL' i ' 'T' 'T' 'T' /T' /T'*' t ' >T' 'T' 'T' 'T' /T' 'T' •T' 'T' 'T' 'T' -T' ^ ^ 'T' ■
’T> 'T* /T' •T' 'T' 'r* / n sr-
•4 ry¡
«7fjà
r i T 1u
^ ^ «
X
*^ (X
*«X^ ^ ^ ^ ^ \X
*^ ^ ^ \Lr
390 VDU3
40 0 M0DE3
410 PR IN T: PRINT
420PRINT "GO TO ZERO ORDER: TYPE Gl"
430 PRINT;PRINT
44 0 PRINT "DO YOU WANT TO CHANGE:"
450 PR IN T: PRINT
4 60 PRINT TAB(2 2 ) "DIVIDING FACTOR D"
4 7 0 PRINT:PRINT
4 80 PRINT TAB(2 2 ) "IN IT IA L VELOCITY I "
49 0 *F X 7, 7
500 REM RECEIVE BAUD RATE
510 *F X 8, 7 ’
520 REM TRANSMIT BAUD RATE
530 * F X 2 2 9 ,1
540
550
560:
570
580
590
600
610
620
630
640
650
660
670
680
690
700
710
720
730
740
750
760
770
780
790
800
810
820
830
840
850
860
870
880
890
900
910
920
930
940
950
960
970
980
990
1000
1010
1020
1030
1040
1050
1060
1070
0SBYTE=&FFF4
REM OSBYTE CALL
L%=0
FOR 11=1 TO 1000
A%=138:X%=2:
REM RS423 O/P BUFFER
*FX 2,2
IF ADVAL( - 1 ) >0 Y%=GET: CALL OSBYTE
IF ADVAL( - 3 ) > 0 Y%=GET: CALL OSBYTE
* F X 2,1
REM GET CHAR FROM KBRD, ENABLE RX
IF ADVAL(- 2 ) > 0 CHAR%=GET:
VDU CHAR%:L%=L%+1:
IF CHAR% =13 VDU10:L%=0
REM CHECKS NO. OF CHARS IN KBRD
REM CHECKS NO. OF CHARS IN RS423
I F L%= 60 VDU10 : VDU13 : L%=0
REM MOVE CURSOR TO NEW LINE
NEXT
:
* F X 2 ,2
* F X 2 2 9 ,0
REM ESCAPE ENABLE
* F X 3 ,4
Z=0
PROCMENU
CLS
R E M ** ** * ** * * * * * * * * * * * * * * * * * *
REM*
*
REM* THE FOLLOWING SETS THE*
REM* MONOCHROMATOR TO A
*
REM* SPECIFIED WAVELENGTH
*
REM*
*
R E M * * * * * * * * * ** ** ** ** * ** ** ** *
PRINT : PRINT
INPUT " W a v e l e n g t h p o s i t i o n (nm )",W
REM W<= 6400 SETS THE MAXIMUM
REM SCAN
TO 800nm
W=W*8: I F W> = 6400 THEN 900
I F W < F THEN 1020
A = Z /8 : PRINT A
B%=(W-F)
F=W
*F X 3 , 3
VDU2
PRINT
;STRn(B%)
GOTO 1070
REM
PRINTF:B%=ABS(W-F)
* F X 3, 3 '
VDU2
P R IN T "-";S T R n (B % )
* F X 3 ,4
G3
1080
1090
VDU3
F=W
1100 GOTD120
1110
1120 REM*
*
1 1 3 0 REM*THE NEXT ROUTINE MAKES*
1 1 4 0 REM*THE MONOCHROMATOR SCAN*
1 1 5 0 REM*BETWEEN TWO S P E C I F I E D *
*
1 1 6 0 REM*WAVELENGTHS
*
1 1 7 0 REM*
1180
1190 INPUT"Starting w a v e le n g th (nm)",S
1200 I NP U T "F i n i s h i n g w a v e l e n g t h ( n m ) " , F
1210 F=F * 8
1220 INPUT" I n c r e m e n t a l r a t e " I n c
1 2 3 0 P 7 . = F - S : I F P 7 . > = 6 4 0 0 THEN GOTO 1 1 9 0
1 2 4 0 I F P7. <0 THEN GOTO 1 1 9 0
1 2 5 0 INPUT" E n t r a n c e s l i t ( u r n ) " S I
1 2 6 0 INPUT" EXI T s l i t ( u m ) " S 2
1 2 7 0 INPUT" PMT s l i t ( u m ) " S 3
12B0 I NP U T "S e n d t o ADC o r C h a r t A / C " , a »
I F a S = " C " THEN PROCCHART
1290
CLS
1300
1 3 1 0 X=0
1 3 2 0 P l = ( F —S ) / ( I n c * 8 )
