Nulling Data Reduction and On-Sky Performance of the Large Binocular Telescope Interferometer

3 MB·

by  D. Defrère

Revised version 2
PreprinttypesetusingLATEXstyleemulateapjv.01/23/15
NULLING DATA REDUCTION AND ON-SKY PERFORMANCE OF THE LARGE BINOCULAR
TELESCOPE INTERFEROMETER
D. Defr`ere1, P.M. Hinz1, B. Mennesson2, W.F. Hoffmann1, R. Millan-Gabet3, A.J. Skemer1, V. Bailey1,4,
W.C. Danchi5, E.C. Downey1, O. Durney1, P. Grenz1, J.M. Hill6, T.J. McMahon1, M. Montoya1, E. Spalding1,
A. Vaz1, O. Absil7, P. Arbo1, H. Bailey8, G. Brusa1, G. Bryden2, S. Esposito9, A. Gaspar1, C.A. Haniff10,
G.M. Kennedy11, J.M. Leisenring1, L. Marion7, M. Nowak3,12, E. Pinna9, K. Powell1, A. Puglisi9, G. Rieke1,
A. Roberge5, E. Serabyn2, R. Sosa1, K. Stapeldfeldt5, K. Su1, A.J. Weinberger12, and M.C. Wyatt11
6 1StewardObservatory,DepartmentofAstronomy,UniversityofArizona,933N.CherryAve,Tucson,AZ85721, USA
1 2JetPropulsionLaboratory,CaliforniaInstituteofTechnology, 4800OakGroveDrive,PasadenaCA91109-8099, USA
0 3NASAExoplanetScienceInstitute, CaliforniaInstitute ofTechnology, 770SouthWilsonAvenue,PasadenaCA91125,USA
4KavliInstituteforParticleAstrophysicsandCosmology,StanfordUniversity,Stanford,CA94305, USA
2
5NASAGoddardSpaceFlightCenter,Exoplanets &StellarAstrophysicsLaboratory,Code667,Greenbelt, MD20771,USA
n 6LargeBinocularTelescopeObservatory,UniversityofArizona,933N.CherryAve,Tucson,AZ85721, USA
7Institutd’AstrophysiqueetdeG´eophysique, Universit´edeLi`ege,19cAll´eeduSixAouˆt,B-4000SartTilman,Belgium
a 8LunarandPlanetaryLaboratory,UniversityofArizona,1541E,UniversityBlvd,Tucson,AZ85721, USA
J 9INAF-OsservatorioAstrofisicodiArcetri,LargoE.Fermi5,I-50125Firenze,Italy
6 10CavendishLaboratory,UniversityofCambridge,JJThomsonAvenue,CambridgeCB30HE,UK
2 11InstituteofAstronomy,UniversityofCambridge,MadingleyRoad,CambridgeCB30HA,UK
12LESIA/ObservatoiredeParis,CNRS,UPMC,Universit´eParisDiderot,5placeJulesJanssen,92195Meudon,Franceand

13DepartmentofTerrestrialMagnetism,CarnegieInstitution ofWashington, 5241BroadBranchRoadNW,Washington, DC,20015,
]
P USA
Revised version 2
E
h. ABSTRACT
p The Large Binocular Telescope Interferometer (LBTI) is a versatile instrument designed for high-
- angular resolution and high-contrast infrared imaging (1.5-13µm). In this paper, we focus on the
o
mid-infrared (8-13µm) nulling mode and present its theory of operation, data reduction, and on-
r
t sky performance as of the end of the commissioning phase in March 2015. With an interferometric
s
baseline of 14.4 meters, the LBTI nuller is specifically tuned to resolve the habitable zone of nearby
a
[ main-sequencestars,wherewarmexozodiacaldustemissionpeaks. Measuringthe exozodiluminosity
functionofnearbymain-sequencestarsisakeymilestonetoprepareforfutureexoEarthdirectimaging
1 instruments. Thankstorecentprogressinwavefrontcontrolandphasestabilization,aswellasindata
v
reduction techniques, the LBTI demonstrated in February 2015 a calibrated null accuracy of 0.05%
6
over a three-hour long observing sequence on the bright nearby A3V star β Leo. This is equivalent
6
to an exozodiacal disk density of 15 to 30 zodi for a Sun-like star located at 10pc, depending on
8
the adopted disk model. This result sets a new record for high-contrast mid-infrared interferometric
6
imaging and opens a new window on the study of planetary systems.
0
. Subject headings: Instrumentation: interferometers, Stars: circumstellar matter.
1
0
6 1. INTRODUCTION break-ups and asteroid collisions. Emission and/or scat-
1
tered light from this dust will be the major source of
: The LargeBinocular Telescope Interferometer (LBTI)
v is an interferometric instrument designed to coherently astrophysicalnoiseforafuturevisiblecoronagraph(e.g.,
Xi combine the beams from the two 8.4-m primary mir- Roberge et al. 2012; Stark et al. 2014) or mid-infrared
interferometer (e.g., Beichman et al. 2006; Defr`ere et al.
rors of the LBT for high-angular resolution imaging
r 2010). As recently discussed by Stark et al. (2015), the
a at infrared wavelengths (1.5-13µm). It leverages the
minimum aperture size for a future exoEarth detection
high sensitivity enabled by LBT’s two large apertures,
coronagraphic mission is dependent on several assumed
high-quality wavefronts delivered by its adaptive optics
astrophysical quantities among which the most impor-
systems, low thermal background due to the adaptive
tantaretheassumedsizeandopticalpropertiesforevery
secondary architecture, and high angular resolution en-
Earth-sized planet residing in the habitable zone (HZ),
abled by the coherent combination of light from the two
LBT primary mirrors (14.4m center-to-center separa- thenumberofHZ Earth-sizedplanets perstar(η⊕),and
the exozodiacal dust cloud surface brightness. While
tion, 22.65m maximum baseline). The primary science
Kepler is currently constraining the two former (e.g.,
goal of the LBTI is to determine the prevalence of exo-
Burke et al. 2015), the prevalence of exozodiacal dust
zodiacaldustaroundnearbymain-sequencestarsinsup-
in the terrestrial planet region of nearby planetary sys-
port of a future space telescope aimed at direct imag-
tems is currently poorly constrained. The bright end
ing and spectroscopy of terrestrial planets (exoEarths)
of the exozodi luminosity function, i.e. several hundred
aroundnearbystars. Thiswarmcircumstellardust,anal-
to several thousand times the dust density of the solar
ogous to the interplanetary dust found in the vicinity
zodiacalcloud,hasbeenmeasuredbyspace-basedsingle-
of the Earth in the Solar system, is produced in comet
dishtelescopes(e.g.,Kennedy & Wyatt2013)butsucha
sensitivity is ordersofmagnitudes too poor to efficiently
[e-mail]
