Calibration is a fundamental step in fringe projection profilometry development. Among various methods, hybrid calibration is a promising solution given its high flexibility and sensing speed. However, existing approaches suffer the problem of limited accuracy and convenience. For example, customized high-accuracy artifacts with complex operations are usually required. This article reports a hybrid method with improved accuracy and operability, based on a unique back-projection and nonlinear epipolar sampling analysis. This method is performed in three steps: stereo calibration, residual distortion analysis, and phase 3-D mapping tabulation; the last two are pure computations without manual operations. The method is straightforward and cost-effective since only a checkerboard-based stereo calibrating operation is required. It is flexible without checkerboard poses to be known and also highly accurate because systematic distortions are almost compensated. The eventually obtained phase 3-D mapping table is computationally efficient for high-speed sensing. Our experiments confirm that a relative measurement error of 0.01% relative to the field-of-view has been finally achieved.