.help fxcor Mar93 noao.rv
.ih
NAME
fxcor -- compute radial velocities via Fourier cross correlation
.ih
USAGE
fxcor objects templates
.ih
PARAMETERS
.ce
INPUT PARAMETERS
.ls objects
The list of image names for the input object spectra.
.le
.ls templates
The list of image names that will be used as templates for the cross
correlation.  This list need not match the object list.  All pairs
between the two lists will be correlated.
.le
.ls apertures = "*"
List of apertures to be correlated in echelle and multispec format spectra.  
This parameter is used for \fIboth\fR the object and reference spectra if both
spectra are two dimensional, otherwise the aperture list applies to the object
only if the template is one-dimensional.  Individual apertures from a
two-dimensional template may be
extracted to 1-D using the \fIonedspec.scopy\fR task, and these new images may
then be used in the template list as separate images.  (See the examples for
how this may be done). The default of '*' means to process all of the
apertures in the spectrum.  Note that the sample regions named by the 
\fIosample\fR and \fIrsample\fR parameters will apply to all apertures.
.le
.ls cursor = ""
Graphics cursor input.
.le

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DATA PREPARATION PARAMETERS
.ls continuum = "both"
Continuum subtract the spectra prior to correlation?  Possible values for
this parameter are any of the strings (or abbreviations) "object" (for object 
spectrum only), "template" (for template spectrum only), "both" for 
continuum flattening both object and template spectra, or "none" for 
flattening neither spectrum.  The \fIcontinpars\fR pset is used to specify 
the continuum fitting parameters.
.le
.ls filter = "none"
Fourier filter the spectra prior to correlation?  Possible values for
this parameter are any of the strings (or abbreviations) "object" (for object 
spectrum only), "template" (for template spectrum only), "both" for 
fourier filtering both object and template spectra, or "none" for 
filtering neither spectrum.  The \fIfiltpars\fR pset holds the parameters 
for the filtering (filter type and width).
.le
.ls rebin = "smallest"
Rebin to which spectrum dispersion?  If the input dispersions are not equal
prior to the correlation,
one of the two spectra in the pair will be rebinned according to the
\fIrebin\fR parameter.  Possible values are "smallest" (to rebin to the
smaller of the two values), "largest" (to rebin to the larger of the two
values), "object" (to force the template to always be rebinned to the object
dispersion), and "template" (to force the object to always be rebinned to the
template dispersion).  Input spectra \fImust be\fR linearly corrected.
Support for non-linear input dispersions is not included in this release.
.le
.ls pixcorr = "no"
Do a pixel-only correlation, ignoring any dispersion information?  If this
parameter is set to \fIyes\fR, then regardless of whether dispersion
information is present in the image headers, the correlation will be done
without rebinning the data to a log-linear dispersion.  This option is useful
when pixel shifts, not velocities, are the desired output.
.le
.ls osample = "*"
Sample regions of the object spectrum to be used in the correlation specified
in pixels if the first character is a 'p', or angstroms if the first
character is an 'a'.  The default (i.e. no 'a' or 'p' as the first
character) if a range is provided, is a range specified in angstroms.
This string value will be updated in an interactive session as sample
regions are re-selected in spectrum mode. The default, '*', is the entire 
spectrum.  The region is specified as a starting value, a '-', and an ending 
value.  If the specified range is out of bounds, the endpoints will be 
modified to the nearest boundary, or else the entire spectrum will be 
correlated if the whole range is out of bounds.
.le
.ls rsample = "*"
Sample regions of the template spectrum to be used in the correlation specified
in pixels if the first character is a 'p', or angstroms if the first
character is an 'a'.  The default (i.e. no 'a' or 'p' as the first
character) if a range is provided, is a range specified in angstroms.
This string value will be updated in an interactive session as sample
regions are re-selected in spectrum mode. The default, '*', is the entire 
spectrum.  The region is specified as a starting value, a '-', and an ending 
value.  If the specified range is out of bounds, the endpoints will be 
modified to the nearest boundary, or else the entire spectrum will be 
correlated if the whole range is out of bounds.
.le
.ls apodize = 0.2
Fraction of endpoints to apodize with a cosine bell when preparing the data
prior to the FFT.
.le

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CORRELATION PEAK FITTING PARAMETERS
.ls function = "gaussian"
Function used to find the center and width of the correlation peak.
Possible choices are "gaussian", "parabola", "lorentzian", "center1d",
or "sinc".  If a center1d fit is selected, then only the center is determined.
A "sinc" function uses a sinc interpolator to find the maximum of the 
peak by interpolating the points selectes.  The FWHM calculation in this
case is computed empirically by finding the half power point according
to the computed peak height and the \fIbackground\fR level.  No FWHM 
will be computed of the background is not set.  The function fitting options
all compute the FWHM from the fitted coefficients of the function.
.le
.ls width = INDEF
Width of the fitting region in pixels.  The fitting weights are
zero at the endpoints so the width should be something
like the expected full width.  If INDEF, then the width is
set by the \fIheight\fR and \fIpeak\fR parameters. If other than INDEF, 
this parameter will override the \fIheight\fR and \fIpeak\fR parameters.
.le
.ls height = 0.
The width of the fitting region is defined by where the correlation
function crosses this height starting from the peak.  The height is
specified as either a normalized correlation level (this is like
the 'y' interactive key) or normalized to the peak.  The type of
level is selected by the \fIpeak\fR parameter.
.le
.ls peak = no
Measure the height parameter relative to the correlation peak value
rather than as a normalized correlation level? If yes, then \fIheight\fR
is a fraction of the peak height with an assumed base of zero.
.le
.ls minwidth = 3., maxwidth = 21.
The minimum and maximum widths allowed when the width is determined
from the height.
.le
.ls weights = 1.
Power of distance defining the fitting weights.  The points used
in fitting the correlation peak are weighted by a power of the
distance from the center as given by the equation
.nf

