; MX ;--------------------------------------------------------------- ;! makes images & deconvolves using UV data directly - replaced ;# TASK OBSOLETE ;----------------------------------------------------------------------- ;; Copyright (C) 1995-1997, 1999, 2002, 2007, 2009 ;; Associated Universities, Inc. Washington DC, USA. ;; ;; This program is free software; you can redistribute it and/or ;; modify it under the terms of the GNU General Public License as ;; published by the Free Software Foundation; either version 2 of ;; the License, or (at your option) any later version. ;; ;; This program is distributed in the hope that it will be useful, ;; but WITHOUT ANY WARRANTY; without even the implied warranty of ;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ;; GNU General Public License for more details. ;; ;; You should have received a copy of the GNU General Public ;; License along with this program; if not, write to the Free ;; Software Foundation, Inc., 675 Massachusetts Ave, Cambridge, ;; MA 02139, USA. ;; ;; Correspondence concerning AIPS should be addressed as follows: ;; Internet email: aipsmail@nrao.edu. ;; Postal address: AIPS Project Office ;; National Radio Astronomy Observatory ;; 520 Edgemont Road ;; Charlottesville, VA 22903-2475 USA ;----------------------------------------------------------------------- MX LLLLLLLLLLLLUUUUUUUUUUUU CCCCCCCCCCCCCCCCCCCCCCCCCCCCC MX: Used to map and CLEAN. IMAGR is a better task to use! Explain file retained since some users may find it of some help. ---------------------------------------------------------------- MX Type: Task: ********** IMAGR is recommended over MX now ********** MX does not apply flag tables or calibration even if FG and/or SN tables accompany the input file. It is also limited in a large number of ways compared to IMAGR even if one does not use thae advanced options of IMAGR. Robust weighting and TV interaction alone are reasons to abandon MX. *************************************************************** Furthermore, DO3DIM = FALSE imaging has been redefined in a more correct fashion which prohibits the use of this task. Therefore, it has been deleted from the system. The EXPLAIN file may still be of utility to some users, so it has been retained. ---------------------------------------------------------------- MX: Task which makes and CLEANs a map from UV data on disk using AP DOCUMENTERS: W. Cotton NRAO (mostly from UVMAP and APCLN) G. Langston NRAO RELATED PROGRAMS: UVLOD,UVSRT,APCLN,UVMAP,BLOAT,HORUS,RSTOR PURPOSE MX combines the functions of mapping, CLEANing and subtracting components from the un-gridded uv data (ie. the functions of UVMAP, APCLN and UVSUB). Because the CLEAN components are subtracted from the un-gridded data, the entire region of a map can be CLEANed; as opposed to the method used in APCLN which can only CLEAN a quarter of the map area. Data in an arbitrary sort order may be deconvolved. MX permits up to 64 independent fields in the antenna beam and 46655 frequency channels to be mapped and CLEANed in one execution. Multi-band data can be gridded together before mapping. If the machine crashes before the end of the execution MX should be fairly easily restartable. MX is recommended over UVMAP and APCLN for the following problems: (1) Snap-shot observations with a small number of visibility points run much faster with MX than UVMAP and APCLN when only the region with the source is mapped. With MX there is no need to confine the source to the inner quarter area of the mapped region, although the source should not extend to the boundary of the field of view. (2) For observations at low frequency and at high sensitivity. Radio emission is often detected over the entire primary beam. It is then prohibitively expensive to make and clean one large map. MX will permit you to choose up to 64 rectangular fields in the sky, map each and then simultaneously clean the entire set. It is often possible to choose a small number of fields which contains virtually all of the radio emission so that the total area processed by MX will be relatively small. MX is particularly valuable for radio maps which contain a few 'confusing' sources at large angular distance from the source of interest. In order to determine the appropriate parameters for MX, first make a very low resolution map in order to determine the approximate location and size of each of the rectangular fields. Insert the appropriate parameters of the fields into MX and run the task at the desired resolution. (3) Only MX can produce and clean 4096X4096 maps at the present time. Make sure you have enough disk space to make these maps! (4) Use MX if you need >1000:1 dynamic range for a relatively extended source. By subtracting components from the un-gridded (u-v) data aliasing of side-lobes inside the field of view is avoided. Finally, components very far from the phase center but near the field center, will be subtracted from the (u-v) data with the proper w-phase terms. (5) MX can average frequency channels in the gridding process by gridding each channel independently onto the same grid; this reduces the delay smearing problem in the maps to the amount due to the individual channel rather than the total bandwidth. This option can also be used to smooth line maps as the number of channels to grid together and the channel increment is independent. (5) Only one Stokes' Parameter map can be made with one execution. If you must have identical coverage for your I, Q, U or V maps, use UVMAP. However, any differences among the different Stokes' parameters are usually minimal. ADVERBS PECULIAR TO MX Most of the adverbs used by MX are duplicates of those used by UVMAP and APCLN and need no further explanation. The adverbs peculiar to MX are: IN2NAME, IN2CLASS, IN2SEQ, IN2DISK MX keeps a scratch file with the current uv data with the current list of components subtracted. This file is cataloged and may be used to restart MX. IN2NAME etc. can be used to specify this file. If an existent version of this file is specified, is compatible with the current