Characterization and design of a freeform holographic optical element

Objective: The aberrations of a conventional lens holographic optical element (HOE) are consid-erable because of the off-axis recording and diffraction nature. A freeform HOE was introduced to alleviate these aberrations. To design and optimize the recording wavefront of a freeform HOE, it is important to figure out the imaging properties of an HOE.Methods: We systematically derived a general characterization of the conjugate imaging equation of an elementary HOE recorded by two spherical wavefronts using the scalar diffraction theory. In our design, each patch of a freeform HOE is considered as an elementary HOE. The recording wavefronts of a freeform HOE is designed by determining each elementary HOE through the conjugate imaging equation.Results: The image position predicted by the imaging equation is consistent with that of the finite ray-tracing method. The error when the imaging equation is applied to off-axis object points and different reconstruction wavelengths is eliminated effectively through coordinate transformation. Furthermore, based on this equation, a freeform HOE with 3 x 3 tiling elementary HOEs is designed to eliminate distortion and astigmatism of the HOE imaging system. A holographic printer to fabricate this freeform HOE is recommended.