Abstract

A method for achieving optimal design of a wide-angle narrow-bandpass optical detection system composed of a spherical interference filter and a circular photodetector is introduced. It was found that there is an optimal photodetector diameter that maximizes the signal-to-noise ratio (SNR) for a given filter configuration. We show how to optimize optical detection systems based on spherical interference filters for all the important parameters simultaneously. The SNR values of these systems are compared with the SNR values of spherical-step-filter-based detection systems. When large silicon photodetectors are used, the two systems have equal SNR values so that the more economical step-filter systems are preferable. The results given here in the near-infrared region can be used for the optimization of any configuration of a detection system based on a spherical interference filter and a silicon photodetector working at the same wavelength range, without further calculations.

© 2000 Optical Society of America

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References

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  1. J. M. Kahn, J. R. Barry, M. D. Audeh, J. B. Carruthers, W. J. Krause, G. W. Marsh, “Non-directed infrared links for high-capacity wireless LANs,” IEEE Pers. Commun. Mag. 1(2), 12–25 (Second Quarter, 1994).
  2. B. N. Brixner, “Wide angle optical system having a telecentric stop and an interference filter,” U.S. patent3,278,752 (11October1966).
  3. A. Grossman, “Wide angle narrow bandpass optical filter system,” U.S. patent4,184,749 (22January1980).
  4. J. W. Howard, D. M. Reilly, “Multi-element spectral filter with curved interior surfaces,” U.S. patent4,554,447 (19November1985).
  5. J. Merchang, “Lens-sphere optical sensing system,” U.S. patent4,935,630 (19June1990).
  6. W. J. Gunning, “Narrow-band wide field-of-view filter study, Rockwell International Science Center,” (Rockwell International, Thousand Oaks, Calif., 1982).
  7. L. Chen, L. S. Alvarez, B. Yin, T. M. Shay, “High-sensitivity direct detection optical communication system that operates in sunlight,” in Free-Space Laser Communication Technologies VI, G. Mecherle, ed., Proc. SPIE2123, 448–454 (1994).
    [CrossRef]
  8. J. R. Barry, Wireless Infrared Communications (Kluwer Academic, Boston, 1994), Chap. 2.
  9. T. Verker, N. Schweitzer, J. Broder, N. Eisenberg, “Construction of a detection system with a wide field-of-view,” in 10th Meeting on Optical Engineering in Israel, I. Shladov, S. R. Rotman, eds., Proc. SPIE3110, 616–621 (1997).
  10. L. Levi, Applied Optics: A Guide to Optical System Design (Wiley, New York,1980), Vol. 2, p. 51.
  11. Oriel Catalog of Optics and Filters (Oriel Corporation, Stratford, Conn., 1984), Vol. 3, p. 19.
  12. “Standard tables for terrestrial solar spectral irradiance air mass 1.5 for a 37° tilted surface,” in ASTM Standards, Designation E892–87 (American Society for Testing and Materials, Philadelphia, 1987), pp. 477–484.

1994

J. M. Kahn, J. R. Barry, M. D. Audeh, J. B. Carruthers, W. J. Krause, G. W. Marsh, “Non-directed infrared links for high-capacity wireless LANs,” IEEE Pers. Commun. Mag. 1(2), 12–25 (Second Quarter, 1994).

Alvarez, L. S.

L. Chen, L. S. Alvarez, B. Yin, T. M. Shay, “High-sensitivity direct detection optical communication system that operates in sunlight,” in Free-Space Laser Communication Technologies VI, G. Mecherle, ed., Proc. SPIE2123, 448–454 (1994).
[CrossRef]

Audeh, M. D.

J. M. Kahn, J. R. Barry, M. D. Audeh, J. B. Carruthers, W. J. Krause, G. W. Marsh, “Non-directed infrared links for high-capacity wireless LANs,” IEEE Pers. Commun. Mag. 1(2), 12–25 (Second Quarter, 1994).

Barry, J. R.

J. M. Kahn, J. R. Barry, M. D. Audeh, J. B. Carruthers, W. J. Krause, G. W. Marsh, “Non-directed infrared links for high-capacity wireless LANs,” IEEE Pers. Commun. Mag. 1(2), 12–25 (Second Quarter, 1994).

