Varifocal lens based on fifth-order XY polynomial freeform surface

Optical system with zooming ability is essential for space exploration. In this paper, we proposed a new varifocal lens design based on the fifth-order X-Y polynomial free-form surface. It can change its focal power by the vertical deflection of the two free-form surfaces. We described the proposed lens’s modulation phase function and aberration based on the first-order optical analysis. Simulation experiments compared the proposed lens with the Alvarez lens regarding surface depth and zoom capability. We further investigate the correspondence between vertical deflection and optical power. The results show that the focal power of the varifocal lens based on the fifth-order X-Y polynomial free-form surface is proportional to the cube of the lateral shift distance, which has a stronger zoom ability than the Alvarez lens. It can achieve a wide range of power changes with a smaller lateral displacement, contributing to the zoom system’s further miniaturization.