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RevMexAA (Serie de Conferencias), 31, 61–70 (2007)

TURBULENCE PROFILES FROM THE SCINTILLATION OF STARS,

PLANETS, AND MOON

Andrei Tokovinin1

RESUMEN

La turbulencia atmosferica puede ser caracterizada por el centelleo de las fuentes astronomicas. Se presentauna breve revision de la fısica del centelleo debil y fuerte. El Sensor de Centelleo Multi-Apertura, MASS, utilizalas propiedades espaciales del centelleo producido por una estrella para reconstruir perfiles de turbulencia debaja resolucion. Se presenta una descripcion del instrumento combinado MASS-DIMM y se evalua la precisionde este metodo. Se describe el experimento de remplazar la estrella por un planeta, ya que en ese caso se puedesensar la turbulencia a unos cuantos cientos de metros sobre el sitio. Sin embargo, de mayor importacia esmedir la turbulencia en la vecindad inmediata de un telescopio o un monitor del sitio. En este caso, un medidorde centelleo lunar es el metodo a elegir. Un medidor de centelleo lunar, LuSci, esta siendo desarrollado por elObservatorio Inter-Americano de Cerro Tololo (CTIO). Se presenta el nuevo metodo para interpretar sus datosy los resultados de las primeras pruebas.

ABSTRACT

Atmospheric turbulence can be characterized by the scintillation of astronomical sources. The physics ofweak and strong scintillation is briefly recalled. The Multi-Aperture Scintillation Sensor, MASS, uses spatialproperties of the scintillation produced by single stars to reconstruct low-resolution turbulence profiles. Adescription of the combined MASS-DIMM instrument is given and the accuracy of this method is evaluated.By replacing a single star with a planet, we can sense turbulence at few hundred meters above the site, and suchan experiment is described. However, of greater importance is to measure the turbulence in the immediatevicinity of a telescope or site monitor. Here, lunar scintillation is the method of choice. A simple lunarscintillometer, LuSci, is under development at CTIO. A new method to interpred its data and the results offirst tests are presented.

Key Words: ATMOSPHERIC EFFECTS — SITE TESTING — TURBULENCE

1. INTRODUCTION

Twinkling of the stars —scintillation— is themost obvious manifestation of atmospheric opticalturbulence which causes “seeing”. Can we use thisphenomenon for a quantitative measurement of see-ing? A scintillation-based device, scintillometer, isinsensitive to the angular pointing and typically hassmall apertures, thus favoring its application for site-testing in the field.

One of the first attempts to extract turbulenceprofiles from scintillation has been undertaken byOchs et al. (1976). It has been established earlierthat the strength of scintillation measured througha 10-cm aperture is closely related to the isoplanaticangle. Krause-Polstorf et al. (1993) compared iso-planatic angles measured by this method with thosederived from the scintillometer of Ochs et al.

Scintillation coming from different layers can bedisentangled by using a double star. This method,

1Cerro Tololo Inter-American Observatory, Casilla 603, LaSerena, Chile (atokovinin@ctio.noao.edu).

called Scidar, has been developed by J. Vernin et al.and appears to be the best direct optical techniqueof turbulence profiling available to date. Originally,Scidar was not sensitive to the near-ground turbu-lence because it does not produce any scintillation.However, a modification of this method proposed byFuchs et al. (1998) and called Generalized Scidar isfree from this problem and can measure completeturbulent path, from the telescope to the top of theatmosphere.

The Scidar method has two problems: it requiressuitably bright double stars and a large (≥ 1m) aper-ture. A need for a simple single-star turbulenceprofiler has driven us to develop a Multi-ApertureScintillation sensor, MASS, described below in § 3.Recently, a new instrument, Single-Star Scidar, hasbeen proposed by Habib et al. (2006). It recordsscintillation of single stars and separates contribu-tions of different turbulent layers by spatio-temporalanalysis.

