Extinction of CO 2 laser radiation by fog and rain Vincent Chimelis Results of extinction measurements of CO 2 laser radiation by fog and rain are discussed. Experimental re- sults obtained in fog with extinction ranging from 1 to 72 dB/km and in rain with extinction ranging from 1.7 to 17 dB/km are reported. Extinction by fog is supported by an extensive particle size data base. Calcu- lations of extinction obtained from size distributions yielded extinction in excess of 290 dB/km. Measure- ments show that transmission losses in dense fog can easily be 6 orders of magnitude greater than losses in heavy rain. I. Introduction Laser propagation through the atmosphere is severely limited by atmospheric effects such as fog and rain. Because of the high power achievable and covertness, CO 2 lasers are finding a multitude of uses in military applications such as target designators, beam riders, moving target indicators, terrain following, weapons delivery, and imaging. CO 2 lasers have also grown in importance in applications such as pollution monitor- ing, optical communications, and earth resources remote sensing. These applications require detailed knowledge of CO 2 laser atmospheric extinction and its dependency upon relevant meteorological parameters associated with adverse weather phenomena. In this paper, results of measurements on the ex- tinction of CO 2 laser radiation by fog and rain are pre- sented. Particle size data for over 150 fog distributions were collected. The extinction efficiency factors for the various density distributions were computed, and these were used in numerical integration to calculate extinc- tion. Results were compared with extinction calcula- tions obtained using an approximation based on the liquid water content of the fog particle distribution. With few exceptions, results differed by <7%. Where applicable, comparison with direct laser measurements gave good results, with extinction differing by <5% during stable fog periods. Extinction by rain with precipitation rates up to 75 mm/h is presented. Using nonlinear regression techniques, an empirical model for determining extinction as a function of precipitation is formulated, and this is compared with results derived from other reported measurements. The author is with U.S. Air Force Wright Aeronautical Laborato- ries, Avionics Laboratory, Electro-Optics Branch, Wright-Patterson AFB, Ohio 45433. Received 18 December 1981. II. Experimental Apparatus The laser transmissometer is shown in Fig. 1. It consists of a multiline CO 2 laser which is mounted coaxially to a He-Ne laser. A 2-deg wedge is used to combine axiallythe CO 2 and He-Ne laser outputs. The signals are modulated at a 1-kHz rate using a WWVB NBS reference time signal which is also used to phase lock the receiver. M 2 and M 3 form a 20X beam ex- pander which provides a 20-cm (8-in.) beam at the re- ceiver. The energy at the receiver is collected by a 60.9-cm (24-in.) f/5 parabolic mirror which is tilted slightly off-axis. The signal is folded and passed through a couple of beam splitters, which are used to limit the energy reaching the detector. In addition, the first beam splitter is used to provide a reference signal for calibration of the receiver and to measure the re- ceived He-Ne signal whenever desired. Lens L is used to relay the CO 2 signal into an f/10 solid recollector R. This arrangement provides a steady signal to the de- tector during periods of high turbulence. When prop- erly aligned, signal variation is -1% in periods of ex- treme turbulence. Pyroelectric detectors (D 1 and D 2 ) are used at both transmitter and receiver,and this limits the dynamic range of the system to 72 dB. The signal processing electronics are shown at the bottom of Fig. 1. The signal conditioning and recording are almost identical, except that in the receiver section a phase-lock amplifier is used to phase lock the receiver to the transmitter. Extinction measurements were conducted over a 1-km atmospheric path. Weather and particle sizedata were collected at the receiver end only. To ensure a nearly isotropic atmospheric path, the receiver signal was visually monitored using a digital voltmeter. Stable voltmeter readings indicated a good probability of a stable atmospheric path, while a varying voltmeter reading indicated an unstable atmospheric path. 15 September 1982 / Vol. 21, No. 18 / APPLIEDOPTICS 3367
Transcript
Extinction of CO2 laser radiation by fog and rain
Vincent Chimelis
Results of extinction measurements of CO2 laser radiation by fog and rain are discussed. Experimental re-sults obtained in fog with extinction ranging from 1 to 72 dB/km and in rain with extinction ranging from1.7 to 17 dB/km are reported. Extinction by fog is supported by an extensive particle size data base. Calcu-lations of extinction obtained from size distributions yielded extinction in excess of 290 dB/km. Measure-ments show that transmission losses in dense fog can easily be 6 orders of magnitude greater than losses inheavy rain.
