Neurological Research A Journal of Progress in Neurosurgery, Neurology and Neurosciences
ISSN: 0161-6412 (Print) 1743-1328 (Online) Journal homepage: http://www.tandfonline.com/loi/yner20
Single optical fibre transducer for pressure measurement Alfred Perlin To cite this article: Alfred Perlin (1992) Single optical fibre transducer for pressure measurement, Neurological Research, 14:1, 62-68, DOI: 10.1080/01616412.1992.11740013 To link to this article: http://dx.doi.org/10.1080/01616412.1992.11740013
Published online: 20 Jul 2016.
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Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=yner20 Download by: [Australian Catholic University]
Date: 16 August 2017, At: 08:44
Single optical fibre transducer for pressure measurement Alfred Perlin
Downloaded by [Australian Catholic University] at 08:44 16 August 2017
Department of Neurosurgery, College of Medicine, The University of Illinois at Chicago, II, USA
In a single optical fibre transducer, light is injected into a fibre through a fibre optic coupler, located at some distance from the distal end of the fibre. Injected light travels toward the front face of the fibre, where it exits in the shape of a cone. then, after reflection from a reflective surface, it is readmitted into the same fibre. The reflected beam of light travels back through the coupler, exits through the distal end of the fibre and illuminates the photosensitive area of a photo diode, where it is converted to an electrical current. Depending on which one of the parameters is allowed to vary the amount of the returning light, one can build a variety of different sensors. Among them are: linear I angular displacement sensors and their derivatives such as pressure or force sensors; transmittance sensors such as turbidity and chemical sensors; reflectance sensors such as temperature sensors, optical encoders and scanners, colourometric and other types of chemical sensors. In the case of the single optic fibre transducer (SOFT) made by Pear/Instruments ( Chicago, II, USA ), the reflective surface is made of a thin metal foil with 6 J..lm thickness and 1.25 mm diameter. Optical fibres are pf the multimode type with 55 J..lm diameter. Their numerical aperture is equal to 0.66. The SOFT head is 1.25 mm in diameter and has an overall length of 50 em. The disposable part of the system contains the head, fibre, protective sheathing and plug. Its operating range is -15 to + 300 mmHg, and + 25 to + 45 °C, and its resolutio n is + I -1 mmHg. Keywords: Fibre optic; transducer
INTRODUCTION With rapid ·advancement in the fields of fibre optic sensing, there is a need for quantitative and qualitative analysis of performance of various types of fibre optic sensors. Computer models can predict behaviour of such sensors with adequate accuracy, thus sparing time and expense on sophisticated equipment needed for such experimentation. MATERIALS AND METHODS The basic principle of a single optical fibre transducer (S OFT) is shown in Figure 1. Light is emitted from the light source (10 ) into the fibre optic coupler spaced some distance from the end of the fibre. A majority of this light travels through the fibre in a forward direction (IF). Light exits the fibre through its distal face in the shape of a cone, and travels through the optical medium until it is reflected back from the reflecting surface. Then, part of this light is reabsorbed back into the fibre (IR ). this returning portion (IR ) traverses the fibre optic coupler, where part of it escapes into the surrounding (IL). The remaining part (Is) leaves the fibre through the proximal end and is absorbed by the photosensor (c.f., Figure 1). The amount of luminous power (in lumens) reabsorbed into the fibre depends on: ( 1) physical properties of optical media (light transmittance etc.); Correspondence and reprint requests to: Dr Alfred Perlin, PH.D, Department of Neurosurgery, College of Medicine, University of Illinois at Chicago, Neuropsychiatric Institute, 912 South Wood Street, chicago, II, 60612, USA. Accepted for publication O ctober 1991.
