  In contemporary imaging systems, achieving optimal auto-focus (AF)
performance hinges on precise lens positioning. Extensive research has delved
into refining algorithms for determining the ideal lens position across
passive, active, and hybrid autofocus systems. This paper explores the
mathematical intricacies and practical considerations essential for optimizing
lens positions during focus searches, addressing overarching challenges
encountered in AF systems, such as balancing speed and accuracy. Moreover, the
lens position calculations proposed herein can be applied to various focus
algorithms, including focus bracketing. The proposed method offers adaptability
and scalability, rendering it suitable for integration into a wide array of
camera systems, ranging from smartphones and DSLRs to microscopes and
industrial imaging devices.
