Abstract

We present a simple method for measuring the effective focal length without determining the location of principle plane of the lens. The method is based on the measurement of confocal backreflection axial responses from the front and back surfaces of a reference plate with known refractive index and thickness. We proved the concept by measuring the effective focal lengths of thin singlet lenses and complex microscope objectives. The theoretical limit of measurement precision varies depending on the numerical aperture of the lens. This method can provide an alternative focal length measurement method for complex lenses or lenses that are permanently attached to other structures. Measurement errors were analyzed theoretically and improvements in measurement accuracy were discussed.

© 2011 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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2010 (1)

D. Malacara-Doblado, D. P. Salas-Peimbert, and G. Trujillo-Schiaffino, “Measuring the effective focal length and the wavefront aberrations of a lens system,” Opt. Eng. 49, 053601 (2010).
[CrossRef]

2009 (1)

2007 (2)

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

I. K. Ilev, “A simple confocal fiber-optic laser method for intraocular lens power measurement,” Eye 21, 819–823 (2007).
[CrossRef]

2005 (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]

2004 (1)

R. Kumar, A. P. Singh, A. Kapoor, and K. N. Tripathi, “Fabrication and characterization of polyvinyl-alcohol-based thin-film optical waveguides,” Opt. Eng. 43, 2134 (2004).
[CrossRef]

2002 (1)

A. A. Camacho, C. Solano, G. Martinez-Ponce, and R. Baltazar, “Simple method to measure the focal length of lenses,” Opt. Eng. 41, 2899–2902 (2002).
[CrossRef]

2001 (1)

H. J. Tiziani, T. Haist, and S. Reuter, “Optical inspection and characterization of micro-optics using confocal microscopy,” Opt. Lasers Eng. 36, 403–415 (2001).
[CrossRef]

1998 (1)

1997 (1)

C. H. Lee and J. Wang, “Noninterferometric differential confocal microscopy with 2 nm depth resolution,” Opt. Commun. 135, 233–237 (1997).
[CrossRef]

1994 (2)

O. Prakash and R. S. Ram, “Determination of focal length of convex lenses using Newton’s method,” J. Opt. 25, 135–138 (1994).
[CrossRef]

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

1992 (1)

A. J. Lewis and D. J. Pugh, “Interferometer light source and alignment aid using single-mode optical fibers,” Meas. Sci. Technol. 3, 929–930 (1992).
[CrossRef]

1988 (1)

1986 (1)

1985 (1)

1981 (1)

R. C. Kaul, “Measurement of focal length through autocollimation method,” J. Photo-Int & Remote Sensing 9, 17–20 (1981).
[CrossRef]

Baltazar, R.

A. A. Camacho, C. Solano, G. Martinez-Ponce, and R. Baltazar, “Simple method to measure the focal length of lenses,” Opt. Eng. 41, 2899–2902 (2002).
[CrossRef]

Camacho, A. A.

A. A. Camacho, C. Solano, G. Martinez-Ponce, and R. Baltazar, “Simple method to measure the focal length of lenses,” Opt. Eng. 41, 2899–2902 (2002).
[CrossRef]

Chatterjee, S.

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]

Chou, G.

Chung, P. S.

Dang, L. K.

Gorle, T.

Haist, T.

H. J. Tiziani, T. Haist, and S. Reuter, “Optical inspection and characterization of micro-optics using confocal microscopy,” Opt. Lasers Eng. 36, 403–415 (2001).
[CrossRef]

Haruna, M.

Hashimoto, H.

Ilev, I. K.

I. K. Ilev, “A simple confocal fiber-optic laser method for intraocular lens power measurement,” Eye 21, 819–823 (2007).
[CrossRef]

Kafri, O.

Kapoor, A.

R. Kumar, A. P. Singh, A. Kapoor, and K. N. Tripathi, “Fabrication and characterization of polyvinyl-alcohol-based thin-film optical waveguides,” Opt. Eng. 43, 2134 (2004).
[CrossRef]

Kaul, R. C.

R. C. Kaul, “Measurement of focal length through autocollimation method,” J. Photo-Int & Remote Sensing 9, 17–20 (1981).
[CrossRef]

Keren, E.

