We use a ray-tracing technique to compute the observed spectrum of a thin accretion disk around a Kerr black hole .
We include all relativistic effects such as frame-dragging , Doppler boost , gravitational redshift , and bending of light by the gravity of the black hole .
We also include self-irradiation of the disk as a result of light deflection .
Assuming that the disk emission is locally blackbody , we show how the observed spectrum depends on the spin of the black hole , the inclination of the disk , and the torque at the inner edge of the disk .
We find that the effect of a nonzero torque on the spectrum can , to a good approximation , be absorbed into a zero-torque model by adjusting the mass accretion rate and the normalization .
We describe a computer model , called KERRBB , which we have developed for fitting the spectra of black hole X-ray binaries .
Using KERRBB within the X-ray data reduction package XSPEC , and assuming a spectral hardening factor f _ { col } = 1.7 , we analyze the spectra of three black hole X-ray binaries : 4U1543-47 , XTE J1550-564 , and GRO J1655-40 .
We estimate the spin parameters of the black holes in 4U1543-47 and GRO J1655-40 to be a / M \sim 0.6 and \sim 0.6 - 0.7 , respectively .
If f _ { col } \sim 1.5 - 1.6 , as in a recent study , then we find a / M \sim 0.7 - 0.8 and \sim 0.8 - 0.9 , respectively .
These estimates are subject to additional uncertainties in the assumed black hole masses , distances and disk inclinations .