Abstract

A new laser differential confocal ultra-large radius measurement (LDCRM) method is proposed for high-precision measurement of ultra-large radii. Based on the property that the zero point of a differential confocal axial intensity curve precisely corresponds to the focus points of focusing beam, LDCRM measures the vertex positions of the test lens and the last optical surface of objective lens to obtain position difference L1, and then measures the vertex positions of the reflector and the last optical surface of objective lens to obtain the position difference L2, finally uses the measured L1 and L2 to calculate the radius of test lens. This method does not require the identification of confocal position. Preliminary experimental results and theoretical analyses indicate that the relative uncertainty is 0.03% for a convex spherical lens with a radius of approximately 20 m. LDCRM provides a novel approach for high-precision ultra-large radius measurement.

© 2016 Optical Society of America

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References

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    [Crossref]
  2. H. Tsutsumi, K. Yoshizumi, and H. Takeuchi, “Ultrahighly accurate 3D profilometer,” Proc. SPIE 5638, 387–394 (2005).
    [Crossref]
  3. Y. P. Kumar and S. Chatterjee, “Application of Newton’s method to determine the focal length of lenses using a lateral shearing interferometer and cyclic path optical configuration setup,” Opt. Eng. 49(5), 053604 (2010).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  9. L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31(9), 1961–1966 (1992).
    [Crossref]
  10. Q. Wang, U. Griesmann, and J. A. Soons, “Holographic radius test plates for spherical surfaces with large radius of curvature,” Appl. Opt. 53(20), 4532–4538 (2014).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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2015 (1)

2014 (1)

2012 (2)

2010 (3)

W. Zhao, R. Sun, L. Qiu, and D. Sha, “Laser differential confocal radius measurement,” Opt. Express 18(3), 2345–2360 (2010).
[Crossref] [PubMed]

Y. P. Kumar and S. Chatterjee, “Application of Newton’s method to determine the focal length of lenses using a lateral shearing interferometer and cyclic path optical configuration setup,” Opt. Eng. 49(5), 053604 (2010).
[Crossref]

D. G. Abdelsalam, M. S. Shaalan, M. M. Eloker, and D. Kim, “Radius of curvature measurement of spherical smooth surfaces by multiple-beam interferometry in reflection,” Opt. Lasers Eng. 48(6), 643–649 (2010).
[Crossref]

2005 (1)

H. Tsutsumi, K. Yoshizumi, and H. Takeuchi, “Ultrahighly accurate 3D profilometer,” Proc. SPIE 5638, 387–394 (2005).
[Crossref]

2004 (1)

U. Griesmann, J. Soons, Q. Wang, and D. DeBra, “Measuring form and radius of spheres with interferometry,” CIRP Annals - Manufacturing Technol 53(1), 451–454 (2004).
[Crossref]

2002 (1)

T. L. Schmitz, C. J. Evans, A. Davies, and W. T. Estler, “Displacement Uncertainty in Interferometric Radius Measurements,” CIRP Annals - Manufacturing Technol 51(1), 451–454 (2002).
[Crossref]

2001 (1)

T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
[Crossref]

1996 (1)

Y. W. Lee, H. M. Cho, and I. W. Lee, “Measurement of a long radius of curvature using a half-aperture bidirectional shearing interferometer,” Opt. Eng. 35(2), 480–483 (1996).
[Crossref]

1992 (2)

1984 (1)

1954 (1)

J. W. Gates, K. J. Habell, and S. P. Middleton, “A precision spherometer,” J. Sci. Instrum. 31(2), 60–64 (1954).
[Crossref]

Abdelsalam, D. G.

D. G. Abdelsalam, M. S. Shaalan, M. M. Eloker, and D. Kim, “Radius of curvature measurement of spherical smooth surfaces by multiple-beam interferometry in reflection,” Opt. Lasers Eng. 48(6), 643–649 (2010).
[Crossref]

Chatterjee, S.

Y. P. Kumar and S. Chatterjee, “Application of Newton’s method to determine the focal length of lenses using a lateral shearing interferometer and cyclic path optical configuration setup,” Opt. Eng. 49(5), 053604 (2010).
[Crossref]

Cho, H. M.

Y. W. Lee, H. M. Cho, and I. W. Lee, “Measurement of a long radius of curvature using a half-aperture bidirectional shearing interferometer,” Opt. Eng. 35(2), 480–483 (1996).
[Crossref]

Davies, A.