J. R. Barry, Wireless Infrared Communications (Kluwer Academic, Boston, 1994), Chap. 2.

Brixner, B. N.

B. N. Brixner, “Wide angle optical system having a telecentric stop and an interference filter,” U.S. patent3,278,752 (11October1966).

Broder, J.

T. Verker, N. Schweitzer, J. Broder, N. Eisenberg, “Construction of a detection system with a wide field-of-view,” in 10th Meeting on Optical Engineering in Israel, I. Shladov, S. R. Rotman, eds., Proc. SPIE3110, 616–621 (1997).

Carruthers, J. B.

J. M. Kahn, J. R. Barry, M. D. Audeh, J. B. Carruthers, W. J. Krause, G. W. Marsh, “Non-directed infrared links for high-capacity wireless LANs,” IEEE Pers. Commun. Mag. 1(2), 12–25 (Second Quarter, 1994).

Chen, L.

L. Chen, L. S. Alvarez, B. Yin, T. M. Shay, “High-sensitivity direct detection optical communication system that operates in sunlight,” in Free-Space Laser Communication Technologies VI, G. Mecherle, ed., Proc. SPIE2123, 448–454 (1994).
[CrossRef]

Eisenberg, N.

T. Verker, N. Schweitzer, J. Broder, N. Eisenberg, “Construction of a detection system with a wide field-of-view,” in 10th Meeting on Optical Engineering in Israel, I. Shladov, S. R. Rotman, eds., Proc. SPIE3110, 616–621 (1997).

Grossman, A.

A. Grossman, “Wide angle narrow bandpass optical filter system,” U.S. patent4,184,749 (22January1980).

Gunning, W. J.

W. J. Gunning, “Narrow-band wide field-of-view filter study, Rockwell International Science Center,” (Rockwell International, Thousand Oaks, Calif., 1982).

Howard, J. W.

J. W. Howard, D. M. Reilly, “Multi-element spectral filter with curved interior surfaces,” U.S. patent4,554,447 (19November1985).

Kahn, J. M.

J. M. Kahn, J. R. Barry, M. D. Audeh, J. B. Carruthers, W. J. Krause, G. W. Marsh, “Non-directed infrared links for high-capacity wireless LANs,” IEEE Pers. Commun. Mag. 1(2), 12–25 (Second Quarter, 1994).

Krause, W. J.

J. M. Kahn, J. R. Barry, M. D. Audeh, J. B. Carruthers, W. J. Krause, G. W. Marsh, “Non-directed infrared links for high-capacity wireless LANs,” IEEE Pers. Commun. Mag. 1(2), 12–25 (Second Quarter, 1994).

Levi, L.

L. Levi, Applied Optics: A Guide to Optical System Design (Wiley, New York,1980), Vol. 2, p. 51.

Marsh, G. W.

J. M. Kahn, J. R. Barry, M. D. Audeh, J. B. Carruthers, W. J. Krause, G. W. Marsh, “Non-directed infrared links for high-capacity wireless LANs,” IEEE Pers. Commun. Mag. 1(2), 12–25 (Second Quarter, 1994).

Merchang, J.

J. Merchang, “Lens-sphere optical sensing system,” U.S. patent4,935,630 (19June1990).

Reilly, D. M.

J. W. Howard, D. M. Reilly, “Multi-element spectral filter with curved interior surfaces,” U.S. patent4,554,447 (19November1985).

Schweitzer, N.

T. Verker, N. Schweitzer, J. Broder, N. Eisenberg, “Construction of a detection system with a wide field-of-view,” in 10th Meeting on Optical Engineering in Israel, I. Shladov, S. R. Rotman, eds., Proc. SPIE3110, 616–621 (1997).

Shay, T. M.

L. Chen, L. S. Alvarez, B. Yin, T. M. Shay, “High-sensitivity direct detection optical communication system that operates in sunlight,” in Free-Space Laser Communication Technologies VI, G. Mecherle, ed., Proc. SPIE2123, 448–454 (1994).
[CrossRef]

Verker, T.

T. Verker, N. Schweitzer, J. Broder, N. Eisenberg, “Construction of a detection system with a wide field-of-view,” in 10th Meeting on Optical Engineering in Israel, I. Shladov, S. R. Rotman, eds., Proc. SPIE3110, 616–621 (1997).

