Astron. Nachr. / AN 331, No. 9-10 (2010) / P58

MISOLFA solar monitor for the ground PICARD program

T. Corbard1,?, A. Irbah2, P. Assus1, C. Dufour2, M. Fodil3, F. Morand1, C. Renaud1, and E. Simon1

1 Universite de Nice Sophia Antipolis, CNRS, Observatoire de la Cote d’Azur, BP 4229 06304 Nice Cedex 4, France2 Universite Versailles St-Quentin, CNRS/INSU, LATMOS-IPSL, Guyancourt, FRANCE3 CRAAG, Observatoire dAlger, BP 63 Bouzareah 16340 Alger, Algerie

Key words Atmospheric effects – methods: observational – site testing – Sun: general

Developed at the Observatoire de la Cote d’Azur (OCA) within the framework of the PICARD space mission (Thuillieret al., 2006) and with support from the french spatial agency (CNES), MISOLFA (Moniteur d’Images Solaires Franco-Algerien) is a new generation of daytime turbulence monitor. Its objective is to measure both the spatial and temporalturbulence parameters in order to quantify their effects on the solar diameter measurements that will be made from groundusing the qualification model of the SODISM (SOlar Diameter Imager and Surface Mapper) instrument onboard PICARD.The comparison of simultaneous images from ground and space should allow us, with the help of the solar monitor, tofind the best procedure possible to measure solar diameter variations from ground on the long term. MISOLFA is nowinstalled at the Calern facility of OCA and PICARD is scheduled to be launched in 2010. We present here the principles ofthe instrument and the first results obtained on the characteristics of the turbulence observed at Calern observatory usingthis monitor while waiting for the launch of the space mission.

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1 Introduction: why a new Solar monitor ?

Diameter measurement analysis revealed a dependence withthe seeing condition as represented by Fried’s parameterr0 (Irbah et al., 1994). Numerical simulations were devel-oped in order to better understand atmospheric effects ondiameter measurements. The error decreases with the see-ing but it is also strongly conditioned by turbulence coher-ence times (Fig.2, Lakhal et al., 1999). The error also showsweak dependence on the outer scale L0 for a small aperturetelescope. Existing solar monitors such as Solar DIfferen-tial Motion Monitors (S-DIMM) or arrays of scintillome-ters (SHABAR) are able to provide useful information onthe spatial scales of the turbulence and are commonly as-sociated for site testing (e.g. Beckers 2001). However ourgoal here is to obtain the accurate turbulence equivalent PSFneeded to properly interpret the ground based radius mea-surements. For this, estimates of the characteristic temporalscales are also needed and it was realized that a single in-strument could provide both the spatial and temporal turbu-lence scales by analysing Angle of Arrival (AA) fluctuationssimultaneously in its image and pupil ways.

2 Atmospheric parameters measured

An illustration of a multi-layer atmosphere model is givenon Fig. 3. MISOLFA will allow us to obtain information onall the following parameters using a Von Karman turbulencemodel:

? Corresponding author: e-mail: Thierry.Corbard@oca.eu

SODISM MountMISOLFA Focal Box

Fig. 1 Picture of MISOLFA monitor and the mountthat will recieve the qualification model of the PI-CARD/SODISM telescope at the Calern facility of OCA.

– The Atmospheric structure constant of the air refractiveindex fluctuations C2

n(h).– Fried’s parameter r0 which is the diameter of the co-

herence zone of the degraded wavefront. It correspondsalso to the image resolution obtained with the telescopeof diameter r0 placed outside the atmosphere.

– The spatial coherence outer scale L0 which defines themaximal size of wavefront perturbations remaining co-herent. It traduces the low frequency evolution of thewavefront.

– The isoplanatic patch θ0 which is the angle where AAor speckles remain correlated.

– The correlation time τ0 which is the time during whichthe atmosphere may be considered as frizzed for theconsidered structures (AA, speckles) i.e. the time dur-ing which they keep their coherence.

c© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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2 T. Corbard et al.: MISOLFA solar monitor for the ground PICARD program

Fig. 2 Estimated errors on diameter estimates as a function of the Fried’s parameter r0 for two values of Rτ (ratiobetween the exposure time and the correlation time) (left) and as a function of Rτ for two values of r0 (right) (Lakhal etal., 1999)

Fried's parameter r0

Telescope pupil D

h1

hk

α 1 ( θ ) α 2 ( θ )

Extended object

Object image Telescope focal planeObserved fluctuations (d(θ ))

Angle of arrival

Characteristic time τ

Wave-front

Layer N

Layer k

Layer 1

Spatial coherence outer scale L0

C2n 1

C2n k

C2n N

θ

Fried's parameter r0

Telescope pupil D

h1

hk

α 1 ( θ ) α 2 ( θ )

Extended object

Object image Telescope focal planeObserved fluctuations (d(θ ))

Angle of arrival

Characteristic time τ

Wave-front

Layer N

Layer k

Layer 1

Spatial coherence outer scale L0

C2n 1

C2n k

C2n N

θ

Fig. 3 Illustration of a multi-layers atmosphere with VonKarman turbulence model (Irbah et al., 2003).

