Wavefront coding (WFC) is a popular technique for extending the depth of field (DOF), where the DOF is extended by the phase modulation of the pupil function using a phase mask and digital processing using a deconvolution filter. We previously proposed an apodized WFC system with a Gaussian aperture that extends the DOF while suppressing artifacts in the reconstructed image. In this study, the influence of aberrations on the proposed WFC system was examined in detail by computer simulation. Then, the image quality was experimentally examined to confirm the effectiveness of the apodized WFC system. In addition, we proposed a new type of aperture, i.e., a generalized Gaussian aperture, to prevent the significant reduction in transmitted light intensity due to apodization, the effectiveness of which was confirmed by computer simulation.