Abstract

The application of multiple-beam shearing interferometry to lens focal-length measurement is described. A coated shearing plate interferometer was used in transmission to produce sharp multiple-beam fringes that rotate as the collimation of the incoming wave front from the lens under test changes. The test lens was used to collimate light from a point source that was translated longitudinally, and the focal length was determined from the rate of rotation of the fringes as the source moved. This method is simple, accurate, and lends itself to automatic determination of focal length.

© 1999 Optical Society of America

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References

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  1. R. Kingslake, ed., Applied Optics and Optical Engineering, (Academic, New York, 1965), Vol. 1, pp. 208–226.
  2. F. M. Dicky, T. M. Harder, “Shearing plate optical alignment,” Opt. Eng. 17, 295–298 (1978).
  3. M. V. R. K. Murty, R. P. Shukla, “Measurement of long radii of curvature,” Opt. Eng. 22, 231–235 (1983).
    [CrossRef]
  4. M. E. Riley, R. A. Gusinow, “Laser beam divergence utilizing a lateral shearing interferometer,” Appl. Opt. 16, 2753–2756 (1977).
    [CrossRef] [PubMed]
  5. J. Choi, M. Perera, M. D. Aggarwal, R. P. Shukla, M. V. Montravadi, “Wedge plate shearing interferometers for collimation testing: use of a moiré technique,” Appl. Opt. 34, 3628–3638 (1995).
    [CrossRef] [PubMed]
  6. H. Zhang, M. J. Lalor, D. R. Burton, “Improved collimation testing technique using a digital moiré method,” Opt. Eng. 36, 3318–3322 (1997).
    [CrossRef]
  7. J. C. Fouere, D. Malacara, “Focusing errors in a collimating lens or mirror: use of a moiré technique,” Appl. Opt. 13, 1322–1326 (1974).
    [CrossRef]
  8. K. Patorski, S. Yokozeki, T. Suzuki, “Collimation test by double grating shearing interferometer,” Appl. Opt. 15, 1234–1240 (1976).
    [CrossRef] [PubMed]
  9. Melles Griot, “Lasers and instruments guide: theory and uses of shear plate collimation testers” (Melles Griot, Irvine, Calif., 1994), pp. 135-12–135-16.
  10. Y. Nakano, K. Murata, “Talbot interferometry for measuring the focal length of a lens,” Appl. Opt. 24, 3162–3166 (1985).
    [CrossRef] [PubMed]
  11. C. W. Chang, D. C. Su, “An improved technique for measuring the focal length of a lens,” Opt. Commun. 73, 257–262 (1989).
    [CrossRef]
  12. 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]
  13. 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]
  14. M. de Angelis, S. de Nicola, P. Ferrao, A. Finizio, G. Pierattini, “A new approach to high accuracy measurement of the focal lengths of lenses using a digital Fourier transform,” Opt. Commun. 136, 370–374 (1997).
    [CrossRef]
  15. S. de Nicola, P. Ferrao, A. Finizio, G. Pierattini, “Reflective grating interferometer for measuring the focal length of a lens by digital moiré effect,” Opt. Commun. 132, 432–436 (1996).
    [CrossRef]
  16. K. Matsuda, M. Roy, P. W. Fekete, T. Eiju, C. J. R. Sheppard, J. W. O’Byrne, “A novel method for beam collimation using multiple beam shearing interferometry” in Flatness, Roughness, and Discrete Defects Characterization for Computer Disks, Wafers, and Flat Panel Displays II, Proc. SPIE3275, 2–8 (1998).
    [CrossRef]

1997

H. Zhang, M. J. Lalor, D. R. Burton, “Improved collimation testing technique using a digital moiré method,” Opt. Eng. 36, 3318–3322 (1997).
[CrossRef]

M. de Angelis, S. de Nicola, P. Ferrao, A. Finizio, G. Pierattini, “A new approach to high accuracy measurement of the focal lengths of lenses using a digital Fourier transform,” Opt. Commun. 136, 370–374 (1997).
[CrossRef]

1996

S. de Nicola, P. Ferrao, A. Finizio, G. Pierattini, “Reflective grating interferometer for measuring the focal length of a lens by digital moiré effect,” Opt. Commun. 132, 432–436 (1996).
[CrossRef]

1995

1992

1990

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

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

1985

1983

M. V. R. K. Murty, R. P. Shukla, “Measurement of long radii of curvature,” Opt. Eng. 22, 231–235 (1983).
[CrossRef]

1978

F. M. Dicky, T. M. Harder, “Shearing plate optical alignment,” Opt. Eng. 17, 295–298 (1978).

1977

1976

1974

Aggarwal, M. D.

Burton, D. R.

H. Zhang, M. J. Lalor, D. R. Burton, “Improved collimation testing technique using a digital moiré method,” Opt. Eng. 36, 3318–3322 (1997).
[CrossRef]

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 for measuring the focal length of a lens,” Opt. Commun. 73, 257–262 (1989).
[CrossRef]

Choi, J.

de Angelis, M.