         weight = 1 - (distance / (width/2)) ** \fIweights\fR

.fi
Note that a weight parameter of zero is equivalent to uniform weights.
The center1d fitting algorithm uses it's own weighting function.
.le
.ls background = 0.0
Background level, in normalized correlation units, for a Gaussian or 
Lorentzian fitting function.  If set to INDEF, the background is a free 
parameter in the fit.
.le
.ls window = INDEF
Size of the window in the correlation plot.  The peak will be displayed
with a window centered on the peak maximum and two times \fIwindow\fR 
pixels wide if no dispersion information is present in the image header.
If dispersion information is present, \fIwindow\fR is specified in Km/s.
A value of INDEF results in a default window size of 20 pixels.  If the
window proves to be too small for the number of points to be fit selected 
with the \fIwidth\fR, \fIheight\fR, and/or \fIpeak\fR parameters, a message
will be written to the ".log" file and/or screen explaining that points
outside the window bounds were used in the fit.  The user may wish to
review this fit or increase the window size.
.le
.ls wincenter = INDEF
Center of the peak search window specified in pixel lags if no dispersion
information is present, or specified in Km/s if dispersion information is
present.  If set to the default INDEF, the maximum peak in the cross-correlation
function will be fit by default.  If set to other than INDEF, the maximum peak 
within a window centered on \fIwincenter\fR and two times \fIwindow\fR 
lags wide will be used.  Note that this parameter can be used to constrain
the velocities computed to a certain range in non-interactive mode.
.le

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OUTPUT PARAMETERS
.ls output = ""
Name of the file to which output will be written.  If no file name is given
then no log files will be kept, but the user will be queried for a file name
if a write operation is performed.  Tabular text output will have a ".txt" 
suffix appended to the \fIoutput\fR name, a verbose description of each fit
will have ".log" suffix appended and will be written only if the \fIverbose\fR
parameter is set, and the graphics metacode file will be appended with 
a ".gki" suffix. (NOTE: Image names will be truncated to 10 characters in the
output file because of space considerations.  Verbose output logs will
truncate the image names to 24 characters.  Object names are similarly
truncated to 15 characters.  If a relative velocity is calculated with a
redshift of more than 0.2, output will be redshift z values rather than
velocities in Km/s.)
.le
.ls verbose = "long"
Set level of verbosity and types of files to create.  The \fIverbose\fR
parameter is an enumerated string whose values determine the number and type
of output files created.  Up to three files are created: the ".txt", ".log",
and ".gki" files (see the description for the \fIoutput\fR parameter).
Possible values  for \fIverbose\fR and the files created are as follows:
.nf

    Value:      Files Created:

    short       (an 80-char .txt file and a .gki file)
    long        (a 125-char .txt file, a .log file, a .gki file)
    nolog       (a 125-char .txt file and a .gki file)
    nogki       (a 125-char .txt file and a .log file)
    txtonly     (a 125-char .txt file)
    stxtonly    (an 80-char .txt file)

.fi
The \fIfields\fR task 
may be used to strip out selected columns from the .txt files.  The 125-char
.txt output
may be printed without wrapping the lines either in landscape mode for
a laser printer, or on a 132 column lineprinter.
.le
.ls imupdate = "no"
Update the image header with the computed velocities?  If set to yes, then
the image will be updated with the observed and heliocentric velocities
by adding the \fIkeywpars.vobs\fR and \fIkeywpars.vhelio\fR keywords
respectively.  Two-dimensional spectra cannot be updated.  Additional keywords
defined in the \fIkeywpars\fR pset will also be updated.
.le
.ls graphics = "stdgraph"
Output graphics device.
.le

.ce
CONTROL PARAMETERS
.ls interactive = "yes"
Process the spectra interactively?  
.le
.ls autowrite = "yes"
Automatically record the last fit to the log file when moving to the 
next/previous spectrum or quitting? If set to "no", the user will be 
queried whether to write the results if no write was performed, and 
possibly queried for a file name if \fIoutput\fR isn't set.  
.le
.ls autodraw = "yes"
Automatically redraw the new fit after it changes.  If set to the default
"yes" then the old fit is erased and a new one computed and drawn after 
the 'g', 'y', 'd', or 'b' keystrokes.  If set to "no", then old fits are not
erased and the user must redraw the screen with an 'r' keystroke.
.le
.ls ccftype = "image"
Type of output to create when writing out the correlation function with
the ":wccf file" command.  Possible choices are "text" which will be a
simple list of (lag,correlation_value) pairs, or "image" which will be an
IRAF image whose header would describe the lag limits and selected peak.
.le

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ADDITIONAL PARAMETER SETS
.ls observatory = "kpno"
The location of the observations, as defined by the \fInoao.observatory\fR
task.  The image header keyword OBSERVAT will override this parameter, thus
allowing for images which were taken at another observatory to be properly
corrected.  These values are used in the heliocentric correction routines.
.le
.ls continpars = ""
The continuum subtraction parameters as described in the \fIcontinpars\fR 
named pset.
.le
.ls filtpars = ""
The parameter set defining the parameters to be used in filtering the
data prior to the correlation. 
.le
.ls keywpars = ""
The image header keyword translation table as described in 
the \fIkeywpars\fR named pset.
.le

.ce
RV PACKAGE PARAMETERS
.ls dispaxis = 1,  nsum = 1
Parameters for defining vectors in 2D images.  The
dispersion axis is 1 for line vectors and 2 for column vectors.
A DISPAXIS parameter in the image header has precedence over the
\fIdispaxis\fR parameter. 
.le
.ls z_threshold = 0.2
Redshift value at which the output logs switch from printing velocities in 
units of Km/s to redshift z values.
.le
.ls tolerance = 1.0e-5
Fitting tolerance for Least Squares fitting.
.le
.ls maxiters = 100
Maximum number of iterations for Least Squares fitting or any other iterative
algorithm.
.le
.ls interp = "poly5"
Interpolator used when rebinning the data to a log-linear dispersion.   See 
the section on interpolation for more information.  Possible choices are
"nearest", "linear", "poly3", "poly5", "spline3", and "sinc".
.le
.ls line_color = 1
Color index of overlay plotting vectors.  This parameter has no effect on
devices which do not support color vectors.
.le
.ls text_color = 1
Color index of plot text annotation.  This parameter has no effect on
devices which do not support color vectors.
.le
.ls observatory = "observatory"
Observatory at which the spectra were obtained if not specified in the
image header by the keyword OBSERVAT.  This parameter is used by several
tasks in the package through parameter redirection so this parameter may be
used to affect all these tasks at the same time.  The observatory may be
one of the observatories in the observatory database, "observatory" to
select the observatory defined by the environment variable "observatory" or
the parameter \fBobservatory.observatory\fR, or "obspars" to select the
current parameters set in the \fBobservatory\fR task.  See help for
\fBobservatory\fR for additional information.
.le

