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diff --git a/pkg/obsolete/doc/oimcombine.hlp b/pkg/obsolete/doc/oimcombine.hlp new file mode 100644 index 00000000..adc95f83 --- /dev/null +++ b/pkg/obsolete/doc/oimcombine.hlp @@ -0,0 +1,1013 @@ +.help oimcombine May96 obsolete +.ih +NAME +oimcombine -- Combine images using various algorithms +.ih +USAGE +oimcombine input output +.ih +PARAMETERS +.ls input +List of input images to combine. All images must have the same dimensionality +but they may be of different sizes. +.le +.ls output +Output combined image or list of images. If the \fIproject\fR parameter is +no then there will be one output image while if it is yes there will be one +output image for each input image. +.le +.ls rejmask = "" (optional) +Output mask file to contain identifications of which pixels in which input +images were rejected or excluded. The pixel mask will be the size of the +output image and identified pixels will be in the output image pixel +coordinate system. There is on extra dimension with length equal to the +number of input images. Each element of this dimension contains the mask +of the input image. The order is the order of the input images. +.le +.ls plfile = "" (optional) +Output pixel list file or list of files. If no name is given or the +list ends prematurely then no file is produced. The pixel list file +is a map of the number of pixels rejected or, equivalently, +the total number of input images minus the number of pixels actually used. +The file name is also added to the output image header under the +keyword BPM. +.le +.ls sigma = "" (optional) +Output sigma image or list of images. If no name is given or the list ends +prematurely then no image is produced. The sigma is standard deviation, +corrected for a finite population, of the input pixel values (excluding +rejected pixels) about the output combined pixel values. +.le +.ls logfile = "STDOUT" (optional) +Output log file. If no file is specified then no log information is produced. +The special filename "STDOUT" prints log information to the terminal. +.le + +.ls combine = "average" (average|median) +Type of combining operation performed on the final set of pixels (after +offsetting, masking, thresholding, and rejection). The choices are +"average" or "median". The median uses the average of the two central +values when the number of pixels is even. +.le +.ls reject = "none" (none|minmax|ccdclip|crreject|sigclip|avsigclip|pclip) +Type of rejection operation performed on the pixels remaining after offsetting, +masking and thresholding. The algorithms are described in the +DESCRIPTION section. The rejection choices are: + +.nf + none - No rejection + minmax - Reject the nlow and nhigh pixels + ccdclip - Reject pixels using CCD noise parameters + crreject - Reject only positive pixels using CCD noise parameters + sigclip - Reject pixels using a sigma clipping algorithm + avsigclip - Reject pixels using an averaged sigma clipping algorithm + pclip - Reject pixels using sigma based on percentiles +.fi + +.le +.ls project = no +Project (combine) across the highest dimension of the input images? If +no then all the input images are combined to a single output image. If +yes then the highest dimension elements of each input image are combined to +an output image and optional pixel list and sigma images. Each element of +the highest dimension may have a separate offset but there can only be one +mask image. +.le +.ls outtype = "real" (short|ushort|integer|long|real|double) +Output image pixel datatype. The pixel datatypes are "double", "real", +"long", "integer", unsigned short "ushort", and "short" with highest +precedence first. If none is specified then the highest precedence +datatype of the input images is used. When there is a mixture of +short and unsigned short images the highest precedence become integer. +The datatypes may be abbreviated to +a single character. +.le +.ls offsets = "none" (none|wcs|grid|<filename>) +Integer offsets to add to each image axes. The options are: +.ls "none" +No offsets are applied. +.le +.ls "wcs" +The world coordinate system (wcs) in the image is used to derive the +offsets. The nearest integer offset that matches the world coordinate +at the center of the first input image is used. +.le +.ls "grid" +A uniform grid of offsets is specified by a string of the form + +.nf + grid [n1] [s1] [n2] [s2] ... +.fi + +where ni is the number of images in dimension i and si is the step +in dimension i. For example "grid 5 100 5 100" specifies a 5x5 +grid with origins offset by 100 pixels. +.le +.ls <filename> +The offsets are given in the specified file. The file consists +of one line per image with the offsets in each dimension forming the +columns. +.le +.le +.ls masktype = "none" (none|goodvalue|badvalue|goodbits|badbits) +Type of pixel masking to use. If "none" then no pixel masking is done +even if an image has an associated pixel mask. The other choices +are to select the value in the pixel mask to be treated as good +(goodvalue) or bad (badvalue) or the bits (specified as a value) +to be treated as good (goodbits) or bad (badbits). The pixel mask +file name comes from the image header