Fluctuations in backscattered signals due to turbulence innear-IR and visible lidar measurements
S. Fastig and Ariel Cohen
Spectral cross-correlation measurements performed in the near IR and in the visible, X1 = 1.06 ,m and X2
0.53 ,um, show that the main contribution to the fluctuations for the above lidar wavelengths originate inatmospheric turbulence. The measurements were performed in nonsaturation conditions verified by anincrease in the backscattered signal fluctuations with an increase in the target range. Normalized measure-ments as a function of daytime hours representing varying atmospheric turbulence conditions are presentedand discussed.
The physics of laser beam fluctuations in the atmo-sphere, with consideration given to the backscatteredreturns from a distant hard target, has been studied byseveral authors.1-4 In the work by Menyuk et al.2
uncertainties caused by strong fluctuations (due pri-marily to speckle effects) were considered. To reducethe uncertainties, average values were used to deter-mine the effect of signal averaging on the accuracy ofthe measurements. The results of this analysis indi-cate that the averaging process provides relatively lim-ited improvement and consequently that the measure-ments performed in the presence of atmospheric-fluctuations should be carefully examined.
Flamant et al. 3 used a pulsed CO2 lidar to study thestatistical properties of the signal returns from targetsat distances near 2 km. It was shown that the signifi-cant differences in the signal return statistics are aresult of different lidar configurations, all mainly dueto speckle effects.
Methods to improve the accuracy of lidar measure-ments in the presence of atmospheric fluctuations aresummarized in Menyuk et al.
4 In particular theyshowed that the combined effect of signal averagingand temporal cross correlation should be taken intoaccount. This is due to the fact that lidar signals
S. Fastig is with Soreq Nuclear Research Center, AtmosphericOptics Department, Yavne 70600, Israel, and A. Cohen is with He-brew University of Jerusalem, Department of Atmospheric Sciences,Jerusalem 91904, Israel.
propagating through the atmosphere are subject totemporal fluctuations as a result of the atmosphericextinction, scintillation effects of atmospheric turbu-lence,5 speckle or glint effects on the target, and man-made fluctuations at the laser source as well. In thework of Menyuk et al.2 ,
4 and Flamant et al.3 the effect
of fluctuations on CO2 laser beams was discussed.Below we show our measurements of the effect of the
fluctuations on the returned signals, in the visiblerange, where the atmospheric turbulence is expectedto play a significant role.
The lidar used in the course of these studies was abistatic lidar system based on a Nd:YAG laser, capableof transmitting both 1.06-/im and frequency doubled0.53-,Mm radiation (Fig. 1). The system parametersare summarized in Table I.
Two identical 1.5 X 1.5 m2 white-painted hard tar-gets were used in this experiment for measuring in twodifferent ranges. Reflectance characteristics werecompared with those of Eastman Kodak white paintno. 6080, and it was found to be the same, namely,nearly Lambertian, with a reflectance efficiency of 0.9at both wavelengths. Furthermore, the targets werechecked and found to be homogeneous over most oftheir area.
The data recording system was planned to collectthe input laser pulse energy and the returned signalfrom one target at both wavelengths, simultaneously.The system is triggered by the laser and is micro-processor controlled. The operation rate, limited bythe laser capability, was 20 pulses/s and sets of 512-1024 consecutive pulses were permanently stored forlater analysis.
The standard deviation (sd) of the signal fluctua-tion, defined as
Fig. 2. Standard deviation of the fluctuation lidar backscatteredsignal as a function of time. The backscattered signal was measuredin two wavelengths: solid line, XA = 0.53 ,um, dashed line, X2 = 1.06jum; path lengthL = 1100 m. The bars are the estimated experimen-
tal error.
Fig. 1. The Nd:YAG lidar schematic diagram.
N 1/2a = 1N A [V. -V(t,)]2 (1)
[where Vo is the average signal, V(ti) is the ith mea-sured signal, N is the number of measurements], wasmeasured as a function of the time of day. Thechanges in the value of a are summarized in Fig. 2. Itcan be seen that in the morning hours, the value of agenerally increases to a constant value, being reachedabout noon, and in the afternoon hours it decreases at agrowing rate until sunset.
Another aspect of the fluctuation of the signal can bedetected in analyzing the correlation coefficient, de-termined as
Fig. 3 Correlation coefficient relative to time of day calculated forthe normalized signals measured in two wavelengths: X = 0.53 jmand X2 = 1.06 jm (+) and the non-normalized return signal and the
outgoing energy both in the same wavelength X = 0.53 ,um (-).
for two signals in two different wavelengths normal-ized relative to the outgoing energy, and once for thenon-normalized signal in one wavelength against itsoutgoing signal (see Fig. 3).
We note that the correlation coefficient for the twowavelengths as a function of daytime hours is firstrelatively low, reaching a maximal value at noon, thenit decreases gradually until sunset. On the otherhand, the correlation function between the returnedsignal against the outgoing laser energy in one givenwavelength shows a behavior which is just the oppo-site: during the early morning hours-relatively high,reaching a minimum at noon, and then continuouslyincreases until sunset.
