## Radiative flux from a planar multiple point source within a cylindrical enclosure reaching a coaxial circular plane

Optics Express, Vol. 15, Issue 7, pp. 3777-3790 (2007)

http://dx.doi.org/10.1364/OE.15.003777

Acrobat PDF (1898 KB)

### Abstract

A general formula and some special integral formulas were presented for calculating radiative fluxes incident on a circular plane from a planar multiple point source within a coaxial cylindrical enclosure perpendicular to the source. These formula were obtained for radiation propagating in a homogeneous isotropic medium assuming that the lateral surface of the enclosure completely absorbs the incident radiation. Exemplary results were computed numerically and illustrated with three-dimensional surface plots. The formulas presented are suitable for determining fluxes of radiation reaching planar circular detectors, collectors or other planar circular elements from systems of laser diodes, light emitting diodes and fiber lamps within cylindrical enclosures, as well as small biological emitters (bacteria, fungi, yeast, etc.) distributed on planar bases of open nontransparent cylindrical containers.

© 2007 Optical Society of America

## 1. Introduction

1. V.P. Gribkovskii, “Injection lasers,” Prog. Quant. Electr. **23**,41–88 (1995). [CrossRef]

3. R. Szweda, “Lasers at the cutting edge,” III-Vs Rev. **12**,28–31 (1999). [CrossRef]

1. V.P. Gribkovskii, “Injection lasers,” Prog. Quant. Electr. **23**,41–88 (1995). [CrossRef]

3. R. Szweda, “Lasers at the cutting edge,” III-Vs Rev. **12**,28–31 (1999). [CrossRef]

8. C. Curachi, A.M. Toboy, D.V. Magalhaes, and V.S. Bagnato, “Hardness evaluation of a dental composite polymerized with experimental LED-based devices,” Dent. Mat. **17**,309–315 (2001). [CrossRef]

9. G. Glickman, B. Byrne, C. Pineda, W.W. Hauck, and G.C. Brainard, “Light therapy for seasonal affective disorder with blue narrow-band light-emitting diodes (LEDs),” Biol. Psych. **59**,502–507 (2006). [CrossRef]

1. V.P. Gribkovskii, “Injection lasers,” Prog. Quant. Electr. **23**,41–88 (1995). [CrossRef]

3. R. Szweda, “Lasers at the cutting edge,” III-Vs Rev. **12**,28–31 (1999). [CrossRef]

2. A.C. Schuerger, C.S. Brown, and E.C. Stryjewski, “Anatomical futures of pepper plants (*Capsicum annuum* L.) grown under red light emitting diodes supplemented with blue or far-red light,” Ann. Botany **79**,273–282 (1997). [CrossRef]

5. O. Monje, G.W. Stutte, G.D. Goins, D.M. Porterfield, and G.E. Bingham, “Farming in space: environmental and biophysical concerns,” Adv. Space. Res. **31**,151–167 (2003). [CrossRef] [PubMed]

8. C. Curachi, A.M. Toboy, D.V. Magalhaes, and V.S. Bagnato, “Hardness evaluation of a dental composite polymerized with experimental LED-based devices,” Dent. Mat. **17**,309–315 (2001). [CrossRef]

9. G. Glickman, B. Byrne, C. Pineda, W.W. Hauck, and G.C. Brainard, “Light therapy for seasonal affective disorder with blue narrow-band light-emitting diodes (LEDs),” Biol. Psych. **59**,502–507 (2006). [CrossRef]

13. A. Mills, “Trends in HB-LED markets,” III-Vs Rev. **14**,38–42 (2001). [CrossRef]

14. C. Gardner, “The use of misuse of coloured light in the urban environment,” Opt. Lasers Tech. **38**,366–376 (2006). [CrossRef]

13. A. Mills, “Trends in HB-LED markets,” III-Vs Rev. **14**,38–42 (2001). [CrossRef]

12. J.M. Gaines, “Modeling of multichip LED packages for illumination,” Lighting Res. Technol. **38**,152–165 (2006). [CrossRef]

## 2. Definition of variables and some fundamental expressions

*ρφz*, was used to obtain the mathematical formulas presented in the paper. The geometry of the analyzed optical system is shown schematically in Fig. 1. Throughout the paper we assume that the multiple point source of the surface, σ, and illuminated circular planar surface,

*S*, are separated by a homogeneous isotropic medium and that the lateral surface of the enclosure completely absorbs the incident radiation so that only the radiation leaving the enclosure through its open end reaches the surface

*S*.

