Method for calibrating system parameters of a multidirectional interferometers system

Jie Zhang; Koichi Iwata; Atsushi Shibuya; Hisao Kikuta; Choong Sik Park

doi:10.1364/AO.45.000605

Applied Optics
Vol. 45,
Issue 4,
pp. 605-610
(2006)
•https://doi.org/10.1364/AO.45.000605

Method for calibrating system parameters of a multidirectional interferometers system

Jie Zhang, Koichi Iwata, Atsushi Shibuya, Hisao Kikuta, and Choong Sik Park

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Jie Zhang, Koichi Iwata, Atsushi Shibuya, Hisao Kikuta, and Choong Sik Park, "Method for calibrating system parameters of a multidirectional interferometers system," Appl. Opt. 45, 605-610 (2006)

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

Abstract

A multidirectional interferometer system has been proposed and developed to measure the position and orientation of a positioning stage. In this method the system parameters, such as positions of the corner-cube reflectors and directions of the rays in the interferometers, must be determined beforehand. However, it is difficult to find ways to determine the system parameters for each different system with necessary accuracy. This paper proposes a systematic method for calibrating the system parameters when the number of the interferometers is larger than the degrees of freedom of the stage. The method is verified for a two-dimensional stage by both simulation and experiment.

Full Article | PDF Article

More Like This

Measurement by multidirectional interferometers of the position and orientation of a positioning stage

Jie Zhang, Tetsuya Yamaguchi, Koichi Iwata, Hisao Kikuta, and Choong Sik Park
Appl. Opt. 42(28) 5661-5669 (2003)

Two-step calibration method for extrinsic parameters of an airborne camera

Dongming Yuan, Yalin Ding, Guoqin Yuan, Feng Li, Jian Zhang, Yuanchao Wang, and Lei Zhang
Appl. Opt. 60(5) 1387-1398 (2021)

Implementation of multidirectional moiré computerized tomography: multidirectional affine calibration

Yang Song, Jia Wang, Ying Jin, Zhenyan Guo, Yunjing Ji, Anzhi He, and Zhenhua Li
J. Opt. Soc. Am. A 33(12) 2385-2395 (2016)

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 (6)

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 (6)

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 (16)

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

System Parameters	Number of Interferometers
System Parameters	$k = 1$	$k = 2$	$k = 3$	$k = 4$
$θ_{k}$ (deg)^a	90	180	270	0
$ψ_{k}$ (deg)^b	0	90	180	270
$r_{k}$ (mm)^c	50	50	50	50

Data No.	0	1	2	3	4	5	6	7	8	9	10
Translation in the x axis (mm)	0.5	1	2	3	4	5	6	7	8	9	10
Translation in the y axis (mm)	0.5	1	2	3	4	5	6	7	8	9	10
Rotation angle around the z axis (deg)	0.5	1.2	2.3	3.4	4.6	5.7	6.9	8.0	9.2	10.3	11.5

System Parameter		Position and Orientation
$σ_{θ}$	$2.2 \times 10^{- 3} \deg$	$σ_{x}$	$0.27 µm$
$σ_{ψ}$	0.74 deg	$σ_{y}$	$0.073 µm$
$σ_{r}$	$37.7 µm$	$σ_{ϕ}$	$0.8 \times 10^{- 4} \deg$

System Parameters	Number of Interferometers
System Parameters	$k = 1$	$k = 2$	$k = 3$	$k = 4$
$θ_{k}$ (deg)	90	178.299	267.818	1.742
$ψ_{k}$ (deg)	0	79.928	176.832	280.469
$r_{k}$ (mm)	50	49.829	50.173	49.835

Data No.	Instructed Values	Measured Values
Data No.	$(U_{x i}, U_{y i}, ϕ_{i})$ (mm, mm, deg)	$(U_{x}, U_{y}, ϕ)$ (mm, mm, deg)
A	(0.025, 0.025, 1.0816)	(0.025, 0.026, 1.071)
B	(−0.800, −0.025, −1.0816)	(−0.808, −0.022, −1.100)
C	(−0.800, −0.700, −1.0816)	(−0.800, −0.691, −1.100)
D	(0.025, −0.700, 1.0816)	(0.032, −0.643, 1.071)

Data Number	$σ_{x} (µm)$	$σ_{y} (µm)$	$σ_{ϕ} (\deg)$
A	0.29	0.16	<0.0001
B	0.05	0.08	<0.0001
C	0.00	0.05	<0.0001
D	0.23	0.13	0.0001

Abstract

Cited By

Figures (6)

Tables (6)

Equations (16)

Applied Optics