AN IDL TOOL FOR INTERFEROMETRIC VISIBILITY COMPUTATIONS
Gianluca Li Causi
INAF – Osservatorio Astronomico di Roma
1. Introduction
Within the framework of the growing interest of the italian astronomical community in the usage of
interferometric facilities (e.g. VLTI, IOTA, PTI) and facing the lack of available software tools
which can compute visibilities by interfacing with user’s modelling softwares, an IDL (Interactive
Data Language) program for this latter scope is currently under developing by the Rome
Astronomical Observatory. It can be used both as a standing alone tool, equipped of a Graphical
User Interface (GUI), or as a subroutine to be used inside the user’s modelling code.
The program aim is to calculate the interferometric visibility of a modeled source as seen by a given
instrument and its configuration.
The most commonly used softwares for the computation of interferometric data are the VisCalc web
interface from ESO1 and the ASPRO software from JMMC2. These programs are effective in
providing different results, but they have three major drawbacks: i) VisCalc does not allow the user
to insert the Spectral Energy Distribution (SED) of his own model; ii) them both cannot receive
multiple and user defined models as input, other than some trivial ones, so that to perform model
fitting among hundreds of models becomes unpracticable; iii) they cannot be used as subroutines
within the user’s modelling code, in order to perform simultaneous fitting on different observables,
e.g. double fit on interferometric visibilities and spectral observations.
In this document we describe the current status of this software as well the functionalities that we
are going to implement.
2. The IDL Interferometry Visibility Calculator
Our tool tries to overcome the described difficulties of VisCalc and ASPRO by allowing the user to
input his own series of models, having both symmetric or asymmetric morphologies, together with
their proper SEDs.
Lots of models can be given in input, both in the GUI as in the sub-routine modes, thus making it
possible to easily perform chi-squared comparisons with a given set of observations data.
All those computations can be done on the basis of a pre-defined or user-defined description of the
instrument and observing mode to be simulated (e.g. MIDI, AMBER, etc.; slit or circular aperture;
uniform or gaussian FOV).
Hereafter the interface of the program, its input/output and its various functions are described.
1
2
European Southern Observatory, Garching b. Munchen, Germany
Jean-Marie Mariotti Center, Observatoire de Grenoble, France
2.1 The GUI
In Figure 1 a screenshot of the GUI is presented, where we can recognize the following scheme:
a) Command Menu: it collects the commands to load input data and to configure instrument
parameters, as well to launch the computation or exit the program.
b) Graphical Tabs: the various graphical outputs are organized into a number of tabs that the
user can select by clicking on the respective names: both input data and output visibilities
are displayed in these tabs.
c) Control Bars: here a series of droplists and buttons allow the user to browse the various
wavelengths and models of input data and output results, or to analyse how the visibilities
change as a function of the baseline. The graphics update in real time at any user’s
intervention. A further buttons bar is provided for convenience to add annotations and to
save the plots.
d) Information Line: finally, a textual message line is used by the program to write temporary
results and process information.
Figure 1: A screenshot of the GUI of the IDL Interferometry Visibility Calculator, with decription
labels (see text).
2.2 The Input Data
The program is fed by a description of the input source given in two alternative ways: i) by a 2-D
image which represents its intensity distribution on the sky I(x,y), or ii) by a 1-D intensity profile
I(r), if the source has a circular symmetry (Figure 2).
Figure 2: The FILE menu offers both Image and Profile input.
In the case of 2-D images, they must be formatted as FITS files, while for 1-D profiles, textual
ASCII files are expected. For the images, a regularly spaced x, y grid is assumed, while for intensity
profile, both regularly or irregularly spaced r coordinate values are accepted.
A source SED can be given by just providing one image/profile for each different wavelength,
thanks to the multiple files selection capability of the input panel.
Although a minimal set of rules for the files format is required, such ways of input will make very
easy for the user to submit a source model for the computation
The 1-D intensity profiles must be ASCII files of the format shown in Tab. 1: an header must be
present where the tags lambda=, distance= and model= have to be declared (and set to the
current wavelength, distance to the source and model identification, respectively), while any
comment should preceeded by a # sign.
Any unit of measure can be used for the tags and for the x, y, or r coordinates in the image or profile
files, providing that the program is informed (see below).




