Abstract

Radiation dose measurements based on scintillator detection are conveniently made by coupling the light from the scintillator into an optical fiber. The low light levels involved typically require sensitive photodetectors, so it is advantageous to increase the available signal by optimizing the optical coupling efficiency between the scintillator and optical fiber. We model thisprocess using geometric optics and finite-element ray tracing to determine the features that maximize the amount of light coupled to an optical fiber from a cylindrical scintillator. We also address whether the coupling can be improved by using an intermediate optical element such as a lens, and we provide a means for calculating its required optical properties for a given geometry.

© 2007 Optical Society of America

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References

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  1. J. Van Dam and G. Marinello, ESTRO Booklet 1: Methods for in vivo Dosimetry in External Radiotherapy (ESTRO and Garant Publishers, 1994).
  2. American Association of Physicists in Medicine Task Group 62, "Diode in-vivo dosimetry for patients receiving external beam radiation therapy," Rep. 87 (Medical Physics Publishing, Madison, Wisc., 2005).
  3. A. S. Beddar, T. R. Mackie, and F. H. Attix, "Water-equivalent plastic scintillation detectors for high-energy beam dosimetry. I. Physical characteristics and theoretical considerations," Phys. Med. Biol. 37, 1883-1900 (1992).
    [CrossRef] [PubMed]
  4. A. S. Beddar, T. R. Mackie, and F. H. Attix, "Water-equivalent plastic scintillation detectors for high-energy beam dosimetry. II. Properties and measurements," Phys. Med. Biol. 37, 1901-1913 (1992).
    [CrossRef] [PubMed]
  5. J. M. Fontbonne, G. Iltis, G. Ban, A. Battala, J. C. Vernhes, J. Tillier, N. Bellaize, C. Le Brun, B. Tamain, K. Mercier, and J. C. Motin, "Scintillating fiber dosimeter for radiation therapy accelerator," IEEE Trans. Nucl. Sci. 49, 2223-2227 (2002).
    [CrossRef]
  6. S. L. Law, N. Suchowerska, S. C. Fleming, A. S. Beddar, and D. R. McKenzie, "Signal versus noise in fiber coupled radiation dosimeters for medical applications," in Optical Fibers and Sensors for Medical Applications IV, I.Gannot, ed., Proc. SPIE 5317, 105-115 (2004).
  7. S. H. Law, S. C. Fleming, D. R. McKenzie, and N. Suchowerska, "Optical fiber design and the trapping of Cerenkov radiation," Appl. Opt. 45, 9151-9159 (2006).

2002

J. M. Fontbonne, G. Iltis, G. Ban, A. Battala, J. C. Vernhes, J. Tillier, N. Bellaize, C. Le Brun, B. Tamain, K. Mercier, and J. C. Motin, "Scintillating fiber dosimeter for radiation therapy accelerator," IEEE Trans. Nucl. Sci. 49, 2223-2227 (2002).
[CrossRef]

1992

A. S. Beddar, T. R. Mackie, and F. H. Attix, "Water-equivalent plastic scintillation detectors for high-energy beam dosimetry. I. Physical characteristics and theoretical considerations," Phys. Med. Biol. 37, 1883-1900 (1992).
[CrossRef] [PubMed]

A. S. Beddar, T. R. Mackie, and F. H. Attix, "Water-equivalent plastic scintillation detectors for high-energy beam dosimetry. II. Properties and measurements," Phys. Med. Biol. 37, 1901-1913 (1992).
[CrossRef] [PubMed]

Attix, F. H.

A. S. Beddar, T. R. Mackie, and F. H. Attix, "Water-equivalent plastic scintillation detectors for high-energy beam dosimetry. I. Physical characteristics and theoretical considerations," Phys. Med. Biol. 37, 1883-1900 (1992).
[CrossRef] [PubMed]

A. S. Beddar, T. R. Mackie, and F. H. Attix, "Water-equivalent plastic scintillation detectors for high-energy beam dosimetry. II. Properties and measurements," Phys. Med. Biol. 37, 1901-1913 (1992).
[CrossRef] [PubMed]

Ban, G.