keyword BPM. Note that when +combining images by projection of the highest dimension only one +pixel mask is applied to all the images. \fBNote\fR, if the number of +input images becomes too large (currently about 250 .imh or 125 .hhh +images) then the images are temporarily stacked and combined by projection +which also means the bad pixel mask from the first image will be used +for all images. +.le +.ls maskvalue = 0 +Mask value used with the \fImasktype\fR parameter. If the mask type +selects good or bad bits the value may be specified using IRAF notation +for decimal, octal, or hexadecimal; i.e 12, 14b, 0cx to select bits 3 +and 4. +.le +.ls blank = 0. +Output value to be used when there are no pixels. +.le + +.ls 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, multiply by the reciprocal of 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 images. +.le +.ls 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 the 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 images. File or keyword zero offset +values do not allow a correction to the weights. +.le +.ls 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 images and the only adjustment made by the task is for the number of +images previously combined. In this case the weights should be those +appropriate for the scaled images which would normally be the inverse +of the variance in the scaled image. +.le +.ls statsec = "" +Section of images to use in computing image statistics for scaling and +weighting. If no section is given then the entire region of the input is +sampled (for efficiency the images are sampled if they are big enough). +When the images are offset relative to each other one can precede the image +section with one of the modifiers "input", "output", "overlap". The first +interprets the section relative to the input image (which is equivalent to +not specifying a modifier), the second interprets the section relative to +the output image, and the last selects the common overlap and any following +section is ignored. +.le +.ls expname = "" +Image header keyword to be used with the exposure scaling and weighting +options. Also if an exposure keyword is specified that keyword will be +added to the output image using a weighted average of the input exposure +values. +.le + +.ce +Algorithm Parameters +.ls 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. +.le +.ls nlow = 1, nhigh = 1 (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 images +so that if no rejections have taken place the specified number of pixels +are rejected while if pixels have been rejected by masking, thresholding, +or nonoverlap, then the fraction of the remaining pixels, truncated +to an integer, is used. +.le +.ls 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. The latter is in addition to pixels +missing due to non-overlapping offsets, bad pixel masks, or thresholds. +.le +.ls 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. +.le +.ls 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. +.le +.ls rdnoise = "0.", gain = "1.", snoise = "0." (ccdclip, crreject) +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. The noise model for a pixel is: + +.nf + variance in DN = (rdnoise/gain)^2 + DN/gain + (snoise*DN)^2 + variance in e- = (rdnoise)^2 + (gain*DN) + (snoise*(gain*DN))^2 + = rdnoise^2 + Ne + (snoise * Ne)^2 +.fi + +where DN is the data number and Ne is the number of electrons. Sensitivity +noise typically comes from noise introduced during flat fielding. +.le +.ls sigscale = 0.1 (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. +.le +.ls pclip = -0.5 (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. +.le +.ls grow = 0. +Radius in pixels for additional pixel to be rejected in an image with a +rejected pixel from one of the rejection algorithms. This applies only to +pixels rejected by one of the rejection algorithms and not the masked or +threshold rejected pixels. +.le +.ih +DESCRIPTION +A set of images or the highest dimension elements (for example the planes +in an image cube) are combined by weighted averaging or medianing. Pixels +may be rejected from the combining by using pixel masks, threshold levels, +and rejection algorithms. The images may be scaled multiplicatively or +additively based on image statistics, image header keywords, or text files +before rejection. The images may be combined with integer pixel coordinate +offsets, possibly determined using the world coordinate system of the +images, to produce an image bigger than any of the input images. + +The input images to be combined are specified by a list. If the +\fBproject\fR parameter is yes then the highest dimension elements of each +input image are combined to make an output image of one lower dimension. +There is no limit to the number of elements combined in this case. If +\fBproject\fR is no then the entire input list is combined to form a single +output image. In this case the images must all have the same +dimensionality but they may have different sizes. There is a software +limit of approximately 100 images in this case. + +The output image header is a copy of the first image in the combined set. +In addition, the number of images