Phase Recovery Algorithm Based on Pupil Diversity

Qian Li; Zhen Wu; Jiesu Xu; Honglan Li

doi:10.3788/AOS201939.0626001

Journals >Acta Optica Sinica >Volume 39 >Issue 6 >Page 0626001 > Article

Acta Optica Sinica
Vol. 39, Issue 6, 0626001 (2019)

Phase Recovery Algorithm Based on Pupil Diversity

Qian Li^1、2、3, Zhen Wu^1、2、*, Jiesu Xu^1、2、3, and Honglan Li^1、2、3

Author Affiliations

¹ National Astronomical Observatories, Nanjing Institute of Astronomical Optics & Technology, Chinese Academy of Sciences, Nanjing, Jiangsu 210042, China;

² Key Laboratory of Astronomical Optics & Technology, Chinese Academy of Sciences, Nanjing, Jiangsu 210042, China;

³ University of Chinese Academy of Sciences, Beijing 100049, China

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DOI: 10.3788/AOS201939.0626001 Cite this Article Set citation alerts

Qian Li, Zhen Wu, Jiesu Xu, Honglan Li. Phase Recovery Algorithm Based on Pupil Diversity[J]. Acta Optica Sinica, 2019, 39(6): 0626001 Copy Citation Text

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Principle diagram of NRM-GS algorithm. (a) Original wavefront; (b) I (ξ,η); (c) wavefront after mask; (d) INRM(ξ,η); (e) fMT of INRM(ξ,η); (f) principle of NRM-GS algorithm

Fig. 1. Principle diagram of NRM-GS algorithm. (a) Original wavefront; (b) I (ξ,η); (c) wavefront after mask; (d) INRM(ξ,η); (e) fMT of INRM(ξ,η); (f) principle of NRM-GS algorithm

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Fig. 2. Flow chart of data processing based on NRM-GS algorithm

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Fig. 3. Iteration processes for NRM-GS algorithm with and without phase constraints or ordinary GS algorithm. (a) S curves; (b) ERMS curves

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Fig. 4. Recovery of astigmatism aberration. (a) Original wavefront; (d) wavefront after mask; (b)(e) recovered wavefronts by NRM-GS algorithm and GS algorithm; (c)(f) recovered residual wavefronts by NRM-GS algorithm and GS algorithm

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Fig. 5. Iteration processes for NRM-GS algorithms with and without phase constraints or ordinary GS algorithm. (a) S curves; (b) ERMS curves

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Fig. 6. Recovery of randomly combined wavefront (first 15 terms). (a) Original wavefront; (d) wavefront after mask; (b)(e) recovered wavefronts by NRM-GS algorithm and GS algorithm; (c)(f) recovered residual wavefronts by NRM-GS algorithm and GS algorithm

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Fig. 7. Comparison of Zernike polynomial coefficients (first 15 items) of original wavefront with those by NRM-GS algorithm and GS algorithm

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Fig. 8. Recovery results of co-phase errors on synthetic aperture telescope. (a) Original wavefront; (b) recovered wavefront by NRM-GS algorithm; (c) recovered residual wavefront by NRM-GS algorithm; (d) wavefront after mask; (e) recovered wavefront by GS algorithm; (f) recovered residual wavefront by GS algorithm

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Fig. 9. Iteration processes for NRM-GS algorithms with and without phase constraints or ordinary GS algorithm when co-phase errors on synthetic aperture telescope are detected. (a) S curves; (b) ERMS curves of residual wavefronts on three sub-telescopes

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Sub-aperture	Original phase	Initial phase		Initial phase error
Sub-aperture	Original phase	NRM-GS piston component	GS random initial phase	NRM-GS piston component	GS random initial phase
1	0.1789λ	0.1787λ		0.1261λ		-0.0002λ	0.0526λ
2	0.0439λ	0.0437λ		0.1197λ		-0.0002λ	-0.0757λ
3	0.2589λ	0.2587λ		0.1248λ		-0.0002λ	-0.1341λ
4	-0.0870λ	-0.0872λ		0.1265λ		-0.0002λ	-0.2135λ
5	-0.3021λ	-0.3023λ		0.0278λ		-0.0002λ	-0.3229λ

Table 1. Original wavefront phases, initial phases of NRM-GS and ordinary GS algorithms and their errors for six-sub-aperture centers