© 1992 Forefront Publishing Group 0161-6412/ 92/ 010062-07 62
Neurological Research, 1992, Volume 14, March
(2) physical properties of fibre (critical angle CJ.. , etc. ); ( 3) physical properties of reflective surface (reflectivity, et c.); (4) geometry of the opt ical media gap between reflective surface and optical fibre (thickness of the gap (X), cross-section of fibre (a), radius of curvature (p) or reflective su rface, incidence angle (/3 ), etc. COMPUTATIONAL MODEL OF SINGLE OPTIC FIBRE OPTIC TRANSDUCER For the sake of simplicity one can assume: (1) luminous power in any cross section of t he cone of the light is constant; (2 ) there are no secondary reflections ; (3 ) radiant areance (once was called illuminance and its units is w I m 2 ) of the incoming light varies in linear fashion across the illuminated area on the face of the fibre; (4 ) angle of incidence of absorbed light is represented by the angle of the incident ray passing through the center of the illuminated area. For cases where all physical properties of this system are constant, their influences can be represented by a single coefficient (K). The coupling efficiency of sensory head (s ), is a ratio of luminous power of the light
Figure 1:
Basic model of single optical fibre transducer (SOFT)
Single optical fibre transducer fo r pressure measurement: Alfred Perlin
1.00
absorbed into the fibre (after reflection from reflective surface), to luminous power of light exiting the distal end of the fibre. For the case when the mirror surface is perpendicular to the axis of the fibre (/3 = 0), and the only variables are distance X and (p) radius of curvature, the coupling efficiency (e) is given by: e
=
K(1
+ (m ±
0.~
o.ao 0.70
,,,,
0.60
(a)
e(1 ± cos (a ±b)))
''
E
0.50
x (tan a· tan(2b ± a)))- 2
0.40
where
0.30
X
-=m ;
!!_ = e ;
ro
ro
A = [ 1
+ j + (;) Ca~
.
X
Q.20
-=I
p
0.10
a) J
0.00 0.00
(1)
''
\
\ \\ \ ' \ \ ',
\ \ ' ',.... "'.... \ '' ........ \ ', \
Downloaded by [Australian Catholic University] at 08:44 16 August 2017
.66
.87
.....
2.00
1.00
10.00 1.00
-w. l ()
(2)
This formula describes the action of a single fibre linear displacement transducer (SFLDT) as shown in Figure 2. Results from computer simulation of the performance of single fibre linear displacement transducer for various fibres are described in Figure 3. Figure 3 also shows dependence of coupling efficiency (e) and its derivative with respect to relative distance (X /r0 ), when the numerical aperture (NA) is 0.3, 0.5, 0.66 and 0.87. To be able to compare performance of transducer based on single and multifibres arrangements, one has built computational model of multi fibre optical transducer (MFOT). Such a model should be based on the same assumptions as model of SOFT. Figure 4 shows a schematic drawing of the basic (two fibre) MOFT. For MOFT case, coupling efficiency (e) is described by different formulas for each one of the four regions of displacement (X).
f,,
.30 .50
xlr.
Remark : Top sign in equation belongs to case of convex mirror surface. For a flat reflective surface (p -+ oo) and when f3 = 0 this ratio (e) becomes:
+ 2 · m ·tan a)- 2
N.A. • N.A. • N.A. • N.A.•
' '' ',' ' ' ,,.................._----..... .................... ............................ __ _ -----
b = 5/ N[ -1A sin a)
e = K·(1
-------
\,
-
1.00 7.00
:- 1..00
(b)
5.00
)(
~
4.00
v
).()()
w
-------
N.A. • .30 N.A. • .50 N.A. • .66 N.A- .87
2.00 1.00 0.00 0.00
0.50
1.00
xlr. Figure 3: Characteristic of single fibre linear displacement transducer (p = oo, f3 = 0). (a) variation of (e) versus relative displacement X/r0 (b) variation of (de/ dx) versus relative displacement (X,,)
100%
0. X
Figure 4: Basic model of multiple fibre linear displacement transducer (8 = 0 and p = oo )
Region/: Figure 2: General principle of action of single fibre linear displacement transducer with flat reflective surface (p = oo) and angle f3 = 0
0
~
N- 2r X ~ - - - = XcR 2 tan a (3a)
e=O
Neurological Research, 1992, Volume 14, March
63
Single optical fibre transducer for pressure measurement: Allred Perlin
Region If:
+ ,-2)1/2 _
(N2
XcR
r
< X ~ -----2 tan
IX
K
e = --{R2 [2 cos- 1 (8)- sin(2 cos- 1 (8))] 2rcR2
+ ?[cos- 1 (A)- sin(2 cos- 1 (Alll}
(3b)
Region Ill: (N2
+ ,-2 )1/2 -
r
N
------
ISSN: 0161-6412 (Print) 1743-1328 (Online) Journal homepage: http://www.tandfonline.com/loi/yner20
Single optical fibre transducer for pressure measurement Alfred Perlin To cite this article: Alfred Perlin (1992) Single optical fibre transducer for pressure measurement, Neurological Research, 14:1, 62-68, DOI: 10.1080/01616412.1992.11740013 To link to this article: http://dx.doi.org/10.1080/01616412.1992.11740013
Published online: 20 Jul 2016.
