functional form of gaussian in DAOPHOT/psf

ameisner wrote on Oct 10, 2008

When I make a psf with a gaussian core in DAOPHOT/psf, it gives me the following parameters: X, Y, Height, Psfmag, Par1 and Par2. However, I can't find what the functional form is in terms of these parameters in any of the documentation. I imagine it's something like:

counts(x,y) = Height*exp{-[(x - X)^2]/2*(Par1)^2 - [(y - Y)^2]/2*(Par2)^2}

But I have no way of knowing with certainty the correspondence between X/Y, Par1/Par2 and horizontal/vertical directions or for that matter the units of X, Y, Par1, Par2. I'm guessing this info. is in the documentation somewhere but I can't seem to find it. Thanks.

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Mike Fitzpatrick wrote on Oct 10, 2008

The best documentation is of course the source code. From daophot$daolib/profile.x we find:

        # Compute the analytic part of the profile for a given x and y.

        switch (ipstyp) {

        # Evaluate the Gaussian function
        #     f = erfx * erfy / (par[1] * par[2])
        #     par[1] is the hwhm in x; sigma(x) = 0.8493218 * hwhm
        #     par[2] is the hwhm in y; sigma(y) = 0.8493218 * hwhm

        case FCTN_GAUSS:

            p1p2 = par[1] * par[2]
            erfx = daoerf (dx, 0.0, par[1], dhdxc, dhdsx)
            erfy = daoerf (dy, 0.0, par[2], dhdyc, dhdsy)
            profile = erfx * erfy / p1p2
            dhdxc = dhdxc * erfy / p1p2
            dhdyc = dhdyc * erfx / p1p2
            if (ideriv > 0) {
                term[1] = (dhdsx - erfx / par[1]) * erfy / p1p2
                term[2] = (dhdsy - erfy / par[2]) * erfx / p1p2
            }

Where the daoerf() function is in the erf.x file in the same directory, the comments for which describe it as:

# DAOERF -- Numerically integrate a Gaussian function from xin-0.5 to xin+0.5
# using 4 point Gauss-Legendre integration. Beta is the half-width at
# half-maximum which is equal to 1.17741 * sigma. The Gaussian function is
# shown below.
#
#      erf = exp (-0.5 *((x - x0) / beta) ** 2))
#
#                          or
#
#      erf = exp (-0.6931472 * [(x - xo) / beta] ** 2)
#
# Also provide the first derivative of the integral with respect to xo and beta.

Hope this helps.

-Mike

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Last post on Oct 10, 2008