NOTES · SEE_ALSO

## NAME

scombine -- Combine spectra

## USAGE

`scombine input output`

## PARAMETERS

- input
- List of input images containing spectra to be combined. The spectra
in the images to be combined are selected with the
*apertures*and*group*parameters. Only the primary spectrum is combined and the associated band spectra are ignored.

- output
- List of output images to be created containing the combined spectra. If the grouping option is "all" or "apertures" then only one output image will be created. In the first case the image will contain only one spectrum and in the latter case there will be a spectrum for each selected aperture. If the grouping option is "images" then there will be one output spectrum per input spectrum.

- noutput = ""
- List of output images to be created containing the number of spectra combined.
The number of images required is the same as the
*output*list. Any or all image names may be given as a null string, i.e. "", in which case no output image is created.

- logfile = "STDOUT"
- File name for recording log information about the combining operation. The file name "STDOUT" is used to write the information to the terminal. If the null string is specified then no log information is printed or recorded.

- apertures = ""
- List of apertures to be selected for combining. If none is specified then all apertures are selected. The syntax is a blank or comma separated list of aperture numbers or aperture ranges separated by a hyphen.

- group = "apertures" (all|images|apertures)
- Option for grouping input spectra for combining (after selection by aperture)
from one or more input images. The options are:
- "all"
- Combine all spectra from all images in the input list into a single output spectrum.

- "images"
- Combine all spectra in each input image into a single spectrum in separate output images.

- "apertures"
- Combine all spectra of the same aperture from all input images and put it into a single output image with the other selected apertures.

- combine = "average" (average|median|sum)
- Option for combining pixels at the same dispersion coordinate. after any rejection operation. The options are to compute the "average", "median", or "sum" of the pixels. The first two are applied after any pixel rejection. The sum option ignores the rejection and scaling parameters and no rejection is performed. In other words, the "sum" option is simply the direct summation of the pixels. The median uses the average of the two central values when the number of pixels is even.

- reject = "none" (none|minmax|ccdclip|crreject|sigclip|avsigclip|pclip)
- Type of rejection operation performed on the pixels which overlap at each
dispersion coordinate. The algorithms are discussed in the
DESCRIPTION section. The rejection choices are:
none - No rejection minmax - Reject the nlow and nhigh pixels sigclip - Reject pixels using a sigma clipping algorithm avsigclip - Reject pixels using an averaged sigma clipping algorithm ccdclip - Reject pixels using CCD noise parameters crreject - Reject only positive pixels using CCD noise parameters pclip - Reject pixels using sigma based on percentiles

- first = no
- Use the first input spectrum of each set to be combined to define the
dispersion coordinates for combining and output? If yes then all other
spectra to be combined will be interpolated to the dispersion of this
reference spectrum and that dispersion defines the dispersion of the
output spectrum. If no, then all the spectra are interpolated to a linear
dispersion as determined by the following parameters. The interpolation
type is set by the package parameter
*interp*.

- w= INDEF, w2=INDEF, dw = INDEF, nw = INDEF, log = no
- The output linear or log linear wavelength scale if the dispersion of the first spectrum is not used. INDEF values are filled in from the maximum wavelength range and minimum dispersion of the spectra to be combined. The parameters are aways specified in linear wavelength even when the log parameter is set to produce constant pixel increments in the log of the wavelength. The dispersion is interpreted in that case as the difference in the log of the endpoints divided by the number of pixel increments.

- scale = "none" (none|mode|median|mean|exposure|@<file>|!<keyword>)
- Multiplicative image scaling to be applied. The choices are none, multiply by the reciprocal of the mode , median, or mean of the specified statistics section, scale by the exposure time in the image header, multiply by the values in a specified file, or multiply by a specified image header keyword. When specified in a file the scales must be one per line in the order of the input spectra.

- zero = "none" (none|mode|median|mean|@<file>|!<keyword>)
- Additive zero level image shifts to be applied. The choices are none, add the negative of the mode, median, or mean of the specified statistics section, add the values given in a file, or add values given by an image header keyword. When specified in a file the zero values must be one per line in the order of the input spectra. File or keyword zero offset values do not allow a correction to the weights.

