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Mathematical model for optimum fibre optic probe design and characterisation
Spectrochimica Acta Part A 54 (1998) 1369 – 1374
Mathematical model for optimum fibre optic probe design and characterisation Uwe Bu¨nting *, Peter Karlitschek Laser Laboratorium Go¨ttingen, Hans-Adolf-Krebs Weg 1, D-37077 Go¨ttingen, Germany Received 23 September 1997; accepted 12 February 1998
Abstract A mathematical model for the optimisation and characterisation of a fibre optic probe is described. The application of the optimisation model to an in situ fibre optic laser fluorometer for the detection of water pollutants is presented. The computational results are verified through experiments. © 1998 Elsevier Science B.V. All rights reserved. Keywords: Fibre optic sensor; Geometry optimisation calculation; Laser-induced fluorescence (LIF); Water pollutant monitoring; Polycyclic aromatic hydrocarbons (PAH)
1. Introduction In the last 10 years there has been an increased interest in the use of spectroscopy for an in situ and on-line monitoring of environmental pollutants. In particular, sensitive fluorometric sensors with lasers as excitation source have been constructed using optical fibres to guide the excitation and fluorescence light [1 – 10]. Only a few studies, however, have been devoted to the optimisation of the design of the fibre optic probe used by such instruments, and it is difficult or impossible to transfer the results to other applications or set-up requirements [11 – 13]. As will be shown, a well chosen geometry can significantly increase the amount of collected * Corresponding author. Tel.: + 49 551 503553; fax: + 49 551 503599; e-mail: [email protected]
fluorescence light. Unfortunately, the optimum geometry is rather difficult to obtain experimentally, requiring a large set of measurements and specially designed apparatus allowing precise modifications of the experimental parameters. Furthermore, some characteristics of a given geometry are not directly measurable, such as the total observation volume or the influence of certain parts of the observation volume as a function of location and size. The motivation and application for this work was the need for an optimally designed probe for a newly developed fibre optic laser fluorometer. The fluorometer was designed as a portable, battery powered system that consists of a small diode-pumped solid state laser with up-conversion into the UV (266 nm), and a time and spectrally resolving detection unit. The systems probe uses optical fibres to guide the excitation light from the
1386-1425/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S1386-1425(98)00043-2
U. Bu¨nting, P. Karlitschek / Spectrochimica Acta Part A 54 (1998) 1369–1374
1370
laser into the water and the fluorescence light from the water into the detection unit [14]. All the parameters of the probe-fibre diameter, numerical aperture, excitation and detection fibre separation and the number of excitation and detection fibres (see Fig. 1), were subject to optimisation as they all have a direct influence on the amount of fluorescence light collected. In order to optimise the geometry of the probe, several geometries were modelled and evaluated according to the amount of fluorescence light the corresponding probe could collect.
2. Theoretical To compute the quality of a given geometry, the observation volume is divided into small unit cubes. Each cube is then rated according to its contribution to the total measured fluorescence light reaching the detection unit. The total size (in mm3) of the rated observation volume —the sum of the ratings — is called the collection efficiency (CE). For this model, some basic assumptions are made: (i) the fluorescence is isotropic; (ii) the water is free from light scattering particles; and (iii) the absorption and scattering of excitation light in the observation volume is negligible. These conditions are essentially met for distilled water with a low concentration of fluorescing molecules (typically 10 ppm or less) and an observation volume of 1 cm3 or smaller. For symmetry reasons, only one detection fibre is taken into consideration. The area outside the intersection of the excitation and detection cone is rated zero, the rating for the area inside depends on the excitation energy density r(r ) (r R3), and the probability h(r )for a photon to hit the surface of the detection fibre within the acceptance angle u. The rating function f(r ) can be written as f(r )= r(r ) h(r )
with E0 the excitation energy and bb the virtual spire of the excitation cone (see Fig. 1): bb x = bb y = 0, bb z = −
¥EF . 2 cos(p/2 −u)
To form an expression for h(r ), let H be the front surface of the detection fiber, and Hb its area vector. A cone with the spire at point r , the axis parallel to Hb and an angle of spread of 2u produces an area A1 on a unit sphere around r (see Fig. 2). Projecting H (seen from r ) on this sphere results in the ellipse A2. The intersection of A1 and A2 gives the solid angle b. The probability for a photon to hit H and be guided within the fibres is then h(r )=
b(r ) 4p
(4)
Integrating f(r ) over the unrated observation volume for a given geometry results in the collection efficiency CE for this geometry: CE=
&& &
0
−
−
f(r (x, y, z)) dx dy dz
(1)
Previous experiments show that the energy density at r can be approximated using r(r )=
!
