Download infrared studies with the lbt interferometer

PRELIMINARY FEASIBILITY STUDIES
FOR A BEAM COMBINER COUPLED TO AN INFRARED
CAMERA AT THE LBT INTERFEROMETER
(an answer to the call of the LBT Corporation)
Prepared by:
1) Osservatorio Astronomico di Torino (OATo), (Italy)
2) Dipartimento di Scienze dell'Informazione, Università di Genova (DSI), (Italy)
3) Istituto Metrologico G. Colonnetti del CNR di Torino (IMGC), (Italy).
Abstract
The Consortium of Institutes (hereafter identified simply as the "Consortium") made by
the Osservatorio Astronomico di Torino (OATo), the Dipartimento di Scienze
dell'Informazione dell'Università di Genova (DSI), and the Istituto Metrologico G.
Colonnetti del CNR di Torino (IMGC) wishes to answer, with the present document,
to the "call for proposals and ideas" for instrumentation of the LBT telescope. Scope of
this proposal is that of providing some ideas for a feasibility study of an IR imager
coupled with a beam combiner for the common focus of LBTI. We first outline the
present status of studies already performed on the subject thanks to the financial support
obtained in Italy by the Consorzio Nazionale per l'Astronomia e l'Astrofisica. Then we
address the problem of applying this existing expertise and further laboratory
experiments to the preparation of a detailed description and project for the instrument.
This result will essentially come out from a careful tolerance analysis of a few possible
designs. The Consortium expresses its intention to work, after completion of the
preliminary study, in the preparation of the instrument itself, and collaborate to this goal
with any other interested Institute of the LBT collaboration.
The topics that will be addressed in the various sections are those specified in the index
here below.
i)
general outline (Introduction)
Part I
ii)
studies made so far on image quality and possible scientific targets (section 2)
iii)
results on image simulations and reconstruction (section 3)
iv)
results on beam combiner design (section 4)
Part II
v)
design and laboratory work on beam combining: experiments foreseen (section
5)
vi)
image simulation and reconstruction: next steps of development (section 6)
vii)
system monitoring and metrology (section 7)
viii) defining the observing program (section 8)
xi)
references (section 9)
1. Introduction
Our interest in ground based interferometric observations in the Infrared (hereafter IR)
descends from two different series of motivations. Generally speaking, the highly
promising possibilities offered by such a technique for the study of several astrophysical
problems in which high resolution is an essential condition, naturally require that the
international astronomical community prepares itself to exploit them. On the other hand,
specific activity in either infrared imaging or high resolution astrometry was carried out
in the recent past by the proponents, and is still underway for both ground based and
space borne projects. As examples of such activities, we mention here the work done by
two of the proponent Institutes (OATo and IMGC) under ESA contract for the GAIA
(Global Astrometric Interferometer for Astrophysics) mission, involving metrology and
optical requirements similar to those involved in the LBT interferometer. Similarly, we
recalled the activity that has been going on at the Observatory of Torino in mid-IR and
near-IR imaging, including the development of three infrared cameras (TC-MIRC and
Tircam I and II) for the TIRGO national telescope.
In the present document we shall not discuss those arguments in detail; interested
readers are solicited to refer to [1] (specifically chapter 3). We want simply to underline
here that, thanks to the “rigid” single mounting of the two mirrors, LBTI will be able to
achieve cophasing of the two beams over a field of view (hereafter FOV) considerably
larger than the point spread function of each telescope; hence this project appears as the
ideal site where to combine new ideas and solutions for both imaging (probably IR
imaging) and interferometry .
If financed, the final product of this work will be a design study accompanied by a
specific solution suggested and tested both in the laboratory and with a dedicated
tolerance and metrology analysis. After this, but also during the completion of this
work, any collaboration with other interested Institutes will be welcome.
Let us discuss, in the following sections, what has been done so far to achieve a
preliminary expertise on the specific LBTI problems (part I of the document), and what
remains to be done for a complete understanding of the problems that have to be faced,
i.e. for arriving at a complete feasibility study (part II).
PART I
(PRELIMINARY STUDIES AND EXPERTISE
ALREADY AVAILABLE)
2. Image characteristics and feasible scientific projects
2a - LBT interferometric focal plane issues
We start from an analysis of the general features of the LBTI Interferometric configuration, which
are summarized in Table 1. The expected number of fringes really visible will be 3 (see Figure 1),
out of a nominal number:
DA /TY = 4.18
where side portions of fringes cannot be counted. As a consequence of the values reported in Table
1, it is straightforward to derive the extension in milli-arcseconds (hereafter mas) of the Airy disc
and of the Young period for different representative wavelengths. This is done in Table 2.
Individual
Diameter
Airy Disk
Table 1
Primary
Baseline (center to center)
Young Period:
8.41 m
DA = 2.44  / D
B = 14.42 m
TY =  / B
Table 2
Wavelength [m] Airy [mas]
0.55
32.89
1.1
65.77
1.7
101.65
2.2
131.55
3.5
209.28
4.7
281.03
8.2
490.31
10.3
615.88
11.5
687.63
13.5
807.22
16.8
1004.54
22.
1315.47
25.
1494.85
Young [mas]
7.87
15.74
24.32
31.48
50.07
67.24
117.32
147.36
164.53
193.15
240.36
314.76
357.68
Figure 1
Location algorithms, developed in the framework of the GAIA project, and then applied to the
present problem, show that significant location accuracy degradation arises in case the sampling
resolution is lower than 3 - 4 pixels per fringe period, optimal performance being achieved for at
least 5 pixels per fringe period (see Figure 2). A compromise value of 4 pixels per fringe period
will be used in the following considerations:
Sp = TY/4.
Although the above result was verified only for
location of point-like sources, it seems likely that
similar requirements will arise from image
reconstruction problems in case of complex
(realistic) targets.
Figure 2
2b – Detector Limitations
The expected format (in number of pixels) of available near-future devices is likely to be still rather
small, e.g. of the order of 3002 for the MIR bands (10-20 m) and 1k2 for the NIR bands (1-5 m).
