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      This is a utility routine to perform an inverse hyperbolic sine
      function intensity transformation on an image. I think of this
      as a sort of "tuned" gamma or power-law function. The algorithm,
      and notion of "asinh magnitudes", comes from a paper by Lupton,
      et. al, in The Astronomical Journal, 118:1406-1410, 1999 September.
      I've relied on the implementation of Erin Sheldon, found here:
      I'm also grateful of discussions with Marshall Perrin on the IDL
      newsgroup with respect to the meaning of the "softening parameter", beta,
      and for finding (and fixing!) small problems with the code.
      Essentially this transformation allow linear scaling of noise values,
      and logarithmic scaling of signal values, since there is a small
      linear portion of the curve and a much large logarithmic portion of
      the curve. (See the EXAMPLE section for some tips on how to view this
      transformation curve.)


      David Fanning, Ph.D.
      1645 Sheely Drive
      Fort Collins, CO 80526 USA
      Phone: 970-221-0438
      E-mail: david@idlcoyote.com
      Coyote's Guide to IDL Programming: http://www.idlcoyote.com



Calling Sequence

      outputImage = ASINHSCL(image)


      image: The image or signal to be scaled. Written for 2D images, but arrays
                      of any size are treated alike.


      BETA: This keyword corresponds to the "softening parameter" in the Lupon et. al paper.
                      This factor determines the input level at which linear behavior sets in. Beta
                      should be set approximately equal to the amount of "noise" in the input signal.
                      IF BETA=0 there is a very small linear portion of the curve; if BETA=200 the
                      curve is essentially all linear. The default value of BETA is set to 3, which
                      is appropriate for a small amount of noise in your signal. The value is always
      NEGATIVE: If set, the "negative" of the result is returned.
      MAX: Any value in the input image greater than this value is
                      set to this value before scaling.
      MIN: Any value in the input image less than this value is
                      set to this value before scaling.
      OMAX: The output image is scaled between OMIN and OMAX. The
                      default value is 255.
      OMIN: The output image is scaled between OMIN and OMAX. The
                      default value is 0.

Return Value

      outputImage: The output, scaled into the range OMIN to OMAX. A byte array.

Common Blocks



      Plot, ASinhScl(Indgen(256), Beta=0.0), LineStyle=0
      OPlot, ASinhScl(Indgen(256), Beta=0.1), LineStyle=1
      OPlot, ASinhScl(Indgen(256), Beta=1.0), LineStyle=2
      OPlot, ASinhScl(Indgen(256), Beta=10.), LineStyle=3
      OPlot, ASinhScl(Indgen(256), Beta=100), LineStyle=4


    Requires SCALE_VECTOR from the Coyote Library:
    Incorporates ASINH from the NASA Astronomy Library and renamed ASINHSCL_ASINH.

Modification History

      Written by: David W. Fanning, 24 February 2006.
      Removed ALPHA keyword and redefined the BETA keyword to correspond
        to the "softening parameter" of Lupton et. al., following the
        suggestions of Marshall Perrin. 25 April 2006. DWF.

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