Abstract: According to the design theory of wavefront coding, taking the imaging restorability into consideration, we used the angle in Hilbert space between infocus PSF and several defocus PSFs as an evaluation for making the shape and intensity of point spread function (PSF) insensitive with defocus over a wide range of defocus parameter values. The angle in Hilbert space is capable of evaluating similarity of the PSFs of different defocus parameter values and was used to optimize the design of phase mask in real wavefront coding systems. A doublet-wavefront coding system was designed based on a finite focused doublet system. The simulation results show that the phase mask can extend the depth of focus by an order of magnitude more than that of Hopkins defocus criterion. Better and more stable imaging quality over a large depth of focus is acquired with the optimized pupil phase mask.