Scaling the above estimates to the formats of specific detectors (or mosaics) is straight-forward. In
the case of single detectors, assuming square pixels, as usual, the low resolution direction is
oversampled by a factor ~4. In particular, the Airy disk is covered by ~230 pixels over a square
region of 17x17 (~290) pixels. Therefore, in near-optimal sampling conditions, the FOV achievable
by a single detector is rather small: 300 pixels / 17 pixels = 18 times the Airy diameter in the MIR
bands, providing about 12” at 10 m, whereas it is about 1024/17 = 60 Airy diameters in the near
infrared (18” at 5 m). These results are somewhat surprising: the field on realistic detectors is
quite small!
2c - Effective Focal Length
One can then estimate the equivalent scale on the focal plane and therefore the required effective
focal length (EFL). The following table (Table 3) is obtained assuming a pixel size of 10 m in the
visible, of 40 m in the 1-5 m region, and of 80 m for the MIR bands. Several relay optics may
be required in order to achieve the best sampling over a large bandwidth.
The announced availability of (2k)2 format NIR detectors, with pixel size ~18 m, reduces the
optical design requirement to an EFL of 200-500 m, which is nonetheless very challenging!
Table 3
m Pixel size [m] Pixel size [mas]
0.55
10
1.97
2.2
40
7.87
5.6
40
20.03
10.3
80
36.84
22.
80
78.69
EFL [m]
1048
1048
412
448
210
The simple analysis performed here is the necessary condition not only for the design of any beam
combining device, but also for the development of realistic scientific projects to be carried out with
the LBT interferometer. Compact sources, in which the goal is to resolve a central structure, or in
which a number of different astrophysical objects are clustered in a small region and must be
separated are the typical affordable scientific targets. We refer to [1] for a list of such targets; in
order to exploit LBTI possibilities for each of them a detailed preliminary study must be performed.
As an outcome of the above considerations, we therefore started a specific research work in order to
understand, for a number of scientific problems satisfying the above requirements, what kind of
information can be achieved at high resolution, and what kind of possibly new physical processes
are expected to take place. An interesting example of this work concerns circumstellar envelopes
around evolved stars. This is outlined in the following sub-section, but we underline that it is only
an example out of a series of studies that clearly require to be afforded (for compact star formation
regions, small clusters, quasars with surrounding faint galaxies, Jovian-like objects around close-by
stars etc...).
2d - Identification of suitable targets: an example
As a typical scientific problem that will certainly strongly benefit from IR interferometry at the
resolution and FOV reached by LBTI, we summarize here a study of the circumstellar envelopes of
evolved stars, using CW Leo as an example. The source is a bright, carbon rich Asymptotic Giant
Branch (AGB) star, whose mass loss builds up a huge circumstellar shroud of gas and dust that
absorbs and re-emits radiation from the photosphere.. Present-day Mid-IR imaging can already
resolve the source (Busso et al., 1996; Marengo et al., 1997), even with telescopes of moderate size.
The extension of the circumstellar dusty region, though variable in time, has typical dimensions of
some arcseconds. Radiative transfer models of the envelope require information on the optical
properties of dust particles. There is now a wide literature on that, but opacities of acceptable
quality are known only for a limited number of compounds (graphite, amorphous carbon, some
variety of silicates and a few oxides). At the level of uncertainty permitted by IR photometry, and
by our knowledge of the optical properties of dust and of condensation sequences, the actual
composition of the envelopes cannot be derived precisely. This is even more so for oxygen-rich
AGB stars. This is a problem, because circumstellar grains (SiC, AL2O3, graphite, ecc...), clearly
carrying the signatures of AGB star nucleosynthesis, have been recovered in pristine meteorites
(see e.g. Zinner, 1997) and are today the most precise source of information about nuclear and
chemical processes in such red giants (Gallino et al., 1990; 1997). It would be extremely useful to
observe directly the innermost regions of circumstellar envelopes, where dust condenses: different
compounds condense in different ( T) conditions and at different distances from the central
source, and one could recover information on individual species, instead of assuming a mixture,
which is often only a measure of our incapability to disentangle the various contributions. This
would require observations down to resolutions of about 0.1 arcsec at 10 m, and would yield a
clear identification of which compounds can form, hence a definite correlation between grains
measured from meteorites in laboratory, and their equivalent in circumstellar environments. In turn,
this would resolve several uncertainties in condensation sequences and opacities, as well as provide
a picture of red giant composition and processes of unprecedented detail. When the difficulties in
understanding critical problems like mass loss and light element isotopic compositions of evolved
stars are considered, this would have enormous effects on our knowledge of the last phases of
stellar evolution.
What can LBT say on such topics? Figure 3 is a sketch of what can be done with a single 8.4m
mirror. Each panel represents a quadrant of an image, (3.5 x3.5) arcsec in size. Panel a) is the
result of the radiative transfer model, computed with a resolution better than 0.05 arcsec. We can
Figure 3
assume it provides the ‘real’ view of the source. Panel b) shows the diffraction limited PSF at 10
m (Airy disc of 0.3 arcsec), while panel c) is a convolution of the two. Finally, panel d) is the
result of projecting the image on a two-dimension detector array with pixels of 0.15 arcsec in size
(minimum Nyquist criterium). Figure 4 represents what will be seen by LBTI, after image
reconstruction from the fringes. Pixels of 0.05 arcsec are considered (slightly larger than in Table 3:
they correspond to 3 pixels per Young period, instead of 4, to limit integration time). The bright
inner portion of Figure 3a) shows rather clearly a ring predicted by the model, representing the shell
where dust condenses. It is not appreciated in Figure 3d), i.e. with a single 8.4 mirror, but is clearly
put in evidence in Figure 4, i.e. in the final image of LBTI, with reasonable assumptions for the
scale and the pixel size. Should one observe this object with different narrow filters, or with a
moderate spectral resolution such as provided by Circular Variable Filters in IR (R = 50 – 100) the
nature of dust grains emitting in the ring would be understood.
