Highly efficient method for cutting position selection of an x-ray mono-capillary lens based on an improved SCA-CSA algorithm

Yi Huang; Zhaofei Zhang; Chuanlu Deng; Zhenyi Chen; Hai Yang; Chengyong Hu; Xiaobei Zhang; Tingyun Wang

doi:10.1364/AO.488807

Applied Optics
Vol. 62,
Issue 13,
pp. 3275-3283
(2023)
•https://doi.org/10.1364/AO.488807

Highly efficient method for cutting position selection of an x-ray mono-capillary lens based on an improved SCA-CSA algorithm

Yi Huang, Zhaofei Zhang, Chuanlu Deng, Zhenyi Chen, Hai Yang, Chengyong Hu, Xiaobei Zhang, and Tingyun Wang

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Yi Huang, Zhaofei Zhang, Chuanlu Deng, Zhenyi Chen, Hai Yang, Chengyong Hu, Xiaobei Zhang, and Tingyun Wang, "Highly efficient method for cutting position selection of an x-ray mono-capillary lens based on an improved SCA-CSA algorithm," Appl. Opt. 62, 3275-3283 (2023)

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Abstract

In order to efficiently select the optimal cutting position of x-ray mono-capillary lenses, an improved sine cosine algorithm-crow search algorithm (SCA-CSA) algorithm is proposed, which combines the sine cosine algorithm with the crow search algorithm, with further enhancements. The fabricated capillary profile is measured using an optical profiler; then the surface figure error for interest regions of the mono-capillary can be evaluated using the improved SCA-CSA algorithm. The experimental results indicate that the surface figure error in the final capillary cut region is about 0.138 µm, and the runtime is 2.284 s. When compared with the traditional metaheuristic algorithm, the particle swarm optimization algorithm, the improved SCA-CSA algorithm, enhances the surface figure error metric by two orders of magnitude. Furthermore, the standard deviation index of the surface figure error metric for 30 runs also improves by more than 10 orders of magnitude, demonstrating the superior performance and robustness of the algorithm. The proposed method provides significant support for the development of precise cuttings of mono-capillaries.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Number	$x_{P}$ (mm)	$x_{Q}$ (mm)	$E_{s}$ ( $\times 10^{- 3} m m$ )	a (mm)	b (mm)	Relative Error (%)
1	100	120	0.138	201.031	0.29947	0.08523
2	105	125	0.617	207.491	0.29554	0.39190
3	109	129	0.881	209.829	0.29389	3.09011
4	110	125	0.654	210.932	0.29318	0.42774
5	99	119	0.372	200.273	0.29999	0.13253
6	100	125	0.588	205.710	0.30056	2.54730

	PSO		SCA		CSA		SCA-CSA		Improved SCA-CSA
Sample Number	AVG	STD	AVG	STD ( $\times 10^{- 2}$ )	AVG	STD ( $\times 10^{- 7}$ )	AVG	STD ( $\times 10^{- 7}$ )	AVG	STD ( $\times 10^{- 7}$ )
1	81.74	90.19	0.13	1.22	0.11	27.34	0.11	4.85	0.11	1.36
2	91.26	117.78	0.21	5.11	0.14	13.40	0.14	2.29	0.14	$2.\bf 51 \times 1 0^{- 9}$
3	83.67	87.16	0.31	1.65	0.29	7.46	0.29	0.04	0.29	$5.\bf 12 \times 1 0^{- 2}$
4	108.33	81.38	0.20	1.11	0.19	38.62	0.19	361.83	0.19	133.31
sum	364.99	376.51	0.85	9.08	0.73	86.82	0.73	369.01	0.73	134.72

	PSO		SCA		CSA		SCA-CSA		Improved SCA-CSA
Sample Number	AVG	STD	AVG	STD	AVG	STD	AVG	STD	AVG	STD
1	2.45	0.28	4.43	0.20	2.02	0.17	2.36	0.18	2.21	0.11
2	3.34	0.36	4.61	0.20	2.24	0.17	2.58	0.10	2.28	0.10
3	2.38	0.23	4.32	0.21	2.20	0.08	2.39	0.05	2.11	0.04
4	2.49	0.23	4.38	0.29	2.04	0.15	2.40	0.13	2.08	0.13
sum	10.66	1.10	17.74	0.90	8.50	0.57	9.73	0.46	8.68	0.38

Number	$x_{P}$ (mm)	$x_{Q}$ (mm)	$E_{s}$ ( $\times 10^{- 3} m m$ )	a (mm)	b (mm)	Relative Error (%)
1	100	120	0.138	201.031	0.29947	0.08523
2	105	125	0.617	207.491	0.29554	0.39190
3	109	129	0.881	209.829	0.29389	3.09011
4	110	125	0.654	210.932	0.29318	0.42774
5	99	119	0.372	200.273	0.29999	0.13253
6	100	125	0.588	205.710	0.30056	2.54730

	PSO		SCA		CSA		SCA-CSA		Improved SCA-CSA
Sample Number	AVG	STD	AVG	STD ( $\times 10^{- 2}$ )	AVG	STD ( $\times 10^{- 7}$ )	AVG	STD ( $\times 10^{- 7}$ )	AVG	STD ( $\times 10^{- 7}$ )
1	81.74	90.19	0.13	1.22	0.11	27.34	0.11	4.85	0.11	1.36
2	91.26	117.78	0.21	5.11	0.14	13.40	0.14	2.29	0.14	$2.\bf 51 \times 1 0^{- 9}$
3	83.67	87.16	0.31	1.65	0.29	7.46	0.29	0.04	0.29	$5.\bf 12 \times 1 0^{- 2}$
4	108.33	81.38	0.20	1.11	0.19	38.62	0.19	361.83	0.19	133.31
sum	364.99	376.51	0.85	9.08	0.73	86.82	0.73	369.01	0.73	134.72

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Applied Optics