Author Affiliations
1 State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China2 Beijing Key Laboratory of Precision/Ultra-Precision Manufacturing Equipments and Control, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, Chinashow less
Fig. 1. Schematic of SBIL system
Fig. 2. Relationship between beam waist radius and waist-to-substrate distance
Fig. 3. Diagram of single light path design
Fig. 4. Far-field interference of Gaussian beams
Fig. 5. Wavefront curvature distribution curve of Gaussian beam
Fig. 6. Nonlinear error distribution of phase without assembly error (unit of error data in curves is nm)
Fig. 7. Nonlinear error distribution of phase with waist-to-substrate assembly errors (unit of error data in curves is nm). (a) dR: -1 mm; (b) dR: -20 mm, dL: -20 mm; (c) dR: -21 mm, dL: -20 mm
Fig. 8. Nonlinear error distribution of phase with waist radius errors (unit of error data in curves is nm)
Fig. 9. Nonlinear error distribution of phase with two kind of assembly errors (unit of error data in curves is nm)
Fig. 10. Nonlinear error distribution of phase with worst assembly errors (unit of error data in curves is nm)
Fig. 11. Schematic of Gaussian beam through circular aperture
Fig. 12. Curves of approximate characteristics of Gaussian beam versus aperture radius
Fig. 13. Nonlinear error distribution of phase when ωo=37.05 μm (unit of error data in curves is nm)
Fig. 14. Nonlinear error distribution of phase when d=275 mm (unit of error data in curves is nm)
Parameter | ω' /mm | z' /m | β /mrad | b /m |
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Input | 0.35 | 0.743 | 0.65 | 1.084 | Output | 0.05 | 0.187 | 4.5 | 0.02217 |
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Table 1. Property changes of beams after passing through lens with a focal length of 175 nm
Figure No. | Assembly error | Maximumnonlinearerror /nm |
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Fig. 6 | - | 1.273 | Fig. 7(a) | dR: -1 mm | 2.183 | Fig. 7(b) | dR: -20 mm, dL: -20 mm | 1.398 | Fig. 7(c) | dR: -21 mm, dL: -20 mm | 2.397 | Fig. 8 | ωoR: -1 μm, ωoL: +1 μm | 1.436 | Fig. 9 | dR: -21 mm, dL: -20 mmωoR: -1 μm, ωoL: +1 μm | 2.585 | Fig. 10 | ωoR: -1 μm, ωoL: +1 μmθR: -200 μrad, θL: +200 μraddR: -21 mm, dL: -20 mm | 2.918 |
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Table 2. Nonlinear error analysis results of phase of interference fringe