Abstract

This paper proposes a laser differential confocal cylindrical radius of curvature measurement (DCCRM) method for high accuracy measurement of the radius of curvature of the cylindrical lens. Based on the property that the null point of an axial intensity curve precisely corresponds to the focus of the objective in a differential confocal system (DCS), the DCCRM uses the null point of the DCS axial intensity curve to precisely identify the cat’s eye position and confocal position of the test cylindrical lens. The distance between the two positions is measured accurately using a laser distance instrument, thus achieving high precision radius measurement. In comparison with existing measurement methods, the proposed DCCRM has high measurement precision and strong environmental anti-interference capability. Theoretical analyses and preliminary experimental results indicate that the DCCRM has a relative measurement uncertainty of better than 0.03% and provides a new approach for a high precision radius measurement of the cylindrical lens.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  14. C. B. Lin, S. H. Yan, Z. G. Du, G. C. Wang, and C. H. Wei, “Symmetrical short-period and high signal-to-noise ratio heterodyne grating interferometer,” Chin. Opt. Lett. 13(10), 100501 (2015).
    [Crossref]
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    [Crossref] [PubMed]
  16. J. Peng, H. Xu, Y. Yu, and M. Chen, “Stitching interferometry for cylindrical optics with large angular aperture,” Meas. Sci. Technol. 26(2), 025204 (2015).
    [Crossref]
  17. W. Zhao, J. Tan, and L. Qiu, “Bipolar absolute differential confocal approach to higher spatial resolution,” Opt. Express 12(21), 5013–5021 (2004).
    [Crossref] [PubMed]
  18. D. Malacara, Optical Shop Testing (Wiley Interscience Publication, 2007).

2015 (2)

C. B. Lin, S. H. Yan, Z. G. Du, G. C. Wang, and C. H. Wei, “Symmetrical short-period and high signal-to-noise ratio heterodyne grating interferometer,” Chin. Opt. Lett. 13(10), 100501 (2015).
[Crossref]

J. Peng, H. Xu, Y. Yu, and M. Chen, “Stitching interferometry for cylindrical optics with large angular aperture,” Meas. Sci. Technol. 26(2), 025204 (2015).
[Crossref]

2013 (1)

2012 (1)

H. Liu, “Measurement accuracy verification of aspheric surface test with computer-generated hologram,” Chin. Opt. Lett. 10(7), 0171201 (2012).

2007 (1)

2005 (1)

R. Schreiner, T. Herrmann, J. Roder, S. Muller-Pfeiffer, and O. Falkenstorfer, “Computer generated holograms for optical shop testing of aspheres,” Proc. SPIE 5856, 503–508 (2005).
[Crossref]

2004 (1)

2002 (1)

S. Reichelt, C. Pruss, and H. J. Tiziani, “New design techniques and calibration methods for CGH-null testing of aspheric surfaces,” Proc. SPIE 4778, 158–168 (2002).
[Crossref]

2001 (3)

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]

R. P. Shukla, D. V. Udupa, and A. K. Sinha, “Simple method for measuring long radius of curvature of metal cylindrical surface,” J. Opt. 30(2), 73–83 (2001).
[Crossref]

N. Lindlein, J. Lamprecht, K. Mantel, and J. Schwider, “Interferometrical measurement of cylindrical lens with the help of computer generated holograms,” Proc. SPIE 440, 127–134 (2001).
[Crossref]

1998 (1)

S. Brinkmann, R. Schreiner, T. Dresel, and J. Schwider, “Interferometric testing of plane and cylindrical workpieces with computer-generated holograms,” Opt. Eng. 37(9), 2506–2511 (1998).
[Crossref]

1996 (1)

S. G. Shiue, T. S. Liao, S. T. Chang, C. F. Kao, and Y. F. Chen, “Apparatus for measuring the curvature of spherical and cylindrical surfaces,” Rev. Sci. Instrum. 67(4), 1688 (1996).
[Crossref]

1995 (1)

1992 (2)

Adibi, A.

Brinkmann, S.

S. Brinkmann, R. Schreiner, T. Dresel, and J. Schwider, “Interferometric testing of plane and cylindrical workpieces with computer-generated holograms,” Opt. Eng. 37(9), 2506–2511 (1998).
[Crossref]

Bülow, H.

Chang, S. T.

