Jacobi-Fourier phase masks to increase performance of wavefront-coded optical systems for random or varying aberration alleviation

Wavefront coding is a hybrid optical-digital technique proposed to increase the effective depth of focus of optical systems. The key to wavefront coding lies in the design of a suitable phase mask placed at the system's aperture to achieve invariant imaging properties over a range of defocus. In systems limited by temporally or spatially varying aberrations the use of wavefront coding has not yet been demonstrated. Here, we propose the use of Jacobi-Fourier shaped phase masks to produce sharp and clear images for optical systems affected by random and varying aberrations. When choosing the mask, noise levels must be taken into account too. In order to illustrate the potential use of the masks we will show by experimental simulations that a Jacobi-Fourier mask can be designed to alleviate temporally varying aberrations due to atmospheric turbulences being robust to noise while keeping acceptable resolution and reducing image artifacts.