2 Defr`ere et al.
Fig.1.—System-levelblockdiagramofLBTIarchitectureinnullingmodeshowingtheopticalpaththroughthetelescope,beamcombiner
(redbox),andtheNICcryostat(bluebox). AfterbeingreflectedonLBTprimaries,secondaries,andtertiaries,thevisiblelightisreflected
on the entrance window and used for wavefront sensing while the infrared light is transmitted into LBTI, where all subsequent optics
are cryogenic. The beam combiner directs the light with steerable mirrorsand can adjust pathlength for interferometry. Inside the NIC
cryostat, the thermal near-infrared (3-5 µm) light is directed to LMIRCam for exoplanet imaging, the near-infrared (1.5-2.5 µm) light is
directedtothephasesensor,whichmeasuresthedifferentialtip/tiltandphasebetweenthetwoprimarymirrors,andthemid-infrared(8-13
µm)lightisdirectedtoNOMICfornullinginterferometry. Bothoutputsofthebeamcombineraredirectedtothephaseandtip/tiltsensor,
whileonlythenulledoutput of theinterferometer isreflected to theNOMICcamera withashort-pass dichroic. Thevariouscameras are
shownindarkgreyandfeed-backsignalsdrivingthedeformablesecondarymirrorsandtip-tilt/OPDcorrectorsarerepresentedbydashed
lines. Notethatthisdiagramisschematiconlyanddoesnotshowseveraladditionaloptics.
prepare future exoEarth imaging missions. ductiontechniquethanthatusedforthefirststudy. This
In order to measure fainter exozodiacal disks, a technique, called Nulling Self Calibration(NSC) and pi-
survey of nearby main sequence stars has been car- oneeredonthePalomarFiberNuller(PFN,Hanot et al.
ried out with the Keck Interferometer Nuller (KIN). 2011;Mennesson et al. 2011), was adaptedfor the LBTI
Science results from the KIN were reported recently and showed to significantly reduce the impact of impor-
(Millan-Gabet et al. 2011; Mennesson et al. 2014) and tantsystematicerrors. Followingtheseresults,theLBTI
indicatethatthemedianlevelofexozodiacaldustaround achieved a calibrated null accuracy that is sufficient to
such stars is no more than 60 times the solar value with start the exozodi survey, called the Hunt for Observable
high confidence (95%, assuming a log-normal luminos- Signature of Terrestrial Systems (HOSTS). The survey
ity distribution). Yet, the state-of-the-art exozodi sensi- will start with a one year science validation phase that
tivity achieved per object by the KIN is approximately will also include some engineering tasks to further im-
one orderof magnitude largerthan that requiredto pre- prove the performance of the instrument. Overall (in-
pare future exoEarth imaging instruments. The LBTI cluding both observations obtained during the commis-
is designed to reach the required level. The first obser- sioning and science validation phases), the HOSTS sur-
vations, based on commissioning data, were reported re- vey will be carried out over the next two to three years
centlyandshowedasensitivitysimilartothatoftheKIN on a sample of 35 to 40 carefully chosen nearby main-
(Defr`ere et al.2015b). Theseobservationswereobtained sequence stars (Weinberger et al. 2015).
using a coarse fringe tracking algorithm (equivalent to ThispaperprovidesadescriptionofLBTI’sinstrumen-
group delay tracking), which is limited to a closed-loop tal setup in nulling mode, data reduction, data calibra-
optical path difference (OPD) residual of approximately tion, and on-sky performance in support of the HOSTS
1µm RMS. Phase tracking was commissioned later that science survey. Section 2 describes the overall architec-
yearandsignificantlyimprovedthe OPDstability of the ture of the LBTI with a particular focus on the nulling
system (∼400nm RMS). During the same period, im- mode and its on-sky response. The method used for
provements in the telemetry tracking also allowed us to fringe and tip/tilt tracking is also discussed. Section 3
test and validate a much more powerful nulling data re- discussesthe level0 (L0) data products andsome obser-
3
vational details including the observing sequence, which
was specifically designed for the NSC. Then, the core of
this section is dedicated to the level 1 (L1) data reduc-
tion process, which consists in converting a set of raw
images of various types to raw null measurements. Sec-
tion4 is dedicatedto the null calibration,orlevel2 (L2)
data reduction, which basically consists in removing the
contribution of the instrument from the raw null depth
measurementsin orderto be left withonly the contribu-
tion from the astrophysical object (or source null). Fi-
nally, Section 5 presents on-sky performance of the sys-
temattheendofthecommissioningphase. Thisincludes
throughput, photometric sensitivity, and OPD stability,
which are the most relevant metrics to reach high con-
trasts. Appendices A, B, and C provide additional in- Fig.2.— Conceptual schematic of the nullingand PHASECam
formation on the choice of calibrator stars, the spectral beam combination. Beam combination is done in the pupil plane
ona50/50beamsplitter(BS),whichcanbetranslatedtoequalize
transmission of the instrument, and the impact of the
the pathlengths between the two sides of the interferometer. To
backgroundregion used for aperture photometry. achieveanachromaticsuppressionoflightoverasufficientlylarge
bandwidth(8-13µm),acompensatorwindow(CW)withasuitable
2. OPTICALSETUPANDMETHODOLOGY tthheickinnteesrsfeorfodmieelteecrtrairceisdiirnetcrtoedducteodtihneonneearb-einamfra.rBedotphhoausetpsuetnssoorf
2.1. Overall architecture (PHASECam)whileoneoutputisreflectedtotheNOMICscience
detectorwithashort-passdichroic. Notethatthissketchdoesnot
The LBTI is located at the bent center Gregorian showseveralfoldmirrorsandbiconics. Thecompletediagramcan
focal station of the Large Binocular Telescope (LBT, befoundinHinzetal.(2008).