M. de Angelis, S. de Nicola, P. Ferrao, A. Finizio, G. Pierattini, “A new approach to high accuracy measurement of the focal lengths of lenses using a digital Fourier transform,” Opt. Commun. 136, 370–374 (1997).
[CrossRef]

de Nicola, S.

M. de Angelis, S. de Nicola, P. Ferrao, A. Finizio, G. Pierattini, “A new approach to high accuracy measurement of the focal lengths of lenses using a digital Fourier transform,” Opt. Commun. 136, 370–374 (1997).
[CrossRef]

S. de Nicola, P. Ferrao, A. Finizio, G. Pierattini, “Reflective grating interferometer for measuring the focal length of a lens by digital moiré effect,” Opt. Commun. 132, 432–436 (1996).
[CrossRef]

Dicky, F. M.

F. M. Dicky, T. M. Harder, “Shearing plate optical alignment,” Opt. Eng. 17, 295–298 (1978).

Eiju, T.

K. Matsuda, M. Roy, P. W. Fekete, T. Eiju, C. J. R. Sheppard, J. W. O’Byrne, “A novel method for beam collimation using multiple beam shearing interferometry” in Flatness, Roughness, and Discrete Defects Characterization for Computer Disks, Wafers, and Flat Panel Displays II, Proc. SPIE3275, 2–8 (1998).
[CrossRef]

Fekete, P. W.

K. Matsuda, M. Roy, P. W. Fekete, T. Eiju, C. J. R. Sheppard, J. W. O’Byrne, “A novel method for beam collimation using multiple beam shearing interferometry” in Flatness, Roughness, and Discrete Defects Characterization for Computer Disks, Wafers, and Flat Panel Displays II, Proc. SPIE3275, 2–8 (1998).
[CrossRef]

Ferrao, P.

M. de Angelis, S. de Nicola, P. Ferrao, A. Finizio, G. Pierattini, “A new approach to high accuracy measurement of the focal lengths of lenses using a digital Fourier transform,” Opt. Commun. 136, 370–374 (1997).
[CrossRef]

S. de Nicola, P. Ferrao, A. Finizio, G. Pierattini, “Reflective grating interferometer for measuring the focal length of a lens by digital moiré effect,” Opt. Commun. 132, 432–436 (1996).
[CrossRef]

Finizio, A.

M. de Angelis, S. de Nicola, P. Ferrao, A. Finizio, G. Pierattini, “A new approach to high accuracy measurement of the focal lengths of lenses using a digital Fourier transform,” Opt. Commun. 136, 370–374 (1997).
[CrossRef]

S. de Nicola, P. Ferrao, A. Finizio, G. Pierattini, “Reflective grating interferometer for measuring the focal length of a lens by digital moiré effect,” Opt. Commun. 132, 432–436 (1996).
[CrossRef]

Fouere, J. C.

Griot, Melles

Melles Griot, “Lasers and instruments guide: theory and uses of shear plate collimation testers” (Melles Griot, Irvine, Calif., 1994), pp. 135-12–135-16.

Gusinow, R. A.

Harder, T. M.

F. M. Dicky, T. M. Harder, “Shearing plate optical alignment,” Opt. Eng. 17, 295–298 (1978).

Kothiyal, M. P.

Lalor, M. J.

H. Zhang, M. J. Lalor, D. R. Burton, “Improved collimation testing technique using a digital moiré method,” Opt. Eng. 36, 3318–3322 (1997).
[CrossRef]

Malacara, D.

Matsuda, K.

K. Matsuda, M. Roy, P. W. Fekete, T. Eiju, C. J. R. Sheppard, J. W. O’Byrne, “A novel method for beam collimation using multiple beam shearing interferometry” in Flatness, Roughness, and Discrete Defects Characterization for Computer Disks, Wafers, and Flat Panel Displays II, Proc. SPIE3275, 2–8 (1998).
[CrossRef]

Montravadi, M. V.

Murata, K.

Murty, M. V. R. K.

M. V. R. K. Murty, R. P. Shukla, “Measurement of long radii of curvature,” Opt. Eng. 22, 231–235 (1983).
[CrossRef]

Nakano, Y.

O’Byrne, J. W.

K. Matsuda, M. Roy, P. W. Fekete, T. Eiju, C. J. R. Sheppard, J. W. O’Byrne, “A novel method for beam collimation using multiple beam shearing interferometry” in Flatness, Roughness, and Discrete Defects Characterization for Computer Disks, Wafers, and Flat Panel Displays II, Proc. SPIE3275, 2–8 (1998).
[CrossRef]

Patorski, K.

Perera, M.

Pierattini, G.

M. de Angelis, S. de Nicola, P. Ferrao, A. Finizio, G. Pierattini, “A new approach to high accuracy measurement of the focal lengths of lenses using a digital Fourier transform,” Opt. Commun. 136, 370–374 (1997).
[CrossRef]

S. de Nicola, P. Ferrao, A. Finizio, G. Pierattini, “Reflective grating interferometer for measuring the focal length of a lens by digital moiré effect,” Opt. Commun. 132, 432–436 (1996).
[CrossRef]

Riley, M. E.

