Abstract

Straightness measurement is a very important technique in the field of mechanical engineering. A particular application for straightness measurement is high-accuracy machining on a diamond-turning lathe. We propose a novel, to our knowledge, optical method for measuring the straightness of motion, and its mathematical analysis is outlined. The technique is based on measurement of the lateral displacement of point images by use of reflection confocal optical systems. The advantages of this method are that (i) the lateral displacements in the direction of the two axes perpendicular to the optical axis can be measured, (ii) the rotation angles around all three axes can be measured, and (iii) reflection optical systems are more compact in length than are transmission optical systems.

© 1999 Optical Society of America

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References

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  1. Hewlett-Packard, Laser Precision Measurement System 5526A Operating Manual (Hewlett Packard, 3000 Hanover Street, Palo Alto, Calif. 94304-1185, 1976).
  2. J. M. Burch, D. C. Williams, “A focal lens systems for straightness measurement,” Opt. Laser Technol. 6, 166–168 (1974).
    [CrossRef]
  3. K. Matsuda, K. Tenjinbayashi, T. Kohno, T. Eiju, “Straightness measurement using holographic real time interferometry,” in International Commission for Optics-13 Conference Digest, H. Ohzu, ed. (Organizing Committee of ICO-13, Sapporo, Hokkaido, Japan, 1984), pp. 316–317.
  4. K. Takada, H. Takeyama, “Accuracy control of machine-tool by means of independent optical axes,” Ann. CIRP 27, 271–276 (1978).
  5. H. H. Sakuma, H. Wada, “Straightness measurement using a heterodyne moiré method,” Precis. Eng. 9, 19–22 (1987).
    [CrossRef]
  6. N.a., “A new laser-based straightness measuring system,” Machin. Product. Eng.15July1975, pp. 62–63.
  7. N. Ikawa, S. Shimada, H. Morooka, “Laser beam as a straight datum and its application to straightness measurement at nanometer level,” Ann. CIRP 37, 523–526 (1998).
    [CrossRef]
  8. M. Yamauchi, K. Matsuda, “Interferometric straightness measurement system using a holographic grating,” Opt. Eng. 33, 1078–1083 (1994).
    [CrossRef]

1998 (1)

N. Ikawa, S. Shimada, H. Morooka, “Laser beam as a straight datum and its application to straightness measurement at nanometer level,” Ann. CIRP 37, 523–526 (1998).
[CrossRef]

1994 (1)

M. Yamauchi, K. Matsuda, “Interferometric straightness measurement system using a holographic grating,” Opt. Eng. 33, 1078–1083 (1994).
[CrossRef]

1987 (1)

H. H. Sakuma, H. Wada, “Straightness measurement using a heterodyne moiré method,” Precis. Eng. 9, 19–22 (1987).
[CrossRef]

1978 (1)

K. Takada, H. Takeyama, “Accuracy control of machine-tool by means of independent optical axes,” Ann. CIRP 27, 271–276 (1978).

1975 (1)

N.a., “A new laser-based straightness measuring system,” Machin. Product. Eng.15July1975, pp. 62–63.

1974 (1)

J. M. Burch, D. C. Williams, “A focal lens systems for straightness measurement,” Opt. Laser Technol. 6, 166–168 (1974).
[CrossRef]

Burch, J. M.

J. M. Burch, D. C. Williams, “A focal lens systems for straightness measurement,” Opt. Laser Technol. 6, 166–168 (1974).
[CrossRef]

Eiju, T.

K. Matsuda, K. Tenjinbayashi, T. Kohno, T. Eiju, “Straightness measurement using holographic real time interferometry,” in International Commission for Optics-13 Conference Digest, H. Ohzu, ed. (Organizing Committee of ICO-13, Sapporo, Hokkaido, Japan, 1984), pp. 316–317.

Ikawa, N.

N. Ikawa, S. Shimada, H. Morooka, “Laser beam as a straight datum and its application to straightness measurement at nanometer level,” Ann. CIRP 37, 523–526 (1998).
[CrossRef]

Kohno, T.

K. Matsuda, K. Tenjinbayashi, T. Kohno, T. Eiju, “Straightness measurement using holographic real time interferometry,” in International Commission for Optics-13 Conference Digest, H. Ohzu, ed. (Organizing Committee of ICO-13, Sapporo, Hokkaido, Japan, 1984), pp. 316–317.

Matsuda, K.

M. Yamauchi, K. Matsuda, “Interferometric straightness measurement system using a holographic grating,” Opt. Eng. 33, 1078–1083 (1994).
[CrossRef]

K. Matsuda, K. Tenjinbayashi, T. Kohno, T. Eiju, “Straightness measurement using holographic real time interferometry,” in International Commission for Optics-13 Conference Digest, H. Ohzu, ed. (Organizing Committee of ICO-13, Sapporo, Hokkaido, Japan, 1984), pp. 316–317.

Morooka, H.

N. Ikawa, S. Shimada, H. Morooka, “Laser beam as a straight datum and its application to straightness measurement at nanometer level,” Ann. CIRP 37, 523–526 (1998).
[CrossRef]

Sakuma, H. H.

H. H. Sakuma, H. Wada, “Straightness measurement using a heterodyne moiré method,” Precis. Eng. 9, 19–22 (1987).
[CrossRef]

Shimada, S.

N. Ikawa, S. Shimada, H. Morooka, “Laser beam as a straight datum and its application to straightness measurement at nanometer level,” Ann. CIRP 37, 523–526 (1998).
[CrossRef]

Takada, K.

K. Takada, H. Takeyama, “Accuracy control of machine-tool by means of independent optical axes,” Ann. CIRP 27, 271–276 (1978).

