; SAD ;--------------------------------------------------------------- ;! finds and fits Gaussians to portions of an image ;# TASK ANALYSIS MODELING ;----------------------------------------------------------------------- ;; Copyright (C) 1995-1996, 1999, 2001-2005, 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 ;----------------------------------------------------------------------- SAD LLLLLLLLLLLLUUUUUUUUUUUU CCCCCCCCCCCCCCCCCCCCCCCCCCCCC SAD: Task to fit Gaussian models to an image by least-squares INNAME Input image name (name) INCLASS Input image name (class) INSEQ 0.0 9999.0 Input image name (seq. #) INDISK 0.0 9.0 Input image disk drive # INVERS -1.0 46655.0 Input image MF ext. version <= 0 => new BLC 0.0 4096.0 Bottom Left corner of fit TRC 0.0 4096.0 Top Right corner of fit DORESID -1.0 2.0 >0 => 1 Catalog residual map OUTNAME Output image name (name) OUTCLASS Output image name (class) OUTSEQ -1.0 9999.0 Output image name (seq. #) OUTDISK 0.0 9.0 Output image disk drive # NGAUSS 0.0 40000.0 Max. Number of components CPARM 0.0 9999.0 Flux cutoff levels in descending order ICUT 0.0 9999.0 Retry level BWSMEAR -0.1 0.1 Bandwidth smearing corr. SORT Sort Order of output ' '=RA DOCRT -3.0 132.0 >0 => print fits on CRT > 72 => terminal width =0 => print suppressed <0 => line printer FITOUT Disk file to save fit info OUTVERS -1.0 46655.0 CC file version # for solutions: -1 => none, 0 new DOALL -1.0 1.0 >0 => fit multiple peaks DOWIDTH -1.0 2.0 >0 => fit widths GAIN 0.0 1.0 Amp-dependent part of retry and warning levels DPARM Reject components with (1) peak < D(1) (2) flux < D(2) (3) rms > D(3) + GAIN * flux (in quadrature) (4) widths > D(4) cells (5) peaks > D(5) cells outside interior area (6) peaks > D(6) cells outside image (7) total residual flux in the fitting box [no default] (9) Use IN2NAME etc to set image of rms >= 2 => CPARM is in S/N (see HELP) (10) Expand fit box pixels IN2NAME RMS image name (name) IN2CLASS RMS image name (class) IN2SEQ 0.0 9999.0 RMS image name (seq. #) IN2DISK 0.0 9.0 RMS image disk drive # PRTLEV 0.0 1023.0 Debug print level PBPARM Primary beam parameters: (1) level to believe - <= 0 means do not apply a primary beam (2) > 0 use (3)-(7) ---------------------------------------------------------------- SAD Type: Task Use: SAD (Search And Destroy) is a task to find a number of potential sources in a (sub)image, fit Gaussian components to these, and optionally print the results, store them in a CC file, and create a residual file. The searching may be restarted with different parameters to remove additional sources. Only one plane of a cube is fit at one time. However, the MF file keeps track of the plane number and may contain data for more than one plane. With additional tasks (to be written yet), one should be able to use this feature to do spectral fitting of the objects found spatially by SAD. The display produced by SAD shows the results of the fitting, estimates of the uncertainties in the answers (based on the actual noise and theory rather than the quality of the fitting), and attempts to deconvolve the Clean beam from the fit sources. When the residual image near a source exceeds a limit controlled by the cutoff (CPARM) and GAIN parameters, an H, L, or S will be shown near the fit peak value. H is for a high point in the residual, L for a rather negative point, and S for a large rms. If the width of the display allows, the max residual is displayed with the deconvolution results and an * is placed near excessive residuals. Adverbs: INNAME......First image name (name). Standard defaults. INCLASS.....First image name (class). Standard defaults. INSEQ.......First image name (seq. #). 0 => highest. INDISK......Disk drive # for the first image. 0 => any. INVERS......Version number of a MF table extension file attached to the input image and copied to the ouput residual image (if any). <= 0 => create a new one, > 0 => use a pre-existing one and subtract the components in it before searching for more. BLC.........Bottom left corner of area of image to fit. TRC.........Top right corner of area of image to fit. DORESID.....