use, and has the same number of components subtracted as the requested number for restarting then the existing file will be used as the input uv data for the current frequency channel. Note that IN2SEQ especially should be specified. This will speed restarting MX considerably. The MX uv work file will, in general, be different in many ways from the original input data and may give difficulties to some of the existing uv data handling routines. The data will be in the form of a single Stokes' (or circular) polarization with the number of frequency channels being summed into one grid. The direction of the baseline (but not the BASELINE code) will have been flipped as appropriate to make U positive. The data will have been selected by the criterion given explicitly or implicitly to MX. The weights will have the uniform weighting correction made. CHANNEL This adverb, if >0, is used to restart MX. If CHANNEL=N, then restart MX at frequency channel N (N=1 for continuum). When restarting a clean, use BCOMP as described below. NCHAV The number of channels to be combined on the same grid before mapping. Use this option to obtain one map from several channels of uv data at slightly different frequencies. Up to 2048 channels can be combined in the gridding stage. CHINC The number of (u-v) planes to skip between maps. If NCHAV>1, CHINC refers to the first plane going into the map. STOKES Only one Stokes' parameter can be made at one time. A beam is made for each polarization and each frequency channel. BIF,EIF These define the first and last IFs to be included in a bandwidth synthesis average. An IF consists of a set of one or more equally spaced frequency channels; multiple IFs with arbitrary frequency spacings are allowed. IMSIZE The minimum desired size for all of the fields. The limits are 32x32 to 4096x4096 and must be a power of 2. The adverb FLDSIZE define the region over which clean components are searched for. NFIELD The number of independent fields to map. Up to 64 are permitted for each frequency channel specified by BCHAN, ECHAN and CHINC. Each field comes out as a separate cataloged file. Clean components subtracted from one field will not be restored to other fields even if the images overlap. FLDSIZE, RASHIFT, DECSHIFT For each independent field, specify the center of the field by its RA offset and DEC offset in arc-seconds from the phase center. A positive RA and DEC offset means that the field center is East and North of the phase center. The FLDSIZE is the area in each image where clean components will be searched for. It is limited to the range 32x32 to 4096x4096 but need not be a power of 2. The output image size will be increase to the next power of 2 or to IMSIZE if it is larger. For maps smaller than 256x256, the size may be doubled for more accurate cleaning. THE DO3DIMAG OPTION OF IMAGR IS NOT SUPPORTED BY MX. NBOXES, CLBOX (TVBOX) For the first field, up to 50 CLEAN windows can be specified via CLBOX as an alternate to FLDSIZE. This allows more flexibility than a single window centered on the phase center. If NBOXES is greater than 0 then the contents of CLBOX is used to specify the input window. Since these values are in pixels care should be taken that they are determined from an image made with the same cellsize and shift. NOTE: the values contains in CLBOX are not used to determine the size of the image for field 1. IMSIZE and/or FLDSIZE must be used for this. In the case that CLBOX and NBOXES are used, this is the only use made of FLDSIZE for field 1. Its use for higher numbered fields is unaffected. If CLBOX is 0's then the value of FLDSIZE (or its default) is used for CLBOX. NBOXES and CLBOX specify the size and location of the rectangular boxes comprising the "CLEAN Window" area A. You make the best use of prior knowledge about the source to help MX do its job when you restrict A as closely as possible to the true boundaries of its emission. Recall that CLEAN attempts to optimize F(n) as a representation of the sky, with zeroes everywhere else. The more information you provide about where the "real" emission is, the more likely MX is to converge on a unique, credible solution. The verb TVBOX may conveniently be used to set the BLC and TRC limits of the boxes after NBOXES has been typed in. Following a prompt on your terminal, position the TV cursor at the BLC of the first CLBOX and press any track-ball button. Then position the cursor at the TRC of this box and press button B. Repeat this for all desired boxes. This will fill the CLBOX array for the MX inputs. The terminal prompt will also give instructions for resetting any previously set corners should you need to do so. Note: since MX will remake the image, be sure to run TVBOX on an image made with the same cellsize and shift as will be used for MX. UVWTFN When using MX to make several small maps over a large field of view, use Natural weighting rather than Uniform weighting in order to obtain the signal to noise and resolution which are comparable to that obtained from one large map over the field of view. For map sizes of 256 or less, the loss of signal to noise using Uniform weighting can be a factor of two or three. Uniform weighting in MX, HORUS and UVMAP is defined as dividing the weights of visibilities in a UV grid cell by the number of visibilities in that UV grid cell. (Note: this is not defined as the dividing by the sum of the weights of the visibilities, unless all visibilities have the same weight.) The result of this weighting is to decrease the significance of UV data falling in regions of the UV plane where large amounts of UV data are present. (For the VLA, the region is near U=V=0.) MX also allows the input UV weights data to be reset in two ways. The first is to reset all visibility weights to One. This is useful in the high signal-to-noise case. It also forces all UV grid cells to have the same contribution to the image after Uniform Weighting. (UVWTFN='O' or UVWTFN='NO') The second weighting is "VLBI" weighting which resets the weights to sqrt(sqrt(input weight)). This is important