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      Compute concentric aperture photometry (adapted from DAOPHOT)


    APER can compute photometry in several user-specified aperture radii.
    A separate sky value is computed for each source using specified inner
    and outer sky radii.

Calling Sequence

    APER, image, xc, yc, [ mags, errap, sky, skyerr, phpadu, apr, skyrad,
                      badpix, /NAN, /EXACT, /FLUX, PRINT = , /SILENT,
                      /MEANBACK, MINSKY=, SETSKYVAL = ]


    IMAGE - input image array
    XC - vector of x coordinates.
    YC - vector of y coordinates

Optional Inputs

    PHPADU - Photons per Analog Digital Units, numeric scalar. Converts
              the data numbers in IMAGE to photon units. (APER assumes
              Poisson statistics.)
    APR - Vector of up to 12 REAL photometry aperture radii.
    SKYRAD - Two element vector giving the inner and outer radii
              to be used for the sky annulus. Ignored if the SETSKYVAL
              keyword is set.
    BADPIX - Two element vector giving the minimum and maximum value
              of a good pixel. If badpix is not supplied or if BADPIX[0] is
              equal to BADPIX[1] then it is assumed that there are no bad
              pixels. Note that fluxes will not be computed for any star
              with a bad pixel within the aperture area, but that bad pixels
              will be simply ignored for the sky computation. The BADPIX
              parameter is ignored if the /NAN keyword is set.

Optional Keyword Inputs

    CLIPSIG - if /MEANBACK is set, then this is the number of sigma at which
            to clip the background. Default=3
    CONVERGE_NUM: if /MEANBACK is set then if the proportion of
          rejected pixels is less than this fraction, the iterations stop.
          Default=0.02, i.e., iteration stops if fewer than 2% of pixels
    /EXACT - By default, APER counts subpixels, but uses a polygon
            approximation for the intersection of a circular aperture with
            a square pixel (and normalizes the total area of the sum of the
            pixels to exactly match the circular area). If the /EXACT
            keyword, then the intersection of the circular aperture with a
            square pixel is computed exactly. The /EXACT keyword is much
            slower and is only needed when small (~2 pixels) apertures are
            used with very undersampled data.
    /FLUX - By default, APER uses a magnitude system where a magnitude of
              25 corresponds to 1 flux unit. If set, then APER will keep
              results in flux units instead of magnitudes.
    MAXITER if /MEANBACK is set then this is the ceiling on number of
            clipping iterations of the background. Default=5
    /MEANBACK - if set, then the background is computed using the 3 sigma
            clipped mean (using meanclip.pro) rather than using the mode
            computed with mmm.pro. This keyword is useful for the Poisson
            count regime or where contamination is known to be minimal.
      MINSKY - Integer giving mininum number of sky values to be used with MMM
            APER will not compute a flux if fewer valid sky elements are
              within the sky annulus. Default = 20.
    /NAN - If set then APER will check for NAN values in the image. /NAN
            takes precedence over the BADPIX parameter. Note that fluxes
            will not be computed for any star with a NAN pixel within the
            aperture area, but that NAN pixels will be simply ignored for
            the sky computation.
    PRINT - if set and non-zero then APER will also write its results to
              a file aper.prt. One can specify the output file name by
              setting PRINT = 'filename'.
    READNOISE - Scalar giving the read noise (or minimum noise for any
              pixel. This value is passed to the procedure mmm.pro when
              computing the sky, and is only need for images where
              the noise is low, and pixel values are quantized.
    /SILENT - If supplied and non-zero then no output is displayed to the
    SETSKYVAL - Use this keyword to force the sky to a specified value
              rather than have APER compute a sky value. SETSKYVAL
              can either be a scalar specifying the sky value to use for
              all sources, or a 3 element vector specifying the sky value,
              the sigma of the sky value, and the number of elements used
              to compute a sky value. The 3 element form of SETSKYVAL
              is needed for accurate error budgeting.


    MAGS - NAPER by NSTAR array giving the magnitude for each star in
              each aperture. (NAPER is the number of apertures, and NSTAR
              is the number of stars). If the /FLUX keyword is not set, then
              a flux of 1 digital unit is assigned a zero point magnitude of
    ERRAP - NAPER by NSTAR array giving error for each star. If a
              magnitude could not be determined then ERRAP = 9.99 (if in
                magnitudes) or ERRAP = !VALUES.F_NAN (if /FLUX is set).
    SKY - NSTAR element vector giving sky value for each star in
              flux units
    SKYERR - NSTAR element vector giving error in sky values


      Determine the flux and error for photometry radii of 3 and 5 pixels
      surrounding the position 234.2,344.3 on an image array, im. Compute
      the partial pixel area exactly. Assume that the flux units are in
      Poisson counts, so that PHPADU = 1, and the sky value is already known
      to be 1.3, and that the range [-32767,80000] for bad low and bad high
      IDL> aper, im, 234.2, 344.3, flux, eflux, sky,skyerr, 1, [3,5], -1, $
            [-32767,80000],/exact, /flux, setsky = 1.3

Procedures Used



      Reasons that a valid magnitude cannot be computed include the following:
      (1) Star position is too close (within 0.5 pixels) to edge of the frame
      (2) Less than 20 valid pixels available for computing sky
      (3) Modal value of sky could not be computed by the procedure MMM
      (4) *Any* pixel within the aperture radius is a "bad" pixel
      (5) The total computed flux is negative. In this case the negative
          flux and error are returned.
      For the case where the source is fainter than the background, APER will
      return negative fluxes if /FLUX is set, but will otherwise give
      invalid data (since negative fluxes can't be converted to magnitudes)
      APER was modified in June 2000 in two ways: (1) the /EXACT keyword was
      added (2) the approximation of the intersection of a circular aperture
      with square pixels was improved (i.e. when /EXACT is not used)

Revison History

      Adapted to IDL from DAOPHOT June, 1989 B. Pfarr, STX
      FLUX keyword added J. E. Hollis, February, 1996
      SETSKYVAL keyword, increase maxsky W. Landsman, May 1997
      Work for more than 32767 stars W. Landsman, August 1997
      Don't abort for insufficient sky pixels W. Landsman May 2000
      Added /EXACT keyword W. Landsman June 2000
      Allow SETSKYVAL = 0 W. Landsman December 2000
      Set BADPIX[0] = BADPIX[1] to ignore bad pixels W. L. January 2001
      Fix chk_badpixel problem introduced Jan 01 C. Ishida/W.L. February 2001
      Set bad fluxes and error to NAN if /FLUX is set W. Landsman Oct. 2001
      Remove restrictions on maximum sky radius W. Landsman July 2003
      Added /NAN keyword W. Landsman November 2004
      Set badflux=0 if neither /NAN nor badpix is set M. Perrin December 2004
      Added READNOISE keyword W. Landsman January 2005
      Added MEANBACK keyword W. Landsman October 2005
      Correct typo when /EXACT and multiple apertures used. W.L. Dec 2005
      Remove VMS-specific code W.L. Sep 2006
      Add additional keywords if /MEANBACK is set W.L Nov 2006
      Allow negative fluxes if /FLUX is set W.L. Mar 2008
      Previous update would crash if first star was out of range W.L. Mar 2008
      Fix floating equality test for bad magnitudes W.L./J.van Eyken Jul 2009
      Added MINSKY keyword W.L. Dec 2011
      Don't ever modify input skyrad variable W. Landsman Aug 2013

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