combined is recorded under the keyword +NCOMBINE, an image header keyword selected by the \fIexpname\fR parameters +(which is usually an exposure time) is updated as the weighted average of +the input header keywords, and any pixel list file created is recorded +under the keyword BPM. The output pixel type is set by the parameter +\fIouttype\fR. If left blank then the input datatype of highest precision +is used. If there is a mixture of short and unsigned short images then +the highest precision is integer. + +In addition to one or more output combined images there are some optional +output files which may be specified. A pixel mask identifying each pixel +rejected or excluded may be created. This mask will match the output +image in size except there is one extra dimension. The extra dimension +indexes the input images in the order in which they are specified and +combined. What this means is that each element of the extra dimension +is a mask of the pixel rejected in a particular input image (or lower +dimensional element in the case of projection) but in the offset and +sized to the output image. For example, if the input consists of +two dimensional images then the rejected pixel mask will be three +dimensional and each plane will be for a particular input image. +If one wants to separate this file the task \fBimslice\fR may be used. +If there are no offsets then the masks will also be registered with the +input image. If there are offsets then the masks will be offset +also. + +Another pixel mask may be produced giving just the total number of pixels +rejected at each output pixel. An image containing the sigmas of the +pixels combined about the final output combined pixels may also be +created. The sigma computation is the standard deviation corrected for a +finite population (the n/(n-1) factor) including weights if a weighted +average is used. Finally a log file may be produced. + +An outline of the steps taken by the program is given below and the +following sections elaborate on the steps. + +.nf +o Set the input image offsets and the final output image size. +o Set the input image scales and weights +o Write the log file output +.fi + +For each output image line: + +.nf +o Get input image lines that overlap the output image line +o Reject masked pixels +o Reject pixels outside the threshold limits +o Reject pixels using the specified algorithm +o Reject neighboring pixels along each line +o Combine remaining pixels using the weighted average or median +o Compute sigmas of remaining pixels about the combined values +o Write the output image line, rejected pixel masks, and sigmas +.fi + + +OFFSETS + +The images to be combined need not be of the same size or overlap. They +do have to have the same dimensionality which will also be the dimensionality +of the output image. Any dimensional images supported by IRAF may be +used. Note that if the \fIproject\fR flag is yes then the input images +are the elements of the highest dimension; for example the planes of a +three dimensional image. + +The overlap of the images is determined by a set of integer pixel offsets +with an offset for each dimension of each input image. For example +offsets of 0, 10, and 20 in the first dimension of three images will +result in combining the three images with only the first image in the +first 10 columns, the first two images in the next 10 columns and +all three images starting in the 21st column. At the 21st output column +the 21st column of the first image will be combined with the 11th column +of the second image and the 1st column of the third image. + +The output image size is set by the maximum extent in each dimension +of any input image after applying the offsets. In the above example if +all the images have 100 columns then the output image will have 120 +columns corresponding to the 20 column offset in the third image. + +The input image offsets are set using the \fIoffset\fR parameter. There +are four ways to specify the offsets. If the word "none" or the empty +string "" are used then all offsets will be zero and all pixels with the +same coordinates will be combined. The output image size will be equal to +the biggest dimensions of the input images. + +If "wcs" offsets are specified then the world coordinate systems (wcs) +in the image headers are used to derived the offsets. The world coordinate +at the center of the first input image is evaluated. Then integer pixel +offsets are determined for each image to bring the same world coordinate +to the same point. Note the following caveats. The world coordinate +systems must be of the same type, orientation, and scale and only the +nearest integer shift is used. + +If the input images have offsets in a regular grid or one wants to make +an output image in which the input images are "mosaiced" together in +a grid then the special offset string beginning with the word "grid" +is used. The format is + +.nf + grid [n1] [s1] [n2] [s2] ... +.fi + +where ni is the number of images in dimension i and si is the step in +dimension i. For example "grid 5 100 5 100" specifies a 5x5 grid with +origins offset by 100 pixels. Note that one must insure that the input +images are