Abstract

A device measuring the optical power of simple lenses by means of moiré phenomena is described. The relevant equations are derived, and a working instrument is presented. A power measuring accuracy better than 0.25 m-1 in the range of ±10 m-1 is demonstrated.

© 2003 Optical Society of America

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References

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  1. International Organization for Standardization, “Optics and optical instruments—test lenses for calibration of focimeters,” Document 9342 (International Organization for Standardization, Geneva, 1996).
  2. V. Greco, G. Molesini, “Characterization of test lenses for calibration of focimeters,” Meas. Sci. Technol. 10, 583–586 (1999).
    [Crossref]
  3. W. J. Smith, Modern Optical Engineering, 2nd ed. (McGraw-Hill, New York1990), pp. 495–497.
  4. O. Kafri, I. Glatt, “Moire deflectometry; a ray deflection approach to optical testing,” Opt. Eng. 24, 944–960 (1985).
    [Crossref]
  5. I. Glatt, O. Kafri, “Determination of the focal length of nonparaxial lenses by moire deflectometry,” Appl. Opt. 26, 2507–2508 (1987).
    [Crossref] [PubMed]
  6. E. Keren, K. M. Kreske, O. Kafri, “Universal method for determining the focal length of optical systems by moire deflectometry,” Appl. Opt. 27, 1383–1385 (1988).
    [Crossref] [PubMed]
  7. Y. Nakano, K. Murata, “Talbot interferometry for measuring the focal length of a lens,” Appl. Opt. 24, 3162–3166 (1985).
    [Crossref] [PubMed]
  8. 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]
  9. K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Direct determination of focal length by using Talbot interferometry,” Appl. Opt. 28, 5984–5987 (1992).
    [Crossref]
  10. O. Bryngdahl, “Moiré: formation and interpretation,” J. Opt. Soc. Am. 64, 1287–1294 (1974).
    [Crossref]
  11. Bureau International des Poids et Mesures, International Electrotechnical Commission, International Federation of Clinical Chemistry, International Organization for Standardization, International Union for Pure and Applied Physics, International Union for Pure and Applied Chemistry, and International Organization of Legal Metrology, Guide to the Expression of Uncertainty in Measurements (International Organization for Standardization, Geneva, 1993).

1999 (1)

V. Greco, G. Molesini, “Characterization of test lenses for calibration of focimeters,” Meas. Sci. Technol. 10, 583–586 (1999).
[Crossref]

1992 (1)

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

1988 (2)

1987 (1)

1985 (2)

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

O. Kafri, I. Glatt, “Moire deflectometry; a ray deflection approach to optical testing,” Opt. Eng. 24, 944–960 (1985).
[Crossref]

1974 (1)

Bernardo, L. M.

Bryngdahl, O.

Glatt, I.

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

O. Kafri, I. Glatt, “Moire deflectometry; a ray deflection approach to optical testing,” Opt. Eng. 24, 944–960 (1985).
[Crossref]

Greco, V.

V. Greco, G. Molesini, “Characterization of test lenses for calibration of focimeters,” Meas. Sci. Technol. 10, 583–586 (1999).
[Crossref]

Kafri, O.

Keren, E.

Kothiyal, M. P.

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

Kreske, K. M.

Molesini, G.

V. Greco, G. Molesini, “Characterization of test lenses for calibration of focimeters,” Meas. Sci. Technol. 10, 583–586 (1999).
[Crossref]

Murata, K.

Nakano, Y.

Sirohi, R. S.

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

Smith, W. J.

W. J. Smith, Modern Optical Engineering, 2nd ed. (McGraw-Hill, New York1990), pp. 495–497.

Soares, O. D. D.

Sriram, K. V.

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

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

Meas. Sci. Technol. (1)

V. Greco, G. Molesini, “Characterization of test lenses for calibration of focimeters,” Meas. Sci. Technol. 10, 583–586 (1999).
[Crossref]

Opt. Eng. (1)

O. Kafri, I. Glatt, “Moire deflectometry; a ray deflection approach to optical testing,” Opt. Eng. 24, 944–960 (1985).
[Crossref]

Other (3)

International Organization for Standardization, “Optics and optical instruments—test lenses for calibration of focimeters,” Document 9342 (International Organization for Standardization, Geneva, 1996).

W. J. Smith, Modern Optical Engineering, 2nd ed. (McGraw-Hill, New York1990), pp. 495–497.

Bureau International des Poids et Mesures, International Electrotechnical Commission, International Federation of Clinical Chemistry, International Organization for Standardization, International Union for Pure and Applied Physics, International Union for Pure and Applied Chemistry, and International Organization of Legal Metrology, Guide to the Expression of Uncertainty in Measurements (International Organization for Standardization, Geneva, 1993).

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Figures (6)

Fig. 1
Fig. 1

Schematic layout of the measuring principle. O, observation point; G1, G2, Ronchi rulings; s, x 1 , x 2 , axial distances.

Fig. 2
Fig. 2

Characteristic curve of the optical power Φ as a function of the measured quantity tan α.

Fig. 3
Fig. 3

Fringe viewer arrangement with rotating hand and scale.

Fig. 4
Fig. 4

Laboratory version of the lens meter.

Fig. 5
Fig. 5

Measurement uncertainty σϕ (standard deviation) as a function of the optical power Φ.

Fig. 6
Fig. 6

Instrument verification. Full line: theoretical curve computed from the values of the parameters. Marked dots: data from experiments.

Equations (18)

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x1= x1ff-x1,
M1= ff-x1;
P1= M1ps+x1= fpsf-x1+f x1.
P2= fpsf-x2+f x2.
tan α= 1tanθ2P1-P2P1+P2.
x1=x, x2=x+d,
tan α= 1tanθ2-d2 s fs-f-2x+d,
Φ= d-tan α tanθ22s+2x+dsd-tan α tanθ22x+d.
tanα=- dθf;
A= 1s,
B=- 2 tanθ2d.
tan αΦ=0= dtanθ22s+2x+d;
Φ tan α= -2d tanθ2d-tan α tanθ22x+d2,
Φθ= -d tan αcos2θ2d-tan α tanθ22x+d2,
Φ s=- 1s2,
Φ x= -4 tan2 α tan2θ2d-tan α tanθ22x+d2,
Φ d= 2 tan α tanθ21-tan α tanθ2d-tan α tanθ22x+d2.
σΦ=Φ tan α2σtan α2+Φθ2σθ2+Φs2σs2+Φx2σx2+Φd2 σd21/2,

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