T. L. Schmitz, C. J. Evans, A. Davies, and W. T. Estler, “Displacement Uncertainty in Interferometric Radius Measurements,” CIRP Annals - Manufacturing Technol 51(1), 451–454 (2002).
[Crossref]

Davies, A. D.

T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
[Crossref]

DeBra, D.

U. Griesmann, J. Soons, Q. Wang, and D. DeBra, “Measuring form and radius of spheres with interferometry,” CIRP Annals - Manufacturing Technol 53(1), 451–454 (2004).
[Crossref]

Du, Z.

Eloker, M. M.

D. G. Abdelsalam, M. S. Shaalan, M. M. Eloker, and D. Kim, “Radius of curvature measurement of spherical smooth surfaces by multiple-beam interferometry in reflection,” Opt. Lasers Eng. 48(6), 643–649 (2010).
[Crossref]

Estler, W. T.

T. L. Schmitz, C. J. Evans, A. Davies, and W. T. Estler, “Displacement Uncertainty in Interferometric Radius Measurements,” CIRP Annals - Manufacturing Technol 51(1), 451–454 (2002).
[Crossref]

Evans, C. J.

T. L. Schmitz, C. J. Evans, A. Davies, and W. T. Estler, “Displacement Uncertainty in Interferometric Radius Measurements,” CIRP Annals - Manufacturing Technol 51(1), 451–454 (2002).
[Crossref]

T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
[Crossref]

Gates, J. W.

J. W. Gates, K. J. Habell, and S. P. Middleton, “A precision spherometer,” J. Sci. Instrum. 31(2), 60–64 (1954).
[Crossref]

Griesmann, U.

Q. Wang, U. Griesmann, and J. A. Soons, “Holographic radius test plates for spherical surfaces with large radius of curvature,” Appl. Opt. 53(20), 4532–4538 (2014).
[Crossref] [PubMed]

U. Griesmann, J. Soons, Q. Wang, and D. DeBra, “Measuring form and radius of spheres with interferometry,” CIRP Annals - Manufacturing Technol 53(1), 451–454 (2004).
[Crossref]

Habell, K. J.

J. W. Gates, K. J. Habell, and S. P. Middleton, “A precision spherometer,” J. Sci. Instrum. 31(2), 60–64 (1954).
[Crossref]

Kim, D.

D. G. Abdelsalam, M. S. Shaalan, M. M. Eloker, and D. Kim, “Radius of curvature measurement of spherical smooth surfaces by multiple-beam interferometry in reflection,” Opt. Lasers Eng. 48(6), 643–649 (2010).
[Crossref]

Kothiyal, M. P.

Kumar, Y. P.

Y. P. Kumar and S. Chatterjee, “Application of Newton’s method to determine the focal length of lenses using a lateral shearing interferometer and cyclic path optical configuration setup,” Opt. Eng. 49(5), 053604 (2010).
[Crossref]

Lee, I. W.

Y. W. Lee, H. M. Cho, and I. W. Lee, “Measurement of a long radius of curvature using a half-aperture bidirectional shearing interferometer,” Opt. Eng. 35(2), 480–483 (1996).
[Crossref]

Lee, Y. W.

Y. W. Lee, H. M. Cho, and I. W. Lee, “Measurement of a long radius of curvature using a half-aperture bidirectional shearing interferometer,” Opt. Eng. 35(2), 480–483 (1996).
[Crossref]

Lin, C.

Middleton, S. P.

J. W. Gates, K. J. Habell, and S. P. Middleton, “A precision spherometer,” J. Sci. Instrum. 31(2), 60–64 (1954).
[Crossref]

Murata, K.

Nakano, Y.

Qiu, L.

Schmitz, T. L.

T. L. Schmitz, C. J. Evans, A. Davies, and W. T. Estler, “Displacement Uncertainty in Interferometric Radius Measurements,” CIRP Annals - Manufacturing Technol 51(1), 451–454 (2002).
[Crossref]

T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
[Crossref]

Selberg, L. A.

L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31(9), 1961–1966 (1992).
[Crossref]

Sha, D.

Shaalan, M. S.

D. G. Abdelsalam, M. S. Shaalan, M. M. Eloker, and D. Kim, “Radius of curvature measurement of spherical smooth surfaces by multiple-beam interferometry in reflection,” Opt. Lasers Eng. 48(6), 643–649 (2010).
[Crossref]

Sirohi, R. S.

Soons, J.

