Efficient metric for pupil-phase engineering.

Pupil-phase engineering is a design process in which pupil-phase masks are optimized for performance characteristics by minimizing a cost function. To reduce computational complexity for optimizing focal depth, a cost function based on the second derivative of the optical transfer function with respect to misfocus at the origin is proposed. Efficient formulas for computing this metric are derived, and a design is presented to demonstrate that this metric can be used to predict insensitivity of the system to large values of misfocus.