E 0bb 2 r −bb − 2 : r in V 0 : otherwise
(2)
(3)
Fig. 1. Parameters of the probe geometry.
(5)
U. Bu¨nting, P. Karlitschek / Spectrochimica Acta Part A 54 (1998) 1369–1374
Fig. 2. The formation of b.
To obtain the influence of the x – y-plane at a distance z from the probe front surface, f(r ) is integrated in this plane: A(z)=
& &
−
−
f(r (x, y, z)) dx dy
(6)
1371
various parameters showed that the results do not change significantly if the integration step width of the volume is decreased below 50 mm. Therefore 50 mm was chosen as the integration step width. Initially, the collection efficiency was calculated as a function of d and g with NA = 0.22 and ¥DF = 400 mm. The result is shown in Fig. 3. As could be expected, the maximum is obtained when d=0. The optimum angle for a typical minimum distance d= 150 mm is g=14°. For angles above 17° (roughly twice the acceptance angle of the fibres in water) the optimum distance is greater than zero and increases with increasing angle. The influence of the parameters of the detection fibre was then evaluated. Collection efficiency CE increases roughly quadratically with increasing diameter of the detection fibre. To obtain the optimum diameter, the average efficiency per unit area is plotted against ¥DF. The numerical aperture NA and fibre separation d remained constant throughout this stage at 0.22 and 150 mm, respectively. The result can be seen in Fig. 4. The third set of calculations allowed the collection efficiency to be determined as a function of g and NA whilst the other parameters were kept constant at d= 150 mm and ¥DF = 400 mm. The result is shown in Fig. 5. As can be seen,
The search for the highest collection efficiency is now reduced to an optimisation problem.
3. Calculations The following parameters were taken into consideration in order to obtain an optimal geometry for the probe: 1. The distance d between the excitation and detection fibres, 2. the angle g between the excitation and detection fibres, 3. the diameter ¥DF of the detection fibre and 4. the numerical aperture NA of the excitation and detection fibres. Throughout the analysis, the diameter of the excitation fibre was kept constant at ¥EF=600 mm. The calculations were performed numerically, implemented using C+ + and running on a standard PC (Intel Pentium). A set of test runs with
Fig. 3. Collection efficiency (in mm3) as a function of angle g and fibre distance d (NA = 0.22, ¥EF =400 mm).
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U. Bu¨nting, P. Karlitschek / Spectrochimica Acta Part A 54 (1998) 1369–1374
Fig. 4. Collection efficiency divided by the square of the detection fibre diameter as a function of detection fibre diameter for different angles g (NA =0.22, d =150 mm).
Fig. 6. Rated observation volume L as a function of depth z and influence of the x – y-plane in distance z. The unrated volume between probe and z is shown by a dotted line (NA = 0.22, g = 20°, d = 150 mm, ¥DF =400 mm).
L(z)=
&
z
A(z) dz
(7)
0
the optimum angle g remains at approximately the same as the acceptance angle (u =sin − 1 (NA)/ 1.33). Finally, the observation volume for a given set-up was calculated. If we use A from Eq. (6) to define the function L(z) as
we obtain a value for the influence of the observation volume between the probe front surface and the depth z. The calculations were performed with d= 150 mm, g= 20° and ¥DF = 400 mm (the parameters of the probe we finally realized as an outcome of this work). The results of the calculations are presented in Fig. 6. Comparisons of CE, L(z) and the unrated observation volume for this probe geometry permit some statements to be made about the physical size of the observation volume. Even if the unrated observation volume for this probe is quite large, the main contribution is due to a very limited area: 50% of the fluorescence signal is gained from 0.67 mm3 and 95% of the signal from 5.32 mm3. This area starts at approximately 0.6 mm from the end of the detection fibre, and finishes at approximately 1.7 mm for 50% and at 5.30 mm for 95% of the signal.
