Selection Method of Risley Prisms Scanning Trajectory Based on Velocity Ratio

Linsen Duan; Hongbo Xie; Jun Ma; Lei Yang

doi:10.3788/AOS231834

Acta Optica Sinica, Volume. 44, Issue 7, 0722003(2024)

Selection Method of Risley Prisms Scanning Trajectory Based on Velocity Ratio

Linsen Duan¹, Hongbo Xie¹, Jun Ma^2、*, and Lei Yang¹

¹Key Laboratory of Optoelectronics Information Technology, School of Precision Instrument and Optoelectronics Engineering, Tianjin University, Tianjin 300072, China

²School of Armament Science and Technology, Xi an Technological University, Xi an 710021, Shaanxi , China

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Figures & Tables(14)

Fig. 1. Arrangement of two-element Risley prisms and establishment of coordinate system

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Fig. 2. Number of points of scanning trajectories. (a) $ω_{1} = 3 (°) / s$ , $ω_{2} = - 4.5 (°) / s$ ; (b) $ω_{1} = 3 (°) / s$ , $ω_{2} = 13.92 (°) / s$

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Fig. 3. Number of petals of scanning trajectories. (a) $ω_{1} = 3 (°) / s$ , $ω_{2} = - 4.5 (°) / s$ ; (b) $ω_{1} = 3 (°) / s$ , $ω_{2} = 13.92 (°) / s$

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Fig. 4. Scanning trajectories at different velocity ratios. (a) M=-6; (b) M=2.5; (c) M=-4.75; (d) M=1.3; (e) M=1.04; (f) M=-2.02

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Fig. 5. Scanning trajectories with the same number of petals. (a) M=1.7; (b) M=2.4; (c) M=4.5; (d) M=1.07; (e) M=1.14; (f) M=1.35

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Fig. 6. Points of scanning trajectories in the same shape. (a) M=0.25; (b) M=4; (c) M=-0.4; (d) M=-2.5

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Fig. 7. Scanning trajectories when $M_{1} = M_{2}$ . (a) $M_{1} = M_{2} = 1.35$ ; (b) $M_{1} = M_{2} = - 4.06$

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Fig. 8. Scanning trajectories when $M_{1} = - M_{2}$ . (a) $M_{1} = - M_{2} = 1.7$ ; (b) $M_{1} = - M_{2} = 3.24$

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Fig. 9. Random scanning trajectories when $|M_{1}| \neq |M_{2}|$ . (a) M₁=6.3, M₂=12.6; (b) M₁=-6.3, M₂=-24.9; (c) M₁=2.8, M₂=-5.7; (d) M₁=2.18, M₂=-5.36

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Fig. 10. Regular and symmetrical scanning trajectories when $|M_{1}| \neq |M_{2}|$ . (a) M₁=6.4, M₂=11.8; (b) M₁=5.04, M₂=9.08; (c) M₁=-3.5, M₂=-1.25; (d) M₁=-3.04, M₂=-7.08; (e) M₁=8.1, M₂=-6.1; (f) M₁=6.02, M₂=-4.02

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Table 1. Number of points and petals of scanning trajectories with $ω_{1} = 1 (°) / s$ at different velocity ratios

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Table 1. Number of points and petals of scanning trajectories with $ω_{1} = 1 (°) / s$ at different velocity ratios

Condition	$M$	$N_{g}$	$N_{h}$
$M$ is an integer	3	360	2
	-4	360	5
	5	360	4
	-6	360	7
$M$ is a decimal, $m \times 10^{n}$ is a multiple of 5	2.5	720	3
	-2.15	7200	63
	0.45	7200	11
	-3.35	7200	87
$M$ is a decimal, $m \times 10^{n}$ is a multiple of 25	1.25	1440	1
	-1.75	1440	11
	3.25	1440	9
	-4.75	1440	23
$M$ is a decimal, $m \times 10^{n}$ is the rest of the odd numbers	0.9	3600	1
	-1.03	36000	203
	1.3	3600	3
	-1.17	36000	217
$M$ is a decimal, $n = 2$ and $m \times 10^{n}$ is a multiple of 4	1.04	9000	1
	-2.24	9000	81
	2.48	9000	37
	-3.36	9000	109
$M$ is a decimal, $m \times 10^{n}$ is the rest of the even numbers	2.2	1800	6
	-1.06	18000	103
	2.8	1800	9
	-2.02	18000	151

