IRAF help page for package noao.imred.echelle, program dofoe

Aperture Definitions

The first operation is to define the extraction apertures, which include the aperture width, background regions, and position dependence with wavelength, for the object and arc orders of interest. This is done on a reference spectrum which is usually a flat field taken through both fibers. Other spectra will inherit the reference apertures and apply a correction for any shift of the orders across the dispersion. The reference apertures are defined only once unless the redo option is set.

The selected number of orders are found automatically by selecting the highest peaks in a cut across the dispersion. Note that the specified number of orders is multiplied by two in defining the apertures. Apertures are assigned with a limits set by the lower and upper parameter and numbered sequentially. A query is then given allowing the aperture limits to be "resized" based on the profile itself (see apresize).

A cut across the orders is then shown with the apertures marked and an interactive aperture editing mode is entered (see apedit). For dofoe the aperture identifications and numbering is particularly critical. All "pairs" of object and arc orders in the region of interest must be defined without skipping any orders. The orders must also be numbered sequentially (though the direction does not matter) so that the arc apertures are either all even or all odd as defined by the arcaps parameter (the default is even numbers for the arc apertures). The 'o' key will provide the necessary reordering. If local background subtraction is used the background regions should also be checked with the 'b' key. Typically one adjusts all the background regions at the same time by selecting all apertures with the 'a' key first. To exit the background and aperture editing steps type 'q'.

Next the positions of the orders at various points along the dispersion are measured and "trace functions" are fit. The user is asked whether to fit each trace function interactively. This is selected to adjust the fitting parameters such as function type and order. When interactively fitting a query is given for each aperture. After the first aperture one may skip reviewing the other traces by responding with "NO". Queries made by dofoe generally may be answered with either lower case "yes" or "no" or with upper case "YES" or "NO". The upper case responses apply to all further queries and so are used to eliminate further queries of that kind.

The above steps are all performed using tasks from the apextract package and parameters from the params parameters. As a quick summary, the dispersion direction of the spectra are determined from the package dispaxis parameter if not defined in the image header. The default line or column for finding the orders and the number of image lines or columns to sum are set by the line and nsum parameters. A line of INDEF (the default) selects the middle of the image. The automatic finding algorithm is described for the task apfind and basically finds the strongest peaks. The resizing is described in the task apresize and the parameters used are also described there and identified in the PARAMETERS section. The tracing is done as described in aptrace and consists of stepping along the image using the specified t_step parameter. The function fitting uses the icfit commands with the other parameters from the tracing section.

Background or Scattered Light Subtraction

In addition to not subtracting any background scattered light there are two approaches to subtracting this light. The first is to determine a smooth global scattered light component. The second is to subtract a locally determined background at each point along the dispersion and for each aperture. Note that background subtraction is only done for object images and not for arc images.

The global scattered light fitting and subtraction is done with the task apscatter. The function fitting parameters are set interactively using the aperture reference spectrum. All other subtractions are done noninteractively with the same set of parameters. The scattered light is subtracted from the input images, thus modifying them, and one might wish to first make backups of the original images.

The scattered light is measured between the apertures using a specified buffer distance from the aperture edges. The scattered light pixels are fit by a series of one dimensional functions across the dispersion. The independent fits are then smoothed along the dispersion by again fitting low order functions. These fits then define the smooth scattered light surface to be subtracted from the image. The fitting parameters are defined and recorded in the two parameter sets apscat1 and apscat2. The scattered light algorithm is described more fully in apscatter. This algorithm is relatively slow.

Local background subtraction is done during extraction based on background regions and parameters defined by the default background parameters or changed during interactive review of the apertures. The background subtraction options are to subtract the average, median, or minimum of the pixels in the background regions, or to fit a function and subtract the function from under the extracted object pixels. The background regions are specified in pixels from the aperture center and follow changes in center of the spectrum along the dispersion. The syntax is colon separated ranges with multiple ranges separated by a comma or space. The background fitting uses the icfit routines which include medians, iterative rejection of deviant points, and a choice of function types and orders. Note that it is important to use a method which rejects cosmic rays such as using either medians over all the background regions (background = "median") or median samples during fitting (b_naverage < -1). The background smoothing parameter b_smooth is may be used to provide some additional local smoothing of the background light. The background subtraction algorithm and options are described in greater detail in apsum and apbackground.

