Whole atmospheric-turbulenceprofiling with generalized scidar
Remy Avila, Jean Vernin, and Elena Masciadri
Statistical analysis of stellar scintillation on the pupil of a telescope, known as the scidar ~scintillation,detection, and ranging! technique, is sensitive only to atmospheric turbulence at altitudes higher than a fewkilometers. With the generalized scidar technique, recently proposed and tested under laboratory condi-tions, one can overcome this limitation by analyzing the scintillation on a plane away from the pupil. Wereport the first experimental implementation of this technique, to our knowledge, under real atmosphericconditions as a vertical profiler of the refractive-index structure constant CN
The basic data for explaining the effects of atmosphericturbulence in optical and near-infrared astronomyare the vertical profiles of the refractive-index struc-ture constant CN
2~h! and the wind velocity v~h!.From these profiles one can calculate1 the Fried pa-rameter r0, the isoplanatic angle u0, and the coher-ence time t0. These are fundamental parameters inhigh angular resolution techniques such as adaptiveoptics and interferometry. Various methods existfor the measurement of CN
2~h! and v~h!, but for prac-tical reasons the most convenient method for astro-nomical purposes is to retrieve them by opticalmeans. This can be achieved with the scidar ~scin-tillation, detection, and ranging! technique. Onecan obtain CN
2~h! profiles by analyzing statisticallythe spatioangular properties of the scintillation of adouble star.2–6 In the case of velocity measure-ments, a spatiotemporal analysis of a single-star scin-tillation is performed.2,7,8
Until now the scidar technique ~which we refer to
The authors are with the Unite Mixte de Recherche 6525 Astro-physique, Universite de Nice-Sophia Antipolis, Centre National dela Recherche Scientifique, Parc Valrose, 06108 Nice Cedex 2,France. R. Avila is on leave from the Instituto de Astronomıa,Universidad Nacional Autonoma de Mexico, Apdo. Postal 70-264,04510 Mexico Distrito Federal, Mexico.
Received 24 February 1997; revised manuscript received 21 July1997.
7898 APPLIED OPTICS y Vol. 36, No. 30 y 20 October 1997
as classical scidar from now on! has been based on thedetection of scintillation on the telescope entrancepupil. Turbulence of as much as a few kilometers is,in this case, undetectable because the scintillation itinduces is very weak, as its variance1 is proportionalto h5y6. This is a severe disadvantage because tur-bulence near the ground ~boundary layer and surfacelayer! and in the telescope dome makes a strong con-tribution to the total phase perturbations.9,10 Toovercome this limitation, a few authors11–13 proposedto detect scintillation on a plane at some distanceaway from the pupil. This new technique, alreadyproved under laboratory conditions,12 is called gener-alized scidar.
Our purpose here is to report the experimentaldemonstration of the generalized scidar as a profilerof CN
2~h! under real atmospheric conditions. Aforthcoming article will be devoted to measurementsof v~h!.
The instrumental setup of the generalized scidar issimple, and the data analysis for obtaining profiles ofthe turbulence along the entire optical path can al-most be done in real time. This instrument might bea helpful companion to adaptive-optics systems, op-timizing their performances, and may be necessary inmulticonjugate adaptive-optics systems.14–16
2. Principle: Brief Resume
A. Classical Scidar
The principle of the classical scidar has been exten-sively explained elsewhere.2–5 When a plane wave
coming from a star crosses a turbulent layer ~acting asa phase screen! at an altitude h, the diffraction patternobserved on the ground is called scintillation or anatmospheric speckle pattern. A second star, a few arcseconds u away, casts onto the ground a second iden-tical speckle pattern shifted by a distance uh in thedirection of the line joining the stars. In that samedirection the autocorrelation function of this doublespeckle pattern shows, at a distance uh, a peak whoseamplitude is proportional to CN
2~h!. In the case ofmultiple layers, each one produces independent phaseperturbations, and the autocorrelation function C**~r!is the sum of the contribution of each layer. It hasbeen shown2 that the difference of the sections ofC**~r! parallel and perpendicular to the stars’ separa-tion, Ci** and C'**, respectively, can be written as
Bpp~x! ; Ci** 2 C'**
5 *0
1`
dhK~x, h!CN2~h! 1 N~x!. (1)
This is an integral relationship between CN2~h! and
Bpp~x!, where the kernel K~x, h! is the theoreticalautocorrelation function produced by a single layer atan altitude h with a unit CN
2 and N~x! is the esti-mated noise. K~x, h! has a bump all along the diag-onal line x 5 uh. Measuring Bpp~x! on the telescopepupil and calculating theoretically K~x, h!, one mustinvert Eq. ~1! ~a Fredholm type! to retrieve CN
2~h! bymeans of a maximum entropy algorithm, for example.The inversion is simplified because there are diago-nal components in K~x, h!.
