Abstract

Relationships between visibility and an extinction coefficient that is due to fog in optical windows that are free from molecular absorption are derived. The extinction coefficients in the visible (0.55 µm), the near IR (1.2 µm), and the mid IR (3.7 µm) are comparable to and roughly twice as much as that in the far IR (10.6 µm) when visibility is less than a few hundred meters. The advantage of far-IR radiation compared with shorter wavelengths grows as visibility exceeds 500 m. Correspondingly, the relationship between extinction coefficient and visibility becomes more sensitive to variations in the particle-size distribution of fog.

© 2005 Optical Society of America

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2003 (3)

M. D’Amico, A. Leva, B. Micheli, “Free-space optics communication systems: first results from a pilot field-trial in the surrounding area of Milan, Italy,” IEEE Microwave Wireless Compon. Lett. 13, 305–307 (2003).
[CrossRef]

S. Arnon, “The effects of atmospheric turbulence and building sway on optical wireless communication systems,” Opt. Lett. 28, 129–131 (2003).
[CrossRef] [PubMed]

S. Arnon, “Optimization of urban optical wireless communication systems,” IEEE Trans. Wireless Commun. 2, 626–629 (2003).
[CrossRef]

2002 (2)

F. Capasso, R. Paiella, R. Martini, R. Colombelli, C. Gmachl, T. L. Myers, M. S. Taubman, R. M. Williams, C. G. Bethea, K. Unterrainer, H. Y. Hwang, D. L. Sivco, A. Y. Cho, A. M. Sergent, H. C. Liu, E. A. Whittaker, “Quantum cascade lasers: ultrahigh-speed operation, optical wireless communication, narrow linewidth, and far-infrared emission,” IEEE J. Quantum Electron. 38, 511–532 (2002).
[CrossRef]

X. Zhu, J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50, 1293–1300 (2002).
[CrossRef]

1998 (1)

A. Acampora, S. H. Bloom, S. Krishnamurthy, “UniNet: a hybrid approach for universal broadband access using small radio cells interconnected by free-space optical links,” IEEE J. Sel. Areas Commun. 16, 973–987 (1998).
[CrossRef]

1996 (2)

P. L. Eardley, D. R. Wisely, “1 Gbit/s optical free space link operating over 40 m—system and applications,” IEE Proc. Op-toelectron. 143, 330–333 (1996).
[CrossRef]

H. Vasseur, C. J. Gibbins, “Inference of fog characteristics from attenuation measurements at millimeter and optical wavelengths,” Radio Sci. 31, 1089–1097 (1996).
[CrossRef]

1982 (4)

G. G. Gimmestad, L. W. Winchester, W. K. Choi, S. M. Lee, “Correlation between infrared and visible extinction coefficients of fog,” Opt. Letters 7, 471–474 (1982).
[CrossRef]

D. A. Stewart, O. M. Essenwanger, “A survey of fog and related optical propagation characteristics,” Rev. Geophys. 20, 481–495 (1982).
[CrossRef]

W. G. Tam, A. Zardecki, “Multiple scattering corrections to the Beer–Lambert law. 1. Open detector,” Appl. Opt. 21, 2405–2412 (1982).
[CrossRef] [PubMed]

A. Zardecki, W. G. Tam, “Multiple scattering corrections to the Beer–Lambert law. 2. Detector with a variable field of view,” Appl. Opt. 21, 2413–2420 (1982).
[CrossRef] [PubMed]

1981 (1)

1980 (1)

J. Abele, H. Raidt, D. H. Höhn, “Studies on the influence of meteorological parameters on atmospheric laser transmission,” Opt. Acta 27, 1445–1464 (1980).
[CrossRef]

1979 (1)

R. G. Pinnick, S. G. Jennings, P. Chýllek, H. J. Auvermann, “Verification of a linear relationship between IR extinction, absorption and liquid water content of fogs,” J. Atmos. Sci. 36, 1577–1586 (1979).
[CrossRef]

1976 (2)

C. Tomasi, F. Tampieri, “Features of the proportionality coefficient in the relationship between visibility and liquid water content in haze and fog,” Atmosphere 14, 61–76 (1976).

F. Tampieri, C. Tomasi, “Size distribution models of fog and cloud droplets and their volume extinction coefficients at visible and infrared wavelengths,” Pure Appl. Geophys. 114, 571–586 (1976).
[CrossRef]

1975 (2)

G. H. Ruppersberg, R. Schellhase, H. Schuster, “Calculations about the transmittance window of clouds and fog at about 10.5 µm wavelength,” Atmos. Environ. 9, 723–730 (1975).
[CrossRef]

D. Deirmendjian, “Far-infrared and submillimeter wave attenuation by clouds and rain,” J. Appl. Meteorol. 14, 1584–1593 (1975).
[CrossRef]

1970 (1)

1969 (2)

1968 (1)

T. S. Chu, D. C. Hogg, “Effect of precipitation on propagation at 0.63, 3.5 and 10.6 microns,” Bell. Syst. Tech. J. 47, 723–759 (1968).
[CrossRef]

1960 (1)

1957 (1)

1944 (1)

F. Löhle, “Über die lichtzerstreuung im nebel,” Phys. Z. 45, 199–205 (1944).

1938 (1)

M. Wolff, “Die lichttechnischen Eigenschaften des Nebels,” Das Light 8, 105–109, 128–130 (1938).

1929 (1)

A. Ångström, “On the atmospheric transmission of sun radiation and on dust in the air,” Geograf. Ann. Deut. 11, 156–166 (1929).
[CrossRef]

Abele, J.