*Φ*

_{σ→S}, enclosed within the spectral region between wavelengths

*λ*

_{min}and

*λ*

_{max}and incident on the surface

*S*from the planar circular coaxial multiple point source of surface σ can be calculated as [17]

*Φ*

_{λ,σ→S}= d

*Φ*

_{σ→S}/ d

*λ*is the spectral radiative flux of wavelength

*λ*from all point emitters given by

*Φ*

_{λ,P→S}(

*ρ*,

_{i}*ϕ*) in the above equation represents the spectral radiative flux at wavelength

_{j}*λ*reaching the plane

*S*from the single point emitter

*P*(

*ρ*,

_{i}*ϕ*) while the symbols

_{j}*N*

_{λ,ρ}and

*N*

_{λ,ϕ}denote the number of point emitters radiating at wavelength

*λ*and positioned at radial distances

*ρ*and horizontal angles

_{i}*ϕ*, respectively.

_{j}*Φ*,

*P*→

*S*(

*ρ*,

_{i}*ϕ*) incident on the surface

_{j}*S*from the single point emitter

*P*(

*ρ*,

_{i}*ϕ*) is described by

_{j}*I*(

_{λ, P}*ρ*,

_{i}*ϕ*,

_{j}*θ*,

*φ*,

*H*,

*α*) denotes the radiant intensity of wavelength

_{λ, at}*λ*at the point where

*P*′(

*ρ*,

_{i}*ϕ*,

_{j}*r*,

*φ*) and d

*ω*

_{P-dS}(

*θ*,

*φ*) is an infinitesimal solid angle subtended at

*P*by the surface element d

*S*′ and is given as follows

*S*′ represents the surface

*S*or its part limited by the rays passing through the upper edge of the cylindrical enclosure. The symbol

*α*denotes the coefficient describing the attenuation of the radiation along the ray between

_{λ, at}*P*(

*ρ*,

_{i}*ϕ*) and

_{j}*P*′(

*ρ*,

_{i}*ϕ*,

_{j}*r*,

*φ*) usually expressed as [16, 17]

*α*and

_{λ, ab}*α*are the absorption and scattering coefficients, respectively. In a homogeneous medium the intensity

_{λ, sc}*I*(

_{λ, P}*ρ*,

_{i}*ϕ*,

_{j}*θ*,

*φ*,

*H*,

*α*) obeys the Bouguer–Lambert exponential law of intensity attenuation [16]

_{λ, at}*I*(

_{λ, P}*ρ*,

_{i}*ϕ*,

_{j}*θ*,

*φ*) is the intensity of radiation emitted by the emitter

*P*(

*ρ*,

_{i}*ϕ*) and

_{j}## 3. The radiative flux reaching the circular plane from the single point emitter within a coaxial cylindrical enclosure

21. S. Tryka, “Angular distribution of the solid angle at a point subtended by a circular disk,” Optics Comm. **137**,317–333 (1997). [CrossRef]

*S*with the radius

*R*and by the top circular edge of the cylindrical enclosure with the radius

*a*, as shown in Fig. 1, we obtain a set of seven double-definite integral expressions:

*h*=

*H*= 0 and

*a*= 0,

*h*≤

*H*and

*a*= 0,

*h*=

*H*= 0 and

*a*> 0,

*h*≤

*H*and

*h*<

*H*and

*h*<

*H*and

*h*≤

*H*and

*R*<

*a*, where the limiting horizontal angles

*γ*and

_{a, ρi}*γ*in Eqs. (9a) and (9b) obey the cosines law of trigonometry as shown in Figs. 2(a) and (b). The angles

_{R, ρi}*γ*

_{2a}and

*γ*

_{2R}in Eqs. (9c) and (9d) are defined similarly to

*γ*and

_{a, ρi}*γ*at

_{R, ρi}*ρ*=

_{i}*a*and

*ρ*=

_{i}*R*, respectively.

