Optimized circularly symmetric phase mask to extend the depth of focus.

We propose a novel design method for a circularly symmetric phase mask to extend the depth of focus. Using the free-form rational function as the solution space, we optimize the profile of the phase mask by analysis of the axial intensity distribution, which can be calculated efficiently by employing the fast Fourier transform algorithm. Numerical comparisons prove the resulting rational phase mask's superiority to the existing quartic phase mask in intensity distribution and imaging performance.