Hill et al. 2014; Veillet et al. 2014). The LBT is located
on Mount Graham in southeastern Arizona and is op-
160µmofopticalpathdifference(OPD)correction. The
erated by an international collaboration among institu-
right mirror provides a larger stroke (40 mm of motion)
tions in the United States, Italy, and Germany. It con-
for slow pathlength correction. In practice, the SPC is
sistsoftwo8.4-mapertureopticaltelescopesinstalledon
usedto acquire the fringeswhile the FPC is used to cor-
a single steerable altitude-azimuth mount. This design
rectforpathlengthvariationsathighspeed(upto1kHz,
provides an ideal platform for interferometric observa-
depending on the magnitude of the star). The SPC can
tions since it does not require long delay lines and con-
also be used in closed-loop to offload the FPC when it
tains relatively few warm optical elements. Both aper-
reaches the end of its range.
tures are equipped with deformable secondary mirrors,
Downstream of the UBC, the infrared light enters the
which are driven with the LBT’s adaptive optics system
cryogenic Nulling and Imaging Camera (NIC), which
to correct atmospheric turbulence (Esposito et al. 2010;
is equipped with two scientific cameras, i.e. LMIR-
Bailey et al. 2014). Each deformable mirror uses 672
Cam(the L andM InfraredCamera,Wilson et al. 2008;
actuators that routinely correct 500 Zernike modes and
Leisenring et al. 2012) and NOMIC (Nulling Optimized
provide Strehl ratios as high as 80%, 95%, and 99% at
Mid-InfraredCamera,Hoffmann et al.2014),andanear-
1.6µm, 3.8µm, and 10µm, respectively (Esposito et al.
infraredfast-readoutPICNIC detector (PHASECam) to
2012; Skemer et al. 2014).
measure the tip/tilt and phase variations between the
The overall LBTI system architecture is based on the
LBT apertures. At the entrance of NIC, a trichroic
heritage of the Bracewell Infrared Nulling Cryostat on
transmits the thermal near-infrared light (3.0-5.0µm)
the MMT (BLINC, Hinz et al. 2000) and will be de-
to the LMIRCam channel and reflects the near-infrared
scribed in a forthcoming paper (Hinz et al. in prep). In
(1.5-2.5µm) and mid-infrared light (8-13µm) to the
this paper, we focus on the parts relevant for nulling in-
NOMIC channel (see transmission and reflection curve
terferometry. The LBTI system architecture in nulling
in Skemer et al. 2014). To minimize non-common path
mode is represented by the block diagram in Figure 1.
errors, we split the near-infrared and mid-infrared light
Starlight bounces off the LBT primaries, secondaries,
after beam combination. Both interferometric outputs
and tertiaries on either side of this figure before com-
are directed to the phase and tip/tilt sensor, while only
ing into the LBTI. Visible light reflects off the LBTI en-
thenulledoutputoftheinterferometerisreflectedtothe
trance windows and into the adaptive optics wavefront
NOMICcamerawithashort-passdichroic(seeFigure2).
sensors,whichcontrolthedeformablesecondarymirrors.
The other output is discarded. In the NOMIC channel,
The infrared light transmits into LBTI’s universalbeam
a series of wheels are available to select the wavelength
combiner(UBC,seeredbox)inwhichallopticsarecryo-
(see list of available filters in Defr`ere et al. 2015a), cold
genic. The UBC can direct the light with steerable mir-
stops (pupil wheel), and grisms for low-resolution spec-
rors and provides a combined focal plane from the two
troscopy. In the PHASECam channel, there are several
LBT apertures. Beam alignment is done via the Fast
wheels to select the wavelengths (e.g., standard H and
Pathlength Corrector (FPC) located in the left part of
K filters), the pupil size, and neutral densities. A more
the UBC and the Slow Pathlength Corrector (SPC) lo-
detailed description about these modes can be found in
cated in the right side. Both the FPC and the SPC can
Hinz et al. (2008).
adjust pathlength for interferometry. The FPC provides
aPiezo-electrictransducer(PZT)fastpathlengthcorrec-
2.2. Nulling mode
tionwith80µmofphysicalstroke,capableofintroducing
4 Defr`ere et al.
One of the main limitations to detect faint circum-
stellar emission with an infrared interferometer resides
in the high dynamic range that must be achieved (e.g.,
∼10000:1forLBTI’s HOSTSsurvey). Apossible avenue
to tackle this observing challenge is to use the undula-
torynature oflightto performadestructive interference
of the starlight. The technique was first proposed by
Bracewell (1978) to image extra-solar planets and has
since then been implemented at various telescopes such
as the MMT (e.g., Hinz et al. 1998), the Keck observa-
tory (e.g., Colavita et al. 2009), and Hale telescope at
MountPalomar(e.g.,Mennesson et al.2011). The basic
Fig.3.— Illustration of LBTI monochromatic single-aperture
principle is to combine the beams in phase opposition PSF(left)andinterferometrictransmissionmap(right)computed
in order to strongly reduce the on-axis starlight while forawavelengthof11.1µmovera1′.′5x1′.′5fieldofview,assuming
transmitting the flux of off-axis sources located at an- apurelyeast-west14.4mbaseline(northisup,eastistotheleft).
Thedashedredlinesindicatethepositionofthefirsttwominimaof
gular spacings given by odd multiples of 0.5λ/B (where
thesingle-aperturePSF.Thesolidbluelineindicates theposition
B =14.4mis the distance betweenthe telescope centers of Earth’s orbit around a sun located at 10pc and seen face-on.
and λ is the wavelength of observation, see transmis- Itisresolvedbytheinterferometer butnotbythesingle-aperture
sion pattern in Figure 3). The high-angular resolution PSF. The PSF is displayed with a square root stretch to better
showthefirstAiryringwhilethetransmissionmapisshownwith
information on the observed object is then encoded in
alinearstretch.
the null depth, which is defined as the ratio of the flux
measured in destructive interference and that measured
2.3. Differential pathlength and tip/tilt sensing
in constructive interference. The advantage of obtaining
null depth measurements is that they are more robust Differential tip-tilt and phase variations between the
against systematic errors than visibility measurements two AO-correctedapertures are measuredwith PHASE-
andhence leadto a better accuracy(e.g., Colavita et al. Cam, LBTI’s near-infrared camera. PHASECam uses
2010b). a fast-readout PICNIC detector that receives the near-
The LBTI nulling beam combination scheme is rep- infraredlightfrombothinterferometricoutputs. Theop-
resented in Figure 2. The beams are combined in the tics provide a field of view of 10×10 arcsec2 with pixels
pupil plane on a 50/50 beamsplitter that can be trans- 0.078arcsec wide and can be adapted to create different
lated to equalize the pathlengths between the two sides setups for pathlength sensing. Three options are cur-
of the interferometer. To achieve an achromatic sup- rently built into the LBTI to allow a flexible approach
pression of light over a sufficiently large bandwidth (8- to phase sensing: 1) use the relative intensity between
13µm),aslightexcessofpathlengthinonebeamiscom- the two interferometric outputs, 2) use dispersed fringes
pensated with a suitable thickness of dielectric material via a low-dispersion prism, or 3) use an image of the
in the opposite beam, which allows us to balance the combined pupils via a reimaging lens. Various neutral
dispersion in the pathlength difference. This technique density filters are also available together with standard
permits a very simple beam combination while allowing H and K filters.