1 3 3 0 FOR i = l TO P I
1340 *FX3,3
1 3 5 0 PRI NT " + " ; S T R B ( P 7 . / P 1 )
1360 *FX 3,4
PROCDATA
1370
FOR
L l = l TO 1 0 0 : NEXT
1380
1390 *FX 21,1
1 4 0 0 NEXT i
1410 *FX3,4
1 4 2 0 PROCSAVE: PROCDRAW: PROCMENU
1 4 3 0 REM MANUAL SCAN
1440
*
1 4 5 0 REM*
REM*THE
NEXT
SEGMENT
ALLOWS*
1460
1 4 7 0 REM*MANUAL SCAN
*
1 4 8 0 REM*
*
i~~m
\ L, I
1 4 9 0 rl*>
1 5 0 0 P R I N T " T d s c a n f o r w a r d p r e s s "CHRS( 9 3 )
1 5 1 0 PRI NT"To s c a n b a c k w a r d p r e s s "CHRQ( 9 1 )
1520 PRINT:"Press Q t o f i n i s h "
1530 *FX4,1
1 5 4 0 Q8=GETS
1 5 5 0 I F Qa=CHRH( &8 9 ) THEN PROCFORWARD
1 5 6 0 I F QB=CHR3( & B 8 ) THEN PROCBACK
1 5 7 0 I F QB="Q" THEN PROCFI NI SH
1 5 8 0 DEF PROCFORWARD
1 5 9 0 V7.= 1 0
1600 *FX3,1
1 6 1 0 PRI NT " + " ; S T R H( V 7 . )
GC
1620 *FX 3,4
1 6 3 0 GOTO 1 5 4 0
1 6 4 0 ENDPROC
1 6 5 0 DEF PROCBACK
1 6 6 0 P*/.=10
1670 *FX3,1
1 6 8 0 PRI NT
; STRH( P7. )
1690 #FX3,4
1 7 0 0 GOTO 1 5 4 0
1 7 1 0 ENDPROC
1 7 2 0 DEF PROOF I NI S H
1730 *FX4,0
1740 *FX3,4
1750 *FX21,0
1 7 6 0 GOTO 1 2 0
1 7 7 0 ENDPROC
1 7 8 0 DEF PROCCHART
1790 *FX 3,1
1 8 0 0 PRI NT " + " ; STRH( P7. )
1 8 1 0 )KFX3,4
1 8 2 0 PROCMENU
1 8 3 0 ENDPROC
1 8 4 0 VDU3
1 8 5 0 C L O S E # 0 : A=&FCC0
Data p o i n t s s t o r e d
###
1 8 6 0 REM
1 8 7 0 REM
in array Y(D).
JK>K#
jji )(i )|i i(!
I 8 6 0 IÌ ^ [^] j|( # )ji )j( )j( )ji )|( )jç )|( j|î îjç )j( )ji )j( jji l)( )ji )|( )|( jji )j( îjc lj(
1 8 9 0 DEF PROCDATA
1 9 0 0 a= 0
1910 *FX3,4
1 9 2 0 FOR 1 = 1 TO 6 0
1 9 3 0 A=&FCC0
1940 A ?0=0:Y=( ( A ? 0 ) # 1 6 ) + ( (A ?1)DIV16)
1 9 5 0 a=a+Y
1 9 6 0 NEXT
1970 Y( i ) = ( a / 6 0 )
1 9 8 0 MOVE X , Y ( i ) / 2
1 9 9 0 DRAW X , Y ( i ) / 2 : X = X + 1 2 0 0 / P 1
2000 ENDPROC
M
r I I
2010 I□\ C
^
q» / p ^
ip #p rp ip f p
ip ^
fp ip *p ' l ' / p *p rp rp /p
20 20 DEF PROCSAVE
2030 S=B/B:F = F /8 :
2 0 4 0 PRINTrPRINT
2 0 5 0 PRI NT TAB( 1 5 ) "I NSERT DATA DISK"
2 0 6 0 I NPUT"Name o f f i l e " B £ : Y=OPENOUT( BE
2 0 7 0 FOR D=1 TO P I
2 0 8 0 PRI N T # Y , Y ( D ) : N E X T : CLOSE#0
2 0 9 0 FOR i = l TO P I
2100 I F Y ( i ) > YMAX THEN YMAX=Y( i )
2110 NEXT
2120 DEF PROCDRAW
2 1 3 0 CLS
2 1 4 0 X= 5 0
2 1 5 0 FOR 1 1 = 1 TO PI
G5
2 1 6 0 MOVE X , Y( I I ) * 9 0 0 / Y M A X + 5 0
2 1 7 0 DRAW X , Y ( 1 1 ) # 9 0 0 / YMAX+50
21B0 X=X+1100/P1
2 1 9 0 NEXT
2200 VDU5
2210 MOVE 5 0 , 5 0 : DRAW 1 2 0 0 , 5 0
2 2 2 0 DRAW 1 2 0 0 , 1 0 0 0 : DRAW 5 0 , 1 0 0 0 :
2 2 3 0 DRAW 5 0 , 5 0
2 2 4 0 FOR 1 2 = 1 TO 4
2 2 5 0 MOVE 5 0 , 2 3 7 . 5 * 1 2 : PR I N T "
2 2 6 0 NEXT
2 2 7 0 MOVE 2 0 0 , 9 5 0 :
