NAME
evelin - the main SAX/LECS EVEnt LINearization module
SYNOPSIS
evelin [infiles=] <file_names>
[parameter=value ...]
DESCRIPTION
evelin
is the main linearization module of the SAX/LECS data analysis system.
It transforms raw event list FITS files (type: rev) into a
linearized form (type: lev) in which several basic corrections have
been applied to the data. These are:
- All events outside the detector's FOV have been removed.
- The raw PHA values have been corrected for
temporal changes in the energy gain (based on continuous monitoring of
Fe calibration sources).
- The PHA values are corrected for spatial variations in the energy gain
across the detector's focal plane (based on spatial gain maps from
calibration database).
- A basic event filtering has been performed to remove "non-scientific"
events from the data.
- A BL-dependent correction has been applied to the already gain-corrected
PHA values.
- The focal-plane coordinates of detected photons have been "linearized"
to account for intrinsic distortions that are inherent to the detector.
- Instrumental dead-time effects have been taken into account.
- The corrected focal-plane coordinates have been mapped onto sky
coordinates (standard tangent-plane projection)
The default behavior is to perform all tasks in one run, although,
each individual correction can be suppressed by setting a corresponding boolean
command line switch. The program is able to deal with two different
types of event files that are symbolized by the name extensions
_rev and _lev. _rev is the default extension for a
raw event file which is the primary output from the
ingestor modules foting and
teleing respectively. _lev stands
for "linearized events" and this represents the primary output of
evelin. The _lev type files differ
from the raw version by five additional Bintable columns that
have been added to the event extension. These are (see
[1] for further details):
PI | - the Pulse Invariant of the event in units
of detector channels
|
PIC | - the Pulse Invariant of the event corrected
for penetration effects
|
DETX | - the linearized X-coordinate of the event
|
DETY | - the linearized Y-coordinate of the event
|
X | - sky-projected X coordinate of photon
|
Y | - sky-projected Y coordinate of photon
|
Thus, evelin
accepts its own output again as input which is needed if one wants to
do the aforementioned multi-step linearization process successively in
more than one run. If the user requests a linearization step
that has already been performed in a previous run, a warning
message is issued and the request is ignored.
The various linearization stages
of evelin are described in more detail in the following sections.
EVENTS REMOVAL
This first processing step simply removes all events outside the detector's
FOV. Note that this pertains also to the events from the calibration sources
which ly in the outermost corners of the focal plane. The detector's FOV is
defined as a circular region with a raw pixel radius of 100 (alterable via
command line parameter fovradius) centered
around the point where the optical axis intersects the focal plane
(approx. raw coordinates: 132/125).
TEMPORAL GAIN CORRECTION
This correction accounts for temporal changes in the detector's energy
gain as a consequence of changes in operating conditions, e.g. temperature,
pressure etc. The actual time-dependent energy gain is calculated using
the pipeline module calcgain
and contained as column data in a HK FITS file of type _hkg. Thus,
evelin
first attempts to open a _hkg file corresponding to the current
event list file and read the gain information from
a Bintable column named GAIN_AVG (can be changed via command line
parameter tgaincol).
The time granularity of those data is always greater than
25s and, therefore, they have
to be interpolated which can either be done by means of a
linear regression function or a cubic spline (controlled via command line
parameter tgainint).
Prior to actually performing the temporal gain correction on the
PHA values, the interpolation function together with the gain data can be
plotted (see parameter tgainplot).
After the plot the user is prompted for an acceptance confirmation.
If this is answered positively, the actual correction is done, i.e., each
event #i will be assigned a PI channel number according to the
relation:
PI_i = PHA_i / gain_t(t_i)
where PI is a new Bintable column in the event extension of the newly
created output file. Since the PHA and PI values are integer quantities
performing the above prescription as is leads to an artificial
"integer quantization effect". In order to avoid this, a random value
in the range [-0.5, 0.5] is added to each PHA value before it is divided
by the actual gain factor.
Further information about gain related issues can be found in
[3].
SPATIAL GAIN CORRECTION
In addition to the time dependence, the energy gain is spatially not
homogeneous, i.e., varies across the detector's focal plane. Hence,
the energy channel of each photon has to be corrected according to its
detection coordinates. This is done with the aid of a pre-processed
spatial gain map file which, either, stems from the SAX/LECS calibration
database, or can be explicitly specified (see command line parameter
sgainfile).
