Abstract

A new laser differential reflection-confocal focal-length measurement (DRCFM) method is proposed for the high-accuracy measurement of the lens focal length. DRCFM uses weak light reflected from the lens last surface to determine the vertex position of this surface. Differential confocal technology is then used to identify precisely the lens focus and vertex of the lens last surface, thereby enabling the precise measurement of the lens focal length. Compared with existing measurement methods, DRCFM has high accuracy and strong anti-interference capability. Theoretical analyses and experimental results indicate that the DRCFM relative measurement error is less than 10 ppm.

© 2012 OSA

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  1. E. Keren, K. M. Kreske, and O. Kafri, “Universal method for determining the focal length of optical systems by moire deflectometry,” Appl. Opt.27(8), 1383–1385 (1988).
    [CrossRef] [PubMed]
  2. C.-W. Chang and D.-C. Su, “An improved technique of measuring the focal length of a lens,” Opt. Commun.73(4), 257–262 (1989).
    [CrossRef]
  3. P. Singh, M. S. Faridi, C. Shakher, and R. S. Sirohi, “Measurement of focal length with phase-shifting Talbot interferometry,” Appl. Opt.44(9), 1572–1576 (2005).
    [CrossRef] [PubMed]
  4. K. V. Sriram, M. P. Kothiyal, and R. S. Sirohi, “Direct determination of focal length by using Talbot interferometry,” Appl. Opt.31(28), 5984–5987 (1992).
    [CrossRef] [PubMed]
  5. F. Lei and L. K. Dang, “Measuring the focal length of optical systems by grating shearing interferometry,” Appl. Opt.33(28), 6603–6608 (1994).
    [CrossRef] [PubMed]
  6. M. Thakur and C. Shakher, “Evaluation of the focal distance of lenses by white-light Lau phase interferometry,” Appl. Opt.41(10), 1841–1845 (2002).
    [CrossRef] [PubMed]
  7. C. J. Tay, M. Thakur, L. Chen, and C. Shakher, “Measurement of focal length of lens using phase shifting Lau phase interferometry,” Opt. Commun.248(4-6), 339–345 (2005).
    [CrossRef]
  8. S. Zhao, J. F. Wen, and P. S. Chung, “Simple focal-length measurement technique with a circular Dammann grating,” Appl. Opt.46(1), 44–49 (2007).
    [CrossRef] [PubMed]
  9. Y. P. Kumar and S. Chatterjee, “Technique for the focal-length measurement of positive lenses using Fizeau interferometry,” Appl. Opt.48(4), 730–736 (2009).
    [CrossRef] [PubMed]
  10. Y. Xiang, “Focus retrocollimated interferometry for focal-length measurements,” Appl. Opt.41(19), 3886–3889 (2002).
    [CrossRef] [PubMed]
  11. I. K. Ilev, “Simple fiber-optic autocollimation method for determining the focal lengths of optical elements,” Opt. Lett.20(6), 527–529 (1995).
    [CrossRef] [PubMed]
  12. D.-H. Kim, D. Shi, and I. K. Ilev, “Alternative method for measuring effective focal length of lenses using the front and back surface reflections from a reference plate,” Appl. Opt.50(26), 5163–5168 (2011).
    [CrossRef] [PubMed]
  13. J.- Wu, J.- Chen, A.- Xu, X.-y. Gao, and S. Zhuang, “Focal length measurement based on Hartmann-Shack principle,” Optik (Stuttg.)123(6), 485–488 (2012).
    [CrossRef]
  14. J. Wu, J. Chen, A. Xu, and X. Gao, “Uncollimated light beam illumination during the ocular aberration detection and its impact on the measurement accuracy by using Hartmann-Shack wavefront sensor,” Proc. SPIE7508, 75080V, 75080V-12 (2009).
    [CrossRef]
  15. T. G. Parham, T. J. McCarville, and M. A. Johnson, “Focal length measurements for the National Ignition Facility large lenses,” Optical Fabrication and Testing (OFT 2002), paper: OWD8.
  16. W. Zhao, R. Sun, L. Qiu, and D. Sha, “Laser differential confocal ultra-long focal length measurement,” Opt. Express17(22), 20051–20062 (2009).
    [CrossRef] [PubMed]
  17. W. Zhao, J. Tan, and L. Qiu, “Bipolar absolute differential confocal approach to higher spatial resolution,” Opt. Express12(21), 5013–5021 (2004).
    [CrossRef] [PubMed]

2012 (1)

J.- Wu, J.- Chen, A.- Xu, X.-y. Gao, and S. Zhuang, “Focal length measurement based on Hartmann-Shack principle,” Optik (Stuttg.)123(6), 485–488 (2012).
[CrossRef]

2011 (1)

2009 (3)