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62 TOKOVININ

Planets, unlike stars, do not scintillate. Their an-gular diameter effectively averages scintillation pro-duced by high turbulent layers. However, some weakscintillation originating mostly in low layers does re-main. It can be measured and used to probe low-altitude turbulence. Such experiment is described in§ 5. Pushing this idea to the extreme, we can evenmeasure the scintillation of the Sun or Moon. Inthis case, the amplitude of the scintillation is verysmall, and it probes air in the immediate vicinity(few tens of meters) from the ground. The idea touse solar scintillation for turbulence measurementshas been developed by Beckers (2001) and imple-mented in the instrument called Shabar. It provedto be decisive in the modern campaign of day-timesite testing (Socas-Navarro et al. 2005). We discussthe use of lunar scintillation in § 6.

2. PHYSICS OF SCINTILLATION

Corrugations of the wave-front produced by theturbulence can be thought of as weak lenses. Whensuch a lens is positive, it focuses the light and theintensity at the ground increases, while a negativelens does the opposite. This simple geometric-opticsview is correct for large-scale perturbations (Fig-ure 1). For perturbations comparable to or smallerthan the Fresnel radius

√λz (λ is the wavelength,

z is the propagation distance) the interference oflight becomes significant, hence such “lenses” actrather as diffraction gratings. Consequently, scintil-lation at small spatial scales r <

√λz is wavelength-

dependent, but at larger scales it is achromatic.The theory of light propagation through weak

turbulence is well developed (Tatarskii 1961; Rod-dier 1981). It predicts that the spatial spectrum ofthe light-wave amplitude χ passing through a weakphase screen and propagating over a distance z is

Φχ(f) = 0.0229r−5/3

0 |f |−11/3 sin2(πλz|f |2) . (1)

The spectrum of intensity fluctuations (scintillation)is ΦI = 4Φχ. Here, f is the 2-dimensional spatial

frequency (in m−1) and r−5/3

0 = 0.423(2π/λ)2C2ndz

is the Fried parameter of a turbulent layer withrefractive-index fluctuations C2

n and thickness dz.An example of the spectrum (1) is shown in Fig-

ure 2. The first maximum is at a frequency f ≈(λz)−1/2, i.e. inverse of the Fresnel radius. At lowerspatial frequencies, in the geometric-optics regime,we can replace the sine by its argument, so thespectrum becomes proportional to f−11/3+4 = f1/3.This is the spectrum of the wave-front curvature,which is nearly white for Kolmogorov turbulence.

Inte

nsity

dilute

interfere

Wavefront

concentrate(focus)

Fig. 1. Qualitative explanation of the scintillation fromthe geometric-optics (left) and wave optics (right) per-spectives.

The curvature is achromatic, r−5/3

0 ∝ λ−2. Interest-ingly, atmospheric errors in photometry and differ-ential astrometry are also proportional to the large-scale wave-front curvature, and hence can be directlyinferred from scintillation (Kenyon et al. 2006).

An aperture of diameter D acts as a spatial fil-ter, admitting only fluctuations with |f | < D−1. Tocalculate the total scintillation power, we have tomultiply the spectrum (1) with a suitable aperturefilter, integrate it, and multiply by 4. The result willbe a scintillation index s2

A, defined as

s2A =

〈∆I2A〉

〈IA〉2, (2)

where IA is the instantaneous light intensity receivedthrough some aperture A, ∆IA is its fluctuation. Thedefinition is equivalent to the variance of log I forweak scintillation. Although the turbulence theoryusually operates with the variances of the logarithm,in practice formula (2) must be used because it per-mits correct treatment of photon counts rather thanintensities (Tokovinin et al. 2003).