4. Experiment Fig. 5. Collection efficiency CE as a function of angle g for different numerical apertures NA (d=150 mm, ¥DF =400 mm).
To verify the theoretical results, the influence of the angle g on the collection efficiency was examined by experiment.
U. Bu¨nting, P. Karlitschek / Spectrochimica Acta Part A 54 (1998) 1369–1374
The excitation fibre and the detection fibre were fixed to a retainer similar to a pair of compasses: Two metal legs are connected with a hinge and the angle between the legs is adjustable to an accuracy of 0.1 degrees using a screw. The fibres were carefully adjusted to keep their separation distance d at 150 mm with an error of less than 10 mm. Distance and angle were controlled using a microscope. Because water turbidity should have an effect on the size of the observation volume, it was expected to affect the optimum value for g. Therefore, the collection efficiency as a function of angle g was measured for different grades of water turbidity. The turbidity of natural water is mainly caused by suspended stray particles which are large compared to the wavelength of the scattered light [15]. This can be accurately modelled using Bentonit (Carl Roth GmbH, Karlsruhe, Germany), which contains no fluorescing components and exhibits good suspension properties. Gentle agitation of the suspension (using a magnetic stirrer at 120 rpm) prevents the particles from settling. To model realistic grades of turbidity, samples of water were taken from rivers, springs and lakes, and the mean free path was measured and compared with Bentonit suspensions. The smallest mean free path (for the 365 nm Hg-line) was determined to be 0.10 m, corresponding to an concentration of 97 mg l − 1 Bentonit. The collection efficiency was measured by evaluating the integral over the fluorescence signal of 0.1 mg l − 1 fluorescence dye FB28 (Aldrich) in distilled water. The Bentonit concentrations and the angle g were adjusted between 0 and 120 mg l − 1 and 10 and 40°, respectively. For excitation, pulses with 266 nm from a frequency converted Nd:YAGLaser were used. The results can be seen in Fig. 7. Scattering particles in the water shift the optimum angle towards larger values. For the fibres used (¥EF =600 mm, ¥DF =400 mm, NA=0.22) the optimum angle g was between 17° (clear water) and 28° (muddy water). The results of the calculations and the experiments were used to define the probe geometry for our laser fluorometer. Because the instrument is designed to work with both clear and turbid water, the optimum geometry — especially the optimum
1373
Fig. 7. Measured integral over the intensity of the fluorescence signal (the collection efficiency) as a function of the angle between excitation and detection fibre for three different Bentonit concentrations. The underlaid curves are quadratic regressions, the maxima are normalized on 1.
g—can only be a compromise. We have chosen g to be 20°, because at this angle the collection efficiency is close to the maximum for both clear and turbid water. The optimum distance d between the fibres for this angle is 100 mm (see Fig. 3), but due to manufacturing problems the smallest separation possible was 150 mm, for which the collection efficiency is still close to the maximum.
Fig. 8. The final fibre optic probe. Excitation fibre with 600 mm diameter, detection fibres with 400 mm diameter.
1374
U. Bu¨nting, P. Karlitschek / Spectrochimica Acta Part A 54 (1998) 1369–1374
To ensure good UV-transmission, silica clad fibres with a NA of 0.22 were used. The laser energy of 100 mJ pulse − 1 fixes the diameter of the excitation fibre at ¥EF =600 mm [16] and the size of the entrance slit of the detection unit (250× 1600 mm) allows either eight detection fibres of ¥DF = 200 mm or four fibres of ¥DF = 400 mm. The results of the calculations shown in Fig. 4 clearly favour the second possibility. The outcome of this work is the fibre optic probe shown in Fig. 8. The four detection fibres are lead to the entrance slit of the detection unit, an optical multichannel analyzer. With the completed system it is possible to detect a large number of water pollutants (PAH, BTX, oil, fuel or oil-based lubricants) in the ppb and sub-ppb range. The system is described in more detail in Refs. [14,17].
5. Conclusion A mathematical model for the characterisation and optimisation of a fibre optic probe has been presented. Using this model, the collection efficiency of various probe geometries and set-ups has been evaluated. For some of the model’s parameters, the collection efficiency was determined experimentally. On the whole, the behavior of the calculated collection efficiency as a function of the angle g reflects the experimental findings, although the optimum angle determined experimentally is a few degrees larger than the calculated one. Taking the results from Fig. 5 into consideration, this can be explained through a slightly larger effective numerical aperture of the fibres. To allow further related work not described in this paper, the executable computer program together with the C+ + source code is available upon request from the authors.
