Abstract

Using grating shearing interferometry, a new and simple technique to measure the effective focal length of optical systems is described. The diffraction pattern of a phase grating positioned at the focal point of the lens under test is evaluated for this purpose. The relative lateral shift between the undiffracted zero order and the diffracted first orders caused by the grating is measured. By utilizing knowledge of the wavelength of light, the grating period, and the diameter of an aperture stop placed in front of the test lens, we can determine the effective focal length of the test lens. Results of measurements are presented and compared with calculated values. The dependence of the focal length on the wavelength of the light is shown by using two laser sources of different wavelengths. An analysis of the measurement accuracy is given.

© 1994 Optical Society of America

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References

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  1. D. Malacara, ed., Optical Shop Testing, 2nd ed. (Wiley, New York, 1992), Chap. 4.
  2. Y. Nakano, K. Murata, “Talbot interferometry for measuring the focal length of a lens,” Appl. Opt. 24, 3162–3166 (1985).
    [CrossRef] [PubMed]
  3. K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Talbot interferometry in noncollimated illumination for curvature and focal length measurements,” Appl. Opt. 31, 75–79 (1992).
    [CrossRef] [PubMed]
  4. K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Direct determination of focal length by using Talbot interferometry,” Appl. Opt. 31, 5984–5987 (1992).
    [CrossRef] [PubMed]
  5. D. C. Su, C. W. Chang. “A new technique for measuring the effective focal length of a thick lens or a compound lens,” Opt. Commun. 78, 118–122 (1990).
    [CrossRef]
  6. C. W. Chang, D. C. Su, “An improved technique of measuring the focal length of a lens,” Opt. Commun. 73, 257–262 (1989).
    [CrossRef]
  7. L. M. Bernardo, O. D. D. Soares, “Evaluation of the focal distance of a lens by Talbot interferometry,” Appl. Opt. 27, 296–301 (1988).
    [CrossRef] [PubMed]
  8. J. C. Bhattacharya, A. K. Aggarwal, “Measurement of the focal length of a collimating lens using the Talbot effect and the moiré technique,” Appl. Opt. 30, 4479–4480 (1991).
    [CrossRef] [PubMed]
  9. E. Keren, K. M. Kreske, O. Kafri, “Universal method for determining the focal length of optical systems by moiré deflectometry,” Appl. Opt. 27, 1383–1385 (1988).
    [CrossRef] [PubMed]
  10. I. Glatt, O. Kafri, “Determination of the focal length of nonparaxial lenses by moiré deflectometry,” Appl. Opt. 26, 2507–2508 (1987).
    [CrossRef] [PubMed]
  11. J. L. Horner, “Collimation invariant technique for measuring the focal length of a lens,” Appl. Opt. 28, 1047–1048 (1989).
    [CrossRef] [PubMed]
  12. R. S. Sirohi, H. Kumar, N. K. Jain, “Focal length measurement using diffraction at a grating,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1332, 50–55 (1990).
  13. Y. Tanaka, Y. Nagaoka, M. Ueda, “Lens and optics for optical disk system,” in Proceedings of the International Symposium on Optical Memory, Jpn. J. Appl. Phys. Suppl. 26-4, 121–126 (1987).
  14. S. Ando, S. Sekine, M. Mita, S. Katsuo, “Optical computing using optical flip-flops in Fourier processors: use in matrix multiplication and discrete linear transforms,” Appl. Opt. 28, 5363–5373 (1989).
    [CrossRef] [PubMed]
  15. B. Hillerich, “Shape analysis and coupling loss of microlenses on single-mode fiber tips,” Appl. Opt. 27, 3102–3106 (1988).
    [CrossRef] [PubMed]
  16. C. W. Barnard, J. W. Y. Lit, “Single-mode fiber microlens with controllable spot size,” Appl. Opt. 30, 1958–1962 (1991).
    [CrossRef] [PubMed]
  17. K. Rastani, C. Lin, J. S. Patel, “Active-fiber star coupler that uses arrays of microlenses and liquid-crystal modulators,” Appl. Opt. 31, 3046–3050 (1992).
    [CrossRef] [PubMed]
  18. V. Ronchi, “Forty years of history of a grating interferometer,” Appl. Opt. 3, 437–451 (1964).
    [CrossRef]
  19. F. Lei, L. K. Dang, “Measurement of the numerical aperture and f-number of a lens system by using a phase grating,” Appl. Opt. 32, 5689–5691 (1993).
    [CrossRef] [PubMed]
  20. D. E. Silva, “A simple interferometric method of beam collimation,” Appl. Opt. 10, 1980–1982 (1971).
    [CrossRef]

