The use of alternating phase shifting masks (alt-PSM) can significantly improve lithographic process windows. However, the existence of phase error between the nominal 0 and 180 degree phase regions can cause printed lines to shift laterally toward each other in pairs at image planes away from the best focus. Such asymmetry, especially evident with small ground rules, challenges both overlay and critical dimension (CD) control. To minimize such effect, tight control in phase angle has been implemented, which contributes to the higher fabrication cost for an alt-PSM. Since the effect of the phase error varies with different lithographic conditions, knowing how much phase control is necessary for a given lithographic situation becomes essential to the reduction of the mask fabrication cost. Although this phenomenon has been studied in the past with a number of simulations and experiments, a systematic understanding of its mechanism, especially its interaction with CD and numerical aperture has not been reported. This paper explores the theoretical relationship between phase error and important parameters of photolithographic processes, such as CD, numerical apertures (NA), and overlay tolerance. A simple equation of the phase error is developed, which indicates that the effect of the phase error is inversely proportional to both phase error and defocus. We have compared the predictions of this theory to our first experimental results from a test mask and a good agreement is found. Based on this theory, we develop the quantity “tolerable phase error” relating the effect of the phase error to the CD, pitch, and depth of focus of the imaging system. We have found that for a system with depth of focus of +/- 300 nm, a phase error control about 2 degrees is necessary to realize a line shift control of less than 2.5% of the CD for the most aggressive feature size at any NA. We also note that the control of phase error can be relaxed at high NA. Calculations for 193 nm as well as 157 nm lithography are presented.