3 Measurement principles

The MISOLFA principle is based on the statistical analy-sis of AA fluctuations, which are fluctuations at each pointof the normal of the perturbed wavefronts. The AA fluctu-ations can directly be observed in the image plane (case ofShack-Hartmann’s sensors used in adaptive optics) but alsoin the pupil plane if the observed source present an intensitydistribution with a strong discontinuity like the Solar limb.The intensity fluctuations observed in the pupil image are,at first order, proportional to AA fluctuations (Borgnino &Martin 1977, Borgnino 1978).

Fig. 4 MISOLFA optical design. See text for details.

Fig. 5 Illustration of the formation of several solar imagesby the entrance prismatic blade. The CCD camera is posi-tioned accross the two first solar images.

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Astron. Nachr. / AN (2010) 3

Pixels

Pixe

lsImage acquise à '2009-07-01T07:09:09.484' - EXPOSURE = 2 ms

100 200 300 400 500 600

50

100

150

200

250

300

350

400

450

0 100 200 300 400 500 600 700100

150

200

250

300

350

400

PixelsInt

ensit

y (AD

U)

Coupe de l'image à mi-hauteur

α1(θ1)

α2(θ2)

Fig. 6 Image sample from the MISOLFA monitor (left)and horizontal cut (right). Arrows illustrate the motionsused to compute the transverse covariance between to an-gular positions (see text).

4 MISOLFA Instrument design

Figure 4 illustrates the optical design of MISOLFA. It ismade of a Cassegranian telescope of 25 cm aperture equipedwith an alt-azimuth mount to which is associated a derotat-ing system. A flat glass blade with non parallels faces allowsthe formation of separate images of the sun (Fig. 5). In thefocal box, a first beam (image way) is imaging two oppositeparts of solar limb on a 480x640 CCD. A tipycal sequenceis 1.5mn long with 32 images per second and a resolutionof 0.2 arcseconds per pixel. A second beam (pupil way) isimaging the pupil after passing through a spatial filter (slit)in the image of a part of solar limb. In the pupil image 4optical fibers (with diameters 2mm, 1mm and 2x0.5 mm)guide the light to 4 diodes. In addition, in the image of theslit a 2mm fiber measure global flux passing through theslit.

5 Analysis Method

In the image way we estimate r0, L0 and θ0 from directmeasurement of AA fluctuations on the limb images:

– r0 is directly related to the variance σ2s of the mean AA

fluctuations by:

r0 = 8.25105 D−1/5λ6/5(σ2s)−3/5

where D is the pupil diameter and λ the wavelength.– The AA transverse covariance is computed from the ob-

served limb fluctuations by (Fig. 6):

Cα(θ) =< α1(θ1)α2(θ2) >

L0 and θ0 = r0/h are then obtained by adjusting theobserved covariance to the theoretical one given, in thecase of the one-layer model and Von Karman theory, by:

Cα(θ) = 0.0716 λ2 r− 5

30

∫ ∞0

f3(f +

1

L20

)− 116

. . .

. . . [J0(2πfθh) + J2(2πfθh)][2J1(πDf)πDf

]2df

where h is the altitude of the equivalent impulse layergiving at ground level the same optical effects than thewhole turbulent terrestrial atmosphere.

– The turbulence profile C2n(h) is then obtained by invert-

ing (Bouzid et al., 2000) the structure function which, ina multi-layer model, is given by:Dα(θ) = 2 [Cα(0)− Cα(θ)]

= 2.4

∫ ∞0

C2n(h)K(θ, h,D,L0)dh

with:

K(θ, h,D,L0) =

∫ ∞0

f3(f +

1

L20

)− 116

. . .

