Author Affiliations
State Key Laboratory of Precision Measuring Technology & Instruments, Centre of MicroNano Manufacturing Technology, Tianjin University, Tianjin 300072, Chinashow less
Fig. 1. Schematic diagram of the ultra-precision three-axis machine
Fig. 2. Flowchart of machining error influence analysis model of ultra-precision machine
Fig. 3. Conversion relationship between different optical performance indexes
Fig. 4. Model diagram of off-axis three-mirror system
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
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
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
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
Axis | Error item |
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X axis | δxx,δxy,δxz,θxx,θxy,θxz | Z axis | δzx,δzy,δzz,θzx,θzy,θzz | C axis | δcx,δcy,δcz,θcx,θcy,θcz | Squareness errors among three axes | αzx,βcx,βcy | Tool alignment errors among three axes | Xt,Yt,Zt |
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Table 1. Geometric errors and tool errors of ultra-precision three-axis machine
Error | Primary mirror | Secondary mirror | Tertiary mirror |
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Tool alignment error in X direction | 1.915052 | 1.558613 | 0.490417 | Squareness error between X and C axis | 0.000175 | 0.000461 | 0.000245 | Tool alignment error in Y direction | 10.847730 | / | 2.868905 | Pitch error of X axis | 0.005656 | / | 0.003096 | Squareness error between X and Z axis | 0.029297 | 0.053046 | 0.003486 |
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Table 2. Ratio of machining errors to surface-shape errors
Error item | Tolerance of surface-shape errors' PV values /μm | Tolerance of machining errors |
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Error 1 | -4.026-1.069 | Xt:-7.71-2.981 μmβcx:-0.000703°-0.000274° | Error 2 | -7.467-18.185 | Yt:81-197 μmθxy:0.042237°-0.102920° | Error 3 | -1.836-5.524 | αzx:-0.053667°-0.161528° |
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Table 3. Tolerances of surface-shape errors' PV values and machining errors for primary mirror
Error item | Tolerance of surface-shape errors' PV values /μm | Tolerance of machining errors |
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Error 1 | -0.981-1.656 | Xt:-1.529-2.581 μmβcx:-0.000452°-0.000763° | Error 3 | -3.624-1.899 | αzx:-0.192242°-0.102832° |
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Table 4. Tolerances of surface-shape errors' PV values and machining errors for secondary mirror
Error item | Tolerance of surface-shape errors' PV values /μm | Tolerance of machining errors |
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Error 1 | -3.369-1.263 | Xt:-1.651-0.619 μmβcx:-0.000826°-0.000310° | Error 2 | -4.020-5.121 | Yt: -11.553-14.717 μmθxy:0.012449°-0.015859° | Error 3 | -0.975-3.274 | αzx:-0.003399°-0.011379° |
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Table 5. Tolerances of surface-shape errors' PV values and machining errors for tertiary mirror