a suitably wide bandpass for starlight suppression. One So far, fringe sensing has been mainly performed us-
output of the interferometer is reflected on a short-pass ingaK-bandimageofpupilfringes(equivalenttowedge
dichroic and focused on the NOMIC camera. NOMIC fringes). Because of angular dispersion between 2 µm
uses a 1024x1024Raytheon Aquarius detector that cov- and 10 µm in the beamsplitter, a well overlapped set
ers a field of view (FOV) of 12×12 square arcsec with of images at 10 µm corresponds to a tilt difference of
a plate-scale of 0.018 arcsec. However, to improve the roughly 3 fringes across the pupil at 2 µm. This has the
data acquisition efficiency, only a small portion of the nice feature of providing a signal in the Fourier plane
array is read and saved (generally a 256x256 sub-array well separated from the zero-frequency component and
corresponding to a field-of-view of 4′.′6×4′.′6). allow us to separate differential tip/tilt and phase vari-
Compared to other ground-based nulling instruments, ations via a Fourier transform of the detected light.The
the LBTI re-images the nulled output of the beamsplit- peak position in the amplitude of the Fourier transform
ter rather than integratingovera single pixel (or several gives a measurement of the differential tip/tilt while the
pixels for dispersed data). Therefore, the LBTI forms argument of the Fourier transform at the peak position
an image of the nulled output at the angular resolution gives a measurement of the optical path delay. While
of a single aperture with the high-angular resolution in- both outputs are read simultaneously by the detector,
formation encoded in the flux of the star. This image only one has been processed for the data presented in
corresponds to the object brightness multiplied by the this paper. This approach is represented in Figure 4 for
transmission pattern of the nuller (see Figure 3, right) a noise-free model (left column) and on-sky data from
and convolved with the point spread function (PSF) of March 17th 2014 (right column).
the individual elements (see Figure 3, left). Because the Due to the nature of the Fourier transform measure-
PSF is broader than the transmission pattern and the ment,thederivedphaseislimitedtovaluesinthe[−π,π]
source is relatively compact, the interference fringes are range while the phase fluctuations have a typical ampli-
not visible in the focal plane and images are formed. It tudeof∼5µm(i.e.,∼4πatKband,seeSection5.3). To
is hence possible to study the spatial structure of the get around this issue, the measured phase is unwrapped
detected excesses at the angular resolution of a single using a first-order derivative estimate (Colavita et al.
aperture. 2010a). The unwrapped phase generally follows closely
5
Fig. 5.—BlockdiagramofLBTIOPDcontroller. Themeasured
phase is first unwrapped and then goes through a classical PID
controller. Apeakingfilterisalsousedtoimprovetherejectionof
specific vibration frequencies. An outer loop running at typically
1Hz is used to monitor the group delay and capture occasional
fringe jumps. In addition, real-time OPD variations induced by
the LBT structure are measured by accelerometers all over the
telescope (OVMS system) and feedforwarded to the FPC. Differ-
entialtip/tiltiscontrolledfollowingthesameprinciple,exceptfor
theunwrapperandtheouterloop.
interferometer) to derive the group delay.
Tip/tilt and phase delay tracking are carried out at
full speed (i.e., ∼1kHz) using a classical proportional-
integral-derivative (PID) controller (see Figure 5). The
PID controller continuously computes the difference be-
tween the measured unwrapped phase and differential
tip/tilt and their setpoints. Currently, the setpoints are
optimizedmanuallybysearchingforthevaluesthatmin-
imize the real-time null depth estimate. The differential
tip/tiltsetpointisfoundto bestablefromnighttonight
and is generally checked only once at the beginning of
the night. The phase setpoint is checked at the begin-
Fig. 4.— LBTI’s phase sensing approach (noise-free model on
the left and on-sky K-band data from March 17th 2014 on the ning of each observing sequence and adjusted if neces-
right). Pupilimagesofthetwointerferometricoutputsareformed sary. The procedure consists in scanning the phase set-
onPHASECam(oneoutputshownontop)andtheFouriertrans- point by increments of 10-20◦ until the minimum real-
formis computed to sense both tip/tilt and phase. The peak po-
time null depth estimate is reached. The PID gain pa-
sitioninthe amplitude ofthe Fourier image(middleimages)pro-
videsthedifferentialtip/tilterrorsignalwhiletheargumentofthe rameters are optimized manually to minimize the error
Fourier image (bottom images) at the peak position provides the signal and generally consist of a large integral gain, a
phase(greyscalerangingfrom-π toπ). Thecentral regionofthe small proportional gain, and no derivative gain.
pupil is excluded from the FFT (location of the secondary mir-
In addition to the real-time control described above,
rors). Note that the camera image is padded in order to increase
theresolutionintheFourierspace. OPD and tip/tilt vibrations induced by the telescope
structure,whicharemeasuredinreal-timebyaccelerom-
etersalloverthetelescope(OVMSsystem,Ku¨rster et al.
the phase fluctuations but on-sky verification tests have 2010), are feedforwarded to the FPC. For the data pre-
shownthatlargephasejumpscanoccasionallyoccurand sented in this study, we only used the accelerometers
cause fringe jumps (evenwith the phase loop running at located on the secondary mirrors,which produce signifi-
1kHz). To capture eventual fringe jumps, the envelope cantOPD variationsat a frequency of ∼12Hz (typically
ofinterference(or the groupdelay)is trackedsimultane- a few hundred nanometers RMS, Defr`ere et al. 2014).
