Vortex Beam Phase Correction Based on Deep Phase Estimation Network

Juan Liu; Qian Du; Fangning Liu; Ke Wang; Jiayi Yu; Dongmei Wei

doi:10.3788/AOS221804

Journals >Acta Optica Sinica >Volume 43 >Issue 6 >Page 0601013 > Article

Acta Optica Sinica
Vol. 43, Issue 6, 0601013 (2023)

Vortex Beam Phase Correction Based on Deep Phase Estimation Network

Juan Liu, Qian Du, Fangning Liu, Ke Wang, Jiayi Yu^**, and Dongmei Wei^*

Author Affiliations

Shandong Provincial Engineering and Technical Center of Light Manipulations, School of Physics and Electronics, Shandong Normal University, Jinan 250358, Shandong, China

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DOI: 10.3788/AOS221804 Cite this Article Set citation alerts

Juan Liu, Qian Du, Fangning Liu, Ke Wang, Jiayi Yu, Dongmei Wei. Vortex Beam Phase Correction Based on Deep Phase Estimation Network[J]. Acta Optica Sinica, 2023, 43(6): 0601013 Copy Citation Text

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Fig. 1. Schematic diagram of beam transmission through multiple phase screens

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Fig. 2. Simulated phase diagram

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Fig. 3. Influence of atmospheric turbulence on beam transmission

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Fig. 4. Mode purity of LG (l=5) under different turbulence intensities

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Fig. 5. Block diagrams of phase compensation process. (a) Source pre-compensation; (b) direct compensation at receiving end

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Fig. 6. DPEnet network structure

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Fig. 7. Simulated and predicted phase screens with different turbulence intensities. (a)

1 \times 10^{- 14} m^{- 2 / 3}

; (b)

2.5 \times 10^{- 14} m^{- 2 / 3}

; (c)

5 \times 10^{- 14} m^{- 2 / 3}

; (d)

7.5 \times 10^{- 14} m^{- 2 / 3}

; (e)

1 \times 10^{- 13} m^{- 2 / 3}

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Fig. 8. Compensation results. (a) Intensity profile in source plane; uncompensated and compensated intensity profiles with turbulence intensities of (b)

1 \times 10^{- 14} m^{- 2 / 3}

, (c)

2.5 \times 10^{- 14} m^{- 2 / 3}

, (d)

5 \times 10^{- 14} m^{- 2 / 3}

, (e)

7.5 \times 10^{- 14} m^{- 2 / 3}

, and (f)

1 \times 10^{- 13} m^{- 2 / 3}

, respectively

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Fig. 9. Mode purity before and after compensation

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Fig. 10. Phases before and after compensation. (a) Phase in source plane; uncompensated and compensated phases with turbulence intensities of (b)

1 \times 10^{- 14} m^{- 2 / 3}

, (c)

2.5 \times 10^{- 14} m^{- 2 / 3}

, (d)

5 \times 10^{- 14} m^{- 2 / 3}

, (e)

7.5 \times 10^{- 14} m^{- 2 / 3}

, and (f)

1 \times 10^{- 13} m^{- 2 / 3}

, respectively

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Data set	$C_{n}^{2}$ / $(10^{- 14} m^{- 2 / 3})$ of LG	Sample size of LG	$C_{n}^{2}$ / $(10^{- 14} m^{- 2 / 3})$ of GB	Sample size of LG
Train set	$[1,10]$	30000	$[1,10]$	30000
Test set 1	$1$	1000	$1$	1000
Test set 2	$2.5$	1000	$2.5$	1000
Test set 3	$5$	1000	$5$	1000
Test set 4	$7.5$	1000	$7.5$	1000
Test set 5	$10$	1000	$10$	1000

Table 1. Database

$C_{n}^{2}$ / $(10^{- 14} m^{- 2 / 3})$	$1$	$2.5$	$5$	$7.5$	$10$
MSE of LG	0.07	0.15	0.25	0.38	0.53
MSE of GB	0.06	0.14	0.31	0.48	0.67

Table 2. Comparison of MSE between predicted phase screen and simulated phase screen

$C_{n}^{2}$ / $(10^{- 14} m^{- 2 / 3})$	MSE without compensation	MSE with compensation for LG	MSE with compensation for GB
$1$	246.8	50.3	48.4
$2.5$	527.8	68.1	64.1
$5$	931.3	98.9	109.0
$7.5$	1259.0	151.9	166.5
$10$	1557.9	228.9	243.1

Table 3. Comparison of MSE of intensity profiles before and after compensation

Juan Liu, Qian Du, Fangning Liu, Ke Wang, Jiayi Yu, Dongmei Wei. Vortex Beam Phase Correction Based on Deep Phase Estimation Network[J]. Acta Optica Sinica, 2023, 43(6): 0601013

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