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The measurement of cosmic shear using weak gravitational lensing is achallenging task that involves a number of complicated procedures. We study indetail the systematic errors in the measurement of weak lensing MinkowskiFunctionals (MFs). Specifically, we focus on systematics associated with galaxyshape measurements, photometric redshift errors, and shear calibrationcorrection. We first generate mock weak-lensing catalogs that directlyincorporate the actual observational characteristics of theCanada-France-Hawaii Lensing Survey (CFHTLenS). We then perform a Fisheranalysis using the large set of mock catalogs for various cosmological models.We find that the statistical error associated with the observational effectsdegrades the cosmological parameter constraints by a factor of a few. TheSubaru Hyper Suprime-Cam (HSC) survey with a sky coverage of ~1400 deg2 willconstrain the dark energy equation of the state parameter with an error ofDelta w_0 ~ 0.25 by the lensing MFs alone, but biases induced by thesystematics can be comparable to the 1-sigma error. We conclude that thelensing MFs are powerful statistics beyond the two-point statistics, only ifwell-calibrated measurement of both the redshifts and the shapes of sourcegalaxies is performed. Finally, we analyze the CFHTLenS data to explore theability of the MFs to break degeneracies between a few cosmological parameters.Using a combined analysis of the MFs and the shear correlation function, wederive the matter density Omega_m0= 0.256+0.054-0.046.

Statistical and Systematic Errors in Measurement of Weak-Lensing Minkowski Functionals: Application to Canada-France-Hawaii Lensing Survey