Abstract

Focus retrocollimated interferometry is developed for the measurement of focal lengths of optical lenses and systems, and achievable accuracy is discussed. It is shown that this method can be used to measure both short and long focal lengths simply and with high accuracy.

© 2002 Optical Society of America

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References

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  1. Y. Nakano, K. Murata, “Talbot interferometry for measuring the focal length of a lens,” Appl. Opt. 24, 3162–3166 (1985).
    [CrossRef] [PubMed]
  2. 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]
  3. C. W. Chang, D. C. Su, “An improved technique of measuring the focal length of a lens,” Opt. Commun. 73, 257–262 (1989).
    [CrossRef]
  4. K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Curvature and focal length measurements using compensation of a collimated beam,” Opt. Laser Technol. 23, 241–245 (1991).
    [CrossRef]
  5. 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]
  6. K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Direct determination of focal length using Talbot interferometry,” Appl. Opt. 31, 5984–5987 (1992).
    [CrossRef] [PubMed]
  7. K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Optical measurements using Talbot interferometry,” J. Opt. (India) 21, 93–106 (1992).
  8. K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Use of a non-collimated beam for determining the focal length of a lens by Talbot interferometry,” J. Opt. (India) 22, 61–66 (1993).
  9. L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31, 1961–1966 (1992).
    [CrossRef]
  10. H. H. Hopkins, Wave Theory of Aberrations (Oxford University, London, 1950), p. 14.

1993

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Use of a non-collimated beam for determining the focal length of a lens by Talbot interferometry,” J. Opt. (India) 22, 61–66 (1993).

1992

1991

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Curvature and focal length measurements using compensation of a collimated beam,” Opt. Laser Technol. 23, 241–245 (1991).
[CrossRef]

1989

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

1988

1985

Bernardo, L. M.

Chang, C. W.

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

Hopkins, H. H.

H. H. Hopkins, Wave Theory of Aberrations (Oxford University, London, 1950), p. 14.

Kothiyal, M. P.

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Use of a non-collimated beam for determining the focal length of a lens by Talbot interferometry,” J. Opt. (India) 22, 61–66 (1993).

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Direct determination of focal length using Talbot interferometry,” Appl. Opt. 31, 5984–5987 (1992).
[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, “Optical measurements using Talbot interferometry,” J. Opt. (India) 21, 93–106 (1992).

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Curvature and focal length measurements using compensation of a collimated beam,” Opt. Laser Technol. 23, 241–245 (1991).
[CrossRef]

Murata, K.

Nakano, Y.

Selberg, L. A.

L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31, 1961–1966 (1992).
[CrossRef]

Sirohi, R. S.

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Use of a non-collimated beam for determining the focal length of a lens by Talbot interferometry,” J. Opt. (India) 22, 61–66 (1993).

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Optical measurements using Talbot interferometry,” J. Opt. (India) 21, 93–106 (1992).

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 using Talbot interferometry,” Appl. Opt. 31, 5984–5987 (1992).
[CrossRef] [PubMed]

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Curvature and focal length measurements using compensation of a collimated beam,” Opt. Laser Technol. 23, 241–245 (1991).
[CrossRef]

Soares, O. D. D.

Sriram, K. V.

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Use of a non-collimated beam for determining the focal length of a lens by Talbot interferometry,” J. Opt. (India) 22, 61–66 (1993).

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Direct determination of focal length using Talbot interferometry,” Appl. Opt. 31, 5984–5987 (1992).
[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, “Optical measurements using Talbot interferometry,” J. Opt. (India) 21, 93–106 (1992).

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Curvature and focal length measurements using compensation of a collimated beam,” Opt. Laser Technol. 23, 241–245 (1991).
[CrossRef]

Su, D. C.

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

Appl. Opt.

J. Opt. (India)

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Optical measurements using Talbot interferometry,” J. Opt. (India) 21, 93–106 (1992).

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Use of a non-collimated beam for determining the focal length of a lens by Talbot interferometry,” J. Opt. (India) 22, 61–66 (1993).

Opt. Commun.

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

Opt. Eng.

L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31, 1961–1966 (1992).
[CrossRef]

Opt. Laser Technol.

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Curvature and focal length measurements using compensation of a collimated beam,” Opt. Laser Technol. 23, 241–245 (1991).
[CrossRef]

Other

H. H. Hopkins, Wave Theory of Aberrations (Oxford University, London, 1950), p. 14.

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Figures (6)

Fig. 1
Fig. 1

Principle of the focus retrocollimated focal-length measurements.

Fig. 2
Fig. 2

Focal-length measurement configuration and procedures.

Fig. 3
Fig. 3

Variation of |Δf/ f| with f for R = 20 mm. |ΔR/ R| equals 0.1% in (a) and 0.01% in (b). For |Δx|, the filled squares represent 5 µm, the filled circles represent 10 µm, the filled triangles represent 20 µm.

Fig. 4
Fig. 4

Variation of |Δf/ f| with f for R = 200 mm. |ΔR/ R| equals 0.1% in (a), 0.01% in (b), 0.001% in (c). The symbols have the same meaning as in Fig. 3.

Fig. 5
Fig. 5

Variation of |Δf/ f| with f for R = 800 mm. The values of |ΔR/ R| are the same as in Fig. 4, and the symbols have the same meaning as in Fig. 3.

Fig. 6
Fig. 6

Variation of |Δf/ f| with f for R = 5000 mm. |ΔR/ R| equals 0.1% in (a) and 0.01% in (b). The symbols have the same meaning as in Fig. 3.

Tables (2)

Tables Icon

Table 1 Relations between ΔW and Wave Aberration

Tables Icon

Table 2 Effect of Interferometry Sensitivity on Null Position Determination

Equations (6)

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

ff=Rx.
f=f,
f=x×R,
δff=12Δxx+ΔRR.
Δff=±12Δxx2+ΔRR21/2=±12Rf22Δx2+ΔRR21/2.
Δx=8fD2ΔW,

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