Abstract

A new accurate method for long focal-length measurement based on Talbot interferometry is proposed. A divergent beam and two Ronchi gratings of different periods are employed, as the alternative of the collimated beam and two identical gratings, to achieve higher measurement accuracy. Moreover, with divergent beam, lenses of large aperture can be easily measured without scanning, which is required when it comes to traditional collimated beam. Numerical analysis and experiments were carried out. The results demonstrate the proposed method features remarkably high accuracy and repeatability.

© 2014 Optical Society of America

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References

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  1. W. Zhao, R. Sun, L. Qiu, and D. Sha, “Laser differential confocal ultra-long focal length measurement,” Opt. Express 17(22), 20051–20062 (2009).
    [Crossref] [PubMed]
  2. P. Singh, M. S. Faridi, C. Shakher, and R. S. Sirohi, “Measurement of focal length with phase-shifting Talbot interferometry,” Appl. Opt. 44(9), 1572–1576 (2005).
    [Crossref] [PubMed]
  3. V. I. Meshcheryakov, M. I. Sinel’nikov, and O. K. Filippov, “Measuring the focal-lengths of long-focus optical systems,” J. Opt. Technol. 66(5), 458–459 (1999).
    [Crossref]
  4. B. DeBoo and J. Sasian, “Precise focal-length measurement technique with a reflective Fresnel-zone hologram,” Appl. Opt. 42(19), 3903–3909 (2003).
    [Crossref] [PubMed]
  5. B. DeBoo and J. Sasian, “Novel method for precise focal-length measurement,” in International Optical Design Conference, 2002 OSA Technical Digest Series (Optical Society of America, 2002), paper IMCS5.
    [Crossref]
  6. W. Zhao, R. Sun, L. Qiu, and D. Sha, “Laser differential confocal radius measurement,” Opt. Express 18(3), 2345–2360 (2010).
    [Crossref] [PubMed]
  7. S. Yokozeki and T. Suzuki, “Shearing interferometer using the grating as the beam splitter,” Appl. Opt. 10(7), 1575–1580 (1971).
    [Crossref] [PubMed]
  8. D. E. Silva, “Talbot interferometer for radial and lateral derivatives,” Appl. Opt. 11(11), 2613–2624 (1972).
    [Crossref] [PubMed]
  9. J. Liao and Q. Gu, “Diffraction self-imaging phenomenon of the grating in the optical system: general Talbot effect,” Acta Opt. Sin. 4, 009 (1985).
  10. Y. Nakano and K. Murata, “Talbot interferometry for measuring the focal length of a lens,” Appl. Opt. 24(19), 3162–3166 (1985).
    [Crossref] [PubMed]
  11. Y. Nakano and K. Murata, “Measurements of phase objects using the Talbot effect and Moiré techniques,” Appl. Opt. 23(14), 2296–2299 (1984).
    [Crossref] [PubMed]
  12. Y. Nakano and K. Murata, “Talbot interferometry for measuring the small tilt angle variation of an object surface,” Appl. Opt. 25(15), 2475–2477 (1986).
    [Crossref] [PubMed]
  13. Y. Nakano, “Measurements of the small tilt-angle variation of an object surface using Moiré interferometry and digital image processing,” Appl. Opt. 26(18), 3911–3914 (1987).
    [Crossref] [PubMed]
  14. C.-W. Chang and D.-C. Su, “An improved technique of measuring the focal-length of a lens,” Opt. Commun. 73(4), 257–262 (1989).
    [Crossref]
  15. J. C. Bhattacharya and A. K. Aggarwal, “Measurement of the focal length of a collimating lens using the Talbot effect and the moiré technique,” Appl. Opt. 30(31), 4479–4480 (1991).
    [Crossref] [PubMed]
  16. K. V. Sriram, M. P. Kothiyal, and R. S. Sirohi, “Direct determination of focal length by using Talbot interferometry,” Appl. Opt. 31(28), 5984–5987 (1992).
    [Crossref] [PubMed]
  17. Y. Wu, “Measurement of the focal length with collimation method,” Opto-Elecron. Engin. 4, 27–29 (1997).
  18. K. Yang, Z. Liao, and T. Tao, “Analysis of Talbot image symmetry about Fourier spectrum plane and measurement of focal length,” Acta Opt. Sin. 14, 50–54 (1994).
  19. C. Hou, J. Bai, and X. Hou, “Novel method for testing the long focal length lens of large aperture,” Opt. Lasers Eng. 43(10), 1107–1117 (2005).
    [Crossref]
  20. X. Jin, J. Zhang, J. Bai, C. Hou, and X. Hou, “Calibration method for high-accuracy measurement of long focal length with Talbot interferometry,” Appl. Opt. 51(13), 2407–2413 (2012).
    [Crossref] [PubMed]