Takeyama, H.

K. Takada, H. Takeyama, “Accuracy control of machine-tool by means of independent optical axes,” Ann. CIRP 27, 271–276 (1978).

Tenjinbayashi, K.

K. Matsuda, K. Tenjinbayashi, T. Kohno, T. Eiju, “Straightness measurement using holographic real time interferometry,” in International Commission for Optics-13 Conference Digest, H. Ohzu, ed. (Organizing Committee of ICO-13, Sapporo, Hokkaido, Japan, 1984), pp. 316–317.

Wada, H.

H. H. Sakuma, H. Wada, “Straightness measurement using a heterodyne moiré method,” Precis. Eng. 9, 19–22 (1987).
[CrossRef]

Williams, D. C.

J. M. Burch, D. C. Williams, “A focal lens systems for straightness measurement,” Opt. Laser Technol. 6, 166–168 (1974).
[CrossRef]

Yamauchi, M.

M. Yamauchi, K. Matsuda, “Interferometric straightness measurement system using a holographic grating,” Opt. Eng. 33, 1078–1083 (1994).
[CrossRef]

Ann. CIRP (2)

K. Takada, H. Takeyama, “Accuracy control of machine-tool by means of independent optical axes,” Ann. CIRP 27, 271–276 (1978).

N. Ikawa, S. Shimada, H. Morooka, “Laser beam as a straight datum and its application to straightness measurement at nanometer level,” Ann. CIRP 37, 523–526 (1998).
[CrossRef]

Machin. Product. Eng. (1)

N.a., “A new laser-based straightness measuring system,” Machin. Product. Eng.15July1975, pp. 62–63.

Opt. Eng. (1)

M. Yamauchi, K. Matsuda, “Interferometric straightness measurement system using a holographic grating,” Opt. Eng. 33, 1078–1083 (1994).
[CrossRef]

Opt. Laser Technol. (1)

J. M. Burch, D. C. Williams, “A focal lens systems for straightness measurement,” Opt. Laser Technol. 6, 166–168 (1974).
[CrossRef]

Precis. Eng. (1)

H. H. Sakuma, H. Wada, “Straightness measurement using a heterodyne moiré method,” Precis. Eng. 9, 19–22 (1987).
[CrossRef]

Other (2)

K. Matsuda, K. Tenjinbayashi, T. Kohno, T. Eiju, “Straightness measurement using holographic real time interferometry,” in International Commission for Optics-13 Conference Digest, H. Ohzu, ed. (Organizing Committee of ICO-13, Sapporo, Hokkaido, Japan, 1984), pp. 316–317.

Hewlett-Packard, Laser Precision Measurement System 5526A Operating Manual (Hewlett Packard, 3000 Hanover Street, Palo Alto, Calif. 94304-1185, 1976).

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Figures (7)

Fig. 1
Fig. 1

Optical arrangement for the straightness measurement by use of confocal optical systems: (a) top view and (b) side view. Three channels feed position sensors PS1, PS2, and PS3. Each channel relays a point source, P 01 or P 02, by means of a concave (Mc) or a convex (Mv) mirror to point images P, P′, and P″, which are in front of the various sensors.

Fig. 2
Fig. 2

Schematic of the imaging process for reflection confocal optical systems: The optical system including (a) a convex mirror (Mv) and (b) a concave mirror (Mc).

Fig. 3
Fig. 3

Convex-mirror system that shows (a) lateral displacement in the direction of the x axis and (b) rotation around the y axis.

Fig. 4
Fig. 4

Rotation of the optical axis when the table rotates around the y axis.

Fig. 5
Fig. 5

Concave-mirror system that shows (a) lateral displacement in the direction of the x axis and (b) rotation around the y axis.

Fig. 6
Fig. 6

Convex-mirror system that shows (a) lateral displacement in the direction of the y axis and (b) rotation around the x axis.

Fig. 7
Fig. 7

Concave-mirror system that shows (a) lateral displacement in the direction of the y axis and (b) rotation around the x axis.

Equations (33)

Equations on this page are rendered with MathJax. Learn more.

1a+fL+1fL+b=1fL,
1b+1c=1fM,
1fL+c+1fL+d=1fL,
b=fL2a.
c=fMfL2fL2-afM.
d=fL2fM-a.
a+d=fL2fM.
m1=b+fLa+fL=fLa.
m2=cb=afMfL2-afM.
m3=fL+dc+f2=fL2-afMfMfL.
m=m1m2m3=1.
1a+fL+1b+fL=1fL,
-1b-2fM+1c=1fM,
1fL+2fM-c+1fL+d=1fL,
a+d=fL2fM,  m=1.
δx1=PPmx¯=PG¯+GPmx¯=PG¯+ΔθyP01A1¯,
FD0¯=h tanΔθy2hΔθy2.
PG¯=ΔθyD0P¯-hΔθy2ΔθyD0P¯.
Δθy=δx1z0,
PPx¯=2Δx.
PPmx¯=PG¯-GPmx¯=PG¯-ΔθyP02A2¯,
δx2=PPx¯+PPm¯=2Δx+ΔθyD0P¯-P02A2¯.
Δx=12δx2-δx1+δx1P01A1¯z0,
PPy¯=2Δy.
Δyx,convex=Δθxz0-P01A1¯-P01A1¯,
Δyz=Δθzh,
δy1=2Δy+Δθxz0-2P01A1¯+Δθzh,
PPy=0.
Δyx,concave=ΔθxA2P+P02A02¯=Δθxz0,
δy2=Δθxz0+Δθzh.
Δθx=δy3z0,
Δθz=1hδy2-δy3.
Δy=12δy1-δy2+δy3P01A1¯z0.

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