Fast and High-Precision Measurement Method of Optical Parameters of Parallel Flat Plates

Fig. 2. Schematic of two-step absolute measurement method of surface interference flat plate optical parameters. (a) With flat plate;(b) cavity structure

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Fig. 3. Feature maps in the calculation of optical thickness change. (a) Step 1; (b) step 2; (c) step 3; (d) step 4

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Fig. 4. Feature map in the calculation of front surface shape

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Fig. 5. Feature map in the calculation of rear surface shape

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Fig. 6. Evaluation functions. (a) W₂ wave surface information; (b) W₁ wave surface information; (c) W₆ wave surface information

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Fig. 7. Residual wave surface data calculated by 77-step phase shift algorithm at different linearities

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Fig. 8. Diagram of the experimental setup

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Fig. 9. Comparison of actual non-uniform sampling intervals with the ideal uniform sampling interval for different parallel plates. (a) 40 mm parallel plate; (b) 5 mm parallel plate

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Fig. 10. Four continuous interference sampling plots for different parallel plates. (a) 40 mm parallel plate; (b) 5 mm parallel plate

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Fig. 11. Four continuous cavity interference sampling plots for different parallel plates. (a) 40 mm parallel plate; (b) 5 mm parallel plate

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Fig. 12. Optical parameter wave surface diagrams of 40 mm parallel flat panel. (a) Comparison of surface shape information on the front surface; (b) comparison of optical thickness change information; (c) comparison of optical uniformity

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Fig. 13. Optical parameter wave surface diagrams of 5 mm parallel flat panel. (a) Comparison of surface shape information on the front surface; (b) comparison of optical thickness change information; (c) comparison of optical uniformity

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Table 1. Frequency distribution for each group of interference signals in four-surface interference system
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Table 1. Frequency distribution for each group of interference signals in four-surface interference system
Interference level Length of interference cavity Frequency ratio $v_{k} / v_{1}$
$1^{s t}$ $2 L_{1}$ 2
$2 L_{2}$ 2s
$2 n t$ 2r
$2 L_{1} + 2 n t$ 2+2r
$2 L_{2} + 2 n t$ 2r+2s
$2 L_{1} + 2 L_{2} + 2 n t$ 2+2r+2s

Table 2. Optical path difference and interference cavity length of each group of fringes

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Table 2. Optical path difference and interference cavity length of each group of fringes

Interference surface	Wave surface information	Length of interference cavity
$T$ and $A$	$W_{1} = 2 A - 2 T$	$h_{1} = 2 L_{1}$
$A$ and $B$	$W_{2} = 2 n (B - A) + 2 Δ n t$	$h_{2} = 2 n t$
$T$ and $B$	$W_{3} = 2 A - 2 T + 2 n (B - A) + 2 Δ n t$	$h_{3} = 2 (L_{1} + n t)$
$T$ and $R$	$W_{4} = 2 R - 2 T + 2 n (B - A) + 2 Δ n t + 2 A - 2 B$	$h_{4} = 2 (L_{1} + L_{2} + n t)$
$A$ and $R$	$W_{5} = 2 R + 2 n (B - A) + 2 Δ n t - 2 B$	$h_{5} = 2 (L_{2} + n t)$
$B$ and $R$	$W_{6} = 2 R - 2 B$	$h_{6} = 2 L_{2}$

Table 3. Cavity length parameters
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Table 3. Cavity length parameters
t /mm L₁ /mm L₂ /mm L₁+t+L₂/mm
5 22.5 67.5 95
40 180 540 760

Table 4. Comparison of calculation results of OPL algorithm and 77-step phase shift algorithm

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Table 4. Comparison of calculation results of OPL algorithm and 77-step phase shift algorithm

Thickness of parallel flat panel /mm	Algorithm	Front surface shape $W_{1}$		Thickness change $W_{2}$		Optical uniformity $Δ n$
Thickness of parallel flat panel /mm	Algorithm	$P V / λ$	$R M S / λ$	$P V / λ$	$R M S / λ$	$P V$	$R M S$
40	OPL algorithm	0.0943	0.00980	0.276	0.0512	$0.330 \times 10^{- 6}$	$0.514 \times 10^{- 8}$
40	77-step phase shift algorithm	0.0916	0.00940	0.267	0.0499	$0.300 \times 10^{- 6}$	$0.487 \times 10^{- 8}$
5	OPL algorithm	0.414	0.0759	0.737	0.113	$1.47 \times 10^{- 5}$	$0.656 \times 10^{- 6}$
5	77-step phase shift algorithm	0.416	0.0764	0.733	0.111	$1.48 \times 10^{- 5}$	$0.671 \times 10^{- 6}$

Table 5. Comparison of running time between 77-step phase shift algorithm and OPL algorithm
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Table 5. Comparison of running time between 77-step phase shift algorithm and OPL algorithm
Thickness of parallel flat panel /mm Running time /s
77-step phase shift algorithm OPL algorithm
40 9.45 29.9
5 18.2 66.3

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Yu Qian, Renhui Guo, Jinwei Jiang, Liang Xue, Yang Liu, Jiangxin Li. Fast and High-Precision Measurement Method of Optical Parameters of Parallel Flat Plates[J]. Acta Optica Sinica, 2024, 44(3): 0312002

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Paper Information

Category: Instrumentation, Measurement and Metrology

Received: Aug. 24, 2023

Accepted: Nov. 19, 2023

Published Online: Mar. 4, 2024

The Author Email: Guo Renhui (grh@njust.edu.cn)

DOI:10.3788/AOS231468

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Frequency distribution for each group of interference signals in four-surface interference system

Table 1. Frequency distribution for each group of interference signals in four-surface interference system

Table 2. Optical path difference and interference cavity length of each group of fringes

Table 2. Optical path difference and interference cavity length of each group of fringes

Table 3. Cavity length parameters

Table 3. Cavity length parameters

Table 4. Comparison of calculation results of OPL algorithm and 77-step phase shift algorithm

Table 4. Comparison of calculation results of OPL algorithm and 77-step phase shift algorithm

Table 5. Comparison of running time between 77-step phase shift algorithm and OPL algorithm

Table 5. Comparison of running time between 77-step phase shift algorithm and OPL algorithm