The classical scidar is based on the measurement ofBpp~x! on the pupil of a telescope. Because scintilla-tion is a diffraction phenomenon, some distance be-tween the turbulent layer and the pupil is necessaryfor any intensity fluctuations to be detected. It iswell known1 that the scintillation variance is propor-tional to h5y6. Because of this, the classical scidar isinsensitive to turbulence in the first few kilometers.
B. Generalized Scidar
Few authors11–13 have suggested the concept of thegeneralized scidar. What differs between classicaland generalized scidars is the altitude of the planewhere scintillation is detected. Using a simple op-tical setup ~see Subsection 3.A!, one can make theplane of the detector the conjugate of a plane ~anal-ysis plane! at a distance hgs ~for the generalized sci-dar! either above or below the telescope pupil. Aturbulent layer at an altitude h produces on thisplane scintillation with a variance proportional touh 2 hgsu
5y6, enabling detection of turbulence near theground ~h 5 0!. When observing a double star, onecan see that a bump in the autocorrelation function ofthe speckle pattern appears at a distance of
d 5 uuh 2 hgsu. (2)
For a unit CN2 this function is described by K~x, uh 2
hgsu!. For multiple layers by analogy with Bpp~x! the
autocorrelation function relevant to the generalizedscidar is
Bgspp~x! 5 B *0
1`
dhK~x, uh 2 hgsu!CN2~h! 1 N~x!. (3)
When the analysis plane is located a few kilometersbelow the pupil ~hgs , 0!, the space between them isturbulence-free because it is virtual, and the CN
2~h!profile in the whole optical path can be retrieved. Inthis configuration h 2 hgs is positive, which allows usto rewrite Eq. ~3! as
Bgspp~x! 5 B*2hgs
1`
dhK~x, h!CN2~h 2 hgs! 1 N~x!. (4)
Applying the same data analysis as in the case of theclassical scidar, i.e., inverting Eq. ~1!, one can shiftthe turbulence profile obtained toward a higher alti-tude by uhgsu and correct it to retrieve the true profile.
When the analysis plane is placed above the pupil~hgs . 0!, a turbulent layer Dh higher than this planeproduces a speckle pattern with the same autocorre-lation function as a turbulent layer Dh lower, as rep-resented by the absolute values in Eq. ~3!. If bothlayers are present, the speckle patterns add up.When the generalized scidar is run under this con-figuration, the resulting turbulence profile is equal tothe true profile but folded around the analysis plane.
In both cases, hgs , 0 and hgs . 0, the distancerelevant to scintillation is uh 2 hgsu.
3. Observation Campaign
Data reported here were recorded during an inten-sive observation campaign at La Palma Observatory,Canary Islands, in November 1995. The general-ized scidar from the Departement d’Astrophysique del’Universite de Nice-Sophia Antipolis ~DAUNSA! wasinstalled at the Nordic Optical Telescope ~NOT! focusfor nine nights. The observing time was shared be-tween the generalized scidar and a Shack–Hartmannwave-front sensor from the Office Nationale d’Etudeset Recherches Aerospatiales ~ONERA!. Simulta-neously, an instrumented mast ~DAUNSA, ONERA!and free-flying balloons ~DAUNSA! were used tomeasure the open-air seeing. Finally, two differen-tial image motion monitors ~DIMM’s! from the Insti-tuto de Astrofısica de Canarias ~IAC! and ONERAwere operated. Later, the generalized scidar wasalso adapted to the William Hershel Telescope ~WHT!for three nights shared with another scidar devel-oped17 at Blackett Laboratory of the Imperial College,London.