*Φ*

_{λ, P→S}(

*ρ*,

_{i}*ϕ*) reaching the planar circular surface

_{j}*S*from a given point emitter

*P*(

*ρ*,

_{i}*ϕ*) within the coaxial cylindrical enclosure perpendicular to the source σ provided that the lateral surface of the enclosure completely absorbs the incident radiation. Putting

_{j}*R*= ∞ in Eqs. (8a)-(8g) and assuming that the radius

*a*, height

*h*and distance

*H*are not infinite, we obtain Eqs. (8a)-(8d) for calculating the total radiative fluxes,

*Φ*

_{λ, σ}(

*ρ*,

_{i}*ϕ*), at wavelength

_{j}*λ*emitted by any point emitter

*P*(

*ρ*,

_{i}*ϕ*) into the space surrounding the cylindrical enclosure.

_{j}*Φ*

_{λ, σ→S}from Eq. (2) for arbitrary distributed point emitters

*P*(

*ρ*,

_{i}*ϕ*) composing the source σ within the cylindrical enclosure if the attenuation coefficient

_{j}*α*of the homogeneous medium is defined and the radiant intensities

_{λ, at}*I*(

_{λ, P}*ρ*,

_{i}*ϕ*,

_{j}*θ*,

*φ*) from each point emitter are known. However the radiative fluxes

*Φ*

_{λ, P→S}(

*ρ*,

_{i}*ϕ*) in Eq. (2) must be calculated at given wavelengths

_{j}*λ*from Eqs. (8a)-(8g). Obviously by substituting Eqs. (8a)-(8d) into (2) at

*R*= ∞ and finite

*a*,

*h*and

*H*, we obtain a formula for calculating the radiative flux,

*Φ*

_{λ, σ}, emitted by the source σ into the space surrounding this source within the enclosure.

*I*(

_{λ, P}*ρ*,

_{i}*ϕ*,

_{j}*θ*,

*φ*) Eqs. (8a)-(8g) can be integrated with respect to the angle

*φ*and expressed by single definite integrals. Even though these equations can be expressed by single definite integrals, further computation of the radiative fluxes

*Φ*

_{λ, σ→S}for large numbers of emitters

*P*(

*ρ*,

_{i}*ϕ*) composing the source σ from general Eq. (2) may be time-consuming and impractical. Therefore, it is desirable to look for a simpler analytical solution to the problem outlined above. We obtain such a solution when the emitters

_{j}*P*(

*ρ*,

_{i}*ϕ*) are spread uniformly and each of them emits identically angularly distributed radiation.

_{j}## 4. Identically radiating emitters of a uniformly spread multiple point source

*N*represents the total number of point emitters radiating at wavelength

_{λ}*λ*and

*P*(

*ρ*,

_{i}*ϕ*) radiating at wavelength

_{j}*λ*.

*P*(

*ρ*,

_{i}*ϕ*) from a uniformly distributed multiple point source we can divide the surface σ into the surface elements

_{j}*π*(

*ρ*

^{2}

_{i}-

*ρ*

^{2}

_{i-1}) containing

*N*(

_{λ}*ρ*) emitters so that

_{i}*m*is the number of elements Δ

*ρ*and

_{i}*a*is the radius of the source σ or radius of the cylindrical enclosure. Then due to the uniform distribution we have

*R*> 0 Eq. (12) obtains the following form

*a*= 0, and

*a*> 0, where

*Φ*

_{λ, P→S}(

*ρ*) is the radiative flux from the point emitter

_{i}*P*(

*ρ*) lying at a distance

_{i}*ρ*. For extremely small elements Δ

_{i}*ρ*→0 we obtain

_{i}*m*→∞ so that Eq. (14) becomes

*a*≤

*h R*/(2

*H*-

*h*) ≤

*R*,

*R*≤

*h R*/(2

*H*-

*h*)≤

*a*≤

*h R*/

*H*,

*h R*/

*H*<

*a*<

*R*,

*R*≤

*a*/2, and

*a*/2 <

*R*<

*a*. The limiting angles

*γ*and

_{a, ρ}*γ*are described by Eqs. (9a)-(9b) without the subscript

_{R, ρ}*i*.