ously via the change in contrast of the fringes. A metric Peaking filters are also used to improve the rejection of
calledcontrastgradient(CG)hasbeendefinedasfollows: specific vibration frequencies not captured by the feed-
foward system (e.g., at ∼15Hz due to the tertiary mir-
|I −hIi|(x −hxi) rors). They are biquad filters applied directly to the
CG= i i i ; (1)
control algorithm that drives the FPC. Finally, note
I
P i i that PHASECam does not capture phase and differen-
whereIi isthe intensityofaPparticularpixelinthe pupil tialtip/tiltvariationsthatarevariablebetweenthenear-
andx isthecoordinateinthehorizontaldirectionofthat infrared, where it operates, and the mid-infrared, where
i
pixel. Thecontrastgradientisusedtomonitorthegroup the null depth measurements are obtained (see more in-
delay and detect fringe jumps at a typical frequency of formation in Section 5.3). Commissioning observations
1-2Hz. In the future, we plan to replace this algorithm have shown that the loop can run at full speed down
and use instead the phases measured at two different to a magnitude of K∼6.5, which is sufficient to observe
near-infrared wavelengths (one from each output of the all targets of the HOSTS survey sample. The loop fre-
6 Defr`ere et al.
Fig.6.— Typical observing sequence used for the HOSTS survey. The sequence is divided in basic observing blocks (OB) consisting
of one to two thousand frames, each having an integration time of typically 10 to 100ms (depending on the brightness of the star). The
complete sequence iscomposed of several successiveOBs atnull,i.e.withthebeams fromboth apertures coherently overlapped inphase
opposition, one OB of photometric measurements with the beams separated on the detector, and one OB of background measurements
with the beams nodded off the detector. Each square represents a 256 x 256 subframe of the NOMIC detector that covers a region of
approximately 4′.′6 x 4′.′6. The beams are aligned vertically in the middle of a given channel (see blue stars) to maximize the effective
field of view and nodded back and forth by 2′.′3 (up-down to preserve the differential pathlength). The dashed lines represent the limits
ofdifferentdetector channels. Therightchannels ofthedetector arenotuseddirectlyforthenulldepthmeasurements butareusefulfor
diagnosticsandframeselection.
quency can in principle be decreased down to ∼30Hz to 3.2. L0 image reduction
observefainterobjectsbutthishasneverbeentestedand
Reduction of detector frames consists of several well-
requires more investigation.
definedstepsthatgenerallyincludebiassubtraction,bad
pixel removal, and flat fielding. For our mid-infrared
3. DATAREDUCTION observations, these steps are either not necessary or
3.1. Level 0 Data Products achieved by nodding subtraction. For instance, the de-
tector bias is removed via nodding subtraction occur-
The raw data from the nuller (Level 0) consist of sin-
ringeveryfewminutes atmost,whichis fastenoughnot
gle detector frames saved in the fits format. Each fits
toworryaboutvariabilitydue to temperaturevariations
file consists of an image, which contains generally 256 x
(related to the telescope elevation). Flat fielding can in
256 pixels, and header information, which contains ap-
principle be derived from observations of the sky at dif-
proximately 160 keywords and associated data. These
ferent airmasses (using for instance the background OB
keywords are grouped according to their origin and in-
of each pointing, see Figure 6). However, it is generally
cludeforinstancethetargetinformation(e.g.,name,RA,
notpossibletofindasatisfactorymethodofcreatingim-
DEC),thetelescopetelemetry(e.g.,elevation,azimuth),
age flats that do not also significantly increase the noise
the AO telemetry (e.g., loopstatus,loopfrequency, loop
level in the images. Besides, the detector response is in-
gains), the detector and filter information (e.g., integra-
trinsically flat over the whole detector, of which we are
tion time, filter position, gain), the PHASECam teleme-
only interested in a very small region (∼ 50 x 50 pixels
try (e.g., loop status, loop frequency, measured phase
for a typical HOSTS star). In addition, thanks to some
and differential tip/tilt), and weather information (e.g.,
flexibilityinthe alignmentofthe instrument,this region
seeing, wind). The science frames are acquired accord-
is chosen to be very clean and contains very few bad
ing to a pre-definedobserving sequence as shownin Fig-
pixels. While the reduction software has the capability
ure 6. The basic observing block (OB) consists of one
to perform these steps, they are generally not executed
totwothousandframes,eachhavinganintegrationtime
andtheL0imagereductiononlyconsistsingroupingthe
of typically 10 to 100ms, depending on the brightness
framesofthe samenodpositioninasingledatacubefor
of the star. The observing sequence is composed of sev-
faster data access in the following step.
eralsuccessiveOBsatnull,i.e.withthebeamsfromboth
aperturescoherentlyoverlappedinphaseopposition,one
OB of photometric measurements with the beams sepa- 3.3. Background subtraction
rated on the detector, and one OB of background mea- A critical step for obtaining accurate null depth mea-
surements with the beams nodded off the detector. In surementsistocorrectlyestimateandsubtracttheback-
order to estimate and subtract the mid-IR background, ground level at the position of the nulled image. In the
the OBs at null are acquired in two telescope nod posi- mid-infrared,thisisachallengingtaskduetothestrong,
tions separated by 2′.′3 on the detector (see background non-uniform, and rapidly varying background emission
subtraction strategy in Section 3.3). All successive OBs (seetoppanelofFigure7). Undertypicalobservingcon-
on the same target define a pointing and the plan for ditionsandoperatingparametersfortheLBTIinnulling
the HOSTS survey is to acquire three pointings on the mode, the total instrumental emissivity in the N’ band
science object, interleaved with pointings on reference (10.22-12.49µm, see transmission curve in Appendix B)
starstomeasureandcalibratetheinstrumentalnullfloor isapproximately27%whenthe beamcombineris warm,
(e.g.,CAL1-SCI-CAL2-SCI-CAL1-SCI-CAL3sequence). which was the case for all the observations presented in
Tominimizesystematicerrors,calibratortargetsarecho- this paper. Including the atmosphere, the total ther-
sen close to the science target, both in terms of sky mal background is equivalent to a 240Jy source over
position and magnitude, using the SearchCal software a photometric aperture with a diameter of 0′.′28 (LBT
(Bonneau et al.2011, seeAppendix Afor moreinforma- PSF diameter). This is 3200 Jy/arcsec2, or 1 Jy/pixel.
