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diff --git a/noao/twodspec/longslit/doc/lslit.ms b/noao/twodspec/longslit/doc/lslit.ms new file mode 100644 index 00000000..de35424f --- /dev/null +++ b/noao/twodspec/longslit/doc/lslit.ms @@ -0,0 +1,712 @@ +.nr PS 9 +.nr VS 10 +.ps 9 +.vs 10 +.po 0.50i +.nr PO 0.50i +.ll 7.0i +.nr LL 7.0i +.nr PD 1v +.EQ +delim $$ +.EN +.TL +Reduction of long slit spectra with IRAF +.AU +Francisco Valdes +.AI +IRAF Group, Central Computer Services, National Optical Astronomy Observatories +P.O. Box 26732, Tucson, Arizona, 85726 +March 1986 +.AB +Tools for the reduction of long slit spectra within the Interactive +Data Reduction and Analysis Facility (IRAF) at the National Optical +Astronomy Observatory (NOAO) are described. The user interface +(commands and special features) and the algorithms are discussed. +Application of the reduction package to multi-slit images is briefly +outlined. The author developed and supports the package at NOAO. +.AE +.LP + +.ce +\fB1. Introduction\fR +.PP +This paper describes the tools currently available within the Interactive Data +Reduction and Analysis Facility (IRAF) at the National Optical +Astronomy Observatories (NOAO) for the reduction of long slit spectra. +The reduction tools, called tasks, are organized as an IRAF package +called \fBlongslit\fR. The tasks in the package are summarized below. + +.TS +center; +n n. +apdefine \&- Define apertures for 1D aperture extraction identify \&- Identify features +apextract \&- Extract 1D aperture spectra illumination \&- Determine illumination calibration +background \&- Fit and subtract a line or column background reidentify \&- Reidentify features +extinction \&- Apply atmospheric extinction corrections to images response \&- Determine response calibration +fitcoords \&- Fit user coordinates to image coordinates setimhdr \&- Set longslit image header parameters +fluxcalib \&- Apply flux calibration to images transform \&- Transform longslit images to user coordinates +.TE + +.PP +Since there are many types of long slit spectra, detectors, and +astronomical goals we do not describe a reduction procedure or path. +Reduction manuals giving cookbook instructions for the reduction of +certain types of data at NOAO are available from the Central Computer +Services Division. Instead, each task is discussed separately. The +primary emphasis is on the algorithms. +.PP +The following terminology is used in this paper. A \fIlong slit +spectrum\fR is a two dimensional image. The two image axes are +called \fIaxis 1\fR and \fIaxis 2\fR and the pixel coordinates are +given in terms of \fIcolumns\fR and \fIlines\fR. The long slit +axes are called the \fIdispersion axis\fR and the \fIslit +axis\fR. The reduction tasks do not require a particular orientation +of the dispersion and slit axes, however, these axes should be +fairly closely aligned with the image axes. \fBIn the remainder of +this paper the slit axis will correspond to image axis 1 and +the dispersion axis with image axis 2\fR. +.PP +There are five types of operations performed by the tasks in the +\fBlongslit\fR package: (1) detector response calibration, (2) geometric +distortion and coordinate rectification, (3) background sky subtraction, +(4) flux calibration, and (5) aperture extraction of one dimensional spectra. +These are listed in the order in which they are usually performed and in +which they are discussed in this paper. There is also an initialization +task, \fBsetimhdr\fR, and a general routine, \fBicfit\fR, used in may of the +long slit tasks. These are described first. +.SH +SETIMHDR - Set long slit image header parameters +.PP +The tasks in the \fBlongslit\fR package use information contained in the IRAF +image header. The task \fBsetimhdr\fR sets a required parameter in the image +header advising the long slit tasks which image axis corresponds to the +dispersion axis; the tasks work equally well with the dispersion axis +aligned with the image lines or the image columns. This is generally +the first task executed when reducing long slit spectra. +.SH +ICFIT - The IRAF Interactive Curve Fitting routine +.PP +Many of the tasks in the IRAF which fit a one dimensional function +utilize the same powerful interactive curve fitting routine called +\fBicfit\fR. This routine allows the user to perform sophisticated +function fitting interactively and graphically or to specify the +function fitting parameters in advance and run the task +non-interactively. That this routine is used in many tasks also has +the advantage that the user need not learn a new set of commands and +features for each task requiring function fitting. +.PP +The features of the this curve fitting tool include: +.IP (1) +A choice of four fitting functions; Chebyshev polynomial, Legendre polynomial, +a linear spline, and a cubic spline. +.nr PD 0v +.IP (2) +A choice of the polynomial order or the number of spline pieces. +.IP (3) +Deletion of individual points from the fit. +.IP (4) +Selection of a sample or subset of points to be fit (excluding the rest). +.IP (5) +Iterative deletion of points with large residuals