for observations were one telescope has significantly higher signal-to-noise ratio that others. If the range of the input weights was not compressed by this weighting, the Fourier transform of the UV data consists only of baselines with the dominant antenna. (UVWTFN='V' or UVWTFN='NV')n BCOMP The default (BCOMP=0) restarts the CLEAN from scratch. Other values of BCOMP are used when MX is to be restarted from an intermediate step in the process. When set >0, it specifies the maximum number of components from each subfield of a previous clean to be subtracted from the uv data to obtain the residual map for the first new iteration. Each value in BCOMP corresponds to a field. Restarts are sometimes needed after the computer has crashed during a long MX. Under these circumstances, the iteration number at the end of the last major cycle is stored in the AIPS clean components file headers. Provided that the crash has not destroyed relevant image files (or the CC extension file) on disk, the CLEAN may be restarted by setting BCOMP equal to the number of iterations shown in the image header for the CLEAN map - if this disagrees with the number in the internal file header (as may happen if the crash comes at an unfortunate point in a cycle), AIPS will adjust BCOMP downwards in a "fail-safe" way. (PRTCC might be run to check the state of the components list in such cases). To restart MX cleaning from a set of fields set BCOMP to the highest of the number of clean components from the set. When you set BCOMP>0, you must set the OUTNAME and OUTSEQ parameters explicitly to those of the Clean Map(s) whose CC extension file(s) contains the components which are to be subtracted. This Clean Map file will be overwritten by the new Clean Map, so if you wish to preserve it you should either write it to tape using FITTP or create a second copy of it on disk using SUBIM. NOTE: there is one CC file per output frequency channel with version number = output channel number. A components file F(N) can be re-convolved with a different Clean Beam H by restarting MX with NITER=BCOMP=n. This is an effective tool for making SMALL changes the resolution of a Clean Map. Do NOT use it for making large (factors >2) changes in resolution, e.g. to "find" extended components of a source. If a structure has been resolved out over the longer baselines, these baselines contribute only noise, not signal, to maps of that structure, and should be excluded from any search for the structure. CLEANing a noisy map and then convolving it to much lower resolution makes no sense. In such cases, you should re-map with an appropriate taper and run MX on a dirty map with a more appropriate resolution. BMAJ, BMIN, BPA IF BMAJ is less than zero, the output image will be the residual image without the clean components restored. Examining this image for waves or other artifacts is helpful for finding bad UV data. The task RSTOR can quickly restore the clean components. CMETHOD MX has two different routines for computing the model visibility from the CLEAN components. The first ('DFT ') method does a direct Fourier transform of the CLEAN components for each visibility point. This method probably gives slightly better accuracy but can be slow if there are many components and/or visibilities. (See TIMING section for more detail). The second model computation method is to grid the CLEAN components, do a hybrid DFT/FFT ('GRID') onto a grid and interpolate each visibility measurement form the grid using (currently) ninth order Lagrange interpolation and a uv grid with half the spacing of the mapping grid. This method is called the gridded-FFT method and CAN be MUCH faster than the DFT method for large data bases and large numbers of components. Since the w correction must be done for each field separately the length of time this routine takes is proportional to the number of fields in which there are CLEAN components in any major cycle. To increase the accuracy of the interpolation, the size of the model grid used for the interpolation is twice the size of the data grid for images up to 2048x2048. This means the output scratch files (three of them) may be four times the size of the largest output file. CMETHOD allows the user to specify the method desired or to allow MX to decide which one will be faster. CMETHOD equal to ' ' (or any values but 'DFT 'or 'GRID') indicates that the decision is left to MX, CMETHOD = 'GRID' causes MX to use the gridded-FFT method and CMETHOD = 'DFT ' forces MX to use the DFT method. In cases where there are bright, localized regions far from the map center (eg. strong hot spots in double lobed sources) the gridded subtraction may be inadequate. The principle failure should be to over estimate the brightness of the bright regions far from the map center (should be under a percent) and slightly increase the noise elsewhere. This problem will be greatly reduced if the first few major cycles use the DFT subtraction method until the brightest regions are removed. If CMETHOD is set to ' ' the first few major cycles will probably use the DFT. EXAMPLES OF COMMON MX PARAMETERS 1) Emulate UVMAP and APCLN: Set the appropriate parameters for normal UVMAP and APCLN execution. To emulate a 1024x1024 map and with a clean of the inner 512x512 (500X500) use the following adverbs; IMSIZE=512; NFIELD=1 FLDSIZE=500; RASHIFT=0; DECSHIFT=0 NITER=200; CMETHOD=''; UVWTFN='UN' MX will effectively clean nearly all of a 512x512 map with 200 iterations. MX will decide (CMETHOD='') which of the two component subtraction methods is most economical. For a data base with less than about 1,000,000 data points, MX will run much faster than UVMAP and APCLN on a 1024x1024 map. Furthermore, the cleaning subtraction in MX is more accurate than that in APCLN. The relative execution time between MX and (UVMAP and APCLN) depend on the number of visibility points and clean components and are given in the TIMING section. Uniform weight was chosen to give highest resolution. 