For non-core-collapse clusters, as identified in Table 2 in the paper
(and lacking the notation 'c' after the cluster name in Table 1---but
note that clusters with 'c?' use the following transformation), the
log (r/arcsec) values must be transformed using the following formula:

x=log(1+10**(2*(logr-logrc')))

where all logs are base-10 logarithms, logr=log (r/arcsec), and the
tricky (and undocumented bit) is

logrc'=logrc-log(2)=logrc-0.301

(for the life of me, I have no idea where this extra factor of 1/2
came from) and logrc is the 'r_c' value given in Table 1 (not Table 2)
on the line

"Power-of-x coeffients a(0)+a(1)x+a(2)x^2+..., where x=1+(r/r_c)^2, r_c= 1.42"

for the case of 47 Tuc.  I.e., r_c=log(r_c/arcsec).  However, note
that this r_c is NOT the core radius given in Table 2, but rather a
first guess used to compute the polynomials given in Table 1.

For core-collapsed clusters (denoted by a 'c' after the cluster name
in Table 1),

x=logr

and there is no correction applied.

After the radial coordinate is transformed as required, the minimum
and maximum values of x taken as the minimum and maximum values of log
(r/arcsec) given for each cluster in Table 1 (transformed as required
above) are then used to transform final the radial coordinate onto the
interval [-1,1].  The Chebyshev T_n(x) coefficients given at the top
of each cluster entry can then be used to give the "mu_V (fitted)"
values in the table.

There has been no correction for reddening in the tables.