2012 (1)

2010 (1)

2009 (1)

2005 (2)

P. Singh, M. S. Faridi, C. Shakher, and R. S. Sirohi, “Measurement of focal length with phase-shifting Talbot interferometry,” Appl. Opt. 44(9), 1572–1576 (2005).
[Crossref] [PubMed]

C. Hou, J. Bai, and X. Hou, “Novel method for testing the long focal length lens of large aperture,” Opt. Lasers Eng. 43(10), 1107–1117 (2005).
[Crossref]

2003 (1)

1999 (1)

1997 (1)

Y. Wu, “Measurement of the focal length with collimation method,” Opto-Elecron. Engin. 4, 27–29 (1997).

1994 (1)

K. Yang, Z. Liao, and T. Tao, “Analysis of Talbot image symmetry about Fourier spectrum plane and measurement of focal length,” Acta Opt. Sin. 14, 50–54 (1994).

1992 (1)

1991 (1)

1989 (1)

C.-W. Chang and D.-C. Su, “An improved technique of measuring the focal-length of a lens,” Opt. Commun. 73(4), 257–262 (1989).
[Crossref]

1987 (1)

1986 (1)

1985 (2)

Y. Nakano and K. Murata, “Talbot interferometry for measuring the focal length of a lens,” Appl. Opt. 24(19), 3162–3166 (1985).
[Crossref] [PubMed]

J. Liao and Q. Gu, “Diffraction self-imaging phenomenon of the grating in the optical system: general Talbot effect,” Acta Opt. Sin. 4, 009 (1985).

1984 (1)

1972 (1)

1971 (1)

Aggarwal, A. K.

Bai, J.

X. Jin, J. Zhang, J. Bai, C. Hou, and X. Hou, “Calibration method for high-accuracy measurement of long focal length with Talbot interferometry,” Appl. Opt. 51(13), 2407–2413 (2012).
[Crossref] [PubMed]

C. Hou, J. Bai, and X. Hou, “Novel method for testing the long focal length lens of large aperture,” Opt. Lasers Eng. 43(10), 1107–1117 (2005).
[Crossref]

Bhattacharya, J. C.

Chang, C.-W.

C.-W. Chang and D.-C. Su, “An improved technique of measuring the focal-length of a lens,” Opt. Commun. 73(4), 257–262 (1989).
[Crossref]

DeBoo, B.

Faridi, M. S.

Filippov, O. K.

Gu, Q.

J. Liao and Q. Gu, “Diffraction self-imaging phenomenon of the grating in the optical system: general Talbot effect,” Acta Opt. Sin. 4, 009 (1985).

Hou, C.

X. Jin, J. Zhang, J. Bai, C. Hou, and X. Hou, “Calibration method for high-accuracy measurement of long focal length with Talbot interferometry,” Appl. Opt. 51(13), 2407–2413 (2012).
[Crossref] [PubMed]

C. Hou, J. Bai, and X. Hou, “Novel method for testing the long focal length lens of large aperture,” Opt. Lasers Eng. 43(10), 1107–1117 (2005).
[Crossref]

Hou, X.

X. Jin, J. Zhang, J. Bai, C. Hou, and X. Hou, “Calibration method for high-accuracy measurement of long focal length with Talbot interferometry,” Appl. Opt. 51(13), 2407–2413 (2012).
[Crossref] [PubMed]

C. Hou, J. Bai, and X. Hou, “Novel method for testing the long focal length lens of large aperture,” Opt. Lasers Eng. 43(10), 1107–1117 (2005).
[Crossref]

Jin, X.