2 2 B 0 P R I N T " I n t e n s i t y v s W a v e l e n g t h ( nm) "
2 2 9 0 REM F = 1 6 0 0 : S = B 0 0
2 3 0 0 B = ( F —B ) / ( 8 0 0 )
2 3 1 0 FOR 1 2 = 0 TO B
2 3 2 0 MOVE 3 7 + 1 1 5 0 / ( ( B ) ) * 12 , 6 0 : P R I N T "6"
2 3 3 0 NEXT
2 3 4 0 £■/.=& 10
2 3 5 0 FOR 1 2 = 0 TO 2
2 3 6 0 MOVE - 4 2 0 + ( 1 1 5 0 / ( ( B ) ) ) # 1 2 * ( B / 2 ) , 3 0
2 3 7 0 PRINT S + I 2 * ( F - S ) / ( B ) # ( B / 2 )
2 3 8 0 NEXT
2 3 9 0 VDU4
2 4 0 0 PRI NT T A B ( 3 , 5 ) "REPEAT SCAN Y/ N"
2 4 1 0 INPUT G S : I F G«="Y" GOTO 2 4 3 0
2 4 2 0 GOTO 1 2 0
2 4 3 0 B'/.= ( F - S ) * 8
2440 *FX3,3
2 4 5 0 VDU2
2 4 6 0 P R I N T " - " ; STRR( B7. )
2470 #FX3,4
2 4 8 0 VDU3
2 4 9 0 PRI NT- ' PRESS ANY KEY TO REPEAT SCAN"
2 5 0 0 K=GET
2510 F=F*B:S=S*8
2 5 2 0 GOTO 1 3 0 0
2 5 3 0 END
G6
10 REM
20 REM **
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
1B0
190
200
***
**
**
T HI S PROGRAM CORRECTS
SPECTRA BY D I V I D I N G
THE **
##
RECORDED SPECTRA BY
**
THE SYSTEM RESPONSE.
A HARDCOPY I S OBTAINED
**
**
ON A RI KADI NKI PLOTTER.
*#
)jc)|i )|i )j())( )jf )|( )jc))i l)( )j( )|( ))()ji )|( )|c)(C)j^]|( )(( )ji )|i )|( )ji >K 3(i
REM * *
REM **
REM # *
REM * *
REM # *
REM **
REM **
REM Jji
VDU14
CLOSE#0
£'/.=131B50
#.
PRI N T : P R I NT
PROCSUBTRACT
PROCSAVE
CLOSE#0
END
DEF PROCSUBTRACT
2 10
22 0 INPUT"NAME OF F I L E " , BH
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
410
420
430
440
450
460
470
480
490
500
510
520
530
L=OPENIN(BS)
K=0PENIN"SYSF9”
Pl=300
XMAX=0
DIM Y 1 ( P I ) , X I ( P I ) , X ( P I )
CLS
FOR 1 = 1 TO P I
I N P U T # K , Y1 ( I ) : I N P U T # L , X I ( I )
REM MOVE X , Y 1 ( I ) : DRAW X , Y 1 ( I )
REM MOVE X , X1 ( I ) : DRAW X , X 1 ( I )
REM X = X + 1 2 0 0 / P 1
NEXT
X1 = 0
CLS
V D U 29,0;50;
FOR 1 = 1 0 TO P I
X( I ) =X1 ( I ) / Y 1 ( I )
NEXT
FOR I = 1 0 TO P I
I F X( I ) > XMAX THEN XMAX = X( I )
NEXT
FDR 1 = 1 0 TO
PI
X ( I ) = X ( I ) /XMAX
NEXT
FOR 1 = 1 0 ' TO P I
MOVE X1 , X ( I ) Xt 5 0 0 : DRAW X 1 , X ( I ) * 5 0 0
X1=X1 + 1 2 0 0 / P I
Q7
540
550
560
570
580
590
600
610
620
630
640
650
660
670
680
690
700
710
720
730
740
750
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900
910
920
930
940
950
960
970
980
990
1000
1010
1020
1030
1040
1050
1060
1070
NEXT
ENDPROC
DEF PROCSAVE
PRINT:PRINT
PRINT : PRINT
INPUT-NAME OF F I L E " B n : Y=OPENOUT(Bn)
FOR D=10 TO P I
PRINT # Y , X (D ) : NEXT : CLOSE#0:
PRINT"PRESS P FOR A PLOT“
PRINT'TRESS C TO DIVIDE ANOTHER SPECTRUM"
Bn=GETn : I F Bn="P" GOTO 660
IF B a= "C “ THEN GOTO 200 ELSE 2330
REM RIKADENKI PLOTTER PROGRAM
*DRIVE0
VDU15
*.