J. M. Fontbonne, G. Iltis, G. Ban, A. Battala, J. C. Vernhes, J. Tillier, N. Bellaize, C. Le Brun, B. Tamain, K. Mercier, and J. C. Motin, "Scintillating fiber dosimeter for radiation therapy accelerator," IEEE Trans. Nucl. Sci. 49, 2223-2227 (2002).
[CrossRef]

Battala, A.

J. M. Fontbonne, G. Iltis, G. Ban, A. Battala, J. C. Vernhes, J. Tillier, N. Bellaize, C. Le Brun, B. Tamain, K. Mercier, and J. C. Motin, "Scintillating fiber dosimeter for radiation therapy accelerator," IEEE Trans. Nucl. Sci. 49, 2223-2227 (2002).
[CrossRef]

Beddar, A. S.

A. S. Beddar, T. R. Mackie, and F. H. Attix, "Water-equivalent plastic scintillation detectors for high-energy beam dosimetry. II. Properties and measurements," Phys. Med. Biol. 37, 1901-1913 (1992).
[CrossRef] [PubMed]

A. S. Beddar, T. R. Mackie, and F. H. Attix, "Water-equivalent plastic scintillation detectors for high-energy beam dosimetry. I. Physical characteristics and theoretical considerations," Phys. Med. Biol. 37, 1883-1900 (1992).
[CrossRef] [PubMed]

S. L. Law, N. Suchowerska, S. C. Fleming, A. S. Beddar, and D. R. McKenzie, "Signal versus noise in fiber coupled radiation dosimeters for medical applications," in Optical Fibers and Sensors for Medical Applications IV, I.Gannot, ed., Proc. SPIE 5317, 105-115 (2004).

Bellaize, N.

J. M. Fontbonne, G. Iltis, G. Ban, A. Battala, J. C. Vernhes, J. Tillier, N. Bellaize, C. Le Brun, B. Tamain, K. Mercier, and J. C. Motin, "Scintillating fiber dosimeter for radiation therapy accelerator," IEEE Trans. Nucl. Sci. 49, 2223-2227 (2002).
[CrossRef]

Fleming, S. C.

S. L. Law, N. Suchowerska, S. C. Fleming, A. S. Beddar, and D. R. McKenzie, "Signal versus noise in fiber coupled radiation dosimeters for medical applications," in Optical Fibers and Sensors for Medical Applications IV, I.Gannot, ed., Proc. SPIE 5317, 105-115 (2004).

S. H. Law, S. C. Fleming, D. R. McKenzie, and N. Suchowerska, "Optical fiber design and the trapping of Cerenkov radiation," Appl. Opt. 45, 9151-9159 (2006).

Fontbonne, J. M.

J. M. Fontbonne, G. Iltis, G. Ban, A. Battala, J. C. Vernhes, J. Tillier, N. Bellaize, C. Le Brun, B. Tamain, K. Mercier, and J. C. Motin, "Scintillating fiber dosimeter for radiation therapy accelerator," IEEE Trans. Nucl. Sci. 49, 2223-2227 (2002).
[CrossRef]

Iltis, G.

J. M. Fontbonne, G. Iltis, G. Ban, A. Battala, J. C. Vernhes, J. Tillier, N. Bellaize, C. Le Brun, B. Tamain, K. Mercier, and J. C. Motin, "Scintillating fiber dosimeter for radiation therapy accelerator," IEEE Trans. Nucl. Sci. 49, 2223-2227 (2002).
[CrossRef]

Law, S. H.

S. H. Law, S. C. Fleming, D. R. McKenzie, and N. Suchowerska, "Optical fiber design and the trapping of Cerenkov radiation," Appl. Opt. 45, 9151-9159 (2006).

