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Paraxial diffraction modeling based on the Fourier transform has seen widespread implementation for simulating the response of a diffraction-limited optical system. For systems where the paraxial assumption is not sufficient, a class of algorithms has been developed that employs hybrid propagation physics to compute the propagation of an elementary beamlet along geometric ray paths. These "beamlet decomposition" algorithms include the well-known Gaussian beamlet decomposition (GBD) algorithm, of which several variants have been created. To increase the computational efficiency of the GBD algorithm, we derive an alternative expression of the technique that utilizes the analytical propagation of beamlets to tilted planes. We then use this accelerated algorithm to conduct a parameter-space search to find the optimal combination of free parameters in GBD to construct the analytical Airy function. The experiment is conducted on a consumer-grade CPU, and a high-performance GPU, where the new algorithm is 34 times faster than the previously published algorithm on CPUs, and 67,513 times faster on GPUs.

The surface quality of optical lenses is highly required in imaging functions. Normally, ultra-precision turning is employed to fabricate the optical lenses. However, ultra-precision turning cannot meet the surface quality demands due to the tool marks. In this study, a new damping-clothed (DC) tool and chemical enhanced non-Newtonian ultrafine (CNNU) slurry for non-contact polishing are proposed to achieve sub-nanometer roughness on aspherical optical molds. A material removal model based on the hydrodynamic pressure and velocity simulation was established to calculate the dwell time in curved surface machining. The formation mechanism of sub-nanometer roughness is clarified. The proposed method and slurry were verified by the experiments in processing NiP alloy aspheric optical mold. After the process, surface roughness Sa achieved 0.54 nm and the form accuracy is less than PV 600 nm.