*Φ*

_{λ, σ→S}> from any uniformly distributed multiple point source, provided that each point emitter of this source identically emits angularly distributed radiation with respect to the

*z*-axis. When the number

*N*of point emitters is known it is simple to obtain the total spectral radiative flux

_{λ}*Φ*

_{λ, σ→S}using Eq. (11).

*Φ*

_{λ, σ}>, emitted into the space surrounding the source σ within a cylindrical enclosure is described by Eqs. (13) and (16a) because the remaining Eqs. (16b)-(16e) disappear for

*R*= ∞ and finite values of

*a*,

*h*, and

*H*.

*I*(

_{λ, P}*θ*,

*φ*) not dependent on the horizontal angle

*φ*, as in the case of radiation rotationally symmetrical around

*z*-axis, the inner integrals with respect to the angle

*φ*and distance

*ρ*in Eqs. (16a)-(16e) can be expressed by simple elementary functions and we obtain single integral solutions to Eq. (12). In the following two subsections, we present such solutions for radiation not dependent on the angle

*φ*and then for isotropic radiation.

### 4.1 Rotationally symmetrical radiation with respect to the z-axis

*I*(

_{λ, P}*θ*,

*φ*) not dependent on the horizontal angle

*φ*we have

*I*(

_{λ, P}*θ*,

*φ*) =

*I*(

_{λ, P}*θ*) and Eqs. (13) and (16a)-(16e) simplify to

*a*= 0,

*a*≤

*h R*/(2

*H*-

*h*) ≤

*R*,

*R*≤

*h R*/(2

*H*-

*h*) ≤

*a*≤

*h R*/

*H*,

*h R*/

*H*<

*a*<

*R*,

*R*<

*a*, where

*Φ*

_{λ, σ→S}> if the radiant intensity

*I*(

_{λ, P}*θ*) is defined. Figures 3(a)–3(d) demonstrate four examples of such calculations obtained for the point emitters of the source σ emitting rotationally symmetrical radiation around

*z*-axis and when the radiant intensity is given by the expression

*I*(

_{λ, P}*θ*) =

*I*cos

_{λ, P}^{2}

*θ*. The data plotted in Figs. 3(a) and 3(c) were computed for nonattenuated radiation while the data shown in Figs. 3(b) and 3(d) were calculated for radiation attenuated within a homogeneous isotropic medium.

*Φ*

_{λ, σ→S}> in a non-attenuating medium is always greater at the lower distance

*H*and clearly depends on both radii

*R*and

*a*. The flux <

*Φ*

_{λ, σ→S}> shown in Fig. 3(a) increases with increased

*R*and obtains maximal value at a small distance

*H*in the region limited by the relation

*R*>

*a*. In Fig. 3(c) we observe that at a given distance

*H*the flux <

*Φ*

_{λ, σ→S}> monotonically increases with increasing

*a*until

*a*≤

*R*. Then the flux <

*Φ*

_{λ, σ→S}> monotonically decreases.

*Φ*

_{λ, σ→S}> of the radiation propagated in an attenuated homogeneous medium is dependent on the radii

*R*,

*a*, and distance

*H*, similarly to the flux <

*Φ*

_{λ, σ→S}> propagated in an non-attenuating medium. However, it is clearly seen that the fluxes <

*Φ*

_{λ, σ→S}> in Figs. 3(b) and 3(d) are lower in comparison to those presented in Figs. 3(a) and 3(c) and this effect is due to the attenuation phenomena described by Eq. (6).