Kino, G.

Kreske, K.

Kumar, R.

R. Kumar, A. P. Singh, A. Kapoor, and K. N. Tripathi, “Fabrication and characterization of polyvinyl-alcohol-based thin-film optical waveguides,” Opt. Eng. 43, 2134 (2004).
[CrossRef]

Kumar, Y. P.

Lee, C. H.

C. H. Lee and J. Wang, “Noninterferometric differential confocal microscopy with 2 nm depth resolution,” Opt. Commun. 135, 233–237 (1997).
[CrossRef]

Lei, F.

Lewis, A. J.

A. J. Lewis and D. J. Pugh, “Interferometer light source and alignment aid using single-mode optical fibers,” Meas. Sci. Technol. 3, 929–930 (1992).
[CrossRef]

Malacara-Doblado, D.

D. Malacara-Doblado, D. P. Salas-Peimbert, and G. Trujillo-Schiaffino, “Measuring the effective focal length and the wavefront aberrations of a lens system,” Opt. Eng. 49, 053601 (2010).
[CrossRef]

Martinez-Ponce, G.

A. A. Camacho, C. Solano, G. Martinez-Ponce, and R. Baltazar, “Simple method to measure the focal length of lenses,” Opt. Eng. 41, 2899–2902 (2002).
[CrossRef]

Maruyama, H.

Mitsuyama, T.

Murata, K.

Nakano, Y.

Ohmi, M.

Prakash, O.

O. Prakash and R. S. Ram, “Determination of focal length of convex lenses using Newton’s method,” J. Opt. 25, 135–138 (1994).
[CrossRef]

Pugh, D. J.

A. J. Lewis and D. J. Pugh, “Interferometer light source and alignment aid using single-mode optical fibers,” Meas. Sci. Technol. 3, 929–930 (1992).
[CrossRef]

Ram, R. S.

O. Prakash and R. S. Ram, “Determination of focal length of convex lenses using Newton’s method,” J. Opt. 25, 135–138 (1994).
[CrossRef]

Reuter, S.

H. J. Tiziani, T. Haist, and S. Reuter, “Optical inspection and characterization of micro-optics using confocal microscopy,” Opt. Lasers Eng. 36, 403–415 (2001).
[CrossRef]

Salas-Peimbert, D. P.

D. Malacara-Doblado, D. P. Salas-Peimbert, and G. Trujillo-Schiaffino, “Measuring the effective focal length and the wavefront aberrations of a lens system,” Opt. Eng. 49, 053601 (2010).
[CrossRef]

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]

Singh, A. P.

R. Kumar, A. P. Singh, A. Kapoor, and K. N. Tripathi, “Fabrication and characterization of polyvinyl-alcohol-based thin-film optical waveguides,” Opt. Eng. 43, 2134 (2004).
[CrossRef]

Solano, C.

A. A. Camacho, C. Solano, G. Martinez-Ponce, and R. Baltazar, “Simple method to measure the focal length of lenses,” Opt. Eng. 41, 2899–2902 (2002).
[CrossRef]

Tajiri, H.

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]

Tiziani, H. J.

H. J. Tiziani, T. Haist, and S. Reuter, “Optical inspection and characterization of micro-optics using confocal microscopy,” Opt. Lasers Eng. 36, 403–415 (2001).
[CrossRef]

Tripathi, K. N.

R. Kumar, A. P. Singh, A. Kapoor, and K. N. Tripathi, “Fabrication and characterization of polyvinyl-alcohol-based thin-film optical waveguides,” Opt. Eng. 43, 2134 (2004).
[CrossRef]

Trujillo-Schiaffino, G.

D. Malacara-Doblado, D. P. Salas-Peimbert, and G. Trujillo-Schiaffino, “Measuring the effective focal length and the wavefront aberrations of a lens system,” Opt. Eng. 49, 053601 (2010).
[CrossRef]

Wang, J.

C. H. Lee and J. Wang, “Noninterferometric differential confocal microscopy with 2 nm depth resolution,” Opt. Commun. 135, 233–237 (1997).
[CrossRef]

Wen, J. F.

