Local tolerance analysis for freeform optical systems containing diffractive phase elements

Freeform surfaces and diffractive phase elements offer significant potential to enhance optical system performance, but their use also presents manufacturing challenges. Freeform surfaces are typically manufactured using sub-aperture machining tools, which may result in localized errors. When applied to the substrate of phase elements or holographic elements (HOE) recording paths, these errors lead to localized phase errors. To address this, a local tolerance analysis method for freeform optical systems with diffractive phase elements is proposed. The method computes local phase tolerances, substrate surface figure tolerances, and grating line spacing error tolerances at different regions on the diffractive element. It can also calculate surface figure tolerances for the auxiliary mirror in the HOE or holographic grating recording path. The method's effectiveness is demonstrated in a freeform surface holographic grating imaging spectrometer.