Extraction

The actual extraction of the spectra is done by summing across the fixed width apertures at each point along the dispersion. The default is to simply sum the pixels using partial pixels at the ends. There is an option to weight the sum based on a Poisson noise model using the readnoise and gain detector parameters. Note that if the clean option is selected the variance weighted extraction is used regardless of the weights parameter. The sigma threshold for cleaning are also set in the params parameters.

The cleaning and variance weighting options require knowing the effective (i.e. accounting for any image combining) read out noise and gain. These numbers need to be adjusted if the image has been processed such that the intensity scale has a different origin (such as a scattered light subtraction) or scaling (such as caused by unnormalized flat fielding). These options also require using background subtraction if the profile does not go to zero. For optimal extraction and cleaning to work it is recommended that any scattered light be accounted for by local background subtraction rather than with the scattered light subtraction and the fitflat option be used. The b_smooth parameter is also appropriate in this application and improves the optimal extraction results by reducing noise in the background signal. For further discussion of cleaning and variance weighted extraction see apvariance and approfiles as well as apsum.

Flat Field Correction

Flat field corrections may be made during the basic CCD processing; i.e. direct division by the two dimensional flat field observation. In that case do not specify a flat field spectrum; use the null string "". The dofoe task provides an alternative flat field response correction based on division of the extracted object spectra by the extracted flat field spectra. A discussion of the theory and merits of flat fielding directly verses using the extracted spectra will not be made here. The dofoe flat fielding algorithm is the recommended method for flat fielding since it works well and is not subject to the many problems involved in two dimensional flat fielding.

The first step is extraction of the flat field spectrum, if one is specified, using the reference apertures. Only one flat field is allowed so if multiple flat fields are required the data must be reduced in groups. When the fitflat option is selected (the default) the extracted flat field spectra are fit by smooth functions and the ratio of the flat field spectra to the smooth functions define the response spectra. The default fitting function and order are given by the parameters f_function and f_order. If the parameter f_interactive is "yes" then the fitting is done interactively using the fit1d task which uses the icfit interactive fitting commands.

If the fitflat option is not selected the extracted and globally normalized flat field spectra are directly divided in the object spectra. This removes the blaze function, thus altering the data counts, and introduces the reciprocal of the flat field spectrum in the object spectra.

The final step is to normalize the flat field spectra by the mean counts over all the fibers. This normalization step is simply to preserve the average counts of the extracted object and arc spectra after division by the response spectra.

Dispersion Correction

If dispersion correction is not selected, dispcor=no, then the object spectra are simply extracted. If it is selected the arc spectra are used to dispersion calibrate the object spectra. There are four steps involved; determining the dispersion functions relating pixel position to wavelength, assigning the appropriate dispersion function to a particular observation, determining a zero point wavelength shift from the arc fiber to be applied to the object fiber dispersion function, and either storing the nonlinear dispersion function in the image headers or resampling the spectra to evenly spaced pixels in wavelength.

The first arc spectrum in the arc list is used to define the reference dispersion solution. It is extracted using the reference aperture definitions. Note extractions of arc spectra are not background or scattered light subtracted. The interactive task ecidentify is used to define the dispersion function in one fiber. The idea is to mark some lines in a few orders whose wavelengths are known (with the line list used to supply additional lines after the first few identifications define the approximate wavelengths) and to fit a function giving the wavelength from the aperture number and pixel position. The dispersion function for the second fiber is then determined automatically by reference to the first fiber using the task ecreidentify.