References [1] R.M. Measures, W.R. Houston., Laser induced fluorescent decay spectra—a new form of environmental signature, Opt. Eng. 13 (6) (1974) 494–501.
[2] T.F. van Geel, J.D. Winefordner., Pulsed nitrogen laser in analytical spectrometry of molecules in the condensed phase, Anal. Chem. 48 (2) (1976) 335 – 338. [3] J.H. Richardson, M.E. Ando., Sub-part-per-trillion detection of polycylic aromatic hydrocarbons by laser induces molecular fluorescence, Anal. Chem. 49 (7) (1977) 955– 959. [4] W.A. Chudyk, M.M. Carrabba, J.E. Kenny., Remote detection of groundwater contaminants using far-ultraviolet laser-induced-fluorescence, Anal. Chem. 57 (1985) 1237 – 1242. [5] S.M. Inman, P. Thibado, G. Theriault, S.H. Lieberman., Development of a pulsed-laser fiber-optic-based fluorometer: determination of fluorescence decay times of polycylic aromatic hydrocarbons in sea water, Anal. Chim. Acta 239 (1990) 45 – 51. [6] G.A. Theriault, R. Newberry, J.M. Andrews, S.E. Apitz, S.H. Lieberman., Fiber optic fluorometer based on a dual wavelength laser excitation source, SPIE-Proc. 1796 (1992) 115 – 123. [7] W. Schade, J. Bublitz., Trace analysis of oil pollution by time-resolved laser spectroscopy-first results of field measurements, Inst. Phys. Conf. Ser. 9 (128) (1992) 317–320. [8] S.E. Apitz, G.A. Theriault, S.H. Lieberman., Optimization of the optical characteristics of a fiber-optic guided laser fluorescence technique for the in situ evaluations of fuels in soils, SPIE-Proc. 1637 (1992) 241 – 254. [9] G. Hillrichs, W. Neu, UV-laser induced fluorescence to determine organic pollutions in water, in: C. Werner, W. Waidlich (Eds.), Laser in der Umweltmesstechnik, Springer-Verlag, Berlin, 1993, pp. 109 – 112. [10] E.M. Filippova, V.V. Chubarov, V.V. Fadeev., New possibilities of laser fluorescence spectroscopy for diagnostics of petroleum hydrocarbons in natural water, Can. J. Appl. Spectrosc. 38 (5) (1993) 139 – 144. [11] P. Plaza, Nguyen Quy Dao, M. Jouan, H. Fevrier, H. Saisse, Simulation et optimisation des capteurs a´ fibres optiques adjacentes, Appl. Opt. 25 (19) (1986) 3448 –3454. [12] R. Niessner, U. Panne, H. Schro¨der., Fibre-optic sensor for the determination of polynuclear aromatic hydrocarbons with time-resolved laser-induced fluorescence, Anal. Chim. Acta 225 (1991) 213 – 243. [13] S.E. Nave, P.E. O’Rourke, and W.R. Toole, Sampling probes enhance remote chemical analyses. Laser Focus World, (1995) 83 – 88. [14] P. Karlitschek, U. Bu¨nting, T. No¨rthemann, and G. Hillrichs. Fluorimetric detection of water pollutants with a fiber coupled solid-state UV-laser,in: Laser methods for biological and environmental applications, SPIE Proceedings, Heraklion, 1996. [15] C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles, Wiley, New York, 1985. [16] P. Karlitschek, G. Hillrichs, K.-F. Klein., Photodegradation and nonlinear effects in optical fibers induced by pulsed UV-laser radiation, Opt. Commun. 116 (1995) 219 – 230. [17] P. Karlitschek, Faseroptische Untersuchungen der UVLaser-gestu¨tzten Schadstoffsensorik, PhD thesis, Georg August Universita¨t, Go¨ttingen, 1996.