2) Piecemeal mapping and cleaning using MX Set the usual input and output parameters, then IMSIZE=128; NFIELD=3 FLDSIZE=32,32,256,256,20,20 RASHIFT=-40,5,200 DECSHIFT=120,2,400 UVWTFN='NA' NITER=500; CMETHOD='' MX will produce the following set of maps. a. 64x64 map centered on (-40",120") with clean components searched in the inner 32x32 area. b. 256x256 map centered on (5",2") with clean components searched over the entire 256x256 area. c. 64x64map centered on (200",400") with clean components searched over the inner 20x20 area. d. 256x256 beam centered on (0",0"). The beam size is taken to be the size of the biggest map or 1024, whichever is smaller. It may be best to choose Natural weighting for the UV weight function. In making relatively small fields over a wide area, Natural weight emulates the resolution and signal to noise of a single map made over the wide area. The uniform weighted map for the 64x64 fields may be several times more noise than the naturally weighted map. 3) MX used with a multi-frequency u-v data base. A range of spectral channels to image can be given by BCHAN and ECHAN which are the low and high channel numbers to be imaged in the the input file. If CHINC is greater than 1 then every CHINC'th channel is selected between BCHAN and ECHAN. If NCHAV is greater than 1 then NCHAV channels will be averaged starting with each channel selected by BCHAN, ECHAN and CHINC. If MX needs to be restarted then CHANNEL specifies the first channel that needs to be processed. An image and a beam are made for each channel. There is a limit of 46655 channels in an output image. The default value for BCHAN is 1, for ECHAN is BCHAN, CHINC is 1 and NCHAV is 1. Example: BCHAN=1; ECHAN=6; NCHAV=2; CHINC=2; STOKES='I' Will cause channels 1&2, 3&4, 5&6 to be combined and imaged using the Stokes' I polarization data. Prudence If running MX on a complicated source with low GAIN you may need to work to large final values of NITER. As MX is the major consumer of CPU time in most map analyses, it is prudent to preserve intermediate clean maps by writing them to a FITS tape with FITTP. This allows you to recover from disasters such as crashes, over CLEANing, etc. with minimal impact on total execution time, your time, and on disk space. TIMING The amount of time it takes for MX to run depends on the amount of data, the size and complexity of the source and the current load on the computer. The following formula give the approximate times for specific operations measured on an otherwise empty VAX11/780 plus an FPS AP-120B array processor: Making maps, gridding correction, statistics etc. T(real) = No. Fields * ( No. vis. * 0.4E-3 + (SQRT(NX*NY)/1024)**1.3 * 180 seconds Subtraction (DFT method) T(real) = 6.0E-6 * No. vis * No. CLEAN components seconds Subtraction (FFT method) T(real) = No. Fields * (No. vis * 0.4E-3 + SQRT (4*NX*NY) * 4.0E-2 + No. Clean components * 1.0E-3 seconds Cleaning (in-AP) T(real) = 3.0E-6 * No. Clean components * No. residual map points seconds GENERAL COMMENTS General comments concerning mapping and cleaning follow. Most of the comments have been taken from the EXPLAIN files for UVMAP and APCLN. MAPPING MX makes dirty maps and beams from (u,v) data using a Fast Fourier Transform (FFT). The data may be in any sort order. The data are convolved onto the regularly spaced grid which is used for the Fourier transform. Maps of several frequency channels, and a beam, can be made with one execution. One polarization per execution. A fairly complete description of the mapping functions performed by MX is given in Lecture 2 of the Proceedings of the NRAO-VLA Workshop on Synthesis Mapping. Observers who are unfamiliar with interferometry are recommended to study this volume. OUTDISK : If OUTDISK = 0, the map and beam will be put on the same disk. FLDSIZE,IMSIZE,CELLSIZE : For effective CLEANing of the maps, the number of pixels per beam should be such that the pixel value immediately north or east of the beam center is no less than about 50% of the peak. However, if tapering is used, the outlying (u,v) points may not have any significant weight in the map. Strong aliased sources should be CLEANed in separate fields unless they are close to the object of interest. MX will make maps which have a power of two pixels on a side; between 32 and 4096 on the X-axis and between 32 and 4096 on the Y-axis. FLDSIZE defines the region to be searched for CLEAN components. If for some reason it is desirable to map a region much larger than the region being CLEANed, IMSIZE can specify the minimum size of a map. Components will be CLEANed from the region specified by FLDSIZE but the output image size will be as specified by IMSIZE. Values in IMSIZE must be powers of 2. STOKES : If you do not expect your source to show significant circular polarization, as is normally the case with galactic and extra-galactic continuum sources, making a V map can be a useful diagnostic for calibration problems, correlator offsets, etc. The V map should be a pure noise map close to the theoretical sensitivity if your data base is well calibrated and edited. UVWTFN : The default uniform weighting option gives higher resolution than natural weighting. However, uniform weighting gives a lower signal to noise ratio. Natural weighting is therefore preferable for detection experiments. With uniform weighting the dirty beam size decreases slightly with larger maps, other parameters remaining unchanged. In cases of very centrally condensed uv coverage such as that resulting from the VLA in the D array uniform weighting with a UVBOX greater than 0.0 may be desirable. ZEROSP : To improve CLEANing of extended sources, the zero-spacing flux should be included in MX. The weight assigned should normally be in the range 10-100 but you may need to experiment, as the optimal value depends on your (u,v) coverage. Inclusion of the zero-spacing flux will allow CLEAN to interpolate into the inner region of the (u,v) plane more accurately, provided that this flux does not exceed the average visibility at the short spacing by too much. You must also CLEAN deeply to derive the full benefit of this (see the EXPLAIN