S. G. Shiue, T. S. Liao, S. T. Chang, C. F. Kao, and Y. F. Chen, “Apparatus for measuring the curvature of spherical and cylindrical surfaces,” Rev. Sci. Instrum. 67(4), 1688 (1996).
[Crossref]

Chen, M.

J. Peng, H. Xu, Y. Yu, and M. Chen, “Stitching interferometry for cylindrical optics with large angular aperture,” Meas. Sci. Technol. 26(2), 025204 (2015).
[Crossref]

J. Peng, D. Ge, Y. Yu, K. Wang, and M. Chen, “Method of misalignment aberrations removal in null test of cylindrical surface,” Appl. Opt. 52(30), 7311–7323 (2013).
[Crossref] [PubMed]

Chen, Y. F.

S. G. Shiue, T. S. Liao, S. T. Chang, C. F. Kao, and Y. F. Chen, “Apparatus for measuring the curvature of spherical and cylindrical surfaces,” Rev. Sci. Instrum. 67(4), 1688 (1996).
[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]

Dresel, T.

S. Brinkmann, R. Schreiner, T. Dresel, and J. Schwider, “Interferometric testing of plane and cylindrical workpieces with computer-generated holograms,” Opt. Eng. 37(9), 2506–2511 (1998).
[Crossref]

Du, Z. G.

Evans, C. J.

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]

Falkenstorfer, O.

R. Schreiner, T. Herrmann, J. Roder, S. Muller-Pfeiffer, and O. Falkenstorfer, “Computer generated holograms for optical shop testing of aspheres,” Proc. SPIE 5856, 503–508 (2005).
[Crossref]

Fan, P. Z.

Ge, D.

Guo, X.

Herrmann, T.

R. Schreiner, T. Herrmann, J. Roder, S. Muller-Pfeiffer, and O. Falkenstorfer, “Computer generated holograms for optical shop testing of aspheres,” Proc. SPIE 5856, 503–508 (2005).
[Crossref]

Hsieh, C.

Jin, R. S.

Kao, C. F.

S. G. Shiue, T. S. Liao, S. T. Chang, C. F. Kao, and Y. F. Chen, “Apparatus for measuring the curvature of spherical and cylindrical surfaces,” Rev. Sci. Instrum. 67(4), 1688 (1996).
[Crossref]

Lamprecht, J.

N. Lindlein, J. Lamprecht, K. Mantel, and J. Schwider, “Interferometrical measurement of cylindrical lens with the help of computer generated holograms,” Proc. SPIE 440, 127–134 (2001).
[Crossref]

Liao, T. S.

S. G. Shiue, T. S. Liao, S. T. Chang, C. F. Kao, and Y. F. Chen, “Apparatus for measuring the curvature of spherical and cylindrical surfaces,” Rev. Sci. Instrum. 67(4), 1688 (1996).
[Crossref]

Lin, C. B.

Lindlein, N.

N. Lindlein, J. Lamprecht, K. Mantel, and J. Schwider, “Interferometrical measurement of cylindrical lens with the help of computer generated holograms,” Proc. SPIE 440, 127–134 (2001).
[Crossref]

Liu, H.

H. Liu, “Measurement accuracy verification of aspheric surface test with computer-generated hologram,” Chin. Opt. Lett. 10(7), 0171201 (2012).

Mantel, K.

N. Lindlein, J. Lamprecht, K. Mantel, and J. Schwider, “Interferometrical measurement of cylindrical lens with the help of computer generated holograms,” Proc. SPIE 440, 127–134 (2001).
[Crossref]

Momtahan, O.

Muller-Pfeiffer, S.

R. Schreiner, T. Herrmann, J. Roder, S. Muller-Pfeiffer, and O. Falkenstorfer, “Computer generated holograms for optical shop testing of aspheres,” Proc. SPIE 5856, 503–508 (2005).
[Crossref]

Peng, J.

J. Peng, H. Xu, Y. Yu, and M. Chen, “Stitching interferometry for cylindrical optics with large angular aperture,” Meas. Sci. Technol. 26(2), 025204 (2015).
[Crossref]

J. Peng, D. Ge, Y. Yu, K. Wang, and M. Chen, “Method of misalignment aberrations removal in null test of cylindrical surface,” Appl. Opt. 52(30), 7311–7323 (2013).
[Crossref] [PubMed]

Pruss, C.