J. Abele, H. Raidt, D. H. Höhn, “Studies on the influence of meteorological parameters on atmospheric laser transmission,” Opt. Acta 27, 1445–1464 (1980).
[CrossRef]

Acampora, A.

A. Acampora, S. H. Bloom, S. Krishnamurthy, “UniNet: a hybrid approach for universal broadband access using small radio cells interconnected by free-space optical links,” IEEE J. Sel. Areas Commun. 16, 973–987 (1998).
[CrossRef]

Ångström, A.

A. Ångström, “On the atmospheric transmission of sun radiation and on dust in the air,” Geograf. Ann. Deut. 11, 156–166 (1929).
[CrossRef]

Arnon, S.

S. Arnon, “The effects of atmospheric turbulence and building sway on optical wireless communication systems,” Opt. Lett. 28, 129–131 (2003).
[CrossRef] [PubMed]

S. Arnon, “Optimization of urban optical wireless communication systems,” IEEE Trans. Wireless Commun. 2, 626–629 (2003).
[CrossRef]

Arnulf, A.

Auvermann, H. J.

R. G. Pinnick, S. G. Jennings, P. Chýllek, H. J. Auvermann, “Verification of a linear relationship between IR extinction, absorption and liquid water content of fogs,” J. Atmos. Sci. 36, 1577–1586 (1979).
[CrossRef]

Bethea, C. G.

F. Capasso, R. Paiella, R. Martini, R. Colombelli, C. Gmachl, T. L. Myers, M. S. Taubman, R. M. Williams, C. G. Bethea, K. Unterrainer, H. Y. Hwang, D. L. Sivco, A. Y. Cho, A. M. Sergent, H. C. Liu, E. A. Whittaker, “Quantum cascade lasers: ultrahigh-speed operation, optical wireless communication, narrow linewidth, and far-infrared emission,” IEEE J. Quantum Electron. 38, 511–532 (2002).
[CrossRef]

Bloom, S. H.

A. Acampora, S. H. Bloom, S. Krishnamurthy, “UniNet: a hybrid approach for universal broadband access using small radio cells interconnected by free-space optical links,” IEEE J. Sel. Areas Commun. 16, 973–987 (1998).
[CrossRef]

Bricard, J.

Capasso, F.

F. Capasso, R. Paiella, R. Martini, R. Colombelli, C. Gmachl, T. L. Myers, M. S. Taubman, R. M. Williams, C. G. Bethea, K. Unterrainer, H. Y. Hwang, D. L. Sivco, A. Y. Cho, A. M. Sergent, H. C. Liu, E. A. Whittaker, “Quantum cascade lasers: ultrahigh-speed operation, optical wireless communication, narrow linewidth, and far-infrared emission,” IEEE J. Quantum Electron. 38, 511–532 (2002).
[CrossRef]

Cho, A. Y.

F. Capasso, R. Paiella, R. Martini, R. Colombelli, C. Gmachl, T. L. Myers, M. S. Taubman, R. M. Williams, C. G. Bethea, K. Unterrainer, H. Y. Hwang, D. L. Sivco, A. Y. Cho, A. M. Sergent, H. C. Liu, E. A. Whittaker, “Quantum cascade lasers: ultrahigh-speed operation, optical wireless communication, narrow linewidth, and far-infrared emission,” IEEE J. Quantum Electron. 38, 511–532 (2002).
[CrossRef]

Choi, W. K.

G. G. Gimmestad, L. W. Winchester, W. K. Choi, S. M. Lee, “Correlation between infrared and visible extinction coefficients of fog,” Opt. Letters 7, 471–474 (1982).
[CrossRef]

Chu, T. S.

T. S. Chu, D. C. Hogg, “Effect of precipitation on propagation at 0.63, 3.5 and 10.6 microns,” Bell. Syst. Tech. J. 47, 723–759 (1968).
[CrossRef]

Chýllek, P.

R. G. Pinnick, S. G. Jennings, P. Chýllek, H. J. Auvermann, “Verification of a linear relationship between IR extinction, absorption and liquid water content of fogs,” J. Atmos. Sci. 36, 1577–1586 (1979).
[CrossRef]

Clay, M. R.

Colombelli, R.