- weight = "none" (none|mode|median|mean|exposure|@<file>|!<keyword>)
- Weights to be applied during the final averaging. The choices are none, the mode, median, or mean of the specified statistics section, the exposure time, values given in a file, or values given by an image header keyword. When specified in a file the weights must be one per line in the order of the input spectra.

- sample = ""
- Wavelength sample regions to use in computing spectrum statistics for scaling and weighting. If no sample regions are given then the entire input spectrum is used. The syntax is colon separated wavelengths or a file containing colon separated wavelengths preceded by the @ character; i.e. @<file>.

Algorithm Parameters

- lthreshold = INDEF, hthreshold = INDEF
- Low and high thresholds to be applied to the input pixels. This is done before any scaling, rejection, and combining. If INDEF the thresholds are not used.

- nlow = 1, nhigh = (minmax)
- The number of low and high pixels to be rejected by the "minmax" algorithm. These numbers are converted to fractions of the total number of input spectra so that if no rejections have taken place the specified number of pixels are rejected while if pixels have been rejected by thresholding or nonoverlap, then the fraction of the remaining pixels, truncated to an integer, is used.

- nkeep = 1
- The minimum number of pixels to retain or the maximum number to reject when using the clipping algorithms (ccdclip, crreject, sigclip, avsigclip, or pclip). When given as a positive value this is the minimum number to keep. When given as a negative value the absolute value is the maximum number to reject. This is actually converted to a number to keep by adding it to the number of images.

- mclip = yes (ccdclip, crreject, sigclip, avsigcliip)
- Use the median as the estimate for the true intensity rather than the average with high and low values excluded in the "ccdclip", "crreject", "sigclip", and "avsigclip" algorithms? The median is a better estimator in the presence of data which one wants to reject than the average. However, computing the median is slower than the average.

- lsigma = 3., hsigma = 3. (ccdclip, crreject, sigclip, avsigclip, pclip)
- Low and high sigma clipping factors for the "ccdclip", "crreject", "sigclip", "avsigclip", and "pclip" algorithms. They multiply a "sigma" factor produced by the algorithm to select a point below and above the average or median value for rejecting pixels. The lower sigma is ignored for the "crreject" algorithm.

- rdnoise = "0.", gain = "1.", snoise = "0." (ccdclip, crreject)
- Effective CCD readout noise in electrons, gain in electrons/DN, and sensitivity noise as a fraction. These parameters are used with the "ccdclip" and "crreject" algorithms. The values may be either numeric or an image header keyword which contains the value. Note that if the spectra have been extracted from a 2D CCD image then the noise parameters must be adjusted for background and the aperture summing.

- sigscale = 0.(ccdclip, crreject, sigclip, avsigclip)
- This parameter determines when poisson corrections are made to the computation of a sigma for images with different scale factors. If all relative scales are within this value of unity and all relative zero level offsets are within this fraction of the mean then no correction is made. The idea is that if the images are all similarly though not identically scaled, the extra computations involved in making poisson corrections for variations in the sigmas can be skipped. A value of zero will apply the corrections except in the case of equal images and a large value can be used if the sigmas of pixels in the images are independent of scale and zero level.

- pclip = -0.(pclip)
- Percentile clipping algorithm parameter. If greater than one in absolute value then it specifies a number of pixels above or below the median to use for computing the clipping sigma. If less than one in absolute value then it specifies the fraction of the pixels above or below the median to use. A positive value selects a point above the median and a negative value selects a point below the median. The default of -0.5 selects approximately the quartile point. See the DESCRIPTION section for further details.

- grow = 0
- Number of pixels to either side of a rejected pixel to also be rejected. This applies only to pixels rejected by one of the rejection algorithms and not the threshold rejected pixels.

- blank = 0.
- Value to use when there are no input pixels to combine for an output pixel.

## DESCRIPTION

**Scombine**
combines input spectra by interpolating them (if necessary)
to a common dispersion sampling, rejecting pixels exceeding specified low
and high thresholds, scaling them in various ways, applying a rejection
algorithm based on known or empirical noise statistics, and computing the
sum, weighted average, or median of the remaining pixels. Note that
the "sum" option is the direct summation of the pixels and does not
perform any rejection or scaling of the data regardless of the parameter
settings.

