Abstract

A laser reflection-confocal focal-length measurement (LRCFM) is proposed for the high-accuracy measurement of lens focal length. LRCFM uses the peak points of confocal response curves to precisely identify the lens focus and vertex of the lens last surface. LRCFM then accurately measures the distance between the two positions to determine the lens focal length. LRCFM uses conic fitting, which significantly enhances measurement accuracy by inhibiting the influence of environmental disturbance and system noise on the measurement results. The experimental results indicate that LRCFM has a relative expanded uncertainty of less than 0.0015%. Compared with existing measurement methods, LRCFM has high accuracy and a concise structure. Thus, LRCFM is a feasible method for high-accuracy focal-length measurements.

© 2013 Optical Society of America

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References

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2012 (2)

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

J. Yang, L. Qiu, W. Zhao, and H. Wu, “Laser differential reflection-confocal focal-length measurement,” Opt. Express 20, 26027–26036 (2012).
[CrossRef]

2011 (1)

2009 (1)

2008 (1)

2006 (1)

I. Ilev, “A simple confocal fibre-optic laser method for intraocular lens power measurement,” Eye 21, 819–823 (2006).
[CrossRef]

2005 (2)

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, 339–345 (2005).
[CrossRef]

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

2002 (2)

1995 (1)

1994 (1)

1992 (1)

Calogero, D.

Chatterjee, S.

Chen, J.-b.

J.-j. Wu, J.-b. Chen, A.-c. Xu, X.-y. Gao, and S. Zhuang, “Focal length measurement based on Hartmann–Shack principle,” Optik 123, 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, 339–345 (2005).
[CrossRef]

Dang, L. K.

Faaland, R. W.

Faridi, M. S.

Gao, X.-y.

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

Ilev, I.

I. Ilev, “A simple confocal fibre-optic laser method for intraocular lens power measurement,” Eye 21, 819–823 (2006).
[CrossRef]

Ilev, I. K.

James, R. H.

Kim, D.-H.

Kothiyal, M. P.

Kumarand, Y. P.

Lei, F.

Qiu, L.

Shakher, C.

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, 339–345 (2005).
[CrossRef]

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

Shi, D.

Singh, P.

Sirohi, R. S.

Sriram, K. V.

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, 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, 339–345 (2005).
[CrossRef]

Thakurand, M.

Wilson, T.

T. Wilson, “Confocal microscopy,” in Confocal Microscopy, T. Wilson, ed. (Academic, 1990), Chap. 1, pp. 1–64.

Wu, H.

Wu, J.-j.

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

Xiang, Y.

Xu, A.-c.

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

Yang, J.

Zhao, W.

Zhuang, S.

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

Appl. Opt. (7)

Chin. Opt. Lett. (1)

Eye (1)

I. Ilev, “A simple confocal fibre-optic laser method for intraocular lens power measurement,” Eye 21, 819–823 (2006).
[CrossRef]

Opt. Commun. (1)

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, 339–345 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Optik (1)

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

Other (1)

T. Wilson, “Confocal microscopy,” in Confocal Microscopy, T. Wilson, ed. (Academic, 1990), Chap. 1, pp. 1–64.

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Figures (8)

Fig. 1.
Fig. 1.

LRCFM principle. SF is the single-mode fiber, AS is the aperture stop, PBS is the polarized beam splitter, P is the quarter wave plate, Lc is the collimating lens, Lt is the test lens, R is the reflector, MO and CCD are the microscope objective and detector of the VPH, respectively, and DMI is the distance measurement interferometer.

Fig. 2.
Fig. 2.

Confocal response signals IA(u) and IB(u).

Fig. 3.
Fig. 3.

Light path schematic with VPH deviating from the Lc focus; labels as in Fig. 1.

Fig. 4.
Fig. 4.

Angles between LRCFM axes.

Fig. 5.
Fig. 5.

Confocal response signals influenced by a Gaussian beam: (a) confocal response signals near the Lt focus and (b) confocal response signals near the vertex of Lt last surface.

Fig. 6.
Fig. 6.

Experimental setup.

Fig. 7.
Fig. 7.

Signal back focal-length measurement result.

Fig. 8.
Fig. 8.

Repeatability of measurement data.

Equations (21)

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lF=2|zAzB|,
IA(u)=|0{01Pt(ρ)Pc(ρ)exp(iuρ22)J0(ν1ρ)ρdρ}2ν1dν1|2,
{ν1=πλDftr1u=π2λzD2ft2.
IA(u)=[sin(u/2)u/2]2.
IB(u)=[sin(u)u]2.
IA(u,uδM)={sin(u/2uδM/4)u/2uδM/4}2,
IB(u,uδM)={sin(uuδM/4)uuδM/4}2,
uδM=π2λδMD2fc2,
Δu1=uδM2andΔu2=uδM4.
Δl1=12ft2fc2δMandΔl2=14ft2fc2δM.
Δdeviation=2(Δl1Δl2)=12ft2fc2δM.
u1=Δdeviation3=123ft2fc2δM.
Δaxialft(cosβcosα1),
u2=Δaxial3=ft3(cosβcosα1),
IA(u)=|0[01ULC(ρ)Pt(ρ)Pc(ρ)exp(iuρ22)J0(ν1ρ)ρdρ]×[01Pt(ρ)Pc(ρ)exp(iuρ22)J0(ν1ρ)ρdρ]ν1dν1|2,
IB(u)=|0[01ULC(ρ)Pt(ρ)Pc(ρ)exp(iuρ2)J0(ν1ρ)ρdρ]×[01Pt(ρ)Pc(ρ)exp(iuρ2)J0(ν1ρ)ρdρ]ν1dν1|2,
ULC(r)={aexp(r2124.122),|r|50mm0,|r|>50mm,
ULC(ρ)={aexp(ρ26.16),|ρ|10,|ρ|>1.
u=u12+u22+u32.
u=u12+u22+u32=0.122+0.022+0.72=0.71μm.
δ=Ul¯F×100%=1.42147.4198×1000×100%0.001%,

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