; UTESS ;--------------------------------------------------------------- ;! deconvolves images by maximizing emptiness ;# TASK IMAGING ;----------------------------------------------------------------------- ;; Copyright (C) 1995-1996, 2002-2003, 2005, 2012 ;; 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 ;----------------------------------------------------------------------- UTESS LLLLLLLLLLLLUUUUUUUUUUUU CCCCCCCCCCCCCCCCCCCCCCCCCCCCC UTESS : Task which deconvolves images by maximising emptiness Dirty image INNAME Image name (name) INCLASS Image name (class) INSEQ 0.0 9999.0 Image name (seq. #) INDISK Image disk drive # Beam image IN2NAME Image name (name) IN2CLASS Image name (class) IN2SEQ -1.0 9999.0 Image name (seq. #) IN2DISK Image disk drive # Default level image IN3NAME Image name (name) IN3CLASS Image name (class) IN3SEQ -1.0 9999.0 Image name (seq. #) IN3DISK Image disk drive # Output UTESS image OUTNAME Image name (name) OUTCLASS Image name (class) OUTSEQ -1.0 9999.0 Image name (seq. #) OUTDISK Image disk drive # Restored image OUT2NAME Image name (name) OUT2CLAS Image name (class) OUT2SEQ -1.0 9999.0 Image name (seq. #) OUT2DISK Image disk drive # NMAPS 1.0 4087.0 Number of maps to deconvolve NITER * Maximum # of iterations NOISE * 0.0 Required residual, units are * (Jy/BEAM) FLUX Zero spacing Flux (Jy) BLC 0.0 4096 Bottom left corner of UTESS TRC 0.0 4096 Top right corner of UTESS DOTV * -1.0 2.0 TV display of UTESS image ? PRTLEV * -1.0 1.0 Lots of messages ? PBSIZE PB FWHM in arcseconds CHANGED < 0 - no PB correction (int. or single dish images) = 0 - use PBPARM > 0 - use Gaussian BMAJ FWHM (asec) Convolving beam BMIN FWHM (asec) Convolving beam BPA PA (degrees) Convolving beam PBPARM Beam parameters: (1) Cutoff 0 -> 0.07 (2) > 0 -> Use (3)-(7) (3)-(7) Beam shape BADDISK Disks to avoid for scratch. ---------------------------------------------------------------- UTESS Type: Task Use: UTESS performs a non-linear deconvolution of dirty beams from dirty images by maximising emptiness. It is specially designed for different types of images which have been interpolated to the same grid. It can combine single dish and interferometer images ! It will also now add residuals a la CLEAN. Unlike VTESS, UTESS does not constrain the image to be positive and can, therefore be used to deconvolve polarization maps or spectral-line absorbtion maps. Adverbs: INNAME......The dirty image name. Standard defaults. INCLASS.....The dirty image class. Standard defaults. INSEQ.......The dirty image seq. #. 0 => highest. If NMAPS > 1 then images having sequence numbers INSEQ,INSEQ+1,...,INSEQ+NMAPS-1 are operated on. INDISK......The dirty image disk drive #. 0 => any. IN2NAME.....The beam image name. blank => INNAME, otherwise standard behavior. IN2CLASS....The beam image class. Standard behavior except blank => 'RBEAM' if INCLASS = 'RMAP' 'LBEAM' if INCLASS = 'LMAP' 'IBEAM' if INCLASS = anything else IN2SEQ......The beam image seq . #. 0 => INSEQ, use -1 to get highest. If NMAPS > 1 then images having sequence numbers INSEQ,INSEQ+1,...,INSEQ+NMAPS-1 are operated on. IN2DISK.....The beam image disk drive #. 0 => any. ******** If a default image is not specified completely, then a flat default will be used. Usually the flat default will work satisfactorily. ********* IN3NAME.....The default image name. Standard defaults. except blank => use flat default. IN3CLASS....The default image class. Standard defaults. except blank => use flat default. IN3SEQ......The default image seq. #. 0 => use flat default, set IN3SEQ to -1 to get highest. IN3DISK.....The default image disk drive #. 0 => use flat default. OUTNAME.....The UTESS image name. Standard defaults. OUTCLASS....The UTESS image class. Standard behavior with default = 'xUT' if INCLASS = 'xMAP', where x is any character 'UT' if INCLASS = anything else OUTSEQ......The UTESS image seq. #. 0 => highest unique. If >0; image will be created if new, overwritten if image name exists. OUTDISK.....The UTESS disk drive no. 0 => highest with space OUT2NAME....The convolved image name. Standard defaults. OUT2CLAS....The convolved image class. Standard behavior with default = 'xUTC' if INCLASS = 'xMAP' 'UTC' if INCLASS = anything else OUT2SEQ.....The convolved image seq. #. 