• Acta Optica Sinica
  • Vol. 37, Issue 8, 0812005 (2017)
Xianlei Liu, Xiaodong Zhang*, Hangyu Xu, and Zhen Zeng
Author Affiliations
  • State Key Laboratory of Precision Measuring Technology & Instruments, Centre of MicroNano Manufacturing Technology, Tianjin University, Tianjin 300072, China
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    DOI: 10.3788/AOS201737.0812005 Cite this Article Set citation alerts
    Xianlei Liu, Xiaodong Zhang, Hangyu Xu, Zhen Zeng. Machining Error Analysis of Freeform Surface Off-Axis Three-Mirror System Based on Optical Performance Evaluation[J]. Acta Optica Sinica, 2017, 37(8): 0812005 Copy Citation Text show less
    Schematic diagram of the ultra-precision three-axis machine
    Fig. 1. Schematic diagram of the ultra-precision three-axis machine
    Flowchart of machining error influence analysis model of ultra-precision machine
    Fig. 2. Flowchart of machining error influence analysis model of ultra-precision machine
    Conversion relationship between different optical performance indexes
    Fig. 3. Conversion relationship between different optical performance indexes
    Model diagram of off-axis three-mirror system
    Fig. 4. Model diagram of off-axis three-mirror system
    Surface-shape error and its effect on MTF for primary mirror. (a) Surface-shape error map; (b) variation diagram of meridional MTF with PV value of surface-shape error; (c) variation diagram of sagittal MTF with PV value of surface-shape error
    Fig. 5. Surface-shape error and its effect on MTF for primary mirror. (a) Surface-shape error map; (b) variation diagram of meridional MTF with PV value of surface-shape error; (c) variation diagram of sagittal MTF with PV value of surface-shape error
    Machining errors' effect on MTF for secondary mirror. (a) Variation diagram of meridional MTF with PV value of surface-shape error; (b) variation diagram of sagittal MTF with PV value of surface-shape error
    Fig. 6. Machining errors' effect on MTF for secondary mirror. (a) Variation diagram of meridional MTF with PV value of surface-shape error; (b) variation diagram of sagittal MTF with PV value of surface-shape error
    Machining errors' effect on MTF for tertiary mirror. (a) Variation diagram of meridional MTF with PV value of surface-shape error; (b) variation diagram of sagittal MTF with PV value of surface-shape error
    Fig. 7. Machining errors' effect on MTF for tertiary mirror. (a) Variation diagram of meridional MTF with PV value of surface-shape error; (b) variation diagram of sagittal MTF with PV value of surface-shape error
    Effects of angle errors on MTF of the system. (a) Effects of angle errors of the primary mirror on MTF of the system; (b) effects of angle errors of the secondary mirror on MTF of the system; (c) effects of angle errors of the tertiary mirror on MTF of the system
    Fig. 8. Effects of angle errors on MTF of the system. (a) Effects of angle errors of the primary mirror on MTF of the system; (b) effects of angle errors of the secondary mirror on MTF of the system; (c) effects of angle errors of the tertiary mirror on MTF of the system
    AxisError item
    X axisδxx,δxy,δxz,θxx,θxy,θxz
    Z axisδzx,δzy,δzz,θzx,θzy,θzz
    C axisδcx,δcy,δcz,θcx,θcy,θcz
    Squareness errors among three axesαzx,βcx,βcy
    Tool alignment errors among three axesXt,Yt,Zt
    Table 1. Geometric errors and tool errors of ultra-precision three-axis machine
    ErrorPrimary mirrorSecondary mirrorTertiary mirror
    Tool alignment error in X direction1.9150521.5586130.490417
    Squareness error between X and C axis0.0001750.0004610.000245
    Tool alignment error in Y direction10.847730/2.868905
    Pitch error of X axis0.005656/0.003096
    Squareness error between X and Z axis0.0292970.0530460.003486
    Table 2. Ratio of machining errors to surface-shape errors
    Error itemTolerance of surface-shape errors' PV values /μmTolerance of machining errors
    Error 1-4.026-1.069Xt:-7.71-2.981 μmβcx:-0.000703°-0.000274°
    Error 2-7.467-18.185Yt:81-197 μmθxy:0.042237°-0.102920°
    Error 3-1.836-5.524αzx:-0.053667°-0.161528°
    Table 3. Tolerances of surface-shape errors' PV values and machining errors for primary mirror
    Error itemTolerance of surface-shape errors' PV values /μmTolerance of machining errors
    Error 1-0.981-1.656Xt:-1.529-2.581 μmβcx:-0.000452°-0.000763°
    Error 3-3.624-1.899αzx:-0.192242°-0.102832°
    Table 4. Tolerances of surface-shape errors' PV values and machining errors for secondary mirror
    Error itemTolerance of surface-shape errors' PV values /μmTolerance of machining errors
    Error 1-3.369-1.263Xt:-1.651-0.619 μmβcx:-0.000826°-0.000310°
    Error 2-4.020-5.121Yt: -11.553-14.717 μmθxy:0.012449°-0.015859°
    Error 3-0.975-3.274αzx:-0.003399°-0.011379°
    Table 5. Tolerances of surface-shape errors' PV values and machining errors for tertiary mirror
    Xianlei Liu, Xiaodong Zhang, Hangyu Xu, Zhen Zeng. Machining Error Analysis of Freeform Surface Off-Axis Three-Mirror System Based on Optical Performance Evaluation[J]. Acta Optica Sinica, 2017, 37(8): 0812005
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