Inverse solutions for a Risley prism scanner with iterative refinement by a forward solution

Anhu Li; Xinjian Gao; Wansong Sun; Wanli Yi; Yongming Bian; Hongzhan Liu; Liren Liu

doi:10.1364/AO.54.009981

Applied Optics
Vol. 54,
Issue 33,
pp. 9981-9989
(2015)
•https://doi.org/10.1364/AO.54.009981

Inverse solutions for a Risley prism scanner with iterative refinement by a forward solution

Anhu Li, Xinjian Gao, Wansong Sun, Wanli Yi, Yongming Bian, Hongzhan Liu, and Liren Liu

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Anhu Li, Xinjian Gao, Wansong Sun, Wanli Yi, Yongming Bian, Hongzhan Liu, and Liren Liu, "Inverse solutions for a Risley prism scanner with iterative refinement by a forward solution," Appl. Opt. 54, 9981-9989 (2015)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Related Topics
Table of Contents Category
- Instrumentation, Measurement, and Metrology
Optics & Photonics Topics
?

The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: August 7, 2015
- Revised Manuscript: October 26, 2015
- Manuscript Accepted: October 27, 2015
- Published: November 19, 2015

Abstract

Risley prism scanners are increasingly used for laser beam steering due to their wide angular scanning range and high resolution. However, the inverse problem, which focuses on obtaining the required prisms’ orientations for a given target position, has not been perfectly solved so far. The existing inverse solutions are not accurate or efficient enough for high-accuracy and real-time tracking. An iterative method that combines an approximate inverse solution with an iterative refinement by the forward solution is set forth in this paper. Two case studies indicate that the rotation motions of Risley prism pairs controlled by iterative solutions can slew the beam to create the desired tracking pattern quickly and accurately. Based on this method, a Risley prism scanner developed as a standard trajectory generator is implemented for the error measurement of a robotic manipulator in our experiments. The simulation and experimental results show that the inverse solution for one target point can be obtained within nine iterations for a prescribed tracking error threshold.

Full Article | PDF Article

More Like This

Forward and inverse solutions for three-element Risley prism beam scanners

Anhu Li, Xingsheng Liu, and Wansong Sun
Opt. Express 25(7) 7677-7688 (2017)

Laser coarse-fine coupling tracking by cascaded rotation Risley-prism pairs

Anhu Li, Wansong Sun, Xingsheng Liu, and Wei Gong
Appl. Opt. 57(14) 3873-3880 (2018)

Tilting double-prism scanner driven by cam-based mechanism

Anhu Li, Wanli Yi, Wansong Sun, and Liren Liu
Appl. Opt. 54(18) 5788-5796 (2015)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (7)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (5)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (24)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Iterations	Exiting Points		Scanning Points		Deviations	Rotation Angles
Iter	$x_{r n} (mm)$	$y_{r n} (mm)$	$x_{r p} (mm)$	$y_{r p} (mm)$	$Δ (mm)$	$θ_{r 1} (°)$	$θ_{r 2} (°)$
1	6.830350	2.312234	6.830350	22.312234	7.211110	195.936655	344.383475
2	5.609818	4.516284	−1.220532	22.204051	2.519432	216.204930	366.329188
3	5.861903	4.149227	0.252086	19.632943	0.445284	212.988204	367.110193
4	5.807144	4.231077	−0.054760	20.081850	0.098479	213.715934	367.148334
5	5.818955	4.213569	0.011812	19.982491	0.021120	213.560311	367.145861
6	5.816402	4.217359	−0.002553	20.003790	0.004570	213.594012	367.146756
7	5.816954	4.216540	0.000552	19.999181	0.000987	213.586734	367.146578
8	5.816835	4.216717	−0.000119	20.000177	0.000213	213.588307	367.146617
9	5.816861	4.216679	0.000026	19.999962	0.000046	213.587967	367.146608

No.	Target Points		First Group of Solutions
No.	$X_{p} (mm)$	$Y_{P} (mm)$	Iter	$x_{p} (mm)$	$y_{p} (mm)$	$Δ (mm)$	$θ_{1} (°)$	$θ_{2} (°)$
1	2.25853	7.27660	9	2.25858	7.27657	0.00006	233.75	409.95
2	−0.15719	9.52251	9	−0.15724	9.52255	0.00006	233.61	404.73
3	−3.74620	10.79714	7	−3.74622	10.79715	0.00002	243.73	411.16
4	−8.08428	10.60293	9	−8.08425	10.60293	0.00003	257.24	421.38
5	−12.56009	8.62808	9	−12.56004	8.62808	0.00004	272.51	433.53
6	−16.45399	4.81079	9	−16.45395	4.81080	0.00005	288.84	446.84
7	−19.03724	−0.62866	9	−19.03720	−0.62863	0.00005	305.87	460.90
8	−19.67871	−7.19379	9	−19.67868	−7.19376	0.00005	323.38	475.48

