Imaging with extended focal depth by means of lenses with radial and angular modulation.

The paper presents imaging properties of modified lenses with the radial and the angular modulation. We analyze three following optical elements with moderate numerical apertures: the forward logarithmic axicon and the axilens representing the radial modulation as well as the light sword optical element being a counterpart of the axilens with the angular modulation. The abilities of the elements for imaging with extended depth of focus are discussed in detail with the help of structures of output images and modulation transfer functions corresponding to them. According to the obtained results only the angular modulation of the lens makes possible to maintain the acceptable resolution, contrast and brightness of the output images for a wide range of defocusing. Therefore optical elements with angular modulations and moderate numerical apertures seem to be especially suitable for imaging with extended focal depth.