Law, S. L.

S. L. Law, N. Suchowerska, S. C. Fleming, A. S. Beddar, and D. R. McKenzie, "Signal versus noise in fiber coupled radiation dosimeters for medical applications," in Optical Fibers and Sensors for Medical Applications IV, I.Gannot, ed., Proc. SPIE 5317, 105-115 (2004).

Le Brun, C.

J. M. Fontbonne, G. Iltis, G. Ban, A. Battala, J. C. Vernhes, J. Tillier, N. Bellaize, C. Le Brun, B. Tamain, K. Mercier, and J. C. Motin, "Scintillating fiber dosimeter for radiation therapy accelerator," IEEE Trans. Nucl. Sci. 49, 2223-2227 (2002).
[CrossRef]

Mackie, T. R.

A. S. Beddar, T. R. Mackie, and F. H. Attix, "Water-equivalent plastic scintillation detectors for high-energy beam dosimetry. II. Properties and measurements," Phys. Med. Biol. 37, 1901-1913 (1992).
[CrossRef] [PubMed]

A. S. Beddar, T. R. Mackie, and F. H. Attix, "Water-equivalent plastic scintillation detectors for high-energy beam dosimetry. I. Physical characteristics and theoretical considerations," Phys. Med. Biol. 37, 1883-1900 (1992).
[CrossRef] [PubMed]

Marinello, G.

J. Van Dam and G. Marinello, ESTRO Booklet 1: Methods for in vivo Dosimetry in External Radiotherapy (ESTRO and Garant Publishers, 1994).

McKenzie, D. R.

S. H. Law, S. C. Fleming, D. R. McKenzie, and N. Suchowerska, "Optical fiber design and the trapping of Cerenkov radiation," Appl. Opt. 45, 9151-9159 (2006).

S. L. Law, N. Suchowerska, S. C. Fleming, A. S. Beddar, and D. R. McKenzie, "Signal versus noise in fiber coupled radiation dosimeters for medical applications," in Optical Fibers and Sensors for Medical Applications IV, I.Gannot, ed., Proc. SPIE 5317, 105-115 (2004).

Mercier, K.

J. M. Fontbonne, G. Iltis, G. Ban, A. Battala, J. C. Vernhes, J. Tillier, N. Bellaize, C. Le Brun, B. Tamain, K. Mercier, and J. C. Motin, "Scintillating fiber dosimeter for radiation therapy accelerator," IEEE Trans. Nucl. Sci. 49, 2223-2227 (2002).
[CrossRef]

Motin, J. C.

J. M. Fontbonne, G. Iltis, G. Ban, A. Battala, J. C. Vernhes, J. Tillier, N. Bellaize, C. Le Brun, B. Tamain, K. Mercier, and J. C. Motin, "Scintillating fiber dosimeter for radiation therapy accelerator," IEEE Trans. Nucl. Sci. 49, 2223-2227 (2002).
[CrossRef]

Suchowerska, N.

S. L. Law, N. Suchowerska, S. C. Fleming, A. S. Beddar, and D. R. McKenzie, "Signal versus noise in fiber coupled radiation dosimeters for medical applications," in Optical Fibers and Sensors for Medical Applications IV, I.Gannot, ed., Proc. SPIE 5317, 105-115 (2004).

S. H. Law, S. C. Fleming, D. R. McKenzie, and N. Suchowerska, "Optical fiber design and the trapping of Cerenkov radiation," Appl. Opt. 45, 9151-9159 (2006).

Tamain, B.

J. M. Fontbonne, G. Iltis, G. Ban, A. Battala, J. C. Vernhes, J. Tillier, N. Bellaize, C. Le Brun, B. Tamain, K. Mercier, and J. C. Motin, "Scintillating fiber dosimeter for radiation therapy accelerator," IEEE Trans. Nucl. Sci. 49, 2223-2227 (2002).
[CrossRef]

Tillier, J.

