Three-dimensional coherent ladar based on FMCW and its flight demonstration

Zhiyong Lu; Wei Lu; Yu Zhou; Jianfeng Sun; Qian Xu; Lijuan Wang

doi:10.3788/COL201917.092801

Journals >Chinese Optics Letters >Volume 17 >Issue 9 >Page 092801 > Article

Chinese Optics Letters
Vol. 17, Issue 9, 092801 (2019)

Three-dimensional coherent ladar based on FMCW and its flight demonstration

Zhiyong Lu^*, Wei Lu, Yu Zhou, Jianfeng Sun, Qian Xu, and Lijuan Wang

Author Affiliations

Key Laboratory of Space Laser Communication and Detection Technology, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China

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DOI: 10.3788/COL201917.092801 Cite this Article Set citation alerts

Zhiyong Lu, Wei Lu, Yu Zhou, Jianfeng Sun, Qian Xu, Lijuan Wang. Three-dimensional coherent ladar based on FMCW and its flight demonstration[J]. Chinese Optics Letters, 2019, 17(9): 092801 Copy Citation Text

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Abstract

A scanning three-dimensional coherent laser radar (ladar) based on the frequency modulated continuous wave (FMCW) is proposed and demonstrated, which can obtain many three-dimensional high-quality images. The system utilizes an electro-optic modulator and an optical filter to output a linear FMCW with a bandwidth of 2 GHz. The flexible and variable rotating double prism is used for beam scanning. The images of flight demonstration are formed by attitude compensation correction. The experiment result validates the performance of our system for airborne three-dimensional scanning imaging.

E_{o u t} = E_{0} \exp [j 2 π ω_{0} t + j φ (t) + j ϕ_{l}],

(1)

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V (t) = \frac{1}{2} V_{s} V_{f} \sin [2 π (ω_{f} + \frac{ω_{H} - ω_{L}}{2 τ} t) t],

(2)

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E_{o u t} = E_{0} \exp {j 2 π ω_{0} t + j β \sin [2 π (\frac{ω_{H} - ω_{L}}{2 τ} t + ω_{f}) t] + j ϕ_{l}},

(3)

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E_{o u t} = E_{0} J_{0} (β) \exp (j 2 π ω_{0} t + j ϕ_{l}) + E_{0} \sum_{m = 1}^{\infty} {(- 1)}^{m} J_{m} (β) \exp {j 2 π [ω_{0} - m (\frac{ω_{H} - ω_{L}}{2 τ} t + ω_{f})] t + j ϕ_{l}} + E_{0} \sum_{m = 1}^{\infty} J_{m} (β) \exp {j 2 π [ω_{0} + m (\frac{ω_{H} - ω_{L}}{2 τ} t + ω_{f})] t + j ϕ_{l}},

(4)

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E_{o u t} = E_{0} J_{2} (β) \exp {j 2 π [ω_{0} + 2 (\frac{ω_{H} - ω_{L}}{2 τ} t + ω_{f})] t + j ϕ_{l}} .

(5)

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i (t) \approx E_{L O} E_{S} \exp {j {2 π [(ω_{0} + 2 ω_{f}) \cdot (- Δ t) - \frac{2 M ω_{H} - 2 M ω_{L}}{τ} Δ t \cdot t]}},

(6)

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f_{u p} = [(ω_{0} + 2 ω_{f}) (\frac{2 υ}{c}) - \frac{B}{t} \frac{2 z}{c}],

(7)

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f_{d o w n} = [(ω_{0} + 2 ω_{f}) (\frac{2 υ}{c}) + \frac{B}{t} \frac{2 z}{c}] .

(8)

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z = \frac{c t}{2 B} \frac{f_{d o w n} - f_{u p}}{2} .

(9)

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[\begin{matrix} x_{S L} \\ y_{S L} \\ z_{S L} \end{matrix}] = [\begin{matrix} 0 \\ 0 \\ z \end{matrix}] .

(10)

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[\begin{matrix} x_{L H} \\ y_{L H} \\ z_{L H} \end{matrix}] = [\begin{matrix} z \sin φ \sin θ \cos H \cos P + z \sin φ \cos θ (\cos H \sin P \sin R + \sin H \cos R) + z \cos φ (- \cos H \sin P \cos R + \sin H \sin R) \\ - z \sin φ \sin θ \sin H \cos P + z \sin φ \cos θ (\cos H \cos R - \sin H \sin P \sin R) + z \cos φ (\sin H \sin P \cos R + \cos H \sin R) \\ z \sin φ \sin θ \sin P - z \sin φ \cos θ \cos P \sin R + z \cos φ \cos P \cos R \end{matrix}] .

(11)

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[\begin{matrix} x_{48} \\ y_{48} \\ z_{48} \end{matrix}] = [\begin{matrix} - x_{L H} \cos L \sin M - y_{L H} \sin L - z_{L H} \cos L \cos M + (N + H) \cos M \cos L \\ - x_{L H} \sin L \sin M + y_{L H} \cos L - z_{L H} \sin L \cos M + (N + H) \cos M \sin L \\ x_{L H} \cos M - z_{L H} \sin M + [N (1 - e^{2}) + H] \sin M \end{matrix}] .

(12)

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Zhiyong Lu, Wei Lu, Yu Zhou, Jianfeng Sun, Qian Xu, Lijuan Wang. Three-dimensional coherent ladar based on FMCW and its flight demonstration[J]. Chinese Optics Letters, 2019, 17(9): 092801

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