file for APCLN). Jacqueline van Gorkom claims that the only proper weight for the zero spacing flux density is the number of cells missing in the center of the uv plane as long as the zero spacing flux density doesn't greatly exceed the amount observed on the shortest baselines. UVBOX : UVBOX MUST be 0 for UV data which is NOT XY sorted! If uniform weighting (UVWTFN other than 'NA') is requested, the weight of each visibility is divided by the number of visibilities occurring in a box in uv space centered on the box containing the visibility point in question. If UVBOX=0 the counting box is the same as the uv cell, UVBOX=1 uses 3X3 uv grid cells centered on the cell containing the visibility UVBOX=2 uses 5X5 cells etc. The effect of increasing UVBOX is to further down weight data occurring in densely populated regions of the uv plane. Since must arrays have centrally condensed uv coverage the effect of increasing UVBOX is to decrease the beam size at a cost of reduced sensitivity and a slightly messier beam. UVBOX=2 occasionally appears to have a dramatic effect on the beam size for VLA data from the D array. XTYPE,YTYPE : The default convolution function Spheroidal (5) is now recommended for nearly all maps. CLEANing MX de-convolves a dirty beam from a dirty map image using the CLEAN algorithm [Hogbom 1974] as modified to take advantage of the Array Processor [Clark 1980] and doing the subtraction from the un-gridded uv data. CLEAN iteratively constructs discrete approximant F(n) to a solution F of the convolution equation: B^F = D (1) where D denotes the discrete representation of the dirty map, B of the dirty beam, the symbol ^ here denoting convolution. The initial approximant F(0)=0 everywhere. At the n'th iteration, CLEAN searches for the extremum of the residual map R determined at the (n-1)'th iteration: R(n-1) = D - B^F(n-1) (2) A delta-function "CLEAN component", centered at this extremum, and of amplitude g (the loop GAIN) times its value, is added to F(n-1) to yield F(n). The search over R is restricted to an area A called the "CLEAN window". A is specified as a number NFIELD of rectangular sub-areas. Iterations continue until either the number of iterations n reaches a preset limit N (=NITER), or the absolute value of the extremum of the residual map decreases to a preset value FLUX. If FLUX is negative, the clean stops at the first negative Clean Component. To diminish any spurious high spatial frequency features in the solution, F(N) is normally convolved with a "hypothetical" Gaussian "Clean Beam" H to construct a final "Clean Map" C: C = H^F(N) + R(N) (3) The clean beam H may be specified by the user through the parameters BMAJ, BMIN, BPA, or it may be defaulted to an elliptical Gaussian fitted to the central region of the dirty beam B. MX writes the array of "Clean Components" F(N) to the CC extension files of the clean map image file. The Clark algorithm speeds up the deconvolution process by splitting it into "major" and "minor" iteration cycles. At the beginning of the m'th major cycle, it loads into the AP a RESTRICTED residual map R'(m) containing only the LARGEST (positive and negative) values in the current residual map R(m). It then performs a "minor" cycle of iterations wherein new CLEAN components are sought with (a) the restricted residual map R'(m) replacing the full residual map R and (b) the dirty beam B being approximated by its values inside a small area (the "beam PATCH") with zeroes outside. A minor cycle is terminated at iteration n' when the peak in the restricted residual map R'(n') falls to a given multiple [Clark 1980] of the largest value that was ignored in R(m) when R'(m) was passed to the the AP. At the end of the cycle of minor iterations, the current clean component list F(n') is Fourier transformed, subtracted from the ungridded uv data, re-gridded and FFT-ed back the map plane, thereby performing step (2) EXACTLY with the components list F(n') obtained at the end of the minor cycle. Errors introduced in the minor cycle through use of the restricted beam patch are corrected to some extent at this step. This ends the m'th major cycle, the (m+1)th beginning when the new restricted residual map R'(m+1) is loaded into the AP. CLEANing ends (with the transform steps used at the end of a major cycle) when either the total number of minor iterations reaches NITER, or the residual value being CLEANed at a minor iteration reaches FLUX. Prussian Hats When dealing with two-dimensional extended structures, CLEAN can produce artifacts in the form of low-level high frequency stripes running through the brighter structure. These stripes derive from poor interpolations into unsampled or poorly sampled regions of the (u,v) plane. [When dealing with quasi one-dimensional sources (jets), the artifacts resemble knots (which may not be so readily recognized as spurious)]. MX invokes a modification of CLEAN that is intended to bias it towards generating smoother solutions to the deconvolution problem while preserving the requirement that the transform of the CLEAN components list fits the data. The mechanism for introducing this bias is the addition to the dirty beam of a delta-function (or "spike") of small amplitude (PHAT) while searching for the CLEAN components. [The beam used for the deconvolution thereby resembles the helmet worn by German military officers in World War I, hence the name "Prussian Helmet Clean"]. The theory underlying the algorithm is given by Cornwell (1982, 1983), where it is described as the Smoothness Stabilized CLEAN (SSC). Don't CLEAN =================== If there is so little signal in your map that no side-lobes of any source in it exceed the thermal noise, then no side-lobe deconvolution is necessary, and CLEANing is a waste of your time and of CPU cycles. General - You can help CLEAN when you map =============================================== Other things being equal, the accuracy of the deconvolution process is greatest when the shape of the dirty beam is well sampled. When mapping complicated fields, it is often