Research on turbulent phase detection method based on phase generated carrier and unwrapping technology

Fig. 3. Comparison of the demodulated phase of the two algorithms with the simulated phase (left) and comparison of the absolute error between the two algorithms (right) under the conditions of strong turbulence (a)(b),medium turbulence (c)(d) and weak turbulence (e)(f)

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Fig. 4. Before (a)(b) and after (c)(d) dynamic tracking of modulation frequency, comparison of demodulation phase (left) and absolute difference (right) between the two algorithms

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Fig. 5. Schematic diagram of the fiber optic turbulence system measurement device

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Table 1. Comparison of mean error and variance between PGCU and DCM algorithms under different turbulence intensities

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Table 1. Comparison of mean error and variance between PGCU and DCM algorithms under different turbulence intensities

Parameter	Strong turbulence		Medium turbulence		Weak turbulence
	PGCU	DCM	PGCU	DCM	PGCU	DCM
Mean / $r a d$	$- 2.7984 \times 10^{- 8}$	$- 3.1650 \times 10^{- 1}$	$\begin{matrix} - 1.1103 \end{matrix} \times 10^{- 11}$	$4.71 \times 10^{- 2}$	$\begin{matrix} 2.7968 \times 10^{- 14} \end{matrix}$	$- 2.4017 \times 10^{- 3}$
Variance / $r a d^{2}$	$3.5831 \times 10^{- 6}$	$1.6021 \times 10^{- 3}$	$\begin{matrix} 2.5500 \times 10^{- 12} \end{matrix}$	$1.0231 \times 10^{- 4}$	$2.8263 \times 10^{- 18}$	$2.9646 \times 10^{- 7}$

Table 2. Comparison of absolute demodulation error of sine wave signals with different frequencies and amplitudes between PGCU and DCM algorithms

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Table 2. Comparison of absolute demodulation error of sine wave signals with different frequencies and amplitudes between PGCU and DCM algorithms

		Absolute error/rad
Amplitude/rad		100 Hz	200 Hz	300 Hz	400 Hz	500 Hz	600 Hz	700 Hz	800 Hz	900 Hz
4	PGCU	$4.77 \times 10^{- 4}$	0.25	0.84	3.89	3.55	3.97	4.47	4.38	5.24
4	DCM	0.0302	0.919	3.14	4.48	3.89	4.05	4.25	4.63	4.93
0.4	PGCU	$2.60 \times 10^{- 12}$	$5.29 \times 10^{- 6}$	$9.29 \times 10^{- 5}$	$2.82 \times 10^{- 3}$	$1.26 \times 10^{- 2}$	$2.57 \times 10^{- 2}$	$2.57 \times 10^{- 2}$	$2.21 \times 10^{- 2}$	$2.57 \times 10^{- 2}$
0.4	DCM	0.0289	0.029	0.0292	0.0346	0.00429	0.0337	0.0348	0.728	0.0375
0.04	PGCU	$2.29 \times 10^{- 12}$	$5.46 \times 10^{- 11}$	$5.63 \times 10^{- 9}$	$2.68 \times 10^{- 6}$	$1.33 \times 10^{- 5}$	$1.68 \times 10^{- 4}$	$1.68 \times 10^{- 4}$	$1.56 \times 10^{- 4}$	$1.68 \times 10^{- 4}$
0.04	DCM	0.01261	0.01263	0.01264	0.01274	0.01265	0.01277	0.01286	0.01287	0.01287

Table 3. Comparison of absolute demodulation errors between PGCU and DCM algorithms when modulation frequency increases in strong turbulence

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Table 3. Comparison of absolute demodulation errors between PGCU and DCM algorithms when modulation frequency increases in strong turbulence

Modulation frequency/Hz	Range of error/rad		Mean/rad		Variance/rad²
Modulation frequency/Hz	PGCU	DCM	PGCU	DCM	PGCU	DCM
2000	$- 0.020 ~ 0.017$	0.353 $~$ 0.532	$- 4.854 \times 10^{- 8}$	0.443	$2.927 \times 10^{- 6}$	0.001
3000	$- 3.540 \times 10^{- 3} ~ 3.547 \times 10^{- 3}$	0.438 $~$ 0.451	$- 8.832 \times 10^{- 9}$	0.445	$9.253 \times 10^{- 8}$	$7.299 \times 10^{- 7}$
4000	$- 7.362 \times 10^{- 4} ~ 6.921 \times 10^{- 4}$	0.442 $~$ 0.444	$1.713 \times 10^{- 10}$	0.443	$2.238 \times 10^{- 9}$	$2.970 \times 10^{- 8}$
5000	$- 1.890 \times 10^{- 4} ~ 1.904 \times 10^{- 4}$	0.442 $~$ 0.444	$- 9.260 \times 10^{- 11}$	0.443	$9.293 \times 10^{- 11}$	$2.658 \times 10^{- 8}$
6000	$- 3.317 \times 10^{- 6} ~ 3.791 \times 10^{- 6}$	0.442 $~$ 0.444	$1.996 \times 10^{- 15}$	0.443	$\begin{matrix} 2.816 \times 10^{- 14} \end{matrix}$	$2.649 \times 10^{- 8}$
7000	$- 1.238 \times 10^{- 6} ~ 1.316 \times 10^{- 6}$	0.442 $~$ 0.444	$9.288 \times 10^{- 14}$	0.443	$1.092 \times 10^{- 15}$	$2.648 \times 10^{- 8}$

Table 4. Comparison of demodulation phase from PGCU algorithm and measurement phase

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Table 4. Comparison of demodulation phase from PGCU algorithm and measurement phase

The actual phase difference/rad	6.76	7.90	8.85	10.51	10.53	12.19	12.39	12.56	13.70	15.30	17.53	18.34	19.66
Demodulation phase difference/rad	6.84	7.71	8.68	9.29	9.96	10.94	12.14	12.82	13.93	14.84	16.06	16.86	17.86
Absolute difference/rad	0.08	0.19	0.17	1.22	0.57	1.25	0.25	0.26	0.23	0.46	1.47	1.48	1.8
Relative difference value/%	1.18	2.41	1.92	11.61	5.41	10.25	2.02	2.07	1.68	3.00	8.39	8.07	9.18

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Jie TONG, Haiping MEI, Yichong REN, Zhiwei TAO. Research on turbulent phase detection method based on phase generated carrier and unwrapping technology[J]. Chinese Journal of Quantum Electronics, 2025, 42(2): 265

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Paper Information

Category:

Received: Feb. 3, 2023

Accepted: --

Published Online: Apr. 1, 2025

The Author Email: Haiping MEI (hpmei@aiofm.ac.cn)

DOI:10.3969/j.issn.1007-5461.2025.02.012

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laser devices and laser physics

Lasers and Laser Optics

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Instrumentation, Measurement and Metrology