0 => highest unique. If >0; image will be created if new, overwritten if image name exists. OUT2DISK....The UTESS disk drive no. 0 => highest with space NMAPS.......Number of maps to be deconvolved. Must be in sequence starting at INSEQ. NITER.......UTESS iteration limit. 0 => 5. If less than Zero then will go to ABS(NITER) iterations or stop at soluton, else increase accuracy of solution as iteration proceeds. Can be changed by TELL. NOISE.......The target R.M.S. residuals for each image are ERROR (Jy/beam). Note this controls the quality of the final UTESS image. UTESS tries to get fit to be less than 1.05 SIGMA. Can be changed by TELL. NOISE(64) is used for all fields > 64. The first value should correspond to the only single dish image. Although it is put on the last (NMAPS) place The other values correspond to the interferometric images (the second=>the first image; the third=>the second..... FLUX........Zerospacing of the UTESS image. Three cases : a. > 0 = >UTESS tries to get within 5% of FLUX b. = 0 => UTESS estimates it. Often does well. c. < 0 => UTESS estimates it using ABS(FLUX) as an initial guess (better than putting zero) BLC.........Bottom left corner of UTESS image, BLC(3) gives the channel number to deconvolve. TRC.........Top right corner of image; both BLC and TRC default do that the inner quarter is chosen. DOTV........Display UTESS map on TV channel 1. >= 0 => yes. If true, you may stop the UTESSing with TV button D after each map is displayed. To see residual image set DOTV = 2. Can be changed by TELL. PRTLEV......Print lots of informative messages ? > 0 => yes. Can be changed by TELL. PBSIZE......Size of primary beam in arcsec, FWHM of Gaussian model. One number per field. If = 0, use PBPARM beam with defaults suitable to the VLA. If < 0, do no primary beam correction, e.g. usually for fields that are not interferometer data but can be specified for interferometer images if desired If > 0, use a Gaussian of FWHM of PBSIZE(I). PBSIZE(64) is used for fields > 64. The first value (-1) should correspond to the only single dish image. Although it is put on the last (NMAPS) place. The other values correspond to the interferometric images (the second=>the first image; the third=>the second..... BMAJ........FWHM in arcseconds of the restoring beam. The final image is convolved with this beam, and the residuals are added to form a pseudo-CLEAN image. If BMAJ < 0.0 then no restoration if performed. If BMAJ = 0.0 then the beam is fitted to obtain BMAJ, BMIN, BPA. BMIN........FWHM in arcseconds of the minor axis of the restoring beam. BPA.........Position angle in degrees of the restoring beam. PBPARM......Primary beam parameters: (1) Lowest beam value to believe: 0 -> 0.07 Sources outside this range are ignored. (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 BADDISK.....This array contains the numbers of disks on which it is desired that scratch files not be located. BADDISK has no effect on input and output maps. ---------------------------------------------------------------- UTESS : Task which deconvolves sets of images DOCUMENTOR: T.J.Cornwell NRAO/VLA DATE OF DOCUMENTATION: 30 Nov 1987 RELATED PROGRAMS: UVMAP,VM,APCLN,MX,APVC,STESS,LTESS VERSION: 15JAN88 PURPOSE UTESS is a variant of VM designed to handle the deconvolution of different types of images. It can handle up to 4087 different dirty images and beams which have been calculated on the same size grid. Both interferometric and focal plane images can be treated, and for the former, primary beam attenuation can be corrected. UTESS performs a deconvolution of the dirty beam from the dirty map by the Maximum Entropy Method MEM. There are, in general, many solutions to the deconvolution problem; of these UTESS selects the solution having the greatest entropy: H = Sum over all pixels ( h(pixel Brightness)) where h has the form : - f*log(f/m) where m is the default brightness and f is the pixel brightness. This measures the lack of dispersion in pixel values and thus the maps tend to be smooth in this