PRINTCHRn(1 3 0 ) "NAME OF F I L E " : INPUTBn
PRINTCHRn(130)"ADDITIONAL IN F O " : INPUT An
L=OPENIN(Bn)
IN P U T "S tart " . S t a r t
INPUT"End " ,E n d
V = S ta rt
U=End
N=End - S t a r t
DX=N-1
X=0 : S t a r t = S t a r t - ( V - l ) : End=End-V
VDU2 9 , 0 ; 5 0 0 ;
FOR I = S t a r t TO End
INPUT#L, A
X (I)= A
X (I)= -l* L O G (X (I> )
MOVE X ,X (I)*3:D R A W X , X ( I ) * 3
X = X + 1 2 0 0 /(E n d -S ta rt+ l)
NEXT I
INPUT "TYPE IN TITLE";NAMEn
PRINT : PRINT
INPUT”Do you w a n t a s p e c i f i c w a v e l e n g t h r a n g e ”
IF GETn="Y" THEN PROCSPEC
REM PLOTTER PROGRAM BEGINS HERE
SX = 10
PRINT:PRINT
PRINT "PRESS R FOR RIKI COPY"
PRINT"PRESS L FOR LINE PROFILE ONLY"
Bn= GETn : IF Bn = "R" GOTO 990
I F Bn=,,L" THEN GOTO 1040 ELSE GOTO 1090
PROCWINDOW
PROCGRAD
PROCTITLE
PRINT "PRESS J FOR LINE THRU POINTS"
Bn = GETn : I F Bn = " J " THEN GOTO 1040 ELSE GOTO 1050
PROCLINE
PRINT "PRESS B FOR BOX"
Bn=GETn:
IF Bn="B" THEN GOTO 1080 ELSE GOTO 1090
GS
1080
1090
1100
1110
1120
1130
1140
1150
1160
1170
1180
1190
1200
1210
1220
1230
1240
1250
1260
1270
1280
1290
1300
1310
1320
1330
1340
1350
1360
1370
1380
1390
1400
1410
1420
1430
1440
1450
1460
1470
1480
1490
1500
1510
1520
1530
1540
1550
1560
1570
1580
1590
PROCBOX
END
REM PROCEDURES BEGIN HERE
DEF PROCWINDOW
VDU2
PRINT "S 4 "
PRINT 11M400 , 2 0 0 "
PRINT " 0 2 3 0 0 , 2 0 0 "
PRINT "D 2 3 0 0 , 1 6 0 0 "
PRI NT " D 4 0 0 , 1 6 0 0 "
PRINT "D 4 0 0 , 2 0 0 "
FOR I = 1 TO 4
L = ( 2 0 0 + ( 3 5 0 * 1 ) ) —2 0
REM 2 0 TO BRING TO CENTRE OF GRAD
K =0.25*1
PRI NT
" M 1 2 0 , " L ""
PRINT 11Q 0 P " K" "
NEXT I
A=V
B=((U-V)/4)+V
C=((U-V)/2)+V
D=((U-V)*3/4)+V
R=U
PRI NT " M 2 0 0 , 1 3 0 "
PRINT " P " A m"
PRI NT " M 6 7 5 , 1 3 0 "
PRI NT " P " B " "
PRI NT " M 1 1 5 0 , 1 3 0 "
PRI NT "P'-C""
PRINT " M 1 6 2 5 , 1 3 0 "
PRINT "P "D ""
PRINT "M 2 1 0 0 , 1 3 0 "
PRINT "P "R ""
PRI NT "H"
VDU3
ENDPROC
DC
r\
1 i(VI| ir'r'p'P'i'TTT^'r'I'T*^*'n'p“ T'r
DEF PROCPOINT
VDU2
FOR I = 1 TO N
L = I N T ( 1 9 0 0 * ( 1 - 1 ) / D X + 4 0 0 . 5)
K = I N T ( 1 4 0 0 * ( Y ( i ) ) + 2 0 0 . 5)
PRINT " M" L" , " K " "
PRINT "N3"
NEXT I
VDU3
ENDPROC
1□^CM
I|^^TT*T*n''nTT*Tn''n*'n*TT'l'
DEF PROCTITLE
VDU2
PRINT " M 1 0 0 0 , 5 S 4 , 5"
PRI NT "Q0PW A V E L E N G T H
PRINT"Ml5 5 7 , 4 5 S 1 ,2 "
P R I N T "Q 0 P 0 "
09
( n m) "
1620
1630
1640
1650
1660
1670
16B0
1690
1700
1710
1720
1730
1740
1750
1760
1770
1780
1790
1B00
PRINT "M 1 8 B 8 , 1 7 5 S 5 "
PRINT "M l 6 0 0 , 1 1 0 0 S 4 , 5"