tion about calibrator selection). This is nearly a million times brighter than the faintest
7

detectable level of zodiacal dust planned for the LBTI 1.220 AVG: 1.2E+06
RMS: 2101.5
survey. To reach background-limited noise performance, U] 1.218
the background is estimated in a two step process: the AD 1.216
first step uses simultaneous background measurements Flux [ 1.214
owbhtialeintehdeinseacnonadnnsutelupseasrtoimunadtetshethpeosbiaticokngroofutnhdebateatmhes 10 x -6 1.212
same position as the beams but at a different time (af- 1.210
ter the telescope has been nodded). The first step deals 0 2000 4000 6000 8000 0 10 20 30 40 50

withbackgroundtimevariations,whichmostlyoriginate -800
from the atmosphere, while the second step deals with U] -1000
the non-uniformity of the background across the detec- D
taorre,dwehscicrihbeisdminosmtloyredudeettaoiltahsepianrsttroufmtheentfl.uTxhceosmepstuetpas- Flux [A --11420000 AVG: -1160.2
RMS: 111.4
tion in the next section. -1600
3.3.1. Flux computation 0 2000 4000 6000 8000 0 50100150 200250300
600
Fluxcomputationisperformedineveryframebycircu- 400
laraperturephotometryusingtheaper.proIDLastrolib U] 200
D
rDouistitnhee.dWiaemuesteeraonftahpeerptruimrearraydaiupserotfur0e.5.1T4hλi/sDis,ewqhueivre- Flux [A -2000
alent to a radius of 140mas (or 8 pixels) at 11.1µm and -400 ARMVGS:: 1 05.54.6
-600
anareaof201pixels. Becausetheflux ofthestaratnull
is usually too faint for precise beam centroid determina- 0 2000 4000 6000 8000 0 20 40 60 80100120
Elapsed time [s] Number of occurence
tion in a single frame, the beam centroid is computed
Fig.7.—Top: exampleofon-skyrawthermalbackgroundmea-
on the median-combined image of all consecutive frames
surements obtained inthe N’ bandwith thetelescope pointing at
of the same nod position. We apply a double-pass cen- anemptyregionoftheskyandcoveringapproximately15degrees
troid function that applies first a coarse Gaussian fit to ofelevationchangeduringthewholedurationofthesequence. The
the whole detector frame to find the approximate beam leftpanelshowsthefluxintegratedoveraphotometricapertureof
8 pixels in radius while the right panel shows the corresponding
position and then uses the non-linear least squares fit-
distribution. Middle: same measurements after subtraction of si-
ter MPFIT (Markwardt 2009) around this position for multaneous background measurements (left). The corresponding
sub-pixel accuracy. Aperture noise resulting from the distribution (right) is now Gaussian and shows a relatively large
intersection of the circular aperture with square pixels offset. Theblacklinerepresentsarunningaverageof100secondsto
bettershowthelow-frequencydriftduetoslowly-changinginstru-
is taken into account in aper.pro, which computes the
mentalbackground. Bottom,samemeasurementsaftersubtraction
exact fraction of each pixel that falls within the photo- of simultaneous background measurements and nod subtraction
metric aperture. (left). For this example, nod subtraction has been performed at
Aperturephotometryhastheadvantagetoremovethe the maximum frequency (i.e., using adjacent frames). The corre-
sponding distribution (right) is now Gaussian and centered on 0.
real-time background fluctuations using a circular an-
Thesedatahavebeenobtainedusinganintegrationtimeof28ms
nulus centered around the photometric aperture. The (onMay14,2014).
sigma-clippedaverageofallpixelsinthebackgroundan-
nulus is computed and subtracted on a per-pixel basis
from each pixel in the photometric aperture. To mini- detector (now pointing to an empty region of the sky)
mize photon and readout noise, the inner radius of the and the resulting flux is subtracted from the flux of the
backgroundregions is generally chosen as close as possi- star at null. Because of the slow drift, it is important
ble to the photometric aperture but can be extended for to minimize the nodding period so that we only use the
bright nearby stars for which the habitable zone is ex- n closest frames in time of the adjacent nods, where n
tended and photometric errors are not dominant. The is the number of frames in the current nod. The result
outer radius of the regions is generally chosen as the obtained with both aperture photometry and nod sub-
smallestdistancetoachanneledgebutcanbeadaptedin traction is shown for the maximum nodding frequency
presenceofanobviousbackgroundbias(seeAppendixC in the bottom panel of Figure 7, where the residual off-
formoreinformation). Theresultofthisprocessisshown set is now close to 0 and no low-frequency drift is vis-
in Figure 7 (see middle panel), where most of the back- ible. In practice, there is a trade-off between observ-
ground fluctuations are now corrected. There remains ing efficiency and nodding frequency. If everything goes
however a slow drift around a relatively large negative smoothly, it takes generally 5 to 10 seconds to close the
value. This offset between the background region and AOandphaseloopssothatwestayatleast60to90sec-
the photometric aperture comes from the spatial struc- onds ina givennodposition. This is sufficiently longfor
ture of the background while the drift is due to slowly- thebackgroundtochangebetweenthetwonodpositions
moving optics inside the LBTI (related to the telescope due to slowly-movingoptics inside the LBTI. Therefore,
elevation). These effects must be corrected or they will the background illumination is not necessarily perfectly
create a flux-dependent background bias between stars uniformafternoddingsubtraction,whichcreatesasmall
of different magnitudes. offset between the backgroundestimated from the back-
To correct for this offset and slow drift, we apply a groundannulusandthatinthephotometricregion. This
second step of background subtraction using a median- offset,calledbackgroundbias inthe following,is present
combined image of frames in adjacent nods. Aperture in most of our commissioning data and can be up to ten
photometry is applied at the exact same position on the times largerthan the photometric noise. New alignment
8 Defr`ere et al.
procedures will be developed during the science valida-
tion phase to mitigate this bias.
100.0
3.4. Null depth computation %]
ThelaststepintheL0datareductionistoconvertthe pth [ 10.0
e
flanudx cmoeraressuproemndeinntgs eartronrubllaorsf.eaTchheOcBlastsoicaslinwglaeyvtaoludeos null d
thatistocomputetheaverageormodeofthenulldepth ous
e
measurements,i.e.thefluxmeasurementsatnulldivided an 1.0
nt
by the constructive flux I+: nsta
I
I =I +I +2 I I , (2)
+ 1 2 1 2 0.1
0 10 20 30 40 50 60
whereI1 andI2 arethe meanindpividualintensities mea- Elapsed time [s]
sured during the same pointing. While straightforward
to implement, the classical technique is also very sensi-
tivetoinstrumentalimperfectionsthatvarybetweenthe 140
calibratorandthesciencestars. InthecaseoftheLBTI,
120
amajorerrortermcomesfromthe meanphasesetpoint,
e
c
which varies from one OB to the next and is indistin- en 100
guishablefromatrueextendedemissionwithclassicalre- cur
duction techniques. This setpoint offset appears for two of oc 80
reasons. First, the fringe tracker computes the Fourier er 60
b
transformofthe combinedpupil imageby defininga cir- m
Nu 40
cle around the illuminated portion of the detector. This
circle is only defined to a precision of one pixel at the 20
beginning of each OB at null so that any sub-pixel drift 0
of the beams is interpreted as a setpoint change. Since -2 0 2 4 6
Instantaneous null depth [%]
thereareapproximately4pixelsperfringe,onepixelcor-

responds to a pathlength offset of ∼0.5µm (or ∼0.3rad Fig.8.— Top: null depth sequence obtained on β Leo (typical
at 11µm). Second, the water vapor component of the results, 2015 February) vs elapsed time in seconds. The largeex-
cursions in the null depth are dominated by variable precipitable
atmospheric seeing creates a variable differential phase
watervapor. Bottom: measurednulldepthdistribution(solidline)
between the K band, where the phase is measured and and best-fit synthetic null depth distribution (dashed line). The
tracked,and the N band, where the null depth measure- reduced χ2 (χ2) amounts to 0.56 (see definition in Hanotetal.
