  The intrinsic alignment (IA) of galaxies has been shown to be a significant
barrier to precision cosmic shear measurements. (Zhang, 2010, ApJ, 720, 1090)
proposed a self-calibration technique for the power spectrum to calculate the
induced gravitational shear-galaxy intrinsic ellipticity correlation (GI) in
weak lensing surveys with photo-z measurements which is expected to reduce the
IA contamination by at least a factor of 10 for currently proposed surveys. We
confirm this using an independent analysis and propose an expansion to the
self-calibration technique for the bispectrum in order to calculate the
dominant IA gravitational shear-gravitational shear-intrinsic ellipticity
correlation (GGI) contamination. We first establish an estimator to extract the
galaxy density-density-intrinsic ellipticity (ggI) correlation from the galaxy
ellipticity-density-density measurement for a photo-z galaxy sample. We then
develop a relation between the GGI and ggI bispectra, which allows for the
estimation and removal of the GGI correlation from the cosmic shear signal. We
explore the performance of these two methods, compare to other possible sources
of error, and show that the GGI self-calibration technique can potentially
reduce the IA contamination by up to a factor of 5-10 for all but a few bin
choices, thus reducing the contamination to the percent level. The
self-calibration is less accurate for adjacent bins, but still allows for a
factor of three reduction in the IA contamination. The self-calibration thus
promises to be an efficient technique to isolate both the 2-point and 3-point
intrinsic alignment signals from weak lensing measurements.