Table 2. Number of points and petals of scanning trajectories with $ω_{1} = 1 (°) / s$ at different velocity ratios
View table
Table 2. Number of points and petals of scanning trajectories with $ω_{1} = 1 (°) / s$ at different velocity ratios
$M$ is positive $M$ is negative
$M$ $N_{g}$ $N_{h}$ $M$ $N_{g}$ $N_{h}$
1.7 3600 7 -4.7 3600 57
4.5 720 7 -27.5 720 57
1.14 18000 7 -1.28 9000 57
2.4 1800 7 -10.4 1800 57
1.07 36000 7 -0.14 18000 57
1.35 7200 7 -1.85 7200 57

Table 3. Number of points and petals of scanning trajectories with $ω_{1} = 1 (°) / s$ at different velocity ratios
View table
Table 3. Number of points and petals of scanning trajectories with $ω_{1} = 1 (°) / s$ at different velocity ratios
$M$ $N_{g}$ $N_{h}$ $M$ $N_{g}$ $N_{h}$
0.25 1440 3 4 360 3
-0.4 1800 7 -2.5 720 7

Table 4. Number of points and petals of scanning trajectories with $ω_{1} = 1 (°) / s$ at different velocity ratios

View table

Table 4. Number of points and petals of scanning trajectories with $ω_{1} = 1 (°) / s$ at different velocity ratios

Condition	$M_{1}$	$N_{g 1}$	$N_{h 1}$	$M_{2}$	$N_{g 2}$	$N_{h 2}$	$N_{g}$	$N_{h}$
$M_{1}$ and $M_{2}$ are both positive	6.4	1800	27	11.8	1800	54	1800	54
$M_{1}$ and $M_{2}$ are both positive	5.04	9000	101	9.08	9000	202	9000	202
$M_{1}$ and $M_{2}$ are both negative	-3.5	720	9	-1.25	1440	9	1440	18
$M_{1}$ and $M_{2}$ are both negative	-3.04	9000	101	-7.08	9000	202	9000	202
One of $M_{1}$ and $M_{2}$ is positive, and the other is negative	8.1	3600	71	-6.1	3600	71	3600	142
	6.02	18000	251	-4.02	251	18000	18000	502

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Linsen Duan, Hongbo Xie, Jun Ma, Lei Yang. Selection Method of Risley Prisms Scanning Trajectory Based on Velocity Ratio[J]. Acta Optica Sinica, 2024, 44(7): 0722003

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Paper Information

Category: Optical Design and Fabrication

Received: Nov. 24, 2023

Accepted: Jan. 22, 2024

Published Online: Apr. 18, 2024

The Author Email: Ma Jun (majun@xatu.edu.cn)

DOI:10.3788/AOS231834

CSTR:32393.14.AOS231834

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Number of points and petals of scanning trajectories with ω1=1 °/s at different velocity ratios

Table 1. Number of points and petals of scanning trajectories with ω1=1 °/s at different velocity ratios

Table 2. Number of points and petals of scanning trajectories with ω1=1 °/s at different velocity ratios

Table 2. Number of points and petals of scanning trajectories with ω1=1 °/s at different velocity ratios

Table 3. Number of points and petals of scanning trajectories with ω1=1 °/s at different velocity ratios

Table 3. Number of points and petals of scanning trajectories with ω1=1 °/s at different velocity ratios

Table 4. Number of points and petals of scanning trajectories with ω1=1 °/s at different velocity ratios

Table 4. Number of points and petals of scanning trajectories with ω1=1 °/s at different velocity ratios

Table 1. Number of points and petals of scanning trajectories with $ω_{1} = 1 (°) / s$ at different velocity ratios

Table 1. Number of points and petals of scanning trajectories with $ω_{1} = 1 (°) / s$ at different velocity ratios

Table 2. Number of points and petals of scanning trajectories with $ω_{1} = 1 (°) / s$ at different velocity ratios

Table 2. Number of points and petals of scanning trajectories with $ω_{1} = 1 (°) / s$ at different velocity ratios

Table 3. Number of points and petals of scanning trajectories with $ω_{1} = 1 (°) / s$ at different velocity ratios

Table 3. Number of points and petals of scanning trajectories with $ω_{1} = 1 (°) / s$ at different velocity ratios

Table 4. Number of points and petals of scanning trajectories with $ω_{1} = 1 (°) / s$ at different velocity ratios

Table 4. Number of points and petals of scanning trajectories with $ω_{1} = 1 (°) / s$ at different velocity ratios