The input spectra are specified using an image list in which each image
may contain multiple spectra. The set of spectra may be restricted
by the *aperture*
parameter to specific apertures. The set of input
spectra may then be grouped using the *group*
parameter and each
group combined separately into a final output spectrum. The grouping
options are to select all the input spectra regardless of the input
image or aperture number, select all spectra of the same aperture,
or select all the spectra from the same input image.

The output consists of either a single image with one spectrum for each combined group or, when grouping by image, an image with the single combined spectra from each input image. The output images and combined spectra inherit the header parameters from the first spectrum of the combined group. In addition to the combined spectrum an associated integer spectrum containing the number of pixels combined and logfile listing the combined spectra, scaling, weights, etc, may be produced.

The spectral combining is done using pixels at common dispersion
coordinates rather than physical or logical pixel coordinates. If the
spectra to be combined do not have identical dispersion coordinates then
the spectra are interpolated to a common dispersion sampling before
combining. The interpolation conserves pixel values rather pixel fluxes.
This means that flux calibrated data is treated correctedly and that
spectra in counts are not corrected in the interpolation for changes
in pixel widths.
The default interpolation function is a 5th order polynomial. The
choice of interpolation type is made with the package parameter "interp".
It may be set to "nearest", "linear", "spline3", "poly5", or "sinc".
Remember that this applies to all tasks which might need to interpolate
spectra in the **onedspec**
and associated packages. For a discussion of
interpolation types see **onedspec**
.

There are two choices for the common dispersion coordinate sampling. If the
*first*
parameter is set then the dispersion sampling of the first
spectrum is used. This dispersion system may be nonlinear. If the
parameter is not set then the user specified linear or log linear
dispersion system is used. Any combination of starting wavelength, ending
wavelength, wavelength per pixel, and number of output pixels may be
specified. Unspecified values will default to reasonable values based on
the minimum or maximum wavelengths of all spectra, the minimum dispersion,
and the number of pixels needed to satisfy the other parameters. If the
parameters overspecify the linear system then the ending wavelength is
adjusted based on the other parameters. Note that for a log linear system
the wavelengths are still specified in nonlog units and the dispersion is
finally recalculated using the difference of the log wavelength endpoints
divided by the number pixel intervals (the number of pixels minus one).

There are several stages to combining a selected group of spectra. The first is interpolation to a common dispersion sampling as discussed above. The second stage is to eliminate any pixels outside the specified thresholds. Note that the thresholds apply to the interpolated spectra. Scaling and zero offset factors are computed and applied to the spectra if desire. The computation of these factors as well as weights is discussed in the following section. Next there is a choice of rejection algorithms to identify and eliminate deviant pixels. Some of these are based on order statistics and some relative to the distance from an initial median or average using a noise model cutoff. A growing factor may be applied to neighbors of rejected pixels to reject additional pixels. The various algorithms are described in detail in a following section. Finally, the remaining pixels are combined by summing (which may not be appropriate when pixels are rejected), computing a median, or computing a weighted or unweighted average. The combined spectrum is written to an output image as well the number of pixels used in the final combining.

SCALES AND WEIGHTS

In order to combine spectra with rejection of pixels based on deviations
from some average or median they must be scaled to a common level. There
are two types of scaling available, a multiplicative intensity scale and an
additive zero point shift. The intensity scaling is defined by the
*scale*
parameter and the zero point shift by the *zero*
parameter. These parameters may take the values "none" for no scaling,
"mode", "median", or "mean" to scale by statistics of the spectrum pixels,
"exposure" (for intensity scaling only) to scale by the exposure time
keyword in the image header, any other image header keyword specified by
the keyword name prefixed by the character `!`, and the name of a file
containing the scale factors for the input image prefixed by the
character `@`.

Examples of the possible parameter values are shown below where "myval" is the name of an image header keyword and "scales.dat" is a text file containing a list of scale factors.

scale = none No scaling zero = mean Intensity offset by the mean scale = exposure Scale by the exposure time zero = !myval Intensity offset by an image keyword scale = @scales.dat Scales specified in a file

The spectrum statistics factors are computed within specified sample
regions given as a series of colon separated wavelengths. If no
regions are specified then all pixels are used. If the
wavelength sample list is too long the regions can be defined in a file and
specified in the *sample*
parameter using the syntax @<file> where file
is the filename.