Yin, B.

L. Chen, L. S. Alvarez, B. Yin, T. M. Shay, “High-sensitivity direct detection optical communication system that operates in sunlight,” in Free-Space Laser Communication Technologies VI, G. Mecherle, ed., Proc. SPIE2123, 448–454 (1994).
[CrossRef]

IEEE Pers. Commun. Mag.

J. M. Kahn, J. R. Barry, M. D. Audeh, J. B. Carruthers, W. J. Krause, G. W. Marsh, “Non-directed infrared links for high-capacity wireless LANs,” IEEE Pers. Commun. Mag. 1(2), 12–25 (Second Quarter, 1994).

Other

B. N. Brixner, “Wide angle optical system having a telecentric stop and an interference filter,” U.S. patent3,278,752 (11October1966).

A. Grossman, “Wide angle narrow bandpass optical filter system,” U.S. patent4,184,749 (22January1980).

J. W. Howard, D. M. Reilly, “Multi-element spectral filter with curved interior surfaces,” U.S. patent4,554,447 (19November1985).

J. Merchang, “Lens-sphere optical sensing system,” U.S. patent4,935,630 (19June1990).

W. J. Gunning, “Narrow-band wide field-of-view filter study, Rockwell International Science Center,” (Rockwell International, Thousand Oaks, Calif., 1982).

L. Chen, L. S. Alvarez, B. Yin, T. M. Shay, “High-sensitivity direct detection optical communication system that operates in sunlight,” in Free-Space Laser Communication Technologies VI, G. Mecherle, ed., Proc. SPIE2123, 448–454 (1994).
[CrossRef]

J. R. Barry, Wireless Infrared Communications (Kluwer Academic, Boston, 1994), Chap. 2.

T. Verker, N. Schweitzer, J. Broder, N. Eisenberg, “Construction of a detection system with a wide field-of-view,” in 10th Meeting on Optical Engineering in Israel, I. Shladov, S. R. Rotman, eds., Proc. SPIE3110, 616–621 (1997).

L. Levi, Applied Optics: A Guide to Optical System Design (Wiley, New York,1980), Vol. 2, p. 51.

Oriel Catalog of Optics and Filters (Oriel Corporation, Stratford, Conn., 1984), Vol. 3, p. 19.

“Standard tables for terrestrial solar spectral irradiance air mass 1.5 for a 37° tilted surface,” in ASTM Standards, Designation E892–87 (American Society for Testing and Materials, Philadelphia, 1987), pp. 477–484.

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Figures (4)

Fig. 1
Fig. 1

Hemispherical glass lens and spherical interference filter. R, filter radius; r, photodetector radius. α, angle between incoming collimated radiation and optical axis of the lens; θ, θ′, angles of incidence and refraction, respectively, at the filter; θ m , maximum angle of incidence of detected rays.

Fig. 2
Fig. 2

Normalized SNR of spherical interference-filter detection systems as a function of photodetector radius r. R, radius of curvature of the filter; Δλ F , filter bandwidth. Peak wavelength of laser radiation and filter transmission λ = 900 nm. Index of refraction of hemispherical lens n = 1.5. Angle between transmitter and optical axis of the lens α = 30°.

Fig. 3
Fig. 3

Ratio of SNR values of a spherical interference-filter detection system to SNR values of a step-filter detection system, as a function of photodetector radius. R = 2 cm, n = 1.5, λ F = 900 nm, Δλ F = 5 nm.

Fig. 4
Fig. 4

Maximum normalized SNR values of fully optimized spherical interference-filter detection system as a function of photodetector radius r. R = 2 cm, n = 1.5, α = 30°.

Tables (1)

Tables Icon

Table 1 Optimal Values of Spherical Interference-Filter Peak Transmission Wavelength λ F and Bandwidth Δλ F as a Function of the Photodetector Radius r for (a) α = 0°, (b) α = 30°, (c) α = 60°

Equations (5)

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λθ=λ01-n0/n*2 sin2 θ1/2,
sin θm=nr cosθm-θmR,
τθ, λ=τθexp(-λ-λFθ/ΔλF2),
SNRI=ΔλL EλSλx,y τθ, λdxdydλ2eΔλSunSunλSλx,y τθ, λdxdydλ1/2,
ΔλFλF-λL.

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