Off-Axis Three-Mirror Anastigmatic System Alignment and Application Based on Principal Component Analysis

Jikai Guo; Zhile Wang; Min Lu

doi:10.3788/AOS201939.0322002

Journals >Acta Optica Sinica >Volume 39 >Issue 3 >Page 0322002 > Article

Acta Optica Sinica
Vol. 39, Issue 3, 0322002 (2019)

Off-Axis Three-Mirror Anastigmatic System Alignment and Application Based on Principal Component Analysis

Jikai Guo^*, Zhile Wang, and Min Lu

Author Affiliations

Research Center for Space Optical Engineering, School of Astronautics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China

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DOI: 10.3788/AOS201939.0322002 Cite this Article Set citation alerts

Jikai Guo, Zhile Wang, Min Lu. Off-Axis Three-Mirror Anastigmatic System Alignment and Application Based on Principal Component Analysis[J]. Acta Optica Sinica, 2019, 39(3): 0322002 Copy Citation Text

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Fig. 1. Schematic of off-axis three-mirror anastigmatic system

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Fig. 2. Flow chart of PCA

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Fig. 3. Simulated wave-front maps. (a) Before alignment; (b) afer alignment

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Zernike polynomial	D_x₂	D_y₂	T_x₂	T_y₂	D_x₃	D_y₃	T_x₃	T_y₃	D₂	D_f	D₃
Z₅₀	0.31486	0.46487	1.80531	-0.60036	0.74743	0.95358	-4.82906	3.94319	-0.54295	0.25935	-0.31383
Z₆₀	-0.52872	-0.34597	-0.24714	1.77598	-1.02581	0.37120	-3.27161	-4.73697	-1.07602	0.67464	-0.70732
Z₇₀	-0.06317	-0.03223	-0.05213	0.21715	-0.01349	-0.01396	0.01612	0.03531	-0.05357	0.03416	-0.03388
Z₈₀	-0.00977	0.01583	0.02058	0.03139	-0.00523	0.00794	-0.05523	-0.00700	0.04632	-0.00755	0.00681
Z₉₀	0.00049	0.00659	0.02540	0.00026	-0.00011	0.00351	-0.00614	-0.00066	-0.00284	-0.00028	0.00011
Z₅₁	0	-0.34399	-0.03201	0	0	0.86515	-6.31798	0	-1.79175	1.13489	-1.20276
Z₆₁	-0.67445	0	0	1.99736	-1.60045	0	0	-7.94097	0	0	0
Z₇₁	-0.05868	0	0	0.20938	-0.01260	0	0	0.03345	0	0	0
Z₈₁	0	0.02309	-0.03427	0	0	0.01195	-0.06807	0	0.08036	-0.03505	0.03458
Z₉₁	0	-0.00044	-0.00728	0	0	0.00001	-0.00515	0	0.00356	-0.00023	0.00023
Z₅₂	-0.31022	-0.79446	-2.03727	0.85579	-0.63397	0.72350	-6.01166	-3.44206	-1.98652	1.25104	-1.31498
Z₆₂	-0.29098	0.65879	2.07534	0.50309	-1.59013	0.08424	1.11993	-8.18076	1.17988	-0.72176	0.73270
Z₇₂	-0.03368	0.01991	0.03604	0.15435	-0.00670	0.00703	-0.00786	0.04266	0.02071	-0.01622	0.01609
Z₈₂	0.01047	0.03470	0.04195	-0.02962	0.00300	0.02013	-0.06012	0.00311	0.04869	-0.03631	0.03561
Z₉₂	-0.00052	0.00216	0.01044	0.00283	-0.00025	0.00161	-0.00217	-0.00041	-0.00505	0.00053	-0.00062

Table 1. Sensitivity matrix A

Principal component	Characteristic value	Contribution rate	Cumulative contribution rate
F₁	5.47037154901298	0.364691436600865	0.364691436600865
F₂	3.84204230941265	0.256136153960843	0.620827590561709
F₃	3.01726718697149	0.201151145798100	0.821978736359808
F₄	1.97697745862482	0.131798497241654	0.953777233601463

Table 2. Characteristic value, contribution rate, and cumulative contribution rate corresponding to principal component with cumulative contribution rate greater than 95%

Adjustment sorting	T_x₃	T_y₃	T_x₂	T_y₂	D₂	D_x₃	D_x₂	D_y₃	D_f	D₃	D_y₂
Corresponding score	8.9529	8.6439	8.5334	8.1599	4.2834	3.6721	3.3978	3.2574	3.1500	3.1127	2.3299

Table 3. Adjustment sorting and corresponding score

Mirror	D	D_x	D_y	T_x	T_y
Second mirror	0.0500	0.0200	-0.0500	0.0700	0.0900
FM	0.0300
Third mirror	-0.0400	0.0600	0.0800	-0.0600	0.1000

Table 4. Given misalignment

Mirror	D	D_x	D_y	T_x	T_y
Second mirror	0.0500	0.0200	-0.0500	0.0700	0.0900
FM	0.0300
Third mirror	-0.0400	0.0600	0.0800	-0.0600	0.1000

Table 5. Calculated misalignment based on inverse optimization method

Mirror	D	D_x	D_y	T_x	T_y
Second mirror	0.0046	-0.0111	-0.0211	0.0050	-0.0002
FM	-0.2000
Third mirror	-0.2000	0.0341	-0.0041	0.0140	-0.0060

Table 6. Difference between given misalignment and calculated misalignment

Data number	Misalignment /mm	D_x₂	D_y₂	T_x₂	T_y₂	D_x₃	D_y₃	T_x₃
1	Set value		-0.0500	0.0700	0.0900		0.0800	-0.0600
	Solution 1			0.0622	-0.0742			0.0900
	Solution 2		-0.0452		0.0900		0.5000
	Solution 3		-0.0497	0.0726			0.0700	-0.0628
2	Set value	0.0200	-0.0500	0.0700	0.0900	0.0600	0.0800	-0.0600
	Solution 1	0.0201		0.0596	0.0900	0.0609	-0.0517	-0.0870
	Solution 2			0.0613	0.0834	0.0470		-0.0761
	Solution 3			0.0669	0.0807			-0.0718
Data number	Misalignment /mm	T_y₃	D₂	D_f	D₃	Wave-front of three fields of view
1	Set value	0.1000				0.0965,0.0704,0.0484
	Solution 1	0.1000				0.0990,0.0762,0.0489
	Solution 2	0.1000				0.1451,0.0574,0.0870
	Solution 3					0.2321,0.2606,0.3305
2	Set value	0.1000	0.0500	0.03	-0.04	0.0965,0.0704,0.0484
	Solution 1	0.0998	0.0276			0.0983,0.0589,0.0491
	Solution 2	0.1027	0.0178			0.1003,0.0518,0.0555
	Solution 3	0.1115				0.3767,0.5009,0.4932

Table 7. Calculation results of different alignment schemes

Jikai Guo, Zhile Wang, Min Lu. Off-Axis Three-Mirror Anastigmatic System Alignment and Application Based on Principal Component Analysis[J]. Acta Optica Sinica, 2019, 39(3): 0322002

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