from the fitted function. +.IP (6) +Binning sets of neighboring points into averages or medians which are then +fit instead of the individual points. +.nr PD 1v +.LP +In addition to the above features the interactive graphics mode allows +the user to: +.IP (1) +Iterate any number of times on the fitting parameters. +.nr PD 0v +.IP (2) +Display the fit in several different ways; residuals, ratios, and the fit +overplotted on the data points. +.IP (3) +Manipulate the graphs using a large set of commands for formating and +expanding any part of a graph for detailed examination. +.IP (4) +Produce copies of the graphs with a snap-shot command. +.nr PD 1v +.PP +For the applications described in this paper the most important features +are the ability to adjust the function order, exclude bad points, and +select subsets of points to be fit. Other useful features are taking the +median or average of a set of points before fitting and iteratively +rejecting deviant points. When used non-interactively the user +selects the function and the order. The \fBlongslit\fR tasks using the +interactive curve fitting routine are \fBbackground\fR, \fBidentify\fR, +\fBillumination\fR, and \fBresponse\fR. + + +.ce +\fB2. Detector Response Calibrations\fR +.PP +The relative response of the pixels in the detector and the transmission +of the spectrograph along the slit are generally not uniform. Outside +of the \fBlongslit\fR package are IRAF tasks for creating \fIflat fields\fR +from quartz lamp calibration images which correct for small scale response +variations. Flat fields, however, do not correct for spectrograph +transmission variations or any large scale response patterns. The tasks +\fBresponse\fR and \fBillumination\fR are specially designed for long slit +spectra to correct both the small scale variations as well as +larger scale response patterns and slit illumination and transmission effects. +.PP +These algorithms make the assumption that the wavelength and slit axis +are very nearly aligned with the image lines and columns. If this is +not true then the images must be aligned first or alternate response +calibration methods used. +.SH +RESPONSE - Determine response calibration +.PP +The task \fBresponse\fR is used with calibration images which (1) +do not have any intrinsic structure along the slit dimension and (2) +have a smooth spectrum without emission or absorption features. +Typically the calibration images consist of quartz lamp exposures. +The idea is to determine a response correction that turns an observed +calibration image into one which is identical at all points along the +slit. +.PP +From (1) a one dimensional spectrum is obtained by averaging along the +slit; i.e. averaging the columns. Based on (2) a smoothing function is +fit to the one dimensional spectrum to reduce noise and eliminate +response effects which are coherent in wavelength such as fringing. +The response correction for each pixel is then obtained by dividing +each point along the slit (the columns) by the smoothed one dimensional +spectrum. +.PP +The purpose of fitting a function to the one dimensional spectrum is to +reduce noise and to remove coherent response effects which are not part +of the true quartz spectrum. Examples of coherent response effects are +fringing and regions of low or high response running along the slit +dimension which are, therefore, not averaged out in the one dimensional +spectrum. The choice of smoothing function is dictated by the behavior +of the particular detector. Difficult cases are treated with the +interactive graphical function fitting routine \fBicfit\fR. For the +automated case the user specifies the smoothing function and order. +.PP +This calibration algorithm has the advantage of removing spatial +frequencies at almost all scales; in particular, there is no modeling +of the response pattern along the slit dimension. The only modeling is +the fit to the \fBaverage\fR spectrum of the calibration source. In +tests at NOAO this algorithm was able to reduce the response variations +to less 0.2%, to correct for a broad diagonal region of low response in +one of the CCD detectors (the CRYOCAM), and to remove strong fringing +in spectra taken in the red portion of the spectrum where the detector +is particularly subject to fringing. +.PP +One feature common to \fBresponse\fR and \fBillumination\fR is that +the algorithm can be restricted to a section of the calibration image. +The response corrections are then determined only within that section. +If a response image does not exist initially then the response values outside +the section are set to unity. If the response image does exist then +the points outside the section are not changed. This feature is used +with data containing several slits on one image such as produced by +the multi-slit masks at Kitt Peak National Observatory. +.PP +When there are many calibration images this algorithm may be applied to +each image separately or to an average of the images. If applied +separately the response images may be averaged or applied to the +appropriate long slit spectra; typically the one nearest the