necessary to compromise between cell size and field of view; if you are going to CLEAN a map image, you should set up your mapping parameters in MX so that there will be at least three or four cells across the main lobe of the dirty beam. It is also important to make the CLEANed region large enough that no strong sources whose side-lobes will affect your map have been aliased by the FFT. This can be done by making a small map field around each confusing source. Consider making a strongly tapered map of a wide field around your source at low resolution to diagnose confusion before running MX on a high resolution map(s) (especially when processing snapshot data from the lower VLA frequencies). It is helpful to regard CLEAN as an attempt to interpolate missing samples in the (u,v) plane. The accuracy of the interpolation is greatest where the original sampling is dense or where the visibility function varies slowly. The accuracy is least where you ask CLEAN to Extrapolate into poorly sampled or unsampled regions of the (u,v) plane where the visibility function changes rapidly. One such region is the center of the (u,v) plane in any map made from data where all of the fringe visibilities were less than the integrated flux density of the source. You can help CLEAN to guess what may have happened in the center of the (u,v) plane (and thus to guess what the more extended structure on your map should look like) by including a zero-spacing flux density when you make your map. This gives CLEAN a datum to "aim at" in the center of the (u,v) plane. Extended structure can often be reconstructed well by deep CLEANing when the zero-spacing flux density is between 100% and 125% of the average visibility amplitude at the shortest spacings. If your data do not meet this criterion, there may be no RELIABLE way for you to reconstruct the more extended structure. (Some cases with higher ratios of zero-spacing flux density to maximum visibility amplitude can be successfully CLEANed, but success is difficult to predict). If you see an increase in the visibility amplitudes on the few shortest baselines in your data, but not to near the integrated flux density, you may get better maps of the FINE structure by excluding these innermost baselines. Another unsampled region lurks in the outer (u,v) plane in many VLA maps of sources at declinations south of +50, if the source has complicated fine structure. To see why, consult the plots of (u,v) coverage for the VLA in Section 4 of the "Green Book" [Hjellming 1982]. At lower declinations, some sectors of the outer (u,v) plane are left poorly sampled, or unsampled, even by "full synthesis" mapping. (There are missing sectors in the outer (u,v) plane in ANY snapshot map). If the visibility function of your source has much structure in the unsampled sectors, CLEAN may work poorly on a high resolution map unless it gets good "clues" about the source structure from the well-sampled domain. If the clues are weak, badly extrapolated visibilities in the unsampled regions can cause high frequency ripples on the CLEAN map. In such cases, CLEAN may give maps with better dynamic range if you are not too resolution-greedy, and restrict your data to the well-sampled "core" of the (u,v) plane. Before applying CLEAN, examine your (u,v) coverage and think whether you will be asking the algorithm to guess what happened in such unsampled regions. Frailties, Foibles and Follies ============================== There are excellent discussions of CLEAN's built-in idiosyncrasies by Schwarz (1978, 1979), by Clark (1982) and by Cornwell (1982). Another way of looking at CLEAN is to think of it as attempting to answer the question "What is the distribution of amplitudes at the CLEAN component positions [F(N)] which best fits the visibility data, if we define the sky to be blank everywhere else ?" The algorithm can then be thought of as a "search" for places where F should be non-zero, and an adjustment of the intensities in F(N) to obtain the "best" agreement with the data. The re-convolution of F(N) with the hypothetical "clean beam" H produces a "clean map" C whose transform is no longer a "best fit" to the data (due to differences between the transforms of H and of the dirty beam B). The merit of the re-convolution is that it produces maps whose noise properties are pleasing to the eye. It may also be used to "cover up" instabilities in CLEAN stemming from poor extrapolation into the unsampled regions of the (u,v) plane, by making H significantly wider than the main lobe of B. Note also that step (3) of the standard CLEAN combines this re-convolution with the residual map, which contains faint sky features convolved with the DIRTY beam B. If there is significant signal remaining in the residual map, the effective resolution of the Clean Map C varies with brightness. You must therefore be particularly careful when comparing Clean maps made at different frequencies or in different polarizations; you should CLEAN all such maps sufficiently deeply that the integrated flux density in the CLEAN components F(N) is much greater than that in the residual map R(N). A recurrent question about CLEAN concerns the uniqueness of the Clean Map. In the absence of noise, CLEAN could adjust the amplitudes of the components in F(N) to minimize the rms difference between the observed visibility function and the transform of F(N) [Schwarz 1978, 1979]. If the number of degrees of freedom in F(N) is less than the number in the data, CLEAN can (and in many practical cases does) converge on a solution that is sensibly independent of your input parameters. Noise and approximations in the algorithms complicate this [Cornwell 1982], but realize that the solution CANNOT be unique if the number of positions at which you end up with CLEAN components exceeds the number of independent (u,v) data points. Be suspicious if your Clean Map contains structures which resemble those of the dirty beam. This may mean either that you have not CLEANed deeply enough,or that CLEAN has had difficulty in some unsampled sector of the (u,v) plane in your case. This test is particularly important in the case of snapshot maps,for which the side-lobes of the dirty beam have a pronounced star (snowflake) structure. GAIN and NITER The depth to which CLEAN carries out its deconvolution is approximately measured by the product NITER*GAIN. The first CC extension file version corresponds to the first output frequency channel. A value of 0 for NITER is recognized to indicate that no CLEANing is desired. In this case the dirty beam is always the size of the largest field and the CLASS of the output images are "IIMnnn" rather than "ICLnnn". The value of NITER and the execution time needed to reach a given CLEANing depth are minimized by setting GAIN = 1.0, but setting GAIN > 0.5 is recommended only when removing the side-lobes of a single bright unresolved component from surrounding fainter structure. Note that TELL may be used to lower the GAIN after the first major cycles have removed the bright point objects. When CLEANing diffuse emission, GAIN = 0.1 (the default) will be much better, for the following reason. The search step of the algorithm begins its work at the highest peak (which in an extended source may be a random noise "spike"). After one iteration, the spike is replaced in R by a negative beam shape, so the next highest peaks are more likely to be found where the spike would have had its biggest negative side-lobes [see the diagram on p.11 of Clark (1982)]. If GAIN is high, subsequent iterations tend to populate F(n) around the negative sidelobe regions of the highest peaks. This "feedback" can be turned off by making GAIN small enough that the negative sidelobes of the first peaks examined in an extended structure are lost in the noise, i.e. GAIN * (worst negative sidelobe level) < signal-to-noise on the extended structure. In practice setting GAIN << 0.1 makes CLEAN unacceptably slow (NITER too large for a given CLEANing depth) so a compromise is needed. GAINs in the range 0.1 to 0.25 are most commonly used. If the source has some very bright compact features embedded in weaker diffuse emission, it is illuminating to examine the Clean Map when only the brightest structure has been CLEANed, to check whether subsequent CLEANing of weaker diffuse emission causes it to "go lumpy" via the sidelobe feedback effect. This could be done with GAIN = 0.3-0.5, using either NITER or the FIELD selection to ensure that the search does not stray into the extended emission. Then MX can be restarted with lower GAIN, higher NITER and wider fields to tackle the diffuse structure. TELL may be used to lower the gain during execution of MX. If the weak emission "goes lumpy" you may need to rerun MX with different combinations of GAIN and NITER to find the most effective one for your particular case. Ultimately you will stop MX when the new CLEAN component intensities approach the noise level on your map. On a map of Stokes I, the appropriate stopping point will be indicated by comparable numbers of positive and negative components appearing in the CC list. On maps of Stokes Q and U, which can and will be legitimately negative, you need to know the expected sensitivity level of your observation to judge how deep to go. It is NEVER worth increasing NITER and restarting MX once many negative CLEAN components appear in the CC list of an I map. When this occurs, you are using CLEAN to shuffle the noise in the residual map, which is about as sensible as rearranging the deck chairs on the Titanic after it hit the iceberg. FLUX This provides an alternative to NITER for terminating the iterations in a given run of CLEAN. In practice, most users prefer to control CLEAN by limiting each execution with NITER. FLUX should then be set to your expected rms noise level times the dynamic range of the dirty beam (peak/worst sidelobe), to ensure that you do not inadvertently waste time iterating to a high value of NITER while in fact CLEANing emission whose sidelobes are lost in the noise. If FLUX is between -99 and -1, then clean stops on first negative clean component. If FLUX < -99, then FLUX is milli-precent change in total flux density between major cycles (ie FLUX=-1000 => stop clean if < 1 % change) A new adverb will be added to replace the convoluted FLUX logic. BMAJ, BMIN, BPA The default values of 0 for these parameters invoke an algorithm whereby the central portion of the dirty beam B is fitted with an elliptical Gaussian function whose parameters are then used to specify the Clean Beam H. The algorithm can be "fooled" by positive or negative sidelobes near the main lobe of B, and has been known to prescribe unsatisfactory forms for H, particularly for snapshot maps. It is normally preferable to specify BMAJ, BMIN and BPA explicitly from your own examination of the dirty beam, or after a trial fit using the default. The Clean Map C may be easier to interpret if BMIN is set equal to BMAJ, so that H is a circular Gaussian, and any elongated structures are therefore seen in their correct orientation. The frailties of CLEAN's deconvolution will be least apparent if both are set equal to the LONGEST dimension of the dirty beam. Attempts to "super resolve" the source by setting BMAJ and BMIN to the SHORTEST dimension of the dirty beam (or shorter) skate on the proverbial thin ice, the more so if the number of clean components in F(N) is comparable to, or larger than, the number of independent visibility data used to make the dirty map. Note that if BMAJ, BMIN and BPA differ greatly from those of the main lobe of the dirty beam, the parts of the Clean Map derived from F(N) and from R(N) at step (3) will have greatly different resolutions. This is very dangerous if R(N) contains significant residual emission. If BMAJ is set <0, then the output map contains the residual map R(N) instead of the clean map C. This option allows you to display, take hard copy of, or back up, the residual map while deciding further strategy, retaining the ability to regenerate the Clean Map later. NFIELD, FLDSIZE A practical detail: when NFIELD=1 and FLDSIZE specifies