1993 (1)

1992 (3)

1991 (2)

1990 (1)

D. C. Su, C. W. Chang. “A new technique for measuring the effective focal length of a thick lens or a compound lens,” Opt. Commun. 78, 118–122 (1990).
[CrossRef]

1989 (3)

1988 (3)

1987 (2)

I. Glatt, O. Kafri, “Determination of the focal length of nonparaxial lenses by moiré deflectometry,” Appl. Opt. 26, 2507–2508 (1987).
[CrossRef] [PubMed]

Y. Tanaka, Y. Nagaoka, M. Ueda, “Lens and optics for optical disk system,” in Proceedings of the International Symposium on Optical Memory, Jpn. J. Appl. Phys. Suppl. 26-4, 121–126 (1987).

1985 (1)

1971 (1)

1964 (1)

Aggarwal, A. K.

Ando, S.

Barnard, C. W.

Bernardo, L. M.

Bhattacharya, J. C.

Chang, C. W.

D. C. Su, C. W. Chang. “A new technique for measuring the effective focal length of a thick lens or a compound lens,” Opt. Commun. 78, 118–122 (1990).
[CrossRef]

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

Dang, L. K.

Glatt, I.

Hillerich, B.

Horner, J. L.

Jain, N. K.

R. S. Sirohi, H. Kumar, N. K. Jain, “Focal length measurement using diffraction at a grating,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1332, 50–55 (1990).

Kafri, O.

Katsuo, S.

Keren, E.

Kothiyal, M. P.

Kreske, K. M.

Kumar, H.

R. S. Sirohi, H. Kumar, N. K. Jain, “Focal length measurement using diffraction at a grating,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1332, 50–55 (1990).

Lei, F.

Lin, C.

Lit, J. W. Y.

Mita, M.

Murata, K.

Nagaoka, Y.

Y. Tanaka, Y. Nagaoka, M. Ueda, “Lens and optics for optical disk system,” in Proceedings of the International Symposium on Optical Memory, Jpn. J. Appl. Phys. Suppl. 26-4, 121–126 (1987).

Nakano, Y.

Patel, J. S.

Rastani, K.

Ronchi, V.

Sekine, S.

Silva, D. E.

Sirohi, R. S.

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Talbot interferometry in noncollimated illumination for curvature and focal length measurements,” Appl. Opt. 31, 75–79 (1992).
[CrossRef] [PubMed]

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

R. S. Sirohi, H. Kumar, N. K. Jain, “Focal length measurement using diffraction at a grating,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1332, 50–55 (1990).

Soares, O. D. D.

Sriram, K. V.

Su, D. C.

D. C. Su, C. W. Chang. “A new technique for measuring the effective focal length of a thick lens or a compound lens,” Opt. Commun. 78, 118–122 (1990).
[CrossRef]

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

Tanaka, Y.

Y. Tanaka, Y. Nagaoka, M. Ueda, “Lens and optics for optical disk system,” in Proceedings of the International Symposium on Optical Memory, Jpn. J. Appl. Phys. Suppl. 26-4, 121–126 (1987).

Ueda, M.

Y. Tanaka, Y. Nagaoka, M. Ueda, “Lens and optics for optical disk system,” in Proceedings of the International Symposium on Optical Memory, Jpn. J. Appl. Phys. Suppl. 26-4, 121–126 (1987).

