Wave-front coding technology is a novel jointly optical and digital imaging technology which can greatly extend the
depth of focus of optical systems. The image restoration process is an important part of wave-front coding technology.
Using wave-front coding makes the modulation transfer function(MTF) values of the optical systems change little over a
range of several times the depth of focus, which means the system MTF is quite insensitive to defocus, and there is no
zero in the passband. So we can design a single filter for the restoration of images in different defocus positions.
However, it's hard to avoid noise during image acquisition and transmission processes. These noises will be amplified in
the image restoration, especially in the high frequency part when the MTF drop is relatively low. The restoration process
significantly reduces the system signal to noise ratio this way. Aimed at the problem of noise amplification, a new
algorithm was proposed which incorporated wavelet denoising into the iterative steps of Lucy-Richardson algorithm.
Better restoration results were obtained through the new algorithm, effectively solving the noise amplification problem of
original LR algorithm. Two sets of identical triplet imaging systems were designed, in one of which the
cubic-phase-plate was added. Imaging experiments of the manufactured systems were carried, and the images of a
traditional system and a wave-front coded system before and after decoding were compared. The results show that the
designed wave-front coded system can extend the depth of focus by 40 times compared with the traditional system while
maintaining the light flux and the image plane resolution.