Numerical investigation of three-dimensional pupil model impact on the relative illumination in panomorph lenses

Abstract

One of the key issues in conventional wide-angle lenses is the well-known cosine-fourth power law problem causing the illumination falloff at its image space. This paper explores methods of improving illumination in the image space in panomorph lenses. By tracing skew rays within the defined field of view and pupil diameter, we obtained the actual position of the three-dimensional pupil model of the entrance pupil (EP) and exit pupil (XP). Based on the law of irradiance transport conservation, the relation between the area of the EP projection and illumination in the image space is derived to investigate the factors affecting the illumination on the peripheral field. A panomorph lens has been optimized as an example by providing a self-defined operation in the optimization process. The characteristic of the EP and XP in panomorph lenses is qualitatively analyzed. Compared with the conventional design method, the proposed design strategy can enhance the illumination with and without polarized light based on qualitatively evaluating the area of projected EP. It is demonstrated that this method enables the enhancement of the illumination without additional film coating.