A. Experimental Setup
The principle of the experimental setup has been de-scribed in detail by Fuchs et al.11,12 At the back ofthe telescope a rotating optical bench is attached,composed of two fixed lenses and a movable electro-optic device. The first lens, a field lens set exactly atthe telescope focus, displaces the image of the tele-
20 October 1997 y Vol. 36, No. 30 y APPLIED OPTICS 7899
scope pupil to provide access, in the image space, tothe conjugate part of the atmosphere where the anal-ysis plane is placed. The second lens is used to col-limate the beam. The bench can be rotated to alignthe lines of the detector with the double-star orien-tation. One can move the detector back and forth toset the analysis plane in the pupil plane ~classicalscidar!, above it ~folded profile!, or below it ~shiftedprofile!.
The optical magnification G 5 ftelyfcol ratio betweenthe focal lengths of the telescope and the collimatinglens is an important parameter. It determines thesampling area on the telescope entrance pupil if weknow the pixel size of the detector. G2 gives the ratiobetween the vertical domain H through the atmo-sphere, explored by the analysis plane, and its conju-gate domain Z on the optical bench: H 5 G2Z.
Following Vernin and Azouit,3 it is shown that thevertical resolution of the CN
2~h! profiles obtainedwith the generalized scidar is given by
DH 5+~uh 2 hgsu!
u5
0.5u
~luh 2 hgsu!1y2, (5)
where +~uh 2 hgsu! is the equivalent width of thescintillation spatial autocorrelation function, relatedto the first Fresnel zone, and l is the wavelength.
During the observation campaign we used an inten-sified CCD equipped with an electronic shutter set to1-ms exposure time to freeze the scintillation. Wepacked the pixels into 4 3 4 squares to lower the res-olution and accelerate the image processing. The fi-nal size of each effective pixel on the entrance pupilwas 3.8 cm for the NOT and 3.2 cm for the WHT. Theequivalent width +~uh 2 hgsu!, given by Eq. ~5!, is 4.5 cmfor an efficient altitude of uh 2 hgsu 5 10 km and l 5 0.5mm. When looking at the double star g-Arietis ~u 57.82 arc sec!, one finds that the vertical resolutioncorresponding to this example is DH 5 1200 m.
Images captured by the camera are sampled andsent to digital signal processors that can be used tocalculate the autocorrelation functions Bgspp~x! in realtime.
B. Data Analysis
Data analysis for the generalized scidar is basically thesame as it is for the classical scidar. It consists ofinverting Eq. ~4! with a maximum entropy algorithm,where Bgspp ~x! represents the measured constraints,K~x, h! is the kernel, and N~x! is the noise. Theinversion algorithm stops when the solution fitswithin the expected noise, which depends on thenumber of images processed and the photon noiserelated to the flux of the double star. The kerneltakes into account the point-spread function of theintensified CCD camera. The zenith angle is alsoincluded for the altitude scale to be correctly estab-lished. For negative hgs the turbulence profile re-sulting from the inversion of Eq. ~4! is shifted by uhgsudownward for CN
2~h! to be correctly calibrated inaltitude. As stated by Vernin et al.,4 with the max-imum entropy approach it is possible to improve by a
7900 APPLIED OPTICS y Vol. 36, No. 30 y 20 October 1997
factor of 2 the natural vertical resolution DH given byEq. ~5!.
For positive hgs no attempt to reconstruct the trueCN
2~h! is made because of the ambiguity in the mea-sured folded profile.
4. Results
A. Visual Inspection
Simple visual inspection of images focused below theground level gives qualitative information of phasedistortions occurring inside the telescope dome. Animage of the scintillation of the double star Castor ~u5 3.6 arc sec! focused on the NOT pupil ~hgs 5 0! isshown in Fig. 1~a!. Only a few pairs of speckles,denoting the presence of a turbulent layer approxi-mately 9 km above the pupil, are noticeable. Figure1~b! was taken later and focused 3.4 km below ~hgs 523.4 km! ground level. The diffraction pattern ap-pears close to the borders of the pupil. The spiderlooks fuzzier. The pupil images produced by thedouble star are separated horizontally by a distanceof uuhgsu 5 6 cm. This small effect is noticeable onthe vertical spider, which appears doubled. Theconcentric rings, far from the diffraction rings, can beattributed to polishing defects of high spatial fre-quency, producing a static intensity pattern at a dis-tance uhgsu. When the focused plane is moveddownward, the speckles acquire higher contrast andlook sharper, which leads us to believe that they come
Fig. 1. Images of 1-ms exposure time ~a! focused on the pupilplane and ~b! 3.4 km lower obtained on the NOT during observa-tion of the double star Castor ~u 5 3.6 arc sec!.