S. Reichelt, C. Pruss, and H. J. Tiziani, “New design techniques and calibration methods for CGH-null testing of aspheric surfaces,” Proc. SPIE 4778, 158–168 (2002).
[Crossref]

Qiu, L.

Reichelt, S.

S. Reichelt, C. Pruss, and H. J. Tiziani, “New design techniques and calibration methods for CGH-null testing of aspheric surfaces,” Proc. SPIE 4778, 158–168 (2002).
[Crossref]

Roder, J.

R. Schreiner, T. Herrmann, J. Roder, S. Muller-Pfeiffer, and O. Falkenstorfer, “Computer generated holograms for optical shop testing of aspheres,” Proc. SPIE 5856, 503–508 (2005).
[Crossref]

Schellhorn, M.

Schmitz, T. L.

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]

Schreiner, R.

R. Schreiner, T. Herrmann, J. Roder, S. Muller-Pfeiffer, and O. Falkenstorfer, “Computer generated holograms for optical shop testing of aspheres,” Proc. SPIE 5856, 503–508 (2005).
[Crossref]

S. Brinkmann, R. Schreiner, T. Dresel, and J. Schwider, “Interferometric testing of plane and cylindrical workpieces with computer-generated holograms,” Opt. Eng. 37(9), 2506–2511 (1998).
[Crossref]

Schwider, J.

N. Lindlein, J. Lamprecht, K. Mantel, and J. Schwider, “Interferometrical measurement of cylindrical lens with the help of computer generated holograms,” Proc. SPIE 440, 127–134 (2001).
[Crossref]

S. Brinkmann, R. Schreiner, T. Dresel, and J. Schwider, “Interferometric testing of plane and cylindrical workpieces with computer-generated holograms,” Opt. Eng. 37(9), 2506–2511 (1998).
[Crossref]

Selberg, L. A.

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

Shiue, S. G.

S. G. Shiue, T. S. Liao, S. T. Chang, C. F. Kao, and Y. F. Chen, “Apparatus for measuring the curvature of spherical and cylindrical surfaces,” Rev. Sci. Instrum. 67(4), 1688 (1996).
[Crossref]

Shukla, R. P.

R. P. Shukla, D. V. Udupa, and A. K. Sinha, “Simple method for measuring long radius of curvature of metal cylindrical surface,” J. Opt. 30(2), 73–83 (2001).
[Crossref]

Sinha, A. K.

R. P. Shukla, D. V. Udupa, and A. K. Sinha, “Simple method for measuring long radius of curvature of metal cylindrical surface,” J. Opt. 30(2), 73–83 (2001).
[Crossref]

Tan, J.

Tiziani, H. J.

S. Reichelt, C. Pruss, and H. J. Tiziani, “New design techniques and calibration methods for CGH-null testing of aspheric surfaces,” Proc. SPIE 4778, 158–168 (2002).
[Crossref]

Udupa, D. V.

R. P. Shukla, D. V. Udupa, and A. K. Sinha, “Simple method for measuring long radius of curvature of metal cylindrical surface,” J. Opt. 30(2), 73–83 (2001).
[Crossref]

Wang, G. C.

Wang, K.

Wei, C. H.

Xu, H.

J. Peng, H. Xu, Y. Yu, and M. Chen, “Stitching interferometry for cylindrical optics with large angular aperture,” Meas. Sci. Technol. 26(2), 025204 (2015).
[Crossref]

Xu, Z. Z.

Yan, S. H.

Yu, Y.

J. Peng, H. Xu, Y. Yu, and M. Chen, “Stitching interferometry for cylindrical optics with large angular aperture,” Meas. Sci. Technol. 26(2), 025204 (2015).
[Crossref]

J. Peng, D. Ge, Y. Yu, K. Wang, and M. Chen, “Method of misalignment aberrations removal in null test of cylindrical surface,” Appl. Opt. 52(30), 7311–7323 (2013).
[Crossref] [PubMed]

Zhang, Z. Q.

Zhao, W.

Zhou, J. Z.

Appl. Opt. (2)

Chin. Opt. Lett. (2)

C. B. Lin, S. H. Yan, Z. G. Du, G. C. Wang, and C. H. Wei, “Symmetrical short-period and high signal-to-noise ratio heterodyne grating interferometer,” Chin. Opt. Lett. 13(10), 100501 (2015).
[Crossref]

H. Liu, “Measurement accuracy verification of aspheric surface test with computer-generated hologram,” Chin. Opt. Lett. 10(7), 0171201 (2012).