The statistics are as indicated by their names. In particular, the mode is a true mode using a bin size which is a fraction of the range of the pixels and is not based on a relationship between the mode, median, and mean. Also thresholded pixels are excluded from the computations as well as during the rejection and combining operations.

The "exposure" option in the intensity scaling uses the value of the image header keyword (EXPTIME, EXPOSURE, or ITIME). Note that the exposure keyword is also updated in the final image as the weighted average of the input values. If one wants to use a nonexposure time keyword and keep the exposure time updating feature the image header keyword syntax is available; i.e. !<keyword>.

Scaling values may be defined as a list of values in a text file. The file name is specified by the standard @file syntax. The list consists of one value per line. The order of the list is assumed to be the same as the order of the input spectra. It is a fatal error if the list is incomplete and a warning if the list appears longer than the number of input spectra. Consideration of the grouping parameter must be included in generating this list since spectra may come from different images, some apertures may be missing, and, when there are multiple output spectra or images, the same list will be repeatedly used.

If both an intensity scaling and zero point shift are selected the multiplicative scaling is done first. Use of both makes sense for images if the intensity scaling is the exposure time to correct for different exposure times and with the zero point shift allowing for sky brightness changes. This is less relevant for spectra but the option is available.

The spectrum statistics and scale factors are recorded in the log file unless they are all equal, which is equivalent to no scaling. The intensity scale factors are normalized to a unit mean and the zero point shifts are adjusted to a zero mean. When scal factors or zero point shifts are specified by the user in an @file or by an image header keyword, no normalization is done.

Scaling affects not only the mean values between spectra but also the relative pixel uncertainties. For example scaling an spectrum by a factor of 0.5 will reduce the effective noise sigma of the spectrum at each pixel by the square root of 0.5. Changes in the zero point also changes the noise sigma if the spectrum noise characteristics are Poissonian. In the various rejection algorithms based on identifying a noise sigma and clipping large deviations relative to the scaled median or mean, one may need to account for the scaling induced changes in the spectrum noise characteristics.

In those algorithms it is possible to eliminate the "sigma correction"
while still using scaling. The reasons this might be desirable are 1) if
the scalings are similar the corrections in computing the mean or median
are important but the sigma corrections may not be important and 2) the
spectrum statistics may not be Poissonian, either inherently or because the
spectra have been processed in some way that changes the statistics. In the
first case because computing square roots and making corrections to every
pixel during the iterative rejection operation may be a significant
computational speed limit the parameter *sigscale*
selects how
dissimilar the scalings must be to require the sigma corrections. This
parameter is a fractional deviation which, since the scale factors are
normalized to unity, is the actual minimum deviation in the scale factors.
For the zero point shifts the shifts are normalized by the mean shift
before adjusting the shifts to a zero mean. To always use sigma scaling
corrections the parameter is set to zero and to eliminate the correction in
all cases it is set to a very large number.

If the final combining operation is "average" then the spectra may be weighted during the averaging. The weights are specified in the same way as the scale factors. The weights, scaled to a unit sum, are printed in the log output.

The weights are only used for the final weighted average and sigma image output. They are not used to form averages in the various rejection algorithms. For weights in the case of no scaling or only multiplicative scaling the weights are used as given or determined so that images with lower signal levels will have lower weights. However, for cases in which zero level scaling is used the weights are computed from the initial weights (the exposure time, image statistics, or input values) using the formula:

weight_final = weight_initial / (scale * zero)

where the zero values are those before adjustment to zero mean over all images. The reasoning is that if the zero level is high the sky brightness is high and so the S/N is lower and the weight should be lower.

THRESHOLD REJECTION

There is an initial threshold rejection step which may be applied. The
thresholds are given by the parameters *lthreshold*
and
*hthreshold*
. Values of INDEF mean that no threshold value is
applied. Threshold rejection may be used to exclude very bad pixel values
or as a way of masking images. The former case is useful to exclude very
bright cosmic rays. Some of the rejection algorithms, such as "avsigclip",
can perform poorly if very strong cosmic rays are present. For masking one
can use a task like **imedit**
or **imreplace**
to set parts of the
spectra to be excluded to some very low or high magic value.

