Abstract

A simple three-dimensional (3D) laser angle sensor for 3D measurement of small angles based on the diffraction theorem and on ray optics analysis is presented. The possibility of using position-sensitive detectors and a reflective diffraction grating to develop a 3D angle sensor was investigated and a prototype 3D laser angle sensor was designed and built. The system is composed of a laser diode, two position-sensitive detectors, and a reflective diffraction grating. The diffraction grating, mounted upon the rotational center of a 3D rotational stage, divides an incident laser beam into several diffracted rays, and two position-sensitive detectors are set up for detecting the positions of ±1st-order diffracted rays. According to the optical path relationship between the three angular motions and the output coordinates of the two position-sensitive detectors, the 3D angles can be obtained through kinematic analysis. The experimental results show the feasibility of the proposed 3D laser angular sensor. Use of this system as an instrument for high-resolution measurement of small-angle rotation is proposed.

© 2004 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2004

X. Y. Fang, M. S. Cao, “Theoretical analysis of 2D laser angle sensor and several design parameters,” Opt. Laser Technol. 34, 225–229 (2004).

2002

K. M. Abedin, M. Wahadoszamen, A. F. M. Y. Haider, “Measurement of in-plane motions and rotations using a simple electronic speckle pattern interferometer,” Opt. Laser Technol. 34, 293–298 (2002).
[CrossRef]

2001

E. W. Bae, J. A. Kim, S. H. Kim, “Multi-degree-of-freedom displacement measurement system for milli-structures,” Meas. Sci. Technol. 12, 1495–1502 (2001).
[CrossRef]

1999

1998

1997

1992

1989

1978

A. E. Ennos, “Speckle interferometry,” Prog. Opt. 16, 233–288 (1978).
[CrossRef]

1976

C. A. Sciammarella, J. A. Gilbert, “A holographic-moiré technique to obtain separate patterns for components of displacement,” Exp. Mech. 16, 215–219 (1976).
[CrossRef]

1968

A. E. Ennos, “Measurement of in-plane surface strain by hologram interferometry,” J. Sci. Instrum. 1, 713–717 (1968).

Abedin, K. M.

K. M. Abedin, M. Wahadoszamen, A. F. M. Y. Haider, “Measurement of in-plane motions and rotations using a simple electronic speckle pattern interferometer,” Opt. Laser Technol. 34, 293–298 (2002).
[CrossRef]

Bae, E. W.

E. W. Bae, J. A. Kim, S. H. Kim, “Multi-degree-of-freedom displacement measurement system for milli-structures,” Meas. Sci. Technol. 12, 1495–1502 (2001).
[CrossRef]

Cao, M. S.

X. Y. Fang, M. S. Cao, “Theoretical analysis of 2D laser angle sensor and several design parameters,” Opt. Laser Technol. 34, 225–229 (2004).

Chen, W. Y.

Y. L. Lay, W. Y. Chen, “Rotation measurement using a circular moiré grating,” Opt. Laser Technol. 30, 539–544 (1998).
[CrossRef]

Cornet, A.

Dai, X.

Ennos, A. E.

A. E. Ennos, “Speckle interferometry,” Prog. Opt. 16, 233–288 (1978).
[CrossRef]

A. E. Ennos, “Measurement of in-plane surface strain by hologram interferometry,” J. Sci. Instrum. 1, 713–717 (1968).

Fang, X. Y.

X. Y. Fang, M. S. Cao, “Theoretical analysis of 2D laser angle sensor and several design parameters,” Opt. Laser Technol. 34, 225–229 (2004).

Gilbert, J. A.

C. A. Sciammarella, J. A. Gilbert, “A holographic-moiré technique to obtain separate patterns for components of displacement,” Exp. Mech. 16, 215–219 (1976).
[CrossRef]

Haider, A. F. M. Y.

K. M. Abedin, M. Wahadoszamen, A. F. M. Y. Haider, “Measurement of in-plane motions and rotations using a simple electronic speckle pattern interferometer,” Opt. Laser Technol. 34, 293–298 (2002).
[CrossRef]

Huang, P. S.

Jabconaki, R.

R. Jabconaki, “Angle interference measurement,” presented at the First International Symposium on Metrology for Quality Control in Production, Tokyo, July 10–13, 1984).

Joannes, L.

Jones, R.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1989).

Kamada, O.

Kim, J. A.

E. W. Bae, J. A. Kim, S. H. Kim, “Multi-degree-of-freedom displacement measurement system for milli-structures,” Meas. Sci. Technol. 12, 1495–1502 (2001).
[CrossRef]

Kim, S. H.

E. W. Bae, J. A. Kim, S. H. Kim, “Multi-degree-of-freedom displacement measurement system for milli-structures,” Meas. Sci. Technol. 12, 1495–1502 (2001).
[CrossRef]

Kiyono, S.

Lay, Y. L.

Y. L. Lay, W. Y. Chen, “Rotation measurement using a circular moiré grating,” Opt. Laser Technol. 30, 539–544 (1998).
[CrossRef]

Li, Y.

Nassim, A. K.

Pirodda, L.

Sciammarella, C. A.

C. A. Sciammarella, J. A. Gilbert, “A holographic-moiré technique to obtain separate patterns for components of displacement,” Exp. Mech. 16, 215–219 (1976).
[CrossRef]

Wahadoszamen, M.