F. Capasso, R. Paiella, R. Martini, R. Colombelli, C. Gmachl, T. L. Myers, M. S. Taubman, R. M. Williams, C. G. Bethea, K. Unterrainer, H. Y. Hwang, D. L. Sivco, A. Y. Cho, A. M. Sergent, H. C. Liu, E. A. Whittaker, “Quantum cascade lasers: ultrahigh-speed operation, optical wireless communication, narrow linewidth, and far-infrared emission,” IEEE J. Quantum Electron. 38, 511–532 (2002).
[CrossRef]

Curé, E.

D’Amico, M.

M. D’Amico, A. Leva, B. Micheli, “Free-space optics communication systems: first results from a pilot field-trial in the surrounding area of Milan, Italy,” IEEE Microwave Wireless Compon. Lett. 13, 305–307 (2003).
[CrossRef]

Deirmendjian, D.

D. Deirmendjian, “Far-infrared and submillimeter wave attenuation by clouds and rain,” J. Appl. Meteorol. 14, 1584–1593 (1975).
[CrossRef]

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).

Eardley, P. L.

P. L. Eardley, D. R. Wisely, “1 Gbit/s optical free space link operating over 40 m—system and applications,” IEE Proc. Op-toelectron. 143, 330–333 (1996).
[CrossRef]

Eldridge, R. G.

R. G. Eldridge, “Mist—the transition from haze to fog,” Bull. Am. Meteorol. Soc. 50, 422–426 (1969).

Essenwanger, O. M.

D. A. Stewart, O. M. Essenwanger, “A survey of fog and related optical propagation characteristics,” Rev. Geophys. 20, 481–495 (1982).
[CrossRef]

Gebhardt, F. G.

R. E. Turner, F. G. Gebhardt, J. L. Manning, R. E. Meredith, S. M. Singer, F. G. Smith, P. C. Vavra, “Model development for EOSAEL: natural aerosol, contrast, laser transmission, and turbulence,” (U.S. Government Printing Office, Washington, D.C., 1980).

Gibbins, C. J.

H. Vasseur, C. J. Gibbins, “Inference of fog characteristics from attenuation measurements at millimeter and optical wavelengths,” Radio Sci. 31, 1089–1097 (1996).
[CrossRef]

Gimmestad, G. G.

G. G. Gimmestad, L. W. Winchester, W. K. Choi, S. M. Lee, “Correlation between infrared and visible extinction coefficients of fog,” Opt. Letters 7, 471–474 (1982).
[CrossRef]

Gmachl, C.

F. Capasso, R. Paiella, R. Martini, R. Colombelli, C. Gmachl, T. L. Myers, M. S. Taubman, R. M. Williams, C. G. Bethea, K. Unterrainer, H. Y. Hwang, D. L. Sivco, A. Y. Cho, A. M. Sergent, H. C. Liu, E. A. Whittaker, “Quantum cascade lasers: ultrahigh-speed operation, optical wireless communication, narrow linewidth, and far-infrared emission,” IEEE J. Quantum Electron. 38, 511–532 (2002).
[CrossRef]

Gowar, J.

J. Gowar, Optical Communication Systems, 2nd ed. (Prentice-Hall, Engelwood Cliffs, N.J., 1993).

Griggs, D. J.

D. J. Griggs, D. W. Jines, M. Ouldrige, W. R. Sparks, “The first WMO intercomparison of visibility measurements,” Instruments and Observing Methods Rep. 41, (World Meteorological Organisation, Geneva, 1990).

Hogg, D. C.

T. S. Chu, D. C. Hogg, “Effect of precipitation on propagation at 0.63, 3.5 and 10.6 microns,” Bell. Syst. Tech. J. 47, 723–759 (1968).
[CrossRef]

Höhn, D. H.

J. Abele, H. Raidt, D. H. Höhn, “Studies on the influence of meteorological parameters on atmospheric laser transmission,” Opt. Acta 27, 1445–1464 (1980).
[CrossRef]

Hwang, H. Y.

F. Capasso, R. Paiella, R. Martini, R. Colombelli, C. Gmachl, T. L. Myers, M. S. Taubman, R. M. Williams, C. G. Bethea, K. Unterrainer, H. Y. Hwang, D. L. Sivco, A. Y. Cho, A. M. Sergent, H. C. Liu, E. A. Whittaker, “Quantum cascade lasers: ultrahigh-speed operation, optical wireless communication, narrow linewidth, and far-infrared emission,” IEEE J. Quantum Electron. 38, 511–532 (2002).
[CrossRef]

Jennings, S. G.

R. G. Pinnick, S. G. Jennings, P. Chýllek, H. J. Auvermann, “Verification of a linear relationship between IR extinction, absorption and liquid water content of fogs,” J. Atmos. Sci. 36, 1577–1586 (1979).
[CrossRef]

Jines, D. W.

D. J. Griggs, D. W. Jines, M. Ouldrige, W. R. Sparks, “The first WMO intercomparison of visibility measurements,” Instruments and Observing Methods Rep. 41, (World Meteorological Organisation, Geneva, 1990).

Kahn, J. M.

X. Zhu, J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50, 1293–1300 (2002).
[CrossRef]

Kim, I. I.