Mathematical model for optimum fibre optic probe design and characterisation Uwe Bu¨nting *, Peter Karlitschek Laser Laboratorium Go¨ttingen, Hans-Adolf-Krebs Weg 1, D-37077 Go¨ttingen, Germany Received 23 September 1997; accepted 12 February 1998
Abstract A mathematical model for the optimisation and characterisation of a fibre optic probe is described. The application of the optimisation model to an in situ fibre optic laser fluorometer for the detection of water pollutants is presented. The computational results are verified through experiments. © 1998 Elsevier Science B.V. All rights reserved. Keywords: Fibre optic sensor; Geometry optimisation calculation; Laser-induced fluorescence (LIF); Water pollutant monitoring; Polycyclic aromatic hydrocarbons (PAH)
1. Introduction In the last 10 years there has been an increased interest in the use of spectroscopy for an in situ and on-line monitoring of environmental pollutants. In particular, sensitive fluorometric sensors with lasers as excitation source have been constructed using optical fibres to guide the excitation and fluorescence light [1 – 10]. Only a few studies, however, have been devoted to the optimisation of the design of the fibre optic probe used by such instruments, and it is difficult or impossible to transfer the results to other applications or set-up requirements [11 – 13]. As will be shown, a well chosen geometry can significantly increase the amount of collected * Corresponding author. Tel.: + 49 551 503553; fax: + 49 551 503599; e-mail: [email protected]
fluorescence light. Unfortunately, the optimum geometry is rather difficult to obtain experimentally, requiring a large set of measurements and specially designed apparatus allowing precise modifications of the experimental parameters. Furthermore, some characteristics of a given geometry are not directly measurable, such as the total observation volume or the influence of certain parts of the observation volume as a function of location and size. The motivation and application for this work was the need for an optimally designed probe for a newly developed fibre optic laser fluorometer. The fluorometer was designed as a portable, battery powered system that consists of a small diode-pumped solid state laser with up-conversion into the UV (266 nm), and a time and spectrally resolving detection unit. The systems probe uses optical fibres to guide the excitation light from the
1386-1425/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S1386-1425(98)00043-2
U. Bu¨nting, P. Karlitschek / Spectrochimica Acta Part A 54 (1998) 1369–1374
1370
laser into the water and the fluorescence light from the water into the detection unit [14]. All the parameters of the probe-fibre diameter, numerical aperture, excitation and detection fibre separation and the number of excitation and detection fibres (see Fig. 1), were subject to optimisation as they all have a direct influence on the amount of fluorescence light collected. In order to optimise the geometry of the probe, several geometries were modelled and evaluated according to the amount of fluorescence light the corresponding probe could collect.
2. Theoretical To compute the quality of a given geometry, the observation volume is divided into small unit cubes. Each cube is then rated according to its contribution to the total measured fluorescence light reaching the detection unit. The total size (in mm3) of the rated observation volume —the sum of the ratings — is called the collection efficiency (CE). For this model, some basic assumptions are made: (i) the fluorescence is isotropic; (ii) the water is free from light scattering particles; and (iii) the absorption and scattering of excitation light in the observation volume is negligible. These conditions are essentially met for distilled water with a low concentration of fluorescing molecules (typically 10 ppm or less) and an observation volume of 1 cm3 or smaller. For symmetry reasons, only one detection fibre is taken into consideration. The area outside the intersection of the excitation and detection cone is rated zero, the rating for the area inside depends on the excitation energy density r(r ) (r R3), and the probability h(r )for a photon to hit the surface of the detection fibre within the acceptance angle u. The rating function f(r ) can be written as f(r )= r(r ) h(r )
with E0 the excitation energy and bb the virtual spire of the excitation cone (see Fig. 1): bb x = bb y = 0, bb z = −
¥EF . 2 cos(p/2 −u)
To form an expression for h(r ), let H be the front surface of the detection fiber, and Hb its area vector. A cone with the spire at point r , the axis parallel to Hb and an angle of spread of 2u produces an area A1 on a unit sphere around r (see Fig. 2). Projecting H (seen from r ) on this sphere results in the ellipse A2. The intersection of A1 and A2 gives the solid angle b. The probability for a photon to hit H and be guided within the fibres is then h(r )=
b(r ) 4p
(4)
Integrating f(r ) over the unrated observation volume for a given geometry results in the collection efficiency CE for this geometry: CE=
&& &
0
−
−
f(r (x, y, z)) dx dy dz
(1)
Previous experiments show that the energy density at r can be approximated using r(r )=
!