sense. Given no data the output image is just the default image. There are other justifications for maximising H but these are not widely accepted. The pragmatic view is that UTESS maps of extended emission seem to be more aesthetically pleasing than those produced by the CLEAN deconvolution algorithm. In particular, CLEAN maps of large sources seem to show a mottled structure, which is caused by the assumptions inherent in the CLEAN algorithm, and which is not present on the corresponding UTESS maps. UTESS may run faster than APCLN on images spanning many (>100,000) resolution elements. There are several undesirable features of UTESS maps of which the user should be aware. First, the response to a point source in the map is manifestly signal-to-noise dependent, the resolution decreasing with signal strength. To some extent this can be masked by convolving with a beam of known resolution as is done in the CLEAN algorithm. The consequence is that comparison with other maps is difficult. Secondly, the map is totally positive and biased. A map will always show some emission in nominally blank regions but this background will be very flat if FLUX has been chosen correctly. This bias is negligible on regions of emission which are much brighter than the noise level. Thus, the map is mainly useful for qualitative information unless it is convolved down to lower resolution. On the other hand, the images may often be superior in quality to CLEAN images and may take less CPU time to compute. This is especially true for large images where the sidelobe level is quite low e.g. rms less than 1%. Quite often UTESS produces the most useful image. UTESS actually maximises H subject to the constraints that the r.m.s. residual be equal to one sigma ( using the Lagrange Multiplier ALPHA ) and that the total flux be FLUX ( using the multiplier BETA ). For the maximisation of the objective function a modified Newton-Raphson approach is used. Non-diagonal elements of the Hessian matrix are neglected. For one input image, each step or iteration requires two 2-D FFTs and so is roughly equivalent to one major cycle of APCLN. The cost of extra fields is roughly proportional. This is an experimental program and so all feedback is welcome. Send any comments, abusive or complimentary, to Tim Cornwell at the Array Operations Center. COMMENTS MAPUNITS : The final units of the map are Jansky per pixel. If you prefer other units of brightness such as Kelvin then AXDEFINE can be used to change the header. To obtain an image which can be compared with the CLEAN image set BMAJ >= 0.0. If BMAJ = 0.0 then a fit will be made to the dirty beam to find a suitable CLEAN beam, otherwise the specified beam will be used. This restored image will come out as OUT2NAME.OUT2CLAS.OUT2SEQ on dish OUT2DISK. ALIASING : To overcome aliasing problems, which can be disastrous in an algorithm which enforces positivity, only a quarter of the map is allowed to be non-zero. BLC and TRC control the location of the quarter within the dirty image. The default is such that the inner quarter is choosen. If TRC is more than half an axis length from BLC then it will be truncated. CONVERGENCE : For maps of reasonable signal to noise 100 - 1000 about 15 - 30 iterations are needed. An automatic stopping criterion is included. It stops if: 1. NITER < 0 2. ABS(total flux-FLUX) < 0.05*FLUX *** only if FLUX > 0 *** 3. rms residual < 1 sigma This criterion has developed by trial and error, and has no real theoretical justification. It may be too optimistic in that the image is still changing significantly. If you believe this to be the case then restart with NITER > 0 and stop by hand. Note however that the minimum brightness is poorly defined and has little meaning so don't worry too much about it. Some combinations of inputs parameters will not allow a UTESS image. For example, in nearly all cases there is no positive image with the correct flux (FLUX) which fits the data exactly (NOISE=0.0). However if you set FLUX too large then an exact fit can be achieved. DEFAULT IMAGE : ************************************************************* NORMALLY YOU CAN IGNORE THIS POSSIBILITY