With apertures of different size, we can distin-guish the altitude where the scintillation was pro-duced (e.g., Kornilov & Tokovinin 2001). An evenbetter method is to measure the differential scintil-lation index s2

AB between two apertures A and B,

s2AB = 〈

(

∆IA

〈IA〉− ∆IB

〈IB〉

)2

〉 . (3)

Again, for weak scintillation this is equivalent tothe variance of log(IA/IB), but the definition (3)is preferable. It has been shown that the differen-tial index in two concentric annular apertures is al-most independent of the propagation distance z forz >

√λDA, where DA is the diameter of the smallest

aperture (Tokovinin 1998, 2002b, 2003). The differ-ential index in such apertures in nothing else but

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TURBULENCE PROFILES FROM SCINTILLATION 63

Fig. 2. Power spectra of scintillation produced at theground. Smooth curves – analytical theory, Equation 1,“noisy” curves – direct numerical simulation. Top panel– weak turbulent layer at 10 km, bottom panel – strongscintillation when a 2′′ seeing is created by two equallayers at 2 km and 10 km.

the scintillation power filtered in the frequency bandfrom 1/DB to 1/DA. Thus, MASS with its cen-timetric apertures is sensitive to the turbulence ofcentimetric scales.

In the framework of the small-perturbation the-ory, both normal and differential scintillation indicess2

k depend on the turbulence profile C2n (z) linearly

as

s2k =

∫

Wk(z) C2n (z)dz , (4)

where the weighting function (WF), Wk(z), describesthe altitude response of a given aperture or aperturecombination k (Tokovinin 2002b, 2003). If the WF isconstant, it means that the scintillation index gives adirect measure of the turbulence integral, hence see-ing. The differential index has this attractive prop-erty and thus provides a more-or-less direct measureof the seeing in the free atmosphere. This idea waspublished by Tokovinin (1998) and first tested the

same year at Mt. Maidanak with a Double-ApertureScintillation Sensor, DASS (Kornilov & Tokovinin2001).

For normal scintillation indices, W (z) increasesas z5/6 for small apertures or as z2 for large ones(Roddier 1981). Steep dependence of the scintilla-tion strength on altitude was an obstacle for mea-suring seeing by this method because we could notdistinguish weak and high turbulence from the lowand strong one. Differential indices have solved thisproblem.

The above formulae are valid only for weak scin-tillation, s � 1. This is so-called single-scattering,or Rytov approximation. In reality, the scintillationis not always weak, even at zenith. In this case,the spatial structure of the intensity fluctuations de-viates from (1), sometimes quite significantly (Fig-ure 2, bottom panel). Qualitatively, the deviationcan be understood as a strong focusing, when tur-bulent “lenses” can produce bright, small spots atthe ground. The size of such spots is smaller thanthe size of the lenses, so the power migrates to highfrequencies. Alternatively, the effect can be seen asan appearance of second harmonics or combinationfrequencies in the intensity pattern created by strongphase gratings. Under strong scintillation, the com-bined effect of several layers is no longer additive, aspredicted by Equation 4: high layers cross-modulatethe scintillation produced by lower layers. There isno theory describing these effects in a quantitativemanner, despite many years of theoretical work onstrong scintillation (e.g., Andrews et al. 1999). Notethat the low-frequency part of the spatial spectrumis not affected by saturation, so large-scale inten-sity fluctuations are still a simple consequence of thewave-front curvature, as prescribed by the geometri-cal optics.

Considering the scintillation of an extendedsource, say a disk of angular diameter θ, we must ad-ditionally multiply the spectrum (1) by a filter corre-sponding to a circle of diameter θz. At low altitudeswhere θz <

√λz this additional filter has little ef-

fect, but at higher altitudes it dominates, admittingonly low spatial frequencies. As a result, the scin-tillation is weakened, being produced only by largelenses. This is the regime where geometric optics isapplicable, so such scintillation is achromatic (Kaiser2004).

3. THE MASS INSTRUMENT

In the Multi-Aperture Scintillation Sensor(MASS) turbulence profiler (Kornilov et al. 2003),the light of a single bright star is detected by fourconcentric apertures which act as a spatial filter

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64 TOKOVININ

*

BA C D

Photon Counters

Turbulent Layer

Propagation

Computer

Bright Star

aperturesAnnular

Fig. 3. Principle of the Multi-Aperture Scintillation Sen-sor, MASS.

(Figure 3). Photon counts in each aperture regis-tered with an exposure time of 1 ms are processedto calculate 4 normal and 6 differential scintillationindices. These indices are then fitted to a modelof 6 turbulent layers (Tokovinin et al. 2003) usingEquation 4.