Kothiyal, M. P.

Liao, J.

J. Liao and Q. Gu, “Diffraction self-imaging phenomenon of the grating in the optical system: general Talbot effect,” Acta Opt. Sin. 4, 009 (1985).

Liao, Z.

K. Yang, Z. Liao, and T. Tao, “Analysis of Talbot image symmetry about Fourier spectrum plane and measurement of focal length,” Acta Opt. Sin. 14, 50–54 (1994).

Meshcheryakov, V. I.

Murata, K.

Nakano, Y.

Qiu, L.

Sasian, J.

Sha, D.

Shakher, C.

Silva, D. E.

Sinel’nikov, M. I.

Singh, P.

Sirohi, R. S.

Sriram, K. V.

Su, D.-C.

C.-W. Chang and D.-C. Su, “An improved technique of measuring the focal-length of a lens,” Opt. Commun. 73(4), 257–262 (1989).
[Crossref]

Sun, R.

Suzuki, T.

Tao, T.

K. Yang, Z. Liao, and T. Tao, “Analysis of Talbot image symmetry about Fourier spectrum plane and measurement of focal length,” Acta Opt. Sin. 14, 50–54 (1994).

Wu, Y.

Y. Wu, “Measurement of the focal length with collimation method,” Opto-Elecron. Engin. 4, 27–29 (1997).

Yang, K.

K. Yang, Z. Liao, and T. Tao, “Analysis of Talbot image symmetry about Fourier spectrum plane and measurement of focal length,” Acta Opt. Sin. 14, 50–54 (1994).

Yokozeki, S.

Zhang, J.

Zhao, W.

Acta Opt. Sin. (2)

J. Liao and Q. Gu, “Diffraction self-imaging phenomenon of the grating in the optical system: general Talbot effect,” Acta Opt. Sin. 4, 009 (1985).

K. Yang, Z. Liao, and T. Tao, “Analysis of Talbot image symmetry about Fourier spectrum plane and measurement of focal length,” Acta Opt. Sin. 14, 50–54 (1994).

Appl. Opt. (11)

J. C. Bhattacharya and A. K. Aggarwal, “Measurement of the focal length of a collimating lens using the Talbot effect and the moiré technique,” Appl. Opt. 30(31), 4479–4480 (1991).
[Crossref] [PubMed]

K. V. Sriram, M. P. Kothiyal, and R. S. Sirohi, “Direct determination of focal length by using Talbot interferometry,” Appl. Opt. 31(28), 5984–5987 (1992).
[Crossref] [PubMed]

Y. Nakano and K. Murata, “Talbot interferometry for measuring the focal length of a lens,” Appl. Opt. 24(19), 3162–3166 (1985).
[Crossref] [PubMed]

Y. Nakano and K. Murata, “Measurements of phase objects using the Talbot effect and Moiré techniques,” Appl. Opt. 23(14), 2296–2299 (1984).
[Crossref] [PubMed]

Y. Nakano and K. Murata, “Talbot interferometry for measuring the small tilt angle variation of an object surface,” Appl. Opt. 25(15), 2475–2477 (1986).
[Crossref] [PubMed]

Y. Nakano, “Measurements of the small tilt-angle variation of an object surface using Moiré interferometry and digital image processing,” Appl. Opt. 26(18), 3911–3914 (1987).
[Crossref] [PubMed]

P. Singh, M. S. Faridi, C. Shakher, and R. S. Sirohi, “Measurement of focal length with phase-shifting Talbot interferometry,” Appl. Opt. 44(9), 1572–1576 (2005).
[Crossref] [PubMed]

B. DeBoo and J. Sasian, “Precise focal-length measurement technique with a reflective Fresnel-zone hologram,” Appl. Opt. 42(19), 3903–3909 (2003).
[Crossref] [PubMed]

S. Yokozeki and T. Suzuki, “Shearing interferometer using the grating as the beam splitter,” Appl. Opt. 10(7), 1575–1580 (1971).
[Crossref] [PubMed]