.ih
DESCRIPTION
\fIFxcor\fR performs a Fourier cross-correlation on the input list of object
and template spectra.  Object spectra may be either one or two dimensional
(in `echelle' or `multispec' format), and may be correlated against a one
or two dimensional template.  If the template spectrum is only one dimensional
but the object is two dimensional, the template is used to correlate each of
the apertures specified by the \fIapertures\fR parameter in the object 
spectrum.  Two dimensional templates will correlate corresponding apertures.

If the input spectra are not dispersion corrected (DC-FLAG parameter missing
or less than zero), or the \fIpixcorr\fR parameter is turned on, then only 
a pixel space correlation is done.  This is
appropriate for a simple cross-correlation of images whether spectra or not.
If the spectra are dispersion corrected, a log binned correlation is
performed and various radial velocity measurements are made. At a minimum,
a relative velocity between the object and template spectra is produced.
If the image headers contain sufficient information for heliocentric
velocity corrections (see help for \fBkeywpars\fR), the corrections are
computed and possibly recorded in the image header (see below for a full
explanation of the computed velocities).  If the value of the 
heliocentric velocity is returned as INDEF, the user may use the 'v'
keystroke to see the full results of the correlation, including errors
which occured causing the corrections to not be done.

A number of operations may be performed to prepare the data for
correlation.  If a linear wavelength dispersion is defined, the spectra are
rebinned to a log-linear dispersion using the interpolant set by the package
parameter \fIinterp\fR (See the section on interpolation for details).  
At this time only linear input dispersions are supported for rebinning.
The starting and ending wavelength for
both spectra will remain the same, but the dispersion in log space will be
determined from the \fIrebin\fR parameter if the input disersions aren't
equal, or from the spectrum's endpoints and number of pixels if they are
equal.  For example, assuming \fIrebin\fR is set to "smallest", if object
one and the template have the same input log dispersion of 0.5e-4 A/pix the
data will not be rebinned.  Object two with a wpc of 0.4e-4 A/pix will force
the template to be rebinned to a common wpc of 0.4e-4 A/pix.  If the third
object on the list then has a dispersion of 0.3e-4 A/pix, the template will
again be rebinned from the original 0.5e-4 A/pix dispersion to a new 0.3e-4
A/pix dispersion.  If object three and the template are the same star, the
template spectrum will suffer from interpolation errors that should be
considered when analyzing the results.  The output .txt file will update
every time the common dispersion is changed.  The suggested course of action
is to bin all spectra to the same dispersion, preferably a log-linear one,
prior to executing this package.

If the \fIcontinuum\fR flag is set to something other than 
"none", the object and/or template data will
be continuum subtracted using the fitting parameters found in the
\fIcontinpars\fR pset on input.  The data are zeroed outside the sample
region specified by the \fIosample\fR and \fIrsample\fR parameters, 
the ends of each region are apodized, and the bias is then subtracted.
If the \fIfilter\fR flag is set to something other than
"none", the data are Fourier filtered according to the parameters in 
the \fIfiltpars\fR pset prior to the correlation computation.

Once the correlation is computed, the maximum peak within the window
specified by the \fIwincenter\fR and \fIwindow\fR parameters is found and
fit according to the \fIwidth\fR or \fIheight\fR and \fIpeak\fR parameters.
A small, unlabeled plot of the entire cross correlation function (hereafter
CCF) is drawn above a larger, expanded plot centered on the peak in a window
of size specified by the \fIwindow\fR parameter.  The dashed lines in the
small plot show the limits of the expanded plot.  The bottom axis of the
expanded plot is labeled with pixel lag and, if dispersion information is
present, the top axis is labeled with relative velocity.  To choose a
different peak to fit, move the cursor to the top plot of the whole ccf and
hit the 'z' keystroke at the desired peak.  The plot will be redrawn with
the new peak now centered in the window and a fit automatically done.  The
status line will contain a summary of the pixel shift from the fit and
optional velocity information.  The 'v' keystroke may be used to suspend
graphics and get a more detailed description of the correlation and fit, and
the '+' keystroke will toggle the status line output.  To view the
antisymmetric noise component of the correlation function, simply hit the
'a' keystroke followed by any keystroke to return to the correlation plot.
Similarly, the 'e' keystroke may be used to preview the summary plot of the
correlation, again hitting any key to return to the correlation.  An
overplot of the subtracted fit (residuals) may be seen with the 'j'
keystroke.

If the user is dissatisfied with the fit to the peak, he can mark the left
and right side of the peak with the 'g' keystroke to redo the fit, or else
set the cursor to mark a cutoff with the 'y' keystroke, and all points from
the peak maximum to the cursor will be fit.  To fix the background of a
Gaussian fit (i.e. change the \fIbackground\fR parameter graphically), type
the 'b' keystroke at the desired level, and a new fit will be done.  The 'r'
keystroke may be used at any time to redraw the plot, and the 'x' keystroke
can be used to compute a new correlation if any of the parameters relating
to the correlation are changed (e.g. the apodize percentage).  New
correlations are automatically computed when new images are read in, the
data are continuum subtracted, a different region is selected for
correlation, or Fourier filtering is done.  Certain colon commands from
within the Fourier or Spectrum mode will also cause a new correlation to be
computed when these modes are exited.

The 'c' keystroke may be used to get a printout of the cursor position in both 
lag and relative velocity.  The cursor may be positioned in either the
unlabeled CCF plot on the top, or in the zoomed plot on the bottom.  This is
useful for judging the FWHM calculation, or estimating the velocity of a
peak without using the 'z' keystroke to zoom and fit.  Note that because of
the plotting implementation, the normal cursor mode keystroke \fIshift-C\fR
should not be used as it may return erroneous results depending upon cursor
position.  Note also that velocities printed are only approximate relative
velocities, and the user should properly fit a peak or use the ":correction"
command to get a true heliocentric velocity.