Most MASS instruments built to date are com-bined with a Differential Image Motion Monitor,DIMM (Sarazin & Roddier 1990) in a single device(Figure 4). It is attached to a small telescopes of25-cm diameter or larger and shares the pupil be-tween MASS and DIMM channels. The image ofthe exit pupil is formed by a lens inside the instru-ment on the pupil plate, where two DIMM mirrorsand 4 concentric annular mirrors of MASS, segmen-tator, are located. The segmentator sends 4 beamsA, B, C, and D to light detectors – miniature photo-multipliers R74000 from Hamamatsu. The detectorsand their photon-counting circuits are assembled ina very compact module which can be detached andreplaced if necessary. The diameter of the outerMASS aperture (in projection on the entrance pupil)is about 8 cm, its inner aperture is about 2 cm.

An essential part of the MASS is its software,Turbina. Individual photon counts are not saved onthe disk (although this can be done for technical pur-pose), but rather processed in real time to computescintillation indices every second. After each minute,the average indices are calculated and the turbulenceparameters are determined. The raw data (indices)

From telescope Segmentator

Pupil plateTo CCD (DIMM)

PMTs &electronics

Fig. 4. MASS-DIMM instrument and main elements ofits MASS channel.

and turbulence profiles are saved in the text filestogether with accompanying information which per-mits various sanity checks of the data.

4. ACCURACY OF MASS

MASS is essentially a fast photometer. However,its useful signal is not the flux, but rather its fluctu-ations, scintillation indices. Of course, even a con-stant light will produce fluctuating photon countsbecause of the shot noise, but this bias is subtractedin the data processing. Useful, atmospheric fluctu-ations are measured from T = 1 min. integrations.The relative error of the indices is determined bythe statistics of the signal and is on the order of(T/τ)−1/2, where τ is the characteristic time of sig-nal fluctuations. In practice, this error is about 2–3%, independently of the strength of scintillation.Thus, the relative random errors of MASS are essen-tially constant, except situations when the shot noisedominates (very weak turbulence and faint stars, es-pecially for the sAB index). In the restoration pro-cess, these errors translate to a random error of tur-bulence in each layer reaching 10% of the total in-tegral (Tokovinin et al. 2003). Hence, turbulencestrength of less than 10−15 m1/3 in the MASS datafiles should be treated as zero.

The absolute calibration of MASS relies on theknowledge of the aperture geometry and spectral re-sponse – these quantities define the weighting func-tions and are used to translate measured scintillationindices into turbulence profiles. Practice and simula-tion show that the magnification factor defining thediameters of projected apertures must be measuredto an accuracy of ∼ 3%. Needless to say that nochange of the aperture geometry (e.g. by vignetting

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TURBULENCE PROFILES FROM SCINTILLATION 65

0 1 2 3 4 5 6 7UT

0.25

0.5

1

2

4

8

16

Alti

tude

, km

MD20+RCX400 (up) and ELT-DS+C11 (down)Cerro Tololo, March 11/12 2006

MD21 MD23 MD22

Fig. 5. Inter-comparison of MASS instruments (March2006, Cerro Tololo). The length of the bars is propor-tional to the C2

ndh integrals in each layer and plotted

against time. One MASS instrument was working con-tinuously as a reference (upper bars), while three otherinstruments were use sequentially on a different telescope(lower bars).

or non-uniform dust) is allowed. The spectral re-sponse is determined from the known properties ofthe detectors and optics and is checked by compar-ing the fluxes of stars of different colors with theirexpected fluxes. Of course, the color of the star itselfinfluences the overall spectral response and is takeninto account in the MASS software.

