Author Affiliations
School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou, Guangdong 510006, Chinashow less
Fig. 1. Polarized light reflection on the crystal surface
Fig. 2. Flow chart of improved simulated annealing simplex joint algorithm
Fig. 3. Variation of ellipsometric parameters of quartz crystal with incident angle. (a) Ψ; (b) Δ
Fig. 4. Variation of ellipsometric parameters of calcite crystal with incident angle. (a) Ψ; (b) Δ
Fig. 5. Variation of ellipsometric parameters of quartz crystal with optical axis azimuth angle. (a) Ψ; (b) Δ
Fig. 6. Variation of ellipsometric parameters of calcite crystal with optical axis azimuth angle. (a) Ψ; (b) Δ
Fig. 7. Relationship between standard deviation of crystal optical parameters and rotation angle. (a) quartz crystal; (b) calcite crystal
Fig. 8. Relation between the angular position error and the optical axis azimuth angle of crystal. (a) quartz crystal; (b) calcite crystal
Optical parameter | no | ko | ne | ke | ϕ /° |
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No noise | 1.5427±0 | 0±0 | 1.5517±0 | 0±0 | 59.998±0 | Add 0.02° noise | 1.5414±0.001 | 0.00009±0.0001 | 1.5511±0.0007 | 0.00004±0.0006 | 62.100±3.2 |
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Table 1. Inversion data of quartz crystal
Optical parameter | no | ko | ne | ke | ϕ /° |
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No noise | 1.6605±0 | 0.02±0 | 1.4874±0 | 0.02±0 | 60.001±0 | Add 0.02° noise | 1.6606±0.002 | 0.02±0.0003 | 1.4874±0.0005 | 0.02±0.00007 | 60.040±0.2 |
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Table 2. Inversion data of calcite crystal
Ellipsometricparameter | Initial angle | Rotate 30° | Rotate 60° |
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Ψ1 | Δ1 | Ψ2 | Δ2 | Ψ3 | Δ3 |
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Quartz crystal | 19.226±0.006 | 358.132±0.020 | 19.443±0.003 | 358.041±0.003 | 19.375±0.008 | 358.0433±0.02 | Calcite crystal | 18.851±0.003 | 359.669±0.002 | 16.830±0.007 | 0.492±0.001 | 18.478±0.004 | 359.925±0.008 |
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Table 3. Repeated measurement results of ellipsometric parameters of crystalunit: (°)
Optical parameter | no | ko | ne | ke | ϕ /(°) |
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Quartz crystal | 1.5524±0.0001 | 0.027±0.0000500 | 1.5664±0.0002 | 0.026±0.000400 | 174.93±0.40 | Calcite crystal | 1.6518±0.0002 | 0.0009±0.000001 | 1.4857±0.0003 | 0.007±0.000009 | 180.45±0.02 |
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Table 4. Inversion results of crystal optical parameters
Initial angle /(°) | Rotate 30°/(°) | Rotate 60°/(°) | no | ko | ne | ne | ϕ /(°) |
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30 | 60 | 90 | 1.5521 | 0.027 | 1.5635 | 0.025 | 143.61 | 90 | 120 | 150 | 1.5522 | 0.027 | 1.5611 | 0.025 | 206.43 | 120 | 150 | 180 | 1.5520 | 0.027 | 1.5611 | 0.026 | 240.30 | 180 | 210 | 240 | 1.5521 | 0.025 | 1.5617 | 0.026 | 289.30 | 240 | 270 | 300 | 1.5552 | 0.025 | 1.5626 | 0.025 | 358.93 | 300 | 330 | 360 | 1.5583 | 0.025 | 1.5648 | 0.026 | 57.23 | Average value | 1.5535 | 0.026 | 1.5629 | 0.025 | | Standard deviation | 0.003 | 0.002 | 0.002 | 0.0005 | |
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Table 5. Quartz crystal measurement results of multiple experiments
Initial angle /(°) | Rotate 30°/(°) | Rotate 60°/(°) | no | ko | ne | ke | ϕ /(°) |
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30 | 60 | 90 | 1.6534 | 0.00080 | 1.4878 | 0.0068 | 151.25 | 90 | 120 | 150 | 1.6525 | 0.00200 | 1.4851 | 0.0160 | 210.15 | 120 | 150 | 180 | 1.6563 | 0.00500 | 1.4881 | 0.0085 | 241.03 | 180 | 210 | 240 | 1.6500 | 0.00000 | 1.4858 | 0.0058 | 301.61 | 210 | 240 | 270 | 1.6551 | 0.00073 | 1.4885 | 0.0059 | 330.87 | 240 | 270 | 300 | 1.6554 | 0.00040 | 1.4892 | 0.0033 | 360.65 | Average value | 1.6538 | 0.0015 | 1.4874 | 0.0077 | | Standard deviation | 0.002 | 0.002 | 0.002 | 0.004 | |
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Table 6. Calcite crystal measurement results of multiple experiments