Appl. Opt. (15)

Y. Nakano, K. Murata, “Talbot interferometry for measuring the focal length of a lens,” Appl. Opt. 24, 3162–3166 (1985).
[CrossRef] [PubMed]

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Talbot interferometry in noncollimated illumination for curvature and focal length measurements,” Appl. Opt. 31, 75–79 (1992).
[CrossRef] [PubMed]

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

L. M. Bernardo, O. D. D. Soares, “Evaluation of the focal distance of a lens by Talbot interferometry,” Appl. Opt. 27, 296–301 (1988).
[CrossRef] [PubMed]

J. C. Bhattacharya, A. K. Aggarwal, “Measurement of the focal length of a collimating lens using the Talbot effect and the moiré technique,” Appl. Opt. 30, 4479–4480 (1991).
[CrossRef] [PubMed]

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

I. Glatt, O. Kafri, “Determination of the focal length of nonparaxial lenses by moiré deflectometry,” Appl. Opt. 26, 2507–2508 (1987).
[CrossRef] [PubMed]

J. L. Horner, “Collimation invariant technique for measuring the focal length of a lens,” Appl. Opt. 28, 1047–1048 (1989).
[CrossRef] [PubMed]

S. Ando, S. Sekine, M. Mita, S. Katsuo, “Optical computing using optical flip-flops in Fourier processors: use in matrix multiplication and discrete linear transforms,” Appl. Opt. 28, 5363–5373 (1989).
[CrossRef] [PubMed]

B. Hillerich, “Shape analysis and coupling loss of microlenses on single-mode fiber tips,” Appl. Opt. 27, 3102–3106 (1988).
[CrossRef] [PubMed]

C. W. Barnard, J. W. Y. Lit, “Single-mode fiber microlens with controllable spot size,” Appl. Opt. 30, 1958–1962 (1991).
[CrossRef] [PubMed]

K. Rastani, C. Lin, J. S. Patel, “Active-fiber star coupler that uses arrays of microlenses and liquid-crystal modulators,” Appl. Opt. 31, 3046–3050 (1992).
[CrossRef] [PubMed]

V. Ronchi, “Forty years of history of a grating interferometer,” Appl. Opt. 3, 437–451 (1964).
[CrossRef]

F. Lei, L. K. Dang, “Measurement of the numerical aperture and f-number of a lens system by using a phase grating,” Appl. Opt. 32, 5689–5691 (1993).
[CrossRef] [PubMed]

D. E. Silva, “A simple interferometric method of beam collimation,” Appl. Opt. 10, 1980–1982 (1971).
[CrossRef]

Opt. Commun. (2)

D. C. Su, C. W. Chang. “A new technique for measuring the effective focal length of a thick lens or a compound lens,” Opt. Commun. 78, 118–122 (1990).
[CrossRef]

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

Proceedings of the International Symposium on Optical Memory (1)

Y. Tanaka, Y. Nagaoka, M. Ueda, “Lens and optics for optical disk system,” in Proceedings of the International Symposium on Optical Memory, Jpn. J. Appl. Phys. Suppl. 26-4, 121–126 (1987).

Other (2)

D. Malacara, ed., Optical Shop Testing, 2nd ed. (Wiley, New York, 1992), Chap. 4.

R. S. Sirohi, H. Kumar, N. K. Jain, “Focal length measurement using diffraction at a grating,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1332, 50–55 (1990).

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Figures (5)

Fig. 1
Fig. 1

Optical configuration for measuring the focal length of a positive lens using a phase grating that causes the undiffracted zero order and the diffracted first orders.

Fig. 2
Fig. 2

Schematic of the experimental arrangement for measuring the focal length of a test lens: L1, L2, lenses to collimate the laser beam; L3, an imaging lens.

Fig. 3
Fig. 3

Diffracted aperture images observed through a plano–convex lens for (a) 632.8-nm wavelength, (b) 780-nm wavelength.

Fig. 4
Fig. 4

Diffracted aperture images observed through a cylindrical plano–convex lens for (a) 632.8-nm wavelength, (b) 780-nm wavelength.

Fig. 5
Fig. 5

Maximum relative error Δf′/f′ versus xr by using a positive test lens (spherical or cylindrical) for d = 200, 300, 400, 500, and 600 pixels.

Tables (2)

Tables Icon

Table 1 Specifications of Test Lenses

Tables Icon

Table 2 Results of Focal-Length Measurement of Test Lenses

Equations (6)

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

f D = l d ,
sin θ = λ p = x ( l 2 + x 2 ) 1 / 2 ,
l = x [ ( p λ ) 2 1 ] 1 / 2 .
f = D x d [ ( p λ ) 2 1 ] 1 / 2 .
f = D x r ( p n 2 1 ) 1 / 2 .
Δ f f = ± ( | Δ D D | + | Δ x x | + | Δ d d | ) .

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