header: 








data: 




# Lambda in micron:
lambda = 10.5
# Distance in parsec:
distance = 190.0
# Model number:
model = 01
# Any other comment
0.316888
0.362316
0.414392
0.473947
0.542089
0.620203
........
6.583E+10
6.583E+10
6.583E+10
6.583E+10
6.583E+10
6.583E+10
.........
other_data
other_data
other_data
other_data
other_data
other_data
..........
other_data .....
other_data .....
other_data .....
other_data .....
other_data .....
other_data .....
................
Tab. 1: Format of the input ASCII file containing the Intensity Profile.
After the header, the profile data follow: two columns must contain the radius r and the intensity
profile I(r), expressed in the choosen units. They can be any couple of columns, irrespectively of
their locations, but specified upon request.
The only requirement is that the raws with the data begin after the same number of lines from the
beginning of the file, at least for any file representing the same kind of data.
At the first access to a new kind of ASCII file, the user will be asked to define a template for that
format by means of a suitable dialog panel, otherwise he can simply load a template already
available for that file type.
As already said, the source image and the profile data can be provided in whatever units the user
wants. This obviously implies that units definition must be given via the Parameters Editing dialog
(Figure 3), where the units names (that will also appear as axes labels in the plots) and the units
value (in terms of cm for linear units, and arcsec for angular units) are requested.
Figure 3: Parameters Editing dialog panel.
2.3 Instruments Description
Different interferometric instruments have different properties and observational modes, e.g.
different shapes and sizes of the Field of View (FoV), different maximum baselines and various
wavelength bands. Also these parameters can be edited via the Parameters Editor, where some other
computation parameters are shown as well.
In particular, the user can specify whether the focal plane aperture is circular, giving its radius in
arcsec, or it is a slit, giving its width, length and rotation angle with respect to the projected
baseline.
More, a gaussian FoV can be defined, i.e. having a gaussian illumination function, instead of a
uniform one.
It’s worth nothing to clarify at this point what the phrase “Field of View” actually means when
referred to interferometric instruments.
There are two different meanings in the literature for the word FoV, which the authors refer to,
sometimes making confusion in the not used reader: the so called interferometric FoV, and the so
called detector FoV, defined hereafter.
The interferometric FoV is defined by the following formula:
FoVINTERF 
where:
B
COER
OPDRANGE
OPDRANGE
  COER
B
is the baseline lenght,
is the coherence length of the wave packet in the interferogram,
is the lenght of optical path difference scanned to form the interferogram.
This quantity represents an angle on the sky which depends on the lenght of the scanned optical
path difference and which actually corresponds to some 0/ times the baseline resolution 0/B
(0 is the central wavelength and  is the band width of a single spectral channel of the
instrument) and is tipycally some tenths of milliarcsecs.
The detector FoV instead, is defined by a circular or slit diaphgram (or by a fiber core) placed on
the telescope focal plane to delimit the observation area, of the order of the Airy disk of the unit
telescope: 0 /D (D is the telescope diameter), tipycally one arcsec .
The difference among them is that, while the detector FoV selects the flux which effectively makes
interference, the interferometric FoV just tells what portion of the former is actually registered in
the interferogram. This explains why in the data reduction of interferometric observations is usually
applied a so called visibility correction, to compensate the measured visibilities for the so called
incoherent flux: the total flux within the area from the small interferometric FoV and the wider
detector FoV, flux that is lost outside the scanned part of the OPD:
1