K. M. Abedin, M. Wahadoszamen, A. F. M. Y. Haider, “Measurement of in-plane motions and rotations using a simple electronic speckle pattern interferometer,” Opt. Laser Technol. 34, 293–298 (2002).
[CrossRef]

Wykes, C.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1989).

Zhou, W. D.

Appl. Opt.

Exp. Mech.

C. A. Sciammarella, J. A. Gilbert, “A holographic-moiré technique to obtain separate patterns for components of displacement,” Exp. Mech. 16, 215–219 (1976).
[CrossRef]

J. Sci. Instrum.

A. E. Ennos, “Measurement of in-plane surface strain by hologram interferometry,” J. Sci. Instrum. 1, 713–717 (1968).

Meas. Sci. Technol.

E. W. Bae, J. A. Kim, S. H. Kim, “Multi-degree-of-freedom displacement measurement system for milli-structures,” Meas. Sci. Technol. 12, 1495–1502 (2001).
[CrossRef]

Opt. Laser Technol.

X. Y. Fang, M. S. Cao, “Theoretical analysis of 2D laser angle sensor and several design parameters,” Opt. Laser Technol. 34, 225–229 (2004).

Y. L. Lay, W. Y. Chen, “Rotation measurement using a circular moiré grating,” Opt. Laser Technol. 30, 539–544 (1998).
[CrossRef]

K. M. Abedin, M. Wahadoszamen, A. F. M. Y. Haider, “Measurement of in-plane motions and rotations using a simple electronic speckle pattern interferometer,” Opt. Laser Technol. 34, 293–298 (2002).
[CrossRef]

Prog. Opt.

A. E. Ennos, “Speckle interferometry,” Prog. Opt. 16, 233–288 (1978).
[CrossRef]

Other

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1989).

R. Jabconaki, “Angle interference measurement,” presented at the First International Symposium on Metrology for Quality Control in Production, Tokyo, July 10–13, 1984).

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Figures (9)

Fig. 1
Fig. 1

Simple optical layout and experimental setup of the system.

Fig. 2
Fig. 2

Spatial relationship of 3D diffraction rays on a grating and two PSDs.

Fig. 3
Fig. 3

Setup for PSD calibration tests with two HP interferometers: A/D, analog to digital.

Fig. 4
Fig. 4

Calibration test results for a PSD: A/D, analog to digital.

Fig. 5
Fig. 5

Results of the repeatability tests of a PSD.

Fig. 6
Fig. 6

Photograph of the prototype 3D laser angle sensor.

Fig. 7
Fig. 7

(a) Results of measurement of the angle of rotation about the X axis based on variation of the rotation angle for three runs, (b) standard deviation based on variation of the rotation angle, (c) mean measuring error based on the variation of the rotation angle.

Fig. 8
Fig. 8

(a) Results of measurement of the angle of rotation about the Y axis based on variation of the rotation angle for three runs, (b) standard deviation based on variation of the rotation angle, (c) mean measuring error based on variation of rotation angle.

Fig. 9
Fig. 9

(a) Results of measurement of the angle of rotation about the Z axis based on variation of the rotation angle for three runs, (b) standard deviation based on variation of the rotation angle, (c) mean measuring error based on variation of rotation angle.

Tables (1)

Tables Icon

Table 1 Resolution and Maximum Measuring Range of the 3D Laser Angle Sensor

Equations (21)

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RcI=IxIyIz.
RcRGc=cos α cos βcos α sin β sin γ-sin α cos γsin α sin γ+sin α sin β cos γsin α cos βcos α cos γ+sin α sin β sin γsin α sin β cos γ-cos α sin γ-sin βcos β sin γcos β cos γ,
GcI=GcRRcRcI=Ix, Iy, IzT,
RcI=00-1.
GcB=bmxbybmz.
bmx=Ix+mλ/d, m=1, -1, by=Iy, bmz=1-bmx2-by21/2, m=1, -1,
RcTPm=cos θm0sin θmam0100-sin θm0cos θmcm0001,
RcP=0001.
PmP=PmTRcRcP=PmxPmyPmz,
PmB=PmRGcGcB=bmpxbmpybmpz.
xmp=Pmx-bmpxbmpz Pmz=fα, β, γ, am, cm, m=1, -1,
ymp=Pmy-bmpybmpz Pmz=fα, β, γ, am, cm, m=1, -1.
y+1p=P+1y-b+1pyb+1pz P+1z=fα, 0, 0, a+1, c+1,
y-1p=P-1y-b-1pyb-1pz P-1z=fα, 0, 0, a-1, c-1.
y+1p+y-1p2=12fα, 0, 0, a+1, c+1+fα, 0, 0, a-1, c-1.
x+1p=P+1x-b+1pxb+1pz P+1z=f0, β, 0, a+1, c+1,
x-1p=P-1x-b-1pxb-1pz P-1z=f0, β, 0, a-1, c-1.
x+1p+x-1p2=12f0, β, 0, a+1, c+1+f0, β, 0, a-1, c-1.
y+1p=P+1y-b+1pyb+1pz P+1z=f0, 0, γ, a+1, c+1,
y-1p=P-1y-b-1pyb-1pz P-1z=f0, 0, γ, a-1, c-1.
y+1p+y-1p2=12f0, 0, γ, a+1, c+1+f0, 0, γ, a-1, c-1.

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