BY LEAVING IN3NAME,IN3CLASS,IN3SEQ,IN3DISK blank. ************************************************************* The default image determines what the image looks like if there is no data. Any data cause perturbations away from this image. The default "default" image is flat and so UTESS tries to make the output image as flat as is allowed by the data. An non-flat default is helpful in cases where a flat default fails. An example is the deconvolution of an image containing a point source in rather diffuse extended emission. Plain UTESS will usually leave the sidelobes of the point source buried in the diffuse emission. A default level of a point source in an extended Gaussian may well help. Another useful mode is to use a low resolution image as the default. Failing such an image, the following procedure gives good results : run to convergence with a flat default, use CONVL to smear out the resulting image (FACTOR=1 to preserve units of Jy/Pixel), then use this smeared image as the default and run to convergence. The resulting image has less bias and suppresses low level noise well. A default image can be generated using the task IMMOD. This is useful for planets, the Sun etc. Note that the units are Jy/pixel. MOSAICING or TESSELATION : One of the most important features of UTESS is its ability to form mosaics of a large object spanning many pointing centers. For example, at 20cm, this allows imaging of objects larger than the size of the primary beam (30'). When observing, you must take data at many different pointing centers. UTESS will then joint them smoooothly. It knows about the VLA primary beam, and uses a model due to Rots and Napier, truncated at the 5% level. Furthermore, singe dish data can be introduced to give the short spacing information missing from the interferometer data. Interferometric data can be corrected for the primary beam pattern. At the moment, the I'th field is corrected for a circular Gaussian of FWHM PBSIZE(I) arcsec centered on the pointing center or, if TELESCOPE='VLA' in the image header then a model of the VLA primary beam is used. Use PUTH with KEYWORD='TELESCOPE', KEYSTR='VLA' to put this in the header if necessary. If PBSIZE(I)=0.0 then no correction is performed. If PBSIZE(I)<0.0 then that field is assumed to refer to a focal plane image such as that measured by an optical telescope or a single dish. The pointing center is specified in the header by the Keywords 'OBSRA', 'OBSDEC'. It will only show up in IMHEADER if it is different from the phase tracking center. UTESS will report the values of the pointing center used after conversion to pixels. The related program STESS will make an image of the sensitivity function for a mosaic. This is the sum of the primary beams, each weighted by the appropriate inverse variance (i.e. NOISE(I)**-2). Once you have set up the parameters for UTESS in mosaicing mode, it is a good idea to run STESS and look at the sensitivity image. It should be fairly smooth and uniform, except for the effects of the cutoff in the primary beam model. Sky-curvature effects will be important in some circumstances and will hinder the use of UTESS. For 20cm and shorter in the C and D configurations, you can usually get away with mapping each primary beam separately. The procedure is: 1. Observe at the requisite number of pointing centers, spaced every HWHM (e.g. 15 arcmin at 20cm). 2. Calibrate, edit each field separately. 3. Run UVMAP on each field separately WITHOUT any phase shifts. The size of each field must be double the full primary beam size (e.g. 512**2 with 15" cellsize is fine for 20cm D-array). 4. Choose one centrally-located field as the center of the coordinate system to be used. Pad the map and beam for this field up to twice the maximum field of view. The task PADIM does this nicely. This resulting image is the reference field image. 5. Put all the other images onto the same grid. HGEOM is very convenient for this: put the reference field image in slot two, and the image to be converted into slot one. 6. Pad the beams out to the required size. Really you should do step 5 on each beam but the shift will come out incorrectly then. 7. Set up the parameters for UTESS, and then run STESS to check the sensitivity function. 