The working principles of off-axis illumination to improve the resolution and depth of focus of optical projection imaging and some foreseeable problems are explained in pictorial and analytical forms in terms of coherent illumination systems. Partial coherent illuminations are used to compare the imaging performance of off-axis illumination systems in the form of quadrapole and ring with the alternating phase-shifting mask technique. Other aspects between these two enhancement techniques are also compared. Some unexpected conclusions have been drawn.