object +exposure in time or telescope position. The task allows a list of +calibration images from which a set of response corrections is +determined. +.PP +Figure 1 shows a portion of an average quartz spectrum ratioed with the +smooth fit to the spectrum. It is one of the graphs which can be +produced with the \fBicfit\fR routine and, with the other figures in +this paper, illustrates the formating, +zooming, and snap-shot capabilities in IRAF. The figure shows considerable +structure of periodic high response lines and fringing which, because +they are primarily aligned with the image lines, are still present in +the average quartz spectrum. Note that this is not the response +since it is the average of all the columns; an actual response column +would have much larger variations including pixel-to-pixel response +differences as well as large scale response patterns such as the diagonal +structure mentioned previously. +.SH +ILLUMINATION - Determine illumination calibration +.PP +The task \fBillumination\fR corrects for large scale variations along +the slit and dispersion dimensions due to illumination or spectrograph +transmission variations (often called the \fIslit profile\fR). When +the detector response function is determined from quartz calibration +images, using \fBresponse\fR, an illumination error may be introduced +due to differences in the way the spectrograph is illuminated by the +quartz lamp compared to that of an astronomical exposure. This +violates the the assumption that the calibration spectrum has no +intrinsic structure along the slit. \fBIllumination\fR is also used +when only the small scale response variations have been removed using a +flat field correction. +.PP +The approach to determining the response correction is similar to that +described for \fBresponse\fR. Namely, the response correction is the +ratio of a calibration image to the expected calibration image. Again, +the expected calibration image is that which has no structure along the +slit. Calibration images may be quartz lamp exposures, assuming there +is no illumination problem, and blank sky exposures. In the worst +case, object exposures also may be used if the extent of the object in +the slit is small. +.PP +There are several important differences between this algorithm and that +of \fBresponse\fR: +.IP (1) +The spectra are not required to be smooth in wavelength and may contain +strong emission and absorption lines. +.nr PD 0v +.IP (2) +The response correction is a smooth, large scale function only. +.IP (3) +Since the signal-to-noise of spectra from blank sky and object images is +lower than quartz calibration images, steps must be taken to minimize noise. +.IP (4) +Care must be taken that the spectral features do not affect the +response determination. +.nr PD 1v +.PP +The algorithm which satisfies these requirements is as follows. First the +calibration spectrum is binned in wavelength. This addresses the +signal-to-noise consideration (3) and is permitted because only large +scale response variations are being determined (2). Next a smoothing +function is fit along the slit dimension in each bin; i.e. each +wavelength bin is smoothed to reduce noise and determine the large +scale slit profile. Then each bin is normalized to the central point +in the slit to remove the spectral signature of the calibration image. +Finally, the binned response is interpolated back to the +original image size. +.PP +The normalization to the central point in the slit is an assumption +which limits the ability of the illumination algorithm to correct +for all wavelength dependent response effects. There is a wavelength +dependence, however, in that the slit profile is a function of the +wavelength though normalized to unity at the central point of the +slit. +.PP +The wavelength bins and bin widths need not be constant. The bins are +chosen to sample the large scale variations in the slit profile as a +function of wavelength, to obtain good signal statistics, and to avoid +effects due to variations in the positions and widths of strong +emission lines. This last point means that bin boundaries should not +intersect strong emission lines though the bin itself may and should +contain strong lines. Another way to put this criterion is that +changes in the data in the wavelength bins should be small when the +bin boundaries are changed slightly. +.PP +The bins may be set interactively using a graph of the average +spectrum or automatically by dividing the dispersion axis into a +specified number of equal width bins. When the number of bins is small +(and the number of wavelength points in each bin is large) bin +boundary effects are likely to be insignificant. +A single bin consisting of all wavelengths, i.e. the sum of all the image +lines, may be used if no wavelength dependence is expected in the +response. Illumination effects introduced with \fBresponse\fR, +however, appear as wavelength dependent variations in the slit +profile. +.PP +Smoothing of each bin along the slit dimension is done with the +interactive curve fitting routine. The curve fitting may be done +graphically and