Fig. 2. Autocorrelation functions Bgspp~x! mea-sured at the WHT with the analysis plane at hgs 50 ~solid curve!, hgs 5 22 km ~dashed curve!, hgs 524 km ~dotted–dashed curve!, and hgs 5 26 km~dotted curve!. Squares and circles represent theexpected positions of the autocorrelation peaks ashgs varies and CN
2 remains constant.
from turbulence at low altitude, because the specklesize is proportional to ~uh 2 hgsu!
1y2, as shown in Eq.~5!. By looking at images on a monitor in real time,one can observe that the sharpest speckles moveslowly around, which is the signature of turbulenceinside the dome, in the tube of the telescope, or closeto the surface of the primary mirror.
Note that constant intensity patterns do not affectthe autocorrelation function Bgspp~x!, because thecontribution of the autocorrelation of the time-average intensity field is suppressed during signalprocessing.3
B. Measured Autocorrelation Functions
Now we investigate the behavior of the measuredautocorrelation functions for different positions of the
analysis plane below the telescope pupil ~hgs # 0! onthe one hand and above it ~hgs $ 0! on the other.
Figure 2 shows autocorrelation functions Bgspp~x!measured at the WHT with the analysis plane atpositions hgs 5 0, 22, 24, and 26 km, at time inter-vals of 6 min, each computed over a set of 2700 im-ages. The double star is g-Arietis. Plots begin atthe third point of the measured Bgspp~x!, becauseBgspp~0! [ 0 as derived from Eq. ~1!, and we are notconfident about the second point owing to instrumen-tal artifacts. For hgs 5 0 ~classical scidar! the plothas a strong peak centered at approximately x 5 0.42m, corresponding to a turbulent layer 11 km abovethe pupil along the optical path. As hgs decreases,this peak is regularly shifted. Near the origin apeak from turbulence at ground level starts to be
Fig. 3. Autocorrelation functions Bgspp~x! mea-sured at the WHT with the analysis plane at fourdifferent positions above the pupil ~hgs $ 0!. Forclarity we determined the values of Bgspp~x! foreach curve by subtracting 0.01n to read values,where n is the integer associated with each plot.Dotted lines represent Bgspp~x! 5 0 for each curve.
20 October 1997 y Vol. 36, No. 30 y APPLIED OPTICS 7901
Fig. 4. CN2~h! profiles retrieved from the auto-
correlation functions shown in Fig. 2 as a functionof the altitude above sea level. The dashed hor-izontal line represents the observatory altitude.The CN
2 values for each plot were obtained bydividing read values by 103n, where n is the inte-ger associated with each plot.
visible for hgs 5 22 km. For the lower values of hgsit is shifted by the same amount as the former peakand is clearly detected. Squares and circles aredrawn at the expected location on the graph on thetop of each peak. Squares correspond to the low-altitude layer and circles to the 11-km layer. Wecalculated their abscissa from Eq. ~2!, taking as ref-erence d 5 0 for the square ~not shown! and d 5 0.42m for the circle ~measured peak! when hgs 5 0. Thecalculated abscissa fall within the uncertainty inter-val of the center of the measured peaks. FollowingRoddier,1 it can be shown theoretically that the max-imum of the autocorrelation peak is proportional touh 2 hgsu
5y6 for a given CN2~h!. We calculated the
vertical coordinates of the squares and circles follow-ing this law and taking as references the values ofBgspp~x! at the top of the peaks indicated by the ar-rows in Fig. 2. For the low-altitude peak we foundgood agreement when extrapolating the peak corre-sponding to hgs 5 22 km. Concerning the 11-kmlayer, CN
2 probably decreased with time between themeasurements recorded for hgs 5 24 and 26 km.
To test for the predicted11 folding of the measuredturbulence profile, we placed the analysis plane suc-cessively at hgs 5 0, 2, 4, and 6 km. Figure 3 showsthe corresponding autocorrelation functions Bgspp~x!.
For hgs 5 0 no turbulence is detected at ground level,but two bumps appear corresponding to layers atapproximately 12 and 16.5 km along the optical path.As hgs increases, the distance between the analysisplane and these layers decreases, and the observedbumps in Bgspp~x! get smaller and closer to the origin.In contrast, as hgs increases, the distance between theanalysis plane and the turbulence near the groundincreases, giving rise to a peak near the origin al-ready detectable for hgs 5 2 km, growing more andmore and moving away from the origin. When hgs 56 km contributions of ground-level and high-altitudelayers add up because they overlap.
