Fourier ptychographic microscopy (FPM) is a computational imaging method that gives a significantly increased space-bandwidth product, in practice high resolution combined with a wide field of view. In this article, we propose an improved Fourier Ptychography algorithm based on Fresnel wave propagation integral for wide field-of-view coherent imaging while correcting for the misalignment of the illuminating LED board and calibration of system parameters. In addition, the wave emanating from the LEDs is taken to be parabolic instead of plane wave as done by others. The advantage of this scheme is that it enables to simulate the transition regions between bright and dark field in wide image patches, and hence this feature can be used to estimate the LED misalignment as well as the distortion of the imaging lens. Experimental results are presented for a USAF resolution target and a biological sample for on-axis and off-axis image patches over a wide sample area showing excellent performance of this scheme when compared to the traditional Fraunhofer-model based Fourier Ptychography algorithm. The article summarizes with high technical detail our experiences with developing and implementing improved FPM methods and will hopefully assist other scientists entering this scientific field.