I. I. Kim, E. J. Korevaar, “Availability of free space optics (FSO) and hybrid FSO/RF systems,” in Optical Wireless Communications IV, E. J. Korevaar, eds., Proc. SPIE4530, 84–95 (2001).
[CrossRef]

I. I. Kim, B. McArthur, E. J. Korevaar, “Comparison of laser beam propagation at 785 nm and 1550 nm in fog and haze for optical wireless communications,” in Optical Wireless Communications III, E. J. Korevaar, ed., Proc. SPIE4214, 26–37 (2001).
[CrossRef]

Korevaar, E. J.

I. I. Kim, B. McArthur, E. J. Korevaar, “Comparison of laser beam propagation at 785 nm and 1550 nm in fog and haze for optical wireless communications,” in Optical Wireless Communications III, E. J. Korevaar, ed., Proc. SPIE4214, 26–37 (2001).
[CrossRef]

I. I. Kim, E. J. Korevaar, “Availability of free space optics (FSO) and hybrid FSO/RF systems,” in Optical Wireless Communications IV, E. J. Korevaar, eds., Proc. SPIE4530, 84–95 (2001).
[CrossRef]

Krishnamurthy, S.

A. Acampora, S. H. Bloom, S. Krishnamurthy, “UniNet: a hybrid approach for universal broadband access using small radio cells interconnected by free-space optical links,” IEEE J. Sel. Areas Commun. 16, 973–987 (1998).
[CrossRef]

Kruse, P. W.

P. W. Kruse, L. D. McGlauchlin, R. B. McQuistan, Elements of Infrared Technology: Generation, Transmission and Detection (Wiley, New York, 1962).

Kurnick, S. W.

Lee, S. M.

G. G. Gimmestad, L. W. Winchester, W. K. Choi, S. M. Lee, “Correlation between infrared and visible extinction coefficients of fog,” Opt. Letters 7, 471–474 (1982).
[CrossRef]

Lenham, A. P.

Leva, A.

M. D’Amico, A. Leva, B. Micheli, “Free-space optics communication systems: first results from a pilot field-trial in the surrounding area of Milan, Italy,” IEEE Microwave Wireless Compon. Lett. 13, 305–307 (2003).
[CrossRef]

Liu, H. C.

F. Capasso, R. Paiella, R. Martini, R. Colombelli, C. Gmachl, T. L. Myers, M. S. Taubman, R. M. Williams, C. G. Bethea, K. Unterrainer, H. Y. Hwang, D. L. Sivco, A. Y. Cho, A. M. Sergent, H. C. Liu, E. A. Whittaker, “Quantum cascade lasers: ultrahigh-speed operation, optical wireless communication, narrow linewidth, and far-infrared emission,” IEEE J. Quantum Electron. 38, 511–532 (2002).
[CrossRef]

Löhle, F.

F. Löhle, “Über die lichtzerstreuung im nebel,” Phys. Z. 45, 199–205 (1944).

Long, R. K.

Manning, J. L.

R. E. Turner, F. G. Gebhardt, J. L. Manning, R. E. Meredith, S. M. Singer, F. G. Smith, P. C. Vavra, “Model development for EOSAEL: natural aerosol, contrast, laser transmission, and turbulence,” (U.S. Government Printing Office, Washington, D.C., 1980).

Martini, R.

F. Capasso, R. Paiella, R. Martini, R. Colombelli, C. Gmachl, T. L. Myers, M. S. Taubman, R. M. Williams, C. G. Bethea, K. Unterrainer, H. Y. Hwang, D. L. Sivco, A. Y. Cho, A. M. Sergent, H. C. Liu, E. A. Whittaker, “Quantum cascade lasers: ultrahigh-speed operation, optical wireless communication, narrow linewidth, and far-infrared emission,” IEEE J. Quantum Electron. 38, 511–532 (2002).
[CrossRef]

McArthur, B.

I. I. Kim, B. McArthur, E. J. Korevaar, “Comparison of laser beam propagation at 785 nm and 1550 nm in fog and haze for optical wireless communications,” in Optical Wireless Communications III, E. J. Korevaar, ed., Proc. SPIE4214, 26–37 (2001).
[CrossRef]

McCoy, J. H.

McGlauchlin, L. D.

P. W. Kruse, L. D. McGlauchlin, R. B. McQuistan, Elements of Infrared Technology: Generation, Transmission and Detection (Wiley, New York, 1962).

McQuistan, R. B.

P. W. Kruse, L. D. McGlauchlin, R. B. McQuistan, Elements of Infrared Technology: Generation, Transmission and Detection (Wiley, New York, 1962).

Meredith, R. E.

R. E. Turner, F. G. Gebhardt, J. L. Manning, R. E. Meredith, S. M. Singer, F. G. Smith, P. C. Vavra, “Model development for EOSAEL: natural aerosol, contrast, laser transmission, and turbulence,” (U.S. Government Printing Office, Washington, D.C., 1980).