>0 -> Create a residual map of subimage OUTNAME.....Residual map name. Standard defaults. OUTCLASS....Residual map class. Standard defaults. OUTSEQ......Residual map seq. #. 0 => highest unique. OUTDISK.....Residual map disk no. 0 => highest with room. NGAUSS......The maximum number of components to search for 0->10. Maximum number is 40000. CPARM.......Search for potential sources down to these levels in units of the input image or in units of S/N (when DPARM(9) >= 2.0 and IN2NAME et al are specified). No defaults - list in descending order, A value of 0 => no more levels. Thus CPARM = 8, 4, 0.666, 0 => 3 rounds of searching. It has been found useful to fit the higest levels first, then look somewhat lower, and then even lower. Low level signal around a strong source can sometimes confuse the fitting. CPARM all 0 -> 3,0 in S/N or 3*rms,0 in image units. ICUT........If the peak residual in an island, after fitting a single Gaussian exceeds ICUT in image or S/N units (as CPARM) adjusted in quadrature by GAIN*flux, then the program will attempt a 2-Gaussian fit to the island. 0 => CPARM(i) for each search level i. BWSMEAR.....If not 0, the Clean beam will be smeared by a Gaussian in the radial direction of FWHM proportional to the radius from the pointing position times abs(BWSMEAR). Set it roughly to the channel bandwidth divided by the center frequency. The Clean beam is used as an initial estimate of the source size and is used in the deconvolution attempt to find the true size from the fit size. The peak intensity printed will be corrected for this effect; set BWSMEAR < 0 to suppress this correction. SORT........Sort order of output. ' ' -> 'R'-> Right Ascension 'D' -> Declination 'X' -> X pixel (~RA if no rotation) 'Y' -> Y pixel (~Dec if no rotation) 'S' -> Flux DOCRT.......False (< 0) use the line printer if FITOUT = ' ' else write named FITOUT file only. -2 causes the line feed characters in FITOUT to be suppressed -3 causes the documentation lines to be suppressed Null (= 0) print suppressed. True (> 0) use the terminal interactively. The task will use the actual terminal width as a display limit unless 72 < DOCRT < width. In that case, the display limit will be DOCRT characters. FITOUT......Disk file name in which to save the fit (line printer) output. ' ' => use scratch and print immediately for interactive jobs - batch jobs use FITOUT = 'PRTFIL:BATCHjjj.nnn' (jjj = job #, nnn = user #). When FITOUT is not blank, multiple outputs are concatenated and the file is not actually printed. OUTVERS.....= 0 => Create a new CC file on input image. < 0 => do not write any CC file > 0 => append components to pre-existing CC file SAD writes the deconvolved widths (0 on failure of deconvolution) into the CC files, if the input image is a Clean image. If DOWIDTH <= 0, then it writes point components into the CC file. DOALL.......>0 -> If an island has multiple (up to 4) peaks, fit multiple gaussians. Otherwise fit 1 gaussian to each island. DOWIDTH.....<= 0 -> Fit all sources with Clean beam >0 & <=1 -> Let fit find size of source starting with the Clean beam >1 -> Let program guess the sizes and then fit them (this can be somewhat unstable) GAIN........Retry, cutoff and warning levels are computed by SQRT ( level**2 + (GAIN*flux)**2 ) where the level is the no-signal retry (ICUT), cutoff (DPARM(2)) or warning (CPARM cutoff) level and flux is the peak of the component in question. No default. DPARM.......Components are fit within islands that are rectangular in shape. It may be possible to get bad solutions, so the program will reject components with: (1) peak <= DPARM(1). No default; 0 is okay if you mean it. Units are image units unless DPARM(9)>=2, in which case they are in S/N. (2) flux <= DPARM(2). No default; 0 okay (3) rms in the box > sqrt (DPARM(3)**2 + (GAIN*flux)**2). 0 => 1000. Units are image units unless DPARM(9)>=2, in which case they are in S/N. (4) widths > DPARM(4) cells. 