We want to study a polychromatic inverse problem method with nulling interferometers to obtain information on the structures of the exozodiacal light. For this reason, during the first semester of 2013, thanks to the support of the consortium PERSEE, we launched a campaign of laboratory measurements with the nulling interferometric test bench PERSEE, operating with 9 spectral channels between J and K bands. Our objective is to characterise the transfer function, i.e. the map of the null as a function of wavelength for an off-axis source, the null being optimised on the central source or on the source photocenter. We were able to reach on-axis null depths better than 10(exp 4). This work is part of a broader project aiming at creating a simulator of a nulling interferometer in which typical noises of a real instrument are introduced. We present here our first results

Cassaing, F.

Danchi, W. C.

Jacquinod, S.

Lhome, E.

Lopez, B.

Lozi, J.

Marcotto, A.

Menut, J.-L.

Millour, F.

Parisot, J.

Petrov, R.

Reess, J.-M.

Vedova, G. Dalla

NASA Technical Reports Server

Improving the performances of current optical interferometers & future designs
Proceedings of Haute Provence Observatory Colloquium (23-27 September 2013)
Edited by L. Arnold, H. Le Coroller & J. Surdej
Oﬀ-axis nulling transfer function measurement: a ﬁrst
assessment
G. Dalla Vedova1, J.-L. Menut1, F. Millour1, R. Petrov1, F. Cassaing2,
W. C. Danchi3, S. Jacquinod4, E. Lhome5, B. Lopez1, J. Lozi6, A.
Marcotto1, J. Parisot4, J.-M. Reess4
1 Laboratoire LAGRANGE, Universite´ de Nice-Sophia Antipolis, OCA,
06108 Nice, France, 2 ONERA, F-92322 Chaˆtillon, France, 3 NASA
Goddard Space Flight Center, Greenbelt, MD 20771, USA, 4 LESIA,
Observatoire de Paris, 5 Place J. Janssen, 92195 Meudon, France, 5 ING,
Apartado de correos 321 E-38700 Santa Cruz de la Palma, Canary Islands,
Spain, 6 The University of Arizona, 1077 N Highland, Tucson Arizona
85721, USA
Abstract. We want to study a polychromatic inverse problem method with
nulling interferometers to obtain information on the structures of the exo-
zodiacal light. For this reason, during the ﬁrst semester of 2013, thanks to
the support of the consortium PERSEE, we launched a campaign of labo-
ratory measurements with the nulling interferometric test bench PERSEE,
operating with 9 spectral channels between J and K bands. Our objective is
to characterise the transfer function, i.e. the map of the null as a function
of wavelength for an oﬀ-axis source, the null being optimised on the central
source or on the source photocenter. We were able to reach on-axis null
depths better than 10−4. This work is part of a broader project aiming at
creating a simulator of a nulling interferometer in which typical noises of a
real instrument are introduced. We present here our ﬁrst results.
1. Introduction
The observation and the characterisation of dusty debris disks, extrasolar planets,
and planetary systems around stars is one of the major astronomical challenge
of the 21st century. Direct detection, model ﬁtting, and ultimately imaging of
these objects require instruments with very high dynamic range and high angular
resolution in order to comply the combination of two major physical constraints.
First, there is large ﬂux ratio between the star and the planet or the circumstellar
disk, typically ∼ 1010 in the visible, and ∼ 107 in the infrared. Second, the
angular separation between a host star and exoplanet in the habitable zone is
typically small. For example, the system Earth-Sun at maximum elongation at
the distance of 10 pc has an angular separation of the order of 100 mas or 0.5
μrad which needs an interferometer with a baseline of 20 m at 10 μm.
Currently, there is a large eﬀort to develop concepts able to detect and char-
acterise Earth-like planets (Quirrenbach 2001). In this context, nulling interfer-
ometry could play a key role (Bracewell & MacPhie 1979). In last decades, nulling
67
https://ntrs.nasa.gov/search.jsp?R=20140012655 2019-08-31T18:50:02+00:00Z
68 G. Dalla Vedova et al.
interferometry has been one of the most studied techniques (Angel & Woolf 1997;
Le´ger et al. 1996a) and these studies led to consider two major projects named
DARWIN (Le´ger et al. 1996b) and TPF-I (Lawson et al. 2007). The goal of
these two missions is to detect Earth-like planets into the habitable region and
characterise their spectra with eventually markers of the possible presence of life
(Danchi et al. 2003). As these instruments are extremely demanding for technical
and operational requirements, some intermediate class projects, such as PEGASE
(Ollivier et al. 2009) and FKSI (Danchi & Lopez 2007) have been considered.
The initial speciﬁcation was to ensure the exozodiacal light with an accuracy of
1 zodi, i.e. the intensity for a system identical to the solar system, for all Darwin
potential targets in order to assess Darwin observations feasibility and priority.