Roy, M.

K. Matsuda, M. Roy, P. W. Fekete, T. Eiju, C. J. R. Sheppard, J. W. O’Byrne, “A novel method for beam collimation using multiple beam shearing interferometry” in Flatness, Roughness, and Discrete Defects Characterization for Computer Disks, Wafers, and Flat Panel Displays II, Proc. SPIE3275, 2–8 (1998).
[CrossRef]

Sheppard, C. J. R.

K. Matsuda, M. Roy, P. W. Fekete, T. Eiju, C. J. R. Sheppard, J. W. O’Byrne, “A novel method for beam collimation using multiple beam shearing interferometry” in Flatness, Roughness, and Discrete Defects Characterization for Computer Disks, Wafers, and Flat Panel Displays II, Proc. SPIE3275, 2–8 (1998).
[CrossRef]

Shukla, R. P.

Sirohi, R. S.

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 for measuring the focal length of a lens,” Opt. Commun. 73, 257–262 (1989).
[CrossRef]

Suzuki, T.

Yokozeki, S.

Zhang, H.

H. Zhang, M. J. Lalor, D. R. Burton, “Improved collimation testing technique using a digital moiré method,” Opt. Eng. 36, 3318–3322 (1997).
[CrossRef]

Appl. Opt.

Opt. Commun.

M. de Angelis, S. de Nicola, P. Ferrao, A. Finizio, G. Pierattini, “A new approach to high accuracy measurement of the focal lengths of lenses using a digital Fourier transform,” Opt. Commun. 136, 370–374 (1997).
[CrossRef]

S. de Nicola, P. Ferrao, A. Finizio, G. Pierattini, “Reflective grating interferometer for measuring the focal length of a lens by digital moiré effect,” Opt. Commun. 132, 432–436 (1996).
[CrossRef]

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

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]

Opt. Eng.

H. Zhang, M. J. Lalor, D. R. Burton, “Improved collimation testing technique using a digital moiré method,” Opt. Eng. 36, 3318–3322 (1997).
[CrossRef]

F. M. Dicky, T. M. Harder, “Shearing plate optical alignment,” Opt. Eng. 17, 295–298 (1978).

M. V. R. K. Murty, R. P. Shukla, “Measurement of long radii of curvature,” Opt. Eng. 22, 231–235 (1983).
[CrossRef]

Other

Melles Griot, “Lasers and instruments guide: theory and uses of shear plate collimation testers” (Melles Griot, Irvine, Calif., 1994), pp. 135-12–135-16.

K. Matsuda, M. Roy, P. W. Fekete, T. Eiju, C. J. R. Sheppard, J. W. O’Byrne, “A novel method for beam collimation using multiple beam shearing interferometry” in Flatness, Roughness, and Discrete Defects Characterization for Computer Disks, Wafers, and Flat Panel Displays II, Proc. SPIE3275, 2–8 (1998).
[CrossRef]

R. Kingslake, ed., Applied Optics and Optical Engineering, (Academic, New York, 1965), Vol. 1, pp. 208–226.

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Figures (7)

Fig. 1
Fig. 1

Optical arrangement for lens focal-length measurement with multiple-beam lateral shearing interferometry.

Fig. 2
Fig. 2

Rotation of the fringes as a function of the relative values of z 0 and f.

Fig. 3
Fig. 3

Calculation of the shear, a, in multiple-beam shearing interferometry.

Fig. 4
Fig. 4

Experimental setup.

Fig. 5
Fig. 5

Fringes obtained with the interferometer. The shear is 0.65 mm; the focal length of the collimating lens is 335 mm; and the shear plate wedge angle is 2.7 arc sec.

Fig. 6
Fig. 6

Results with a computer-optimized achromatic doublet lens of a nominal focal length of 160 mm. The shear, a, is (a) 1.7 mm and (b) 0.85 mm.

Fig. 7
Fig. 7

Results with a simple doublet lens of a nominal focal length of 200 mm. The shear, a, is (a) 1.7 mm and (b) 0.85 mm.

Equations (14)

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

φx, y=12z0x-x02+y-y02-12fx2+y2+z0,
Iγ=11+F sin2γ/2,
γ=4πλ nh cos θ+2πλ ny sin 2α+2πaλφx, yx+ϕ,
F=4R1-R2.
γ-4πλ nh cos θ+ϕ=2πm where m is an integer,
ny sin 2αλ+aλφx, yx=m.
y=-an sin 2α1z0-1fx+an sin 2αx0z0+mλn sin 2α.
dy=λn sin 2α.
tan ω=yx=an sin 2αΔzff-Δz=adyλΔzff-Δz.
fadyΔzλ tan ω1/2,
a=2h tan θ cos θ=h sin 2θn2-sin2 θ1/22θhn when θ  1.
f=-Δz±Δz2+4adyΔzλ tan ω1/22,
δfδΔz2+f4λ2dy2a2δω21/2,
tan ωadyΔzλf2.

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