Y. P. Kumar and S. Chatterjee, “Technique for the focal-length measurement of positive lenses using Fizeau interferometry,” Appl. Opt.48(4), 730–736 (2009).
[CrossRef] [PubMed]

W. Zhao, R. Sun, L. Qiu, and D. Sha, “Laser differential confocal ultra-long focal length measurement,” Opt. Express17(22), 20051–20062 (2009).
[CrossRef] [PubMed]

J. Wu, J. Chen, A. Xu, and X. Gao, “Uncollimated light beam illumination during the ocular aberration detection and its impact on the measurement accuracy by using Hartmann-Shack wavefront sensor,” Proc. SPIE7508, 75080V, 75080V-12 (2009).
[CrossRef]

2007 (1)

2005 (2)

P. Singh, M. S. Faridi, C. Shakher, and R. S. Sirohi, “Measurement of focal length with phase-shifting Talbot interferometry,” Appl. Opt.44(9), 1572–1576 (2005).
[CrossRef] [PubMed]

C. J. Tay, M. Thakur, L. Chen, and C. Shakher, “Measurement of focal length of lens using phase shifting Lau phase interferometry,” Opt. Commun.248(4-6), 339–345 (2005).
[CrossRef]

2004 (1)

2002 (2)

1995 (1)

1994 (1)

1992 (1)

1989 (1)

C.-W. Chang and D.-C. Su, “An improved technique of measuring the focal length of a lens,” Opt. Commun.73(4), 257–262 (1989).
[CrossRef]

1988 (1)

Chang, C.-W.

C.-W. Chang and D.-C. Su, “An improved technique of measuring the focal length of a lens,” Opt. Commun.73(4), 257–262 (1989).
[CrossRef]

Chatterjee, S.

Chen, J.

J. Wu, J. Chen, A. Xu, and X. Gao, “Uncollimated light beam illumination during the ocular aberration detection and its impact on the measurement accuracy by using Hartmann-Shack wavefront sensor,” Proc. SPIE7508, 75080V, 75080V-12 (2009).
[CrossRef]

Chen, J.-

J.- Wu, J.- Chen, A.- Xu, X.-y. Gao, and S. Zhuang, “Focal length measurement based on Hartmann-Shack principle,” Optik (Stuttg.)123(6), 485–488 (2012).
[CrossRef]

Chen, L.

C. J. Tay, M. Thakur, L. Chen, and C. Shakher, “Measurement of focal length of lens using phase shifting Lau phase interferometry,” Opt. Commun.248(4-6), 339–345 (2005).
[CrossRef]

Chung, P. S.

Dang, L. K.

Faridi, M. S.

Gao, X.

J. Wu, J. Chen, A. Xu, and X. Gao, “Uncollimated light beam illumination during the ocular aberration detection and its impact on the measurement accuracy by using Hartmann-Shack wavefront sensor,” Proc. SPIE7508, 75080V, 75080V-12 (2009).
[CrossRef]

Gao, X.-y.

J.- Wu, J.- Chen, A.- Xu, X.-y. Gao, and S. Zhuang, “Focal length measurement based on Hartmann-Shack principle,” Optik (Stuttg.)123(6), 485–488 (2012).
[CrossRef]

Ilev, I. K.

Kafri, O.

Keren, E.

Kim, D.-H.

Kothiyal, M. P.

Kreske, K. M.

Kumar, Y. P.

Lei, F.

Qiu, L.

Sha, D.

Shakher, C.

Shi, D.

Singh, P.

Sirohi, R. S.

Sriram, K. V.

Su, D.-C.

C.-W. Chang and D.-C. Su, “An improved technique of measuring the focal length of a lens,” Opt. Commun.73(4), 257–262 (1989).
[CrossRef]

Sun, R.

Tan, J.

Tay, C. J.

C. J. Tay, M. Thakur, L. Chen, and C. Shakher, “Measurement of focal length of lens using phase shifting Lau phase interferometry,” Opt. Commun.248(4-6), 339–345 (2005).
[CrossRef]

Thakur, M.

C. J. Tay, M. Thakur, L. Chen, and C. Shakher, “Measurement of focal length of lens using phase shifting Lau phase interferometry,” Opt. Commun.248(4-6), 339–345 (2005).
[CrossRef]

M. Thakur and C. Shakher, “Evaluation of the focal distance of lenses by white-light Lau phase interferometry,” Appl. Opt.41(10), 1841–1845 (2002).
[CrossRef] [PubMed]

Wen, J. F.

Wu, J.