PRINT "P"+NAME8
PR IN T"M 1600,1000S4,5"
PRINT "Ml 6 0 0 , 9 0 0 S 4 , 5 "
PRI NT "P"+AS
PRI NT"M 1 8 0 , 6 5 0 S 4 , 5 "
PRI NT"D1PABSDRBANCE ( A r b )"
PRINT "S3"
PRINT "H"
VDU3
ENDPROC
REM * * * * * * * >|c* * * * * * * * * *
DEF PROCLINE
VDU2
PRI NT "M 4 0 0 , 2 0 0 "
FDR I = 1 TO N
L = I N T ( 1 9 0 0 * ( I - 1 ) / DX + 4 0 0 . 5 )
K = I N T ( 1 4 0 0 * ( X ( I ) ) + 2 0 0 . 5)
PRI NT " D" L " , " K""
NEXT I
PRI NT "H"
VDU3
ENDPROC
REM * * * * * * * * * * * * * * * * * *
DEF PROCBOX
VDU2
PRI NT "M0 , 0 "
PRI NT "D 2 5 0 0 , 0 "
PRI NT " D 2 5 0 0 , 1 8 0 0 "
PRI NT " D 0 , 1 B 0 0 "
PRINT " D 0 , 0 "
PRI NT "H"
VDU3
ENDPROC
REM*******************
1810
1820
1830
1840
1B50
1860
1870
1 BB 0
1B90
1900
1910
1920
1930
1940
1950
1960
1970
1 9 8 0 nC.I l'pT'T^^^'P'r'i’'r,r'P'r'rT''PiP'r,p
1 9 9 0 PROCSPEC
2000 PRI NT : P RI NT
2010 CLS
2 0 2 0 INPUT " W a v e l e n g t h r a n g e ", S t a r t , End
2030 X=0: S t a r t = S t a r t - 5 4 0 0 : End=End-5400
2 0 4 0 FOR i = S t a r t TO End
2 0 5 0 MOVE X , Y ( i ) / 2
2 0 6 0 DRAW X , Y ( i ) / 2
2070 X =X +1200/(E nd-Start)
2 0 8 0 NEXT
2 0 9 0 ENDPROC
2100 R E M * * * * * * * * * * * * * * * * * *
2110 DEF PR0C6RAD
2120 VDU2
2 1 3 0 P R I N T "M 4 0 0 , 2 0 0 "
2 1 4 0 PR IN T "D 400,190"
2 1 5 0 PRINT"M875,200"
2 1 6 0 PR IN T "D 875,190"
2 1 7 0 PRI N T " M 1 3 5 0 , 2 0 0 "
510
2180
2190
2200
2210
2220
2230
2240
2250
2260
2270
2280
2290
2300
2310
2320
2330
P R IN T " D 1 3 5 0 ,190"
PRINT"Ml8 2 5 , 2 0 0 "
PRINT"D1B25,190"
P R I N T "M 2 3 0 0 , 2 0 0 "
P R IN T "D 2300,190"
PRINT"M400,5 5 0 "
P R IN T " D 3 9 0 ,550"
PRINT"M400,9 0 0 "
P R I N T "D 3 9 0 , 9 0 0 "
PRINT"M400,1250"
PRINT"D390,1250"
PRINT"M400, 1 6 0 0 "
PRINT"D390,1600"
PRINT"H"
VDU3
ENDPROC
G11
10 REPI f t* * * * * * * * * * * * * * * * * * * * * * * * * * * *
**
20 REM **
SMOOTH AND **
3 0 REM * * PROGRAMTO
**
4 0 REM * * DI SPLAY STORED SPECTRA
5 0 REM **
**
I ) r—1^4
^ ^ ^ ^
^
^
^ ^
^
lb ^
iL ^
^ >L ^ ^ ^ ^ ^
6 0 I Ll~ I |
7 0 CLS
B0 *DRI VE2
90 * .
: " ; F I LEB
100 P R I N T : : INPUT"ENTER FILENAME
110 PRI NT: I NPUT"NEW FI LENAME: " ; JB
120 DIM A ( 2 0 0 2 )
1 3 0 Y= O P E NI N( F I L E G )
1 4 0 FOR 1=1 TO 4 0 0
1 5 0 INPUT # Y , A ( I )
1 6 0 NEXT I
1 7 0 VDU7
1 B 0 M0DE4
1 9 0 PROCDRAW
2 00 PROCPLOT
210 PROCSMOOTH
2 20 CLS
2 3 0 PROCDRAW
2 4 0 PROCPLOT
2 5 0 CLOSE#0
2 6 0 PROCDRAW
2 7 0 PROCINTERVAL
2B0 PROCENPLOT
2 9 0 * DRI VE2
3 0 0 END
3 1 0 DEF PROCENPLOT
