• Acta Optica Sinica
  • Vol. 45, Issue 3, 0312001 (2025)
Yuan Zhou1, Ying Chen1,*, Liping Sun1, Zixin Zou1..., Yingchang Zou1, Xiqiao Chen1, Shixun Fan2 and Dapeng Fan2|Show fewer author(s)
Author Affiliations
  • 1College of Electronic Communication and Electrical Engineering, Changsha University, Changsha 410022, Hunan , China
  • 2College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, Hunan , China
  • show less
    DOI: 10.3788/AOS241604 Cite this Article Set citation alerts
    Yuan Zhou, Ying Chen, Liping Sun, Zixin Zou, Yingchang Zou, Xiqiao Chen, Shixun Fan, Dapeng Fan. Singularity Problem Analysis of Target Tracking Based on Risley Prisms[J]. Acta Optica Sinica, 2025, 45(3): 0312001 Copy Citation Text show less
    Schematic diagram of Risley-prisms-based beam steering system. (a) Description of system parameters; (b) system arrangement
    Fig. 1. Schematic diagram of Risley-prisms-based beam steering system. (a) Description of system parameters; (b) system arrangement
    Control singularity problem at center zone of field of regard (FOR) for real-time target tracking. (a) Schematic diagram for target moving at center zone of FOR; (b) variations of M required by real-time target tracking as a function of θ; (c) variations of maximum M value Mm as a function of Φ
    Fig. 2. Control singularity problem at center zone of field of regard (FOR) for real-time target tracking. (a) Schematic diagram for target moving at center zone of FOR; (b) variations of M required by real-time target tracking as a function of θ; (c) variations of maximum M value Mm as a function of Φ
    Schematic diagram of target tracking in discrete time domain
    Fig. 3. Schematic diagram of target tracking in discrete time domain
    Required rotation angle of two prisms for tracking target from point A (ΦA=1°, ΘA=0°) to other points at center zone of FOR. (a) Required rotation angle Δϕ1 of prism I when adopting the same set of solutions; (b) required rotation angle Δϕ1 of prism I when switching solutions; (c) required rotation angle Δϕ2 of prism Ⅱ when adopting the same set of solutions; (d) required rotation angle Δϕ2 of prism Ⅱ when switching solutions
    Fig. 4. Required rotation angle of two prisms for tracking target from point A (ΦA=1°, ΘA=0°) to other points at center zone of FOR. (a) Required rotation angle Δϕ1 of prism I when adopting the same set of solutions; (b) required rotation angle Δϕ1 of prism I when switching solutions; (c) required rotation angle Δϕ2 of prism Ⅱ when adopting the same set of solutions; (d) required rotation angle Δϕ2 of prism Ⅱ when switching solutions
    Required values of M¯1 and M¯2 for tracking target from point A (ΦA=1°, ΘA=0°) to other points at center zone of FOR. (a) Required values of M¯1 when adopting the same set of solutions; (b) required values of M¯1 when switching solutions; (c) required values of M¯2 when adopting the same set of solutions; (d) required values of M¯2 when switching solutions; (e) required values of M¯max when adopting the same set of solutions; (f) required values of M¯max when switching solutions
    Fig. 5. Required values of M¯1 and M¯2 for tracking target from point A (ΦA=1°, ΘA=0°) to other points at center zone of FOR. (a) Required values of M¯1 when adopting the same set of solutions; (b) required values of M¯1 when switching solutions; (c) required values of M¯2 when adopting the same set of solutions; (d) required values of M¯2 when switching solutions; (e) required values of M¯max when adopting the same set of solutions; (f) required values of M¯max when switching solutions
    Required values of M¯max for tracking target from point A (ΘA=0°) to other points at center zone of FOR by applying optimal-solution method. (a) ΦA=1°; (b) ΦA=0.5°; (c) ΦA=0.1°; (d) variations of M¯M as a function of ΦA
    Fig. 6. Required values of M¯max for tracking target from point A (ΘA=0°) to other points at center zone of FOR by applying optimal-solution method. (a) ΦA=1°; (b) ΦA=0.5°; (c) ΦA=0.1°; (d) variations of M¯M as a function of ΦA
    Sources of singularity problem for tracking target at center zone of FOR. (a) Schematic diagram for beam steering at center zone; (b) variations of difference between two sets of solutions as a function of Φ
    Fig. 7. Sources of singularity problem for tracking target at center zone of FOR. (a) Schematic diagram for beam steering at center zone; (b) variations of difference between two sets of solutions as a function of Φ
    Schematic diagram of tracking blind zone for rotational double prisms
    Fig. 8. Schematic diagram of tracking blind zone for rotational double prisms
    Yuan Zhou, Ying Chen, Liping Sun, Zixin Zou, Yingchang Zou, Xiqiao Chen, Shixun Fan, Dapeng Fan. Singularity Problem Analysis of Target Tracking Based on Risley Prisms[J]. Acta Optica Sinica, 2025, 45(3): 0312001
    Download Citation