Despite careful calibration, all MASS instru-ments are slightly different, e.g. because of theirindividual detector characteristics. Comparison be-tween two MASSes reveals that the integral param-eters such as free-atmosphere seeing or isoplanaticangle usually match within few percent. The turbu-lence profiles are also similar, but their details maydiffer, sometimes in a systematic way (e.g. Figure 5).For example, one instrument may “think” that mostof the turbulence is at 2 km, while another measuresthe same turbulence distributed between 1 km and2 km. The agreement between instruments is alwaysbetter for the two highest layers (8 km and 16 km)than for the lowest layers, because the scintillationfrom high altitudes is stronger. A direct comparisonbetween MASS and Scidar (Tokovinin et al. 2005)leads to the same conclusion.

The free-atmosphere seeing measured by MASSshould always be better or equal to the full seeingmeasured by DIMM. However, it was found that un-der strong turbulence, MASS typically measures aworse seeing, “over-shoots” (Figure 6). At first, this

3 4 5 6 7 8UT, hours

0

0.5

1

1.5

2

2.5

3

Seei

ng, a

rcse

c

Uncorrected MASS seeingDIMM seeingCorrected MASS seeing

Fig. 6. “Over-shoots” of MASS and their correction. Thedata were taken at Cerro Tololo on October 7/8, 2004when the seeing was dominated by high layers.

seemed counter-intuitive, as we expected that strong,saturated scintillation would under-estimate the tur-bulence strength. Numerical simulations (Figure 2)revealed that in fact under strong scintillation thepower at high frequencies increases (compared to theweak-perturbation theory) and it is wrongly inter-preted by the MASS software as scintillation pro-duced by low layers. The turbulence profile is hencedistorted (shifted to lower altitudes) and the seeingis over-estimated.

In the absence of strong-scintillation theory, theproblem was tackled by numerical simulation. It wasfound that “over-shoots” can be approximately cor-rected if the turbulence integral measured by MASSis divided by (1 + sA). Further study led to a moreelaborate scheme where all measured indices are cor-rected and then used in the standard profile restora-tion procedure (Tokovinin & Kornilov 2007). Thismethod works for moderately strong scintillation,sA < 0.7. Beyond this point, MASS does not givequantitative results, all we can say is that the tur-bulence in the upper atmosphere is very strong.

5. PLANET SCINTILLATION

The smallest MASS aperture is 2 cm, of the or-der of the Fresnel radius

√λh for h = 0.5 km layer.

Can we push this method to lower altitudes by usinga smaller aperture, say 1 cm? In principle, yes, butwe will need stars ∼20 times brighter. Not only theflux will be less, but the scintillation from low alti-tudes is weak, too. It would be difficult to separatethis weak scintillation from the much stronger signaloriginating at high altitudes.

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66 TOKOVININ

AC

D

C

B

2.0, 3.6, 6.6, 13cm

Apertures ABCD

Angular diameter 19.7"AD

A

BD

AB

BC

CD

Fig. 7. Weighting functions for the scintillation of Sat-urn. Apertures and their combinations are marked bysingle and double letters for the normal and differentialindices, respectively.

Planets are extended sources and scintillate muchless because the signal from high-altitude layers isspatially averaged. As a result, the weighting func-tions for the normal indices decline at high altitudes,instead of growing (Figure 7), and the WFs for dif-ferential indices fall down rapidly. Thus, planetaryscintillation “senses” turbulence located mostly inthe first kilometer above ground. Interestingly, thecondition max(D, θz) >

√λz is always fulfilled, so

the scintillation signal is always averaged by eitheraperture (at low altitudes) or by the planet (at highaltitudes) at spatial scales longer than the Fresnel ra-dius. Therefore, planetary scintillation is describedby the geometric optics and is achromatic.

The maxima of the WFs occur when those twoaveraging factors are comparable, i.e. at propagationdistance z ∼ D/θ. If we want to probe a large zoneof altitudes, a correspondingly large span of aperturesizes is needed. Depending on the angular diameterθ of the planet available on the sky, the sensitiv-ity zone of a planetary scintillometer (PlaSci) movescloser or further away from the telescope. Moreover,the sensitivity is a function of the range z = h/ cos γinstead of altitude h, i.e. it depends on the zenithdistance γ. In a MASS, a star sufficiently close tothe zenith can always be selected, so its results arerelated to the altitudes h. In contrast, the param-eters of PlaSci depend on the available planet andchange during the night as the planet moves on thesky.