3 2 0 PLOT 6 9 , ( ( I * . 6 ) + 2 2 ) , 1 0 0 + ( ( A ( I ) * . 5 ) * 0 . B )
3 3 0 ENDPROC
3 4 0 DEF PROCDRAW
3 5 0 MOVE 2 5 , 1 0 0 : DRAW 1 2 2 5 , 1 0 0 :
3 6 0 DRAW 1 2 2 5 , 9 0 0 : DRAW 2 5 , 9 0 0 : DRAW 2 5 , 1 0 0
3 7 0 FOR 1=1 TO 5
3 8 0 PLOT 6 9 , ( I > K 2 0 0 ) + 2 5 , 1 0 0
3 9 0 DRAW ( I * 2 0 0 ) + 2 5 , 8 0
4 0 0 NEXT I
4 1 0 ENDPROC
4 2 0 DEF PROCINTERVAL
4 3 0 P R I N T : P R I N T " D O YOU WANT TO EXAMINE ANY"
PARTICULAR REGION ( Y / N ) " ; A B
4 4 0 INPUT"
4 5 0 I F A B O " Y11 ENDPROC
4 6 0 P R I N T: I NP U T" E NTE R REGION START WAVELENGTH"; X
4 7 0 P RI NT: I NP UT" E NTE R REGION F I N I S H WAVELENGTH"; Y
4B0 j =X: K=Y
4 9 0 N = I N T ( Y—X )
5 0 0 S = 1 2 0 0 / N : P=1
5 1 0 CLS:PROCDRAW
FOR I = J TO K
PLOT 6 9 , 2 5 + ( P * S ) , 1 0 0 + ( A ( I ) * 0 . 5 )
G12
530
540
550
560
570
580
590
600
610
620
630
640
650
660
670
PLOT 6 9 , 2 5 + ( P # S ) , 1 0 0 + ( A ( I ) # 0 . 5 )
P=P+1
NEXT I
ENDPRDC
DEF PROCSMOOTH
P R I N T : " 3 P T . RUNNING AVERAGE UNDER WAY"
* DRI VE2
Y=OPENQUT JB
FÜR 1 = 1 TO 4 0 0
Y l = ( ( A ( 1 - 1 ) + ( 2 # A( I ) ) + A ( 1 + 1 ) ) / 4 )
PRINT#Y,Y1
NEXT I
CLOBE#0
Y=OPENIN JB
FOR 1 = 1 TO 4 0 0
G13
n
r
V ul
ib ib t b \ b kb
ib ib ^
^
ib ^
ib i b ib
t b t b ib ^
^
ib
ib ib %b ^
t b ib
I(t, I I ^ ^ ^ ^
/p^
^^ ^
^^
^ ^ * * T* * *
20 REM ft*
3 0 REM * * T HI S PROGRAM CALCULATES ftft
4 0 REM ft* CONCENTRATION OF
ft*
5 0 REM ft* ABSORBED LI QUI D
ftft
ft*
6 0 REM ftft
Ivi <bit tbils
7 0 n r—
60 Pl=790
9 0 DIM V I ( P I ) , X 1 ( P I )
100 INPUT"NAME OF F I L E " , BH
110 INPUT"ABSORPTI ON CONSTANT " , e
120 INPUT"CELL LENGTH", b
1 3 0 L=OPENIN( BE)
140 P l=400
1 5 0 FOR 1 = 1 TO P I
1 6 0 I N P U T # L , Y1 ( I )
1 7 0 NEXT
1 8 0 B=0
1 9 0 FOR 1 = 1 TO P I
200 B= B + Y1 ( I )
2 1 0 NEXT I
220 A = 4 0 0 - B
230 C = A / ( e f t b )
2 4 0 PRI NT "CONCENTRATION C= " , c
2 5 0 END
014
i> ‘ I t
/p »p n* <p ip
10 nriyi
20 REM * *
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
2 20
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
410
420
430
440
450
460
470
480
490
500
510
520
530
REM * *
REM * *
Pi f—
1^
I\P I |
^4 ^ ^
^ T ’P ' p ' P ^ n * T ' P ' p * T ^ P ' r T ' P T * ' P ' P n ' ' r ' l ' ' r
RIKADENKI
**
PLOTTER PROGRAM#*
**
tb tlf >b lb *b tb lb tb ib ib ib ^ ^ tb ^ kb «b ^ ib ^ kb ib ^ %
b *b ib ^ ^ ^ ^
^ ^ ^
^ * * /p ^
^ ^
^ * 'p ^ * ^P * ® * * * * * »P
REM RIKADENKI PLOTTER PROGRAM
CLOSE#0
DIM Y ( 2 0 0 5 )
# DRI VE 0
M0 DE7 : VDU1 5
i=0
absmax=0
#.