What we have shown above clearly demonstrates that even a single LBTI frame can provide an
entirely new insight in a number of astrophysical problems, if the proper goals chosen, analyzed and
modeled in advance (Busso et al.,1998; Marengo et al., 1998).
Figure 4
2e - Anamorphic Optics
In order to overcome the limitations described in the previous sub-sections (mainly 2c), we have
started a study of non-conventional optical systems that might offer a way out.
An optical system providing different scale in different directions of the image plane is called
‘anamorphic’ (B.N. Begunov, N.P. Zakaznov, S.I. Kiryushin, V.I. Kuzichev, "Optical
Instrumentation - Theory and Design, MIR, 1988). They are usually based on cylindrical lenses or
mirrors, and in particular they can transform the aspect ratio of a rectangle, modifying the relative
values of its sides.
The reason for an interest in such asymmetric properties in the case of LBT arises from the quite
different resolution required in the two directions of the interferometric image and from the
available detector pixel geometry, which is in most cases squared. Therefore, an anamorphic optical
system could be proficiently used in order to achieve the best pixel matching for the LBT detectors;
an appropriate number of detector pixels can be placed in the low resolution direction, e.g. sampling
the Airy disk over 2-3 pixels and the Young period with 7-8 pixels. In such a case, the FOV of a
(2k)2 NIR array would become of the order of 10"x67", whereas for a 300 2 MIR detector the FOV
is 7"x46". Therefore, there would be a very large gain with respect to the case of symmetric scale,
produced by conventional optics, which, with 4 pixels/fringe resolution, would provide a FOV
~16"x16" (NIR) or ~11"x11" (MIR). For example, in K band, in order to obtain an image of about
1'x1', the symmetric scale case would require 4x4 distinct exposures, in a mosaic technique,
whereas using anamorphic optics 6 side-by-side exposures would be sufficient, despite an higher
sampling resolution in the interferometric direction. Moreover, since the signal per pixel is higher,
the detection limit would benefit as well (here, by about the pixel compression factor, i.e. ~6,
corresponding to about 2 magnitudes). Of course, an anamorphic factor ~6 is not trivial to be
achieved, while still preserving the image quality over the field.
3. Image simulation and reconstruction
3a – Simulations at the telescope
In order to simulate the LBT pupil, three masks have been prepared and installed in the pupil wheel
of the MAX camera (Figure 5), a thermal IR imager currently operated at UKIRT (Robberto and
Herbst 1998). This project is part of a collaboration with the Max Planck Institute fuer Astrophysik
of Heidelberg. MAX is based on a 128x128 Rockwell Si:As HF16 array, with 0.265 arcsec/pixel
scale and a field size of ~34x34 arcsec. The pupil masks are shaped in such a way as to reproduce a
scaled version of the LBT, with two 1.4m diameter mirrors approximately 1m edge-to-edge apart.
The three masks correspond to three different orientations of the baseline angle, spaced by 60
degrees. The pixel scale of MAX adapted for a full aperture 4m telescope, slightly over-samples the
fringes. The increased scale decreases the background flux down to a level in which the read-out
noise - in the short exposure time used - becomes significant with respect to the shot noise of the
background. For these reasons, the sensitivity of this kind of interferometer cannot be considered as
Figure 5
optimal, and our results must be used with care to extrapolate the LBT performances. During a
MAX run in fall, 1997, images of a few bright IR sources have been obtained to demonstrate the
principle and to study the temporal behavior of the atmosphere at mid-IR wavelengths. In general,
the pupil mask easily provides the PSF expected for the LBT interferometer (Figure 6). Here the
ghost image (see section 3b) is clearly visible.
Figure 6
The fringe contrast turns out to mainly depend on the filter pass-band and on the source brightness,
and also, as in the case of  Ori, on the presence of a faint circumstellar envelope, already known
from previous measurements. With the usual atmospheric conditions of Mauna Kea, the UKIRT
telescope, recently upgraded with the new tip-tilt system, is known to routinely provide diffraction
limited images at 10 m (Robberto et al. 1997). Therefore, it is not surprising that the fringes
maintain their position for exposure times much longer than the coherence time of the atmosphere.
To study the spatial behavior of the fringe pattern, images of the Becklin-Neugebauer (BN) source
in Orion have been obtained in the night of 22 October 1997. The observations were performed in a
narrow-N band filter, centered at 11.6 m and approximately 3 m wide. The integration time was
25 msec, i.e. coincident with typical rms variation of the atmospheric OPD jitter and approximately
1/4 of the coherence time. The chopping throw was set to about 20 arcsec in the NS direction,
parallel to the dispersion of the fringe pattern. A complete ABBA cycle was performed, taking 100
chopped pairs of frames (source-minus-sky) on each A/B cycle, for a total of 400 frames on source.
The observations were done in the morning twilight with the fast-guide camera switched-off.
Therefore, the secondary mirror was not providing the usual low-order (image-motion and piston)
corrections. However, since the natural seeing at K (2.2 m) was still well below 1 arcsec, the
effects of the image motion at 10m were expected to be negligible. Our data in fact do not show
any significant loss in fringe contrast going from single 25 msec images to the co-adding of 400
frames. In Figure 7 we show the co-adding of 100 frames, 25 msec each. The central source is BN,
almost unresolved with the three fringes expected from the LBT pupil. To the south, some extended
nebulosity is present without any significant sign of fringes. In this raw image, a small number
(about 20) of bad pixels is seen.