Micheli, B.

M. D’Amico, A. Leva, B. Micheli, “Free-space optics communication systems: first results from a pilot field-trial in the surrounding area of Milan, Italy,” IEEE Microwave Wireless Compon. Lett. 13, 305–307 (2003).
[CrossRef]

Middleton, W. E. K.

W. E. K. Middleton, Vision through the Atmosphere (U. of Toronto Press, Toronto, Canada, 1952).

Myers, T. L.

F. Capasso, R. Paiella, R. Martini, R. Colombelli, C. Gmachl, T. L. Myers, M. S. Taubman, R. M. Williams, C. G. Bethea, K. Unterrainer, H. Y. Hwang, D. L. Sivco, A. Y. Cho, A. M. Sergent, H. C. Liu, E. A. Whittaker, “Quantum cascade lasers: ultrahigh-speed operation, optical wireless communication, narrow linewidth, and far-infrared emission,” IEEE J. Quantum Electron. 38, 511–532 (2002).
[CrossRef]

Ouldrige, M.

D. J. Griggs, D. W. Jines, M. Ouldrige, W. R. Sparks, “The first WMO intercomparison of visibility measurements,” Instruments and Observing Methods Rep. 41, (World Meteorological Organisation, Geneva, 1990).

Paiella, R.

F. Capasso, R. Paiella, R. Martini, R. Colombelli, C. Gmachl, T. L. Myers, M. S. Taubman, R. M. Williams, C. G. Bethea, K. Unterrainer, H. Y. Hwang, D. L. Sivco, A. Y. Cho, A. M. Sergent, H. C. Liu, E. A. Whittaker, “Quantum cascade lasers: ultrahigh-speed operation, optical wireless communication, narrow linewidth, and far-infrared emission,” IEEE J. Quantum Electron. 38, 511–532 (2002).
[CrossRef]

Pinnick, R. G.

R. G. Pinnick, S. G. Jennings, P. Chýllek, H. J. Auvermann, “Verification of a linear relationship between IR extinction, absorption and liquid water content of fogs,” J. Atmos. Sci. 36, 1577–1586 (1979).
[CrossRef]

Raidt, H.

J. Abele, H. Raidt, D. H. Höhn, “Studies on the influence of meteorological parameters on atmospheric laser transmission,” Opt. Acta 27, 1445–1464 (1980).
[CrossRef]

Rensch, D. B.

Ruppersberg, G. H.

G. H. Ruppersberg, R. Schellhase, H. Schuster, “Calculations about the transmittance window of clouds and fog at about 10.5 µm wavelength,” Atmos. Environ. 9, 723–730 (1975).
[CrossRef]

Schellhase, R.

G. H. Ruppersberg, R. Schellhase, H. Schuster, “Calculations about the transmittance window of clouds and fog at about 10.5 µm wavelength,” Atmos. Environ. 9, 723–730 (1975).
[CrossRef]

Schuster, H.

G. H. Ruppersberg, R. Schellhase, H. Schuster, “Calculations about the transmittance window of clouds and fog at about 10.5 µm wavelength,” Atmos. Environ. 9, 723–730 (1975).
[CrossRef]

Sergent, A. M.

F. Capasso, R. Paiella, R. Martini, R. Colombelli, C. Gmachl, T. L. Myers, M. S. Taubman, R. M. Williams, C. G. Bethea, K. Unterrainer, H. Y. Hwang, D. L. Sivco, A. Y. Cho, A. M. Sergent, H. C. Liu, E. A. Whittaker, “Quantum cascade lasers: ultrahigh-speed operation, optical wireless communication, narrow linewidth, and far-infrared emission,” IEEE J. Quantum Electron. 38, 511–532 (2002).
[CrossRef]

Singer, S. M.

R. E. Turner, F. G. Gebhardt, J. L. Manning, R. E. Meredith, S. M. Singer, F. G. Smith, P. C. Vavra, “Model development for EOSAEL: natural aerosol, contrast, laser transmission, and turbulence,” (U.S. Government Printing Office, Washington, D.C., 1980).

Sivco, D. L.

F. Capasso, R. Paiella, R. Martini, R. Colombelli, C. Gmachl, T. L. Myers, M. S. Taubman, R. M. Williams, C. G. Bethea, K. Unterrainer, H. Y. Hwang, D. L. Sivco, A. Y. Cho, A. M. Sergent, H. C. Liu, E. A. Whittaker, “Quantum cascade lasers: ultrahigh-speed operation, optical wireless communication, narrow linewidth, and far-infrared emission,” IEEE J. Quantum Electron. 38, 511–532 (2002).
[CrossRef]

Smith, F. G.

R. E. Turner, F. G. Gebhardt, J. L. Manning, R. E. Meredith, S. M. Singer, F. G. Smith, P. C. Vavra, “Model development for EOSAEL: natural aerosol, contrast, laser transmission, and turbulence,” (U.S. Government Printing Office, Washington, D.C., 1980).

Sparks, W. R.