Another parameter, the influence of which on thevarying signal was investigated, was the target dis-tance. During the measurements the target distanceL had been changed by directing the lidar to a secondidentical target to the first but placed at approximate-ly half of the distance. The distances were chosen tobe L, = 1100 m and L2 = 450 m. Typical variationsdue to target distance are shown in Fig. 4. The mainresult of the measurements indicates that by increas-ing the beam path through the turbulent atmosphere,the sd of the backscattered signal was also increased.
Fig. 4. Effect of target distance on the standard deviation for X =
1.06,um.
The effect of the changes in the telescope field ofview (FOV) on the sd of the backscattered signal isshown in Fig. 5. The FOV is controlled by the diame-ter D of an aperture placed in the focal plane of thetelescope. A sharp decrease of the sd level followedthe increase of the aperture, as long as the diameterwas less than D = 4 mm (corresponding to a FOV angleof 1 mrad). When D > 4 mm, no further changes in thesd were detected.
The normalized fluctuations in the backscatteredsignal can be caused by
(1) The atmospheric effect on the laser beam travel-ing from the laser to the target and from the target tothe telescope (see below).
(2) The target reflection inhomogeneities.(3) The speckle effect between the target and the
telescope (due to the laser coherence).(4) System electronic noise including background
noise.The relative contribution of each of the possible
causes listed above depends on the meteorological con-ditions and the optical parameters of the lidar-targetsystem.
Flamant et al.3 and Menyuk et al.2 '4 measured thefluctuations in the standard signal from a fixed targetusing a CO2 laser. They concluded that the speckleeffect is the main cause of the fluctuations.
In our experiment the contribution of the speckleeffect to the fluctuation is much smaller than that ofthe turbulence since the wavelengths used are de-creased by an order of magnitude.
The atmospheric turbulence has a characteristic di-urnal behavior which is dependent on the atmosphericheating. We can, therefore, find the explanation forthe behavior of the sd as a function of time to be almostuniquely governed by the atmospheric turbulence.
During the morning hours when the temperature isrelatively low, the turbulence intensity is also relative-ly small and consequently its influence on the scat-
30
-20 -
10 T
0 1 2gt(mrod)
Fig. 5. Standard deviation of the signal as a function of the tele-scope FOV (0t).
tered signal scintillation is small. This results in a lowsd. The atmospheric heating reaches a maximum atnoon and consequently the turbulence intensity has itshighest value. The degree of the signal scintillationincreases and thus the sd level is also high. During theafternoon hours, approaching sunset, the atmospherebegins to cool and the turbulence intensity decreaseswith a corresponding decrease in the signal sd. (Atypical illustration of the atmospheric heating can befound in Ref. 6, Fig. 18,9, which is a 24-h record ofacoustic echo sounding.)
The behavior of the correlation coefficient can alsobe related to the turbulence effect on the laser pulse.When the turbulence is weak the correlation betweenthe normalized signals in two wavelengths is expectedto be small assuming that the correlation induced bythe atmospheric extinction is small for a target dis-tance of -1 km. Furthermore, when the turbulence isweak for each separate wavelength it is expected thatthe correlation between the backscattered signal andthe outgoing energy signal will be significant. Thiswas indeed the case as described above (see Fig. 3 for X= 0.53 im).
Another indication of the turbulence contribution tothe signal fluctuation can be found by investigating theeffect of the target distance on the fluctuation level. Itwas found that whenever the scintillations are notsaturated, the larger the distance the greater is thefluctuation integral effect (see Fig. 4).
An additional parameter of interest, namely, thetelescope FOV value, was also changed and its influ-ence on the sd level was investigated. By controllingthe FOV, the actual area of the illuminated targetwhich was viewed could be determined. In propagat-ing through the atmosphere, the laser beam is affectedby the integral of all the scintillations to and from thetarget. The fluctuations caused by the scintillationsto the target can be detected by their influence on the
width of the laser spot on the target and the energydistribution within the spot.
For a large value of the telescope FOV the changes inenergy distribution have little effect on the total re-flected light intensity fluctuations. Thus, when theFOV is large enough to cover the total illuminatedtarget area, the turbulence effect on the beam passagebetween the laser and the target is averaged out.However, when the FOV is small and only a fraction ofthe total illuminated target area is seen by the tele-scope, the measured signal fluctuations are also depen-dent on the turbulence effect on the beam passagefrom the laser to the target.
The results of the measurements which emphasizedthe effect of atmospheric turbulence of lidar returnscan be summarized as follows:
(1) The stronger the turbulence, the larger is thetotal effect on the signal fluctuations in the visiblerange. Thus, turbulence is the dominant factor in thedaily change in behavior of the signal fluctuations.