Experiments with PlaSci were conducted atCerro Tololo Inter-American Observatory (CTIO) on4 nights in November-December 2004, when a Slodar

Fig. 8. Response of a planetary scintillometer corre-sponding to some linear combinations of the WFs. Fulllines show the synthetic response for three layers – low,middle, and high. The dashed line is the sum of theseresponse functions.

turbulence profiler was tested and compared to So-dar. The data from Slodar, Sodar and MASS-DIMMprovide a benchmark for evaluating the new method,PlaSci. The only planet available on the sky in thisperiod was Saturn, visible in the morning at highair mass. In the data processing, we neglected therings which contributed only few percent of the light,and calculated WFs for a uniform disk of angular di-ameter 19.7′′. A first-generation MASS instrumentwith apertures from 2 cm to 13 cm was used, witha neutral-density filter in the D-channel to preventsaturation of the photon counts.

Some WFs displayed in Figure 7 have maximain the first kilometer and provide a measure of tur-bulence strength in this zone. A better job of tur-bulence profile restoration can be done by combin-ing linearly the WFs with suitable coefficients. Weused only three indices sAB , sBD, and sC and foundtheir linear combinations that better isolate threepre-selected layers (Figure 8). At air mass of ∼2,the first layers corresponded to altitudes of ∼100 mand ∼200 m above the observatory.

A comparison with MASS-DIMM have shownthat PlaSci gives reasonable results, although the dif-ference in the response functions of these instrumentsprevents a quantitative conclusion. In Figure 9, theseeing in the two PlaSci “layers” is compared to theseeing inferred from the acoustic sounder, Sodar,by integrating its profiles with the same response.Again, we see a qualitative agreement, but somequantitative differences. Note that at that time the

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TURBULENCE PROFILES FROM SCINTILLATION 67

Fig. 9. Comparison between the low-altitude seeing (inarcseconds) measured with PlaSci (lines) and Sodar (as-terisks) on December 1/2, 2004, at Cerro Tololo (hori-zontal axis – universal time). The low and middle layersare at altitudes of ∼100 m and ∼200 m, respectively

absolute calibration of Sodar was still uncertain, butit has improved since (Travouillon 2006).

Planetary scintillometer fulfills the promise to ex-tend the MASS method to lower altitudes. However,the gain in the lower limit is only a factor of 2–4, notenough for a detailed characterization of the groundlayer. The performance of the PlaSci method de-pends on the visibility of a suitable planet and its el-evation. Hence, development of a regular turbulencemonitor based on this idea appears problematic.

6. LUNAR SCINTILLOMETER

Sun with its angular diameter θ ≈ 30′ also scin-tillates. However, this scintillation has very low am-plitude s ∼ 10−8 and originates mostly in the imme-diate vicinity of the instrument, at distances of fewmeters. Beckers (2001) proposed to use solar scin-tillation for turbulence profiling in the ground layerand developed the instrument, Shabar. It consistsof 6 light detectors in a linear non-redundant con-figuration, with baselines up to 47 cm. Covariancesbetween light fluctuations in individual detectors aremeasured and serve to restore the profile from ∼1 mto ∼100 m from the instrument. Shabars were usedin combination with a solar DIMM to select the sitefor a new solar telescope (Socas-Navarro et al. 2005).

A Shabar using Moon as a light source can bebuilt for night-time measurements. Compared to theSun, there are however three additional challenges:

36

9

21

2430

Fig. 10. The weighting functions W (z, b) for the detec-tor configuration 6-9-30 (baselines 0, 3, 6, 9, 21, 24, and30 cm). The full line shows autocorrelation, dashed lines– cross-correlations. Full Moon, 1-cm detector, turbu-lence outer scale L0 = 25 m.

