Enhancing parameter design for full-aperture rapid planar polishing based on fuzzy optimization

Mingchen Cao; Mingchen Cao; Huiying Zhao; Ruiqing Xie; Ruiqing Xie; Ruiqing Xie; Shijie Zhao; Lingyu Zhao; Jinfeng Bai

doi:10.1364/AO.426283

Applied Optics
Vol. 60,
Issue 17,
pp. 5049-5055
(2021)
•https://doi.org/10.1364/AO.426283

Enhancing parameter design for full-aperture rapid planar polishing based on fuzzy optimization

Mingchen Cao, Huiying Zhao, Ruiqing Xie, Shijie Zhao, Lingyu Zhao, and Jinfeng Bai

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Mingchen Cao, Huiying Zhao, Ruiqing Xie, Shijie Zhao, Lingyu Zhao, and Jinfeng Bai, "Enhancing parameter design for full-aperture rapid planar polishing based on fuzzy optimization," Appl. Opt. 60, 5049-5055 (2021)

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Abstract

Full-aperture rapid planar polishing (RPP) has been widely used in optics manufacturing for high-power laser systems. A new, to the best of our knowledge, fuzzy optimization method was presented to assess the precision and productivity of RPP. Unlike the traditional method that can only set one objective, the proposed method can combine different objectives for RPP into one overall indicator. The material removal rate, material removal uniformity, and synthetical fuzzy indicator of RPP (SFIRPP) were selected as the objectives to prove the validity of fuzzy optimization. The rotational speed of optics, polishing pressure, and swing speed were set as the optimized parameters. The orthogonal design was introduced to simplify the operations of experiments. A semi-gamma distribution was used to fit the curve of SFIRPP. The experimental results indicated that the optimized parameters under SFIRPP obtained better manufacturing precision and productivity for flat optics simultaneously. The proposed fuzzy optimization provides the potential for enhancing the optimal parameters of RPP.

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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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	Factors
Level	Rotational Speed of Optics $W$ (rpm)	Polishing Pressure $P$ (kPa)	Swing Speed $V$ (mm/min)
#1	8 ( $W 1$ )	3.96 ( $P 1$ )	50 ( $V 1$ )
#2	16 ( $W 2$ )	7.06 ( $P 2$ )	100 ( $V 2$ )
#3	24 ( $W 3$ )	10.16 ( $P 3$ )	200 ( $V 3$ )

	Experimental Factors			Objective Functions and Satisfaction Degrees
No.	$W$	$P$	$V$	ERMS (nm)	$μ_{ERMS}^{N}$	MRR (µm/h)	$μ_{MRR}^{N}$	$f (x_{i, j})$
1	1	1	1	57.6	0.514	1.19	0.400	0.457
2	1	2	2	60.7	0.505	1.56	0.412	0.459
3	1	3	3	85.5	0.435	3.44	0.474	0.455
4	2	1	2	26.9	0.600	1.72	0.418	0.509
5	2	2	3	48.2	0.540	2.37	0.439	0.490
6	2	3	1	98.1	0.400	5.44	0.540	0.470
7	3	1	3	92.0	0.417	3.06	0.462	0.439
8	3	2	1	69.7	0.480	3.68	0.482	0.481
9	3	3	2	88.9	0.426	7.25	0.600	0.513

	Optimized Parameters for RPP
ERMS	$W$	$P$	$V$
${\bar{K}}_{E R M S 1}$ (nm)	67.9	$\underline{55.4}$	75.1
${\bar{K}}_{E R M S 2}$ (nm)	$\underline{54.3}$	59.5	$\underline{55.4}$
${\bar{K}}_{E R M S 3}$ (nm)	83.5	90.8	75.2
$R_{E R M S}$ (nm)	29.2	35.4	19.9
	Optimized Parameters for RPP
MRR	$W$	$P$	$V$
${\bar{K}}_{M R R 1}$ (µm/h)	2.06	1.99	3.43
${\bar{K}}_{M R R 2}$ (µm/h)	3.18	2.54	$\underline{3.51}$
${\bar{K}}_{M R R 3}$ (µm/h)	$\underline{4.66}$	$\underline{5.37}$	2.96
$R_{MRR}$ (µm/h)	2.60	3.38	0.55
	Optimized Parameters for RPP
SFIRPP	$W$	$P$	$V$
${\bar{K}}_{S F I R P P 1}$	0.457	0.468	0.469
${\bar{K}}_{S F I R P P 2}$	$\underline{0.489}$	0.476	$\underline{0.493}$
${\bar{K}}_{S F I R P P 3}$	0.478	$\underline{0.479}$	0.461
$R_{S F I R P P}$	0.033	0.011	0.032

	Method A-ERMS	Method B-MRR	Method C-SFIRPP
Optimal parameters set	W2P1V2	W3P3V2	W2P3V2
ERMS	$\underline{26.9}$	88.9	67.6
MRR	1.62	$\underline{7.25}$	5.91
SFIRPP	0.507	0.513	$\underline{0.521}$

	Factors
Level	Rotational Speed of Optics $W$ (rpm)	Polishing Pressure $P$ (kPa)	Swing Speed $V$ (mm/min)
#1	8 ( $W 1$ )	3.96 ( $P 1$ )	50 ( $V 1$ )
#2	16 ( $W 2$ )	7.06 ( $P 2$ )	100 ( $V 2$ )
#3	24 ( $W 3$ )	10.16 ( $P 3$ )	200 ( $V 3$ )

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Applied Optics