Modified crossed Dragone optical design of the LiteBIRD low-frequency telescope

<i>LiteBIRD</i> is a JAXA-led international project aimed at measuring the cosmic microwave background (CMB) polarization with high sensitivity to detect polarization <i>B</i> modes. This detection would provide evidence of inflation. <i>LiteBIRD</i> will observe the full sky for three years at the L2 Lagrange point of the Earth-Sun system across 34-448 GHz and is expected to launch in the Japanese fiscal year of 2032. The Low-Frequency Telescope (LFT) will observe in the 34-161 GHz range implementing a modified crossed Dragone (MCD) reflective optical design optimized for high optical performance across a wide 18^∘×9^∘ field of view (FOV). In this paper, we report the LFT optical design details including its optimization and optical performance assessed using optical simulations. The MCD design consists of a paraboloidal primary and a hyperboloidal secondary reflector with polynomial correction terms up to seventh order, achieving Strehl ratios ≥0.97 at 161 GHz across the FOV. The Mueller QU (UQ) cross-polarization response is ≤-26.9<i>d</i><i>B</i> at 34 GHz. The simulated beam sizes are <78^' at 34 GHz. The simulated sidelobe response for the direct and diffuse triple reflection sidelobes is estimated to be <-57<i>d</i><i>B</i> and for the focused triple reflection sidelobe <-37<i>d</i><i>B</i> at 34 GHz. The LFT optical design satisfies all the optical requirements and specifications for the project and is compatible with the <i>LiteBIRD</i> science goals.