PRI NTCHRB( 1 3 0 ) "NAME OF F I L E " : INPUTBB
L = O P E N I N ( BQ)
INPUT"Start", S t a r t
I N P U T "End " , E n d
V=Start
U=End
N=End - S t a r t
DX=N—1
X=0 : S t a r t = S t a r t - ( V - l ) : E n d = E n d - V
M0DE4
V D U 2 9 ,0 ;500;
FOR I = S t a r t TO End
INPUT#L, A
Y ( I ) =A
Y ( I ) = —l # L O G ( Y ( I ) )
MOVE X , Y ( I ) * 3 : DRAW X , Y ( I ) * 3
X =X +1200/(End-Start+1)
NEXT I
I F i = 0 THEN 3 3 0 ELSE 5 2 0
FOR 1= S t a r t TO End
I F Y ( I ) > a b s m a x THEN a b s m a x = Y ( I )
i —1
NEXT I
INPUT "TYPE IN T I T L E " ; NAMES
P R I N T : PR INT
I NPUT"Do y o u w a n t a s p e c i f i c w a v e l e n g t h
I F GETK="Y" THEN PROCSPEC
REM PLOTTER PROGRAM BEGI NS HERE
£ -/.= 10
P R I N T : PRINT
PR I N T " P R E S S R FOR RI KI COPY"
P R I N T "PRESS L FOR LI NE PROFI LE ONLY"
BB= GETS : I F B8 = "R" GOTO 4 9 0
I F B £ = "L " THEN GOTO 5 5 0 ELSE GOTO 6 0 0
£ ‘/.= 1 3 1 8 5 0
PROCWINDOW
PROCGRAD
PROCTITLE
PRI NT "PRESS J FOR LI NE THRU POI NTS"
BB = GETB
G15
range"
540
550
560
570
580
590
600
610
620
630
640
650
660
670
680
690
700
710
720
730
740
750
760
770
780
790
800
810
820
830
840
850
860
870
880
890
900
910
920
930
940
950
960
970
980
990
1000
1010
1020
1030
1040
1050
1060
1070
I F Bn = " J " THEN GOTO 550 ELSE GOTO 560
PROCLINE
PRINT "PRESS B FOR BOX"
Bn=GETn :
IF Bn="B" THEN GOTO 590 ELSE GOTO 600
PROCBOX
GOTO 130
REM PROCEDURES BEGIN HERE
DEF PROCWINDOW
REM
VDU2
PRINT " S4 "
PRINT " M 4 0 0 ,2 0 0 PRINT " 0 2 3 0 0 ,2 0 0 "
PRINT " 0 2 3 0 0 ,1 6 0 0 "
PRINT " D 4 0 0 , 1 6 0 0 "
PRINT " D 4 0 0 ,2 0 0 "
FOR I = 1 TO 4
L = IN T ((2 0 0 + (3 5 0 * I))-2 0 )
REM 20 TO BRING TO CENTRE OF GRAD
K = 0.2 5 * I*absm ax
PRINT "M 120, " L " "
Ë%=131850
PRINT "Q0P"K,‘ "
É%=&10
NEXT I
A=V
B = ( ( U - V ) /4 ) + V
C = ( ( U - V ) /2 ) + V
D = ( ( U - V ) * 3 /4 ) + V
R=U
PRINT M 5 0 ,130"
PRINT P" A" "
PRINT M 5 2 5 ,130"
PRINT P"B" "
PRINT “M 1000, 130"
PRINT P -C " "
PRINT "M 1475. 130"
PRINT " P " D " "
PRINT " M 1 9 5 0 ,130"
PRINT " P " R " "
PRINT "H"
VDU3
ENDPROC
REM
DEF PROCPOINT
VDU2
FOR I = 1 TO N
L = I N T ( 1 9 0 0 * ( I - 1 ) /D X + 4 0 0 . 5 )
K = INT(1400*( Y ( i ) )/a b sm a x + 2 0 0 .5 )
PRINT ,,M,,L" , "K" "
PRINT ' N3‘
NEXT I
VDU3
G16
1080
1090
ENDPROC
«I* tL kh >b X «Li ^ tb «b kb iL ^ tb ^ *b tb ^ ^ tb kb ^ ^
* * /p^ ^ ^
^ ^ ^ ^ ip* * * /p^ ^ *
1100 DEF PROCTITLE
1110 VDU2
1120 PRI NT
"M 1 0 0 0 , 5 S 4 , 5 "
1 1 3 0 PRI NT "Q0PW A V E L E N G T H
( nm)
114 0 P R IN T " M 1 5 5 7 ,4 5 S 1 ,2"
1 1 5 0 P R I N T "Q 0 P 0 "
1 1 6 0 PRI NT "M 1 8 8 8 , 1 7 5 S 5 "
1 1 7 0 PRI NT " M 1 6 0 0 , 1 1 0 0 S 4 , 5"
11B0 PRI NT "P"+NAMEB
1190 PR IN T"M 1600,1000S4,5"
1200 PRI NT "M l 6 0 0 , 9 0 0 B 4 , 5 "
1210 P R I N T " M l 8 0 , 6 5 0 S 4 , 5 "
1220 P R I N T "Q1PABSORBANCE ( A r b ) "
1 2 3 0 PRI NT "S3"
1 2 4 0 PRI NT "H"
1 2 5 0 VDU3
1 2 6 0 ENDPROC
1 2 7 0 REM
1 2 8 0 DEF PROCLINE
1 2 9 0 VDU2
1 3 0 0 PRI NT " M 4 0 0 , 2 0 0 "
1 3 1 0 FOR I = 1 TO N
1320 L = INT(1900#( I - D /D X + 4 0 0 .5 )
1 3 3 0 K = I N T ( 1 4 0 0 * ( Y ( I ) ) / a b s m a x + 2 0 0 . 5)
1 3 4 0 PRI NT " D " L " , " K""
1 3 5 0 NEXT I
1 3 6 0 PRI NT "H"
1 3 7 0 VDU3
1 3 8 0 ENDPROC
1 3 9 0 REM
1 4 0 0 DEF PROCBOX
1 4 1 0 VDU2
1 4 2 0 PRINT "M0, 0 "