Figure 7
When compared with standard images obtained with the full UKIRT aperture, this one shows little
signs of background gradient. This is due to the fact that the warm parts of the telescope are
efficiently masked by the small sub-pupils. In Figure 8 we present the final combination of 400
frames, i.e. the result of a complete ABBA cycle. The image is stretched in order to display the
faintest details, and the fringes on the BN object therefore appear to be saturated. At the upper edge
of the frame, the negative ghost arises from the nodded B pair, taken by pointing the telescope to
the south at the ``sky'' position. The structure of the region is now clearly understandable: BN is at
the center of the figure, whereas the Kleinman-Low object (IRC4) is at the bottom. Between these
Figure 8
two sources, from left to right IRC2, IRC7 and IRC3 are visible. The faint emission just south of
BN is IRC6. A faint negative ghost to the west (right) of BN is due to a bright stellar source outside
the field, to the north. Each source provides fringes with different contrast, ranging from 0.4 for BN
to roughly 0 for KL, which is known to be fairly elongated in the NS direction. Unfortunatly, it was
impossible to obtain other images of this region in the past winter with the other masks, to
reconstruct the final image. However, these data clearly show that the most critical problem
affecting the image reconstruction in LBT comes from the presence of negative images due to the
chopping/nodding observing strategy necessary in mid-IR. Simple algorithms for fringe restoration
are already available, but no one allows to manage the negative ghosts. In fact, reconstruction of
chopped/nodded images is up to now a classical unsolved problem of IR astronomy. Therefore, a
specific activity, reported in the next section, was dedicated to this issue.
.
3b – Numerical simulations and image reconstruction
A problem that may become crucial in Interferometry applied to thermal Infrared studies, is the
reconstruction of chopped and nodded images. Indeed, the technique of chopping and nodding,
which is used for subtracting the background due to the thermal emission of the telescope and of the
overlying gray atmosphere, allows one to obtain accurate observations of isolated sources but not
of extended sources, as a consequence of the superposition of the negative dual images. With this
addition, the various restoration problems which must be considered in connection with the LBT
interferometer are the following :
1) restoration of a chopped and nodded image
2) deconvolution of this restored image using the space-variant PSF which describes the effect of
the adaptive optics
3) simultaneous deconvolution of several images of the same object, corresponding to various
orientations of the LBT, again in the case of adaptive optics.
Therefore the final goal is a method which compensates the effect of chopping and nodding for the
various images provided by the interferometer and then combines these images to produce a high
resolution and high sensitivity image of the object under observation.
We have so far mainly investigated problem 1) and problem 3), the latter in the simpler case of
space-invariant PSF's. Concerning problem 1) we have proposed a very simple mathematical model
describing the formation of a chopped/nodded image and we have used a very simple constrained
iterative method, the projected Landweber method, with constraint of positivity, for the inversion of
the chopped/nodded matrix. Preliminary results obtained both in the case of simulated images and
in the case of real images taken at the UKIRT telescope with the MAX camera, are very promising
and have been presented at the Kona meeting on Astronomical Instrumentation (M.Bertero,
P.Boccacci and M.Robberto, 1998, “An inversion method for the restoration of chopped and
nodded images,” Proc. SPIE, vol. 3354, 1998). An example of restoration of the galactic center is
presented in Figure 9. An analysis of the results obtained by means of the method has also
suggested a new observation strategy based on the use of different chop/nodding amplitudes.
Numerical simulations indicate that by combining the corresponding restored images it is possible
to obtain very accurate restorations. The future work in this direction will consist in an accurate
analysis of the artifacts generated by the inversion method and of the effect of noise on the restored
images, as well as in the optimization of various parameters such as the chop/nodding amplitudes
and the number of iterations.
Fiure 9. a) 128x128 chop/nodded image of the Galactic Center obtained with a chopping aperture of
28 pixels (7.56 arcsec); b) restoration of the imaging in a) obtained by means of the projected
Landweber method.
Concerning problem 3), its formulation as a least-squares/maximum-likelihood problem has been
considered in the case of space-invariant PSF's and methods for obtaining regularized solutions
have been implemented. More precisely the following methods are now available :
1)Tikhonov regularization method
2) Projected Landweber method with positivity constraints
3) Lucy-Richardson method.
The input of each one of these programs is a set of images of the same object with the
corresponding PSF, typically the various images provided by the LBT interferometer when rotating
the system and the corresponding rotated PSF. Each method contains a free parameter, namely the
regularization parameter in the case of method 1) and the number of iterations in the case of
methods 2) and 3). When synthetic data are used these parameters can be optimized by minimizing
the distance between the restored image and the true one. The problem of the choice of these
parameters in the case of real data must still be investigated. The numerical simulations have been
performed assuming a space-invariant, diffraction-limited PSF for the LBT interferometer.
Moreover a picture of the M51 galaxy has been used as a test object. Examples of the results of this
simulation, using three images corresponding to three different orientations of the base line of the
interferometer are shown in Figure 10.
Figure 10. a) The image of M51 used as test object; b) a noisy image (Poisson noise) of a)
corresponding to a 45 degrees angle between the base line of the interferometer and the horizontal
line; c) the restoration of M51 obtained by means of three images corresponding to three
orientations spaced by 45 degrees (Lucy-Richardson method); d) the restoration of M51 obtained by
means of three images corresponding to three orientations spaced by 60 degrees (Lucy-Richardson).
The implemented methods can now be used for performing several numerical experiments. The
preliminary step is to define a set of test objects which are of interest in infrared astronomy and, for
each test object, a set of possible orientations of the LBT. By comparing the performance of the
various methods it should be possible to decide which approach is recommended in a given
situation.
4. Beam combiner design
The LBT configuration has been progressively inserted into the Code V Computer Aided Optical
Design software, in order to achieve an overall interferometric macro suitable to the required
tolerance analysis versus wavelength
4a -Telescope Input Parameters
The two telescopes have a Gregorian structure. Primary mirrors are paraboloids (K = -1) with an
effective focal length of 9.6 m, which produces a F/1.142 beam. Secondary mirrors are prolate
ellipsoids with a diameter of 871.2 mm, undersized for infrared optimization. The total system has
an effective aperture of F/15. The two mirrors are separated by a distance of 10.61845 m. The F/15
beam is folded by a flat tertiary mirror which redirects the light towards the beam combiner. This is
composed by two beam collimators and another pair of flat mirrors, which re-direct the collimated
beams parallel to the beam combiner axis. Then a focusing system will provide the superposition of
the beams to obtain interference.