D. J. Griggs, D. W. Jines, M. Ouldrige, W. R. Sparks, “The first WMO intercomparison of visibility measurements,” Instruments and Observing Methods Rep. 41, (World Meteorological Organisation, Geneva, 1990).

Stewart, D. A.

D. A. Stewart, O. M. Essenwanger, “A survey of fog and related optical propagation characteristics,” Rev. Geophys. 20, 481–495 (1982).
[CrossRef]

Tam, W. G.

Tampieri, F.

F. Tampieri, C. Tomasi, “Size distribution models of fog and cloud droplets and their volume extinction coefficients at visible and infrared wavelengths,” Pure Appl. Geophys. 114, 571–586 (1976).
[CrossRef]

C. Tomasi, F. Tampieri, “Features of the proportionality coefficient in the relationship between visibility and liquid water content in haze and fog,” Atmosphere 14, 61–76 (1976).

Taubman, M. S.

F. Capasso, R. Paiella, R. Martini, R. Colombelli, C. Gmachl, T. L. Myers, M. S. Taubman, R. M. Williams, C. G. Bethea, K. Unterrainer, H. Y. Hwang, D. L. Sivco, A. Y. Cho, A. M. Sergent, H. C. Liu, E. A. Whittaker, “Quantum cascade lasers: ultrahigh-speed operation, optical wireless communication, narrow linewidth, and far-infrared emission,” IEEE J. Quantum Electron. 38, 511–532 (2002).
[CrossRef]

Tomasi, C.

F. Tampieri, C. Tomasi, “Size distribution models of fog and cloud droplets and their volume extinction coefficients at visible and infrared wavelengths,” Pure Appl. Geophys. 114, 571–586 (1976).
[CrossRef]

C. Tomasi, F. Tampieri, “Features of the proportionality coefficient in the relationship between visibility and liquid water content in haze and fog,” Atmosphere 14, 61–76 (1976).

Turner, R. E.

R. E. Turner, F. G. Gebhardt, J. L. Manning, R. E. Meredith, S. M. Singer, F. G. Smith, P. C. Vavra, “Model development for EOSAEL: natural aerosol, contrast, laser transmission, and turbulence,” (U.S. Government Printing Office, Washington, D.C., 1980).

Unterrainer, K.

F. Capasso, R. Paiella, R. Martini, R. Colombelli, C. Gmachl, T. L. Myers, M. S. Taubman, R. M. Williams, C. G. Bethea, K. Unterrainer, H. Y. Hwang, D. L. Sivco, A. Y. Cho, A. M. Sergent, H. C. Liu, E. A. Whittaker, “Quantum cascade lasers: ultrahigh-speed operation, optical wireless communication, narrow linewidth, and far-infrared emission,” IEEE J. Quantum Electron. 38, 511–532 (2002).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Vasseur, H.

H. Vasseur, C. J. Gibbins, “Inference of fog characteristics from attenuation measurements at millimeter and optical wavelengths,” Radio Sci. 31, 1089–1097 (1996).
[CrossRef]

Vavra, P. C.

R. E. Turner, F. G. Gebhardt, J. L. Manning, R. E. Meredith, S. M. Singer, F. G. Smith, P. C. Vavra, “Model development for EOSAEL: natural aerosol, contrast, laser transmission, and turbulence,” (U.S. Government Printing Office, Washington, D.C., 1980).

Véret, C.

Whittaker, E. A.

F. Capasso, R. Paiella, R. Martini, R. Colombelli, C. Gmachl, T. L. Myers, M. S. Taubman, R. M. Williams, C. G. Bethea, K. Unterrainer, H. Y. Hwang, D. L. Sivco, A. Y. Cho, A. M. Sergent, H. C. Liu, E. A. Whittaker, “Quantum cascade lasers: ultrahigh-speed operation, optical wireless communication, narrow linewidth, and far-infrared emission,” IEEE J. Quantum Electron. 38, 511–532 (2002).
[CrossRef]

Williams, D. B.

Williams, R. M.

F. Capasso, R. Paiella, R. Martini, R. Colombelli, C. Gmachl, T. L. Myers, M. S. Taubman, R. M. Williams, C. G. Bethea, K. Unterrainer, H. Y. Hwang, D. L. Sivco, A. Y. Cho, A. M. Sergent, H. C. Liu, E. A. Whittaker, “Quantum cascade lasers: ultrahigh-speed operation, optical wireless communication, narrow linewidth, and far-infrared emission,” IEEE J. Quantum Electron. 38, 511–532 (2002).
[CrossRef]

Winchester, L. W.

G. G. Gimmestad, L. W. Winchester, W. K. Choi, S. M. Lee, “Correlation between infrared and visible extinction coefficients of fog,” Opt. Letters 7, 471–474 (1982).
[CrossRef]

Wisely, D. R.

P. L. Eardley, D. R. Wisely, “1 Gbit/s optical free space link operating over 40 m—system and applications,” IEE Proc. Op-toelectron. 143, 330–333 (1996).
[CrossRef]

Wolff, M.

