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High deflection efficiency is one of the urgent requirements for practical liquid crystal optical phased array (LC-OPA). In this paper, we demonstrate that high order grating lobes induced from fringe effect are the most important issue to reduce occupation of main lobe. A novel theoretical model is developed to analyze the feature of grating lobes when the device of LC-OPA is working on the scheme of variable period grating (VPG) or variable blazing grating (VBG). Subsequently, our experiments present the relevant results showing a good agreement with the theoretical analysis.