J. Opt. (1)

R. P. Shukla, D. V. Udupa, and A. K. Sinha, “Simple method for measuring long radius of curvature of metal cylindrical surface,” J. Opt. 30(2), 73–83 (2001).
[Crossref]

Meas. Sci. Technol. (1)

J. Peng, H. Xu, Y. Yu, and M. Chen, “Stitching interferometry for cylindrical optics with large angular aperture,” Meas. Sci. Technol. 26(2), 025204 (2015).
[Crossref]

Opt. Eng. (2)

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

S. Brinkmann, R. Schreiner, T. Dresel, and J. Schwider, “Interferometric testing of plane and cylindrical workpieces with computer-generated holograms,” Opt. Eng. 37(9), 2506–2511 (1998).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Proc. SPIE (4)

N. Lindlein, J. Lamprecht, K. Mantel, and J. Schwider, “Interferometrical measurement of cylindrical lens with the help of computer generated holograms,” Proc. SPIE 440, 127–134 (2001).
[Crossref]

R. Schreiner, T. Herrmann, J. Roder, S. Muller-Pfeiffer, and O. Falkenstorfer, “Computer generated holograms for optical shop testing of aspheres,” Proc. SPIE 5856, 503–508 (2005).
[Crossref]

S. Reichelt, C. Pruss, and H. J. Tiziani, “New design techniques and calibration methods for CGH-null testing of aspheric surfaces,” Proc. SPIE 4778, 158–168 (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]

Rev. Sci. Instrum. (1)

S. G. Shiue, T. S. Liao, S. T. Chang, C. F. Kao, and Y. F. Chen, “Apparatus for measuring the curvature of spherical and cylindrical surfaces,” Rev. Sci. Instrum. 67(4), 1688 (1996).
[Crossref]

Other (2)

T. L. Schmitz, C. J. Evans, A. Davies, and W. T. Estler, “Displacement uncertainty in interferometric radius measurements,” CIRP. Annals-manufacturing technology. 51, 451–454 (2002).
[Crossref]

D. Malacara, Optical Shop Testing (Wiley Interscience Publication, 2007).

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Figures (14)

Fig. 1
Fig. 1 DCCRM principle. S is laser source, PBS is polarized beam splitter, WP is λ/4 wave plate, Lc is collimating lens, CWG is cylindrical wave generator, BS is beam splitter, P1 and P2 are pinholes, D1 and D2 are detector sand Lt is test cylindrical lens.
Fig. 2
Fig. 2 Differential confocal simulation curves.
Fig. 3
Fig. 3 Differential confocal simulation curves for different D.
Fig. 4
Fig. 4 Differential confocal simulation curves for different fo.
Fig. 5
Fig. 5 Differential confocal simulation curves for different pinhole offset zM.
Fig. 6
Fig. 6 Differential confocal simulation curves for different vP. (a) Intensity curves (b) focusing sensitivity.
Fig. 7
Fig. 7 Light path schematics with different offsets.
Fig. 8
Fig. 8 Angles between DCCRM axes.
Fig. 9
Fig. 9 DCCRM simulation curves with figure error w(ρ,θ). (a) Defocus. (b) Primary astigmatism at 0°.
Fig. 10
Fig. 10 Light path schematics with offset of laser source.
Fig. 11
Fig. 11 DCCRM main structure schematic.
Fig. 12
Fig. 12 Experimental setup.
Fig. 13
Fig. 13 Single measurement result of the test cylindrical lens.
Fig. 14
Fig. 14 10 measurement results of the test cylindrical lens.

Tables (1)

Tables Icon

Table 1 Figure measurements of the test cylindrical lens

Equations (22)