r
ments are obtained. Whereas the phase setpoint is opti- 2011,Equation17).
mized regularly to minimize this effect, the water vapor
component of the atmospheric seeing can be sufficiently
fast (typically of the order of a few seconds) to modify to create the synthetic flux distributions. The distribu-
themeanphasesetpointduringtheacquisitionofasingle tion of the unknowninstantaneous sequences (i.e., I (t),
1
OB. I2(t), and B(t)) are estimated by their values measured
To get around this issue of varying mean phase set- at a slightly different time. The observing sequence pre-
point, we use the statistical reduction (or NSC) tech- sented in Figure 6 has been specifically defined for that
niquementionedintheintroduction. Thistechniquecan purpose. Given their excellentstability, the photometric
derivethemeanphasesetpointfromthenulldepthmea- intensities (I1 and I2) are obtained only once per point-
surements themselves and has demonstrated improved ing, generally at the end of the sequence. The back-
calibrated null accuracies over those obtained with clas- ground measurements B(t) on the other hand are esti-
sical reduction techniques in the case of the PFN (up mated at a higher frequency and usually in the closest
to a factor of 10). The idea behind NSC is to produce a adjacentnod(andatthesamepositionasthenulldepth
syntheticsequenceoffluxmeasurementsatnullandcom- measurements). Note that both measured photometric
pare its distribution to that of the measured sequence. intensities are intrinsically affected by the photon noise
The synthetic instantaneous flux sequence I (t) is cre- of the thermal backgroundso that their distributions do
ated using the following expression (e.g., Serabyn 2000; not represent the true intensity variations. Because the
Mennesson et al. 2011): background noise is overwhelmingly dominant and al-
ready included in the term B(t), there are no reasons
I (t)=I (t)+I (t)+2|V| I (t)I (t)cos(∆φ(t))+B(t), to inject the measured distributions of I and I in the
1 2 1 2 1 2
(3) model. Instead,we use twoconstantsderivedby averag-
p
where I (t) and I (t) are the individual instantaneous ing the photometric measurements of each aperture.
1 2
photometries, |V| is the absolute value of the source vis- AsdiscussedbyHanot et al.(2011),Equation3isonly
ibilityattheinstrumentbaseline(whichisrelatedtothe validforinstantaneousfluxmeasurementsorifthe time-
source null as explained later in this section), ∆φ(t) is dependentquantitiesdonotvarywithineachintegration
the instantaneous phase offset (close to π at null), and time. In the case of the LBTI, the instantaneous differ-
B(t)istheinstantaneousmeasuredbackground. Thead- ential phase varies significantly at high frequency (see
vantage of using distributions is that it is not necessary Section 5), which would require integration times pro-
to have access to simultaneous auxiliary measurements hibitively short to “freeze” it. While integration times
9
σ2(t)), a synthetic flux sequencecanbe producedby fix-
ǫ
ing the three remaining parameters in Equation 3, i.e.
0.5 10.00
N, µ (the mean value of ∆φ(t) over all the measure-
φ
ments of the OB), and σ its standard deviation. The
8.57 φ
0.4 method then consists in creating a large grid of models
d] 7.13 over these three parameters and comparing them to the
or [ra 0.3 museinagsuareldeassetqsuqeunacree. eTshtiembaetsotr-fi(it.ep.,arbaymχe2temrsinairmeidzaertiivoend)
hase err 0.2 45..2770 aesptpimlieadtotroistheequwivhaolleentgrtiod.theInmtahxeiomryu,mthleikeleliahsotosdquesatrie-
P
mator only in the presence of Gaussian noise. This is a
0.1 2.83 validassumptioninourcasebecause the noiseterms are
nindependentbinomialvariables(wherenisthenumber
1.40 of bins in the histogram), which follow closely a Gaus-
0.0 0.5 1.0 1.5 sian distribution if the number of occurrences per bin is
Null depth [%]
sufficiently large. For this reason, we only keep the bins

Fig.9.— Example of χ2 map represented as a function of null that have at least 10 occurrences in the histogram fit.
r
depth and RMS phase error σφ (χ2r minimized along the mean Note that it is possible to derive a maximum likelihood
phasedirection). Theregionwhereχ2r >10has beenset to10to estimator that does not rely on this assumption. The
emphasizethelowχ2r region. Thepositionofthebest-fitmodelis derivation of this estimator is beyond the scope of this
representedbythewhitecross.
analysis and will be presented in a forthcoming paper.
Regarding the error bars on the best-fit parameters,
as short as 3ms could be used in practice, this would they are derived by bootstrapping (independent of the
lead to a significant sensitivity loss due to readout noise actual noise properties, Efron 1979). This means that,
and camera overheads. Therefore, we have modified the for each position of the grid, we create a large num-
synthetic null depth expression to include the effect of ber (2000) of “alternative” flux sequences by randomly
varying differential phase over a finite integration time. resampling and replacing the observed flux measure-
The average of the flux at null over an integration time ments at null. Each alternative sequence is compared
T can be expressed from Equation 3 as: to the synthetic null depth histogram and the distribu-
tion of best-fit null depths gives the statistical uncer-
hI (t)i=I +I +2|V| I I hcos(∆φ(t))i+B
1 2 1 2 tainty (68.3%interval). To avoidrunning the fit on pro-
hibitively largegridsandgiventhe requiredprecisionon
=I1+I2+2|V|pI1I2[cos(∆φ0)hcosǫ(t)i
the source null, we first run a coarse searchto find good
−sin(∆φ0)hsipnǫ(t)i]+B starting values for the three parameters and then per-
≃I +I +2|V| I I cos(∆φ )(1−0.5σ2)+B, form a fine search around these values.