E 0bb 2 r −bb − 2 : r in V 0 : otherwise
(2)
(3)
Fig. 1. Parameters of the probe geometry.
(5)
U. Bu¨nting, P. Karlitschek / Spectrochimica Acta Part A 54 (1998) 1369–1374
Fig. 2. The formation of b.
To obtain the influence of the x – y-plane at a distance z from the probe front surface, f(r ) is integrated in this plane: A(z)=
& &
−
−
f(r (x, y, z)) dx dy
(6)
1371
various parameters showed that the results do not change significantly if the integration step width of the volume is decreased below 50 mm. Therefore 50 mm was chosen as the integration step width. Initially, the collection efficiency was calculated as a function of d and g with NA = 0.22 and ¥DF = 400 mm. The result is shown in Fig. 3. As could be expected, the maximum is obtained when d=0. The optimum angle for a typical minimum distance d= 150 mm is g=14°. For angles above 17° (roughly twice the acceptance angle of the fibres in water) the optimum distance is greater than zero and increases with increasing angle. The influence of the parameters of the detection fibre was then evaluated. Collection efficiency CE increases roughly quadratically with increasing diameter of the detection fibre. To obtain the optimum diameter, the average efficiency per unit area is plotted against ¥DF. The numerical aperture NA and fibre separation d remained constant throughout this stage at 0.22 and 150 mm, respectively. The result can be seen in Fig. 4. The third set of calculations allowed the collection efficiency to be determined as a function of g and NA whilst the other parameters were kept constant at d= 150 mm and ¥DF = 400 mm. The result is shown in Fig. 5. As can be seen,
The search for the highest collection efficiency is now reduced to an optimisation problem.
3. Calculations The following parameters were taken into consideration in order to obtain an optimal geometry for the probe: 1. The distance d between the excitation and detection fibres, 2. the angle g between the excitation and detection fibres, 3. the diameter ¥DF of the detection fibre and 4. the numerical aperture NA of the excitation and detection fibres. Throughout the analysis, the diameter of the excitation fibre was kept constant at ¥EF=600 mm. The calculations were performed numerically, implemented using C+ + and running on a standard PC (Intel Pentium). A set of test runs with
Fig. 3. Collection efficiency (in mm3) as a function of angle g and fibre distance d (NA = 0.22, ¥EF =400 mm).
1372
U. Bu¨nting, P. Karlitschek / Spectrochimica Acta Part A 54 (1998) 1369–1374
Fig. 4. Collection efficiency divided by the square of the detection fibre diameter as a function of detection fibre diameter for different angles g (NA =0.22, d =150 mm).
Fig. 6. Rated observation volume L as a function of depth z and influence of the x – y-plane in distance z. The unrated volume between probe and z is shown by a dotted line (NA = 0.22, g = 20°, d = 150 mm, ¥DF =400 mm).
L(z)=
&
z
A(z) dz
(7)
0
the optimum angle g remains at approximately the same as the acceptance angle (u =sin − 1 (NA)/ 1.33). Finally, the observation volume for a given set-up was calculated. If we use A from Eq. (6) to define the function L(z) as
we obtain a value for the influence of the observation volume between the probe front surface and the depth z. The calculations were performed with d= 150 mm, g= 20° and ¥DF = 400 mm (the parameters of the probe we finally realized as an outcome of this work). The results of the calculations are presented in Fig. 6. Comparisons of CE, L(z) and the unrated observation volume for this probe geometry permit some statements to be made about the physical size of the observation volume. Even if the unrated observation volume for this probe is quite large, the main contribution is due to a very limited area: 50% of the fluorescence signal is gained from 0.67 mm3 and 95% of the signal from 5.32 mm3. This area starts at approximately 0.6 mm from the end of the detection fibre, and finishes at approximately 1.7 mm for 50% and at 5.30 mm for 95% of the signal.
4. Experiment Fig. 5. Collection efficiency CE as a function of angle g for different numerical apertures NA (d=150 mm, ¥DF =400 mm).
To verify the theoretical results, the influence of the angle g on the collection efficiency was examined by experiment.
