Abstract

This Letter proposes a laser differential confocal paraboloidal vertex radius measurement (DCPRM) method for the high-accuracy measurement of the paraboloidal vertex radius of curvature. DCPRM constructs an autocollimation vertex radius measurement light path for the paraboloid by placing a reflector in the incidence light path. This technique is based on the principle that a paraboloid can aim a parallel beam at its focus without aberration and uses differential confocal positioning technology to identify the paraboloid focus and vertex accurately. Measurement of the precise distance between these two positions is achieved to determine the paraboloid vertex radius. Preliminary experimental results indicate that DCPRM has a relative expanded uncertainty of less than 0.001%.

© 2014 Optical Society of America

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References

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  1. A. Rakich and N. J. Rumsey, Adv. Opt. Technol. 2, 111 (2013).
    [CrossRef]
  2. J. He, H. Jiang, Y. Hu, Y. Zhao, and J. Wang, “Space laser communication network,” in International Conference on Space Optical Systems and Applications (ICSOS), France, October9, 2012.
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    [CrossRef]
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  7. R. E. Parks, Proc. SPIE 6676, 667603 (2007).
    [CrossRef]
  8. J. Yang, L. Qiu, W. Zhao, and H. Wu, Opt. Express 20, 26027 (2012).
    [CrossRef]

2013 (1)

A. Rakich and N. J. Rumsey, Adv. Opt. Technol. 2, 111 (2013).
[CrossRef]

2012 (1)

2007 (1)

R. E. Parks, Proc. SPIE 6676, 667603 (2007).
[CrossRef]

2005 (1)

2004 (1)

H. Wang, Y. Li, L. Zeng, C. Yin, and Z. Feng, Opt. Commun. 232, 61 (2004).
[CrossRef]

1994 (1)

D. Anderson, J. Burge, D. Ketelsen, B. Martin, S. West, G. Poczulp, J. Richardson, and W. Wong, Proc. SPIE 1994, 193 (1994).
[CrossRef]

1986 (1)

Anderson, D.

D. Anderson, J. Burge, D. Ketelsen, B. Martin, S. West, G. Poczulp, J. Richardson, and W. Wong, Proc. SPIE 1994, 193 (1994).
[CrossRef]

Burge, J.

D. Anderson, J. Burge, D. Ketelsen, B. Martin, S. West, G. Poczulp, J. Richardson, and W. Wong, Proc. SPIE 1994, 193 (1994).
[CrossRef]

Choi, Y.-W.

Cornejo-Rodriguez, A.

Diaz-Uribe, R.

Feng, Z.

H. Wang, Y. Li, L. Zeng, C. Yin, and Z. Feng, Opt. Commun. 232, 61 (2004).
[CrossRef]

He, J.

J. He, H. Jiang, Y. Hu, Y. Zhao, and J. Wang, “Space laser communication network,” in International Conference on Space Optical Systems and Applications (ICSOS), France, October9, 2012.

Hu, Y.

J. He, H. Jiang, Y. Hu, Y. Zhao, and J. Wang, “Space laser communication network,” in International Conference on Space Optical Systems and Applications (ICSOS), France, October9, 2012.

Jiang, H.

J. He, H. Jiang, Y. Hu, Y. Zhao, and J. Wang, “Space laser communication network,” in International Conference on Space Optical Systems and Applications (ICSOS), France, October9, 2012.

Ketelsen, D.

D. Anderson, J. Burge, D. Ketelsen, B. Martin, S. West, G. Poczulp, J. Richardson, and W. Wong, Proc. SPIE 1994, 193 (1994).
[CrossRef]

Kim, E. D.

Li, Y.

H. Wang, Y. Li, L. Zeng, C. Yin, and Z. Feng, Opt. Commun. 232, 61 (2004).
[CrossRef]

Martin, B.

D. Anderson, J. Burge, D. Ketelsen, B. Martin, S. West, G. Poczulp, J. Richardson, and W. Wong, Proc. SPIE 1994, 193 (1994).
[CrossRef]

Parks, R. E.

R. E. Parks, Proc. SPIE 6676, 667603 (2007).
[CrossRef]

Poczulp, G.

D. Anderson, J. Burge, D. Ketelsen, B. Martin, S. West, G. Poczulp, J. Richardson, and W. Wong, Proc. SPIE 1994, 193 (1994).
[CrossRef]

Qiu, L.

Rakich, A.

