512 pixels; the size of each pixel is 30
m.
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PS reprint
Valery V. Vlasyuk
Special Astrophysical Observatory of Rus. Ac. Sci.,
Nyzhnij Arkhyz, RUSSIA 357147
The method of bidimensional spectroscopy, proposed by Prof. G. Courtes (Courtes et al. 1987), allows one to get independent spectra of each contiguous spatial element in a field, using a bidimensional array of lenses that form a grid of micro-pupils instead of a slit as in a classical spectrograph where these images are dispersed into spectra.
The number of spectra, registered simultaneously, as well as the spectral range of data are limited by the size of the detector and the entrance field of the spectrograph. Using square lenses permits optimum data sampling and is ideal for spectrophotometry, allowing complete integration of flux.
The main advantages of integral field spectroscopy are its ability to cover extended sources with the necessary spatial sampling matched with seeing conditions, independence of spectral resolution from seeing, and continuous spatial sampling.
The Multi-Pupil Field Spectrograph (MPFS) was developed at the Special Astrophysical Observatory of the Russian Academy of Sciences in 1990, and is now extensively used for spectral observations with the 6-m telescope (Afanasiev et al. 1995). It provides simultaneous detection of about 100 individual spectra produced by a raster of 9 by 11 (or 8 by 16) lenses.
The spatial sampling of the data is chosen by the observer depending on the seeing quality and may be varied from 0.3-1.6 per lens.
There are two different types of detectors attached to the spectrograph's camera which may be used.
a) a bidimensional photon counting system on the base of a 4-stage EMI image
intensifier and TV head.
The resulting frame is 512512 pixels; the size of each pixel is 30m.
b) a CCD detector, developed at the Observatory, with 530
580 pixels
(pixel size---18
24
m) and a readout noise of
15 e
.
The reduction of the MPFS data consists of the following steps:
-- bias subtraction;
-- cosmic ray removal;
-- flatfielding (of nonuniformities that exceed 2--3%);
-- recognition of the individual spectra on the frame and their extraction;
-- transformation of the spectra onto a uniform wavelength scale;
-- correction for variations in the lenses (transparency and vignetting);
-- spectral analysis, decomposing complex profiles, measurement of astrophysical parameters, image reconstruction, etc.
The software package for data reduction, described here, is written in C and operates on personal computers AT/386 and higher under MS-DOS. No particular hardware is necessary. All procedures may be easily transferred onto another operating system and platform.
Flatfielding for CCD detectors is straightforward, but it becomes a complex problem when data are acquired with a photon counting system. It is widely known that all types of photon detectors on the back of image intensifiers suffer from instabilities, depending on time, orientation of the system in space, etc. The instabilities, causing frame shifts, make useless the ordinary flatfielding procedures. In order to solve this problem the method of preliminary matching of spectral and flatfield accumulations was developed.
As a reference points, the most prominent nonuniformities are used to
indicate differential shifts of the image. To match it with
appropriate accuracy
we decided to use bidimensional cross-correlations, which
are calculated in corresponding fragments of the spectral data and the
flatfield of
64
64 pixels. The position of the cross-correlation maximum yields
the value of the relative shift of one fragment with respect to another.
The total field of the relative shifts is approximated by bidimensional
second-order polynomials.
The regular form of differential shifts suggests the presence of a real correlation between the images. The flatfield image needs a high signal-to-noise ratio; a long exposure of this image is acquired in this manner: individual sub-exposures are correlated with one another and added after corresponding shifts.
This procedure is very delicate as spectra are packed on the detector frame very close to one another: the mean distance between adjacent spectra does not usually exceed 5 pixels. Moreover, some optic deficiences along with the CCD's poor charge transfer cause the spectra to be slightly blurred.
The preliminary step in extraction is defining the approximate location of the spectra on the frame. This is done by means of a description of the spectral trajectories with a bidimensional low-order polynomial, approximating positions of a set of user-predefined references, which are images of arc lamp spectral lines.