The spatial gain map file contains
basically a two-dimensional array which, when indexed with raw X and Y
coordinates, yields the spatial energy gain at that location.
This is used to correct the PI values of each photon according to the
simple prescription:
PI_i = PI_i_old / (const * gain_s(x_i, y_i))
where PI_i_old is the already temporally corrected energy channel of photon
#i and "const" is an alterable correction factor with default value 1 (see
command line parameter sgainfactor).
Similar to the temporal gain correction, a random value in the range
[-0.5, 0.5] is added to the integer PI values before they get divided
by the spatial gain factors.
Further information about gain related issues can be found in
[3].
EVENT SELECTION
Not all events that are detected inside the instrument's FOV are of actual
interest for the further scientific analysis of the data. Examples are
particle events originating from cosmic rays that have been absorbed in
the gas cell or spurious, so-called double events that are detected on
a line joining the two calibration sources. Those events can be identified
through peculiarities in their Veto and BL signals, and
be removed via a discrimination against appropriately chosen interval
thresholds of those quantities. This is done by performing a standard
one-dimensional Veto cut in combination with a two-dimensional selection
in PI-BL space. The event-selection stage is controlled via several
command line parameters, among which the most important one is
blvselfract. It determines the fraction
of photons that will be retained by the combined selection at all energies.
More detailed information on the event selection can be found in
[3].
BURST-LENGTH CORRECTION
Due to the driftless design of the LECS detector, X-rays that penetrate deep
into the gas cell before the get photoelectrically absorbed give rise
to events with lower PI and BL values than events of the same energy
which are detected just beneath the cell entrance window. Analyses
of ground calibration data have shown that the BL information can be
used to correct for that effect, i.e., to effectively enhance the
detector's spectral resolution. A corresponding algorithm
has been developed which is used by evelin to derive
a gain and BL-corrected Pulse Invariant Channel number (PIC channel) for
each event. Information about the BL-correction algorithm together with
related ground calibration results can be found in
[4].
Please note: Although PIC spectra obtained from ground calibration
measurements show the anticipated improvements with regard to the
spectral resolution, early analyses of flight data do not seem to
confirm this finding. It is clear that further investigations by the LECS
team are required to clarify the situation. At present (01/97) observers
are therfore discouraged from using the PIC data for spectral analyses.
COORDINATE LINEARIZATION
Due to intrinsic distortions inherent to the detection mechanism, the raw
spatial event coordinates as yielded by the instrument's electronic
unit do not directly reflect the physical location where the photon has hit the
focal plane. To gain this information, a non-linear correction of the form
C_i = a0_i + a1_i*x + a2_i*y + a3_i*x*y + a4_i*x^2 +
a5_i*y^2 + a6_i*x^2*y + a7_i*x*y^2 + a8_i*x^3 +
a9_i*y^3
has to be applied. Here, i is either x or y,
C_{x/y} are the desired
physical coordinates of the photon in the focal plane (measured from the
center of the FOV),
x/y are the raw detection coordinates referred to the center of
the FOV,
and a0_i to a9_i are constant coefficients. For more
details on the transformation and related issues, see
[3]. Per default, evelin
attempts to read the two sets of a-coefficients from a corresponding
FITS data file in the SAX/LECS calibration database. If this is not
available the file of an alternative coordinate linearization file can
be specified (see command line parameter
lincrdfile).
The above transformation gives the physical X and Y event coordinates
measured in mm from the center of the FOV which will be used to
derive "linearized" pixel coordinates. These
will finally be stored as DETX and DETY table entries
in the event extension of _lev files. Linearized coordinates
run in each dimension from 0.0 to a maximal pixel value Max
which depends on the actually chosen plate scale (see
command line parameter lincrdplatescale).
The point (0.0/0.0) is defined to refer to the corner in the focal plane with
physical coordinates (0mm/0mm) and the point (Max/Max)
represents the diagonally opposite corner at (32.79mm/32.79mm).
Using the "intrinsic" plate scale of 7.8 pixels/mm
(256x256 raw pixels on an active window area of 32.8x32.8 mm) the
dimension of the linearized coordinate space will be [0.0-255.0] x [0.0-255.0].
Another example: A plate scale of 30 pixels/mm leads to an pixel range in
X and Y of [0.0-30*32.79] = [0.0-984.0].