Devices	Parameters
Rotation double prisms	$α = 10 °$
	$n = 1.517$
	$D_{p} = 80 mm$
	$d_{0} = 5 mm$
	$D_{1} = 100 mm$
Two-dimensional slipway	Effective travel of $x$ axis: 300 mm
	Effective travel of $y$ axis: 400 mm
	Precision: superior to 0.02 mm
Collaborative controller	LPC1114
Laser source	Wavelength: 650 nm
	Power: $\geq 2.5 mW$
	Variable focus
Detector	Position precision: superior to 0.01 mm
	Range: 3 mm
	$D_{2} = 400 mm$

No.	A		B		C
No.	$X_{p}$	$Y_{p}$	$θ_{1}$	$θ_{2}$	M	N
1	40.000	0.000	127.91	250.38	0.00007	0.308
2	39.203	11.920	145.33	266.22	0.00007	0.300
3	36.842	23.365	162.27	278.80	0.00005	0.293
4	33.013	33.879	177.87	288.18	0.00003	0.311
5	27.868	43.041	191.85	295.20	0.00003	0.306
6	21.612	50.488	204.25	300.91	0.00007	0.309
7	14.494	55.922	215.13	306.31	0.00003	0.307
8	6.799	59.127	224.54	312.25	0.00004	0.308
9	−1.168	59.974	232.61	319.37	0.00004	0.300
10	−9.088	58.431	239.62	328.10	0.00004	0.309
11	−16.646	54.558	246.04	338.65	0.00003	0.310
12	−23.540	48.510	252.56	351.09	0.00004	0.352
13	−29.496	40.528	260.03	365.42	0.00006	0.343
14	−34.276	30.930	269.35	381.60	0.00004	0.045
15	−37.689	20.099	281.30	399.34	0.00006	0.043
16	−39.600	8.467	296.09	417.77	0.00007	0.043
17	−39.932	−3.502	312.96	435.30	0.00007	0.040
18	−38.672	−15.332	330.38	450.25	0.00006	0.036
19	−35.870	−26.551	346.99	461.84	0.00004	0.046
20	−31.639	−36.711	362.12	470.43	0.00002	0.045
21	−26.146	−45.408	375.64	476.95	0.00003	0.043
22	−19.610	−52.295	387.58	482.48	0.00009	0.030
23	−12.293	−57.096	398.02	487.96	0.00004	0.039
24	−4.486	−59.621	407.03	494.18	0.00004	0.256
25	3.500	−59.770	414.75	501.74	0.00004	0.242
26	11.346	−57.535	421.53	510.99	0.00004	0.284
27	18.741	−53.007	427.90	522.08	0.00002	0.287
28	25.388	−46.366	434.60	535.08	0.00007	0.304
29	31.023	−37.876	442.52	549.96	0.00009	0.298
30	35.421	−27.876	452.54	566.65	0.00004	0.298
31	38.407	−16.765	465.34	584.71	0.00006	0.288
32	39.862	−4.985	480.87	603.07	0.00007	0.286

Iterations	Exiting Points		Scanning Points		Deviations	Rotation Angles
Iter	$x_{r n} (mm)$	$y_{r n} (mm)$	$x_{r p} (mm)$	$y_{r p} (mm)$	$Δ (mm)$	$θ_{r 1} (°)$	$θ_{r 2} (°)$
1	6.830350	2.312234	6.830350	22.312234	7.211110	195.936655	344.383475
2	5.609818	4.516284	−1.220532	22.204051	2.519432	216.204930	366.329188
3	5.861903	4.149227	0.252086	19.632943	0.445284	212.988204	367.110193
4	5.807144	4.231077	−0.054760	20.081850	0.098479	213.715934	367.148334
5	5.818955	4.213569	0.011812	19.982491	0.021120	213.560311	367.145861
6	5.816402	4.217359	−0.002553	20.003790	0.004570	213.594012	367.146756
7	5.816954	4.216540	0.000552	19.999181	0.000987	213.586734	367.146578
8	5.816835	4.216717	−0.000119	20.000177	0.000213	213.588307	367.146617
9	5.816861	4.216679	0.000026	19.999962	0.000046	213.587967	367.146608

Abstract

Cited By

Figures (7)

Tables (5)

Equations (24)

Applied Optics