Aims: We use 12,530 photometrically-selected BHB stars} from Sloan Digital Sky Survey to estimate, the total extinction of the Milky Way in high Galactic latitude, $R_V$ and $A_V$ in each line of sight. Methods: A Bayesian method is developed to estimate the reddening values in the given lines of sight. Based on the most likely values of reddening in multiple colors, we are able to derive the values of $R_V$ and $A_V$. . Results: We select 94 zero-reddened BHB stars from 7 globular cluster as the template. The reddening in the 4 SDSS colors for the northern Galactic cap are estimated by comparing the field BHB stars with the template stars. The accuracy of this estimation is around 0.01\,mag for the most line of sights. We also obtain $<R_V>$ to be around 2.40$\pm1.05$ and $A_V$ map within uncertainty of 0.1\,mag. The results, including reddening values in the 4 SDSS colors, $A_V$, and $R_V$ in each line of sight, are released on line. In this work, we employ an up-to-date parallel technique on GPU card to overcome the time-consuming computation. We plan to release online the C++ CUDA code used for this analysis. Conclusions: The extinction map derived from BHB stars is highly consistent with that from Schlegel, Finkbeiner & Davis(1998). The derived $R_V$ is around 2.40$\pm1.05$. The contamination probably makes the $R_V$ tend to be larger.
Date added: Mon, 14 Oct 13