interactively on any set of bins or automatically by +specifying the function and order initially. The fitting should be +done interactively (at least on the first bin) in order to exclude +objects when the sky is not truly blank and contains faint objects or +when object exposures must be used to determine the slit profile. +.PP +As with \fBresponse\fR, several blank sky images may be available +(though this is less often true in practice). An illumination +correction may be determined for each calibration image or one +illumination correction may be computed from the average of the +calibration images. Also the illumination response correction may be +determined for only a section of the calibration image so as to be +applicable to multi-slit data. +.PP +Figure 2 shows the fit to one of the wavelength bins; lines 1 to 150 have been +summed and the sum is plotted as a function of slit position (column). +The data is from a response image produced by \fBresponse\fR. This +figure illustrates a number of things. \fBIllumination\fR may be run +on a response image to remove the large scale illumination and slit +transmission effects. This creates a flat field in a manner different than +normal surface fitting. The figure shows that response effects occur +at all scales (keeping in mind that the pixel-to-pixel response has +been largely averaged out by summing 150 columns). It also illustrates +how the illumination algorithm works for a typical slit profile. In +this example about half the large scale variation in the slit profile +is due to illumination effects and half is real slit transmission +variations. For a blank sky or object image the main differences +would be larger data values (hundreds to thousands) and possibly +objects present in the slit to be excluded from the fit. + + +.ce +\fB3. Distortion Corrections and Coordinate Transformations\fR +.PP +The removal of geometric distortions and the application of coordinate +transformations are closely related. Both involve applying a +transformation to the observed image to form the desired final image. +Generally, both steps are combined into a single image transformation +producing distortion corrected images with linear wavelength +coordinates (though the pixel interval may be logarithmic). +This differs from other systems (for example, the Kitt Peak IPPS) which +perform distortion corrections on each axis independently and then +apply a dispersion correction on the distortion corrected image. +While this approach is modular it requires several transformations of +the images and does not couple the distortions in each dimension into +a single two dimensional distortion. +.PP +To transform long slit images requires (1) identifying spectral +features and measuring their positions in arc lamp or sky +exposures at a number of points in the image, (2) determining the +distortions in the slit positions at a number of points along the +dispersion axis using either calibration images taken with special +masks or narrow objects such as stars, +(3) determining a transformation function between the image +coordinates and the user coordinates for the measured wavelength and +slit positions, (4) and interpolating the images to a uniform grid in +the user coordinates according to the transformation function. The +coordinate feature information and the transformation functions are +stored in a database. If needed, the database may be examined and +edited. +.PP +An important part of this task is the feature center determination. This +algorithm is described in a separate section below. +.SH +IDENTIFY - Identify features +.PP +The tasks \fBidentify\fR and \fBreidentify\fR are general tools used +for one dimensional, multi-aperture, multi-slit, echelle, and long slit +spectra. The tasks are also general in the sense that they are used to +identify features in any one dimensional vector. For long slit +reductions they are used to identify and trace objects in the slit and +to identify, trace, and determine wavelength solutions for spectral +features from arc calibration images and from sky and object +exposures. +.PP +\fBIdentify\fR is used to identify emission or absorption features in a +one dimensional projection of an image. This projection consists of an +image line or column or the +average of many lines or columns. Averaging is used to increase the +signal in weak features and provide better accuracy in determining the +one dimensional positions of the features. The identified features are +assigned user coordinates. The user coordinates will ultimately define +the final coordinates of the rectified images. +.PP +For determining the distortions along the slit, the positions of object +profiles or profiles obtained with multi-aperture masks in the slit +are measured at a reference line. The user coordinates are then taken to be +the positions at this reference line. The +coordinate rectification will then correct for the distortion to bring the +object positions at the other lines to the same position. +(Note that it is feasible to make an actual coordinate transformation of +the spatial axis to arc seconds or some other