• Moon’s phases and surface detail• Detectability of a small scintillation signal• Methods of profile restoration

Hickson & Lanzetta (2004) prototyped lunarShabar and made first measurements. Later, thisgroup constructed a 12-channel lunar scintillometerand installed it at CTIO.2 We also decided to de-velop a lunar scintillometer, LuSci. The idea wasto address the above three challenges and to findthe simplest possible instrument concept. Our pri-mary motivation was to use such a scintillometer inAntarctica for detailed measurements of its highly-turbulent ground layer.

If the ground layer is blown in front of the de-tector by a steady wind, the temporal correlationfunction of the scintillation signal can be used in-stead of its spatial correlation. However, the windspeed profile V (h) must be known, which is not usu-ally the case. At each altitude h, the typical sizeof “lenses” contributing most of scintillation is θhand corresponds to the time delay t = θh/V (h). IfV (h) = const., there is a unique mapping betweent and h. In the worst case when V (h) ∝ h all lay-ers produce temporal correlations of same width andcannot be disentangled. The idea of LuSci is to takeadvantage of the temporal correlations and to com-bine them with spatial correlations on few baselines.Presently we use only 4 detectors.

Figure 10 shows the WFs corresponding to thecorrelations of the scintillation signal on several base-lines from 3 cm to 30 cm. The detector size is 1 cm

2See http://www.astro.ubc.ca/LMT/alpaca/site.html

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68 TOKOVININ

square. Note that Hickson & Lanzetta (2004) useda simplified, non-rigorous expression for calculatingthe WFs, following Beckers (2001). These authorsalso ignored the finite turbulence outer scale. In factthe averaging size θz reaches 10 m at z > 1 km, andthe deviation of turbulence spectrum from the Kol-mogorov model becomes very significant, reducingthe scintillation. Socas-Navarro et al. (2005) dis-covered this circumstance empirically and had toaccount for it by introducing an extra parameter,“missing scintillation”.

The first challenge – Moon’s phases – was ad-dressed by calculating the scintillation covariancewith actual Moon images. It turns out that for theperiod of ±5 days around full Moon the model ofan elliptical disk reproduces the actual scintillationcovariances with an absolute error of 10% of the vari-ance or less. The largest error at zero baseline (vari-ance) is caused by the neglect of surface details inthe elliptical disk model. Covariances at non-zerobaselines are modeled even more accurately, beingless sensitive to fine details.

The detector for measuring lunar scintillationmust reliably register relative flux fluctuations of10−5 at frequencies of few hundred Hz. A 1-cmSi photo-diode gives a photo-current of 90 nA (or5.5 1011 photo-electrons s−1) from the full Moon.The shot noise of this signal in 1-ms integrationtime corresponds to relative fluctuations ∆I/I ∼4 × 10−5. It turns out that the noise of commonoperational amplifiers (e.g. LT 1464) is much less,so our detector is nearly perfect. Of course, care istaken to avoid any pick-up noise (grounding, shield-ing, etc.). The dynamic range of 16-bit convertersis insufficient for digitizing small signal fluctuations,hence we amplify the fluctuating part by 100 timesand digitize it separately from the DC part, as doneby Hickson & Lanzetta (2004).

The last challenge – profile restoration – is ap-proached by the same method as used for planets,i.e. by finding linear combinations of covariancesthat peak at certain altitudes and are close to zeroelsewhere. It is clear that the WFs have sharp cutoffsat z < θb, where b is the baseline (Figure 10). Evena simple difference of two WFs at baselines b1 and b2

will isolate a range b1/θ < z < b2/θ. Our method offinding suitable linear combinations is more elabo-rate than a simple difference, but essentially similar.Response functions obtained by this technique areplotted in Figure 11. The half-width of the response∆z/z ∼ 1 defines the altitude resolution. With alarger number of detectors and baselines, a higherresolution will be possible.

Fig. 11. Response functions of LuSci for baseline con-figuration 3-10-38 and layers centered at 3, 12, 40, and200 m. The thick line shows a sum of responses.

4 5 6 7 8 9UT, hours

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Fig. 12. Ground-layer seeing measured by LuSci andestimated by the DIMM-MASS on February 5/6, 2007at CTIO. The curves for LuSci depict seeing created byturbulence from the ground up to the indicated altitude.