0 => 1000. (5) peaks > DPARM(5) cells outside the island (fitting area) but interior to the image. No default; < 0 => inside the fitting area required. (6) peaks > DPARM(6) cells outside image. No default. This allows SAD to fit components legitimately on the edge of the whole image while rejecting spurious ones extrapolated to positions outside the fitting rectangle but fully in the image. (7) total residual flux in the fitting box > SQRT (DPARM(7) + (GAIN*flux)**2). No default. *** (9) > 0 => use IN2NAME, IN2CLASS, etc as an image of the RMS so that it may vary with position. = 1 => use the image only to evaluate the uncertainties in the fit components. >= 2 => use the image also to evaluate the noise at each pixel as data are read. In that case CPARM, ICUT, DPARM(1), and DPARM(3) are in S/N units. *** (10) Expand (or contract) the box used to fit the component. IN2NAME.....RMS image name (name). NO DEFAULT. The task RMSD may be used to prepare such an image. Note that the RMS image must be at the same coordinates more or less as the INNAME image but they do not have to allign. The RMS is found by looking up the coordinate of the coponent in the RMS image. If DPARM(9) >= 2, the RMS image is ASSUMED to have the same size and coordinates as the input image. Bad things will happen, perhaps not in obvious ways, if this is not true. In this case, the noise image is used throughout rather than simply in evaluating the uncertainties in the component parameters. IN2CLASS....RMS image name (class). Standard defaults. IN2SEQ......RMS image name (seq. #). 0 => highest. IN2DISK.....RMS drive # for the first image. 0 => any. PRTLEV......To find out which islands are rejected by the above for what reasons, set PTRLEV to the sum of the desired reasons: 1 peak, 2 flux, 4 rms, 8 widths, 16 X position outside interior window, 32 Y position outside interior window, 64 X position outside image, 128 Y position outside image., and 256 for residual flux. 511 does all of them. If you don't want to see the low peak ones, set PRTLEV to an even number. Any that are rejected for low peak will not be displayed even if they are also rejected for a selected reason. PBPARM......Primary beam parameters: (1) Lowest beam value to believe: 0 -> do not do the primary beam correction. This correction is done to the printed parameters only. The beam value used is max (PBPARM(1), that computed from (2)-(7)). (2) > 0 => Use beam parameters from PBPARM(3)-PBPARM(7) Otherwise use default parameters for the VLA (or ATCA where appropriate) (3-7)..For all wavelengths, the beam is described by the function: 1.0 + X*PBPARM(3)/(10**3) + X*X*PBPARM(4)/(10**7) + X*X*X*PBPARM(5)/(10**10) + X*X*X*X*PBPARM(6)/(10**13) X*X*X*X*X*PBPARM(7)/(10**16) where X is (distance from the pointing position in arc minutes times the frequency in GHz)**2. For the VLA, these parms are, by default, given by Perley's fits: 0.0738 GHz -0.897 2.71 -0.242 0.3275 -0.935 3.23 -0.378 1.465 -1.343 6.579 -1.186 4.885 -1.372 6.940 -1.309 8.435 -1.306 6.253 -1.100 14.965 -1.305 6.155 -1.030 22.485 -1.417 7.332 -1.352 43.315 -1.321 6.185 -0.983 For the ATCA, these are by default: 1.5 GHz -1.049 4.238 -0.8473 0.09073 -5.004E-3 2.35 -0.9942 3.932 -0.7772 0.08239 -4.429E-3 5.5 -1.075 4.651 -1.035 0.12274 -6.125E-3 8.6 -0.9778 3.875 -0.8068 0.09414 -5.841E-3 20.5 -0.9579 3.228 -0.3807 0.0 0.0 See explain for details ---------------------------------------------------------------- SAD: Task to find potential sources and fit Gaussian models to an image by least squares. DOCUMENTORS: W. Jaffe, Leiden RELATED PROGRAMS : SLFIT, IMEAN, MAXFIT, IMFIT, JMFIT PURPOSE SAD attempts to find all sources in a subimage whose peak is brighter than a given level. It searches the subimage specified by BLC and TRC for all points above this level and merges such points in contiguous "islands". For each island, initial estimates of the strength and size are generated. Then the gaussian fitting algorithm used in JMFIT is called to determine the least square guassian fit. If DOALL is < 0., only one gaussian is fit per island, with initial estimates generated from 2nd moments. If DOALL is TRUE and multiple peaks (above a cutoff = CPARM(i)) are found within