units). +.PP +For wavelength features arc calibration images are generally used, +though sky and object exposures can also be used if necessary. After +marking a number of spectral features and assigning them wavelength +coordinates a \fIdispersion solution\fR can be computed relating the +image coordinate to the wavelength; $lambda~=~f(l)$, where $lambda$ is +wavelength and $l$ is the image line. The dispersion +solution is determined using the \fBicfit\fR routines described +earlier. This dispersion solution is used in the long slit package +only as an aid in finding misidentified lines and to automatically add +new features from a wavelength list. The dispersion solution actually +used in transforming the images is a two dimensional function +determined with the task \fBfitcoords\fR. +.PP +Figure 3 shows a graph from \fBidentify\fR used on a Helium-Neon-Argon +arc calibration image. Only three lines were identified interactively +and the reminder were added automatically from a standard line list. +Note that the abscissa is in wavelength units and the ordinate is +displayed logarithmically. The latter again illustrates the flexibility +the user has to modify the graph formats. Each marked feature is +stored in a database and is automatically reidentified at other columns +in the image with \fBreidentify\fR. +.SH +REIDENTIFY - Reidentify features +.PP +The task \fBreidentify\fR automatically reidentifies the spectral and +object features and measures their positions at a number of other +columns and lines starting from those identified interactively with +\fBidentify\fR. The algorithms and the feature information produced is +the same as that of \fBidentify\fR including averaging a number of +lines or columns to enhance weak features. The automatic tracing can +be set to stop or continue when a feature fails to be found in a new +column or line; failure is defined by the position either becoming +indeterminate or shifting by more than a specified amount +(\fIcradius\fR defined in the next section). +.SH +CENTER1D - One dimensional feature centering +.PP +The one dimensional position of a feature is determined by solving the equation + +.EQ +define I0 'I sub 0' +define XC 'X sub c' +.EN +.EQ (1) +int ( I - I0 ) f( X - XC ) dX~=~0 +.EN + +where $I$ is the intensity at position $X$, $I0$ is the continuum +intensity, $X$ is the vector coordinate, and $XC$ is the desired +feature position. The convolution function $f(X- XC )$ is a +sawtooth as shown in figure 4. For absorption features the negative of this +function is used. The figure defines the parameter \fIfwidth\fR which +is set to be approximately the width of the feature. If it is too +large the centering may be affected by neighboring features and if it +is too small the accuracy is worse. +.PP +For emission features the continuum, $I0$, is assumed to be zero. +For absorption features the continuum +is the maximum value in the region around the initial guess +for $XC$. The size of the region on each side of the initial guess is +the sum of \fIfwidth\fR/2, to allow for the feature itself, \fIcradius\fR, +to allow for the uncertainty in the feature position, and \fIfwidth\fR, for a +buffer. Admittedly this is +not the best continuum but it contains the fewest assumptions and is +tolerant of nearby contaminating features. +.PP +Equation (1) is solved iteratively starting with the initial position. +When successive positions agree within 0.1% of a pixel the position is +returned. If the position wanders further than the user defined +distance \fIcradius\fR from the initial guess or outside of the data +vector then the position is considered to be indefinite. +.SH +FITCOORDS - Fit user coordinates to image coordinates +.PP +Let us denote the image coordinates of a point in the two dimensional +image as $(c,~l)$ where $c$ is the column coordinate +and $l$ is the line coordinate. Similarly, denote the +long slit coordinates as $(s,~lambda )$ where $s$ is +the slit position and $lambda$ is the wavelength. +The results of \fBidentify\fR and \fBreidentify\fR is a set of points +$(c,~l,~s)$ and $(c,~l,~lambda )$ recorded in the database. +.PP +Two dimensional functions of the image coordinates are fit to the user +coordinates for each set of slit and wavelength features, +$s~=~t sub s (c, l)$ and $lambda~=~t sub lambda (c, l)$, which are +stored in the database. +Note that the second function is a two dimensional dispersion solution. +It is this function which is used to transform the long slit images to +linear wavelength coordinates. Many images may be used to create a +single transformation or each calibration images may be used separately +to create a set of transformations. +.PP +This task has both an interactive and non-interactive mode. For the +non-interactive mode the user specifies the transformation function, +either a two dimensional Chebyshev or Legendre polynomial, and separate +orders for the column and line axes. When run interactively the +user can try different functions and orders, delete bad points, and +examine the data and the transformation in a variety of graphical formats. +The interactive