The arc dispersion function parameters are for ecidentify and it's related partner ecreidentify. The parameters define a line list for use in automatically assigning wavelengths to arc lines, a centering width (which should match the line widths at the base of the lines), the dispersion function type and orders, parameters to exclude bad lines from function fits, and defining whether to refit the dispersion function as opposed to simply determining a zero point shift. The defaults should generally be adequate and the dispersion function fitting parameters may be altered interactively. One should consult the help for the two tasks for additional details of these parameters and the interactive operation of ecidentify.

Once the reference dispersion functions are defined other arc spectra are extracted as they are assign to the object spectra. The assignment of arcs is done either explicitly with an arc assignment table (parameter arctable) or based on a header parameter such as a time. The assignments are made by the task refspectra. When two arcs are assigned to an object spectrum an interpolation is done between the two dispersion functions. This makes an approximate correction for steady drifts in the dispersion. Because the arc fiber monitors any zero point shifts in the dispersion functions it is probably only necessary to have one or two arc spectra, one at the beginning and/or one at the end of the night.

The tasks setjd and setairmass are automatically run on all spectra. This computes and adds the header parameters for the Julian date (JD), the local Julian day number (LJD), the universal time (UTMIDDLE), and the air mass at the middle of the exposure. The default arc assignment is to use the Julian date grouped by the local Julian day number. The grouping allows multiple nights of data to be correctly assigned at the same time.

Defining the dispersion function for a new arc extraction is done with the task ecreidentify. This is done noninteractively with log information recorded about the line reidentifications and the fit.

From the one or two arc spectra come two full dispersion function, one for the object fiber and one for the arc fiber. When an object spectrum is extracted so is the simultaneous arc spectrum. A zero point shift of the arc spectrum relative to the dispersion solution of the dual arc observation is computed using ecreidentify (refit=no). This zero point shift is assumed to be the same for the object fiber and it is added to the dispersion function of the dual arc observation for the object fiber. Note that this does not assume that the object and arc fiber dispersion functions are the same or have the same wavelength origin, but only that the same shift in wavelength zero point applies to both fibers. Once the dispersion function correction is determined from the extracted arc fiber spectrum it is deleted leaving only the object spectrum.

The last step of dispersion correction is setting the dispersion of the object spectrum. There are two choices here. If the linearize parameter is not set the nonlinear dispersion function is stored in the image header. Other IRAF tasks interpret this information when dispersion coordinates are needed for plotting or analysis. This has the advantage of not requiring the spectra to be interpolated and the disadvantage that the dispersion information is only understood by IRAF tasks and cannot be readily exported to other analysis software.

If the linearize parameter is set then the spectra are resampled to a linear dispersion relation either in wavelength or the log of the wavelength. For echelle spectra each order is linearized independently so that the wavelength interval per pixel is different in different orders. This preserves most of the resolution and avoids over or under sampling of the highest or lowest dispersion orders. The wavelength limits are taken from the limits determined from the arc reference spectrum and the number of pixels is the same as the original images. The dispersion per pixel is then derived from these constraints.

The linearization algorithm parameters allow selecting the interpolation function type, whether to conserve flux per pixel by integrating across the extent of the final pixel, and whether to linearize to equal linear or logarithmic intervals. The latter may be appropriate for radial velocity studies. The default is to use a fifth order polynomial for interpolation, to conserve flux, and to not use logarithmic wavelength bins. These parameters are described fully in the help for the task dispcor which performs the correction.