Submit your article to this journal
View related articles
Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=yner20 Download by: [Australian Catholic University]
Date: 16 August 2017, At: 08:44
Single optical fibre transducer for pressure measurement Alfred Perlin
Downloaded by [Australian Catholic University] at 08:44 16 August 2017
Department of Neurosurgery, College of Medicine, The University of Illinois at Chicago, II, USA
In a single optical fibre transducer, light is injected into a fibre through a fibre optic coupler, located at some distance from the distal end of the fibre. Injected light travels toward the front face of the fibre, where it exits in the shape of a cone. then, after reflection from a reflective surface, it is readmitted into the same fibre. The reflected beam of light travels back through the coupler, exits through the distal end of the fibre and illuminates the photosensitive area of a photo diode, where it is converted to an electrical current. Depending on which one of the parameters is allowed to vary the amount of the returning light, one can build a variety of different sensors. Among them are: linear I angular displacement sensors and their derivatives such as pressure or force sensors; transmittance sensors such as turbidity and chemical sensors; reflectance sensors such as temperature sensors, optical encoders and scanners, colourometric and other types of chemical sensors. In the case of the single optic fibre transducer (SOFT) made by Pear/Instruments ( Chicago, II, USA ), the reflective surface is made of a thin metal foil with 6 J..lm thickness and 1.25 mm diameter. Optical fibres are pf the multimode type with 55 J..lm diameter. Their numerical aperture is equal to 0.66. The SOFT head is 1.25 mm in diameter and has an overall length of 50 em. The disposable part of the system contains the head, fibre, protective sheathing and plug. Its operating range is -15 to + 300 mmHg, and + 25 to + 45 °C, and its resolutio n is + I -1 mmHg. Keywords: Fibre optic; transducer
INTRODUCTION With rapid ·advancement in the fields of fibre optic sensing, there is a need for quantitative and qualitative analysis of performance of various types of fibre optic sensors. Computer models can predict behaviour of such sensors with adequate accuracy, thus sparing time and expense on sophisticated equipment needed for such experimentation. MATERIALS AND METHODS The basic principle of a single optical fibre transducer (S OFT) is shown in Figure 1. Light is emitted from the light source (10 ) into the fibre optic coupler spaced some distance from the end of the fibre. A majority of this light travels through the fibre in a forward direction (IF). Light exits the fibre through its distal face in the shape of a cone, and travels through the optical medium until it is reflected back from the reflecting surface. Then, part of this light is reabsorbed back into the fibre (IR ). this returning portion (IR ) traverses the fibre optic coupler, where part of it escapes into the surrounding (IL). The remaining part (Is) leaves the fibre through the proximal end and is absorbed by the photosensor (c.f., Figure 1). The amount of luminous power (in lumens) reabsorbed into the fibre depends on: ( 1) physical properties of optical media (light transmittance etc.); Correspondence and reprint requests to: Dr Alfred Perlin, PH.D, Department of Neurosurgery, College of Medicine, University of Illinois at Chicago, Neuropsychiatric Institute, 912 South Wood Street, chicago, II, 60612, USA. Accepted for publication O ctober 1991.
