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There are many situations where adaptive optic elements are useful for beam steering. When the beam is passed through a lens the resulting focus may be scanned within a three dimensional volume. In this article, we introduce expressions to describe the maximum distance to which a focus may be steered using a deformable mirror with a continuous phase distribution, limited either in its gradient or amplitude. Additionally for liquid crystal spatial light modulators (SLMs), an analytic approach isdoi:10.1080/15599612.2012.758791 fatcat:it3tx3u4qve7jeyhqurnyf74rq