U. Bu¨nting, P. Karlitschek / Spectrochimica Acta Part A 54 (1998) 1369–1374
The excitation fibre and the detection fibre were fixed to a retainer similar to a pair of compasses: Two metal legs are connected with a hinge and the angle between the legs is adjustable to an accuracy of 0.1 degrees using a screw. The fibres were carefully adjusted to keep their separation distance d at 150 mm with an error of less than 10 mm. Distance and angle were controlled using a microscope. Because water turbidity should have an effect on the size of the observation volume, it was expected to affect the optimum value for g. Therefore, the collection efficiency as a function of angle g was measured for different grades of water turbidity. The turbidity of natural water is mainly caused by suspended stray particles which are large compared to the wavelength of the scattered light [15]. This can be accurately modelled using Bentonit (Carl Roth GmbH, Karlsruhe, Germany), which contains no fluorescing components and exhibits good suspension properties. Gentle agitation of the suspension (using a magnetic stirrer at 120 rpm) prevents the particles from settling. To model realistic grades of turbidity, samples of water were taken from rivers, springs and lakes, and the mean free path was measured and compared with Bentonit suspensions. The smallest mean free path (for the 365 nm Hg-line) was determined to be 0.10 m, corresponding to an concentration of 97 mg l − 1 Bentonit. The collection efficiency was measured by evaluating the integral over the fluorescence signal of 0.1 mg l − 1 fluorescence dye FB28 (Aldrich) in distilled water. The Bentonit concentrations and the angle g were adjusted between 0 and 120 mg l − 1 and 10 and 40°, respectively. For excitation, pulses with 266 nm from a frequency converted Nd:YAGLaser were used. The results can be seen in Fig. 7. Scattering particles in the water shift the optimum angle towards larger values. For the fibres used (¥EF =600 mm, ¥DF =400 mm, NA=0.22) the optimum angle g was between 17° (clear water) and 28° (muddy water). The results of the calculations and the experiments were used to define the probe geometry for our laser fluorometer. Because the instrument is designed to work with both clear and turbid water, the optimum geometry — especially the optimum
1373
Fig. 7. Measured integral over the intensity of the fluorescence signal (the collection efficiency) as a function of the angle between excitation and detection fibre for three different Bentonit concentrations. The underlaid curves are quadratic regressions, the maxima are normalized on 1.
g—can only be a compromise. We have chosen g to be 20°, because at this angle the collection efficiency is close to the maximum for both clear and turbid water. The optimum distance d between the fibres for this angle is 100 mm (see Fig. 3), but due to manufacturing problems the smallest separation possible was 150 mm, for which the collection efficiency is still close to the maximum.
Fig. 8. The final fibre optic probe. Excitation fibre with 600 mm diameter, detection fibres with 400 mm diameter.
1374
U. Bu¨nting, P. Karlitschek / Spectrochimica Acta Part A 54 (1998) 1369–1374
To ensure good UV-transmission, silica clad fibres with a NA of 0.22 were used. The laser energy of 100 mJ pulse − 1 fixes the diameter of the excitation fibre at ¥EF =600 mm [16] and the size of the entrance slit of the detection unit (250× 1600 mm) allows either eight detection fibres of ¥DF = 200 mm or four fibres of ¥DF = 400 mm. The results of the calculations shown in Fig. 4 clearly favour the second possibility. The outcome of this work is the fibre optic probe shown in Fig. 8. The four detection fibres are lead to the entrance slit of the detection unit, an optical multichannel analyzer. With the completed system it is possible to detect a large number of water pollutants (PAH, BTX, oil, fuel or oil-based lubricants) in the ppb and sub-ppb range. The system is described in more detail in Refs. [14,17].
5. Conclusion A mathematical model for the characterisation and optimisation of a fibre optic probe has been presented. Using this model, the collection efficiency of various probe geometries and set-ups has been evaluated. For some of the model’s parameters, the collection efficiency was determined experimentally. On the whole, the behavior of the calculated collection efficiency as a function of the angle g reflects the experimental findings, although the optimum angle determined experimentally is a few degrees larger than the calculated one. Taking the results from Fig. 5 into consideration, this can be explained through a slightly larger effective numerical aperture of the fibres. To allow further related work not described in this paper, the executable computer program together with the C+ + source code is available upon request from the authors.
References [1] R.M. Measures, W.R. Houston., Laser induced fluorescent decay spectra—a new form of environmental signature, Opt. Eng. 13 (6) (1974) 494–501.
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