(2) An increase in the target range leads to a similarincrease in the backscattered signal fluctuations.This indicates that the turbulence effect measuredduring this experiment was not in saturation. We notethat the nature of the experiment required nonsatura-tion conditions and the range effect was used to verifythis condition.
(3) When the receiver FOV was smaller than that ofthe laser transmitter, the signal fluctuations werefound to decrease with the increase in the receiverFOV. This effect emphasizes the averaging of theatmospheric scintillation due to turbulence along thebeam path to the target.
(4) The signal fluctuations were measured in eachwavelength and compared with the initial laser sourcefluctuations. The normalized signal relative to theoutgoing pulse of this measurement showed that themeasured fluctuations are related to the atmosphericfluctuations.
References1. D. K. Killinger, N. Menyuk, and W. E. DeFeo, "Experimental
Comparison of Heterodyne and Direct Detection for Pulsed Dif-ferential Absorption CO2 Lidar," Appl. Opt. 22, 682 (1983).
2. N. Menyuk, D. K. Killinger, and C. R. Menyuk, "Limitations ofSignal Averaging Due to Temporal Correlation in Laser Remote-Sensing Measurements," Appl. Opt. 21, 3377 (1982).
3. P. H. Flamant, R. T. Menzies, and M. J. Kavaya, "Evidence forSpeckle Effects on Pulsed CO2 Lidar Signal Returns from Re-mote Targets," Appl. Opt. 23, 1412 (1984).
4. N. Menyuk, D. K. Killinger, and C. R. Menyuk, "Error Reductionin Laser Remote Sensing: Combined Effects of Cross Correla-tion and Signal Averaging," Appl. Opt. 24, 118 (1985).
5. R. J. Hill, R. S. Lawrence, and S. F. Clifford, "Refractive-Indexand Adsorption Fluctuations in the Infrared Caused by Tempera-ture, Humidity, and Pressure Fluctuations," J. Opt. Soc. Am. 70,1192 (1980).
6. V. E. Derr, Ed., Remote Sensing of the Troposphere (U.S. CPO,Washington, DC, 1972).
Books continued from page 1904
Many-Body Aspects of Solid State Spectroscopy. By R. F.WALLIS and M. BALANSKI. North Holland Publishing Co., Am-sterdam, 1986. 423 pp. $70.50.
As the title says, this book is primarily devoted to many-bodytechniques applied to the theory of optical properties of solids. It isnot an introduction to the optical properties of solids; it is not even acomprehensive account of the theoretical models used to describethese properties. It is an exposition of modern theoretical tech-niques of solid-state physics. Written with clarity and considerableattention to detail, it should prove useful to graduate students andphysicists who want to acquire a working knowledge of the theoreti-cal language found in the recent literature of theoretical solid-statephysics.
The first chapter gives a standard account of the macroscopictheory in terms of the complex dielectric function, the Kramers-Kronig relation, and damping constants. The book then turns tothe many-body formalisms with emphasis on Green's functions.These are applied in turn to IR absorption due to optical phonons,optical absorption by free and bound electrons, magnetooptics, andscattering of light, including Raman scattering. Each of these topicsis treated separately with reference to the chapter which introducesthe Green's function techniques. This organization minimizes thedemand placed on the reader; nevertheless the book does not makeeasy reading.
The difficulty is that the emphasis is on the techniques. A com-mon feature of all these problems is that the light interacts withexcitations which themselves-by interacting with other excitationsof the crystal-have a finite lifetime. This causes broadening andshift of the absorption frequencies. The many-body techniquesavoid the phenomenological description of this subsequent interac-tion in favor of a logical and self-consistent treatment, which inactual cases allows a systematic development to all orders of pertur-bation. Although the theory treated here has wider applicabilitythan optical properties of solids, the present scope makes sense,because these properties form such a large part of solid-state physicsand because the authors are eminent experts in this area.
In some ways this is unfortunate even if inevitable. The topicscovered usually have a wider implication. Consider the section onanharmonicity. A general discussion is given of the anharmonicterms of the potential energy of the lattice, paying attention to therequirements of translational and directional symmetry in a wayfound in few other places. These terms are used in the self-consis-tent Green's function approach of IR absorption and Raman scatter-ing. Yet the same anharmonicities are the physical cause of thermalexpansion, of some departures of the high-temperature specific heatfrom the Dulong-Petit limit, of thermal resistance in dielectric crys-tals, of ultrasonic attenuation, and of reversible nonlinear elasticeffects. Furthermore, it is from these properties that much of ouractual knowledge of anharmonicities is derived. The omission ofthese connections leaves the physical model somewhat incomplete.
The book is very instructive for those who already possess a goodbackground in solid-state physics and who want to deepen theirunderstanding of the formal theory, but it cannot serve as an intro-duction to the subject. Even in its coverage of the optical proper-ties, which is its objective, its emphasis on the advanced theorymakes it valuable to a limited audience of theoreticians but unsuitedas an introduction of solid-state optics.
For a clear and comprehensive account of the many-body orGreen's function theory in its several forms, the book is without peer.