C. Retrieved CN2~h!
Figure 4 shows the CN2~h! profiles we retrieved from
the measured autocorrelation functions shown in Fig.2, using the inversion method explained in Subsec-tion 3.B. CN
2 in the horizontal axis is representedas a function of the altitude above sea level hasl, cor-rected from the zenith angle of the observed star.The dashed line represents the altitude of the obser-vatory ~2400 m!. For hgs 5 0 no turbulence is de-tected near the ground, whereas with the othervalues of hgs a strong CN
2 is measured there. Thevertical structure of the turbulence in the free atmo-
Fig. 5. Average of 10 CN2~h! profiles obtained at
the NOT within 10 min with the analysis plane athgs 5 23.4 km. The dashed line represents theobservatory altitude.
7902 APPLIED OPTICS y Vol. 36, No. 30 y 20 October 1997
Fig. 6. Contribution to the seeing of the turbulence NG and FA. Diamonds, lozenges, and stars represent NG seeing ~dome and boundarylayer!, FA seeing, and total seeing, respectively, calculated from the available CN
2~h! profiles measured with the generalized scidar. Eachframe corresponds to a night. Abscissa display decimal time. When greater than 24 h it corresponds to the following date. Data in ~a!and ~b! were recorded at the NOT and data in ~c! and ~d! at the WHT. Solid curves represent simultaneous IAC DIMM seeingmeasurements.
sphere is similar from plot to plot. There is mainlya high-CN
2 layer centered at hasl 5 13 km and twoweaker layers at 9 and 5 km. The layer at groundlevel is poorly measured with hgs 5 22 km becausethe corresponding autocorrelation peak ~dashedcurve in Fig. 2! is not completely detected. Besides,whenever detected, this layer appears slightly shiftedbeneath the ground. Although the position of thelayer center falls inside the uncertainty interval ofthe expected altitude ~hasl 5 0 6 0.7 km!, this errorseems to be systematic. It could be due to insuffi-cient accuracy in the collimation or determination ofthe position of the pupil image. Nevertheless, it isnot a troublesome effect. The portion of the plot at alower altitude than that of the observatory has to beunderstood as part of the response of the instrumentto CN
2 just above the ground.An example of CN
2~h! profiles obtained at the NOTappears in Fig. 5. There are three main layers.The measured low-altitude layer is more accuratelycentered at the observatory altitude.
5. Discussion
The full width at half-maximum of a long-exposureimage of a point source ~seeing! can be calculatedfrom the CN
2~h! profile as1
e 5 5.25l21y5F* dhCN2~h!G3y5
. (6)
We estimated the contribution to the seeing of theturbulence near the ground ~NG! ~dome 1 surfacelayer 1 boundary layer! and that of the free atmo-sphere ~FA! from Eq. ~6!, integrating experimentalCN
2~h! profiles over the peak at ground level and inthe rest of the atmosphere, with all the generalizedscidar data available. The results are shown in Fig.6, where each frame corresponds to a night, ~a! and~b! on the NOT and ~c! and ~d! on the WHT. Dia-monds, lozenges, and stars correspond to the NG see-ing, FA seeing, and total seeing, respectively. Thesolid curves in Figs. 6~a! and 6~d! are the available
20 October 1997 y Vol. 36, No. 30 y APPLIED OPTICS 7903
Fig. 7. Comparison between CN2~h! profiles ob-
tained with the generalized scidar ~stars! and theballoon sounding ~solid curve!. The balloon waslaunched at 1:30 UT on 9 November 1995, and thegeneralized scidar measurement was calculated1 h later. The balloon profile was convolved ~seetext!.