For binary star work, the user may type the 'd' and/or '-' keystrokes to fit
and then subtract up to four Gaussians to the peaks. See the discussion
below for more deatils on the use of this feature.  If multiple peaks were
fit, a separate entry will be made in the log file for each peak with a
comment that it was part of a blended peak.  The metacode file will contain
only one summary plot with each peak marked with it's heliocentric velocity
or pixel shift.

To move to the next spectrum in a list (of images or apertures), simply hit
the 'n' keystroke.  Similary, the 'p' keystroke will move to the previous
spectrum.  These commands have a hitch, though.  By default, the
next/previous commands will move first to the next template in the template
image list.  Once the end of the template image list is reached, the next
spectrum will be the next aperture in the list specified by \fIapertures\fR,
resetting the template image list automatically and possibly updating the
aperture in the template image as well.  Finally, after correlating all of
the templates against all of the apertures, the next/previous command will
move to the next object image, again resetting the template image and/or
aperture list.  To override this sequence, the user may use the ":next" or
":previous" commands and specify one of "aperture", "object", or
"template".  If \fIautowrite\fR is set, the results of the last fit will be
written to the log automatically.  To write any one of the fits explicitly,
use the 'w' keystroke.

The \fIfxcor\fR task also contains three submodes discussed in detail below.
Briefly, the 'f' keystroke will put the user in the "fourier mode",
where he can examine the Fourier transform of the spectra in various
ways and change/examine the filtering parameters.  The 'o' and 't'
keystrokes let the user examine and fit the continuum for the object
and template spectra, respectively, using the \fBicfit\fR commands.
Upon exiting the continuum fitting the spectra are continuum subtracted 
and a new correlation is computed.  Finally the 's' keystroke will put
the user in "spectrum mode", in which he may graphically select the
region to be correlated, compute an approximate shift using the cursor,
or simply examine the two spectra in a variety of ways.  All of these
submodes are exited with the 'q' keystroke, after which the correlation
will be redone, if necessary, and the CCF plot redrawn.

Colon commands may also be used to examine or change parameter values in
any of the \fIfiltpars\fR, \fIcontinpars\fR, or \fIkeywpars\fR
psets.  Simply type a ':' followed by the parameter name and an optional
new value.  The \fIobservatory\fR parameters may only be changed outside
the task.

To exit the task, type 'q'.  Results will be saved
to the logfile automatically if one was specified, otherwise the user will
be asked if he wants to save the results, and if so, queried for a file name
before exiting if no \fIoutput\fR file was defined.

If the \fIoutput\fR parameter is set, several files will be created
depending on the value of the \fIverbose\fR parameter (see the parameter
description for details).  These include a file with a ".gki" suffix
containing metacode output of a summary plot, a ".txt" suffix file
containing text output in the standard IRAF 'list' format containing either
verbose or non-verbose output, and a third file having a ".log" suffix
containing a verbose description of the correlation and fit, as well as any
warning messages.  This contents of the ".log" file is identical to what is
seen with the 'v' keystroke.  If the computed relative velocity exceeds the
package parameter \fIz_threshold\fR, the ".txt" file will contain redshift Z
values rather than the default velocities.  Text file output may be have
selected columns extracted using the iraf \fIfields\fR task (where string
valued fields will have blank spaces replaced with an underscore), and
specific metacode plots may be extracted or displayed with the iraf
\fIgkiextract\fR and/or \fIstdgraph\fR/\fIgkimosaic\fR tasks.

(References: Tonry, J. and Davis, M. 1979 \fIAstron. J.\fR \fB84,\fR 1511, 
and Wyatt, W.F. 1985 in \fIIAU Coll. No 88, Stellar Radial Velocities\fR, 
p 123).

.ih
FOURIER MODE DESCRIPTION
Fourier mode is entered from the main task mode via the 'f' keystroke.  By 
default, the user is presented with a split plot of the power spectra of
the object and template spectra (object on top) and the requested filter
overlayed. The X-axis is double-labeled with wavenumbers on the bottom of
the screen and frequency on top.  The ":log_scale" command can be used to 
toggle the log scaling of the Y-axis of the plot, and the ":overlay" command 
will toggle whether or not the filter function (if specified) is overlayed 
on the plot.  By default the entire power spectrum is displayed, but 
the ":zoom" command may be used to specify a blowup factor for the 
display (e.g. ":zoom 2" will display only the first half of the power 
spectrum).  Plot scaling and content parameters are learned for the next 
invocation of this mode.

The plot contents may also be changed through various keystroke commands.
The 'p' keystroke will display the power spectrum (the default) and the 'f'
keystroke will display the two FFT's.   The 'b' and 'g' 
keystrokes may be used to examine the power spectra and FFT's 
respectively \fIbefore\fR filtering.  The user can determine the period 
trend in the data by placing the cursor at a particular wavenumber/frequency 
and hitting the 'i' keystroke (this command will not work on a plot of 
the filtered spectra).  The 'r' key will redraw whichever plot is currently
selected and a 'q' will return the user to the mode which called the Fourier
mode (i.e. either the main task mode or the Spectrum mode).  The Spectrum
mode may be entered from within Fourier mode via the 's' keystroke.

Colon commands are also used to specify or examine the filtering parameters
by simply typing a ':' followed by the parameter name found in 
the \fIfiltpars\fR pset.

.ih
CONTINUUM MODE DESCRIPTION
Automatic continuum subtraction is controlled by the \fIcontinpars\fR
pset.  These may be reset from the main
correlation function mode.  To interactively fit and modify the continuum
fitting parameters the 'o' and 't' keys are used.  This enters
the ICFIT package which is described elsewhere (see \fIicfit\fR).  
Exiting the fitting,
with 'q', causes a recomputation of the correlation function and peak
fit.  To view the flattened spectra use the spectrum review mode
entered with the 's' key.  Fitting parameters changed while doing the
interactive continuum fitting are learned.