specified in the correct order. This may best be accomplished +using a "@" list. One useful application of the grid is to make a +nonoverlapping mosaic of a number of images for display purposes. Suppose +there are 16 images which are 100x100. The offset string "grid 4 101 4 +101" will produce a mosaic with a one pixel border having the value set +by \fIblank\fR parameter between the images. + +The offsets may be defined in a file by specifying the file name +in the \fIoffset\fR parameter. (Note that the special file name STDIN +may be used to type in the values terminated by the end-of-file +character). The file consists of a line for each input image. The lines +must be in the same order as the input images and so an "@" list may +be useful. The lines consist of whitespace separated offsets one for +each dimension of the images. In the first example cited above the +offset file might contain: + +.nf + 0 0 + 10 0 + 20 0 +.fi + +where we assume the second dimension has zero offsets. + +The offsets need not have zero for one of the images. The offsets may +include negative values or refer to some arbitrary common point. +When the offsets are read by the program it will find the minimum +value in each dimension and subtract it from all the other offsets +in that dimension. The above example could also be specified as: + +.nf + 225 15 + 235 15 + 245 15 +.fi + +There may be cases where one doesn't want the minimum offsets reset +to zero. If all the offsets are positive and the comment "# Absolute" +appears in the offset file then the images will be combined with +blank values between the first output pixel and the first overlapping +input pixel. Continuing with the above example, the file + +.nf + # Absolute + 10 10 + 20 10 + 30 10 +.fi + +will have the first pixel of the first image in the 11th pixel of the +output image. Note that there is no way to "pad" the other side of +the output image. + + +SCALES AND WEIGHTS + +In order to combine images 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 +\fIscale\fR parameter and the zero point shift by the \fIzero\fR +parameter. These parameters may take the values "none" for no scaling, +"mode", "median", or "mean" to scale by statistics of the image 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. + +.nf + 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 +.fi + +The image statistics are computed by sampling a uniform grid of points with +the smallest grid step that yields less than 10000 pixels; sampling is used +to reduce the time needed to compute the statistics. If one wants to +restrict the sampling to a region of the image the \fIstatsec\fR parameter +is used. This parameter has the following syntax: + +.nf + [input|output|overlap] [image section] +.fi + +The initial modifier defaults to "input" if absent. The modifiers are useful +if the input images have offsets. In that case "input" specifies +that the image section refers to each input image, "output" specifies +that the image section refers to the output image coordinates, and +"overlap" specifies the mutually overlapping region of the input images. +In the latter case an image section is ignored. + +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 masked 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 specified by the \fIexpname\fR keyword. As implied +by the parameter name, this is typically the image exposure time since +intensity levels are linear with the exposure time in CCD detectors. +Note that the exposure keyword is also updated in the final image +as the weighted average of the input values. Thus, 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 images. It is a fatal error if the list is incomplete +and a warning if the list appears longer than the number of input images. +Because the scale and zero levels are adjusted only the relative +values are important. + +If both an intensity scaling and zero point shift are selected the +zero point is added first and the scaling is done. This is +important if the scale and offset values are specified by +header keywords or from a file of values. However, +in the log output the zero values are given as the scale times +the offset hence those numbers would be interpreted as scaling +first and zero offset second. + +The image 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 adjust to a zero mean. When scale 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 images but also the +relative pixel uncertainties. For example scaling an image by a +factor of 0.5 will reduce the effective noise sigma of the image +at each pixel by the square root of 0.5. Changes in the zero +point also changes the noise sigma if the image 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 image 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 +image statistics may not be Poissonian, either inherently or because the +images 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 \fIsigscale\fR 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 images may be +weighted during the averaging. The weights are specified in the +same way as the scale factors. In addition +the NCOMBINE keyword, if present, will be used in the