option is quite useful in initially setting the +transformation function parameters and deleting bad points. +The two dimensional function fitting routine is similar in spirit to the +\fBicfit\fR one dimensional function fitting routine. It is possible +that this routine may find uses in other IRAF tasks. +.PP +Figure 5 shows a graph from \fBfitcoords\fR. The feature image coordinates +of four objects in the slit (the first of which is very weak) +from \fBidentify\fR and \fBreidentify\fR are plotted. This information +is used to measure the distortion of the spectrograph in the slit axis. +This example shows particularly gross distortions; often the distortions +would not be visible in such a graph, though expanding it would make +the distortion visible. The transformation surface fit to this data +removes this distortion almost entirely as seen in the residual plot +of figure 6. Figure 7 shows the equivalent residual plot for the +wavelength coordinates; a two dimensional dispersion solution. +.SH +TRANSFORM - Transform long slit images to user coordinates +.PP +The coordinate transformations determined with the task \fBfitcoords\fR are +read from the database. The transformations are evaluated on a grid of +columns and lines, $s sub i~=~t sub s (c sub i , l sub i )$ and +$lambda sub i~=~t sub lambda (c sub i , l sub i )$. +If no transformation is defined for a particular dimension then a unit +transformation is used. If more than one transformation for a dimension +is given then a set of points is computed for each transformation. +The inverse transformations are obtained by fitting transformation +functions of the same type and orders to the set of slit position and +wavelength points. Note how this allows combining separate +transformations into one inverse transformation. +.PP +The inverse transformations, $c~=~t sub c (s, lambda )$ and +$l~=~t sub l (s, lambda )$, are used to rectify a set of input images. +The user specifies a linear grid for the transformed images by defining some +subset of the starting and ending coordinates, the pixel interval, and the +number of points. In addition the pixel interval can be specified to be +logarithmic; used primarily on the wavelength axis for radial +velocity studies. The inverse transformations define the image column +and line to be interpolated in the input image. The user has the choice +of several types of image interpolation; bilinear, bicubic, and biquintic +polynomials and bicubic spline. In addition the interpolation +can be specified to conserve flux by multiplying the interpolated value +by the Jacobian of the transformation. +.PP +The wavelength of the first pixel and the pixel wavelength interval are +recorded in image headers for later use in making plots and in the +\fBonedspec\fR package. In addition a flag is set in the header indicating +that the image has been dispersion corrected. + + +.ce +\fB4. Background Subtraction\fR +.SH +BACKGROUND - Fit and subtract a line or column background +.PP +If required, the background sky at each wavelength is subtracted from +the objects using regions of the slit not occupied by the object. +This must be done on coordinate rectified images since the lines or +columns of the image must correspond exactly to the same wavelength. +A set of points along the slit dimension, which are representative of the +background, are chosen interactively. Generally this will consist of two +strips on either side of the object spectrum. +At each wavelength a low order function is fit to the sky points and then +subtracted from the entire line or column. +.PP +Ideally the response corrections and coordinate rectification will make +the background sky constant at all points on the slit at each +wavelength and the subtracted background is just a constant. However, if +desired a higher order function may be used to correct for +deficiencies in the data. A possible problem is focus variations which +cause the width of the sky emission lines to vary along the slit. One +may partially compensate for the focus variations by using a higher +order background fitting function. +.PP +The background fitting uses the +interactive curve fitting routine \fBicfit\fR described earlier. +Figure 8 shows a graph from \fBbackground\fR illustrating how the user +sets two sample regions defining the sky (indicated a the bottom of +the graph). + + +.ce +\fB5. Flux Calibration\fR +.SH +EXTINCTION - Apply atmospheric extinction corrections to images +.PP +A set of coordinate rectified images is corrected for atmospheric +extinction with the task \fBextinction\fR. The extinction correction +is given by the formula + +.EQ + roman {correction~factor}~=~10 sup {0.4~E sub lambda~A} +.EN + +where $E sub lambda$ are tabulated extinctions values and $A$ is the air +mass of the observation (determined from information in the image +header). The tabulated extinctions are interpolated to the wavelength of +each pixel and the correction applied to the input pixel value to form +the output pixel value. The user may supply the extinction table but +generally a standard extinction table is used. +.PP +The air mass