REJECTION ALGORITHMS

The *reject*
parameter selects a type of rejection operation to
be applied to pixels not thresholded. If no rejection
operation is desired the value "none" is specified. This task is
closely related to the image combining task **imcombine**
and, in
particular, has the same rejection algorithms.
Some the algorithms are more appropriate to images but are available
in this task also for completeness.

MINMAX

A specified fraction of the highest and lowest pixels are rejected. The fraction is specified as the number of high and low pixels, theCCDCLIPnhighandnlowparameters, when data from all the input spectra are used. If pixels are missing where there is no overlap or have been rejected by thresholding then a matching fraction of the remaining pixels, truncated to an integer, are used. Thus,

nl = n * nlow/nspectra + 0.001 nh = n * nhigh/nspectra + 0.001where n is the number of pixels to be combined, nspectra is the number of input spectra, nlow and nhigh are task parameters and nl and nh are the final number of low and high pixels rejected by the algorithm. The factor of 0.001 is to adjust for rounding of the ratio.

As an example with 10 input spectra and specifying one low and two high pixels to be rejected the fractions to be rejected are 0.1 and 0.2 and the number rejected as a function of n is:

n 0 1 2 3 4 5 6 7 8 9 10 nl 0 0 0 0 0 1 1 1 1 1 2 nh 0 0 0 0 0 0 0 0 0 0 1

If the noise characteristics of the spectra can be described by fixed gaussian noise, a poissonian noise which scales with the square root of the intensity, and a sensitivity noise which scales with the intensity, the sigma in data values at a pixel with true value <I>, as approximated by the median or average with the lowest and highest value excluded, is given as:CRREJECT

sigma = ((rn / g) ** 2 + <I> / g + (s * <I>) ** 2) ** 1/2where rn is the read out noise in electrons, g is the gain in electrons per data value, s is a sensitivity noise given as a fraction, and ** is the exponentiation operator. Often the sensitivity noise, due to uncertainties in the pixel sensitivities (for example from the flat field), is not known in which case a value of zero can be used.

This model is typically valid for CCD images. During extraction of spectra from CCD images the noise parameters of the spectrum pixels will be changed from those of the CCD pixels. Currently it is up to the user to determine the proper modifications of the CCD read noise gain, and sensitivity noise.

The read out noise is specified by the

rdnoiseparameter. The value may be a numeric value to be applied to all the input spectra or an image header keyword containing the value for spectra from each image. Similarly, the parametergainspecifies the gain as either a value or image header keyword and the parametersnoisespecifies the sensitivity noise parameter as either a value or image header keyword.The algorithm operates on each output pixel independently. It starts by taking the median or unweighted average (excluding the minimum and maximum) of the unrejected pixels provided there are at least two input pixels. The expected sigma is computed from the CCD noise parameters and pixels more that

lsigmatimes this sigma below orhsigmatimes this sigma above the median or average are rejected. The process is then iterated until no further pixels are rejected. If the average is used as the estimator of the true value then after the first round of rejections the highest and lowest values are no longer excluded. Note that it is possible to reject all pixels if the average is used and is sufficiently skewed by bad pixels such as cosmic rays.If there are different CCD noise parameters for the input images (as might occur using the image header keyword specification) then the sigmas are computed for each pixel from each image using the same estimated true value.

If the images are scaled and shifted and the

sigscalethreshold is exceeded then a sigma is computed for each pixel based on the spectrum scale parameters; i.e. the median or average is scaled to that of the original image before computing the sigma and residuals.After rejection the number of retained pixels is checked against the

nkeepparameter. If there are fewer pixels retained than specified by this parameter the pixels with the smallest residuals in absolute value are added back. If there is more than one pixel with the same absolute residual (for example the two pixels about an average or median of two will have the same residuals) they are all added back even if this means more thannkeeppixels are retained. Note that thenkeepparameter only applies to the pixels used by the clipping rejection algorithm and does not apply to threshold or bad pixel mask rejection.This is the best clipping algorithm to use if the CCD noise parameters are adequately known. The parameters affecting this algorithm are

rejectto select this algorithm,mclipto select the median or average for the center of the clipping,nkeepto limit the number of pixels rejected, the CCD noise parametersrdnoise, gainandsnoise,lsigmaandhsigmato select the clipping thresholds, andsigscaleto set the threshold for making corrections to the sigma calculation for different image scale factors.