I. Introduction
Laser propagation through the atmosphere is severelylimited by atmospheric effects such as fog and rain.Because of the high power achievable and covertness,CO2 lasers are finding a multitude of uses in militaryapplications such as target designators, beam riders,moving target indicators, terrain following, weaponsdelivery, and imaging. CO2 lasers have also grown inimportance in applications such as pollution monitor-ing, optical communications, and earth resources remotesensing. These applications require detailed knowledgeof CO2 laser atmospheric extinction and its dependencyupon relevant meteorological parameters associatedwith adverse weather phenomena.
In this paper, results of measurements on the ex-tinction of CO2 laser radiation by fog and rain are pre-sented. Particle size data for over 150 fog distributionswere collected. The extinction efficiency factors for thevarious density distributions were computed, and thesewere used in numerical integration to calculate extinc-tion. Results were compared with extinction calcula-tions obtained using an approximation based on theliquid water content of the fog particle distribution.With few exceptions, results differed by <7%. Whereapplicable, comparison with direct laser measurementsgave good results, with extinction differing by <5%during stable fog periods. Extinction by rain withprecipitation rates up to 75 mm/h is presented. Usingnonlinear regression techniques, an empirical model fordetermining extinction as a function of precipitation isformulated, and this is compared with results derivedfrom other reported measurements.
The author is with U.S. Air Force Wright Aeronautical Laborato-ries, Avionics Laboratory, Electro-Optics Branch, Wright-PattersonAFB, Ohio 45433.
Received 18 December 1981.
II. Experimental Apparatus
The laser transmissometer is shown in Fig. 1. Itconsists of a multiline CO2 laser which is mountedcoaxially to a He-Ne laser. A 2-deg wedge is used tocombine axially the CO2 and He-Ne laser outputs. Thesignals are modulated at a 1-kHz rate using a WWVBNBS reference time signal which is also used to phaselock the receiver. M 2 and M 3 form a 20X beam ex-pander which provides a 20-cm (8-in.) beam at the re-ceiver. The energy at the receiver is collected by a60.9-cm (24-in.) f/5 parabolic mirror which is tiltedslightly off-axis. The signal is folded and passedthrough a couple of beam splitters, which are used tolimit the energy reaching the detector. In addition, thefirst beam splitter is used to provide a reference signalfor calibration of the receiver and to measure the re-ceived He-Ne signal whenever desired. Lens L is usedto relay the CO2 signal into an f/10 solid recollector R.This arrangement provides a steady signal to the de-tector during periods of high turbulence. When prop-erly aligned, signal variation is -1% in periods of ex-treme turbulence. Pyroelectric detectors (D1 and D2)are used at both transmitter and receiver, and this limitsthe dynamic range of the system to 72 dB. The signalprocessing electronics are shown at the bottom of Fig.1. The signal conditioning and recording are almostidentical, except that in the receiver section a phase-lockamplifier is used to phase lock the receiver to thetransmitter.
Extinction measurements were conducted over a1-km atmospheric path. Weather and particle size datawere collected at the receiver end only. To ensure anearly isotropic atmospheric path, the receiver signalwas visually monitored using a digital voltmeter.Stable voltmeter readings indicated a good probabilityof a stable atmospheric path, while a varying voltmeterreading indicated an unstable atmospheric path.
Measurements of fog-size distributions were madewith a Knollenberg-type counter, PMS model FSSP-100 light-scattering particle-measuring system. Thisinstrument is useful for measuring particles with radiibetween 0.25 and 23.5 .Am. Calibration of the PMScounter is performed with the aid of a Berlund Liu TSI3050 vibrating orifice monodisperse aerosol counterwhich generates particles with diameters between 1.3and 24.3 gm. The diameter of the particles is verifiedby collecting them on a treated glass slide and using ahigh-resolution microscope equipped with a Vickersimage splitting eyepiece. With corrections for dropletspread, this device gives measurements which are ac-curate to within 0.05 m. When properly aligned andadjusted, the PMS counter gives size values that arewithin 10% of those generated for particles with diam-eters larger than 2 gm. For smaller particles the sizedifference varies between 10 and 20%.