*I*(

_{λ, P}*θ*) =

*I*

_{λ, 0}cos

*θ*were similar to the plots in Figs. 3(a)-3(d) although the fluxes <

*Φ*

_{λ, σ→S}> were varied within the wider ranges of the spectral power obtaining maximal values of 1.200 W nm

^{-1}and 0.657 W nm

^{-1}at

*I*

_{λ, 0}= 1 W sr

^{-1}within wavelength interval Δ

*λ*= 1 nm in a non-attenuating and attenuating medium respectively. Therefore from these data, it is easy to deduce that the fluxes <

*Φ*

_{λ, σ→S}> reaching the surface

*S*clearly depend on the angular distribution of the emitted radiation.

*Φ*

_{λ, σ→S}> computed for

*I*(

_{λ, P}*θ*) =

*I*

_{λ, 0}cos

^{2}

*θ*and

*I*(

_{λ, P}*θ*) =

*I*

_{λ, 0}cos

*θ*with accuracy to twelve decimal places when the radii

*R*and

*a*, and height

*H*were expressed in m and when the attenuation coefficient

*α*was expressed in m

_{at}^{-1}are given in the fifth and sixth column of Table 1 in Appendix A. All these data were computed from Eqs. (17a)-(17e) for the radiant intensity

*I*

_{λ, 0}= 1 W∙sr

^{-1}. Therefore one can use the data from Table 1 for checking one’s own calculations from the formulas presented above.

### 4.2 Isotropic radiation

*I*(

_{λ, P}*θ*) does not depend on the angle

*θ*so that

*I*(

_{λ, P}*θ*) =

*I*

_{λ, 0}and Eqs. (17a)-(17e) become

*a*= 0,

*a*≤

*h R*/(2

*H*-

*h*) ≤

*R*,

*R*≤

*h R*/(2

*H*-

*h*) ≤

*a*≤

*h R*/

*H*,

*h R*/

*H*<

*a*<

*R*, and

*R*<

*a*.

*I*(

_{λ, P}*θ*) =

*I*

_{λ, 0}were illustrated identically as the surface-plots in Figs. 3(a)-3(d) for comparison. From these plots we observe that the fluxes <

*Φ*

_{λ, σ→S}> of isotropic radiation at

*I*

_{λ, 0}= 1 W sr

^{-1}and within wavelength interval Δ

*λ*= 1 nm attain significantly higher values than in Figs. 3(a)-(d) and in case of

*I*(

_{λ, P}*θ*) =

*I*

_{λ, 0}cos

*θ*although the plotted dependencies look similar.

*Φ*

_{λ, σ→S}> of isotropic radiation at some radii

*R*,

*a*, height

*H*, and coefficient

*α*are presented in the seventh column of Table 1 in Appendix A. Here it can indeed seen that these data are higher than those obtained for the radiant intensities

_{at}*I*(

_{λ, P}*θ*) =

*I*

_{λ, 0}cos

*θ*and

*I*(

_{λ, P}*θ*) =

*I*

_{λ, 0}cos

^{2}

*θ*.

#### 4.2.1 Isotropic radiation in non-attenuating medium

*τ*

_{P′}(

*θ*,

*H*,

*α*) = 1 and the flux <

_{λ, at}*Φ*

_{λ, σ→S}> at

*a*= 0 is given by Eq. (18a), rewritten here for convenience,

*a*> 0 from Eqs. (18b)-(18e) we obtain

*a*≤

*h R*/(2

*H*-

*h*) ≤

*R*,

*R*≤

*h R*/(2

*H*-

*h*) ≤

*a*≤

*h R*/

*H*,

*h R*/

*H*<

*a*<

*R*, and

*R*<

*a*.

