The three-dimensional correlation function offers an effective way to summarize the correlation of the large-scale structure even for imaging galaxy surveys. We have applied the projected three-dimensional correlation function, ξp to measure the baryonic acoustic oscillations (BAO) scale on the first-three years Dark Energy Survey data. The sample consists of about 7 million galaxies in the redshift range 0.6 p<1.1 over a footprint of 4108 deg2. Our theory modeling includes the impact of realistic true redshift distributions beyond Gaussian photo-z approximation. ξp is obtained by projecting the three-dimensional correlation to the transverse direction. To increase the signal-to-noise of the measurements, we have considered a Gaussian stacking window function in place of the commonly used top-hat. ξp is sensitive to DM(zeff)/rs, the ratio between the comoving angular diameter distance and the sound horizon. Using the full sample, DM(zeff)/rs is constrained to be 19.00 ±0.67 (top-hat) and 19.15 ±0.58 (Gaussian) at zeff=0.835 . The constraint is weaker than the angular correlation w constraint (18.84 ±0.50 ), and we trace this to the fact that the BAO signals are heterogeneous across redshift. While ξp responds to the heterogeneous signals by enlarging the error bar, w can still give a tight bound on DM/rs in this case. When a homogeneous BAO-signal subsample in the range 0.7 p<1.0 (zeff=0.845 ) is considered, ξp yields 19.80 ±0.67 (top-hat) and 19.84 ±0.53 (Gaussian). The latter is mildly stronger than the w constraint (19.86 ±0.55 ). We find that the ξp results are more sensitive to photo-z errors than w because ξp keeps the three-dimensional clustering information causing it to be more prone to photo-z noise. The Gaussian window gives more robust results than the top-hat as the former is designed to suppress the low signal modes. ξp and the angular statistics such as w have their own pros and cons, and they serve an important crosscheck with each other....