To keep the measurement time to a minimum, thePMS counter was kept at a preset range during eachmeasurement. For dense fog measurements, the 1-23.5-gm radius range was used. Neglect of particlesbelow 1 Am in size does not result in significant errors,since Mie computations show that for water dropletsbelow this size, extinction of <0.1 km can be expected.This is of little significance when dealing with densefog.
111. Computation Methods
According to Lambert's law,1 the power received PRfrom a laser beam is related to the power transmittedPT by the relation
PR = PT exp(-axL), (1)
where ad is the extinction coefficient per unit length at
3 B B
M D 2
D, - 7. L4
wavelength X, and L is the propagation path.transmittance in the path length is given by
T = PR/PT = exp(-oxL).
The
(2)
Taking the natural log of both sides yields the expres-sion for the extinction coefficient
¢x = - lnT(km-), (3)
where L in kilometers has been chosen.van de Hulst2 showed that the extinction of electro-
magnetic energy of wavelength X, propagating througha medium which contains scattering and absorbingparticles, is given by
° = J R Qext(a,X,n)N(a)a2da,fRo
where N(a) is the size distribution for the particulatesof radius a and size range R, to R, and Qext(aXn) isthe Mie extinction efficiency factor for spherical par-ticles with refractive index n = - n2 . Qext(aXn)as given by exact Mie theory is difficult to compute andis very time-consuming. For computational purposes,the approximation worked out by van de Hulst,3
Qext(x) = 2 - 4 exp(-a tan:l cos(f/la) sin(a - O)
+ 4 cos2(i/a)[cos23-cos(a-2B) exp(-a tan)], (5)
where
x = 2ira/X, a = 2x(ni - 1), and 3 = tan-ln2/(nl - 1),
is more convenient to use. Because of the assumptions,the van de Hulst approximation overestimates the ex-tinction efficiency factor for small a and underestimatesit in varying degrees as ae approaches and surpasses theposition for the first maximum in Qext(x). Deirmend-jian worked out correction factors, which, when appliedto Eq. (5), give extinction values which are within 6% ofthe values obtained from exact Mie calculations as ap-plied to water particles near the 10.6-um wavelength.4
For particles with radii above 7 Aim, use of the Deir-mendjian correction factors gives answers that arewithin 3% of values obtained by exact Mie theory.However, the error becomes larger for smaller particles,with the error ranging from 0.2 to 6% for particles withradii between 1 and 7 Atm. For particles with radii of<1 Am, the correction factors fail, giving answers thatincrease rather than reduce the error. Deirmendjiancorrection factors were modified to give results whichare within 1.0% of exact Mie calculations for a X of 10.6,um.
5 Complex index of n = 1.185-0.0662j as given byHale and Querry6 is used.
To aid in analysis, it was useful to apply Chylek'srelationship between extinction and the liquid watercontent W of the fog distribution.7 Chylek showedempirically that extinction may be approximated by
, = rc W,=2Xp
Fig. 1. C 2 laser transmissometer.
(6)
where c is the slope of a line approximating Qext(x), and
moved out to be followed by fog with entirely differentcharacteristics. Some of the extinction data obtainedduring this period are tabulated in Tables II, III, and IV.Size distributions representative of the data tabulatedon Table II are plotted on Figs. IV and V. The 0550distribution of Fig. 4 corresponds to an extinction of 66.9dB/km. Shortly after this measurement, the signal waslost and was not detectable during the next 40 min.
Table II. Extinction of CO2 Laser Radiation in Heavy Fog (Data Taken 19Feb. 1981)
Fig. 4. Particle size distribution for dense fog, 19 Feb. 1981,0545-0605 h.
1I
IU)01IiJUH
V
z
010
12
-2210
0.
------ 0620
- - - 0620- ,t-x- 0650- --- 071 n
- -- I __ I I
4. S. 12. 115. 20 4.-
l
0
-v
I l
RADXUS 4MICRONS>
Fig. 5. Particle size distributions for dense fog, 19 Feb. 1981,0620-0710 h.
