Abstract

The power spectrum of the phase difference fluctuations between two IR beams propagating side by side is strongly influence by rain along the path. According to our measurements over a 1.37-km path in convective rainfall averaging 18 mm/h, the power spectrum of phase difference fluctuations in rain extends over the 300-Hz to 2-kHz band, and it is as much as 18 dB above the no-rain spectrum at ~600 Hz during periods of heavier rain (>30 mm/h). The shape of the spectrum is different at different stages of the storm probably because of changing drop size distributions. A simple dimensionless parameter derived from the power spectrum of phase difference fluctuations is 0.186 ± 20% for a rain rate of 41 (mm/h) km ± 25%, but this value may depend on the chopped transmitter waveform. The simple optical design and data analysis procedure allow power spectra to be obtained from a single signal channel. We conclude that measurement of phase difference fluctuations in 10.6-μm propagation should allow the path-averaged rainfall rate to be inferred over path lengths of at least 1.5 km if a properly calibrated system is used.

© 1985 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. F. Clifford, G. M. B. Bouricius, G. R. Ochs, M. H. Ackley, “Phase Variations in Atmospheric Optical Propagation,” J. Opt. Soc. Am. 61, 1279 (1971).
    [CrossRef]
  2. V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation, J. W. Strohbehn, Ed. (Israel Program for Scientific Translations, Jerusalem, 1971), available from NTIS.
  3. G. K. Born, R. Bogenberger, K. D. Erben, F. Frank, F. Mohr, G. Sepp, “Phase-Front Distortion of Laser Radiation in a Turbulent Atmosphere,” Appl. Opt. 14, 2857 (1975).
    [CrossRef] [PubMed]
  4. R. L. Schwiesow, R. F. Calfee, “Atmospheric Refractive Effects on Coherent Lidar Performance at 10.6 μm,” Appl. Opt. 18, 3911 (1979).
    [CrossRef] [PubMed]
  5. H. T. Yura, K. G. Barthel, W. Büchtemann, “Rainfall Induced Optical Phase Fluctuations in the Atmosphere,” J. Opt. Soc. Am. 73, 1574 (1983).
    [CrossRef]
  6. T.-i. Wang, G. Lerfald, R. S. Lawrence, S. F. Clifford, “Measurement of Rain Parameters by Optical Scintillation,” Appl. Opt. 16, 2236 (1977).
    [CrossRef] [PubMed]
  7. T.-i. Wang, R. S. Lawrence, M. K. Tsay, “Optical Rain Gauge Using a Divergent Beam,” Appl. Opt. 19, 3617 (1980).
    [CrossRef] [PubMed]
  8. G. M. B. Bouricius, S. F. Clifford, “An Optical Interferometer Using Polarization Coding to Obtain Quadrature Phase Components,” Rev. Sci. Instrum. 41, 1800 (1970).
    [CrossRef]
  9. T.-i. Wang, G. R. Ochs, S. F. Clifford, “A Saturation-Resistant Optical Scintillometer to Measure Cn2,” J. Opt. Soc. Am. 68, 334 (1978).
    [CrossRef]
  10. K. Barthel, “Experimental Investigation of Aperture Limitations of a Heterodyne CO2 Laser Radar by Atmospheric Turbulence and Rain,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1982), paper FV3.
  11. T.-i. Wang, S. F. Clifford, “Use of Rainfall-Induced Optical Scintillations to Measure Path-Averaged Rain Parameters,” J. Opt. Soc. Am. 65, 927 (1975).
    [CrossRef]
  12. L. G. Kazovsky, “Particle Analysis Using Forward Scattering Data,” Appl. Opt. 23, 448 (1984).
    [CrossRef] [PubMed]
  13. V. Chimelis, “Extinction of CO2 Laser Radiation by Fog and Rain,” Appl. Opt. 21, 3367 (1982).
    [CrossRef] [PubMed]

1984

1983

1982

1980

1979

1978

1977

1975

1971

1970

G. M. B. Bouricius, S. F. Clifford, “An Optical Interferometer Using Polarization Coding to Obtain Quadrature Phase Components,” Rev. Sci. Instrum. 41, 1800 (1970).
[CrossRef]

Ackley, M. H.

Barthel, K.

K. Barthel, “Experimental Investigation of Aperture Limitations of a Heterodyne CO2 Laser Radar by Atmospheric Turbulence and Rain,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1982), paper FV3.

Barthel, K. G.

Bogenberger, R.

Born, G. K.

Bouricius, G. M. B.

S. F. Clifford, G. M. B. Bouricius, G. R. Ochs, M. H. Ackley, “Phase Variations in Atmospheric Optical Propagation,” J. Opt. Soc. Am. 61, 1279 (1971).
[CrossRef]

G. M. B. Bouricius, S. F. Clifford, “An Optical Interferometer Using Polarization Coding to Obtain Quadrature Phase Components,” Rev. Sci. Instrum. 41, 1800 (1970).
[CrossRef]

Büchtemann, W.

Calfee, R. F.

Chimelis, V.

Clifford, S. F.

Erben, K. D.

Frank, F.

Kazovsky, L. G.

Lawrence, R. S.

Lerfald, G.

Mohr, F.

Ochs, G. R.

Schwiesow, R. L.

Sepp, G.

Tatarskii, V. I.

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation, J. W. Strohbehn, Ed. (Israel Program for Scientific Translations, Jerusalem, 1971), available from NTIS.

Tsay, M. K.

Wang, T.-i.

Yura, H. T.

Appl. Opt.

J. Opt. Soc. Am.

Rev. Sci. Instrum.