## 5. Conclusions

15. A. Zukauskas, R. Vaicekauskas, F. Ivanauskas, R. Gaska, and M.S. Shur, “Optimization of white polychromic semiconductors lamps,” Appl. Phys. Lett. **80**,234–236 (2002). [CrossRef]

*Φ*

_{λ, σ→S}>. Examples of numerical computations were presented in Figs. 3(a)-3(d) for the radiant intensity function

*I*(

*θ*) =

*I*

_{0}cos

^{2}

*θ*

_{1}. From these plots, one can see that the flux <

*Φ*

_{λ, σ→S}> decreases generally with increased distance

*H*and decreased radii

*a*and

*R*. A similar dependencies were also observed for the fluxes <

*Φ*

_{λ, σ→S}> calculated for the radiant intensities

*I*(

*θ*) =

*I*

_{0}cos

*θ*

_{1}and

*I*(

*θ*) =

*I*

_{0}. All these dependencies clearly indicate geometrical conditions at which the grater fluxes <

*Φ*

_{λ, σ→S}> reach the plane

*S*. Such conditions are particularly important when extremely weak intensity radiation is measured. Therefore Eqs. (8a)-(8g), (17a)-(17e), (18a)-(18e) and (19a)-(19e) are particularly valuable for optimizing the geometry of the optical system shown schematically in Fig. 1. Additionally, some computed representative data are presented in Appendix A.

## Appendix A

*Φ*

_{λ, σ→S}> computed with accuracy to twelve decimal places by Mathematica 2.2.3 [23] from programmed Eqs. (16a)-(16e), (17a)-(17e), and (18a)-(18e), respectively.

## References and Links

1. | V.P. Gribkovskii, “Injection lasers,” Prog. Quant. Electr. |

2. | A.C. Schuerger, C.S. Brown, and E.C. Stryjewski, “Anatomical futures of pepper plants ( |

3. | R. Szweda, “Lasers at the cutting edge,” III-Vs Rev. |

4. | L. Botter-Jensen, E. Bulur, G.A.T. Duller, and A.S. Murray, “Advances in luminescence instrument systems,” Radiat. Meas. |

5. | O. Monje, G.W. Stutte, G.D. Goins, D.M. Porterfield, and G.E. Bingham, “Farming in space: environmental and biophysical concerns,” Adv. Space. Res. |

6. | K.T. Lau, W.S. Yerazunis, R.L. Shepherd, and D. Diamond, “Quantitative colorimetric analysis of dye mixtures using an optical photometer based on LED array,” Sens. Actuators B-Chem. |

7. | S. Nakamura, S. Pearton, and G. Fasol, |

8. | C. Curachi, A.M. Toboy, D.V. Magalhaes, and V.S. Bagnato, “Hardness evaluation of a dental composite polymerized with experimental LED-based devices,” Dent. Mat. |

9. | G. Glickman, B. Byrne, C. Pineda, W.W. Hauck, and G.C. Brainard, “Light therapy for seasonal affective disorder with blue narrow-band light-emitting diodes (LEDs),” Biol. Psych. |

10. | A. Juzeniene, P. Juzenas, L.-W. Ma, V. Iani, and J. Moan, “Effectiveness of different light sources for 5-aminolevolinic acid photodynamic therapy,” Lasers Med. Sci. |

11. | B. Link, S. Ruhl, A. Peters, A. Junemann, and F.K. Horn, “Pattern reversal ERG and VEP - comparison of stimulation by LED, monitor and a Maxwellian-view system,” Doc. Opthalmol. |

12. | J.M. Gaines, “Modeling of multichip LED packages for illumination,” Lighting Res. Technol. |

13. | A. Mills, “Trends in HB-LED markets,” III-Vs Rev. |

14. | C. Gardner, “The use of misuse of coloured light in the urban environment,” Opt. Lasers Tech. |

15. | A. Zukauskas, R. Vaicekauskas, F. Ivanauskas, R. Gaska, and M.S. Shur, “Optimization of white polychromic semiconductors lamps,” Appl. Phys. Lett. |

16. | F Grum and R.J. Becherer, |

17. | M. Strojnik and G Paez, “Radiometry” in |

18. | E. Sparrow and R. Cess, |

19. | D.H. Sliney, “Laser effect on vision and ocular exposure limit,” App. Occup. Environ. Hyg. |