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I(z, z M )= 1 D 2 | + P c (ξ,η) P c (ξ,η) P o (η) P o (η)exp(i kz f o 2 η 2 )exp(i k z M 2 f c 2 η 2 )dξdη | 2 1 D 2 | + P c (ξ,η) P c (ξ,η) P o (η) P o (η)exp(i kz f o 2 η 2 )exp(i k z M 2 f c 2 η 2 )dξdη | 2
I(z, z M )= I 1 (z, z M ) I 2 (z, z M ) = | 1 π 0 2π 0 1 exp(ik( z f o 2 + z M 2 f c 2 ) D 2 4 ρ 2 cos 2 θ) ρdρdθ | 2 | 1 π 0 2π 0 1 exp(ik( z f o 2 z M 2 f c 2 ) D 2 4 ρ 2 cos 2 θ) ρdρdθ | 2
R= Z A Z B
I( ν p ,z, z M )= 0 ν p [ I 1 (ν,z, z M ) I 2 (ν,z, z M ) ]νdν = 0 ν p [ | 1 π 0 2π 0 1 exp(ik( z f o 2 + z M 2 f c 2 ) D 2 4 ρ 2 cos 2 θ) J 0 (ρν)ρdρdθ | 2 | 1 π 0 2π 0 1 exp(ik( z f o 2 z M 2 f c 2 ) D 2 4 ρ 2 cos 2 θ) J 0 (ρν)ρdρdθ | 2 ]νdν
u 1 = 0.5× 10 6 ×R 2 =2.5× 10 7 R DMI
I A ' (z, z M )= | 1 π 0 2π 0 1 exp( i2π λ ( z f o 2 + z M 2 f c 2 ) D 2 4 ρ 2 cos 2 θ) ρdρdθ | 2 | 1 π 0 2π 0 1 exp( i2π λ ( z f o 2 z M + z σ M 2 f c 2 ) D 2 4 ρ 2 cos 2 θ) ρdρdθ | 2
I B ' (z, z M )= | 1 π 0 2π 0 1 exp( i2π λ ( z f o 2 + z M 2 f c 2 ) D 2 4 ρ 2 cos 2 θ) ρdρdθ | 2 | 1 π 0 2π 0 1 exp( i2π λ ( z f o 2 z M + z σ M 2 f c 2 ) D 2 4 ρ 2 cos 2 θ) ρdρdθ | 2
Δ R A = R M (1cosα)
u 2 = Δ R A 3 = R M (1cosα) 3
w(ρ,θ)= j a j Z j (ρ,θ)
I A (z, z M ) = | 1 π 0 2π 0 1 exp(ik( z f o 2 + z 2 f c 2 ) D 2 4 ρ 2 cos 2 θ) exp(ik[ w(ρ,θ)+w(ρ,π+θ) ])ρdρdθ | 2 | 1 π 0 2π 0 1 exp(ik( z f o 2 z 2 f c 2 ) D 2 4 ρ 2 cos 2 θ) exp(ik[ w(ρ,θ)+w(ρ,π+θ) ])ρdρdθ | 2
I B (z, z M )= | 1 π 0 2π 0 1 exp(ik( z f o 2 + z 2 f c 2 ) D 2 4 ρ 2 cos 2 θ) exp(2ikw(ρ,θ))ρdρdθ | 2 | 1 π 0 2π 0 1 exp(ik( z f o 2 z 2 f c 2 ) D 2 4 ρ 2 cos 2 θ) exp(2ikw(ρ,θ))ρdρdθ | 2
ΔR=Δ R A Δ R B
u 3 = λ 8k =0.04 μm
I A ' (Δ z A , z M )= | 1 π 0 2π 0 1 exp( i2π λ ( Δ z A f o 2 + ΔS 2 f c 2 + z M 2 f c 2 ) D 2 4 ρ 2 cos 2 θ) ρdρdθ | 2 | 1 π 0 2π 0 1 exp( i2π λ ( Δ z A f o 2 + ΔS 2 f c 2 z M 2 f c 2 ) D 2 4 ρ 2 cos 2 θ) ρdρdθ | 2 =0
I B ' (Δ z B , z M )= | 1 π 0 2π 0 1 exp( i2π λ ( Δ z B f o 2 + ΔS 2 f c 2 + z M 2 f c 2 ) D 2 4 ρ 2 cos 2 θ) ρdρdθ | 2 | 1 π 0 2π 0 1 exp( i2π λ ( Δ z B f o 2 + ΔS 2 f c 2 z M 2 f c 2 ) D 2 4 ρ 2 cos 2 θ) ρdρdθ | 2 =0
Δ z A =Δ z B = ΔS 2 f o 2 f c 2
u= u 1 2 + u 2 2 + u 3 2 + u 4 2
ΔR=Δ R A Δ R B =0.00870.0061=0.0026 mm
R=(25.858210.0026)=25.85561 mm
u= u 1 2 + u 2 2 + u 3 2 + u 4 2 =0.003167 mm
U= 2u R ×100%= 2×0.003166 mm 25.85561 mm ×100%=0.024%

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