G. M. B. Bouricius, S. F. Clifford, “An Optical Interferometer Using Polarization Coding to Obtain Quadrature Phase Components,” Rev. Sci. Instrum. 41, 1800 (1970).
[CrossRef]

Other

K. Barthel, “Experimental Investigation of Aperture Limitations of a Heterodyne CO2 Laser Radar by Atmospheric Turbulence and Rain,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1982), paper FV3.

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation, J. W. Strohbehn, Ed. (Israel Program for Scientific Translations, Jerusalem, 1971), available from NTIS.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Schematic representation of the propagation path.

Fig. 2
Fig. 2

Optical layout of the phase difference receiver. BS is a 50% beam splitter for s-polarized light. Each beam has an aperture of 2.2 cm, and the detector to the right operates with an input lens of 62.2-mm focal length and an active area of 6.45 × 10−2 cm2. WP is a wobble plate used to scan the phase difference over ≳2π at a 3-Hz rate. It is used to check interferometer alignment and system operation but not to take data.

Fig. 3
Fig. 3

Received irradiance for a single channel of the setup of Figs. 1 and 2 operating over a path of 1.37 km with radiation of 10.6-μm wavelength. No vertical scale is shown because, although the detector current is proportional to received optical power, the transmitter power, atmospheric attenuation, and beam expansion ratio were not precisely known. In addition to these uncertainties, the ac-coupled preamplifier produces a floating base line for the signal.

Fig. 4
Fig. 4

Superposition of incident (plane-wave in full lines) and scattered (spherical, shown dashed) wave fronts at a receiver aperture. In this elevation view the incident and scattered waves are in phase for a scatterer on the receiver axis (fixed phase changes caused by the scattering process are neglected), but incident and scattered waves are generally out of phase for a scatterer off the axis. The phase of the scattered wave relative to the incident wave depends on distance d from the axis, horizontal distance x between the scatterer and receiver, and wavelength λ.

Fig. 5
Fig. 5

Phase difference between signals received from a single scatterer at two different receiver apertures shown in plan view. The change in relative phase as the scatterer falls approximately perpendicularly to the plane of the figure depends on aperture separation ρ as well as on fall speed and other quantities.

Fig. 6
Fig. 6

Solid line, power spectrum of detector current during a rain, which is proportional to a power spectrum of phase difference fluctuations by Eq. (6). Dashed line, the spectrum immediately after the rain stopped. Dotted section, the spectrum with no input to the spectrum analyzer.

Fig. 7
Fig. 7

Power spectra of phase difference fluctuations showing differences at two stages of the storm. The dashed line is the same as the solid line in Fig. 6, and the solid line is the spectrum taken ~7 min later.

Fig. 8
Fig. 8

Relative spectral power as a result of rain above the no-rain base line (dashed in Fig. 6). Circles are for the spectrum of Fig. 6 and squares for that of Fig. 7. The corresponding power-law slopes are −3.3 and −6.1.

Fig. 9
Fig. 9

Power spectrum of irradiance fluctuations taken during a rain of 15 mm/h ±30% with a single channel. (One beam of the system of Fig. 2 was blocked.) The dashed line is the same as the dashed reference spectrum in Fig. 6, and the peak at 4.3 kHz is at the chopper frequency.

Fig. 10
Fig. 10

Power spectra of phase difference fluctuations with power reference spike from chopped transmitter. The solid line is for a path-averaged rain rate of 30 mm/h ±25%; the dashed for a rate <1 mm/h.

Fig. 11
Fig. 11

Spectral power of the heavy rain case in Fig. 10 above the very light rain reference. The log power is referenced to the chopper peak at 0 dB, and the power law slope is −3.2 ± 0.2.

Equations (13)

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

E j = E 0 exp { i [ ω t + ϕ j ( t ) ] } , j = 1,2 ,
I ( t ) = E E * = dc terms + E 0 2 { exp [ i Δ ϕ ( t ) ] + exp [ i Δ ϕ ( t ) ] } = dc terms + E 0 2 cos Δ ϕ ( t ) ,
Δ ϕ ( t ) = ϕ 1 ( t ) ϕ 2 ( t ) .
Δ ϕ ( t ) = Δ ϕ 0 + δ ( t ) , with δ ( t ) π ,
cos [ Δ ϕ 0 + δ ( t ) ] = cos Δ ϕ 0 cos δ ( t ) sin Δ ϕ 0 sin δ ( t ) = cos Δ ϕ 0 [ 1 δ ( t ) 2 / 2 ! + ] sin Δ ϕ 0 [ δ ( t ) δ ( t ) 3 / 3 ! , ] δ ( t ) sin Δ ϕ 0 , ac only .
F [ a ( t ) b ( t ) ] = ( 1 / 2 π ) A ( f ) * B ( f ) .
P ( Δ ϕ , f ) ¯ P ( δ , f ) ¯ 2 P ( I / E 0 2 , f ) ¯ P ( i , f ) ¯
E j = a j ( t ) E 0 exp { i [ ω t + ϕ j ( t ) ] } , j = 1,2 .
Δ ϕ ( t ) = cos 1 [ I ( t ) / a 1 ( t ) a 2 ( t ) E 0 2 ] ,
E r = E 0 + E 0 a j k ( b k ) exp [ i ϕ j k ( t ) ] , j = 1,2 , k = 1 to n ,
ϕ j k ( t ) = f [ | d k ( t ) | , x k , λ ]
d ( λ x ) 1 / 2 ,
P = ( 1 / B W ) 200 Hz 2.5 kHz [ P ( f ) / P r ] d f ,

Metrics