Later, it has been understood that this type of M-class space interferometer can
have remarkable possibilities to characterise the structures of protoplanetary and
debris disks with various signatures of planet presence or formation. A demon-
strator PERSEE, acronym of Pegase Experiment for Research and Stabilisation
of Extreme Extinction, has been designed and built by a consortium led by CNES
and including IAS, LESIA, ONERA, OCA and Thales Alenia Space in order to
assess the potential and limits of PEGASE, and lately FKSI.
There is a growing interest in the image reconstruction from interferometric
observations, due to the possibility to visualise unsuspected structures and details
of the object of interest. Both in model ﬁtting and image reconstruction, the
knowledge and the characterisation of the transfer function and the covariance
matrix of residuals of the interferometer are critical information, both to optimise
the problem inversion and to characterise the quality of the result (Tallon-Bosc
2007; Thie´baut 2009). As a consequence, characterising the oﬀ-axis transfer
function of a nulling interferometer is of prime interest.
Early in 2013, we started a measurement campaign with the aim of char-
acterising the transfer function with a real nulling interferometer operating in 9
spectral channels in a large spectral band of the infrared. We used the PERSEE
test bench to record transmission maps, simulating angularly oﬀset sources with
diﬀerent ranges of baselines and tilts. We obtained a database of measured multi-
wavelength transmission maps of a nulling interferometer, and are comparing it
with its analytical model (section 3.).
2. Measurement campaign
PERSEE is a ﬁbered nulling interferometer demonstrator built with the aim to
achieve a stabilised nulling ratio better than 10−4 in a large spectrum range be-
tween bands J and K. Lozi et al. (2013) have demonstrated that a polychromatic
nulling depth of 10−6 with a stability of 10−7 could be reached over 10 hours sim-
ulating conditions of typical perturbations of a spacecraft such as PEGASE. The
detailed optical layout made by Thales Alenia Space is recalled in Table 2. and
in Fig.1. The bench is equipped with a fringe sensor (FS) based on the ABCD
modulation technique (Shao et al. 1988) and a tip-tilt sensor (FRAS) in order
to correct respectively internal OPD between the interferometer arms and tilt er-
rors in closed loop. After the combining stage, a Modiﬁed Mach-Zehnder (MMZ)
(Jacquinod et al. 2008), dichroic plates separate the various spectral channels
and direct them in the appropriate detection chains. The H and K channel sig-
nals reach, via a single mode ﬁber, the nitrogen cooled infrared detector. On the
Oﬀ-axis nulling transfer function measurement: a ﬁrst assessment 69
Table 1.: Optical components of PERSEE
M1 45 deg. mirror
M4-M5 nulling periscope
M6 tip-tilt injection
M7-M8 delay line (cat’s eye)
M11 FRAS mirror
M9 30 deg. mirror (MMZ)
L3-L4 separating plates (MMZ)
D2 fringe sensor dichroic
M10 oﬀ-axis parabola
I output of MMZ corresponding to the channel A
II output of MMZ corresponding to the channel B
III output of MMZ corresponding to the channel D
IV output of MMZ corresponding to the channel C
IR camera, we have simultaneously polychromatic measurements in 9 channels
from 1.65μm to 2.45 μm. In order to simulate an oﬀ-axis source, we introduced
on mirrors of PERSEE (M6) a set of commands to drive a displacement in tip-tilt
(α, β) and OPD δ. These tip-tilt and OPD can be associated with a simulated
baseline B by the relationship δ = B · sin(α), where α and β correspond to an
angular position on sky relative to the optical axis of the instrument. With com-
mands injected on mirrors M6, we scanned a near-ﬁeld close to the axis within
an angular separation of two Airy disk diameters, deﬁned by the resolution of the
considered pupils. We simultaneously measured the ﬂux on the dark output of
the MMZ recombiner (III output or channel D, see Table 2.), and a ﬂux reference
for the source ﬂuctuations directly at the output of the collimator (see Fig.1). A
measurement corresponds to a scan of a grid of points in the near-ﬁeld oﬀ-axis
with a ﬁxed baseline and, for each position (α, β, δ), we recorded 20 frames in
0.2 seconds with the IR camera. We make α and δ proportional to each other in
order to simulate the variation of the transfer function along a 2-telescope base-
line. We also measured the photometry of both arms of the interferometer. We
normalised the science channels with ﬂuctuations of the source and we evaluated
the photometry in both arms IA, IB , and the recombination of both beams of
light ID. We deﬁne the measured normalised transfer function T¯
B(α, β) (Eq.1),
and the theoretical transfer function of PERSEE, given in He´nault et al. (2011).
T¯Bmeas(α, β) =
ID(α, β, δ)
IA(α, β, δ) + IB(α, β, δ) + 2