4b – Collimator
Once input parameters are given, it's useful to study different ways of collimating the optical
beams, in order to compare their functionality and sensitivity.
The solutions we have studied so far are:
 Refractive collimator: a simple doublet with a careful choice of materials. It must be designed
and optimized for different wavelength bands.
 Reflective collimator with a Cassegrain structure solution (see Figure 11).
 Reflective collimator with a Gregorian structure solution.
 Reflective collimator with an off axis mirror system with a parabolic element and a flat mirror
(see Figure 12). This solution was originally proposed by Bonaccini et al. (Report.Osservatorio
Astronomico di Arcetri n. 9301).
 Reflective collimator with two mirrors (spheric) and three reflections. Probably the less
interesting solution, for dimensions and quality property.
Figure 11 - Single arm with Cassegrain collimator
Figure 12 - Single arm with off-axis collimator
4c - LBTI Computer Simulations
Figure 13 - NSS Lbt configuration
Our purpose was to exploit the Non-Sequential Surface (NSS) option of the CodeV package in
order to carry out the simulation of the whole system. This option let the definition of the system be
independent from the sequence of surface inputs. CodeV will determine, for each ray, which is the
next surface to be struck in accordance with its coordinates and system topology. With NSS tracing
we can analyze the system behavior and tolerances without making use of auxiliary instruments nor
dividing the study into different phases. Figure 13 is the optical layout of the NSS system: two
Gregorian telescopes followed by collimators (an inverted Cassegrain) and two flat mirrors making
the beams directing towards the combiner, still represented by a single focusing mirror (whose
virtual rays are traced)
4d – LBTI fringes
Figure 14. Display of the LBTI fringed PSF
Figure 15 - 2D plotting of Figure 14
In figure 14 and 15 the fringes of the whole nominal system are showed. The object is on axis.
The point spread function has been computed using the NSS configuration of Figure 13
implemented on CodeV.
4e - Atmospheric effects on the PSF of the LBT telescope
i) THE STRUCTURE FUNCTION
We used a model based on the Kolmogorov turbulence law to simulate the wavefronts at the ground
level for each wavelenght. The model is based on the Karhunen-Loève functions which consitute a
set of eigenfunctions for the structure operator on an annular support. The structure function of a
wavefront passing through a kolmogorovian turbulent layer is:

 2


D       r    r      6.88
 r0



5
3
where  is the distance between two points of the wavefront,  is the phase and r0 is the so called
Fried's parameter (it gives the outer scale of the turbolence eddies). This structure function is
correct only if the diameter of the entrance pupil of the telescope is smaller than r0, otherwise we
must use a modified structure function similar to the Kolmogorov law for small scales and with an
asymptotic value of 6.88 for infinite distance, that is.

r
D     6.881   0











5
3
ii) THE SIMULATION
Exploiting CodeV capability, we have achieved the first results from the simulation of atmosphere
perturbation on LBT's performance. The wavefronts affected by seeing have been generated using
IDL routines proposed by R. C. Cannon. It is possible to estimate system performance form the
visible to the infrared region just changing the parameters involved in calculations. Here's some
example of perturbed PSF for the interferometric configuration
a)
b)
c)
Figure 16 - 2D plot and display of LBTI's PSF at 10 micron without seeing (a), with r0 = 866 cm (b), with r0 = 397 cm
(c). (r0 is the Fried's parameter of seeing)
PART II
(Ideas for a Feasibility Study)
5. Design and experiments for the beam combiner
5a – Optical design and laboratory experiments
In order to arrive at a design for the system, the beam combiner will be assumed to be a diluted
telescope (Fizeau interferometer), used to collect and merge the two beams; the LBT aperture
geometry must be replicated over the appropriate scale. A simplified version might be tested in
laboratory in order to provide an experimental verification of some of the critical degrees of
freedom deduced from the tolerance analysis: they may be fed by a suitable beam splitting system.
Some ideas on the Fizeau interferometer and on the beam splitter are outlined in Figures 17 to 20.
~1m
Figure 17 - Possible Beam Combiner Configuration
FM3
D
BS
Star Simulator
FM2
FM1
~ 1.4 m
Figure 18 – One of the possible beam splitter solutions
D
BS PCP (n1 )
Star Simulator
FM1
~ 1.4 m
Figure 19 – One of the possible beam splitter solutions
BS
FM2
Star Simulator
D
FM1
~ 1.7 m
Figure 20 – One of the possible beam splitter solutions
5b – Atmospheric Perturbations and Interferometric requirements
The main goal of the work on design is probably that of including, at a relatively sophisticated level
atmospheric perturbations and to study the effects on the beams of various system degrees of
freedom. This will allow the final project to be tested for tolerance against predictable disturbances,
and the shortest wavelength still permitting effective interferometry derived.
The local environment disturbances can be separated by time scale or frequency: acoustic waves act
in the bandwidth from several Hz on, whereas convection (associated to local thermal gradients) is
effective on a time scale slower than several seconds. It will be necessary to verify the natural
frequencies of the telescope structure, in particular in the intermediate region (some Hz). High
frequency is likely to be intrinsically damped, whereas lower frequency phenomena (e.g. flexure)
should basically be controlled by the active optics system, as well as the thermal deformations. The
results of a finite element model analysis should be evaluated to define the structure linear
deformation which should be expected in the band from DC to ~10 Hz.