The center of the FOV will become the central pixel in the linearized
image, i.e., in the last example the center of the FOV will be assigned
the coordinates (492.0/492.0).
DEAD-TIME CALCULATION
In this processing step the instrumental dead-time correction factor
Fd, i.e., 1 minus the fraction of the total observing time
during which the instrument was insensitive to incoming X-rays, is calculated.
The actual computation is carried out using the instrument's deadtime
ratemeter counter which is tabulated in the HK file as a standard
parameter with a 1s time granularity. The corresponding Bintable column name
is DEADTIME_RATEMETER, see [1].
The value of Fd is then simply
Fd = 1 - M(DEADTIME_RATEMETER)
where M(DEADTIME_RATEMETER) is the value of the dead-time
ratemeter averaged over the time period covered by the observation.
Fd will be stored in the event extension of the output file as value
of a new header keyword DEADC. In addition, the standard deviation
of Fd and the dead-time corrected observation time will be
calculated (keyword names STDDEADC and LIVETIME/
EXPOSURE). The latter quantity is needed to allow the
true X-ray source strength and variance to be determined.
DETECTOR TO SKY COORDINATE MAPPING
In this stage the program calculates for each event the pixel position
within a two-dimensional sky image and saves this information
in the X and Y table columns of the event extension.
In addition, standard World-Coordinate-System (WCS) header keywords (see
[1] and [5] for details) are
added to the event extension header which enables corresponding FITS readers
such as Ximage or the standard FTOOLS task xy2sky to compute
for each event the actual R.A. and Dec. value. The generated image is a
standard tangent plane projection of the sky with a X and Y pixel range
corresponding to the dimensions of the linearized detector image. Other than
in this, however, X and Y pixel values start at 1. The central pixel
of the sky image shall be the projection's fixed-point, i.e.,
the point where the tangent plane touches the celestial sphere. Via a command
line parameter skypointing) it can
be chosen among the following three alternatives:
- the current nominal pointing direction of the satellite
- the mean pointing of the satellite during the observation
- any fixed point in the sky given as a user-supplied R.A./Dec.
coordinate pair
In the first case, the celestial coordinates of the reference point are
taken as the values of the RA_OBJ and DEC_OBJ keywords
from the primary FITS header. In the second case, they are calculated
as the mean R.A. and Dec. values of the satellite's pointing axis from
the attitude data in the HK file corresponding to the current event file.
In case an arbitrary reference point is requested, the coordinates
are specified via command line parameters
skyranom and
skydecnom.
Once the sky image reference point is known, the calculation of each
event's sky coordinates is carried out in the following manner:
- The satellite's attitude at the photon arrival time is
determined. This is normally done by reading the attitude data from the
Aspect extension in the HK file corresponding to the current event list
file. Those data have a time granularity of 0.5s and the satellite's
attitude at the requested time is calculated using a cubic-spline
interpolation. It is possible to dispense with using the actual attitude
data from the HK file and assume a fixed spacecraft attitude instead (see
command line parameter skyfixedatt).
This must then be given as set of
3-1-3 Euler angles in the celestial,
earth-centered reference frame.
- The actual pointing direction is corrected for the effect
of abberation and the current satellite roll angle is calculated.
- The event is projected onto the tangent plane using its linearized
focal-plane coordinates and the quantities obtained in step 2.
Hereby, the effect of a potential boresight-misalignment, is taken into
account. This is done by means of a 3x3 rotation matrix to align the
LECS's optical axis to the satellite's Z-axis, i.e., the current pointing
direction. Per default the boresight-misalignment matrix is attempted to
read from a corresponding file in the calibration database. This can
be suppressed by specifying an alternative file or by forcing the program
to use a hard-coded default matrix (see command line parameter
opticscalfile).
The final sky image is north-oriented, i.e., the top of the image points
towards the celestial north pole.
PARAMETERS
The following command line parameters are recognized by the program:
- infiles = "" [string: list of existing event list files]
- A blank or colon separated list of event files (of type _rev,
or _lev) to be processed. Note that if blank is used as file name
separator, the list has to be enclosed by "" in order to be considered as
a single command line argument. If a file in infiles
does not exist or is found not to be a valid LECS event file
a warning message is issued and the processing continues with the next
file in the list.