20. | T.R. Fry, “Laser safety,” Vet. Clin. Small Anim. |

21. | S. Tryka, “Angular distribution of the solid angle at a point subtended by a circular disk,” Optics Comm. |

22. | S. Tryka, “Angular distribution of an average solid angle subtended by a circular disc from multiple points uniformly distributed on planar circular surface coaxial to the disc,” J. Mod. Opt. |

23. | S. Wolfram, |

**OCIS Codes**

(080.2720) Geometric optics : Mathematical methods (general)

(120.5240) Instrumentation, measurement, and metrology : Photometry

(120.5630) Instrumentation, measurement, and metrology : Radiometry

(230.6080) Optical devices : Sources

(350.5610) Other areas of optics : Radiation

**History**

Original Manuscript: September 29, 2006

Revised Manuscript: February 16, 2007

Manuscript Accepted: March 1, 2007

Published: April 2, 2007

**Virtual Issues**

Vol. 2, Iss. 5 *Virtual Journal for Biomedical Optics*

**Citation**

Stanislaw Tryka, "Radiative flux from a planar multiple point source within a cylindrical enclosure reaching a coaxial circular plane," Opt. Express **15**, 3777-3790 (2007)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-15-7-3777

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### References

- V. P. Gribkovskii, "Injection lasers," Prog. Quant. Electr. 23, 41-88 (1995). [CrossRef]
- A.C. Schuerger, C.S. Brown and E.C. Stryjewski, "Anatomical futures of pepper plants (Capsicum annuum L.) grown under red light emitting diodes supplemented with blue or far-red light," Ann. Botany 79, 273-282 (1997). [CrossRef]
- R. Szweda, "Lasers at the cutting edge," III-Vs Rev. 12, 28-31 (1999). [CrossRef]
- L. Botter-Jensen, E. Bulur, G. A. T. Duller and A. S. Murray, "Advances in luminescence instrument systems," Radiat. Meas. 32, 523-528 (2000). [CrossRef]
- O. Monje, G. W. Stutte, G. D. Goins, D. M. Porterfield and G. E. Bingham, "Farming in space: environmental and biophysical concerns," Adv. Space. Res. 31, 151-167 (2003). [CrossRef] [PubMed]
- K. T. Lau, W. S. Yerazunis, R. L. Shepherd and D. Diamond, "Quantitative colorimetric analysis of dye mixtures using an optical photometer based on LED array," Sens. Actuators B-Chem. 114, 819-825 (2006). [CrossRef]
- S. Nakamura, S. Pearton and G. Fasol, The blue laser diode: The complete story (Springer-Verlag, Berlin, 2000).
- C. Curachi, A. M. Toboy, D. V. Magalhaes and V.S . Bagnato, "Hardness evaluation of a dental composite polymerized with experimental LED-based devices," Dent. Mat. 17, 309-315 (2001). [CrossRef]
- G. Glickman, B. Byrne, C. Pineda, W. W. Hauck and G. C. Brainard, "Light therapy for seasonal affective disorder with blue narrow-band light-emitting diodes (LEDs)," Biol. Psych. 59, 502-507 (2006). [CrossRef]
- A. Juzeniene, P. Juzenas, L.-W. Ma, V. Iani and J. Moan, "Effectiveness of different light sources for 5-aminolevolinic acid photodynamic therapy," Lasers Med. Sci. 19, 139-149 (2004). [CrossRef] [PubMed]
- B. Link, S. Ruhl, A. Peters, A. Junemann and F. K. Horn, "Pattern reversal ERG and VEP - comparison of stimulation by LED, monitor and a Maxwellian-view system," Doc. Opthalmol. 12,1-11 (2006). [CrossRef]
- J. M. Gaines, "Modeling of multichip LED packages for illumination," Lighting Res. Technol. 38, 152-165 (2006). [CrossRef]
- A. Mills, "Trends in HB-LED markets," III-Vs Rev. 14, 38-42 (2001). [CrossRef]
- C. Gardner, "The use of misuse of coloured light in the urban environment," Opt. Lasers Tech. 38, 366-376 (2006). [CrossRef]
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