The stable nature of the fog between 0620 and 0710 isillustrated on Fig. 5. This is reflected by the good cor-relation between ,,, c, and ,,,. Figure 6 presents sizedistributions taken 10 min apart. As can be seen fromTable IV, the size distributions correspond to extinctionof 173.3, 270.9, 281, and 220.3 dB/km. The highest,extinction computed during this period was 291 dB/kmand occurred at 0735 h. Size distributions corre-sponding to extinction data taken between 0805 and0820 h are plotted in Fig. 7 The fog reached its mini-mum intensity at 080 h and had started to grow in in-
p is the density of water. Using the values c = 0.33 ata value of X = 10.6 Am, and p = 1 g/cm3 , Eq. (6) be-comes
u = 147 W km-,
small shift in the concentration of large particles cancause a large change in the measured extinction. Dis-tribution for 0610 and 0615 h appears to be almostidentical in size, but from Table I it can be seen thatthere is a 31-dB/km difference in extinction betweenthem.
An excellent opportunity for fog measurements wasprovided on 19 Feb. Fog rolled in, stabilized, and then
210
10
A1.
IMm
<0HI-I()W.
a.
(7)
where the validity of Eq. (7) is good for computationswhere the majority of the particles in the fog size dis-tribution have radii equal to or less than 13 gim. Theliquid water content is obtained by numerical integra-tion of the equation
4 j'RmW=- r a3N(a)da.
3
10
-1I
-210
-3100(8)
- 06050610
--- 0615-- 0620
--- - 0625
>N
-
I' Ia 4. e. 12. 1n. 20. 24.
In the accompanying fog distribution plots that fol-low, N(a) is the number of particles per cm3 having amean square radius a2 in the sampling interval beingmeasured. N(a) is obtained by dividing the total par-ticle count in each size range by the volume samplingrate of 7.54 cm3/sec and the sampling time of the mea-surement. For the measurements reported here, asampling time of 60 sec was used. The units of dB/kmare used in this paper. These are obtained by multi-plying the (km'1) units by 4.34.
IV. Extinction by Fog
Extinction data for the morning of 18 Feb. 1981 aretabulated in Table I for indicated size distributionshaving mean radius rrn. Between 0605 and 0655 h, ex-tinction in the optical path exceeded the dynamic rangeof the system. The direct laser extinction values mea-sured are tabulated under am. The extinction com-puted from the size distribution and extinction effi-ciency factors is tabulated under c. The last two col-umns give the fog liquid water content in g/m3 and theextinction obtained by use of Eq. (7). Comparison ofoc and ah gives values which differ by <6% for fogs withliquid water content above 0.09 g/m3. Measurementstaken at 0705 and 0715 show a good correlation betweenam and a, indicating that the fog was very uniform atthese times. Figures 2 and 3 show several size distri-butions corresponding to the data tabulated on TableI. Both of these figures illustrate the bimodal tendencyof some of the distributions. They also show that a
RADIUS CMICRONS>
Fig. 2. Particle size distribution for dense fog, 18 Feb. 1981,0605-0625 h.
102
l10
IUaI
i-M
V
Z
010
-110
-2.10
0.
Fig. 3. Particle
4. S. 12. 18. 20. 24.
RADIZUS CM1 CRONS>
size distribution for dense fog, 18 Feb. 1981,0630-0650 h.
other, yet there is almost a 4 to 1 difference in the ex-tinction produced. Variation in extinction withchanging fog is documented on Table V. Data werecollectedwiththeRl8line (10.2 6Mm). A31X decreasein transmission is observed between 0809 and 0811 h.
V. Extinction by Rain
A plot of extinction at 10.6 gm vs precipitation rateP in mm/h is shown in Fig. 8. The data contain pointsfrom three separate sets of extinction measurementsobtained on 22, 28, and 29 Apr. 1981, in which themaximum precipitation rates measured were 58, 46, and75 mm/h, respectively. The solid line represents thebest fit to the measured data obtained through appli-cation of a nonlinear regression scheme. The derivedequation is given by
U = 1.4P° 6 dB/km.Il
4. . 12. lie. 20. 24.