- indirpath = "" [string: list of directory names]
- A colon separated list of directories to seek for the specified input
files. For each file given in infiles
this is performed by first attempting to open the file as specified in
infiles. If this fails, each directory component in
indirpath is inspected for the location of the desired input file.
- outdir = "=" [string: name of existing directory or "="]
- The destination directory for the FITS output file. If
"=" is specified for outdir
(the default), the output file is written to the directory where the
corresponding input file was found.
Note that write access for outdir is needed.
- clobber = no [boolean: yes|no]
- In case of a raw event input file the name of the output file is
simply derived by changing rev to lev, e.g.
x_rev.fits becomes x_lev.fits. If a _lev file
is to be processed the name is retained causing a name conflict.
clobber = "yes" in this situation triggers that the input
file will get overwritten by the new output file. If clobber
is set to "no" an input file x_lev.fits will be renamed to
x_lev.old.fits prior to creating the output file. In case
a file x_lev.old.fits exists already from a previous run it
will be lost.
- fovradius = 0. [real: >=0.]
- The radius in raw pixels of the circular region defining the detector's
FOV. If it is given as 0. (the default), the actual value will be
obtained from the LECS-optics geometry calibration file
([3]). The value will be close to 100 pixels.
- rmevents = no [boolean: yes|no]
- A boolean switch determining whether the
events removal stage shall be carried out.
- tgain = yes [boolean: yes|no]
- A boolean switch determining whether the
temporal gain correction shall be performed.
- tgaincol = "GAIN_AVG" [string: valid HK parameter column name]
- The name of the Bintable column in the HK file (type: hkg)
containing the time-dependent gain values to be used for the temporal gain
correction.
- tgainint = "POLYNOMIAL" [string: "PLOYNOMIAL"|"SPLINE"]
- This determines the gain interpolation method to be used.
The value "POLYNOMIAL" selects a polynomial with a maximum degree
specified via the tgainpolymaxdeg
parameter. "SPLINE" signifies that the available gain values should be
interpolated using a cubic spline.
- tgainpolymaxdeg = 1 [integer: 0-10]
- This parameters determines the maximum allowed degree of the polynomial
which will be fitted to the gain data. The actual degree will be
optimized by the utilized fitting algorithm. The default for this parameter
is 1 which forces a linear interpolation of the gain data.
- tgainplot = no [boolean: yes|no]
- If set to "yes", a plot showing the interpolating gain function is produced
and the program asks for acceptance before proceeding with the actual
correction.
- sgain = yes [boolean: yes|no]
- A boolean switch determining whether the
spatial gain correction shall be carried out.
- sgainfile = "CALDB" [string: name of existing gain map file]
- The name of a spatial gain map file to be used for performing the spatial
gain correction. Assigning the special value "CALDB" to sgainfile
causes evelin to attempt to interrogate the SAX/LECS calibration
database for the location of this file.
- sgainfactor = 1 [real: 1-100]
- A multiplicative
constant used in the spatial energy gain correction.
- blvsel = yes [boolean: yes|no]
- A boolean switch determining whether the standard
standard event selection shall be carried out.
- blvseldovetocut = yes [boolean: yes|no]
- If set to "no" the Veto selection part in the combined Veto/PI-BL cut
will not be done.
- blvselfract = 0.9 [real: 0.5-1.0]
- This is the fraction of photons that shall be retained in the standard
Veto/PI-BL event selection at all energies. Default is to retain 90%
of the genuine X-ray events.
- blvsele2pifile = "CALDB" [string: name of existing keV->PI
conversion file]
- This must be the name of an existing LECS calibration file of type
CCNM001=KEV2PI used by the program to obtain coefficients
which define the keV->PI conversion relation. This relation is needed
during the event selection stage to convert an energy in keV to the
corresponding PI channel number. Assigning the special value "CALDB"
to blvsele2pifile causes evelin to attempt to interrogate
the SAX/LECS calibration database for the location of this file. If this
fails, a hard-coded default relation will be used to convert energies to
PI channel numbers.
For information on the structure and contents of the KEV2PI
calibration file, please consult Chap. 23 in [2].
- blvselcalfile = "CALDB" [string: name of existing BL-spectra
calibration file]
- This must be the name of an existing LECS calibration file of type
CCNM001=BLSPEC needed by the event selection algorithm which is based
on a combined VETO/BL cut. Assigning the special value "CALDB" to
blvselcalfile will cause evelin to attempt to interrogate
the SAX/LECS calibration database for the location of this file. If the
calibration file is not available the execution will be aborted.