Both the coherence condition: OPD  2 /  and the cophasing condition: OPD   / n
(where n  60  100 and OPD is the Optical Path Difference) must be achieved in order to allow an
actual interferometric measure, but their significance is different: the former must hold in any
position of the FOV and at any time, whereas the latter should be attained over the whole FOV and
along the measure. The limiting values for OPD and OPD (right-hand terms in the above
expressions), assuming a fractional bandwidth  /   10% and a comparably relaxed cophasing
limit n  60 , are:
Table 4
m OPD m
OPD m
0.55
5.50
0.01
2.20
22.00
0.04
5.60
56.00
0.09
10.30
103.00
0.17
22.00
220.00
0.37
The most critical requirements are related to the cophasing condition, and this is much more
stringent in the NIR bands, not only because of the scaling with , but also because at shorter
wavelength it is possible to perform signal-limited integration instead of back-ground limited
elementary exposures. In the latter case, part of the cophasing could be performed in software, by
applying to the sequence of MIR images appropriate monitoring and correction procedures;
conversely, in the former case, the image quality must be necessarily preserved onto the scientific
detector throughout the exposure by direct control of the interferometer.
Most of the work has still to be done, but we derived a considerable experience from an analysis of
the somewhat similar problems encountered in space-borne interferometry, as in the GAIA mission.
Next subsection shows examples of the constraints deduced in this case, that can serve as an
example of the type of work to be performed for LBTI.
5c – Hints derived from the GAIA Interferometer
Several characteristic features can be derived from our previous analysis of the GAIA
interferometric configurations, affected by similar (although scaled) requirements. Currently, the
nominal operating wavelength is eff  750 nm.
Table 5
Individual
Primary 0.65 m
Diameter
Airy Disk
DA = 0”.6
Baseline
B = 2.5 m
Young Period:
TY = 62 mas
Number of Visible Fringes: 8
The result of a perturbation of one of the
arms with respect to the nominal
configuration has been evaluated by means
of ray tracing (Code V, non-sequential
surface mode), providing a variation of the
fringe pattern for an off-axis target as shown
in figure 21. A shift of the fringe pattern
within the Airy disk profile is obtained,
corresponding to about half one period (~30
mas vs. 62 mas), i.e. an equivalent phase
shift of about 160 degrees; however, the
image variation is only partially due to an
actual fringe position variation, because a
Figure 21
relevant contribution is related to an effective deformation of the fringe pattern, with different
relative intensity of the subsequent fringes. It appears that a simple shift-and-add algorithm will
provide only limited improvements, because:
(a) the fringe and photocenter displacements are not linearly linked;
(b) the digital integration (co-adding) will provide a degraded resulting fringe pattern.
The perturbation induced in the system is a -tilt (Figure 22), corresponding to a rotation of one of
the primary mirrors with respect to the center-to-center axis; different field-dependent PSF
variations are originated by different perturbations, such as -tilts, etc. The tilt value is ~1 rad,
corresponding to ~0.2 arcsec, or to a linear displacement of the primary mirror edge of about 0.3
m. Scaling directly the perturbations to the LBT scale, the corresponding scale of effects is of the
order of a few micrometers.
Figure 22
In the LBT case, the -tilt effect can be related either to an effective perturbation acting onto the
telescope structure, or to an instantaneous mismatch between the adaptive optics units, providing an
equivalent line of sight displacement along the X axis of the reference frame depicted in the above
(image motion on the individual telescope). In the same way, an -tilt can be referred either to
internal optical configuration variations, or to external perturbations (mismatch between AOUs,
atmospheric fluctuations), providing image motion along the Y axis. The AOUs can use the same
reference source, each correcting for the respective air column, therefore their performance enters
directly in the error budget related to the two mentioned degrees of freedom (- and tilt).
Unfortunately, AOUs can not take into account the other relevant degrees of freedom associated to
the above simplified model, namely tilt, piston, x- and y-decentering, since they are specific
features of the diluted (interferometric) system. The cophasing information for interferometer
locking can only be obtained from the combined focal plane, possibly reinforced by additional
information on the telescope structure provided by metrology and, in general, auxiliary measures.
6. Image simulation and reconstruction
When describing the activity already performed on similar projects (Part I), we already mentioned
its natural continuation, as concerns the problem of reconstructing chop/nodded images and
deconvolving multiple images of the same object .
Among the problems mentioned in section 3b for image reconstruction, one of the crucial items is
the deconvolution of the restored image (after the treatment for chopping and nodding, and hence
the suppression of ghost images) using the space-variant PSF which describes the effect of the
adaptive optics.
The above problem will be investigated by implementing a method based on a domain
decomposition. More precisely we assume that the space-variant PSF is approximated by different
space-invariant PSF in different domains of the imaged region. Moreover, in order to avoid edge
effects, partially superimposed domains are considered. In each domain where the approximation of
space-invariance holds true, the deconvolution methods mentioned above are used again. The
application of the method to the case of adaptive optics will be based on a mosaic of PSF provided
by the group of "Osservatorio Astronomico di Torino".
After this goal is reached, we shall pass to the extension of the method to the case of multiple
images of the same object.
The final step will be the optimization of the software, providing friendly user interfaces, so that our
simulation and reconstruction techniques can be used not only as a data reduction tool, but also as a
valuable instrument for designing successful observation programs.
7. System Monitoring and Metrology
7a - Fringe tracking studies: Use of Natural and Artificial Stars
In principle, if one (or more) sufficiently bright point-like star were present in the coherent field of
view of LBT, it would be possible to acquire its interferogram at a rate higher than the residual
perturbations from the atmosphere and, possibly, the telescope. Fringe tracking is efficient only in a
small perturbation regime, because at any time the system must be phased, i.e. within the OPD
specifications. In such a case, the variation of the interferogram phase can provide sufficient
information to correct the system to within the OPD specification, achieving the cophased
conditions in which the fringes of any target in the coherent region are temporally and spatially
stable, and therefore the signal integration can be performed in a classical way. The MIR band is
most convenient, because phase interferometry can be used: since in any case the elementary
exposure is fixed to a comparably small interval of time (e.g. 10-20 ms) by the intense thermal
background, for both the reference and the scientific source, the image correction can be applied by
software onto the sequence of elementary images, with an approach similar to the technique of shiftand-add. Moreover, MIR is convenient also because in many cases of interest the targets imply
slightly extended sources with a bright core, as for circumstellar envelopes (see section 2d).