is sought in the image header under the keyword AIRMASS. +If the air mass is not found then it is computed from the zenith +distance, ZD, using the approximation formula from Allen's +"Astrophysical Quantities", 1973, pages 125 and 133 + +.EQ + A = ( cos ( roman ZD ) sup 2~+~2 s~+~1) sup half +.EN + +where $s$, the atmospheric scale height, is set to be 750. If the +zenith distance is not found then it must be computed from the +hour angle, the declination, and the observation latitude. The +hour angle may be computed from the right ascension and the siderial time. +Computed quantities are recorded in the image header. +Flags indicating extinction correction are also set in the image +header. +.SH +FLUXCALIB - Apply flux calibration to images +.PP +The specified images are flux calibrated using a flux calibration file +derived with the \fBonedspec\fR package using standard stars. The +standard stars are extracted from response corrected, coordinate +rectified, and background subtracted long slit images using the tasks +\fBapdefine\fR and \fBapextract\fR. The standard stars must not be +extinction corrected because this is done by the \fBonedspec\fR flux +calibration algorithms. The user may specify flux per unit wavelength, +$roman F sub lambda$, or flux per unit frequency, $roman F sub nu$. +The flux is computed using the exposure time and dispersion from the +image headers and a flux calibration flag is set. + + +.ce +\fB6. Extraction of One Dimensional Spectra\fR +.PP +The user may wish to extract one dimensional spectra at various points +along the slit. As mentioned earlier, this is necessary if observations +of standard stars are to be used to calibrate the fluxes. The flux +calibration values are determined from one dimensional spectra of standard +stars using the \fBonedspec\fR package. The tools to extract +one dimensional aperture spectra from long slit spectra are \fBapdefine\fR and +\fBapextract\fR. +.SH +APDEFINE - Define apertures for 1D aperture extraction +.PP +Extraction apertures are defined as a list consisting of an +aperture number and lower and upper limits for the aperture. The aperture +limits are specified as column or line positions which need not be +integers. The user may create a file containing these +aperture definitions with an editor or use the interactive +graphics task \fBapdefine\fR. +.PP +\fBApdefine\fR graphs the sum of a number of lines or columns (depending +on the dispersion axis) and allows the user to interactively define and +adjust apertures either with the cursor or using explicit commands. +If an aperture definition file exists the apertures are indicated on +the graph initially. When the user is done a new aperture definition +file is written. +.SH +APEXTRACT - Extract 1D aperture spectra +.PP +One dimensional aperture spectra are extracted from a list of +long slit images using an aperture definition file. The extraction +consists of the sum of the pixels, including partial pixels, at +each column or line along the dispersion axis between the aperture limits. +.PP +More sophisticated algorithms than simple strip extraction are available +in IRAF and will soon be incorporated in the long slit package. The +other extraction tasks trace the positions of features, i.e. the aperture +is not fixed at certain columns or lines, and allow weighted extractions +and detecting and removing bad pixels such as cosmic rays. The +weighted extractions can be chosen to be optimal in a statistical sense. + + +.ce +\fBConclusion\fR +.PP +The IRAF long slit reduction tasks have been used at NOAO for about six +months and have yielded good results. The package does not contain specific +analysis tasks. Some analysis task will be added in time. The package +is part of the software distributed with release of the IRAF. The +author of this paper wrote and supports the tasks described here. +Any comments are welcome. +.sp5 +.ll 4.2i +.nr LL 4.2i +.LP +\fBCaptions for Figures:\fP +.sp 1 +Figure 1. Ratio of average quartz spectrum to fit of a 20 piece cubic spline +for determination of response correction using \fBresponse\fR. + +Figure 2. Fit of 4 piece cubic spline to the slit profile from the average +of the first 150 lines in a response image using \fBillumination\fR. + +Figure 3. Identification of emission lines from the central column of a +Helium-Neon-Argon spectrum using task \fBidentify\fR. + +Figure 4. Sawtooth convolution function of width \fIfwidth\fR used in the +profile centering algorithm. + +Figure 5. Graph of stellar object positions identified with \fBidentify\fR, +traced with \fBreidentify\fR, and graphed by \fBfitcoords\fR showing the +spectrograph distortions. + +Figure 6. Residuals of the fit of a two dimensional 6th order Chebyshev +polynomial to the data of figure 5 using \fBfitcoords\fR. + +Figure 7. Residuals of the fit of a two dimensional 6th order Chebyshev +polynomial to the image positions of wavelength features using \fBfitcoords\fR. + +Figure 8. Constant background fit to a line of an object spectrum using +\fBbackground\fR. The marks at the bottom of the graph indicate the +set of points used in the fit. |