Single point diamond turning is a commonly used method for manufacturing harmonic diffractive optical elements (HDOEs). Diffraction efficiency of HDOEs is sensitive to surface-relief profile errors, and a half-round tool can reduce the profile error obviously. Furthermore, the diamond tools also create surface roughness errors. The two errors will produce shadowing and scattering effects. In this paper, the two kinds of errors, especially the surface roughness, are described accurately. A mathematical model is proposed to reveal the relationship among diffraction efficiency, cutting tool radius, feed rate, microstructure zone period widths, and the refractive index of the substrate material and balance the influence of shadowing and scattering effects. The simulation results show that the model can guide the acquisition of high-precision surface topography and high diffraction efficiency, which improves the imaging quality of the optical system. (C) 2020 Optical Society of America.
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