Analytical computation of the derivative of PSF for the optimization of phase mask in wavefront coding system.

Wavefront coding system can realize defocus invariance of PSF/OTF with a phase mask inserting in the pupil plane. Ideally, the derivative of the PSF/OTF with respect to defocus error should be close to zero as much as possible over the extended depth of field/focus for the wavefront coding system. In this paper, we propose an analytical expression for the computation of the derivative of PSF. With this expression, the derivative of PSF based merit function can be used in the optimization of the wavefront coding system with any type of phase mask and aberrations. Computation of the derivative of PSF using the proposed expression and FFT respectively are compared and discussed. We also demonstrate the optimization of a generic polynomial phase mask in wavefront coding system as an example.