For NIR bands, since it is actually possible to perform rather long exposures onto many sources, but
the cophasing requirements are more stringent, requiring control on a short time scale of some
optical component, it appears that a monitoring system cannot be embedded in the main scientific
detection system. It is still possible to implement a fringe tracker as an auxiliary instrument,
operating independently from the main instrument, fed either by a bright enough target close to the
scientific source, or by an artificial source inserted in the system. In the latter case, it is necessary to
ensure that the intrinsic stability of the source is better than the desired system accuracy.
7b - Global vs. Point-to-point Metrology
The implementation of a reference source in the system, often defined as artificial star, requires
particular care because of the tolerancing mentioned below. The alternative is a direct point-to point
Figure 23 – Effects of tip-tilt on Beam Transfer Optics or on an Artificial Star
measure, by linear metrology, of the three-dimensional setup of the whole optical assembly. This is
intrinsically safer, because the individual cavities are intrinsically insensitive to most external
effects, but more complex, since it involves mounting three Fabry-Pérot cavities between each pair
of subsequent optical components. Some simplifications may arise thanks to the geometry of the
transfer optics, which operates basically on parallel beams, and which therefore might be monitored
by a single global subsystem measuring the whole path. An additional factor to be considered is
that, in case refractive optics are used, the laser beams must follow the optical path but must avoid
passing through the dispersive elements, e.g. different cavities may be implemented on both sides of
the lenses, filters, etc. Since the optical path is not in vacuo, the need for a multi-wavelength
monitoring shall be evaluated in more detail; however, it seems to be likely that, since absolute
measure is not strictly necessary for the LBT operations, but only the system symmetry and stability
is to be ensured, residual chromatic effects might be negligible.
As shown in Figure 23, the effects of tip-tilt perturbations in the beam transfer optics, as well as
inthe reference source generation optics, can be evaluated by the simple two-slit model depicted.
Figure 24 – Schematic Interferometer Model
We made so far a preliminary tolerance analysis, based onto the imaging requirements of a system
accuracy corresponding to a comparably large fraction of the fringe period at the operating
wavelength, e.g. OPD  o / 10 ,
OPD
  2
 2 / 10 .
o
such
that
the
phase
variation
is
not
too
large:

The reference source stability must be such that its errors are small with respect to the OPD in the
d
o
 L A  LB  
 OPD 
selected observing band:
2D
10
and the requirements on the tilts (   2  L ) and displacements (   t / 2 ) of its component
become:
 
o D
10 L d
and t 
o D 2
5d
Roughly, in our case, D  200 m is the EFL, o 1  10 m is the wavelength of observation, and
L, d 10 m are typical values of the optical paths and overall dimensions of LBT.
At o 10 m, we get the limiting values
  2 rad  0". 4 and t  60 m,
which can be scaled linearly with the wavelength. The order of magnitude is more relevant than the
actual values (which are to be revised on a more detailed and realistic model). It is comparable with
what can be expected from the intrinsic mechanical stability.
The above tolerances are still stringent with respect to the atmospheric variations: an optical path
variation of 100 m, over a distance of 10 m, comparable with the transfer optics size, can be
associated to a variation of the refraction index of ~10-5. This confirms that either optical path or
environmental temperature/pressure monitoring are required in order to keep track of the cophasing
status, and most likely an active control is to be used on some optical element.
It should be noted that the requirements for high accuracy astrometry, e.g. related to the galactic
center dynamics or the exo-planet detection, corresponding to relative accuracy 10 as, appear to be
more stringent, but since they imply relative measures between targets in the same field the relevant
factors might arise only as higher order effects, provided the elementary image quality is preserved.
This issue is to be analyzed in more detail throughout this study.
7c - Practical solutions for the beam cophasing
The problems and solutions outlined in the previous sub-sections (7a and 7b) require careful
verification in laboratory. Essentially, we have to verify that the internal optical path difference of
the light beams through the two arms of the interferometer (the equality and stability of the external
optical path difference is assumed guaranteed against atmospheric turbulence by active optics) is
kept at zero. A preliminary performance analysis suggests that the optical path difference should be
stable to within, let say, 50 nm. The separation between external and internal optical paths depends
critically on how the adaptive optics of the two telescopes operate, and its definition will be one of
the goals of this study. At present, in order to stabilize the internal optical path difference against
environmental disturbances (acoustic waves, turbulence associated to thermal gradients in the
building, mechanical vibrations and thermal strains, and so on), two main approaches have been
identified and will be studied in detail. In both cases, we plan to design and implement laboratory
experiments and extensive test campaigns and validations which use a scaled breadboard model of
the beam combiner, which is described below.
The first approach is based on the information delivered by the photons of an artificial-star, which is
already planned to be used in order to generate the error signal for the telescope optics. If they are
delivered through the same optics as the star light, recombined, and made to interfere, we obtain
information not only on the distortions of the two interfering wavefronts, but also on the amount
and stability of the relative phase shift. An advantage of this technique is that distinguishing the
optical path in its internal and external parts, which, to some extend, is arbitrary, is no longer
necessary. In the focal planes of each single telescope we cannot found the information necessary to
ensure that the two corrected wavefronts lie on the same "plane" to within 50 nm, a shift that, over
15 m baseline, corresponds to a 0.3 nrad (less than 0.1 mas). In simple words, the interference
pattern of an artificial-star delivers (at least in part) information about the whole 15 m wavefront
and, in principle, the stabilization of the optical path difference and the stabilization of the whole 15
m wavefront by active and adaptive optics can be afforded jointly, as a unique task.
The 'internal' optical path difference, whichever its definition is, can be monitored by laser gauging.
Therefore, the second approach is based on a laser interferometer in which a laser beam is split in
the focal plane of the beam combiner, the two partial beams are delivered back and forth through
the same optics as the star light and recombined again on the beam combiner focal plane. A
practical implementation, although, by no means, the only possible, is a "spherical" wave generated
in the center of the beam combiner focal plane. Hence, two "plane" wavefronts will emerge from
the beam combiner towards the two telescopes. Two retro-reflectors attached to one of the telescope
mirrors fold the laser beams and return them to the focal plane. The advantage of this technique is
its intrinsic higher resolution and bandwidth.
