Programmable birefringent lenses with a liquid-crystal display

We study the properties of a novel birefringent lens constructed by combination of a regular glass lens and a programmable diffractive lens addressed to a liquid-crystal display (LCD). The LCD affects only the vertical polarization state. Consequently the birefringent lens produces two images of an input object with different locations and magnifications for the two orthogonal polarization states. Using a properly oriented analyzer polarizer produces interference fringes. We then show how the imaging system acts as a common-path polarization interferometer for wave-front analysis of objects in the input plane. Finally, we subtract the two images to produce an edge-enhanced version of the input image. All these effects can be controlled because we can program lenses with different focal lengths onto the LCD.