RADIUs CICRCNS)
distributions for extremely dense fog, 19 Feb.1981, 0720-0750 h.
-0805.. . 0810
-- -0815
---- 0820
4. B. 12. 165. 20. 24.
RADIUS CMICRONS)
1981,Fig. 7. Particle size distributions for selected fogs, 19 Feb.0805-0820 h.
tensity at 0810 h. The parts of the distributions withradii <6 gm are almost identical. The small increaseshown in the larger particles between 6 and 23 m isresponsible for more than the 30% rise in extinction. Asimilar analogy may be made for the distributionsshown for 0815 and 0820 h. The most interesting fea-ture of Fig. 7 is that the mean and maximum radii of thedistributions shown are nearly equal in size to each
Table V. Extinction of 10.26-jum CO2 Laser Radation with Time (19 Feb.1981)
Fig. 9. Best fit models for data of Fig. 8, Laws and Parsons as re-ported by Chen, and measurements conducted by Rensch.
The same nonlinear regression scheme was applied torain extinction data published by Chen8 and Renschand Long.9 The resulting curves are plotted on Fig. 9alongside the model given by Eq. (9). Chen's calcula-tions were obtained from data derived from the Lawsand Parsons'0 rainfall measurements. The rain rateswere derived from measurements of drop size and dropterminal velocity." These quantities do not lendthemselves to easy meassurements. The relationshipderived from Chen's results is given by
ax = 1.085P° 6 59 dB/km. (10)
Equation (10) was derived from data with rain rates upto 50 mm/h. The extension to 75 mm/h was done by thecomputed based on the model given by Eq. (10). Datafrom Rensch and Long were obtained from direct pre-cipitation measurements. Their results follow fairlywell with other two results up to rain rates of 25 mm/h,but then it begins to drop off. A best fit model to theirdata is given by
or = 1.84P0 5 0 1 dB/km. (11)
VI. Summary
Extinction of CO2 laser radiation in adverse weatherwas measured using a tunable laser transmissometerhaving a 72-dB dynamic range. Measured results werecompared to extinction values obtained from the cal-culated extinction efficiency factors and the liquid watercontent of the fog size distribution. Calculations ofextinction obtained from density distributions yieldedextinction by fog as high as 291 dB/km.
Extinction by rqin with rain rates up to 75 mm/h wasmeasured. An empirical model was derived for deter-mining extinction as a function of precipitation in
mm/h. Models were also derived from published databy other workers, and these were compared with themodel derived from measurements in this investigation.Measured extinction in heavy rainfall was found to bean order of magnitude less than measured extinction inheavy fog.
The author wishes to thank Jeff Sweet, RussellCampbell, and Richard Norris for help with the com-puter programs, David Rardin who operated the lasertransmitter, and Douglas Redmond who collected theraw particle size data.
This work was performed while the author was agraduate student at the University of Dayton.
References1. M. Holter, S. Nudelman, G. Suits, W. Wolfe, and G. Zissis, Fun-
damentals of Infrared Technology (Macmillan, New York, 1963),p. 72.
2. H. C. van de Hulst, Light Scattering by Small Particles (Wiley,New York, 1957), p. 129.
3. Ref. 2, p. 179.4. D. Deirmendjian, Electromagnetic Scattering on Spherical
Polydispersions (Elsevier, New York, 1969), p. 30.5. V. Chimelis, "Extinction of CO 2 Laser Radiation in Adverse
Weather," Dissertation, U. Dayton, Dayton, Ohio (1981), pp.168-171.
6. G. M. Hale and M. R. Querry, Appl. Opt. 12, 555 (1973).7. P. Chflek, J. Atmos. Sci. 35, 296 (1978).8. C. C. Chen, "Attenuation of Electromagnetic Radiation by Haze,
Fog, Cloud and Rain," Report R-1694-PR, The Rand Corp. (Apr.1975), p. 5.
9. D. B. Rensch and R. K. Long, Appl. Opt. 9, 1563 (1970).10. J. 0. Laws and A. Parsons, Trans. Am. Geophys. Union 24, 452
(1943).11. C. C. Chen, "A Correction for Middleton's Visible and Infrared
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