weights. +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 and the zero levels are determined from image +statistics (not from an input file or keyword) the weights are computed +from the initial weights (the exposure time, image statistics, or input +values) using the formula: + +.nf + weight_final = weight_initial / (scale * sky) +.fi + +where the sky values are those from the image statistics before conversion +to zero level shifts and 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. If any sky value +determined from the image statistics comes out to be negative a warning is +given and the none of the weight are adjusted for sky levels. + +The weights are not adjusted when the zero offsets are input from a file +or keyword since these values do not imply the actual image sky value. +In this case if one wants to account for different sky statistics +in the weights the user must specify the weights in a file taking +explicit account of changes in the weights due to different sky +statistics. + + +PIXEL MASKS + +A pixel mask is a type of IRAF file having the extension ".pl" which +identifies an integer value with each pixel of the images to which it is +applied. The integer values may denote regions, a weight, a good or bad +flag, or some other type of integer or integer bit flag. In the common +case where many values are the same this file is compacted to be small and +efficient to use. It is also most compact and efficient if the majority of +the pixels have a zero mask value so frequently zero is the value for good +pixels. Note that these files, while not stored as a strict pixel array, +may be treated as images in programs. This means they may be created by +programs such as \fBmkpattern\fR, edited by \fBimedit\fR, examined by +\fBimexamine\fR, operated upon by \fBimarith\fR, graphed by \fBimplot\fR, +and displayed by \fBdisplay\fR. + +At the time of introducing this task, generic tools for creating +pixel masks have yet to be written. There are two ways to create a +mask in V2.10. First if a regular integer image can be created +then it can be converted to pixel list format with \fBimcopy\fR: + +.nf + cl> imcopy template plfile.pl +.fi + +by specifically using the .pl extension on output. Other programs that +can create integer images (such \fBmkpattern\fR or \fBccdred.badpiximage\fR) +can create the pixel list file directly by simply using the ".pl" +extension in the output image name. + +To use pixel masks with \fBoimcombine\fR one must associate a pixel +mask file with an image by entering the pixel list file name in the +image header under the keyword BPM (bad pixel mask). This can be +done with \fBhedit\fR. Note that the same pixel mask may be associated +with more than one image as might be the case if the mask represents +defects in the detector used to obtain the images. + +If a pixel mask is associated with an image the mask is used when the +\fImasktype\fR parameter is set to a value other than "none". Note that +when it is set to "none" mask information is not used even if it exists for +the image. The values of \fImasktype\fR which apply masks are "goodvalue", +"badvalue", "goodbits", and "badbits". They are used in conjunction with +the \fImaskvalue\fR parameter. When the mask type is "goodvalue" the +pixels with mask values matching the specified value are included in +combining and all others are rejected. Similarly, for a mask type of +"badvalue" the pixels with mask values matching the specified value are +rejected and all others are accepted. The bit types are useful for +selecting a combination of attributes in a mask consisting of bit flags. +The mask value is still an integer but is interpreted by bitwise comparison +with the values in the mask file. + +If a mask operation is specified and an image has no mask image associated +with it then the mask values are taken as all zeros. In those cases be +careful that zero is an accepted value otherwise the entire image will be +rejected. + +In the case of combining the higher dimensions of an image into a +lower dimensional image, the "project" option, the same pixel mask +is applied to all of the data being combined; i.e. the same 2D +pixel mask is applied to every plane of a 3D image. This is because +a higher dimensional image is treated as a collection of lower +dimensional images having the same header and hence the same +bad pixel mask. It would be tempting to use a bad pixel mask with +the same dimension as the image being projected but this is not +currently how the task works. + +When the number of input images exceeds the maximum number of open files +allowed by IRAF (currently about 250 or 125 .hhh images) the input images +are stacked and combined with the \fIproject\fR option. \fBNote\fR that +this means that the bad pixel mask from the first input image will be +applied to all the images. + + +THRESHOLD REJECTION + +In addition to rejecting masked pixels, pixels in the unscaled input +images which are below or above the thresholds given by the parameters +\fIlthreshold\fR and \fIhthreshold\fR are rejected. Values of INDEF +mean that no threshold value is applied. Threshold rejection may be used +to exclude very bad pixel values or