1 2 1 2 0 ǫ An example of null depth measurements obtained in
(4)
p the N’ band is shown in the top panel of Figure 8. The
whereI , I , andB arerespectivelythe averageofI (t),
1 1 1 correspondingmeasuredandbest-fitsyntheticnulldepth
I (t), and B(t) over the same integration time T. The
2 distributions are shown in the bottom panel. Figure 9
term cos(∆φ(t)) has been replaced by cos(∆φ +ǫ(t)),
0 represents the corresponding parameter grid projected
where∆φ isthemeandifferentialphaseoverT andǫ(t)
0 on the mean phase direction. The null depth measure-
is the instantaneous phase (within T). The standard
ments and error bars for each OB of the β Leo sequence
deviation over time T of the phase, σ , is measured in
ǫ obtained on February 8, 2015, are shown in Figure 10
real-time by PHASECam and recorded in the NOMIC
(left). Interestingly, the error bar on the best-fit null
fits header. At high-frequency (typically >1/60ms ≃
depthdecreaseswiththeratiobetweenthebest-fitphase
16Hz), the contribution of variable water-vapor to the
jitterandthe best-fitmeanphaseasshowninFigure11.
differentialphase is negligiblecomparedtoother sources
This effect, which may seem counterintuitive, is actually
ofvibrationsandthenear-infraredmeasurementisavery
expected from performing the NSC reduction on a finite
good approximation of the differential phase in the mid
number of measurements (see Figure 5 in Hanot et al.
infrared. The phase conversion between the two wave-
2011). It can be understood by realizing that the NSC
bands is achievedby computing the effective wavelength
isunabletodistinguishbetweenameanphaseoffsetand
using the spectrum of the star (using tabulated K-band
a true extended emission in the absence of phase jitter.
spectrafromPickles1998)andthe spectraltransmission
The parameters constraining the minimum number of
ofPHASECam. The resultingphaseisthenusedtopro-
measurementsperOBrequiredtoaccuratelyretrievethe
duce synthetic flux sequences following Equations 3 and
best-fit null depth are known (mainly the background
4. Note that in the future, we plan on using the terms
noise, the phase jitter, and the mean phase offset) but
hcosǫ(t)i and hsinǫ(t)i, which were not yet available at
further investigations are needed to define their sweet
the time of the observations presented in this paper.
spots for the LBTI.
Replacing the visibility by the null depth as
(Mennesson et al. 2011): 3.5. Data gating
1−|V| All the processing steps described in the previous sec-
N = , (5) tions use data that have passed through various data-
1+|V|
quality checks, which vary depending on the nature of
and using the auxiliary data (I (t), I (t), B(t), and the frame (null, photometry,orbackgroundframe). The
1 2
10 Defr`ere et al.
2015/2/8 2015/2/8
1.5
0.8
%]
Measured null per OB [%] 001...050 asured null per pointing [ 0000....0246
-0.5 Me
-0.2
-1.0
11 12 13 14 11 12 13 14
UT hour UT hour
Fig.10.— Left, null depth measurements per OB as a function of UT time obtained on February 8, 2015. The blue squares show the
calibratormeasurementswhilethereddiamondsrepresenttheβLeomeasurements. Theestimatedinstrumentalnullfloorisrepresentedby
thesolidblacklineandthecorresponding1-σuncertaintybythedottedlines. Right,correspondingnulldepthmeasurementsperpointing
(same notation). The longer time spent to acquire the second βLeo pointing increased the background bias and hence the dispersion of
the null depth measurements per OB inthe left-hand plot. This effect results ina larger systematic error for this pointing (see Table 1)
andexplainsthelargererrorbarintheright-handplot.
2015/2/8 than∼1%oftheframesundertypicalconditionswithno
major loop failure. Figure 8 shows an example of gated
null depth measurements (top panel) and corresponding
distribution (bottom panel). The null depth typically
%] 0.3 fluctuatesaroundafewpercentswithlow-frequencyvari-
aN [ ations due to precipitable water vapor (PWV, see Sec-
ull tion 5.3).
n
est-fit 0.2 4. DATACALIBRATION
b
on Datacalibrationconsistsinsubtractingtheinstrument
Error 0.1 null floor from the null depths obtained on the science
object. The instrument null floor, sometimes also called
thetransferfunction,istheresponseoftheinstrumentto
an unresolved object. As explained above, it is not nec-
0.0
essarily zero because of instrumental imperfections such
0 1 2 3 4 5
(Best-fit phase jitter σ)/(Best-fit mean phase µ) as phase errors, intensity mismatch, and tip-tilt varia-
φ φ
tions. Because these perturbations can vary over time
Fig. 11.— Error on the best-fit null depth versus the ratio be- (e.g., phase noise decreasing with elevation), the point-
tween the best-fit phase jitter (σφ) and the best-fit mean phase ings on the science object are interleavedwith pointings
(µφ) (same data as in Figure 10). The error bar increases with
lower values of this ratio as expected from performing the NSC on calibrator stars. We have adopted a total time per
reduction on a finite number of measurements (see Figure 5 in pointing of approximatively 20 to 25 minutes resulting
Hanotetal.2011). from a trade-off between data acquisition efficiency and
the need for measuring the null floor regularly.
Since the calibrators are not fully unresolved, the
first obvious gating consists of the removal of all open- first step to estimate the instrumental null floor is
loop frames using the AO and PHASECam telemetry. to correct the calibrator measurements for the finite
For photometric and null frames, we require both AO extension of the stars. This correction is done using a
systems to be inclosed-loop. For nullframes,we require linearlimb-darkenedmodelforthe geometricstellarnull
in addition that the fringe sensor is in closed loop, that (Absil et al. 2006, 2011):
there were no fringe jumps during the previous integra-
tion time of NOMIC, and that the near-infrared fringe πBθ 2 7u u −1
LD λ λ
quality(trackedby the SNR ofthe fringes)isnotpoorer Nstar = 1− 1− ; (6)
4λ 15 3
than a certain level (3-σ threshold). Since fringe jumps (cid:18) (cid:19) (cid:18) (cid:19)(cid:16) (cid:17)
areonlymonitoredat1Hz(seeSection2.3),wealsogate where B is the interferometric baseline, θ is the limb-
LD
the null frames by removing those showing a null depth darkened angular diameter of the photosphere, λ is the
larger than 20%. The null depth is computed directly effective wavelength,andu is the linear limb-darkening
λ
by dividing the flux measurements at null by the con- coefficient. Given the relatively short interferometric
structive flux estimated using Equation 2. Finally, the baseline of the LBTI, this correction is generally small
lastdatagatingappliestoallkindofframesandconsists inthe mid-infraredandthe effect oflimb-darkeningneg-
in removing the frames which show a high background ligible. Assuming u = 0, the typical geometric stellar
λ
level(5-σthreshold). Thesecriteriagenerallyremoveless nullforourtargetsis∼10−5withanerrorbarof∼10−6,