J. Wu, J. Chen, A. Xu, and X. Gao, “Uncollimated light beam illumination during the ocular aberration detection and its impact on the measurement accuracy by using Hartmann-Shack wavefront sensor,” Proc. SPIE7508, 75080V, 75080V-12 (2009).
[CrossRef]

Wu, J.-

J.- Wu, J.- Chen, A.- Xu, X.-y. Gao, and S. Zhuang, “Focal length measurement based on Hartmann-Shack principle,” Optik (Stuttg.)123(6), 485–488 (2012).
[CrossRef]

Xiang, Y.

Xu, A.

J. Wu, J. Chen, A. Xu, and X. Gao, “Uncollimated light beam illumination during the ocular aberration detection and its impact on the measurement accuracy by using Hartmann-Shack wavefront sensor,” Proc. SPIE7508, 75080V, 75080V-12 (2009).
[CrossRef]

Xu, A.-

J.- Wu, J.- Chen, A.- Xu, X.-y. Gao, and S. Zhuang, “Focal length measurement based on Hartmann-Shack principle,” Optik (Stuttg.)123(6), 485–488 (2012).
[CrossRef]

Zhao, S.

Zhao, W.

Zhuang, S.

J.- Wu, J.- Chen, A.- Xu, X.-y. Gao, and S. Zhuang, “Focal length measurement based on Hartmann-Shack principle,” Optik (Stuttg.)123(6), 485–488 (2012).
[CrossRef]

Appl. Opt. (9)

F. Lei and L. K. Dang, “Measuring the focal length of optical systems by grating shearing interferometry,” Appl. Opt.33(28), 6603–6608 (1994).
[CrossRef] [PubMed]

M. Thakur and C. Shakher, “Evaluation of the focal distance of lenses by white-light Lau phase interferometry,” Appl. Opt.41(10), 1841–1845 (2002).
[CrossRef] [PubMed]

Y. Xiang, “Focus retrocollimated interferometry for focal-length measurements,” Appl. Opt.41(19), 3886–3889 (2002).
[CrossRef] [PubMed]

K. V. Sriram, M. P. Kothiyal, and R. S. Sirohi, “Direct determination of focal length by using Talbot interferometry,” Appl. Opt.31(28), 5984–5987 (1992).
[CrossRef] [PubMed]

P. Singh, M. S. Faridi, C. Shakher, and R. S. Sirohi, “Measurement of focal length with phase-shifting Talbot interferometry,” Appl. Opt.44(9), 1572–1576 (2005).
[CrossRef] [PubMed]

S. Zhao, J. F. Wen, and P. S. Chung, “Simple focal-length measurement technique with a circular Dammann grating,” Appl. Opt.46(1), 44–49 (2007).
[CrossRef] [PubMed]

E. Keren, K. M. Kreske, and O. Kafri, “Universal method for determining the focal length of optical systems by moire deflectometry,” Appl. Opt.27(8), 1383–1385 (1988).
[CrossRef] [PubMed]

Y. P. Kumar and S. Chatterjee, “Technique for the focal-length measurement of positive lenses using Fizeau interferometry,” Appl. Opt.48(4), 730–736 (2009).
[CrossRef] [PubMed]

D.-H. Kim, D. Shi, and I. K. Ilev, “Alternative method for measuring effective focal length of lenses using the front and back surface reflections from a reference plate,” Appl. Opt.50(26), 5163–5168 (2011).
[CrossRef] [PubMed]

Opt. Commun. (2)

C.-W. Chang and D.-C. Su, “An improved technique of measuring the focal length of a lens,” Opt. Commun.73(4), 257–262 (1989).
[CrossRef]

C. J. Tay, M. Thakur, L. Chen, and C. Shakher, “Measurement of focal length of lens using phase shifting Lau phase interferometry,” Opt. Commun.248(4-6), 339–345 (2005).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Optik (Stuttg.) (1)

J.- Wu, J.- Chen, A.- Xu, X.-y. Gao, and S. Zhuang, “Focal length measurement based on Hartmann-Shack principle,” Optik (Stuttg.)123(6), 485–488 (2012).
[CrossRef]

Proc. SPIE (1)

J. Wu, J. Chen, A. Xu, and X. Gao, “Uncollimated light beam illumination during the ocular aberration detection and its impact on the measurement accuracy by using Hartmann-Shack wavefront sensor,” Proc. SPIE7508, 75080V, 75080V-12 (2009).
[CrossRef]

Other (1)

T. G. Parham, T. J. McCarville, and M. A. Johnson, “Focal length measurements for the National Ignition Facility large lenses,” Optical Fabrication and Testing (OFT 2002), paper: OWD8.

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Figures (6)

Fig. 1
Fig. 1

DRCFM principle. PBS is the polarized beam splitter, P is the one-fourth wave plate, Lc is the collimating lens, Lt is the test lens, R is the reflector, BS is the beam splitter, CCD1 and CCD2 are detectors, MO1 and MO2 are microscope objectives, M is the offset of the VPHs from the focus of Lc, and DMI is distance measurement interferometer.