A. Rakich and N. J. Rumsey, Adv. Opt. Technol. 2, 111 (2013).
[CrossRef]

Richardson, J.

D. Anderson, J. Burge, D. Ketelsen, B. Martin, S. West, G. Poczulp, J. Richardson, and W. Wong, Proc. SPIE 1994, 193 (1994).
[CrossRef]

Rumsey, N. J.

A. Rakich and N. J. Rumsey, Adv. Opt. Technol. 2, 111 (2013).
[CrossRef]

Wang, H.

H. Wang, Y. Li, L. Zeng, C. Yin, and Z. Feng, Opt. Commun. 232, 61 (2004).
[CrossRef]

Wang, J.

J. He, H. Jiang, Y. Hu, Y. Zhao, and J. Wang, “Space laser communication network,” in International Conference on Space Optical Systems and Applications (ICSOS), France, October9, 2012.

West, S.

D. Anderson, J. Burge, D. Ketelsen, B. Martin, S. West, G. Poczulp, J. Richardson, and W. Wong, Proc. SPIE 1994, 193 (1994).
[CrossRef]

Wong, W.

D. Anderson, J. Burge, D. Ketelsen, B. Martin, S. West, G. Poczulp, J. Richardson, and W. Wong, Proc. SPIE 1994, 193 (1994).
[CrossRef]

Wu, H.

Yang, J.

Yin, C.

H. Wang, Y. Li, L. Zeng, C. Yin, and Z. Feng, Opt. Commun. 232, 61 (2004).
[CrossRef]

Zeng, L.

H. Wang, Y. Li, L. Zeng, C. Yin, and Z. Feng, Opt. Commun. 232, 61 (2004).
[CrossRef]

Zhao, W.

Zhao, Y.

J. He, H. Jiang, Y. Hu, Y. Zhao, and J. Wang, “Space laser communication network,” in International Conference on Space Optical Systems and Applications (ICSOS), France, October9, 2012.

Adv. Opt. Technol. (1)

A. Rakich and N. J. Rumsey, Adv. Opt. Technol. 2, 111 (2013).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Korea (1)

Opt. Commun. (1)

H. Wang, Y. Li, L. Zeng, C. Yin, and Z. Feng, Opt. Commun. 232, 61 (2004).
[CrossRef]

Opt. Express (1)

Proc. SPIE (2)

R. E. Parks, Proc. SPIE 6676, 667603 (2007).
[CrossRef]

D. Anderson, J. Burge, D. Ketelsen, B. Martin, S. West, G. Poczulp, J. Richardson, and W. Wong, Proc. SPIE 1994, 193 (1994).
[CrossRef]

Other (1)

J. He, H. Jiang, Y. Hu, Y. Zhao, and J. Wang, “Space laser communication network,” in International Conference on Space Optical Systems and Applications (ICSOS), France, October9, 2012.

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Figures (7)

Fig. 1.
Fig. 1.

Paraboloidal vertex radius measurement: (a) concave paraboloid measurement and (b) convex paraboloid measurement. Here, Lo is the objective, R is the partial reflector, and TP is the test paraboloid.

Fig. 2.
Fig. 2.

DCPRM principle. Here, PBS is the polarized beam splitter, P is the quarter-wave plate, Lc is the collimating lens, Lo is the objective, R is the partial reflector, TP is the test paraboloid, BS is the beam splitter, CCD1 and CCD2 are detectors, MO1 and MO2 are microscope objectives, and M is the offset of the VPHs from the focus of Lc.

Fig. 3.
Fig. 3.

Differential confocal response curves with different uM.

Fig. 4.
Fig. 4.

Differential confocal response curves with different D/fo.

Fig. 5.
Fig. 5.

Experimental setup.

Fig. 6.
Fig. 6.

Single vertex radius of curvature measurement.

Fig. 7.
Fig. 7.

Repeatability of measurement data.

Equations (3)

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

IA(u,uM)=|02π01exp[i2kΦ(ρ,θ)]exp(iuρ2iuMρ2/2)ρdρdθ|2|02π01exp[i2kΦ(ρ,θ)]exp(iuρ2+iuMρ2/2)ρdρdθ|2,
IA(u,uM)=[sin(u/2uM/4)u/2uM/4]2[sin(u/2+uM/4)u/2+uM/4]2.
IA(z)=IB(z)=[sin(π4λD2fo2z1.303)π4λD2fo2z1.303]2[sin(π4λD2fo2z+1.303)π4λD2fo2z+1.303]2.

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