Single order Zernike term	NRM-GS algorithm		GS algorithm
Single order Zernike term	Residual wavefront E_RMS	Number of iteration	Residual wavefront E_RMS	Number of iteration
3	0.0040λ		91		0.1523λ	105
5	0.0031λ		112		0.1167λ	191
9	0.0145λ		125		0.1096λ	212
11	0.0056λ		97		0.1244λ	129
12	0.0080λ		109		0.1241λ	136
13	0.0123λ		103		0.1248λ	117
Average	0.0079λ				0.1253λ

Table 2. Six groups of recovery results of single order Zernike polynomial by NRM-GS algorithm and GS algorithm

Sub-aperture	Original phase	Initial phase		Initial phase error
Sub-aperture	Original phase	NRM-GS piston component	GS random initial phase	NRM-GS piston component	GS random initial phase
1	-0.164λ	-0.1521λ		0.1051λ		-0.0119λ	-0.2791λ
2	-0.1284λ	-0.1086λ		0.091λ		-0.0198λ	-0.2194λ
3	0.0907λ	0.0861λ		0.1259λ		0.0046λ	-0.0352λ
4	0.1995λ	0.1924λ		0.1245λ		0.0071λ	0.075λ
5	-0.1301λ	-0.1212λ		0.0051λ		-0.0089λ	-0.1361λ
6	0.0887λ	0.1027λ		0.1244λ		-0.014λ	-0.0357λ

Table 3. Original wavefront phases, initial phases and their errors for six-sub-aperture centers

Number of terms of Zernike polynominals	RMS of original wavefront ϕ₀	NRM-GS		GS
Number of terms of Zernike polynominals	RMS of original wavefront ϕ₀	Residual wavefront E_RMS	Number of iterations	Residual wavefront E_RMS		Number of iterations
1(first 15 terms)	0.1156λ	0.0088λ			95		0.1241λ	98
2(first 20 terms)	0.1919λ	0.0140λ			112		0.1027λ	127
3(first 25 terms)	0.1048λ	0.0240λ			108		0.1556λ	145
4(first 30 terms)	0.1301λ	0.0099λ			99		0.1342λ	165
5(first 37 terms)	0.0800λ	0.0141λ			110		0.1258λ	128

Table 4. Five groups of recovery results of randomly combined wavefronts by NRM-GS algorithm and GS algorithm

Sub-telescope	Piston error	Tip error	Tilt error
123	0.0000λ0.2000λ0.0500λ	0.2000λ0.1254λ0.0752λ	0.0752λ0.0627λ0.1254λ

Table 5. Added co-phase errors on each sub-telescope

Sub-aperture	Original phase	Initial phase		Initial phase error
Sub-aperture	Original phase	NRM-GS piston component	GS random initial phase	NRM-GS piston component		GS random initial phase
1	0.0000λ	0.0000λ			0.0235λ		0.0000λ	-0.0235λ
2	0.0112λ	0.0011λ			0.0453λ		0.0101λ	-0.0341λ
3	0.3734λ	0.3707λ			0.1305λ		0.0027λ	0.2132λ
4	0.0384λ	0.0289λ			0.0973λ		0.0095λ	-0.0589λ
5	0.0461λ	0.0378λ			0.0542λ		0.0083λ	-0.0081λ

Table 6. Original wavefront phases, initial phases and their errors

Co-phase error	Maximum E_RMS		Minimum E_RMS		Average E_RMS			Average number of iteration
Co-phase error	NRM-GS	GS	NRM-GS	GS	NRM-GS		GS	NRM-GS	GS
Piston(10 groups)	0.0078λ					0.0741λ				0.0045λ	0.0424λ	0.0056λ	0.0533λ	37	43
Tip/tilt(10 groups)	0.0100λ					0.1327λ				0.0037λ	0.1240λ	0.0071λ	0.1267λ	38	49
Piston, tip/tilt (10 groups)	0.0064λ					0.0860λ				0.0022λ	0.0423λ	0.0045λ	0.0651λ	40	47

Table 7. Recovery results of multigroup co-phase errors

Qian Li, Zhen Wu, Jiesu Xu, Honglan Li. Phase Recovery Algorithm Based on Pupil Diversity[J]. Acta Optica Sinica, 2019, 39(6): 0626001

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