J. M. Fontbonne, G. Iltis, G. Ban, A. Battala, J. C. Vernhes, J. Tillier, N. Bellaize, C. Le Brun, B. Tamain, K. Mercier, and J. C. Motin, "Scintillating fiber dosimeter for radiation therapy accelerator," IEEE Trans. Nucl. Sci. 49, 2223-2227 (2002).
[CrossRef]

Van Dam, J.

J. Van Dam and G. Marinello, ESTRO Booklet 1: Methods for in vivo Dosimetry in External Radiotherapy (ESTRO and Garant Publishers, 1994).

Vernhes, J. C.

J. M. Fontbonne, G. Iltis, G. Ban, A. Battala, J. C. Vernhes, J. Tillier, N. Bellaize, C. Le Brun, B. Tamain, K. Mercier, and J. C. Motin, "Scintillating fiber dosimeter for radiation therapy accelerator," IEEE Trans. Nucl. Sci. 49, 2223-2227 (2002).
[CrossRef]

IEEE Trans. Nucl. Sci.

J. M. Fontbonne, G. Iltis, G. Ban, A. Battala, J. C. Vernhes, J. Tillier, N. Bellaize, C. Le Brun, B. Tamain, K. Mercier, and J. C. Motin, "Scintillating fiber dosimeter for radiation therapy accelerator," IEEE Trans. Nucl. Sci. 49, 2223-2227 (2002).
[CrossRef]

Phys. Med. Biol.

A. S. Beddar, T. R. Mackie, and F. H. Attix, "Water-equivalent plastic scintillation detectors for high-energy beam dosimetry. I. Physical characteristics and theoretical considerations," Phys. Med. Biol. 37, 1883-1900 (1992).
[CrossRef] [PubMed]

A. S. Beddar, T. R. Mackie, and F. H. Attix, "Water-equivalent plastic scintillation detectors for high-energy beam dosimetry. II. Properties and measurements," Phys. Med. Biol. 37, 1901-1913 (1992).
[CrossRef] [PubMed]

Other

J. Van Dam and G. Marinello, ESTRO Booklet 1: Methods for in vivo Dosimetry in External Radiotherapy (ESTRO and Garant Publishers, 1994).

American Association of Physicists in Medicine Task Group 62, "Diode in-vivo dosimetry for patients receiving external beam radiation therapy," Rep. 87 (Medical Physics Publishing, Madison, Wisc., 2005).

S. L. Law, N. Suchowerska, S. C. Fleming, A. S. Beddar, and D. R. McKenzie, "Signal versus noise in fiber coupled radiation dosimeters for medical applications," in Optical Fibers and Sensors for Medical Applications IV, I.Gannot, ed., Proc. SPIE 5317, 105-115 (2004).

S. H. Law, S. C. Fleming, D. R. McKenzie, and N. Suchowerska, "Optical fiber design and the trapping of Cerenkov radiation," Appl. Opt. 45, 9151-9159 (2006).

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Figures (13)

Fig. 1
Fig. 1

Scintillator butt-coupled to an optical fiber showing the key variables. D S is the diameter of the cylindrical scintillator, L is its length, and D F is the diameter of the optical fiber's core. n a and n b are the refractive indices of the scintillator material and its cladding where this is used. n A and n B are the refractive indices of the core of the optical fiber and its cladding.

Fig. 2
Fig. 2

Critical angles θ S and θ F in the scintillator and fiber, respectively. θ is the projection of θ F into the scintillator.

Fig. 3
Fig. 3

Nomenclature used in the analytical model for the case where the fiber has a small diameter and is located on the axis of the scintillator. A slice of scintillator is shown located at a distance from the fiber of less than the distance Z to the intersection point of the projection of the acceptance angle of the scintillator with the scintillator boundary.

