Odd symmetrical square-root phase mask to extend the depth of field in wavefront-coded imaging systems

Extend-the-depth-of-field imaging can be achieved by wavefront coding technique, which inserts an odd symmetrical phase mask into the pupil plane to generate the invariant imaging property over a wide range of defocus. Obtaining the low sensibility to defocus for wavefront coding systems depends on designing a proper phase profile. Here we proposed a phase mask combining the power function with the square-root function to maximize the invariant imaging property to defocus. Judging by defocused modulation transfer function (MTF) and Hilbert space angle, numerical comparisons with the cubic mask, exponential mask and improved logarithmic mask prove the superiority of proposed square-root phase mask in extending the depth of field.