U. Griesmann, J. Soons, Q. Wang, and D. DeBra, “Measuring form and radius of spheres with interferometry,” CIRP Annals - Manufacturing Technol 53(1), 451–454 (2004).
[Crossref]

Soons, J. A.

Sriram, K. V.

Sun, R.

Takeuchi, H.

H. Tsutsumi, K. Yoshizumi, and H. Takeuchi, “Ultrahighly accurate 3D profilometer,” Proc. SPIE 5638, 387–394 (2005).
[Crossref]

Tsutsumi, H.

H. Tsutsumi, K. Yoshizumi, and H. Takeuchi, “Ultrahighly accurate 3D profilometer,” Proc. SPIE 5638, 387–394 (2005).
[Crossref]

Wang, G.

Wang, Q.

Q. Wang, U. Griesmann, and J. A. Soons, “Holographic radius test plates for spherical surfaces with large radius of curvature,” Appl. Opt. 53(20), 4532–4538 (2014).
[Crossref] [PubMed]

U. Griesmann, J. Soons, Q. Wang, and D. DeBra, “Measuring form and radius of spheres with interferometry,” CIRP Annals - Manufacturing Technol 53(1), 451–454 (2004).
[Crossref]

Wei, C.

Wu, H.

Yan, S.

Yang, J.

Yoshizumi, K.

H. Tsutsumi, K. Yoshizumi, and H. Takeuchi, “Ultrahighly accurate 3D profilometer,” Proc. SPIE 5638, 387–394 (2005).
[Crossref]

Zhao, W.

Appl. Opt. (4)

Chin. Opt. Lett. (1)

CIRP Annals - Manufacturing Technol (2)

T. L. Schmitz, C. J. Evans, A. Davies, and W. T. Estler, “Displacement Uncertainty in Interferometric Radius Measurements,” CIRP Annals - Manufacturing Technol 51(1), 451–454 (2002).
[Crossref]

U. Griesmann, J. Soons, Q. Wang, and D. DeBra, “Measuring form and radius of spheres with interferometry,” CIRP Annals - Manufacturing Technol 53(1), 451–454 (2004).
[Crossref]

J. Sci. Instrum. (1)

J. W. Gates, K. J. Habell, and S. P. Middleton, “A precision spherometer,” J. Sci. Instrum. 31(2), 60–64 (1954).
[Crossref]

Opt. Eng. (3)

Y. P. Kumar and S. Chatterjee, “Application of Newton’s method to determine the focal length of lenses using a lateral shearing interferometer and cyclic path optical configuration setup,” Opt. Eng. 49(5), 053604 (2010).
[Crossref]

L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31(9), 1961–1966 (1992).
[Crossref]

Y. W. Lee, H. M. Cho, and I. W. Lee, “Measurement of a long radius of curvature using a half-aperture bidirectional shearing interferometer,” Opt. Eng. 35(2), 480–483 (1996).
[Crossref]

Opt. Express (2)

Opt. Lasers Eng. (1)

D. G. Abdelsalam, M. S. Shaalan, M. M. Eloker, and D. Kim, “Radius of curvature measurement of spherical smooth surfaces by multiple-beam interferometry in reflection,” Opt. Lasers Eng. 48(6), 643–649 (2010).
[Crossref]

Proc. SPIE (2)

H. Tsutsumi, K. Yoshizumi, and H. Takeuchi, “Ultrahighly accurate 3D profilometer,” Proc. SPIE 5638, 387–394 (2005).
[Crossref]

T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
[Crossref]

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Figures (14)

Fig. 1
Fig. 1 A schematic of ‘cat’s eye and confocal’ radius measurement.
Fig. 2
Fig. 2 Position difference L1 measurement. BS is the beam splitter, LC is the collimating lens, TL is the test spherical lens, LO is the objective lens, PH is the pinhole, DMI is the distance measuring instrument.
Fig. 3
Fig. 3 Position difference L2 measurement.
Fig. 4
Fig. 4 Radius calculation.
Fig. 5
Fig. 5 Error transfer coefficient.
Fig. 6
Fig. 6 The focusing sensitivity for different uM and vPH.
Fig. 7
Fig. 7 The main structure of a LDCRM system.
Fig. 8
Fig. 8 LDCRM system.
Fig. 9
Fig. 9 Measurement results of position difference L2.
Fig. 10
Fig. 10 Repeatability of L2 measurement data.
Fig. 11
Fig. 11 Measurement results of position difference L1.
Fig. 12
Fig. 12 Repeatability of L1 measurement data.
Fig. 13
Fig. 13 Axial misalignment between the LDCRM axes.
Fig. 14
Fig. 14 Schematics of detectors with different offsets.