8. Run UTESS! RESTARTING : UTESS can be restarted by simply filling in OUTNAME, OUTCLASS and OUTSEQ with the parameters of a map. NITER must, of course, be larger than the previous stopping point. Unlike CLEAN one can start from any initial estimate, hence it is efficient to keep iterating on the same image while changing the input dirty map by selfcalibration or by data editting. Similarly any of the control parameters may be changed in flight. UTESS writes the current image to the output file every iteration so that if it crashs, simply clear the write status and start from that iteration. If it crashs while writing the output image then tough luck, you will have to start again. Between iterations the values of ALPHA and BETA are stored in REAL*4 words 127 and 128 of the Catalog header. NOISE : One crucial control parameter is NOISE. This determines the level of fit attempted. It should be comparable to the r.m.s. noise level in a blank region of a CLEAN map thus if the data is reasonably well-calibrated this will be close to the theoretical noise level. Specifying too large a number will lead to an overly smooth map. Too small a number will prevent convergence since there will be no positive map which fits the data to that level. A useful strategy is to initially underestimate NOISE and then stop after a number of iterations and reset it to the level acheived up to that point. FLUX : FLUX specifies how the zero spacing flux is to be estimated. There are three cases : a. You specify a known or guessed value which must be fit to within 5%. Set FLUX to a positive number. This is quite important on weak sources since after accounting for all the power in the source UTESS will put power into the sidelobes thus biasing the total flux by a large amount and overfitting to the other visibility samples. b. If you have no idea what the zero spacing flux is then leave FLUX = 0.0. UTESS will attempt to estimate it. c. If you have a rough idea (within a factor of 2 say) then set FLUX to the negative of your guess e.g. FLUX=-2.0 UTESS will then do a reasonable job of estimating the true value. GENERAL TIPS : If the gradient starts to increase dramatically after a number of iterations then the problem that you have given is probably too difficult. Stop and reconsider the input parameters; in particular, NOISE and FLUX. Usually setting these too low will cause problems. Point sources often cause problems so it is a good idea to remove them using CLEAN. If you set BMAJ to -1 and put BOXs around the points then the output image will be the dirty image minus the point sources. Then put this image into the slot for the dirty image. Preconvolving the dirty image with a CLEAN beam will usually improve the quality of the result and "fix" the resolution to be that of the CLEAN beam. Convergence is also improved. Over-sampling of the image plane will slow UTESS so restrict the number of points per beam to less than about 7 or 8. OPTICAL DATA : UTESS can be used to deconvolve optical images. The main difference from interferometric images is that the noise is independent in the image plane; it assumes that the image is not photon limited i.e. it uses a chi-squared test between the convolved image and the dirty map. You will need a dirty beam to put into IN2NAME,IN2CLASS,IN2SEQ,IN2DISK. There are at least three ways to do this : 1. Guess a simple Gaussian form and use IMMOD to generate an image containing it. 2. Use IMFIT to fit an number of Gaussians to a star in the field. Then use IMFIT as in 1. 