.ih
SPECTRUM MODE DESCRIPTION
Spectrum mode is entered from the main or fourier mode via the 's'
keystroke.  The user may select plots of the original input spectra with the
'i' keystroke, or the continuum subtracted spectra with the 'n' keystroke,
If the data have been rebinned to a log scale, they will still be plotted 
on a linear wavelength scale for clarity.  Pixel data are plotted identically
to how they were read.  (NOTE: For rebinned spectra, a slight slope may be
noticed in the 'original' data because of rebinning effects.)
In addition, a sample regions (if selected) for the correlation are marked
on the bottom of both plots.  To select a new sample region, use the 's'
keystroke to select the endpoints of the region.  An 's' keystroke on the
top plot will select a sample region for the object spectrum, and an 's' on
the bottom plot will select a template sample, using the 'b' keystroke will
select both samples simultaneously.  The regions may be selected
explicitly by using the ":osample" and ":rsample" commands, and selected
sample regions may be cleared entirely using the (e.g.) ":osample *" command,
or individual regions may be unselected by putting the cursor within the
region and typing 'u'.  See the
parameter description for syntax of the sample ranges.  Regions will be
checked and possibly truncated to see if they 
lie within the range of the spectrum.  The 'd'
keystroke may be used to print the difference in pixels (and/or velocity)
between two points on the spectrum.  This is useful for getting an
approximate shift.  Fourier mode may be entered via the 'f' keystroke.  To
return to the correlation simply type 'q' or 'x'.

In addition to the above commands, the user may examine or change the 
parameters in the \fIcontinpars\fR pset by simply typing a ':' followed
by the parameter name. Changing these values will not cause a new correlation
until an explicit command is given to redo the continuum subtraction.

(NOTE: More functionality is planned for this mode.)

.ih
INTERPOLATION
The interpolation type is set by the package parameter \fIinterp\fR.
The available interpolation types are:

.nf
	nearest - nearest neighbor
	 linear - linear
	  poly3 - 3rd order polynomial
	  poly5 - 5th order polynomial
	spline3 - cubic spline
	   sinc - sinc function
.fi

The default interpolation type is a 5th order polynomial (poly5).

The choice of interpolation type depends on the type of data, smooth
verses strong, sharp, undersampled features, and the requirements of
the user.  The "nearest" and "linear" interpolation are somewhat
crude and simple but they avoid "ringing" near sharp features.  The
polynomial interpolations are smoother but have noticible ringing
near sharp features.  They are, unlike the sinc function described
below, localized.

In V2.10 a "sinc" interpolation option is available.  This function
has advantages and disadvantages.  It is important to realize that
there are disadvantages!  Sinc interpolation approximates applying a phase
shift to the fourier transform of the spectrum.  Thus, repeated
interpolations do not accumulate errors (or nearly so) and, in particular,
a forward and reverse interpolation will recover the original spectrum
much more closely than other interpolation types.  However, for
undersampled, strong features, such as cosmic rays or narrow emission or
absorption lines, the ringing can be more severe than the polynomial
interpolations.  The ringing is especially a concern because it extends
a long way from the feature causing the ringing; 30 pixels with the
truncated algorithm used.  Note that it is not the truncation of the
interpolation function which is at fault!

Because of the problems seen with sinc interpolation it should be used with
care.  Specifically, if there are no undersampled, narrow features it is a
good choice but when there are such features the contamination of the
spectrum by ringing is much more severe than with other interpolation
types.

.ih
DEBLENDING
When entering the deblending function, two cursor settings define the
local background, which may be sloping, and the region to be fit.  Note
that both the x and y of the cursor position are used.  The lines to be
fit are then entered either with the cursor ('m'), or by typing the
shifts ('t').  The latter is useful if the shifts of the
lines are known accurately and if fits restricting the absolute or
relative positions of the lines will be used (i.e. 'a', 'b', 'd',
'e').  A maximum of four lines may be fit.  If fewer lines are desired,
exit the marking step with 'q'.

There are six types of fits which may be selected.  This covers all
combinations of fixing the absolute positions, the relative positions,
the sigmas to be the same, and letting all parameters be determined.
In all cases the peak intensities are also determined for each line.
The options are given below with the appropriate key and mnemonic.

.nf
    a=0p1s	Fit intensities and one sigma with positions fixed
    b=1p1s	Fit intensities, one position, and one sigma with
			separations fixed
    c=np1s	Fit intensities, positions, and one sigma
    d=0pns	Fit intensities and sigmas with positions fixed
    e=1pns	Fit intensities, one position, and sigmas with
			separations fixed
    f=npns	Fit intensities, positions, and sigmas
.fi

This list may also be printed with the '?' key when in the deblending
function.

As noted above, sometimes the absolute or relative shifts of the
lines are known a priori and this information may be entered by typing
the shifts explicitly using the 't' option during marking.  In
this case, one should not use the 'c' or 'f' fitting options since they
will adjust the line positions to improve the fit.  Options 'a' and 'd'
will not change the lines positions and fit for one or more sigmas.
Options 'b' and 'e' will maintain the relative positions of the lines
but allow an other than expected shift.

After the fit, the modeled lines are overplotted.  The line center,
flux, equivalent width, and full width half maximum are printed on the
status line for the first line.  The values for the other lines and
the RMS of the fit may be examined by scrolling the status line
using the '+', '-', and 'r' keys.  Velocity information is obtained by
typing the 'v' keystroke.  To continue enter 'q'.

The fitting may be repeated with different options until exiting with 'q'.

The fitted model may be subtracted from the data (after exiting the
deblending function) using the '-' (minus)
keystroke to delimit the region for which the subtraction is to
be performed. This allows you to fit a portion of a peak which may
be contaminated by a blend and then subtract away the entire peak
to examine the remaining components.

The fitting uses an interactive algorithm based on the Levenberg-Marquardt
method.  The iterations attempt to improve the fit by varying the parameters
along the gradient of improvement in the chi square.  This method requires
that the initial values for the parameters be close enough that the
gradient leads to the correct solution rather than an incorrect local
minimum in the chi square.  The initial values are determined as follows:

.nf
    1.  The initial line centers are those specified by the user
	either by marking with the cursor or entering the shifts.
    2.  The initial peak intensities are the data values at the
	given line centers with the marked continuum subtracted.
    3.  The initial sigmas are obtained by dividing the width of
	the marked fitting region by the number of lines and then
	dividing this width by 4.
.fi

Note that each time a new fitting options is specified the initial parameters
are reset.  Thus the results do not depend on the history of previous fits.
However, within each option an iteration of parameters is performed as
described next.

