Increasing depth of field in imaging systems can be beneficial, particularly for systems with high numerical apertures and short depth of field, such as microscopy. Extending depth of field has been previously demonstrated, for example, using non-rotationally symmetric (freeform) components such as cubic and logarithmic phase plates. Such fixed phase plates are generally designed for a specific optical system, so a different phase plate is required for each system. Methods that enable variable extended depth of field for multiple optical systems could provide benefits by reducing the number of required components and costs. In this paper, we explore the design of a single pair of transmissive freeform surfaces to enable extended depth of field for multiple lenses with different numerical apertures through relative translation of the freeform components. This work builds on the concept of an Alvarez lens, in which one pair of transmissive XY-polynomial freeform surfaces generates variable optical power through lateral relative shifts between the surfaces. The presented approach is based on the design of multiple fixed phase plates to optimize the through-focus Modulation Transfer Function (MTF) for imaging lenses of given numerical apertures. The freeform surface equation for the desired variable phase plate pair is then derived and the relative shift amounts between the freeform surfaces are calculated to enable extended depth of field for multiple imaging lenses with different numerical aperture values. Design approaches and simulation results will be discussed.
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