Fig. 2
Fig. 2

Determination of the best offset of the VPHs: (a) focusing sensitivity curves, (b) differential confocal response signals.

Fig. 3
Fig. 3

Angles between DRCFM axes.

Fig. 4
Fig. 4

Light path schematics with different offsets.

Fig. 5
Fig. 5

Experimental setup. (1) He-Ne laser, (2) single-mode fiber, (3) VPH1, (4) VPH2, (5) beam splitter, (6) polarized beam splitter, (7) one-fourth wave plate, (8) aiming system, (9) beam splitter, (10) collimating lens, (11) test lens, (12) reflector, (13) air bearing slider, (14) XL-80 laser interferometer produced by Renishaw, and (15) air sensor of XL-80.

Fig. 6
Fig. 6

Back focal length measurement curves.

Equations (24)

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l F =2| z A z B |,
I A1 ( ν 2 ,u,+ u M )=| 0 { 0 1 P t (ρ) P c (ρ)exp( iu ρ 2 2 ) J 0 ( ν 1 ρ )ρdρ } × { 0 1 P t (ρ) P c (ρ)exp[ i ρ 2 ( u 2 u M 2 ) ] 0 2π J 0 ( ρ ν 1 2 + ν 2 2 +2 ν 1 ν 2 cosθ ) dθρdρ } ν 1 d ν 1 | 2 ,
I A2 ( ν 2 ,u, u M )=| 0 { 0 1 P t (ρ) P c (ρ)exp( iu ρ 2 2 ) J 0 ( ν 1 ρ )ρdρ } × { 0 1 P t (ρ) P c (ρ)exp[ i ρ 2 ( u 2 + u M 2 ) ] 0 2π J 0 ( ρ ν 1 2 + ν 2 2 +2 ν 1 ν 2 cosθ ) dθρdρ } ν 1 d ν 1 | 2 ,
{ ν 1 = π λ D f t r 1 u= π 2λ z D 2 f t 2 and{ ν 2 = π λ D f c r 2 u M = π 2λ M D 2 f c 2 .
I A (u, u M )= I A1 (0,u,+ u M ) I A2 (0,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 B (u, u M )= [ sin( u u M /4 ) u u M /4 ] 2 [ sin( u+ u M /4 ) u+ u M /4 ] 2 .
f t '= l F + r b 2 n(r 2 r 1 )+(n1)b ,
S A (0, u M )=| I A ( u, u M ) u | u=0 |=| 2sin u M 4 ( sin u M 4 u M 4 cos u M 4 ) / ( u M 4 ) 3 |,
S B (0, u M )=| I B ( u, u M ) u | u=0 |=| 4sin u M 4 ( sin u M 4 u M 4 cos u M 4 ) / ( u M 4 ) 3 |.
S Amax = S A (0,5.21)=0.54and S Bmax = S B (0,5.21)=1.08.
σ z A = δ I A ( u, u M ) S A max 2λ π (D/ f t ) 2 = 2λ 0.54πSNR (D/ f t ) 2 ,
σ z B = δ I B ( u, u M ) S B max 2λ π (D/ f t ) 2 = 2λ 1.08πSNR (D/ f t ) 2 ,
σ axial f t ( cosβ cosα 1 ).
I A (u, u M )= { sin( u/2 u M /4 ) u/2 u M /4 } 2 { sin[ u/2 + ( u M u δM ) /4 ] u/2 + ( u M u δM ) /4 } 2 ,
I B (u, u M )= { sin( u u M /4 ) u u M /4 } 2 { sin[ u+ ( u M u δM ) /4 ] u+ ( u M u δM ) /4 } 2 .
Δ u 1 = u δM 4 andΔ u 2 = u δM 8 .
Δ l 1 = 1 4 f t 2 f c 2 δ M andΔ l 2 = 1 8 f t 2 f c 2 δ M .
σ offset =2( Δ l 1 Δ l 2 )= 1 4 f t 2 f c 2 δ M .
σ L =1×L ppm,
σ l F = ( l F L σ L ) 2 + ( l F z A σ z A ) 2 + ( l F z B σ z B ) 2 + σ offset 2 + σ axial 2 .
l F L =2, l F z A =2,and l F z B =2.
σ l F = 4 σ L 2 +4σ z A 2 +4σ z B 2 + σ offset 2 + σ axial 2 .
σ l F = 4 σ L 2 +4σ z A 2 +4σ z B 2 + σ axial 2 + σ offset 2 = 4× 0.1 2 +4× 0.75 2 +4× 0.37 2 + 0.03 2 + 0.1 2 =1.7 μm.
δ= σ l F l F ×100%= 1.7 198.6918×1000 ×100%0.00086%=8.6 ppm.

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