The iteration is more likely to fail if one initially attempts to fit too
many parameters simultaneously.  A constrained approach to the solution
is obtained by iterating starting with a few parameters and then adding
more parameters as the solution approaches the true chi square minimum.
This is done by using the solutions from the more constrained options
as the starting point for the less constrained options.  In particular,
the following iterative constraints are used during each option:

.nf
	a: 0p1s
	b: 0p1s, 1p1s
	c: 0p1s, 1p1s, np1s
	d: 0p1s, 0pns
	e: 0p1s, 1p1s, 1pns
	f: 0p1s, 1p1s, np1s, npns
.fi

For example, the most general fit, 'f', first fits for only a single sigma
and the peak intensities, then allows the lines to shift but keeping the
relative separations fixed. Next, the positions are allowed to vary
independently but still using a single sigma, and then allows all parameters
to vary.

To conclude, here are some general comments.  The most restrictive 'a'
key will give odd results if the initial positions are not close to the
true centers.  The most general 'f' can also lead to incorrect results
by using unphysically different sigmas to make one line very narrow and
another very broad in an attempt to fit very blended lines.  The
algorithm works well when the lines are not severely blended and the
shapes of the lines are close to Gaussian.

.ih
PEAK FITTING/FINDING ALGORITHMS
Determining the center of the cross correlation peak is the key step in
measuring a relative shift or velocity between the object and template.
The width of the correlation peak is also of interest for measuring
a line broadening between the two samples.  Since people have different
preferences and prejudices about these important measurements, a variety
of methods with a range of parameters is provided.

In all cases, one must specify the fitting function and a sample width; i.e.
the range of points about the correlation peak to be used in the
measurement.  Note that the width defines where the fitting weights vanish
and should be something like the full width.  For the CENTER1D algorithm the
maximum weights are at the half width points while for the other methods
(with the exception of "sinc") greater weight is given to data nearer the
center.

The width may be specified in three ways.  The first is as an actual
width in pixels.  This is the most straightforward and is independent
of quirks in the actual shape of the peak.  The second way is to find
where the correlation function crosses a specified height or level.
The height may be specified in normalized correlation units or as a
fraction of the peak height.  The former is equivalent to the
interactive 'y' key setting while the latter may be used to select some
"flux" point.  A value of 0.5 in the latter would be approximately the
full width at half intensity point except that the true zero or base of
the peak is somewhat uncertain and one needs to keep in mind that the
weights go to zero at this point.  Note that a level may be negative.
In this method the actual width may go to zero or include the entire
data range if the level fall above the peak or below the minimum of the
correlation.  The minimum and maximum width parameters are applied to
constrain the fitting region.  The last method is to interactively mark
the fitting region with the 'g' key.

There are five methods for determining the correlation peak position.  The
CENTER1D algorithm has been heavily used in IRAF and is quite stable and
reliable.  It is independent of a particular model for the shape of the peak
or the background determination and is based on bisecting the integral.  It
uses antisymmetric weights with maxima at points half way between the
estimated center and the fitting region endpoint.  A parabola fit and sinc
interpolation is also independent of background determinations.  The
parabola is included because it is a common method of peak centering.

The sinc option uses a sinc interpolator together with a maximization
(actually a minimization algorithm) function to determine the peak height
and center.  A width will be computed only if a background level has been
set and is determined empirically based on the peak height and background.
Point weighting is not used in this option.

The gaussian and lorentzian function fits are model dependent and
determine a center, width, and peak value.  The background may also
be determined simultaneously but this extra degree of freedom
for a function which is not strictly gaussian or lorentzian may
produce results which are sensitive to details of the shape of the
correlation function.  The widths reported are the full width at
half maximum from the fits.

The parabola, gaussian, and lorentzian methods use weights which
vary continuously from 1 at the estimated center to zero at the
endpoints of the fitting region.  The functional form of the
weights is a power law with specified exponent.  A value of zero
for the exponent produces uniform weights.  However, this is
discontinuous at the endpoints and so is very sensitive to the data
window.  A value of one (the default) produces linearly decreasing weights.

All these methods produce centers which depend on the actual
data points and weights used.  Thus, it is important to iterate
using the last determined center as the center of the data window
with continuous weights in order to find a self-consistent center.
The methods are iterated until the center does not change by more
than 0.01 pixels or a maximum of 100 iterations is reached.

Errors in the pixel shift are computed from the center parameter of the fitting
function.  Velocity errors are computed based on the fitted peak height and
the antisymmetric noise as described in the Tonry & Davis paper (1979,
\fIAstron. J.\fR \fB84,\fR 1511). Dispersion/pixel-width errors are 
not computed in this release but are planned for a future release.

The initial peak fit will be the maximum of the CCF.  This will be the only 
peak fit in non-interactive mode but a confidence level will be entered in
the logfile.  In interactive mode, the user may select a different peak with
the 'z' keystroke, and the maximum peak within the specified \fIwindow\fR
(centered on the cursor) will be fit.  The user has full control in interactive
mode over the points used in the fit.  Once the endpoints of the peak have
been selected, the actual data points are shown with '+' signs on the CCF,
the fitted curve drawn, and a horizontal bar showing the location of the
FWHM calculation is displayed.  The status line will show a summary of the 
fit, and the user may type the 'v' keystroke for a more detailed description
of the fit and correlation. 

.ih
VELOCITY COMPUTATION ALGORITHM
Up to three velocities are computed by the task depending on the completeness
of the images headers and the presence of dispersion information.  If only
dispersion information is present, a relative velocity, VREL, and an error
will be computed.  If a full header is present (see the \fIkeywpars\fR
help page), an observed and heliocentric velocity (VOBS and VHELIO
respectively) will be computed.

