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      Estimate the sky background in a stellar contaminated field.


      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]


      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.
      MINSKY - Integer giving mininum number of sky values to be used. MMM
                will return an error if fewer sky elements are supplied.
                Default = 20.
      MAXITER - integer giving maximum number of iterations allowed,default=50
      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).


      (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.


      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
      (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
      Make sure that MESSAGE never aborts W. Landsman January 2008
      Add mxiter keyword and change default to 50 W. Landsman August 2011
      Added MINSKY keyword W.L. December 2011

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