3. Cut a star out from the field using COMB then use GEOM to edge it out to the full size with zeroes. UTESS has two different units that it works with : Jy/beam and Jy/pixel. If the beam volume is normalised to unity then these are the same; if the beam peak is normalised to unity then they differ by the number of pixels per beam. In radio interferometry the latter is the usual convention but in optical work the former will be more convenient so I recommend that you normalise the dirty beam by it's volume and put NPOINTS = 1. For optical data, PBSIZE for that field must be set to a negative number. BMAJ,BMIN,BPA: If BMAJ > 0.0 then a CLEAN-type image is formed by convolving the output image with an elliptical Gaussian and adding the residuals. If the program is mosaicing then the residuals are linearly corrected for the primary beams before this addition. The units of the final restored image are JY/BEAM. Agreement with a CLEAN image will be generally good, but UTESS will slightly underestimate the peaks and will give a smoother restoration. If mosaicing, then the UTESS image will contain significantly more extended emission. EXECUTION TIMES : Typical CPU time for running UTESS in an otherwise empty VAX 11/780 with FPS120B array processor is: 128 x 128 0.20 min/iter/field 256 x 256 0.53 min/iter/field 512 x 512 1.9 min/iter/field 1024 x 1024 7.2 min/iter/field 2048 x 2048 28.5 min/iter/field Typical CPU time for running UTESS in an otherwise empty CONVEX C-1 is: 128 x 128 0.02 min/iter/field 256 x 256 0.1 min/iter/field 512 x 512 0.4 min/iter/field 1024 x 1024 1.6 min/iter/field 2048 x 2048 6.4 min/iter/field Wall clock times will be at least two to three times these numbers. If the map is mainly filled by emission then the APCLN runtimes will be comparable to these. DISK SPACE : The amount of scratch disk space allocated for the following image sizes is : Radio data Optical data 256 x 256 2176 blocks 5376 blocks 512 x 512 8704 blocks 21504 blocks 1024 x 1024 34816 blocks 86016 blocks 2048 x 2048 139264 blocks 344064 blocks NX x NY 4.25*NX*NY/128 10.5*NX*NY/128 REFERENCES Cornwell T.J., and Evans K.F., "A simple Maximum Entropy deconvolution algorithm", Astronomy and Astrophysics, (1985) Burch,S.F, Gull,S.F., and Skilling,J., "Image restoration by a powerful Maximum Entropy method", Computer Vision, Graphics and Image processing, 23, 113-128 (1983). -------------------------------- The function used to model the primary beam for normal VLA frequencies F(x) = 1.0 + parm(1) * 10E-3 * x + parm(2) * 10E-7 * x*x + parm(3) * 10E-10 * x*x*x + parm(4) * 10E-13 * x*x*x*x + parm(5) * 10E-16 * x*x*x*x*x where x is proportional to the square of the distance from the pointing position in units of [arcmin * freq (GHz)]**2, and F(x) is the multiplicative factor to divide into the image intensity at the distance parameter x. For other antennas, the user may read in appropraite constants in DPARM(5) through DPARM(9). The flag, DPARM(4) must be set to a positive number to invoke this option and DPARM(5) must not be zero. This correction scales with frequency and has a cutoff beyond which the map values are set to an undefined pixel value GIVEN IN DPARM(1). At the VLA frequencies the default cutoff is 1.485 GHz 29.8 arcmin 4.885 GHz 9.13 arcmin 15 GHz 2.95 arcmin 22.5 GHz 1.97 arcmin and occurs at a primary beam sensitivity of 2.3% of the value at the beam center. Corrections factors < 1 are forced to be 1. The estimated error of the algorithm is about 0.02 in (1/F(x)) and thus leads to very large errors for x>1500, or at areas outside of the primary response of 20%. The cutoff level may be specified with DPARM(1). RICK PERLEY'S REPORT Polynomial Coefficients from LSq Fit to VLA Primary Beam raster scans. Functional form fitted: 1 + G1.X^2 + G2.X^4 + G3.X^6 where X = r.F, and r = radius in arcminutes F = frequency in GHz. Fits were made to 3% cutoff in power for 24 antennas. Poor fits, and discrepant fits were discarded, and the most consistent subset of antennas had their fitted coefficients averaged to produce the following 'best' coefficients. Freq. G1 G2 G3 ---------------------------------------------------------- 1.285 -1.329E-3 6.445E-7 -1.146E-10 * 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 (old) -1.350 6.526 -1.090 * 22.485 (new) -1.417 7.332 -1.352 43.315 -1.321 6.185 -0.983 ----------------------------------------------------------- The estimated errors (from the scatter in the fitted coefficients) are generally very small: G1: .003 at all bands except Q (.014) G2: .03 to .07 at all bands except Q (.15) G3: .01 to .02 at all bands except Q (.04) R. Perley 21/Nov/00 * The 1.285 and 22.485 old feed values are not used.