. . . [1− J0(2πfθh)− J2(2πfθh)]

[2J1(πDf)

πDf

]2df

In the pupil plane, we perform a spatio-temporal analysisof AA fluctuations (Berdja, 2007). The photodiode detec-tors used represent various collecting surfaces of the pupil-plane. They allow fast recordings (5KHz) and thus an accu-rate intensity signal time sampling. Such measurement timeseries will be used to study temporal properties of the di-urnal turbulence and continuously estimate the correlationtime τ0 of AA-fluctuations from the estimated temporal co-variance assuming the Von Karman model and Taylor’s hy-pothesis of frozen turbulence. Such as for other seeing mon-itors like the well-known S-DIMM or GSM, dual measure-ments from photodiode pairs on the same collecting sur-face will allow also estimate the Fried parameter r0. Theneeded transverse temporal covariance is obtained by doingθh = vτ in the previous formula, v denoting an equiva-lent speed (weighted average of the different layer speeds)and τ a temporal shift (Conan et al., 2000). The goal of us-ing photodiode detectors with different collecting surfacesis to estimate the spatial coherence outer scale L0 from AA-fluctuation statistics.

6 Observations and first results

Sequences of images are recorded at Calern observatorysince june 2009. A typical sequence consists in a set ofabout 2500 images with an angular resolution of 0.2 arc-seconds per pixel recorded at a rate of 32 images per sec-ond. The exposure time of each image is 1ms. The meanlimb position is evaluated for each image in order to cor-rect in real time the guiding errors. The limb profile of eachimage is first extracted using wavelet based denoising andinflexion point identification (Irbah et al. 1999) as illustratedFig. 7. Then, from the temporal evolution of all the points ofthe extracted limb profiles (Fig. 8), the variance of the meanAA fluctuations and the Fried’s parameter are estimated.When estimating the Fried’s parameter from increasing timeintervals, the value decreases while integrating clearly dif-ferent turbulence regimes (Fig. 9). Figure 10 shows Fried’sparameter r0 estimated on a continuous set of two secondsintervals which correspond to the exposure time of the fulldisk images that will be recorded by the SODISM instru-ment. The full time sequence is therefore cuted in 40 inter-vals of two seconds. On these time intervals r0 can reach up

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4 T. Corbard et al.: MISOLFA solar monitor for the ground PICARD program

Fig. 7 The limb profile of each image is extracted usingwavelet based denoising and inflexion point identification(Irbah et al. 1999)

Fig. 8 Temporal evolution of all the points of the ex-tracted limb profiles.

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0

2

3

4

5

6

7

8

T i m e ( s )

r 0 (cm)

D a t e : 2 0 0 9 - 0 7 - 0 1 0 7 : 0 9 - r 0 c a l c u l é s u r d e s p e r i o d e s d ' i n t e g r a t i o n c r o i s s a n t e ( r : p i x e l s a b e r r a n t s c o r r i g é s )

2

3

4

5

6

7

8

R 0 (cm)

Time (s)10 20 30 40 50 60 70 80

Fig. 9 Fried’s parameter r0 estimated from increasingtime intervals.

to 14 cm while over the whole 75 s the value would be about2.6 cm (Fig. 9).

7 Conclusion

MISOLFA is a new type of solar monitor based on the anal-ysis of AA statistic that we record both in the image andpupil plane. It will allow us to get a full characterizationof the spatio-temporal parameters of the turbulence neededto identify the appropriate atmospheric model and build theturbulence + instrument equivalent PSF. The first sequences

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0

2

4

6

8

1 0

1 2

1 4

i n d e x

r 0 (cm)

D a t e : 2 0 0 9 - 0 7 - 0 1 0 7 : 0 9 - r 0 c a l c u l é s u r d e s p e r i o d e s d ' i n t e g r a t i o n c o n s t a n t e ( r : s u p p r e s s i o n b a d p i x e l s )

2

4

6

8

10

12

14

R 0 (cm)

Time interval5 10 15 20 25 30 35 40

Fig. 10 Fried’s parameter r0 estimated on two secondsintervals.

of images obtained where analyzed to extract the Fried’sparameter showing that good condition can eventually bereached at Calern observatory on some intervals for the 2 sexposure time of SODISM. The continuous record of the r0values will help us in the interpretation of ground SODISMimages while the PICARD satellite is operating. The pro-cedure to extract all the other spatial turbulence parametershave been tested and are now being implemented. The pupilway is still not operating properly and lots of effort are cur-rently made to increase the signal to noise ratio by improv-ing the electronic components.

Acknowledgements. This work has been performed with supportof the Observatoire d’Alger - C.R.A.A.G., the French Foreign Af-fair Ministry, the Observatoire de la Cote d’Azur and of the CentreNational d’Etudes Spatiales. We thank the European Helioseismol-ogy and Asteroseismology Network (HELAS) for supporting ourparticipation to the HELAS-4 conference. HELAS is a major in-ternational collaboration funded by the European Commission’sSixth Framework Programme.

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