The high precision determination of the partial width Gamma(H-->gamma gamma
) of an intermediate mass Higgs boson is among the most important measureme
nts at a future photon-photon collider. Recently it was shown that large no
n-Sudakov as well as Sudakov double logarithmic corrections can be summed t
o all orders in the background process gamma gamma-->q (q) over bar, q={b,c
}, from an initially polarized J(z)=0 state. In addition, running coupling
corrections were included exactly to all orders by employing the renormaliz
ation group. Thus all necessary theoretical results for calculating the Hig
gs signal and the non-Higgs continuum background contributions to the proce
ss gamma gamma-->q (q) over bar are now known. We are therefore able to pre
sent for the first time precise predictions for the measurement of the part
ial width Gamma(H-->gamma gamma) at the Compton collider (gamma gamma) opti
on at a future linear e(+)e(-) collider. The interplay between signal and b
ackground is very sensitive to the experimental cuts and the ability of the
detectors to identify b quarks in the final state. We investigate this in
some detail using a Monte Carlo analysis, and conclude that a measurement w
ith a 2% statistical accuracy should be achievable. This could have importa
nt consequences for the discovery of physics beyond the standard model, in
particular for large masses of a pseudoscalar Higgs boson as the decoupling
Limit is difficult and for a wide range of tan beta impossible to cover at
the CERN LHC proton-proton collider.