an area <= 127 by 127, the entire residual map can be loaded into an AP with 64k, and CLEAN can proceed very efficiently. This speeds up execution enormously. If NFIELD>1, even if the area in the fields adds up to less than 127 by 127, this economy is lost. A particularly large economy in run time is achieved when this default is used with 128 by 128 (or smaller) maps. In the 128 by 128 case not only will the Clean Window default to 128 by 128, but the necessary FFTs can be done entirely within the AP; under these circumstances MX proceeds at a headlong gallop. FACTOR This knob protrudes from the inner workings of the Clark algorithm, enabling the user to vary the criterion [Clark 1980] by which minor iteration cycles are ended. [For those with an interest in the gory details - MX first notes the ratio between the brightest point which was ignored when the residual map R'(m) was passed to the AP and the maximum residual R'(n') at some later iteration n'; it then uses the Clark criterion with this ratio raised to the power FACTOR replacing unity in Clark's summation]. FACTOR = 0 (the default) recovers the Clark criterion. FACTOR > 0 allows the minor cycles to go on longer, speeding up the CLEAN slightly (about 20% for FACTOR = 1), but allowing you to get closer to the situation where residuals R' in the AP become smaller than values which were ignored when the AP was loaded. The search for new components becomes less and less accurate (compared with a Hogbom algorithm using all of R in step (2)), and the representation of extended structure in the final F(N) deteriorates. FACTOR < 0 makes the termination criterion more conservative and thus improves the accuracy of the CLEANing at the expense of forcing more major cycles with a corresponding overhead in the FFTs done at the end of each one. It is recommended that experiments with FACTOR normally be confined to the range -0.3 < FACTOR < +0.3, negative values being used when CLEANing complex extended structures, and positive values when CLEANing very simple compact structures. MINPATCH This parameter specifies the minimum half-width of the beam patch that will be allowed in a minor cycle. A smaller beam patch allows the CLEAN to go faster at the expense of less accurate subtraction at each iteration. The inaccuracy can lead to errors which will not be recovered completely at the end of the major cycle, especially if high GAINs are used or the source has complex structure. MINPATCH=51 is recommended for CLEANing complicated sources. If the BEAM has large sidelobes far from the beam center, the MINPATCH should be as large as possible (<= 1024). (The BEAM often has large sidelobes for VLA snap-shot images.) The beam patch and the residuals to be cleaned in each minor iteration must fit in the (pseudo) AP memory. This may limit the number of pixels cleaned when MINPATCH is large. This is not a consideration on most modern computers where we set the AP size to 1 Megaword or more. DOTV Use of DOTV > 0 is STRONGLY recommended when CLEANing a source for the first time. It causes the residual map of field number DOTV to be displayed on the TV after each major cycle, allowing you to monitor what emerges as the CLEAN progresses. DOTV > 0 produces a 15-sec pause after each major cycle to give you time to inspect the display and to assess whether it is reasonable to proceed. Pressing track-ball D during this pause terminates MX in an orderly fashion. Pressing buttons A,B,C (or allowing the pause time to elapse) starts the next major cycle. When CLEANing a very complicated source for the first time, it is often worth going beyond this interactive approach, by taking hard copy of various stages of the CLEAN to compare carefully later. Consider setting NITER to a value in the range 50-200 at first. Then take hard copy of the lightly CLEANed map for later reference, and restart MX with a higher value of NITER. Doing this increasing NITER by factors of order 2 each time can be very instructive in showing you what CLEAN is doing to the extended structures in your source. Spectral line users may wish to CLEAN a typical channel in this way before deciding how best to parameterize MX for their production runs. (Note that the trial channel should be reanalyzed using the final choice of parameters, for consistency; MX's final Clean maps depend in detail on the relative numbers of major and minor cycles which have been performed). Sorting of UV data: For historical reasons, there are two parallel data paths for gridding and model subtraction within MX; one for XY sorted UV data and the other for unsorted UV data. (Data must be Time-Baseline (TB) sorted for the calibration process.) The XY sorted algorithm was written first, and was kept although the newer un-sorted algorithm has the identical functionality. Subroutines UVTBUN, UVGRTB and ALGSTB are process un-sorted data while UVUNIF, UVGRID, and ALGSUB process XY sorted data. REFERENCES Proceedings of the NRAO-VLA Workshop on Synthesis Mapping 1982, ed. A.R.Thompson and L.R.D'Addario. Clark, B.G. (1980). "An Efficient Implementation of the Algorithm "CLEAN", Astron.Ap., 89, 377-378 Clark, B.G. (1982). "Large Field Mapping", Lecture #10 in the NRAO-VLA Workshop on "Synthesis Mapping" Cornwell, T.J. (1982). "Image Restoration (and the CLEAN Technique)", Lecture #9 in the NRAO-VLA Workshop on "Synthesis Mapping" Hjellming,R.M. (1982). "An Introduction to the NRAO Very Large Array", Section 4. Hogbom,J.A. (1974). "Aperture Synthesis with a Non-Regular Distribution of Interferometer Baselines",Astron.Ap.Suppl., 15, 417-426 Schwarz, U.J. (1978). "Mathematical-statistical Description of the Iterative Beam Removing Technique", Astron.Ap.,65, 345. Schwarz, U.J. (1979). "The Method "CLEAN" - Use, Misuse and Variations", in Proc. IAU Colloq. No.49, "Image Formation from Coherence Functions in Astronomy", ed. C. van Schooneveld, (Dordrecht:Reidel), p. 261-275. Cornwell,T.J. (1982). "Can CLEAN be Improved ?",VLA Scientific Memorandum No. 141. Cornwell,T.J. (1983). "A Method of Stabilizing the CLEAN Algorithm", preprint.