Zhao, S.

Appl. Opt. (5)

Eye (1)

I. K. Ilev, “A simple confocal fiber-optic laser method for intraocular lens power measurement,” Eye 21, 819–823 (2007).
[CrossRef]

J. Opt. (1)

O. Prakash and R. S. Ram, “Determination of focal length of convex lenses using Newton’s method,” J. Opt. 25, 135–138 (1994).
[CrossRef]

J. Photo-Int & Remote Sensing (1)

R. C. Kaul, “Measurement of focal length through autocollimation method,” J. Photo-Int & Remote Sensing 9, 17–20 (1981).
[CrossRef]

Meas. Sci. Technol. (1)

A. J. Lewis and D. J. Pugh, “Interferometer light source and alignment aid using single-mode optical fibers,” Meas. Sci. Technol. 3, 929–930 (1992).
[CrossRef]

Opt. Commun. (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]

C. H. Lee and J. Wang, “Noninterferometric differential confocal microscopy with 2 nm depth resolution,” Opt. Commun. 135, 233–237 (1997).
[CrossRef]

Opt. Eng. (3)

D. Malacara-Doblado, D. P. Salas-Peimbert, and G. Trujillo-Schiaffino, “Measuring the effective focal length and the wavefront aberrations of a lens system,” Opt. Eng. 49, 053601 (2010).
[CrossRef]

R. Kumar, A. P. Singh, A. Kapoor, and K. N. Tripathi, “Fabrication and characterization of polyvinyl-alcohol-based thin-film optical waveguides,” Opt. Eng. 43, 2134 (2004).
[CrossRef]

A. A. Camacho, C. Solano, G. Martinez-Ponce, and R. Baltazar, “Simple method to measure the focal length of lenses,” Opt. Eng. 41, 2899–2902 (2002).
[CrossRef]

Opt. Lasers Eng. (1)

H. J. Tiziani, T. Haist, and S. Reuter, “Optical inspection and characterization of micro-optics using confocal microscopy,” Opt. Lasers Eng. 36, 403–415 (2001).
[CrossRef]

Opt. Lett. (2)

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Figures (6)

Fig. 1
Fig. 1

Illustration of the parameters related to the determination of focal length of a lens. Subscripts of D and α correspond to the two different beam paths, (1) and (2).

Fig. 2
Fig. 2

Illustration of the focus from a lens on to a thin dielectric plate and its corresponding confocal axial reflection.

Fig. 3
Fig. 3

Schematic diagram of the experimental setup. (a) Pinhole-based confocal microscope setup for the measurement of single lenses with large diameter; (b) fiber-optic confocal microscope setup for the measurement of microscope objective lenses. L 1 is the lens under test and L 2 is coupling lens for both setups.

Fig. 4
Fig. 4

Axial response intensities using a thin bi-convex lens as L 1 and a 15 μm pinhole. L 2 was a (a)  10 × lens and (b)  5 × lens. A soda-lime glass plate with thickness 0.98 mm was used as the reference plate.

Fig. 5
Fig. 5

(a) Axial response intensities using a 20 × objective lens as L 1 , (b) and for another unit of the same type of lens. The reference plate was a soda-lime glass plate with thickness 1.00 mm .

Fig. 6
Fig. 6

Estimated percentage errors in EFL induced by the errors in parameters.

Equations (7)

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

NA = sin α = sin ( arctan D 2 f ) .
EFL = D 2 tan [ arcsin ( NA ) ] .
n s = [ NA 2 + ( 1 NA 2 ) ( t s / d ) 2 ] 1 / 2 .
NA = [ n s 2 ( t s / d ) 2 1 ( t s / d ) 2 ] 1 / 2 .
EFL = D 2 tan { arcsin [ n s 2 ( t s / d ) 2 1 ( t s / d ) 2 ] 1 / 2 } .
( Δ z ) 1 / 2 = 0.44 λ / ( 1 cos α ) ,
( Δ z ) 1 / 2 < t s [ 1 ( 1 NA 2 n s 2 NA 2 ) 1 / 2 ] < W D lens ,

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