the island, then up to 4 gaussians are fit. If the peak residual of a single Gaussian fit exceeds ICUT then a more complex 2-Gaussian fit ai attempted. The results of the fit are printed on the screen or the line printer and written into a ModelFit (MF) extension table. If DORESID is TRUE, the gaussians are subtracted from the input subimage, and a residual imageis cataloged, using OUTDISK, OUTNAME etc. If DOWIDTH(1) is negative, a gaussian with fixed size = CLEAN beam will be fit. WARNING!!! The list generated by SAD is not COMPLETE in any statistical sense. You will be warned about islands where the fitting algorithm failed. Note that sizes etc. of sources near the noise are very unreliable. For something approaching completeness Walter Jaffe recommends: Start with a well Cleaned map Set DOWIDTH = FALSE and only fit point sources. Do a series of search on progressively more tapered maps and compare results to determine flxes of extended sources. Make residual maps and inspect them to see where SAD blew it. Suggestion from Eric Greisen: DOWIDTH false always produces poor results even for only slightly extended objects. For decent S/N, the width fitting is quite reliable. COMMENTS ABOUT SOME PARAMETERS BLC, TRC: These specify the area to be searched for sources. If an residual file is requested, it covers the entire input image. NGAUSS: The maximum number of sources to find. Currently limited to 40000. CPARM: Search for source peaks down to this level. If specified as 0., SAD will determine the real (i.e. source-free) R.M.S. in the full image area and take CPARM(1) to be 3.0 times this value. If you make some CPARM(i) too small, you'll get lots of nonsense. The task uses CPARM(1), then restarts using CPARM(2), etc so long as the CPARM(i) > 0. This lets you extract the strongest points first without low-level interference and then go after weaker things. DOCRT: DOCRT = 1. will cause a list of fluxes, positions, and extension parameters, with their estimated errors, to be displayed on your terminal. DOCRT = -1. will cause the list to be printed on the line printer. DOCRT = 0. causes listing to be supressed. DORESID Catalog the post-fit residual map. DOWIDTH If you think most sources are unresolved, use DOWIDTH(1) = -1.0. This will fit simple point sources to each peak (and do very badly on those few that are slightly resolved). COMMENTS ON THE USE OF SAD FLUX DENSITY DETERMINATION: When attempting to obtain the flux density of a well-resolved source, the task IMEAN, which integrates the map values in a specified rectangle, is often more accurate than fitting the source with several Gaussian components and summing the integrated flux densities. Of course for a well resolved source a gaussian fit is only a crude approximation in any case. TVSTAT allows you to use an irregular area for this determination. PEAK FLUX DENSITY DETERMINATION: The verb MAXFIT, a simple fitting of the peak of a component with a second degree interpolation, is much faster than JMFIT and useful to obtain the approximate peak and position of a component. ERRORS OF PARAMETERS: The error estimates should be regarded as tentative, but more relaible than those from formal standard error estimates. The latter are meaningless since the objects are normally well fit using only 1-4 Clean beam areas. This means that the number of parameters fit exceeds the number of truly independent samples (neglecting the samples of 0 which were part of the selection of the island but not part of the formal fit of course). The errors are produced using an estimate of the true (signal free) rms R. It is taken from the image header keyword ACTNOISE, if present and positive, or by fitting the histogram of the image with a Gaussian. Note that this fit excludes both blanked and pure zero pixels, thereby allowing blanked pixels to be REMAGed to zero when needed. Using, John Ball's article in Method in Computational Physics, 14, 177, 1975, the noise in the peak of the fit Gaussian is estimated as: Delta(P) = R * (Clean-beam area) / (fit area) the noise in the widths as: Delta(W) = Delta(p) / P * W the noise in the center positions as: Delta(X) = Delta(W) / 2 The noise in the total flux is found by the usual combinatorial formulae and the noise in the position angle is estimated from Condon's article Delta(PA) = Delta(p) / P * sqrt (2 WxWn / (WxWx - WnWn)) where Wx is the maximum width and Wn the minimum width. The estimates from Ball have been replace by more complicated formulae from Condon. The following remarks now apply. An estimate of the each error is determined from theory based on the actual rms of the image (neglecting signal portions) or the rms given in header parameter ACTNOISE (if present and positive). AIPS verb ACTNOISE may be used to set this header parameter. See the explain file for SAD for details. Theory gives expressions for the errors in two limiting cases: point source (the beam area > 0.9*the fitted gaussian area) and expanded source (the beam area < 0.1*the fitted gaussian area). The formulae are taken from J. Condon paper 'Errors in Elliptical Gausian Fit', AA, 1996. The intermediate case is handled by interpolation between the two limit cases. It is not clear if this interpolation provides a good estimation of the error in general relation of beam and fitted gausian sizes and position angle. DECONVOLUTION: When fitting to a Clean map, SAD deconvolves the Clean beam from the fitted component size. The nominal deconvolution is obtained by deconvolving the fit from the Clean beam. A value of 0.0 means that the source is smaller than the Clean beam in some dimension. The minimum and maximum values are obtained by deconvolving the source beam parameters with all combinations of 0.7 * error and listing the extreme values. ON THE MESSAGE OUTPUT FORMAT For readability and compactness the message formats are chosen to fit in the width of the "printer" (real printer or CRT screen width given by DOCRT). The UNITS of the printed flux are scaled so that the weakest found flux lies in the range 1.0 to 999.0. The UNIT will be Jy or milliJY or whatever (indicated in the header to the printout). If another source has a flux greater than 999.999 in this UNIT, the flux will be divided by 1000., before printing, and an asterisk "*" will be printed before the flux to indicate this. A flux greater than 999,999.999 will be divided by 1.e6 and be prefixed by a "#". If non-point sources are fit (DOWIDTH > 0), and a CLEAN beam size can be found in the header, the derived source sizes and are orientations are deconvolved, with the results printed in a second listing. The numbers printed are the deconvolution of the best fit major axis, minor axis and position angle. (arcsec, arcsec, degrees), followed by the one-sigma lower limits on these quantities and the one sigma upper limits. ON THE MEANING OF BMAX, BMIN, AND BPA Formally the position angle of anything, such as the major axis of a gaussian source, is defined as the angle of the thing East from North. But the direction North only coincides with a column of the pixel array when you are on a meridian through the phase center. Thus in general two different positional angles can be defined, either relative to local North, or relative to the local Y-direction of the pixel matrix. Similar small differences can occur in the definition of an astronomical major axis versus a pixel-based major axis. Note for example that the formal astronomical position angle of the point spread function of an unresolved source changes with position in the field, due to the curvature of the North/South coordinate system. Sooooooooo, following the convention in JMFIT, the extention parameters bpa, bmin, and bmax printed in the message file are the astronomical values, relative to local North etc., while the parameters put into the CC file are the pixel based values. This latter so that operations like UVSUB will work correctly. This has the consequence, for example, that for point sources the message file values differ from the values for the BEAM, whereas the CC file values should agree with the BEAM. The MF file contains everything and the kitchen sink, so all parameters are present there.