pro mmm, sky_vector, skymod, sigma , skew, HIGHBAD = highbad, DEBUG = debug, $ ReadNoise = readnoise, Nsky = nsky, INTEGER = discrete, $ SILENT = silent ;+ ; NAME: ; MMM ; PURPOSE: ; Estimate the sky background in a stellar contaminated field. ; EXPLANATION: ; MMM assumes that contaminated sky pixel values overwhelmingly display ; POSITIVE departures from the true value. Adapted from DAOPHOT ; routine of the same name. ; ; CALLING SEQUENCE: ; MMM, sky, [ skymod, sigma, skew, HIGHBAD = , READNOISE=, /DEBUG, ; NSKY=, /INTEGER,/SILENT] ; ; INPUTS: ; SKY - Array or Vector containing sky values. This version of ; MMM does not require SKY to be sorted beforehand. SKY ; is unaltered by this program. ; ; OPTIONAL OUTPUTS: ; skymod - Scalar giving estimated mode of the sky values ; SIGMA - Scalar giving standard deviation of the peak in the sky ; histogram. If for some reason it is impossible to derive ; skymod, then SIGMA = -1.0 ; SKEW - Scalar giving skewness of the peak in the sky histogram ; ; If no output variables are supplied or if /DEBUG is set ; then the values of skymod, SIGMA and SKEW will be printed. ; ; OPTIONAL KEYWORD INPUTS: ; HIGHBAD - scalar value of the (lowest) "bad" pixel level (e.g. cosmic ; rays or saturated pixels) If not supplied, then there is ; assumed to be no high bad pixels. ; READNOISE - Scalar giving the read noise (or minimum noise for any ; pixel). Normally, MMM determines the (robust) median by ; averaging the central 20% of the sky values. In some cases ; where the noise is low, and pixel values are quantized a ; larger fraction may be needed. By supplying the optional ; read noise parameter, MMM is better able to adjust the ; fraction of pixels used to determine the median. ; /INTEGER - Set this keyword if the input SKY vector only contains ; discrete integer values. This keyword is only needed if the ; SKY vector is of type float or double precision, but contains ; only discrete integer values. (Prior to July 2004, the ; equivalent of /INTEGER was set for all data types) ; /DEBUG - If this keyword is set and non-zero, then additional ; information is displayed at the terminal. ; /SILENT - If set, then error messages will be suppressed when MMM ; cannot compute a background. Sigma will still be set to -1 ; OPTIONAL OUTPUT KEYWORD: ; NSKY - Integer scalar giving the number of pixels actually used for the ; sky computation (after outliers have been removed). ; NOTES: ; (1) Program assumes that low "bad" pixels (e.g. bad CCD columns) have ; already been deleted from the SKY vector. ; (2) MMM was updated in June 2004 to better match more recent versions ; of DAOPHOT. ; (3) Does not work well in the limit of low Poisson integer counts ; (4) MMM may fail for strongly skewed distributions. ; METHOD: ; The algorithm used by MMM consists of roughly two parts: ; (1) The average and sigma of the sky pixels is computed. These values ; are used to eliminate outliers, i.e. values with a low probability ; given a Gaussian with specified average and sigma. The average ; and sigma are then recomputed and the process repeated up to 20 ; iterations: ; (2) The amount of contamination by stars is estimated by comparing the ; mean and median of the remaining sky pixels. If the mean is larger ; than the median then the true sky value is estimated by ; 3*median - 2*mean ; ; REVISION HISTORY: ; Adapted to IDL from 1986 version of DAOPHOT in STSDAS, ; W. Landsman, STX Feb 1987 ; Added HIGHBAD keyword, W. Landsman January, 1991 ; Fixed occasional problem with integer inputs W. Landsman Feb, 1994 ; Avoid possible 16 bit integer overflow W. Landsman November 2001 ; Added READNOISE, NSKY keywords, new median computation ; W. Landsman June 2004 ; Added INTEGER keyword W. Landsman July 2004 ; Improve numerical precision W. Landsman October 2004 ; Fewer aborts on strange input sky histograms W. Landsman October 2005 ; Added /SILENT keyword November 2005 ; Fix too many /CON keywords to MESSAGE W.L. December 2005 ; Fix bug introduced June 2004 removing outliers when READNOISE not set ; N. Cunningham/W. Landsman January 2006 ;- compile_opt idl2 On_error,2 ;Return to caller if N_params() EQ 0 then begin print,'Syntax: MMM, sky, skymod, sigma, skew, [/INTEGER, /SILENT' print,' [HIGHBAD = , READNOISE =, /DEBUG, NSKY=] ' return endif silent = keyword_set(SILENT) mxiter = 30 ;Maximum number of iterations allowed minsky = 20 ;Minimum number of legal sky elements nsky = N_elements( sky_vector ) ;Get number of sky elements if nsky LE minsky then message, $ 'ERROR -Input vector must contain at least '+strtrim(minsky,2)+' elements' nlast = nsky-1 ;Subscript of last pixel in SKY array if keyword_set(DEBUG) then $ message,'Processing '+strtrim(nsky,2) + ' element array',/INF sz_sky = size(sky_vector,/structure) integer = keyword_set(discrete) if not integer then integer = (sz_sky.type LT 4) or (sz_sky.type GT 11) sky = sky_vector[ sort( sky_vector ) ] ;Sort SKY in ascending values skymid = 0.5*sky[(nsky-1)/2] + 0.5*sky[nsky/2] ;Median value of all sky values cut1 = min( [skymid-sky,sky[nsky-1] - skymid] ) if N_elements(highbad) EQ 1 then cut1 = cut1 < (highbad - skymid) cut2 = skymid + cut1 cut1 = skymid - cut1 ; Select the pixels between Cut1 and Cut2 good = where( (sky LE cut2) and (sky GE cut1) ) delta = sky[good] - skymid ;Subtract median to improve arithmetic accuracy sum = total(delta,/double) sumsq = total(delta^2,/double) maximm = max( good,MIN=minimm ) ;Highest value accepted at upper end of vector minimm = minimm -1 ;Highest value reject at lower end of vector ; Compute mean and sigma (from the first pass). skymed = 0.5*sky[(minimm+maximm+1)/2] + 0.5*sky[(minimm+maximm)/2 + 1] ;median skymn = sum/(maximm-minimm) ;mean sigma = sqrt(sumsq/(maximm-minimm)-skymn^2) ;sigma skymn = skymn + skymid ;Add median which was subtracted off earlier ; If mean is less than the mode, then the contamination is slight, and the ; mean value is what we really want. skymod = (skymed LT skymn) ? 3.*skymed - 2.*skymn : skymn ; Rejection and recomputation loop: niter = 0 clamp = 1 old = 0 START_LOOP: niter = niter + 1 if ( niter GT mxiter ) then begin sigma=-1.0 & skew = 0.0 message,/CON, NoPrint=Silent, $ 'ERROR - Too many ('+strtrim(mxiter,2) + ') iterations,' + $ ' unable to compute sky' return endif if ( maximm-minimm LT minsky ) then begin ;Error? sigma = -1.0 & skew = 0.0 message,/CON,NoPrint=Silent, $ 'ERROR - Too few ('+strtrim(maximm-minimm,2) + $ ') valid sky elements, unable to compute sky' return endif ; Compute Chauvenet rejection criterion. r = alog10( float( maximm-minimm ) ) r = max( [ 2., ( -0.1042*r + 1.1695)*r + 0.8895 ] ) ; Compute rejection limits (symmetric about the current mode). cut = r*sigma + 0.5*abs(skymn-skymod) if integer then cut = cut > 1.5 cut1 = skymod - cut & cut2 = skymod + cut ; ; Recompute mean and sigma by adding and/or subtracting sky values ; at both ends of the interval of acceptable values. redo = 0B newmin = minimm tst_min = sky[newmin+1] GE cut1 ;Is minimm+1 above current CUT? done = (newmin EQ -1) and tst_min ;Are we at first pixel of SKY? if not done then $ done = (sky[newmin>0] LT cut1) and tst_min if not done then begin istep = 1 - 2*fix(tst_min) repeat begin newmin = newmin + istep done = (newmin EQ -1) or (newmin EQ nlast) if not done then $ done = (sky[newmin] LE cut1) and (sky[newmin+1] GE cut1) endrep until done if tst_min then delta = sky[newmin+1:minimm] - skymid $ else delta = sky[minimm+1:newmin] - skymid sum = sum - istep*total(delta,/double) sumsq = sumsq - istep*total(delta^2,/double) redo = 1b minimm = newmin endif ; newmax = maximm tst_max = sky[maximm] LE cut2 ;Is current maximum below upper cut? done = (maximm EQ nlast) and tst_max ;Are we at last pixel of SKY array? if not done then $ done = ( tst_max ) and (sky[(maximm+1)
0 )) skymn = skymn + skymid ; Determine a more robust median by averaging the central 20% of pixels. ; Estimate the median using the mean of the central 20 percent of sky ; values. Be careful to include a perfectly symmetric sample of pixels about ; the median, whether the total number is even or odd within the acceptance ; interval center = (minimm + 1 + maximm)/2. side = round(0.2*(maximm-minimm))/2. + 0.25 J = round(CENTER-SIDE) K = round(CENTER+SIDE) ; In case the data has a large number of of the same (quantized) ; intensity, expand the range until both limiting values differ from the ; central value by at least 0.25 times the read noise. if keyword_set(readnoise) then begin L = round(CENTER-0.25) M = round(CENTER+0.25) R = 0.25*readnoise while ((J GT 0) and (K LT Nsky-1) and $ ( ((sky[L] - sky[J]) LT R) or ((sky[K] - sky[M]) LT R))) do begin J = J - 1 K = K + 1 endwhile endif skymed = total(sky[j:k])/(k-j+1) ; If the mean is less than the median, then the problem of contamination ; is slight, and the mean is what we really want. dmod = skymed LT skymn ? 3.*skymed-2.*skymn-skymod : skymn - skymod ; prevent oscillations by clamping down if sky adjustments are changing sign if dmod*old LT 0 then clamp = 0.5*clamp skymod = skymod + clamp*dmod old = dmod if redo then goto, START_LOOP ; skew = float( (skymn-skymod)/max([1.,sigma]) ) nsky = maximm - minimm if keyword_set(DEBUG) or ( N_params() EQ 1 ) then begin print, '% MMM: Number of unrejected sky elements: ', strtrim(nsky,2), $ ' Number of iterations: ', strtrim(niter,2) print, '% MMM: Mode, Sigma, Skew of sky vector:', skymod, sigma, skew endif return end
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|Last modified on 2nd Mar 2009 by Richard Massey.|