In short form, here are the equations:
.nf

    ref_rvobs = catalogue_vel_of_template - H(temp)  # obs. vel. of temp.
    VREL = C * (10 ** (wpc * shift) - 1.)	     # relative vel.
    VOBS = ((1+ref_rvobs/C)*(10**(wpc*shift)-1)) * C # observed vel.
    VHELIO = VOBS + H(object)			     # heliocentric vel.

.fi
where H() is the heliocentric correction for that observation.  The
equation used for the relative velocity is derived from the standard
(1+z), and the VOBS equation reflects that the observed velocty is the
product of (1+z) values for the object and template (this allows for high
redshift templates to be used).  The date, time, and position of each
spectrum is found from the image header via the keywords defined in
\fIkeywpars\fR.  In the case of the time the task first looks for a
keyword defining the UT mid-point of the observation
(\fIkeywpars.utmiddle\fR).   If that is not found any time present in the
header DATE-OBS (\fIkeywpars.date_obs\fR) keyword is used at the UT start
point, if there is no time in the keyword value then the mid-point UT is
computed from the exposure time (\fIkeywpars.exptime\fR) and UT of
observation (\fIkeywpars.ut\fR) keywords.

The keyword added to the template header (as defined by the
"vhelio" parameter in the \fIkeywpars\fR pset) should be the catalogue velocity 
of the template.  Since the observation of the template has a slightly
different heliocentric correction, this is subtracted from the template
heliocentric velocity so that the \fIobserved\fR velocity of the template 
is used when correcting the relative velocity computed from the shift.  
This gives the \fIobserved\fR velocity of the object wrt the template.  
Adding the heliocentric correction of the object star then yields the true
heliocentric velocity of the object.

.bp
.ih
CURSOR KEYS AND COLON COMMANDS SUMMARY

.ce
CORRELATION MODE COMMANDS
.nf
?  Print list of cursor key and colon commands
-  Subtract blended component from correlation peak
.  Do the continuum subtraction
+  Toggle status line output
a  Display the antisymmetric noise component of the correlation
b  Fix the background level for the Gaussian fit
c  Read out cursor position in pixel lag and velocity
d  Deblend multiple correlation peak
e  Preview the summary plot of the correlation
f  Fourier filtering and FFT display mode
g  Mark correlation peak lag limits and fit
I  Interrupt
j  Plot the residuals of the fit to the peak
l  Page the current logfile of results
m  Plot polymarkers of actual CCF points on the plot
n  Go to next (template --> aperture --> object)
o  Fit or refit object spectrum continuum for subtraction
p  Go to previous (template --> aperture --> object)
q  Quit task
r  Redraw
s  Examine object/template spectra and display mode
t  Fit or refit template spectrum continuum for subtraction
v  Print full correlation result in text window
w  Write current correlation results to the log file
x  Compute correlation
y  Mark correlation peak lower limit and fit
z  Expand on different correlation peak using full correlation plot

:apertures [range]               Set/Show list of apertures to process
:apnum  [aperture]               Set/Show specific aperture to process
:apodize  [fraction]             Set/Show fraction of endpts to apodize
:autowrite [y|n]                 Set/Show autowrite param
:autodraw  [y|n]                 Set/Show autodraw param
:background  [background|INDEF]  Set/Show background fitting level
:ccftype  [image|text]           Set/Show type of CCF output
:comment  [string]               Add a comment to the output logs
:continuum  [both|obj|temp|none] Set/Show which spectra to normalize
:correction shift                Convert a pixel shift to a velocity
:deltav                          Print the velocity per pixel dispersion
:disp				 Print dispersion info
:filter  [both|obj|temp|none]    Set/Show which spectra to filter
:function [gaussian|lorentzian|  Set/Show CCF peak fitting function
              center1d|parabola]
:height  [height]                Set/SHow CCF peak fit height
:imupdate  [y|n]                 Set/Show image update flag
:maxwidth  [width]               Set/Show min fitting width
:minwidth  [width]               Set/Show max fitting width
:nbang                           :Next command without a write
:next [temp|aperture|object]     Go to next correlation pair
:objects  [list]                 Set/Show object list
:osample  [range]                Set/Show object regions to correlate
:output  [fname]                 Set/Show output logfile
:<parameter> [value]             Set/Show pset parameter value
:peak  [y|n]                     Set/Show peak height flag
:pbang                           :Previous command without a write
:previous [temp|aperture|object] Go to previous correlation pair
:printz [y|n]			 Toggle output of redshift z values
:rebin [small|large|obj|temp]    Set/Show the rebin parameter
:results [file]                  Page results
:rsample  [range]                Set/Show template regions to correlate
:show                            List current parameters
:templates  [list]               Set/Show template list
:tempvel  [velocity]             Set/Show template velocity
:tnum  [temp_code]               Move to a specific temp. in the list
:unlearn                         Unlearn task parameters
:update                          Update task parameters
:version                         Show task version number
:verbose  [y|n]                  Set/Show verbose output flag
:wccf                            Write out the CCF to an image|file
:weights  [weight]               Set/Show fitting weights
:width  [width]                  Set/Show fitting width about peak
:wincenter  [center]             Set/Show peak window center
:window  [size]                  Set/Show size of window
:ymin  [correlation height]      Set/Show lower ccf plot scaling
:ymax  [correlation height]      Set/Show upper ccf plot scaling
.fi

.ce
FOURIER MODE COMMANDS
.nf
?  Print list of cursor key and colon commands
b  Display power spectra before filtering
f  Enter Fourier mode
g  Display Fourier transforms before filtering
i  Print period trend information
o  Display filtered and unfiltered object spectrum
p  Display power spectra after filtering
q  Quit
r  Redraw
s  Enter Spectrum mode
t  Display filtered and unfiltered template spectrum
x  Return to parent mode

:log_scale [y|n]              Plot on a Log scale?
:one_image [object|template]  What plot on screen
:overlay [y|n]                Overlay filt function?
:<parameter> [value]          Set/Show the FILTERPARS parameter value
:plot [object|template]       What type of plot to draw on single plot? 
:split_plot [y|n]             Make a split-plot?               
:when [before|after]          Plot before/after filter?   
:zoom [factor]                FFT zoom parameter
.fi

.ce
CONTINUUM MODE COMMANDS

See \fBicfit\fR.