D. E. Silva, “Talbot interferometer for radial and lateral derivatives,” Appl. Opt. 11(11), 2613–2624 (1972).
[Crossref] [PubMed]

X. Jin, J. Zhang, J. Bai, C. Hou, and X. Hou, “Calibration method for high-accuracy measurement of long focal length with Talbot interferometry,” Appl. Opt. 51(13), 2407–2413 (2012).
[Crossref] [PubMed]

J. Opt. Technol. (1)

Opt. Commun. (1)

C.-W. Chang and D.-C. Su, “An improved technique of measuring the focal-length of a lens,” Opt. Commun. 73(4), 257–262 (1989).
[Crossref]

Opt. Express (2)

Opt. Lasers Eng. (1)

C. Hou, J. Bai, and X. Hou, “Novel method for testing the long focal length lens of large aperture,” Opt. Lasers Eng. 43(10), 1107–1117 (2005).
[Crossref]

Opto-Elecron. Engin. (1)

Y. Wu, “Measurement of the focal length with collimation method,” Opto-Elecron. Engin. 4, 27–29 (1997).

Other (1)

B. DeBoo and J. Sasian, “Novel method for precise focal-length measurement,” in International Optical Design Conference, 2002 OSA Technical Digest Series (Optical Society of America, 2002), paper IMCS5.
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 The sketch of a long focal-length testing system.
Fig. 2
Fig. 2 Schematic representation of the optical system, (a) without testing lens, (b) with testing lens, f w a v e : the focal-length of the divergent beam. f c o m : the combined focal-length of the test lens and the divergent beam.
Fig. 3
Fig. 3 Uncertainty of measured focal-length caused by parameter β .
Fig. 4
Fig. 4 Uncertainties of different measured focal-lengths δ and relative uncertainties Δ S : (a) Traditional method. (b) Presented method.
Fig. 5
Fig. 5 A photograph of our long-focal-length testing system.
Fig. 6
Fig. 6 The flow chart of experimental steps.
Fig. 7
Fig. 7 Fringe patterns recorded with CCD camera. (a) Image at Talbot distance Z without test lens. (b) Image at distance Z with test lens. (c) Image at corresponding Talbot distance Z ' with test lens.
Fig. 8
Fig. 8 Comparative experiments between LFTS and interferometry approach.
Fig. 9
Fig. 9 (a) Experiments for repeatability. (b) Experiments for long-term stability.

Tables (1)

Tables Icon

Table 1 Comparison of the measured values of focal lengths with the standard values of focal lengths.

Equations (11)

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

tan α = p 2 p 1 ' cos θ sin θ .
η = p 1 ' p 1 = f w a v e Z f w a v e ,
f w a v e = Z β sin θ tan α + β cos θ 1 + Z ,
β = p 1 p 2 ,
f c o m = Z ' β sin θ tan α + β cos θ 1 + Z ' .
{ l H = d r 1 / [ n ( r 2 r 1 ) + ( n 1 ) d ] l ' H = d r 2 / [ n ( r 2 r 1 ) + ( n 1 ) d ] d 2 = d 1 d l ' H .
f l e n s = 1 / ( 1 f c o m + d 2 1 f w a v e + d 1 l H ) .
δ = [ ( f l e n s f w a v e Δ f w a v e ) 2 + ( f l e n s d 1 Δ d 1 ) 2 + ( f l e n s Z ' Δ Z ' ) 2 + ( f l e n s θ Δ θ ) 2 + ( f l e n s α Δ α ) 2 + ( f l e n s l H Δ l H ) 2 + ( f l e n s l ' H Δ l ' H ) 2 + ( f l e n s β Δ β ) 2 ] 1 / 2 ,
Δ S = δ / f l e n s .
β = f w a v e ( f w a v e Z ) ( s i n θ tan α + cos θ ) .
Δ β = [ ( β f w a v e Δ f w a v e ) 2 + ( β Z Δ Z ) 2 + ( β θ Δ θ ) 2 + ( β α Δ α ) 2 ] 1 / 2 .

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