  We present a fully differentiable framework for seamlessly integrating wave
optical components with geometrical lenses, offering an approach to enhance the
performance of large-scale end-to-end optical systems. In this study, we focus
on the integration of a metalens, a geometrical lens, and image data. Through
the use of gradient-based optimization techniques, we demonstrate the design of
nonparaxial imaging systems and the correction of aberrations inherent in
geometrical optics. Our framework enables efficient and effective optimization
of the entire optical system, leading to improved overall performance.