1. The following example uses artificial data and may be executed at the terminal (with IRAF V2.10). This is also the sequence performed by the test procedure "demos dofoe". Because the images are small the dispersion solution is somewhat simplistic.

ec> demos mkdofoe
Creating image demoobj ...
Creating image demoflat ...
Creating image demoarc ...
ec> echelle.verbose = yes
ec> dofoe demoobj apref=demoflat flat=demoflat arcs=demoarc 
>>> norders=3 width=5.
Set reference apertures for demoflat
Searching aperture database ...
Finding apertures ...
Mar  4  9:39: FIND - 6 apertures found for demoflat
Resize apertures for demoflat?  (yes):
Resizing apertures ...
Mar  4  9:39: RESIZE - 6 apertures resized for demoflat

Fit traced positions for demoflat interactively?  (yes):
Tracing apertures ...
Fit curve to aperture 1 of demoflat interactively  (yes):

Fit curve to aperture 2 of demoflat interactively  (yes): N
Mar  4  9:39: TRACE - 6 apertures traced in demoflat.
Mar  4  9:39: DATABASE - 6 apertures for demoflat written to database
Create response function demoflatnorm.ec
Extract flat field demoflat
Searching aperture database ...
Mar  4  9:39: DATABASE  - 6 apertures read for demoflat from database
Extracting apertures ...
Mar  4  9:39: EXTRACT - Aperture 1 from demoflat --> demoflat.ec
Mar  4  9:39: EXTRACT - Aperture 2 from demoflat --> demoflat.ec
Mar  4  9:39: EXTRACT - Aperture 3 from demoflat --> demoflat.ec
Mar  4  9:39: EXTRACT - Aperture 4 from demoflat --> demoflat.ec
Mar  4  9:39: EXTRACT - Aperture 5 from demoflat --> demoflat.ec
Mar  4  9:40: EXTRACT - Aperture 6 from demoflat --> demoflat.ec
Fit and ratio flat field demoflat
Create the normalized response demoflatnorm.ec
demoflatnorm.ec -> demoflatnorm.ec  using bzero: 0.  and bscale: 1.
    mean: 1.  median: 0.9990048  mode: 0.9876572
    upper: INDEF  lower: INDEF
Extract arc reference image demoarc
Mar  4  9:40: DATABASE  - 6 apertures read for demoflat from database
Mar  4  9:40: DATABASE - 6 apertures for demoarc written to database
Mar  4  9:40: EXTRACT - Aperture 1 from demoarc --> demoarc.ec
Mar  4  9:40: EXTRACT - Aperture 2 from demoarc --> demoarc.ec
Mar  4  9:40: EXTRACT - Aperture 3 from demoarc --> demoarc.ec
Mar  4  9:40: EXTRACT - Aperture 4 from demoarc --> demoarc.ec
Mar  4  9:40: EXTRACT - Aperture 5 from demoarc --> demoarc.ec
Mar  4  9:40: EXTRACT - Aperture 6 from demoarc --> demoarc.ec
Determine dispersion solution for demoarc
 demoobj.ec
Mar  4  9:54: EXTRACT - Aperture 2 from demoobj --> demoobj.ec
Mar  4  9:54: EXTRACT - Aperture 3 from demoobj --> demoobj.ec
Mar  4  9:54: EXTRACT - Aperture 4 from demoobj --> demoobj.ec
Mar  4  9:54: EXTRACT - Aperture 5 from demoobj --> demoobj.ec
Mar  4  9:54: EXTRACT - Aperture 6 from demoobj --> demoobj.ec
Assign arc spectra for demoobj
[demoobj] refspec1='demoarc'
Reidentify arc fibers in demoobj with respect to demoarc
ECREIDENTIFY: NOAO/IRAF V2.10BETA valdes@puppis Wed 09:54:28 04-Mar-92
  Reference image = demoarcarc.ec, Refit = no
   Image    Found     Fit Pix Shift  User Shift  Z Shift      RMS
  d...ec    8/8     8/8       0.119       0.566  1.69E-6  0.00834
Dispersion correct demoobj
d...ec.imh: ap = 1, w1 = 4959.1, w2 = 4978.5, dw = 0.076, nw = 256
d...ec.imh: ap = 2, w1 = 5003.4, w2 = 5022.1, dw = 0.073, nw = 256
d...ec.imh: ap = 3, w1 = 5049.0, w2 = 5067.0, dw = 0.070, nw = 256