.ce
SPECTRUM MODE COMMANDS
.nf
?  Print list of cursor key and colon commands
b  Select sample regions for both spectra
d  Print velocity difference between two cursor positions
f  Enter Fourier mode
i  Display original input spectra
n  Display continuum subtracted spectra
p  Display the prepared spectra prior to correlation
q  Quit
r  Redraw
s  Select sample region endpoints
u  Unselect a sample region
x  Return to correlation mode

:<parameter> [value]    Set/Show parameters in CONTINPARS pset
:osample [list]         List of object sample regions
:rsample [list]         List of template sample regions
:show                   List current parameters
.fi

.ih
EXAMPLES
.nf
    1. Cross correlate a list of 1-dimensional object spectra against
    three 1-dimensional template spectra, saving results automatically
    and not continuum subtracting or filtering the data:

	rv> fxcor.interactive = no		# Do it in batch mode
	rv> fxcor obj* temp1,temp2,temp3 autowrite+ continuum="no"
	>>> filter="no" output="results"

    2. Compute a velocity for a list of apertures in a 2-dimensional 
    multispec format object image, using only two apertures of a multispec
    image as the templates:

	cl> onedspec
	on> scopy object.ms temp apert="8,9" inform="multi" outform="oned"
	on> rv
	rv> fxcor.interactive = no		# Do it in batch mode
	rv> fxcor object.ms temp.0008,temp.0009 apertures="1-7,10,12-35"

    In this example, apertures 8 and 9 of the object image will be used 
    as the template.  The \fIscopy\fR task is used to extract the aper-
    tures to onedspec format, into two images named "temp.0008" and 
    "temp.0009".  The task is then run with all of the apertures in the 
    aperture list correlated against the onedspec templates.

    3. Compute a velocity by fitting a fixed number of points on the peak,
    using uniform weighting:

	rv> fxcor obj temp width=8 weights=0.

    4. Compute a velocity by fitting a Gaussian to the points on the CCF
    peak above the 0.1 correlation level.  Constrain the number of points
    to be less than 15, and linearly decrease the weights:

	rv> fxcor obj temp func="gaussian" width=INDEF height=0.1 
	>>> maxwidth=15 weights=1.

    5. Compute a velocity by fitting a Lorentzian to the peak, from the
    peak maximum to it's half power point:

	rv> fxcor obj temp func-"lorentz" width=INDEF height=0.5 peak+
	>>> maxwidth=15 weights=1.

    6. Process a 1-dimensional object against a 1-dimensional template
    interactively, examining the FFT, and input spectra to define a sample
    region for the correlation:

	rv> fxcor obj temp inter+ continuum="both" autowrite- output=""
	    Screen is cleared and CCF peak with fit displayed

	... to refit peak, move cursor to left side of peak and type 'g'
	... move cursor to right side of peak and hit any key

	    New fit is drawn and results displayed to the status line

	... type the 'v' key for a detailed description of the correlation

	    Graphics are suspended and the text screen shows various
	    parameters of the correlation and fit. 

	... type 'q' to get back to graphics mode

	... to examine the FFT's of the spectra, type the 'f' keystroke.

	    The screen is cleared and a split plot of the two power spectra
	    after filtering is drawn with the requested filter (if any)
	    overlayed.
	... type the 'f' keystroke
	    The screen is cleared and the absolute value of the two FFT's
	    after filtering is plotted, again with the filter overlayed.
	... type ":overlay no", followed by a 'g' keystroke
	    The spectra are redrawn prior to filtering, with no filter over-
	    lay
	... type 'q' to return to correlation mode

	    The screen is redrawn with the CCF plot and peak fit

	... type 's' to enter spectrum mode

	    The screen is cleared and the input spectra displayed
	... type 's' to mark the endpoints of sample regions for correl-
	... ation.  The user can mark either the top or bottom plot to
	... set sample regions for the object and template respectively.
	... Then type 'q' to quit this mode

	    A new correlation is computed and the peak refit automatically

	... type 'q' to quit the task, satisfied with the results
	    The user is asked whether he wants to save results
	... type 'y' or <cr> to save results
	    The user is prompted for an output file name since one wasn't
	    specified in the parameter set
	... type in a file name
	 
	    The task exits.

    7. Save the correlation function of two galaxy spectra: 

	rv> fxcor obj temp inter+ ccftype="text"
	    Screen is cleared and CCF peak with fit displayed

	... type ":wccf" to write the CCF
	... type in a filename for the text output
	... quit the task

	rv> rspectext ccf.txt ccf.fits dtype=interp
	rv> splot ccf.fits

       The velocity per-pixel-shift is non-linear and is an approximation
       which works well for low-velocity shifts.  In the case of hi-velocity
       correlations (or when there are many points) it is best to save the
       CCF as a text file where the velocity at each shift is written to
       the file,  then use RSPECTEXT to linearize and convert to an image
       format.  This avoids the task interpolating a saved image CCF in
       cases where it may not be required.

    7. Compute a cross-correlation where the template has already been
       corrected to the rest frame and no heliocentric correction is 
       required:

	  Step 1)  Use the HEDIT or HFIX tasks to add the following
		   keywords to the template image:

		        DATE-OBS= '1993-03-17T04:56:38.0'
		        RA      = '12:00:00'
		        DEC     = '12:00:00'
		        EPOCH   = 1993.0
		        OBSERVAT= 'KPNO'
		        VHELIO  = 0.0

		   These values produce a heliocentric correction of zero
		   to within 5 decimal places.  The VHELIO keyword will 
		   default to zero if not present.

	  Step 2)  Use the HEDIT task to add an OBSERVAT keyword to each
		   of the object spectra.  The OBSERVATORY task can be used
		   get a list of recognized observatories.

	Because mixing observatories is not currently well supported, the
	use of the OBSERVAT keyword in \fI both\fR images is the only sure
	way to apply the proper observatory information to each image.  Users
	may wish to derive a zero-valued heliocentric correction for their
	local observatory and use those values instead.
.fi

.ih
SEE ALSO
continpars, filtpars, observatory, keywpars, onedspec.specwcs, center1d, 
dispcor, stsdas.fourier
.endhelp