seeing measurements carried out with the IACDIMM that was located 200 m away from the tele-scope domes. Both instruments were observingclose to the zenith, avoiding any bias caused by large-scale geographical effects.18 On the first night at theNOT @Fig. 6~a!# NG seeing was slightly lower than FAseeing. The total seeing measured with the gener-alized scidar was systematically approximately 0.1arc sec higher than that measured with the DIMM.This small difference could come from the turbulenceinside the dome, detected by the generalized scidarbut not by the DIMM in open air, and would confirmthe previously reported9 low dome seeing of the NOT.On the night beginning 8 November @Fig. 6~b!# bothcontributions to the total seeing were similar to eachother except in the last run. Results obtained withthe WHT, shown in Figs. 6~c! and 6~d!, behave differ-ently. NG seeing is always much higher than seeingfrom the FA. Unfortunately, this is explained notonly by the extremely weak seeing detected in the FAbut also by the high NG seeing. Comparing, in Fig.6~d!, the open-air total seeing measured with theDIMM on 12 November and the total seeing given bythe generalized scidar leads us to suppose that ap-proximately half the NG seeing detected comes fromturbulence inside the dome.
An example of a comparison between CN2~h! pro-
files obtained with the generalized scidar and a free-flying instrumented balloon is shown in Fig. 7. Theballoon was launched on 9 November 1995 at 1:30UT, and the generalized scidar measurement wasrecorded 1 h later when the balloon had reached 17km above sea level. The balloon profile shown ~solidcurve! is the result of the convolution of the originalprofile with a suitable window for the purpose of ob-taining a vertical resolution similar to that of thegeneralized scidar ~stars!. Both instruments de-tected three main turbulent layers. The strongestturbulence was found at the observatory level ~2.4
7904 APPLIED OPTICS y Vol. 36, No. 30 y 20 October 1997
km!, where the balloon measurement might have di-verged owing to some effect during the launching. Aweaker turbulent layer was detected at 6 km by thegeneralized scidar and at 7 km by the balloon. Fi-nally, both instruments detected a layer at 12.5 km.Agreement between the two profiles is reasonablygood, considering that the instruments measuredCN
2 at slightly different times and places. Indeed,the balloon profile was obtained by in situ measure-ments during the ascent at 4-mys vertical speed ~1 h,20 min for 20 km!, whereas the generalized scidarprovided simultaneous CN
2 estimates at all altitudes.Moreover, the balloon, drifting with the wind, fol-lowed a trajectory different from the line of sight ofthe generalized scidar.
6. Conclusion
We have confirmed the theoretically predicted behav-ior of the generalized scidar. A simple optical setupenables the transition from the classical scidar that isinsensitive to low-altitude turbulence to the general-ized scidar that is sensitive to turbulence all alongthe optical path. An example of the importance ofdetecting turbulence near the ground has been shownin Section 5. The previously reported low turbu-lence level inside the NOT dome,9 estimated with adifferent technique from that used here, is confirmed.We are not aware of other measurements of turbu-lence inside the WHT dome. The low resolution inaltitude prevents our discerning turbulence insidethe dome from that of the boundary and surface lay-ers. Measuring the propagation velocity of eachlayer could avoid this ambiguity because index ofrefraction fluctuations inside the dome would show azero mean velocity, whereas turbulence outside thedome would appear as propagating at a low velocity.One can accomplish this by calculating the spatio-temporal cross-correlation function ~instead of thespatial autocorrelation function! of successive scintil-
lation images in the generalized scidar configuration,i.e., focusing below the ground level. A forthcomingarticle will be devoted to that subject.
We are indebted to M. Azouit for managing thetechnical aspects of the scidar and balloons. Wethank C. Munoz-Tunon for giving us valuable help inlogistics and providing the IAC DIMM seeing mea-surements. We acknowledge E. Gizard and the Cen-tre National de la Recherche Meteorologique for theircomplementary operation and loan of their balloon-tracking system. Sharing the observing time in theNOT with the ONERA team was a pleasure thanks totheir valuable cooperation. We appreciate the effi-cient help of M. Andersen from the NOT. We alsothank J. C. Dainty for giving us the opportunity toobserve at the WHT. This study was made possiblewith financial support from the ONERA, NOT, andCentre National de la Recherche Scientifique. Wemake special mention of the late J. F. Manigault forhis part in the successful completion of this research.
References1. F. Roddier, “The effects of atmospheric turbulence in optical
astronomy,” in Progress in Optics, E. Wolf, ed. ~North-Holland,Amsterdam, 1981!, Vol. 19, pp. 281–376.
2. A. Rocca, F. Roddier, and J. Vernin, “Detection of atmosphericturbulent layers by spatiotemporal and spatioangular correla-tion measurements of stellar-light scintillation,” J. Opt. Soc.Am. 64, 1000–1004 ~1974!.