√
IA(α, β, δ)IB(α, β, δ)
(1)
TBtheor(α, β) = | sin(αB/λ) · [BˆD(α, β) ⊗G(α, β)]|
2 (2)
Where BˆD(α, β) is the complex amplitude generated by an individual sub-
aperture and being back-projected onto the sky. For unobstructed pupils as
in PERSEE, it is equal to 2J1(ρ)/ρ where ρ = πD/λ, and J1 is the Bessel
function at the ﬁrst order. G(α, β) is the fundamental mode of the exit ﬁlter-
ing waveguide, after being projected back on-sky. It can be approximated by a
gaussian function. Once we obtain the measured transfer function, we can com-
pare it with the normalised theoretical one T¯B
theor
(α, β) = N · TB
theor
(α, β), where
N = [BˆD(α, β) ⊗G(α, β)]
−1 is the normalisation term.
70 G. Dalla Vedova et al.
Figure 1.: Layout scheme of the ﬁbered nulling interferometer demonstrator
PERSEE designed by Thales Alenia Space.
3. Results
We present preliminary results for the measure with internal tip-tilt from −36 to
36 arcseconds with a maximal OPD of 3.5 μm. The two apertures of PERSEE
have a diameter of 13 mm and are separated by a baseline of 50 mm. It corre-
sponds to a near-ﬁeld oﬀ-axis on the order of  1.4 Airy disk radius and a ratio
of baseline to diameter of pupils equal to B/D = 3.2 that gives ∼ 7 fringes in
an Airy disk region. For example, if we consider two apertures with a diame-
ter of 10 cm the baseline is equal to 32 cm. Using Eq.1 we produced the map
transfer function and its associated variance map shown for the channel λ = 2.45
μm respectively in Fig.2 and Fig.3. Fig.4 shows the theoretical transfer function
obtained using Eq.2. The diﬀerence between measured and theoretical transfer
function is shown in Fig.5. Both theoretical and subtracted maps are obtained for
the channel λ = 2.45 μm. We see that the measured and modeled maps are fairly
similar but with a diﬀerence that is larger than the standard deviation. The next
step is to tune the model with a simple number of perturbation to obtain a good
match with the measures. The value of the best null measured is on the order of
magnitude of 10−4. This value is considered deep enough to detect the zodiacal
light with an accuracy of 1 zodi, comparable with the request for the PEGASE
mission (Defre`re et al. 2008). We hope that this null of 10−4 is suﬃcient for a
comprehensive analysis of the statistic of the transfer function T¯Bmeas(α, β). Note
that the irregular region in the center of the left side of the measured transfer
function has been caused by a sudden slight pressure change in the white room
occurred during the measurements, due to the opening of the entrance door.
Oﬀ-axis nulling transfer function measurement: a ﬁrst assessment 71
Figure 2.: measured normalised trans-
fer function T¯Bmeas(α, β) for λ = 2.45
μm.
Figure 3.: variance of the measured
normalised transfer function.
Figure 4.: theoretical normalised
transfer function T¯B
theor
(α, β), for
λ = 2.45 μm.
Figure 5.: map of the subtraction be-
tween measured and theoretical trans-
fer function.
72 G. Dalla Vedova et al.
4. Conclusions and perspectives
Using the PERSEE test bench, we collected data for a detailed characterisation
of the polychromatic transfer function T¯B(α, β) for a realistic ﬁbered nulling in-
terferometer and study its statistics in time and space. We presented preliminary
results obtained for the measure with the ratio B/D = 3.23. The value of the
best null is on the order of 10−4. If the transfer function is perfectly known, cali-
brated and stable, the performances of the model ﬁtting or image reconstruction
will be limited only by fundamental noises.
The precision and the stability of the transfer function for a nulling interfer-
ometer is the main limiting factor for the dynamic range that can be obtained
for the investigated structures. Our goal is to analyse the variances and the co-
variances in time and between channels to evaluate the additional instrumental
noise and hence the realistic limits of the approach. This is the starting point
for a detailed characterisation of the nulling performances, especially for image
reconstruction with an hyper-spectral approach and model ﬁtting of very high-
dynamic range scenes such as a star plus an exoplanet, or a star plus a debris
disk with gaps.
Acknowledgements. The authors would like to thank the following people for the techni-
cal help, e-mail exchanges and remarks give during and after the work on the bench: T.
Buey1, J.-M. Le Duigou2, J. Montri3, A. Sevin1.
1 LESIA, Observatoire de Paris, 5 Place J. Janssen, 92195 Meudon, France, 2 CNES,
18 Av. E. Belin 31401 Toulouse Cedex 9, France, 3 ONERA, F-92322 Chaˆtillon, France,
3 NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
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Off-Axis Nulling Transfer Function Measurement: A First Assessment

Off-Axis Nulling Transfer Function Measurement: A First Assessment

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