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:: http://cheops1.uchicago.edu/idlhelp/sdssidl/plotting/tvasinh.html 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.)
Image Processing
Plot various values of beta:: cgPlot, cgASinhScl(Indgen(256), Beta=0.0), LineStyle=0 cgOPlot, cgASinhScl(Indgen(256), Beta=0.1), LineStyle=1 cgOPlot, cgASinhScl(Indgen(256), Beta=1.0), LineStyle=2 cgOPlot, cgASinhScl(Indgen(256), Beta=10.), LineStyle=3 cgOPlot, cgASinhScl(Indgen(256), Beta=100), LineStyle=4
FANNING SOFTWARE CONSULTING:: David W. Fanning 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
Change 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. Renamed cgASinhScl from ASinhScl. 27 March 2015. DWF.
Copyright (c) 2008-2015, Fanning Software Consulting, Inc. rn the inverse hyperbolic sine of the argument. Taken from the NASA Astronomy Library and renamed for use in this program. The inverse rbolic sine is used for the calculation of asinh magnitudes, see on et al. (1999, AJ, 118, 1406). Expression given in Numerical Recipes, s et al. (1992), eq. 5.6.7. Note that asinh(-x) = -asinh(x) and that h(0) = 0. and that if y = asinh(x) then x = sinh(y).
A byte scaled image is returned.
image: in, required The image to be scaled. Written for 2D images, but arrays of any size are treated alike.
beta: in, optional, type=float, default=3.0 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 positive. max: in, optional Any value in the input image greater than this value is set to this value before scaling. min: in, optional Any value in the input image less than this value is set to this value before scaling. negative, in, optional, type=boolean, default=0 If set, the "negative" of the result is returned. omax: in, optional, type=byte, default=255 The output image is scaled between OMIN and OMAX. omin: in, optional, type=byte, default=0 The output image is scaled between OMIN and OMAX.