3. J. Vernin and M. Azouit, “Traitement d’image adapte auspeckle atmospherique. II. Analyse multidimensionnelleappliquee au diagnostic a distance de la turbulence,” J. Opt.~Paris! 14, 131–142 ~1983!.
4. J. Vernin, M. Crochet, M. Azouit, and O. Ghebrebrhan, “SCI-DARyradar simultaneous meaurements of atmospheric turbu-lence,” Radio Sci. 25, 953–959 ~1990!.
5. J. Vernin, “Atmospheric turbulence profiles,” in Wave Propa-gation in Random Media ~Scintillation! - Invited Papers, V. I.Tatarskii, A. Ishimaru, and V. U. Zavorotny, eds. SPIE Press~Bellingham, Wash. 1992!, pp. 248–260.
6. R. Racine and B. L. Ellerbroek, “Profiles of nighttime turbu-lence above Mauna Kea and isoplanatism extension in adap-tive optics,” in Adaptive Optical Systems and Applications,R. K. Tyson and R. Q. Fugate, eds., Proc. SPIE 2534, 248–257~1995!.
7. J. L. Caccia, M. Azouit, and J. Vernin, “Wind and CN2 profiling
by single-star scintillation analysis,” Appl. Opt. 26, 1288–1294~1987!.
8. J. L. Caccia and J. Vernin, “Wind fluctuation measurements inthe buoyancy range by stellar scintillation analysis,” J. Geo-phys. Res. 95, 13683–13690 ~1990!.
9. J. Vernin and C. Munoz-Tunon, “Optical seeing at La PalmaObservatory II—Intensive site testing campaign at the NordicOptical Telescope,” Astron. Astrophys. 284, 311–318 ~1994!.
10. C. E. Coulman, J. Vernin, and A. Fuchs, “Optical seeing—mechanism of formation of thin turbulent laminae in the at-mosphere,” Appl. Opt. 34, 5461–5474 ~1995!.
11. A. Fuchs, M. Tallon, and J. Vernin, “Folding-up of the verticalatmospheric turbulence profile using an optical technique ofmovable observing plane,” in Atmospheric Propagation andRemote Sensing III, W. A. Flood and W. B. Miller, eds., Proc.SPIE 2222, 682–692 ~1994!.
12. A. Fuchs, “Contribution a l’etude de l’apparition de la turbu-lence optique dans les couches minces: Concept du SCIDARgeneralise,” Ph.D. dissertation ~Universite de Nice, Nice,France, 1995!.
13. J. D. Bregman, C. M. de Vos, and U. J. Schwartz, “The effectsof pupil refocussing on different atmospheric heights,” in HighResolution Imaging by Interferometry II, Proceedings of ESOConference 39, J. M. Beckers and J. M. Merkle, eds. ~EuropeanSouthern Observatory, Garching, Germany, 1991!, pp. 1067–1071.
14. R. Foy and A. Labeyrie, “Feasibility of adaptive telescope withlaser probe,” Astron. Astrophys. 152, L29–L31 ~1985!.
15. J. M. Beckers, “Increasing the size of the isoplanatic patchwith multiconjugate adaptive optics,” in Very Large Telescopesand their Instrumentation, Proceedings of ESO Conference 30,M.-H. Ulrich, ed. ~European Southern Observatory, Garching,Germany, 1988!, pp. 693–703.
16. M. Tallon, R. Foy, and J. Vernin, “3-D wavefront sensing formulticonjugate adaptive optics,” in Progress in Telescope andInstrumentation Technologies, Proceedings of ESO Conference42, M.-H. Ulrich, ed. ~European Southern Observatory, Garch-ing, Germany, 1992!, pp. 517–521.
17. V. A. Kluckers, N. L. Wooder, M. A. Adcock, and J. C. Dainty,“Results from Scidar observations,” in Image Propagationthrough the Atmosphere, J. C. Dainty and L. R. Bissonnette,eds., Proc. SPIE 2828, 234–243 ~1996!.
18. D. F. Buscher, “A thousand and one nights of seeing on Mt.Wilson,” in Amplitude and Intensity Spatial Interferometry II,J. B. Breckinridge, ed., Proc. SPIE 2200, 407–417 ~1994!.
20 October 1997 y Vol. 36, No. 30 y APPLIED OPTICS 7905