Fig. 4
Fig. 4

Calculated total power coupled from a scintillator to an optical fiber using the analytical model of Eqs. (3) and (4). The horizontal dashed line is the asymptotic power corresponding to an infinitely long scintillator according to Eq. (5). The vertical dashed line is at z = R / tan θ marking the transition from linear dependence. The contribution from wall reflections is not included. The units of coupled power are watts per watt of energy emitted per unit volume.

Fig. 5
Fig. 5

Mesh used to divide the scintillator into volume elements.

Fig. 6
Fig. 6

Use of concentric virtual fiber “rings” conceptually simplifies the geometry for describing internal reflections of light generated within the scintillator. Reflections are replaced by direct paths within scintillator material to the virtual fiber ring pattern.

Fig. 7
Fig. 7

Geometry for analyzing scintillator internal reflections, defining points, lengths, and angles used in the derivation.

Fig. 8
Fig. 8

Fiber acceptance patterns for the locus of the direct and the first three reflected rays as seen by points (a) 0   mm , (b) 0 .4   mm , (c) 0 .5   mm , and (d) 0 .7   mm from the scintillator axis. In all cases, the scintillator diameter is 1 mm and the fiber diameter is 0 .5   mm .

Fig. 9
Fig. 9

Comparison between the analytical (solid curve) and finite-element (circles) models under identical conditions (a small fiber diameter relative to scintillator diameter and no wall reflections). The dashed line is the result of the numerical model under the same conditions when the contribution from wall reflections is included.

Fig. 10
Fig. 10

Experimental setup to assess the predicted linear dependence of coupled optical power with scintillator length.

Fig. 11
Fig. 11

Experimental measurement of coupled power versus scintillator length for a 1   mm anthracene-doped PVT fiber butt-coupled to a 1   mm PMMA fiber. The linear result is in agreement with the theory developed in this paper.

Fig. 12
Fig. 12

(a) Dosimeter showing the fiber acceptance cone. The addition of a lens as shown in (b) will result in a change in the numerical aperture and magnification of the optical fiber. The result is equivalent to the system shown in (c) having a larger diameter optical fiber with a reduced numerical aperture.

Fig. 13
Fig. 13

Coupled power as a function of lens-modified fiber acceptance angle for fiber diameters (a) 1%, (b) 10%, (c) 50%, and (d) 100% of the scintillator diameter. The vertical line is drawn at the acceptance angle of a butt-coupled fiber with no lens with parameters listed in Table 1.

Tables (1)

Tables Icon

Table 1 Typical Parameters for a Scintillator Coupled to a Small-Diameter Polymer Optical Fiber

Equations (18)

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sin θ F = n A 2 n B 2 n A .
sin θ = n A 2 n B 2 n a .
d P ( r , z ) = 2 π r d r I 0 d z d A cos ϕ 4 π ( r 2 + z 2 ) ,
d P ( z ) = 0 R d P ( r , z ) d r = d A 2 I 0 d z ( 1 z R 2 + z 2 ) .
P 1 = 0 L P ( z ) d z = L I 0 d A 2 ( 1 cos θ ) .
P 2 = R S / tan θ L d P ( z ) d z
= I 0 d A 2 ( L R S 2 + L 2 R S tan θ + R S sin θ ) .
P 2 ( L ) = I 0 d A 2 R S sin θ ( 1 cos θ ) .
a ( ψ ) = r cos ψ + 2 r 2 cos 2 ψ 2 ( r 2 R S 2 ) .
c i ( ψ ) = r cos ψ + 2 r 2 cos 2 ψ 2 ( r 2 R F 2 ) .
c ( ψ ) = 2 r cos ψ ,
c o ( ψ ) = c + c i .
H i ( ψ ) = 2 a c i ,
H o ( ψ ) = 2 a + c o .
H i ( ψ ) = k ( 2 a + c ) c o ,
H o ( ψ ) = k ( 2 a + c ) + c i .
n a d f sin θ = n a d f sin θ .
d f = n a d f sin θ n A sin θ .

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