Machining Error Analysis of Freeform Surface Off-Axis Three-Mirror System Based on Optical Performance Evaluation

Xianlei Liu; Xiaodong Zhang; Hangyu Xu; Zhen Zeng

doi:10.3788/AOS201737.0812005

Acta Optica Sinica, Volume. 37, Issue 8, 0812005(2017)

Machining Error Analysis of Freeform Surface Off-Axis Three-Mirror System Based on Optical Performance Evaluation

Xianlei Liu, Xiaodong Zhang^*, Hangyu Xu, and Zhen Zeng

State Key Laboratory of Precision Measuring Technology & Instruments, Centre of MicroNano Manufacturing Technology, Tianjin University, Tianjin 300072, China

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Figures & Tables(13)

Fig. 1. Schematic diagram of the ultra-precision three-axis machine

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Fig. 2. Flowchart of machining error influence analysis model of ultra-precision machine

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Fig. 3. Conversion relationship between different optical performance indexes

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Fig. 4. Model diagram of off-axis three-mirror system

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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

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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

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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

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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

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Table 1. Geometric errors and tool errors of ultra-precision three-axis machine

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Table 1. Geometric errors and tool errors of ultra-precision three-axis machine

Axis	Error item
X axis	δ_xx,δ_xy,δ_xz,θ_xx,θ_xy,θ_xz
Z axis	δ_zx,δ_zy,δ_zz,θ_zx,θ_zy,θ_zz
C axis	δ_cx,δ_cy,δ_cz,θ_cx,θ_cy,θ_cz
Squareness errors among three axes	α_zx,β_cx,β_cy
Tool alignment errors among three axes	X_t,Y_t,Z_t

Table 2. Ratio of machining errors to surface-shape errors

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Table 2. Ratio of machining errors to surface-shape errors

Error	Primary mirror	Secondary mirror	Tertiary mirror
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

Table 3. Tolerances of surface-shape errors' PV values and machining errors for primary mirror

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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
Error 1	-4.026-1.069	X_t:-7.71-2.981 μmβ_cx:-0.000703°-0.000274°
Error 2	-7.467-18.185	Y_t:81-197 μmθ_xy:0.042237°-0.102920°
Error 3	-1.836-5.524	α_zx:-0.053667°-0.161528°

Table 4. Tolerances of surface-shape errors' PV values and machining errors for secondary mirror
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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
Error 1 -0.981-1.656 X_t:-1.529-2.581 μmβ_cx:-0.000452°-0.000763°
Error 3 -3.624-1.899 α_zx:-0.192242°-0.102832°

Table 5. Tolerances of surface-shape errors' PV values and machining errors for tertiary mirror

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Table 5. Tolerances of surface-shape errors' PV values and machining errors for tertiary mirror

Error item	Tolerance of surface-shape errors' PV values /μm	Tolerance of machining errors
Error 1	-3.369-1.263	X_t:-1.651-0.619 μmβ_cx:-0.000826°-0.000310°
Error 2	-4.020-5.121	Y_t: -11.553-14.717 μmθ_xy:0.012449°-0.015859°
Error 3	-0.975-3.274	α_zx:-0.003399°-0.011379°

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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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Paper Information

Category: Instrumentation, Measurement and Metrology

Received: Feb. 10, 2017

Accepted: --

Published Online: Sep. 7, 2018

The Author Email: Zhang Xiaodong (zhangxd@tju.edu.cn)

DOI:10.3788/AOS201737.0812005

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Geometric errors and tool errors of ultra-precision three-axis machine

Table 1. Geometric errors and tool errors of ultra-precision three-axis machine

Table 2. Ratio of machining errors to surface-shape errors

Table 2. Ratio of machining errors to surface-shape errors

Table 3. Tolerances of surface-shape errors' PV values and machining errors for primary mirror

Table 3. Tolerances of surface-shape errors' PV values and machining errors for primary mirror

Table 4. Tolerances of surface-shape errors' PV values and machining errors for secondary mirror

Table 4. Tolerances of surface-shape errors' PV values and machining errors for secondary mirror

Table 5. Tolerances of surface-shape errors' PV values and machining errors for tertiary mirror

Table 5. Tolerances of surface-shape errors' PV values and machining errors for tertiary mirror