© 1992 Forefront Publishing Group 0161-6412/ 92/ 010062-07 62
Neurological Research, 1992, Volume 14, March
(2) physical properties of fibre (critical angle CJ.. , etc. ); ( 3) physical properties of reflective surface (reflectivity, et c.); (4) geometry of the opt ical media gap between reflective surface and optical fibre (thickness of the gap (X), cross-section of fibre (a), radius of curvature (p) or reflective su rface, incidence angle (/3 ), etc. COMPUTATIONAL MODEL OF SINGLE OPTIC FIBRE OPTIC TRANSDUCER For the sake of simplicity one can assume: (1) luminous power in any cross section of t he cone of the light is constant; (2 ) there are no secondary reflections ; (3 ) radiant areance (once was called illuminance and its units is w I m 2 ) of the incoming light varies in linear fashion across the illuminated area on the face of the fibre; (4 ) angle of incidence of absorbed light is represented by the angle of the incident ray passing through the center of the illuminated area. For cases where all physical properties of this system are constant, their influences can be represented by a single coefficient (K). The coupling efficiency of sensory head (s ), is a ratio of luminous power of the light
Figure 1:
Basic model of single optical fibre transducer (SOFT)
Single optical fibre transducer fo r pressure measurement: Alfred Perlin
1.00
absorbed into the fibre (after reflection from reflective surface), to luminous power of light exiting the distal end of the fibre. For the case when the mirror surface is perpendicular to the axis of the fibre (/3 = 0), and the only variables are distance X and (p) radius of curvature, the coupling efficiency (e) is given by: e
=
K(1
+ (m ±
0.~
o.ao 0.70
,,,,
0.60
(a)
e(1 ± cos (a ±b)))
''
E
0.50
x (tan a· tan(2b ± a)))- 2
0.40
where
0.30
X
-=m ;
!!_ = e ;
ro
ro
A = [ 1
+ j + (;) Ca~
.
X
Q.20
-=I
p
0.10
a) J
0.00 0.00
(1)
''
\
\ \\ \ ' \ \ ',
\ \ ' ',.... "'.... \ '' ........ \ ', \
Downloaded by [Australian Catholic University] at 08:44 16 August 2017
.66
.87
.....
2.00
1.00
10.00 1.00
-w. l ()
(2)
This formula describes the action of a single fibre linear displacement transducer (SFLDT) as shown in Figure 2. Results from computer simulation of the performance of single fibre linear displacement transducer for various fibres are described in Figure 3. Figure 3 also shows dependence of coupling efficiency (e) and its derivative with respect to relative distance (X /r0 ), when the numerical aperture (NA) is 0.3, 0.5, 0.66 and 0.87. To be able to compare performance of transducer based on single and multifibres arrangements, one has built computational model of multi fibre optical transducer (MFOT). Such a model should be based on the same assumptions as model of SOFT. Figure 4 shows a schematic drawing of the basic (two fibre) MOFT. For MOFT case, coupling efficiency (e) is described by different formulas for each one of the four regions of displacement (X).
f,,
.30 .50
xlr.
Remark : Top sign in equation belongs to case of convex mirror surface. For a flat reflective surface (p -+ oo) and when f3 = 0 this ratio (e) becomes:
+ 2 · m ·tan a)- 2
N.A. • N.A. • N.A. • N.A.•
' '' ',' ' ' ,,.................._----..... .................... ............................ __ _ -----
b = 5/ N[ -1A sin a)
e = K·(1
-------
\,
-
1.00 7.00
:- 1..00
(b)
5.00
)(
~
4.00
v
).()()
w
-------
N.A. • .30 N.A. • .50 N.A. • .66 N.A- .87
2.00 1.00 0.00 0.00
0.50
1.00
xlr. Figure 3: Characteristic of single fibre linear displacement transducer (p = oo, f3 = 0). (a) variation of (e) versus relative displacement X/r0 (b) variation of (de/ dx) versus relative displacement (X,,)
100%
0. X
Figure 4: Basic model of multiple fibre linear displacement transducer (8 = 0 and p = oo )
Region/: Figure 2: General principle of action of single fibre linear displacement transducer with flat reflective surface (p = oo) and angle f3 = 0
0
~
N- 2r X ~ - - - = XcR 2 tan a (3a)
e=O
Neurological Research, 1992, Volume 14, March
63
Single optical fibre transducer for pressure measurement: Allred Perlin
Region If:
+ ,-2)1/2 _
(N2
XcR
r
< X ~ -----2 tan
IX
K
e = --{R2 [2 cos- 1 (8)- sin(2 cos- 1 (8))] 2rcR2
+ ?[cos- 1 (A)- sin(2 cos- 1 (Alll}
(3b)
Region Ill: (N2
+ ,-2 )1/2 -
r
N
------