1 4 3 0 PRI NT "D 2 5 0 0 , 0 "
1 4 4 0 PRI NT " D 2 5 0 0 , 1 B 0 0 "
1 4 5 0 PRI NT " D 0 , 1 8 0 0 "
1 4 6 0 PRI NT " D 0 , 0 "
1 4 7 0 PRI NT "H"
1 4 8 0 VDU3
1 4 9 0 ENDPROC
1 5 0 0 REM
1 5 1 0 REM
1 5 2 0 PROCSPEC
1 5 3 0 P R I N T : PRINT
1 5 4 0 CLS
1 5 5 0 INPUT " W a v e l e n g t h r a n g e ", S t a r t , End
1 5 6 0 X= 0 : S t a r t = S t a r t - 5 4 0 0 : E n d = E n d - 5 4 0 0
1 5 7 0 FOR i = S t a r t TO End
1 5 8 0 MOVE X , Y ' ( i ) / 2
1 5 9 0 DRAW X , Y ( i ) / 2
1600 X = X + 1 2 0 0 /(E n d -S ta r t)
1 6 1 0 NEXT
G17
1620 ENDPROC
1 O O fTí
1 Q j J )¿J
U/
^ ^
y!/
»!> kU t í / t b ^ %Xr
'I r ^L* <1/ kXs>Xí i l/ ^
^ 'T' ^ ^ ^ 'T' * T 1m' * T 1'T ' 'T' * ' r ' ms 'T1^ 'T' “jp
1640
1650
1660
1670
1680
1690
1700
1710
1720
1730
1740
1750
17 60
1770
1780
1790
1800
1810
1820
1830
1840
1850
1860
DEF PROCGRAD
VDU2
PRIN T"M400,2 0 0 "
P R I N T " D 4 0 0 ,190"
PR IN T "M 875,200 "
P R I N T " D 8 7 5 ,190"
P R IN T "M 1 35 0,200"
P R IN T " D 1 3 5 0 ,190"
P R IN T "M 1 82 5,200"
P R IN T " D 1 8 2 5 ,1 9 0 “
PRIN T"M 2300, 2 0 0 "
P R IN T "D 2 30 03190"
PRINT”M400, 550"
P R IN T "D 3 90 , 5 5 0 ”
PRINT"M 400,9 0 0 "
P R IN T "D 39 0,9 0 0 "
PRINT” M 4 0 0 ,1250"
PRIN T"D 3 9 0 , 1 2 5 0 "
P R IN T -M 4 0 0 ,1600"
P R I N T " D 3 9 0 ,1600"
PRINT"H"
VDU3
ENDPROC
G18
APPENDIX H
The Debye-Hiickel Limiting Law in 3- D .
There
is
general
agreement
that
the
gives the correct description of the
Debye-Hiickel
ion-ion
at the limit of extremely dilute solutions
theory
interactions
(49).
The main
features of the theory are a consideration of the solvent
as a dielectric medium having an electrical permittivity c,
and
of
the
ions
as
point
charges
z^e,
capable
of
approaching each other to a distance of closest approach a
(which
may
ions) . The
be
interpreted
main
as
approximation
the
in
mean
the
diameter
theory
is
of
the
that
the
electrostatic potential energy V of an ion i at a distance
r from
an
ion
j is equal
to the potential
of mean
force
between the ions.
The
spatial
equilibrium
distribution
in
an
where k is Boltzmann's
a
test
charge
charges
electrostatic
n(r)
If
of
zg
potential
in
V
= n Q exp” eV/kT
thermal
is
given
(H.l)
constant.
is
placed
at
the
origin,
then
the
charge density is
p = p.
- i . u
r
K ions + P ^electron
=
z.n. e - n e exp (eV/kT).
1 xo
eo
But for overall neutrality
'( H . 2 )'
Therefore,
p = neQ e (1 - exp(eV/kT)}
1/2! +
= neQe (l-[l-(eV/kT) + (eV/kT)
=
But
V
n
e V
eo kT~
]}
(H.3 )
V = p/e, Poissons equation.
In 3D,
_a
JL
V2 =
r
2
r2 3V
ar
dr
(H. 4)
therefore,
r2 av
r2
- n eo e
kT
3r
ar
tt
V
= v / a;
or
This has the
a2v
ar
|
av
r
3r
(H. 5)
V .
2
general solution
V(r) =
With V(r)
2
0 ar r
{ A e~r/ \ + B
d
}
(H .
6)
, B must be zero.
Therefore,
.
A -r/A
V(r) = — e
d
which is the screened Coulomb potential.
H2
(H. 7)
In cylindrical polar coordinates
y2 _
r
l
a
fr av 1
r ar
ar _
a2v
+ l
r
ar
av
ar
Therefore,
Now
a^V
1_
av_
ar2
r
ar
equations
(H.5)
and
_
V
(H. 8)
A2
D
(H.8)
have
the
same
functional
form so they will have the same form of solution.
Because
of the differing multiplicative constant on the a v / 3 r term,
a slightly modified Ad will arise.
It will only introduce
numerical constant in Ad and not effect the n 2 dependence.
H3