For information on the structure and contents of the BLSPEC
calibration file, please consult Chap. 25 in [2].
- blcorr = yes [boolean: yes|no]
- A boolean switch determining whether the
BL correction stage shall be carried out.
- blcorrestart = 3.0 [real: 0.1-10.]
- The energy in keV below which no BL-correction shall be performed on
the PI data.
- blcorrblpifile = "CALDB" [string: name of existing BL-PI
curve file]
- This must be the name of an existing LECS calibration file of type
CCNM001=BLPICORR which is needed by the BL-correction algorithm.
Assigning the special value "CALDB" to blcorrblpifile
will cause evelin to attempt to interrogate
the SAX/LECS calibration database for the location of this file.
If this fail, execution will continue with hard-coded default values for
the coefficients defining the BL-PI relation.
For information on the structure and contents of the BLPICORR
calibration file, please consult Chap. 24 in [2].
- lineshapefile = "CALDB" [string: name of existing lineshape
parameter file]
- This must be the name of an existing LECS calibration file of type
CCNM001=LINESHAPE which contains the coefficients defining the
shape of a spectral line as a function of energy. This information is
needed by the BL-correction algorithm.
Assigning the special value "CALDB" to lineshapefile
will cause evelin to attempt to interrogate
the SAX/LECS calibration database for the location of this file.
If this fail, execution will continue with hard-coded default values for
all needed coefficients.
For information on the structure and contents of the LINESHAPE
calibration file, please consult Chap. 22 in [2].
- lincrd = yes [boolean: yes|no]
- A boolean switch determining whether the
coordinate linearization shall be carried out.
- lincrdplatescale = "8.0s" [string: number followed by "m" or "s"]
- This defines the actual plate scale for the coordinate linearization,
i.e., the number of linearized pixels per mm on the focal plane.
This parameter is supposed to be given as a number optionally followed by
either of the letters "m" or "s". In the first case or without any suffix,
the numeric value shall be interpreted a pixel-per-mm value,
otherwise as arcsec/pixel.
If 0 is assigned to this parameter the program will use
the intrinsic value 7.8 pixels/mm (256 raw pixels on 32.8mm active entrance
window length) which corresponds to a pixel size of 17.4". This will lead
to a linearized pixel range of [0.0-255.0] in both directions (see
above) and the X/Y sky image coordinates shall run
from [1.0-256]. The default plate scale is 8"/pixel which will lead
to a linearized pixel range of [0.0-511.0] and X/Y sky coordinates in the
range [1-512].
- lincrdcaldb = yes [boolean: yes|no]
- If set to yes, the file containing the coefficients needed for the
coordinate linearization is located by querying the SAX calibration database.
In case this is not desired, lincrdcaldb = no
signals that a set of default coefficients shall be used instead.
- lincrdfile = "CALDB" [string: name of existing FITS file]
- This must be the name of an existing LECS calibration file of type
CCNM001=GMAP containing the coefficients which define the
coordinate linearization transformation described above. Assigning the special
value "CALDB" to lincrdfile causes evelin to attempt to
interrogate the SAX/LECS calibration database for the location of this file.
If this fails, a set of hard-coded default values will be used.
For information on the structure and contents of the GMAP
calibration file, please consult Chap. 20 in [2].
- deadtime = yes [boolean: yes|no]
- A boolean switch determining whether the
dead-time calculation shall be carried out.
- sky = yes [boolean: yes|no]
- A boolean switch determining whether the
detector-to-sky coordinate mapping shall be carried
out.
- skyfixedatt = no [[boolean: yes|no]
- A boolean switch determining whether the spacecraft's attitude shall
be assumed to be fixed during the observation. If set to "yes" the actual
attitude must be specified as set of three 3-1-3 Euler angles in the
celestial, earth-centered reference frame via command line parameters
skyphi, skytheta, and skyphi.
- skyphi = 0. [real: 0.-360.]
- The first 3-1-3 Euler angle to specify the satellite's attitude if
skyfixedatt is set to "yes".
- skytheta = 0. [real: 0.-180.]
- The second 3-1-3 Euler angle to specify the satellite's attitude if
skyfixedatt is set to "yes".