Equations (28)

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I A ( u , u M ) = I 2 ( u , u M ) I 1 ( u , + u M ) = [ sin ( u / 2 + u M / 4 ) ( u / 2 + u M / 4 ) ] 2 [ sin ( u / 2 u M / 4 ) ( u / 2 u M / 4 ) ] 2 ,
{ u = π 2 λ ( D f O ) 2 z u M = π 2 λ ( D f C ) 2 M .
I B ( u , u M ) = I 2 ( u , u M ) I 1 ( u , + u M ) = { sin [ ( 1 + α ) / 2 u + u M / 4 ] [ ( 1 + α ) / 2 u + u M / 4 ] } 2 { sin [ ( 1 + α ) / 2 u u M / 4 ] [ ( 1 + α ) / 2 u u M / 4 ] } 2 ,
α = ( 2 L 2 L 1 L 1 ) 2 .
I A ( u , u M ) = [ sin ( u / 2 + u M / 4 ) ( u / 2 + u M / 4 ) ] 2 [ sin ( u / 2 u M / 4 ) ( u / 2 u M / 4 ) ] 2 .
I C ( u , u M ) = [ sin ( u + u M / 4 ) ( u + u M / 4 ) ] 2 [ sin ( u u M / 4 ) ( u u M / 4 ) ] 2 .
{ L = 2 L 2 θ = arc tan ( ρ D 2 L ) tan θ 1 2 = 2 L R ρ ( 1 - c o s θ 1 ) ρ D [ L 1 R ρ ( 1 cos θ 1 ) ] R ρ = ( L L 1 ) sin ( θ 2 θ 1 ) sin ( θ θ 1 ) sin ( θ 2 θ 1 ) .
R = 0 1 2 π ρ R ρ d ρ 0 1 2 π ρ d ρ = 2 0 1 ρ R ρ d ρ .
σ a x i a l L 1 ( 1 cos β ) .
f ( σ a x i a l ) = { 1 γ 1 ( 1 σ a x i a l ) 2 σ a x i a l [ 0 , 1 cos γ ] 0 else .
u ( L 1 ) a x i a l = 3 × 0.00058 2 × | L 1 | 20 .
I A ( u , u M ) = [ sin ( u / 2 + u M / 4 ) ( u / 2 + u M / 4 ) ] 2 { sin [ u / 2 ( u M u δ ) / 4 ] [ u / 2 ( u M u δ ) / 4 ] } 2 ,
I B ( u , u M ) = { sin [ ( 1 + α ) / 2 u + u M / 4 ] [ ( 1 + α ) / 2 u + u M / 4 ] } 2 { sin [ ( 1 + α ) / 2 u ( u M u δ ) / 4 ] [ ( 1 + α ) / 2 u ( u M u δ ) / 4 ] } 2 .
Δ u A = u δ 4 and Δ u B = u δ 4 ( 1 + α ) .
σ o f f s e t = α 4 ( 1 + α ) f o 2 f c 2 δ .
u ( L 1 ) o f f s e t = σ o f f s e t 3 = α 4 3 ( 1 + α ) f o 2 f c 2 δ .
σ D M I = 1 × 10 6 × L 1 .
u ( L 1 ) D M I = 1 × 10 6 × L 1 3 .
u ( L 1 ) σ 1 = σ L 1 .
u ( L 1 ) = u ( L 1 ) a x i a l 2 + u ( L 1 ) o f f s e t 2 + u ( L 1 ) D M I 2 + u ( L 1 ) σ 1 2 .
u ( L 1 ) = 3.43 × 10 3 mm .
u ( L 2 ) = 1 2 [ ( σ a x i a l 3 ) 2 + ( σ o f f s e t 3 ) 2 + ( σ D M I 3 ) 2 ] + ( σ L 2 10 ) 2
u ( L 2 ) = 1.64 × 10 3 mm .
u c ( R ) = [ c 1 u ( L 1 ) ] 2 + [ c 2 u ( L 2 ) ] 2 ,
u r e l ( R ) = u c ( R ) R × 100 % .
c 1 = 1449.59 and c 2 = 686.68.
u c ( R ) = 5.1 mm .
u r e l ( R ) = 0.026 % .

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