as an alternative way of masking +images. In the latter case one can use a task like \fBimedit\fR +or \fBimreplace\fR to set parts of the images to be excluded to some +very low or high magic value. + + +REJECTION ALGORITHMS + +The \fIreject\fR parameter selects a type of rejection operation to +be applied to pixels not masked or thresholded. If no rejection +operation is desired the value "none" is specified. + +MINMAX +.in 4 +A specified fraction of the highest and lowest pixels are rejected. +The fraction is specified as the number of high and low pixels, the +\fInhigh\fR and \fInlow\fR parameters, when data from all the input images +are used. If pixels have been rejected by offsetting, masking, or +thresholding then a matching fraction of the remaining pixels, truncated +to an integer, are used. Thus, + +.nf + nl = n * nlow/nimages + 0.001 + nh = n * nhigh/nimages + 0.001 +.fi + +where n is the number of pixels surviving offsetting, masking, and +thresholding, nimages is the number of input images, 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 images and specifying one low and two high +pixels to be rejected the fractions to be rejected are nlow=0.1 and nhigh=0.2 +and the number rejected as a function of n is: + +.nf + n 0 1 2 3 4 5 6 7 8 9 10 + nl 0 0 0 0 0 0 0 0 0 0 1 + nh 0 0 0 0 0 1 1 1 1 1 2 +.fi + +.in -4 +CCDCLIP +.in 4 +If the images are obtained using a CCD with known read out noise, gain, and +sensitivity noise parameters and they have been processed to preserve the +relation between data values and photons or electrons then the noise +characteristics of the images are well defined. In this model 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 by: + +.nf + sigma = ((rn / g) ** 2 + <I> / g + (s * <I>) ** 2) ** 1/2 +.fi + +where 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. +See the task \fBstsdas.wfpc.noisemodel\fR for a way to determine +these values (though that task expresses the read out noise in data +numbers and the sensitivity noise parameter as a percentage). + +The read out noise is specified by the \fIrdnoise\fR parameter. The value +may be a numeric value to be applied to all the input images or a image +header keyword containing the value for each image. Similarly, the +parameter \fIgain\fR specifies the gain as either a value or image header +keyword and the parameter \fIsnoise\fR specifies 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 \fIlsigma\fR times this sigma below or \fIhsigma\fR times 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 \fIsigscale\fR threshold +is exceedd then a sigma is computed for each pixel based on the +image 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 +\fInkeep\fR parameter. 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 than \fInkeep\fR pixels are retained. +Note that the \fInkeep\fR parameter 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 \fIreject\fR +to select this algorithm, \fImclip\fR to select the median or average for +the center of the clipping, \fInkeep\fR to limit the number of pixels +rejected, the CCD noise parameters \fIrdnoise, gain\fR and \fIsnoise\fR, +\fIlsigma\fR and \fIhsigma\fR to select the clipping thresholds, +and \fIsigscale\fR to set the threshold for making corrections to the sigma +calculation for different image scale factors. + +.in -4 +CRREJECT +.in 4 +This algorithm is identical to "ccdclip" except that only pixels above +the average are rejected based on the \fIhsigma\fR parameter. This +is appropriate for rejecting cosmic ray events and works even with +two images. + +.in -4 +SIGCLIP +.in 4 +The sigma clipping algorithm computes at each output pixel the median or +average excluding the high and low values. The sigma is then computed +about this estimate (without excluding the low and high values). 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. + +After rejection the number of retained pixels is checked against the +\fInkeep\fR parameter. 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 than \fInkeep\fR pixels are retained. +Note that the \fInkeep\fR parameter only applies to the pixels used +by the clipping rejection algorithm and does not apply to threshold +or bad pixel mask rejection. + +The parameters affecting this algorithm are \fIreject\fR to select +this algorithm, \fImclip\fR to select the median or average for the +center of the clipping, \fInkeep\fR to limit the number of pixels +rejected, \fIlsigma\fR and \fIhsigma\fR to select the +clipping thresholds, and \fIsigscale\fR to set the threshold for +making corrections to the sigma calculation for different image scale +factors. + +.in -4 +AVSIGCLIP +.in 4 +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: + +.nf + sigma(column,line) = sqrt (gain(line) * signal(column,line)) +.fi + +where the \fIestimated\fR signal is the mean or median (hopefully excluding +any bad pixels) and the gain is the \fIestimated\fR proportionality +constant having units of photons/data number. + +This noise model is valid for images whose values are proportional to the +number of photons recorded. In effect this algorithm estimates a +detector gain for each line with no read out noise component when +information