2
Vcorrected
 V 2
m / 2.5 
 1  10

where:
V
Vcorrected
m
2
is the mesured visibility amplitude,
is the corrected visibility amplitude,
is the magnitude difference between the flux in the FoV INTERF to FoVDETECTOR annulus and
the flux inside the FoVINTERF area.
Interferometric computations based on sysnthetic models of the source intensity distribution do
compute the visibility for the whole detector FoV as all the flux from that area will interfere within
the instrument. This means that the simulated visibilities can be put in comparison only with
observations already compensated for the lost incoherent flux.
2.4. Interferometric Computations
Once the input files are selected, the computation starts first by classifying them according to the
header tags. Then an outer cycle, spanning the models, and an inner one, spanning the defined
wavelengths for each model, are set up to perform the following operations:
1. if the input is a 1-D profile, builds a correctly sampled 2-D revolution surface;
2. cuts the 2-D intensity distribution with the defined circular or slit FOV;
3. if a gaussian FOV has been defined, multiplies the intensity distribution by a normalized
gaussian with a sigma equal to the FOV radius.
4. computes the complex Visibility in the (u,v) plane by a 2-D Fast Fourier Transform (FFT) of
the intensity distribution;
5. extracts the 1-D Visibility vs. Baseline profile along the projected baseline direction.
The following plots are drawn in the respective graphic areas, when in GUI mode (see Figure 4):
-
2-D Intensity Distribution;
1-D Source Profile, if circularly symmetric;
2-D Visibility Surface on the (u,v) plane;
1-D Visibility Profile vs. Projected Baseline (in meters);
1-D Visibility Profile vs. Projected Baseline (in M)
1-D Visibility vs. Wavelength, if a baseline has been choosen.
All of these plots can be re-drawn in real-time, for any specific wavelength, baseline, model and
visibility component (modulus, squared modulus, phase, real or imaginary), by just changing their
values via the commands on the Control Bars, thus accessing very quikly to a lots of information.
Figure 4: Examples of the various plots provided by the program. From left to right: 2-D Intensity Distribution, 1-D
Source Profile, if circularly symmetric, 2-D Visibility Surface on the (u,v) plane, 1-D Visibility Profile vs. Projected
Baseline (meters), 1-D Visibility Profile vs. Projected Baseline (M), 1-D Visibility vs. Wavelength for a choosen
Baseline.
2.5 Working with a grid of models
When working with a multiple parametrized model of an astronomical source, the user’s code does
normally produce a wide grid of solutions in the parameters space, which implies a huge number of
profile or image files.
In this case the user could be interested in comparing its grid of models with some available
interferometric observations, in order to find the best 2 fit of them. This can be simply done by our
tool by selecting a Visibility vs. Wavelength or Visibility vs. Baseline observation file (which must
be written in a suitable ASCII format, similar to the one adopted to describe the intensity profile).
The program will add to the results a plot of the 2 vs. model number, with the indication of its
absolute minimum.
A different situation can occur with a grid of models: i.e. the user’s code itself provides a selection
of models based on a 2 fit to some other observations. For example the user’s code could output
the n models which best fit the SED observations and we want to know which of them
simultaneously fits the observed interferometric data. In such case, the minimization must be done
on the squared sum of deviations, 2TOT = 2SED + 2INTERF and not separately on the two 2.
To obtain this result, the user can simply call the present program from inside his code’s cycle on
model parameters, thus using this tool in the not-GUI mode.
3. Conclusions
We have presented a new tool which performs interferometric calculations. It is written in IDL
language (version 6.0) and can be used in two different modes: by calling it as a subroutine from
within other IDL programs, or launching it in a self standing GUI mode both from the IDL
command line, or even outside IDL by using the freely distributed IDL Virtual Machine (IDL VM)
environment3.
Different instruments and observation conditions can be simulated and our tool has been designed
to accept the input data in various types and formats, only imposing very minimal restrictions to the
user.
By using this tool some difficulties inherent to the most common VisCalc and ASPRO softwares are
overcome and models grid analysis can be easily performed. Further improvements are planned,
like the implementation of closure phase and image reconstruction from multiple baselines
telescope sets.
The present software is currently in its final stages of implementation and will be soon
downloadable from the Technology Working Group internet page at the Rome Astronomical
Observatory: .......indirizzo internet........
Rome, May 2005
3
http://www.rsinc.com/idlvm/