This algorithm is identical to "ccdclip" except that only pixels above the average are rejected based on theSIGCLIPhsigmaparameter. This is appropriate for rejecting cosmic ray events and works even with two spectra.

The sigma clipping algorithm computes at each output pixel the median or average excluding the high and low values and the sigma about this estimate. There must be at least three input pixels, though for this method to work well there should be at least 10 pixels. Values deviating by more than the specified sigma threshold factors are rejected. These steps are repeated, except that after the first time the average includes all values, until no further pixels are rejected or there are fewer than three pixels.AVSIGCLIPAfter rejection the number of retained pixels is checked against the

nkeepparameter. If there are fewer pixels retained than specified by this parameter the pixels with the smallest residuals in absolute value are added back. If there is more than one pixel with the same absolute residual (for example the two pixels about an average or median of two will have the same residuals) they are all added back even if this means more thannkeeppixels are retained. Note that thenkeepparameter only applies to the pixels used by the clipping rejection algorithm and does not apply to threshold rejection.The parameters affecting this algorithm are

rejectto select this algorithm,mclipto select the median or average for the center of the clipping,nkeepto limit the number of pixels rejected,lsigmaandhsigmato select the clipping thresholds, andsigscaleto set the threshold for making corrections to the sigma calculation for different spectrum scale factors.

The averaged sigma clipping algorithm assumes that the sigma about the median or mean (average excluding the low and high values) is proportional to the square root of the median or mean at each point. This is described by the equation:PCLIP

sigma(column,line) = sqrt (gain(line) * signal(column,line))where the

estimatedsignal is the mean or median (hopefully excluding any bad pixels) and the gain is theestimatedproportionality constant having units of photons/data number.This noise model is valid for spectra whose values are proportional to the number of photons recorded. In effect this algorithm estimates a photon per data value gain for each spectrum. The gain proportionality factor is computed independently for each output spectrum by averaging the square of the residuals (at points having three or more input values) scaled by the median or mean.

Once the proportionality factor is determined, deviant pixels exceeding the specified thresholds are rejected at each point by estimating the sigma from the median or mean. If any values are rejected the median or mean (this time not excluding the extreme values) is recomputed and further values rejected. This is repeated until there are no further pixels rejected or the number of remaining input values falls below three. Note that the proportionality factor is not recomputed after rejections.

If the spectra are scaled differently and the sigma scaling correction threshold is exceeded then a correction is made in the sigma calculations for these differences, again under the assumption that the noise in an spectra scales as the square root of the mean intensity.

After rejection the number of retained pixels is checked against the

nkeepparameter. If there are fewer pixels retained than specified by this parameter the pixels with the smallest residuals in absolute value are added back. If there is more than one pixel with the same absolute residual (for example the two pixels about an average or median of two will have the same residuals) they are all added back even if this means more thannkeeppixels are retained. Note that thenkeepparameter only applies to the pixels used by the clipping rejection algorithm and does not apply to threshold rejection.This algorithm works well for even a few input spectra. It works better if the median is used though this is slower than using the average. Note that if the spectra have a known read out noise and gain (the proportionality factor above) then the "ccdclip" algorithm is superior. However, currently the CCD noise characteristics are not well propagated during extraction so this empirical algorithm is the one most likely to be useful. The two algorithms are related in that the average sigma proportionality factor is an estimate of the gain.

The parameters affecting this algorithm are

rejectto select this algorithm,mclipto select the median or average for the center of the clipping,nkeepto limit the number of pixels rejected,lsigmaandhsigmato select the clipping thresholds, andsigscaleto set the threshold for making corrections to the sigma calculation for different image scale factors.