M. Wolff, “Die lichttechnischen Eigenschaften des Nebels,” Das Light 8, 105–109, 128–130 (1938).

Zardecki, A.

Zhu, X.

X. Zhu, J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50, 1293–1300 (2002).
[CrossRef]

Zitter, R. N.

Appl. Opt. (5)

Atmos. Environ. (1)

G. H. Ruppersberg, R. Schellhase, H. Schuster, “Calculations about the transmittance window of clouds and fog at about 10.5 µm wavelength,” Atmos. Environ. 9, 723–730 (1975).
[CrossRef]

Atmosphere (1)

C. Tomasi, F. Tampieri, “Features of the proportionality coefficient in the relationship between visibility and liquid water content in haze and fog,” Atmosphere 14, 61–76 (1976).

Bell. Syst. Tech. J. (1)

T. S. Chu, D. C. Hogg, “Effect of precipitation on propagation at 0.63, 3.5 and 10.6 microns,” Bell. Syst. Tech. J. 47, 723–759 (1968).
[CrossRef]

Bull. Am. Meteorol. Soc. (1)

R. G. Eldridge, “Mist—the transition from haze to fog,” Bull. Am. Meteorol. Soc. 50, 422–426 (1969).

Das Light (1)

M. Wolff, “Die lichttechnischen Eigenschaften des Nebels,” Das Light 8, 105–109, 128–130 (1938).

Geograf. Ann. Deut. (1)

A. Ångström, “On the atmospheric transmission of sun radiation and on dust in the air,” Geograf. Ann. Deut. 11, 156–166 (1929).
[CrossRef]

IEE Proc. Op-toelectron. (1)

P. L. Eardley, D. R. Wisely, “1 Gbit/s optical free space link operating over 40 m—system and applications,” IEE Proc. Op-toelectron. 143, 330–333 (1996).
[CrossRef]

IEEE J. Quantum Electron. (1)

F. Capasso, R. Paiella, R. Martini, R. Colombelli, C. Gmachl, T. L. Myers, M. S. Taubman, R. M. Williams, C. G. Bethea, K. Unterrainer, H. Y. Hwang, D. L. Sivco, A. Y. Cho, A. M. Sergent, H. C. Liu, E. A. Whittaker, “Quantum cascade lasers: ultrahigh-speed operation, optical wireless communication, narrow linewidth, and far-infrared emission,” IEEE J. Quantum Electron. 38, 511–532 (2002).
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

A. Acampora, S. H. Bloom, S. Krishnamurthy, “UniNet: a hybrid approach for universal broadband access using small radio cells interconnected by free-space optical links,” IEEE J. Sel. Areas Commun. 16, 973–987 (1998).
[CrossRef]

IEEE Microwave Wireless Compon. Lett. (1)

M. D’Amico, A. Leva, B. Micheli, “Free-space optics communication systems: first results from a pilot field-trial in the surrounding area of Milan, Italy,” IEEE Microwave Wireless Compon. Lett. 13, 305–307 (2003).
[CrossRef]

IEEE Trans. Commun. (1)

X. Zhu, J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50, 1293–1300 (2002).
[CrossRef]

IEEE Trans. Wireless Commun. (1)

S. Arnon, “Optimization of urban optical wireless communication systems,” IEEE Trans. Wireless Commun. 2, 626–629 (2003).
[CrossRef]

J. Appl. Meteorol. (1)

D. Deirmendjian, “Far-infrared and submillimeter wave attenuation by clouds and rain,” J. Appl. Meteorol. 14, 1584–1593 (1975).
[CrossRef]

J. Atmos. Sci. (1)

R. G. Pinnick, S. G. Jennings, P. Chýllek, H. J. Auvermann, “Verification of a linear relationship between IR extinction, absorption and liquid water content of fogs,” J. Atmos. Sci. 36, 1577–1586 (1979).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Acta (1)

J. Abele, H. Raidt, D. H. Höhn, “Studies on the influence of meteorological parameters on atmospheric laser transmission,” Opt. Acta 27, 1445–1464 (1980).
[CrossRef]

Opt. Lett. (1)

Opt. Letters (1)

G. G. Gimmestad, L. W. Winchester, W. K. Choi, S. M. Lee, “Correlation between infrared and visible extinction coefficients of fog,” Opt. Letters 7, 471–474 (1982).
[CrossRef]

Phys. Z. (1)

F. Löhle, “Über die lichtzerstreuung im nebel,” Phys. Z. 45, 199–205 (1944).

Pure Appl. Geophys. (1)

F. Tampieri, C. Tomasi, “Size distribution models of fog and cloud droplets and their volume extinction coefficients at visible and infrared wavelengths,” Pure Appl. Geophys. 114, 571–586 (1976).
[CrossRef]

Radio Sci. (1)

H. Vasseur, C. J. Gibbins, “Inference of fog characteristics from attenuation measurements at millimeter and optical wavelengths,” Radio Sci. 31, 1089–1097 (1996).
[CrossRef]

Rev. Geophys. (1)

D. A. Stewart, O. M. Essenwanger, “A survey of fog and related optical propagation characteristics,” Rev. Geophys. 20, 481–495 (1982).
[CrossRef]

Other (10)

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

U.S. Environmental Protection Agency, “Protecting visibility: an EPA report to Congress,” EPA-450/5-79-008 (U.S. Government Printing Office, Washington, D.C., 1979).