about the detector noise parameters are not known or +available. The gain proportionality factor is computed +independently for each output line by averaging the square of the residuals +(at points having three or more input values) scaled by the median or +mean. In theory the proportionality should be the same for all rows but +because of the estimating process will vary somewhat. + +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 images are scaled differently and the sigma scaling correction +threshold is exceedd then a correction is made in the sigma +calculations for these differences, again under the assumption that +the noise in an image scales as the square root of the mean intensity. + +After rejection the number of retained pixels is checked against the +\fInkeep\fR parameter. 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 than \fInkeep\fR pixels are retained. +Note that the \fInkeep\fR parameter only applies to the pixels used +by the clipping rejection algorithm and does not apply to threshold +or bad pixel mask rejection. + +This algorithm works well for even a few input images. It works better if +the median is used though this is slower than using the average. Note that +if the images have a known read out noise and gain (the proportionality +factor above) then the "ccdclip" algorithm is superior. The two algorithms +are related in that the average sigma proportionality factor is an estimate +of the gain. + +The parameters affecting this algorithm are \fIreject\fR to select +this algorithm, \fImclip\fR to select the median or average for the +center of the clipping, \fInkeep\fR to limit the number of pixels +rejected, \fIlsigma\fR and \fIhsigma\fR to select the +clipping thresholds, and \fIsigscale\fR to set the threshold for +making corrections to the sigma calculation for different image scale +factors. + +.in -4 +PCLIP +.in 4 +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 multiplied by the scale factors \fIlsigma\fR and \fIhsigma\fR +to 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 \fIpclip\fR selects 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 +the \fIpclip\fR parameter 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 images. 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 +offsetting, masking, or thresholding; for example, if the 3rd 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 +\fInkeep\fR parameter. 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 than \fInkeep\fR pixels are retained. +Note that the \fInkeep\fR parameter 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 \fIpclip\fR value of 2 selects the 2nd pixel +above the median (6th) pixel which is the 8th pixel. A \fIpclip\fR +value 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 objects when combining +disregistered observations for a sky flat field, 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. + +The parameters affecting this algorithm are \fIreject\fR to select this +algorithm, \fIpclip\fR to select the percentile pixel, \fInkeep\fR to limit +the number of pixels rejected, and \fIlsigma\fR and \fIhsigma\fR to select +the clipping thresholds. + +.in -4 +GROW REJECTION + +Neighbors of pixels rejected by the rejection algorithms +may also be rejected. The number of neighbors to be rejected +is specified by the \fIgrow\fR parameter which is a radius in pixels. +If too many pixels are rejected in one of the grown pixels positions +(as defined by the \fInkeep\fR parameter) then the value of that pixel +without growing will be used. + +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. + + +SIGMA OUTPUT + +In addition to the combined image and optional sigma image may be +produced. The sigma computed is the standard deviation, corrected for a +finite population by a factor of n/(n-1), of the unrejected input pixel +values about the output combined pixel values. +.ih +EXAMPLES +1. To average and median images without any other features: + +.nf + cl> oimcombine obj* avg combine=average reject=none + cl> oimcombine obj* med combine=median reject=none +.fi + +2. To reject cosmic rays: + +.nf + cl> oimcombine obs1,obs2 Obs reject=crreject rdnoise=5.1, gain=4.3 +.fi + +3. To make a grid for display purposes with 21 64x64 images: + +.nf + cl> oimcombine @list grid offset="grid 5 65 5 65" +.fi + +4. To apply a mask image with good pixels marked with a zero value and +bad pixels marked with a value of one: + +.nf + cl> hedit ims* bpm badpix.pl add+ ver- + cl> oimcombine ims* final combine=median masktype=goodval +.fi + +5. To scale image by the exposure time and then adjust for varying +sky brightness and make a weighted average: + +.nf + cl> oimcombine obj* avsig combine=average reject=avsig \ + >>> scale=exp zero=mode weight=exp expname=exptime +.fi +.ih +REVISIONS +.ls OIMCOMBINE V2.11.4 +The version of IMCOMBINE from V2.11-V2.11.3 was moved to OBSOLETE. +.le +.ih +LIMITATIONS +Though the previous limit on the number of images that can be combined +was removed in V2.11 the method has the limitation that only a single +bad pixel mask will be used for all images. +.ih +SEE ALSO +immatch.imcombine ccdred.combine onedspec.scombine, wpfc.noisemodel +.endhelp |