The percentile clipping algorithm is similar to sigma clipping using the median as the center of the distribution except that, instead of computing the sigma of the pixels from the CCD noise parameters or from the data values, the width of the distribution is characterized by the difference between the median value and a specified "percentile" pixel value. This width is then multipled by the scale factorsGROW REJECTIONlsigmaandhsigmato define the clipping thresholds above and below the median. The clipping is not iterated.The pixel values at each output point are ordered in magnitude and the median is determined. In the case of an even number of pixels the average of the two middle values is used as the median value and the lower or upper of the two is the median pixel when counting from the median pixel to selecting the percentile pixel. The parameter

pclipselects the percentile pixel as the number (if the absolute value is greater than unity) or fraction of the pixels from the median in the ordered set. The direction of the percentile pixel from the median is set by the sign of thepclipparameter with a negative value signifying pixels with values less than the median. Fractional values are internally converted to the appropriate number of pixels for the number of input spectra. A minimum of one pixel and a maximum corresponding to the extreme pixels from the median are enforced. The value used is reported in the log output. Note that the same percentile pixel is used even if pixels have been rejected by nonoverlap or thresholding; for example, if the 3nd pixel below the median is specified then the 3rd pixel will be used whether there are 10 pixels or 5 pixels remaining after the preliminary steps.After rejection the number of retained pixels is checked against the

nkeepparameter. If there are fewer pixels retained than specified by this parameter the pixels with the smallest residuals in absolute value are added back. If there is more than one pixel with the same absolute residual (for example the two pixels about an average or median of two will have the same residuals) they are all added back even if this means more thannkeeppixels are retained. Note that thenkeepparameter only applies to the pixels used by the clipping rejection algorithm and does not apply to threshold or bad pixel mask rejection.Some examples help clarify the definition of the percentile pixel. In the examples assume 10 pixels. The median is then the average of the 5th and 6th pixels. A

pclipvalue of 2 selects the 2nd pixel above the median (6th) pixel which is the 8th pixel. Apclipvalue of -0.5 selects the point halfway between the median and the lowest pixel. In this case there are 4 pixels below the median, half of that is 2 pixels which makes the percentile pixel the 3rd pixel.The percentile clipping algorithm is most useful for clipping small excursions, such as the wings of bright lines when combining disregistered observations, that are missed when using the pixel values to compute a sigma. It is not as powerful, however, as using the CCD noise parameters (provided they are accurately known) to clip about the median. This algorithm is primarily used with direct images but remains available for spectra.

The parameters affecting this algorithm are

rejectto select this algorithm,pclipto select the percentile pixel,nkeepto limit the number of pixels rejected, andlsigmaandhsigmato select the clipping thresholds.

Neighbors of pixels rejected by the rejection algorithms
may also be rejected. The number of neighbors to be rejected on either
side is specified by the *grow*
parameter.

This rejection step is also checked against the *nkeep*
parameter
and only as many pixels as would not violate this parameter are
rejected. Unlike it's application in the rejection algorithms at
this stage there is no checking on the magnitude of the residuals
and the pixels retained which would otherwise be rejected are randomly
selected.

COMBINING

After all the steps of offsetting the input images, masking pixels, threshold rejection, scaling, and applying a rejection algorithms the remaining pixels are combined and output. The pixels may be combined by computing the median or by computing a weighted average.

## EXAMPLES

1. Combine orders of echelle images.

cl> scombine *.ec *%.ec%% group=images combine=sum

2. Combine all spectra using range syntax and scale by the exposure times.

cl> names irs 10-42 > irs.dat cl> scombine @irs.dat irscombine group=all scale=exptime

3. Combine spectra by apertures using exposure time scaling and weighting.

cl> scombine *.ms combine.ms nout=ncombine.ms \\ >>> group=apertures scale=exptime weights=exptime

## REVISIONS

- SCOMBINE V2.10.3
- The weighting was changed from using the square root of the exposure time
or spectrum statistics to using the values directly. This corresponds
to variance weighting. Other options for specifying the scaling and
weighting factors were added; namely from a file or from a different
image header keyword. The
*nkeep*parameter was added to allow controling the maximum number of pixels to be rejected by the clipping algorithms. The*snoise*parameter was added to include a sensitivity or scale noise component to the noise model.

- SCOMBINE V2.10
- This task is new.

## NOTES

The pixel uncertainties and CCD noise model are not well propagated. In particular it would be desirable to propagate the pixel uncertainties and CCD noise parameters from the initial CCD images.

## SEE ALSO

imcombine, odcombine, lscombine