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A focus profile having a steeper peak is more resistant to image noise in the autofocus (AF) process of a digital camera. However, a focus profile of such shape normally has a flatter out-of-focus region on either side of the profile, resulting in a slow AF process due to the lack of clue about where the lens should move when the lens is in such regions. To address the problem, we provide a statistical analysis of the focus profile and show that a strictly monotonic transformation of the focus profile preserves the accuracy of the AF. On the basis of this analysis, we propose a new focus profile representation that transforms the focus profile to the reciprocal domain in which the reciprocal focus profile is modeled by a polynomial function. This transformation makes the AF mathematically tractable and boosts the search speed. Experimental results are shown to demonstrate the advantage of the proposed representation .