- skypsi = 0. [real: 0.-360.]
- The third 3-1-3 Euler angle to specify the satellite's attitude if
skyfixedatt is set to "yes".
- skypointing = "KEYWORD" [string: "KEYWORD"|"MEANATT"|"USER"]
- This determines the method by which the sky image reference point with
the defined coordinates (128.5/128.5) will be chosen. "KEYWORD" signifies
that the celestial coordinates of the reference point shall be taken as
the values of the header keywords RA_OBJ and DEC_OBJ
in the event file's primary header. "MEANATT" means that the coordinates
will be computed as the mean values of R.A. and Dec. of the spacecraft's
pointing axis during the observation. Finally, if "USER" is given as
value of skypointing the celestial coordinates of the image
reference point must be passed to the program via command line parameters
skyranom and skydecnom respectively.
- skyranom = 0. [real: 0.-360.]
- The value of the R.A. of the sky image reference point if
skypointing was chosen as "USER".
- skydecnom = 0. [real: -90.-90.]
- The value of the Dec. of the sky image reference point if
skypointing was chosen as "USER".
- opticsfile = "CALDB" [string: name of existing FITS file]
- This must the name of an existing LECS calibration file of type
CCNM001=OPTICSGEO read by evelin to obtain the
following information:
- 3x3 bore-sight misalignment matrix needed for the
creation of sky images
- detector rotation angle referred to the spacecraft's X/Y reference
frame
- focal plane coordinates of the center of the FOV
- radius of the circle defining the FOV
Assigning the special value "CALDB" to opticsfile
will cause evelin to attempt to interrogate the SAX/LECS calibration
database for the location of this file. If this fails
a set of hard-coded default values will be used for the above quantities.
- caldb = yes [boolean: yes|no]
- If set to "yes" all calibration files needed by the various stages of
evelin will be attempted to locate by querying the SAX/LECS
calibration database. This requires that
- the SAX/LECS calibration database is accessible from the machine on
which evelin is running
- the standard FTOOLS task quzcif is available
- the environment to use the calibration database has been properly
set up (see general HEASARC calibration database documents)
Setting caldb equal to "yes" is equivalent to setting all
of the above command line parameters ending in ...file equal to
"CALDB"
- verbosity = 2 [integer: 0|1|2|3]
- Specifies the program verbosity level, i.e. the amount of screen output
that will be issued during program execution. Level 0 means "mute",
only fatal error messages will be printed. Verbosity level 3 results into
detailed diagnostic messages. Default is level 2.
- plotdev = "/XWIN" [string]
- The default PGPLOT device. All devices supported by the FTOOLS PGPLOT
library can be specified.
- help = no [boolean: yes|no]
- A boolean flag which, when set to yes triggers that the program
prints out a brief on-screen description of all available command line
parameters together with the current program version number and exits
successfully.
EXAMPLES
- Perform event linearization of the two raw event files
kv183_rev.fits and kv550_rev.fits. Suppress the
computation of sky coordinates, use cubic-spline interpolation for temporal
gain values and show the resulting function before proceeding:
evelin "kv183_rev.fits kv550_rev.fits" sky=no tgainint=spline tgainplot=yes
- Perform event linearization of the file xxx_lev.fits
except for the calculation of the total dead time. The input file shall be
sought under /data/sax1/ and /data/sax2/ and program shall
give maximum diagnostic messages as it proceeds through the various stages:
evelin xxx_lev.fits indir=/data/sax1:/data/sax2 verb=3 deadtime=no
FURTHER DOCUMENTATION
- The SAX LECS Data Analysis System -
Software User Manual,
U. Lammers, Doc. SAX/LEDA/0010
- SAX LECS calibration files: formats and contents,
M. Busetta, F. Favata, G. Vacanti, U. Lammers, Doc. SAX/LEDA/0003
-
The Ground Calibration of the Low Energy Concentrator Spectrometer aboard
SAX,
G. Vacanti, Doc. SAX/LEDA/0015
- The low-energy concentrator spectrometer on-board the SAX
X-ray astronomy satellite,
A.N. Parmar, et. al., A&A 1997
-
Representations of celestial coordinates in FITS,
E.W. Greisen and M. Calabretta, A&A, 1995
BUGS
SEE ALSO
U. Lammers (Uwe.Lammers@astro.estec.esa.nl)