The following procedure is done in two stages. First, the accurate position and the current profile for each spectrum are defined by minimizing the observed summary profile, obtained by stacking some detector columns around each spectrum. The second stage consists of fitting the amplitudes of the cross-dispersion profiles for each column, taking into account neighboring spectra, in order to reach the minimum of the residuals between the real and modeled profiles. The observed cross-dispersion profiles are usually fairly represented by a combination of 2 Gaussians, so all fitting procedures are solved as multi-gaussian decomposing tasks.
PYTHEAS-6 is, in essence, an integral field spectrograph, including a scanning Fabry-Perot interferometer which is illuminated by a sharp angular beam that is mounted on the optical axis between an enlarger and a multi-lens array. The basic concept of this instrument is described in le Coarer et al. 1995.
This instrument allows observations of extended sources with a spectral resolution defined by using a scanning Fabry-Perot etalon, which provides spectral channeling and subsequent filling by tuning of the etalon.
It is evident that the choice of an available etalon depends on the used linear dispersion of the spectrograph: successive etalon's spectral orders are separated enough for accurate measurements.
Observations with PYTHEAS-6 consist of a sequence of spectral integrations for
each spectral channel of the etalon,
obtained with the changing distance between its
plates. Input spectra are modulated by the etalon transparency function, where
the wavelength of maximum 
for a particular order p is
defined by the law: 
.
Here n is the refractive index of the internal substance of the etalon,
e is the distance between plates,
i is the angle between the axes of the etalon and the beam (
0).
Therefore, individual spectra are represented on spectral images as a set of spots with various brightness levels corresponding to the spectral intensity: for continuum sources these spots will occupy all of the spectral range; for a line spectrum such spots will be seen only at line locations on the frame.
Following from the main law of etalons, complete coverage of the free spectral range by an individual interference order depends on wavelength. In order to acquire all available information necessary, choose the total scanning distance that corresponds to the reddest wavelength. Some information will be redundant for blue wavelengths as part of the spectra will be scanned twice.
For accurate integration of some overlapped spectra, the method, similar to one of Gaussian extraction, briefly explained above is applied to each individual spectrum over all successive spectral channels. During etalon scanning, the wavelengths which correspond to interference order peaks are increasing and spots will be shifted from one spectral channel to another. Thus the integrated data from successive etalon channels for a particular spectrum, being placed one under another, will show inclined tracks.
Restoration of resulting spectra is provided by the integration of the signal over this image along tracks in the dispersion direction. In order to separate accurately individual interference orders, Gaussian extraction is also applied.
For sampling of spectra with a uniform step in wavelength, it is necessary to reduce the data for the comparison spectrum in much the such style as the object's data. One can assign to these lines the corresponding numbers of the interference orders using information derived from the continuum source data, and define the number of the spectral channel corresponding to each line peak.
Let the first spectral channel correspond to the integer order's number.
Then to
obtain the real (non-integer) order value 
for a particular
i-th line with wavelength
, found in channel 
and assigned to 
,
the following expression is used:
where NumChan is the total number of scanning channels used.
Using the derived values of 
one can get the ``empirical phase
curve'', representing a polynomial, approximating the set of
products 
as a wavelength
function.
Errors to this approximation define the resulting error
of the transformation onto a wavelength scale.
Following from the main etalon law, the zeroth order coefficient is the so-called ``constant of etalon'' (right side of etalon's law) for a particular wavelength; the first order coefficient is the offset (difference between true and assigned values) for the interference order; the coefficients of higher orders represent the phase shifts, i.e., variations of etalon's constant with wavelength.
Finally, the ``empirical phase curve'' allows one to compute for each specified wavelength, a corresponding value for the interference order, and to build a resultant spectrum.
The author wishes to thank V. L. Afanasiev for useful discussions. The creation of the described package was supported by an American Astronomical Society grant.
le Coarer, E., Bensammar, S., Comte, G., Gach, J. L., & Georgelin, Y. 1995, A&AS, 111, 359
Courtes, G., Georgelin, Y., Bacon, R., Monnet, G., & Boulesteix, J. 1987, in Instrumentation for Ground-Based Optical Astronomy: Present and Future, ed. L. Robinson, 266