Data Reduction Software
We present the plans and progress of the reduction software for the SIFS.
We intend to provide the means for doing quick look at the telescope and the data reduction software to reduce the data during the observations or in the next day.
The only step that is specific to SOAR-IFU reduction is the extraction of the fiber spectra from the initial CCD image. It is expected that everything else could be done using standard packages such as IRAF. As for looking at the final 3D data, there are also existing packages that can do this. We intend to develop a task similar to 'ldisplay' in the 'gmisc' package as a quick look tool.
In (1.1) we summarize the main steps of the data reduction procedure and in (1.2) we discuss the problem of the superposition of spectra. This step of data reduction is described in more detail, as it poses new challenges.
1.1. Main steps
Considering that the acquisition system will provide the raw data in FITS.MEF, the steps of the reduction procedure can be summarized as follows:
a. The images are first processed for bias and dark subtraction; flat-field and fiber throughput correction; cosmic ray removal; sky subtraction (in the case of nod-and-shuffle).
b. Extracting the signal from each fiber, by using the multiple-Gaussian fitting code. It is possible that this step takes a relatively long time to be performed, and a simpler extraction could be provided for a quick view of the results.
c. Extraction of the spectra in the two dimensional images and their scattered light subtraction and extraction to one dimensional spectra in multispec format.
d. Wavelength calibration (using 2D spectrum calibration). In the case of sky subtraction using the sky IFU, it may be preferable to perform sky subtraction after this step, since small wavelength shifts may appear between different regions of the slit.
e. Writing reduced data on data cube format.
1.2. Deconvolution of overlapping spectra
In this sub-section we discuss step (b) above in more detail, describing the problem of the superposition of spectra. To solve this problem a solution that uses a code to fit multiple Gaussians is suggested.
We have developed a code based on the ROOT routines and applied it to theoretical curves in order to deconvolve multiple Gaussians. The procedure tries to fit simultaneously the observed profile of the whole set of fibers.
In Figure 1 the cut of a flat-field image obtained with the IFU-prototype is shown. This will illustrate how many pixels are contaminated by the signal of the other fibers.
Figure 1 - The cut of a flat-field image obtained with the IFU-prototype at the OPD. A mask was use in order to assure that the signal detected by one fiber is not contaminated by the signal of the neighboring fibers. As the mask was not roughly located, a small contamination is detected in the right side of the profile. The FWHM is 3.12 pixels.
The first step in the calculations is to determine the center and the FWHM of each fiber profile. In principle, it is expected that the signal of the fiber could be represented by a Gaussian with constant width, which is centered at a fixed position. When these parameters are known, the next step is to fit the real data (representative calibration data). In this case, only the amplitudes of the observed curves are fitted. The final step is to extract the observed signal of each fiber, removing the contamination from the other fibers. A numerical mask should be applied in the case of non-Gaussian profile, in order to correct for the spurious contributions. This could occur in the case of contamination due to the cylindrical curvature of the micro-lens, for example.
If the signal profile of the fibers does not vary appreciably by changing the instrument configuration (changes of gratings , grating angle and camera angle), once the main parameters have been determined, the observed data will be fitted in a fast way. Eventually, a number of files containing the parameters for different configurations could be necessary.
The first tests of the fit of multiple Gaussians are available in Antonio Kanaan's page, where the problem of dealing with the superposition of the spectrum of one fiber with the spectra of its neighbors is described. Some simulations are given to illustrate the solution to this superposition problem, which will be worst as the ratio fwhm/fiber-separation becomes larger.
The simplest case considers one single cut across the spatial dimension of the IFU-gram. The light from only a single fiber should pass through the spectrograph in order to have the signal intensity and shape (width and center of the Gaussian) measured without contamination from the other fibers. In principle, this procedure should be repeated as many times as the number of pixels in the dispersion direction; however, in practice, the parameters will probably vary linearly in the dispersion direction, and 3 to 5 measurements at different wavelengths will be sufficient to describe the width and center as a function of wavelength. Note that if we use a mask in the form of a slit illuminating a row of the lens array, we obtain 26 individual spectra at a time.
The individual spectra will give us the width and center of the profile of each one of the fibers;. The second step is to fit the intensity of each fiber profile in the overlapping spectrum (calibration data) and then to apply the previously measured widths and centers. The more complex fit (intensity, width and center) is done first to the calibration data, which has more photons counting and do not suffer from superposition. In this way, the science data have to be fitted for a single parameter (times the number of fibers in one spatial cut). The fit to the science data will give us the intensity of each fiber at every wavelength, by repeating this procedure several times in the dispersion direction.
Probably the profile of the fibers on the CCD will not be a Gaussian. In order to approximate the profile into an analytic model (a Gaussian for instance) we will need to add a numerical model, by following, for example, the Stetson's model for stars in 'daophot' IRAF procedure.
In the next example the fit parameters obtained with 30 Gaussians are presented.
There is no initial value as these Gaussians were not mathematically created but were the
It may be that we do not need to separate the fibers using the masks. The fit is almost perfect except for the two edges. This implies we must allow for some extra pixels at the CCD edges.
Figure 2. The fit to the flat-field real data obtained during tests of the IFU-prototype at OPD. Blue represents the data and red represents the fit.
1.3 Real data from the SIFS - prototype
The SIFS-prototype, Eucalyptus, has been installed at the OPD 1.6m telescope to test the spectrograph by using the 600 l/mm grating. Several objects were observed, and flat-field and arc comparison data were obtained. The next figures show some of the data, obtained in the February run. These results give us an idea about the alignment of the fibers, the rough profile of the signal, and the degree of the spectra overlapping in the CCD. The images are available in the Eucalyptus page
1.4 - Sharing the Gemini codes
We expect to share the codes to be used in the data reduction of the Gemini IFU spectrograph. We hope to share at least the common tasks that could be applied to the SOAR-IFU. We present here some information that we received from people we have contacted:
(Brian Miller - 4 Dec 2000)
(Frank Valdes - 2 Nov 2000)
The following has been adapted from the discussion list at the home-page http://www.astro.keele.ac.uk. Different ideas are presented.
The common standard for the data cube file will be a multi-extension FITS file. It is a single 3-D image with the axes in the order x/ra (pixels), y/dec (rows), lambda (planes) and the basic FITS keywords - CRVAL1, CD1_1, CRPIX1 etc. The logical extension is to have corresponding 3-D variance and data quality images in extra FITS extensions.
Some people do not think general software should constrain the order of the axes. There should be tools to rotate (tumble?) a data cube to any orientation to optimize the most common access. The software will recognize the axes by CTYPE keywords. However if someone insists the most obvious choice is the first two axes being spatial.
What they expect will happen with IRAF IFU packages is that extraction from the raw data will be a collection of 1D spectra with a position coordinate attached as well as some information about the size and shape of the aperture on the sky. Wavelength and flux calibration will proceed in 1D. Finally there will be a task that will build a data cube from the 1D spectra using the header information.
General software, as written by software developers such as Starlink and IRAF, should be able to find the primary data cube either in the primary HDU or as an extension. Users may provide only a simple primary HDU while more sophisticated systems may provide more complex FITS structures. But an image extension and a primary HDU are basically the same thing. In a pinch it is always possible to extract an image extension into a simple FITS image file. The IRAF syntax for specifying an extension would be nice to use: image[extno] or image[extname] or image [extname,extver] where extno is the extension position in the file (0 for primary), and extname/extver are the extension name and version following the image extension convention. In IRAF it is an error not to specify an extension if extensions exist but other software could adopt a default that no extension means the primary array.