D. J. Griggs, D. W. Jines, M. Ouldrige, W. R. Sparks, “The first WMO intercomparison of visibility measurements,” Instruments and Observing Methods Rep. 41, (World Meteorological Organisation, Geneva, 1990).

P. W. Kruse, L. D. McGlauchlin, R. B. McQuistan, Elements of Infrared Technology: Generation, Transmission and Detection (Wiley, New York, 1962).

I. I. Kim, E. J. Korevaar, “Availability of free space optics (FSO) and hybrid FSO/RF systems,” in Optical Wireless Communications IV, E. J. Korevaar, eds., Proc. SPIE4530, 84–95 (2001).
[CrossRef]

W. E. K. Middleton, Vision through the Atmosphere (U. of Toronto Press, Toronto, Canada, 1952).

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).

I. I. Kim, B. McArthur, E. J. Korevaar, “Comparison of laser beam propagation at 785 nm and 1550 nm in fog and haze for optical wireless communications,” in Optical Wireless Communications III, E. J. Korevaar, ed., Proc. SPIE4214, 26–37 (2001).
[CrossRef]

R. E. Turner, F. G. Gebhardt, J. L. Manning, R. E. Meredith, S. M. Singer, F. G. Smith, P. C. Vavra, “Model development for EOSAEL: natural aerosol, contrast, laser transmission, and turbulence,” (U.S. Government Printing Office, Washington, D.C., 1980).

J. Gowar, Optical Communication Systems, 2nd ed. (Prentice-Hall, Engelwood Cliffs, N.J., 1993).

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Figures (5)

Fig. 1
Fig. 1

Relationship between visibility and extinction coefficient at (a) 0.785 µm and at (b) 1.550 µm according to two empirical models. Also shown is the curve βext = 3.91/V, which defines the visibility as a function of the extinction coefficient at 0.55 µm.

Fig. 2
Fig. 2

Near-IR extinction coefficient versus visibility. Laser transmission data from CL and ABCV have been fitted with a piecewise power-law expression. The thin solid curves are at ± 1 rms (relative) deviation from the best fit. Also depicted are the model proposed by Kim et al. and the relationship βext = 3.91/V, which holds in the visible window (dotted curve).

Fig. 3
Fig. 3

Mid-IR extinction coefficient versus visibility. Laser transmission data from CL, ABCV, and CH have been fitted with a piecewise power-law expression. The thin solid curves are at ± 1 rms (relative) deviation from the best fit. Also depicted are the model proposed by Kim et al. and the relationship βext = 3.91/V, which holds in the visible window (dotted curve).

Fig. 4
Fig. 4

Far-IR extinction coefficient versus visibility. Laser transmission data from CL, ABCV, CH, and A have been fitted with a piecewise power-law expression. The thin solid curves are at ± 1 rms (relative) deviation from the best fit. Also depicted are the model proposed by Kim et al. and the relationship βext = 3.91/V, which holds in the visible window (dotted curve).

Fig. 5
Fig. 5

Maximum link range versus visibility with the system margin allocated to cope with atmospheric losses as a parameter. (a) Curves are related to a system operating in the near-IR window; (b) transmission in the far IR is assumed.

Tables (2)

Tables Icon

Table 1 Summary of Laser Transmission Measurements Analyzed in This Paper

Tables Icon

Table 2 Empirical Coefficients of the Power-Law Expression βext = aVb, Which Relates the Extinction Coefficient (km−1) Due to Fog to Visibility

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

β ext = r 1 r 2 π r 2 Q ext ( m , r / λ ) n ( r ) d r ,
R ω s ( V ) R ω s ( 0 ) = 0.02 .
τ ( 0.55 μ m ) = [ R ω s ( V ) R ω s ( 0 ) ] 0.55 μ m = exp ( β ext V ) .
β ext ( 0.55 μ m ) = 3.91 V [ km 1 ] ,
β ext ( λ ) = A λ q ,
A = 3.91 V ( 0.55 ) q .
β ext ( λ ) = 3.91 V ( λ 0.55 ) q [ km 1 ] ,
q = { 0.585 V 1 / 3 V < 6 km 1.3 6 km V < 50 km . 1.6 V 50 km
q = { 0 V < 500 m V 0.50 500 m V < 1 km . 0.16 V + 0.34 1 km V < 6 km
β ext ( V ) = a V b .
P R = P T L sys + 10 log 10 [ A R ( θ T z ) 2 ] 60 4.34 β atm z ,
M atm = 4.34 β ext z ,
z = M atm 4.34 a V b .

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