Point light source imaging by a three-dimensional long-imaging-depth lens

Based on Fermat's principle, we have designed a three-dimensional long-imaging-depth (LID) lens for point light source imaging. The thickness function of the designed LID lens is given analytically. Imaging properties of the designed LID lens are simulated by the Fresnel diffraction integral method. Numerical simulations demonstrate that the designed LID lens has gained a much longer imaging depth in the axial direction, in comparison with the conventional lens. In addition, compared with the conventional lens, the transverse imaging spot size and the imaging efficiency of the designed LID lens have exhibited weaker reliance on the longitudinal position within the LID region. Finally, the wavelength tolerance and roughness tolerance properties of the designed LID lens are disclosed.