7d Laboratory experiments for validation of the proposed solutions
The above described ideas need to be tested and validated in laboratory before being suggested as
actual solutions for the nulling and stabilization of the real optical path difference at the telescope.
In the first case, the simulator of the artificial-star is simply an He-Ne 633 nm laser beam
superimposed in the middle of the beam of the star simulator before beam splitting. In the second
case, suitable optics will be designed and mounted behind focal plane in order to split and
recombine an He-Ne 633 nm laser beam. The two partial laser beams will be back-reflected, for
example, by a single retro-reflector located in the middle of the front face of the star simulator.
This experimental activity is aimed at developing and validating not only cophasing and optical
path stabilization procedures and techniques, but also the techniques of information processing and
data analysis, for example which solution is best suited, between space and time modulation, for
the processing of the laser interferometer signal.
8. Defining the observing program (OP)
There are three steps which are essential for the implementation of a scientific project into an
observing program:
i)
ii)
iii)
Compile lists of suitable candidates (see section 2d for very preliminary indications);
Describe in details which parameters are to be determined and with what precision/accuracy;
Define an observing strategy.
Below we discuss these items and the activities planned to address them.
8a - Compiling lists of suitable candidates.
This item deserves close attention as it is often underestimated. The issue resides in the difficulty of
having a natural guide star (NGS) in the isoplanatic field of the target object for best tip/tilt
corrections. Recent statistical estimates show that the number of available targets (QSOs, AGNs,
Pre-main sequence stars, semi-regular pulsating stars, Miras, etc...) is quite low everywhere on the
sky (galactic plane included). Statistics does improve for the LBT because of the size of its field-ofview, although Adaptive-Optics (AO) systems quickly degrade their performances as the angular
distance of the NGS increases. Another possibility to increase statistics in the near future will be to
use polychromatic LGS to remove the image motion –tip/tilt- although NGSs should be used
whenever possible for best results.
We will cross-correlate catalogs of potential targets (as defined by the scientific programs), like for
example the VERON-CETTY 96 catalog of Quasars and Active Galactic Nuclei, the DENIS survey
at 2.2 µm, or the ROSAT catalog, with portions of the Guide Star Catalog II (GSC2), which we are
building in collaboration with the Space Telescope Sc. Institute, in order to characterize (the GSC2
2.0 in the North will have 2 colors closely related to B-V and B-R) the LBT FOV around the
candidate targets. This will allow us to decide, given the performances of the AO systems being
developed for the LBT, if the proposed targets will be available for observations and what
efficiency to expect (in terms of the Strehl ratio) from the operation of the OA system.
8b - Parameters and their errors
For each research program it will be necessary to define clearly what is expected from the LBT
observations in interferometric mode (LBTI). We will derive from the scientific desiderata of a
representative set of cases the parameters that have to be measured and the precision/accuracy
which must be achieved. Also, we will try to identify what kind of calibrations (relative and/or
absolute) are required. For example, when observing a binary one might wish to measure relative
distance, magnitude difference of the two components, and the position angle relative to a reference
direction. Distance and magnitude difference might be intrinsically easier to measure while an
absolute orientation might require more difficult calibrations. On the other hand, if the separation
must be known in true arcseconds then an absolute scale calibration would be needed in that case.
We plan to use Hipparcos targets to provide initial absolute scale calibrations good to ~0.5
mas/arcsec. The stability of the scale will be known to a much higher accuracy limited only by the
performances of LBTI. Another example is imaging of diffuse sources (as star formation regions).
Here, it might be sufficient to achieve the highest possible resolution and the largest possible
dynamic range with absolute calibrations needed only for zero-order registrations.
LBTI imaging will be the most demanding in terms of telescope time. Given the complexity (for
example the MTF) of the sources to be imaged we will estimate the minimum number of baseline
configurations required for a reconstruction which will have the resolution properties requested. For
this, it is extremely important to know what are the noise levels that can be tolerated.
8c - Observing strategy.
In this subsection we assume that interferometric time at the LBT will compete with the individual
use of the two 8-m telescopes. Therefore, interferometric observing programs will have to be
optimized so to use the least amount of time to achieve the measurements discussed before. When
imaging a complex structure, for example, the findings from the study phase discussed in 7.2 will
tell us if that particular object can be done in one night or it will be necessary to restart integration
the following night. We will try to push the simulation to a level that it will give us indications on
which conditions must achieved to allow coherent LBTI operation for more than one night. Also, if
multi-night operation is required, the calibration procedures will have to take this into account.
9. References
a) General references, quoted in the text
[1] Busso, M., et al. 1997, IR Studies with the LBT Interferometer, CNAA proposal.
[2] Busso, M., et al. 1996, Astron. Astrophys. 311, 253
[3] Marengo, M. et al., 1997, Astron. Astrophys. 312, 587
[4] Zinner, E. Et al., 1997, in Astrophysical Implications of the Laboratory Study of
Presolar Materials ,T.J. Bernatowicz and E. Zinner (ed.) (New York: AIP), 185.
[5] Gallino, R., Busso, M. et al. 1990, Nature 348, 298
[6] Gallino, R., Busso, M. and Lugaro, M., 1997, in Astrophysical Implications of the
Laboratory Study of Presolar Materials, T.J. Bernatowicz and E. Zinner (ed.) (New
York: AIP), 115.
[7] Robberto, M. and Herbst, T. 1996,
[8] Robberto, M. et al., 1997,
b) Specific on the present research, quoted in the text
[9] Busso, M. et al. 1998, talk at the Annual Meeting of the SAIt, Palermo, April 1998
[10] Bertero, M., Boccacci , P., and Robberto, M. 1998, Proc. SPIE, vol. 3354, 1998,
[11]Marengo, M. et al. 1998, IAU Symposium n. 181, Montpellier, 1998.