The grid of “layers” is defined above as a functionof range, not altitude, so it projects to altitudes witha cos γ compression depending on the Moon’s zenithdistance γ. The distance of the peak response cannotbe selected arbitrary, as it related to the cutoffs of theWFs. Hence, it is not possible to re-define responsein terms of altitude h = z cos γ, as in MASS.

Figure 12 shows how this restoration techniqueworks on the real data. The ground-layer seeing wascalculated by taking the first LuSci layer, sum of thefirst two layers, etc. No correction for the air masswas applied because the thickness of the layers is pro-portional to cos γ and thus compensates for the air-mass effect for a uniform C2

n(h) profile. The seeing in

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the ground layer (GL) up to ∼500 m was measuredsimultaneously by subtracting turbulence integralsdelivered by DIMM and MASS (with 5-min. averag-ing). The results of LuSci show that on that particu-lar night, the ground-layer seeing was not dominatedby turbulence in the first ∼20 m, as one would ex-pect, but was rather produced by the whole 500-mzone. Apparently, the LuSci’s upper sensitivity limitwas lower than 500 m, so sometimes it measured theGL seeing less than the DIMM-MASS. Both instru-ments show correlated details in the temporal varia-tion of the GL seeing.

The temporal auto- and cross-correlations of thelunar scintillation signal at two baselines are shownin Figure 13. The narrow peak is produced by small-scale structures at low altitudes. In the covarianceon a 10-cm baseline this peak is displaced from thecoordinate origin by ∼0.1 s, corresponding to a pro-jected wind of V ∼ 1 m s−1 along the baseline (thewind on February 5/6 was weak). This narrow peakis absent in the covariance at the longest 38-cm base-line because the wind vector was not oriented alongthe baseline. The slow component of the signal cor-responds to a turbulence at few hundred meters, it iscorrelated on all baselines. This example shows thattemporal analysis of the scintillation signal adds sig-nificant information to the spatial covariances. Weplan to further develop this approach.

LuSci is a relatively simple and robust methodfor quantitative measurement of turbulence profilenear the ground. The scintillation signal, althoughweak, can be detected reliably. The theory of lu-nar scintillation is very simple (geometrical optics,no saturation) and the Kolmogorov model is ade-quate in the range of measured spatial scales (fromfew cm to 1 m). The resolution of a simple 4-channelinstrument is already adequate for determining theheight of a telescope dome (see Socas-Navarro et al.2005, for an example of data use) and can be furtherimproved by adding additional detectors or, better,by using the temporal domain. LuSci is cheaper andmore accurate than the micro-thermal mast equip-ment traditionally used for GL turbulence studies.

7. WHAT’S NEXT?

The theory of optical propagation through tur-bulence was established over 50 years ago. Yet, anexplosive development of new techniques for opticalturbulence measurements happened only recently, inthe past few years. A stimulus for such developmentwas provided by the needs of adaptive optics andinterferometry, but an even more important factoris the progress of technology. Without modern de-

Fig. 13. Temporal covariances of Moon’s scintillationwith baselines 10 cm (top) and 38 cm (bottom). Datataken on February 5/6, 2007, at 7:45 UT.

tectors and computers, instruments like MASS andLuSci would not be practical, although in principlethey could be envisioned long time ago.

As new, better and cheaper detectors becomeavailable, new ideas on how to use them for turbu-lence characterization will emerge. Instead of the 4channels of MASS, a complete 2-dimensional analy-sis of the scintillation pattern will become feasible, asalready implemented in the single-star scidar (Habibet al. 2006). The methods of data interpretation willevolve, too.

There is little doubt that the need to monitorturbulence profiles near the ground and in the wholeatmosphere will not vanish – on the contrary, almostevery observatory will eventually want to have a new,advanced site monitor. Among many existing andfuture instruments, the users will prefer the simplestand cheapest options with automatic on-line dataprocessing and robotic control. The MASS-DIMMinstrument comes close to this ideal, but it is notthe last word. The development will continue!

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70 TOKOVININ

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