Abstract

In this paper, we realize an accurate and flexible measurement method for paraxial focal length with a simple apparatus. The proposed method utilizes the established measurement principle which is based on the differentiation of the Gaussian optical formula and geometrical relationship of camera-lens system to obtain the focal length of a lens. Some image processing methods are employed to experimentally realize this measurement principle with high accuracy and practicability. Image sharpness evaluation function is utilized to ensure the system conforms to the Gaussian optical formula. System calibration is adopted to compensate for the errors caused by the simple apparatus. In addition, aberration is considered to obtain a paraxial focal length of a lens. Experimental results indicate that repeatability error of measurement system is less than 0.11% for most lenses.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. R. Kingslake, Applied Optics and Optical Engineering, vol. 1 (Elsevier, 2012).
  2. E. Keren, K. Kreske, and O. Kafri, “Universal method for determining the focal length of optical systems by moiré deflectometry,” Applied Optics 27, 1383–1385 (1988).
    [Crossref]
  3. S. Trivedi, J. Dhanotia, and S. Prakash, “Measurement of focal length using phase shifted moiré deflectometry,” Optics and Lasers in Engineering 51, 776–782 (2013).
    [Crossref]
  4. K. V. Sriram, M. P. Kothiyal, and R. Sirohi, “Direct determination of focal length by using Talbot interferometry,” Applied Optics 31, 5984–5987 (1992).
    [Crossref]
  5. P. Singh, M. S. Faridi, C. Shakher, and R. S. Sirohi, “Measurement of focal length with phase-shifting Talbot interferometry,” Applied Optics 44, 1572–1576 (2005).
    [Crossref]
  6. S. Rasouli, Y. Rajabi, and H. Sarabi, “Microlenses focal length measurement using Z-scan and parallel moiré deflectometry,” Optics and Lasers in Engineering 51, 1321–1326 (2013).
    [Crossref]
  7. F. Lei and L. Dang, “Measuring the focal length of optical systems by grating shearing interferometry,” Applied Optics 33, 6603–6608 (1994).
    [Crossref] [PubMed]
  8. J. Dhanotia and S. Prakash, “Focal length and radius of curvature measurement using coherent gradient sensing and Fourier fringe analysis,” Optik - International Journal for Light and Electron Optics 124, 2115–2120 (2013).
    [Crossref]
  9. C. Tay, M. Thakur, L. Chen, and C. Shakher, “Measurement of focal length of lens using phase shifting Lau phase interferometry,” Optics Communications 248, 339–345 (2005).
    [Crossref]
  10. J. Yang, L. Qiu, W. Zhao, and H. Wu, “Laser differential reflection-confocal focal-length measurement,” Optics Express 20, 26–27 (2012).
    [Crossref]
  11. H.-G. Zimmer, Geometrische Optik (Springer-Verlag, 2013).
  12. N. D. Narvekar and L. J. Karam, “A no-reference image blur metric based on the cumulative probability of blur detection (CPBD),” IEEE Transactions on Image Processing 20, 2678–2683 (2011).
    [Crossref]
  13. Z. Zhang, “A flexible new technique for camera calibration,” Trans. Pat. Anal. Mach. Intel. 22, 1330–1334(2000).
    [Crossref]
  14. A. Miks and P. Pokorny, “Use of diffraction grating for measuring the focal length and distortion of optical systems,” Applied Optics 54, 10200–10206 (2015).
    [Crossref]
  15. A. Miks and J. Novak, “Estimation of accuracy of optical measuring systems with respect to object distance,” Optics Express 19, 14300–14314 (2011).
    [Crossref]
  16. A. Miks, J. Novak, and P. Novak, “Analysis of imaging for laser triangulation sensors under scheimpflug rule,” Optics Express 21, 18225–18235 (2013).
    [Crossref]
  17. C. Harris and M. Stephens, “A combined corner and edge detector,” in “Alvey vision conference,” 10–5244 (1988).
  18. D. Chen and G. Zhang, “A new sub-pixel detector for x-corners in camera calibration targets,” in “WSCG SHORT papers proceedings,” 97–100 (2005).
  19. L. Pedrotti, “Basic geometrical optics,” Society of Photo-Optical Instrumentation Engineers, 2017 (2008).

2015 (1)

A. Miks and P. Pokorny, “Use of diffraction grating for measuring the focal length and distortion of optical systems,” Applied Optics 54, 10200–10206 (2015).
[Crossref]

2013 (4)

A. Miks, J. Novak, and P. Novak, “Analysis of imaging for laser triangulation sensors under scheimpflug rule,” Optics Express 21, 18225–18235 (2013).
[Crossref]

S. Trivedi, J. Dhanotia, and S. Prakash, “Measurement of focal length using phase shifted moiré deflectometry,” Optics and Lasers in Engineering 51, 776–782 (2013).
[Crossref]

S. Rasouli, Y. Rajabi, and H. Sarabi, “Microlenses focal length measurement using Z-scan and parallel moiré deflectometry,” Optics and Lasers in Engineering 51, 1321–1326 (2013).
[Crossref]

J. Dhanotia and S. Prakash, “Focal length and radius of curvature measurement using coherent gradient sensing and Fourier fringe analysis,” Optik - International Journal for Light and Electron Optics 124, 2115–2120 (2013).
[Crossref]

2012 (1)

J. Yang, L. Qiu, W. Zhao, and H. Wu, “Laser differential reflection-confocal focal-length measurement,” Optics Express 20, 26–27 (2012).
[Crossref]

2011 (2)

N. D. Narvekar and L. J. Karam, “A no-reference image blur metric based on the cumulative probability of blur detection (CPBD),” IEEE Transactions on Image Processing 20, 2678–2683 (2011).
[Crossref]

A. Miks and J. Novak, “Estimation of accuracy of optical measuring systems with respect to object distance,” Optics Express 19, 14300–14314 (2011).
[Crossref]

2005 (2)

C. Tay, M. Thakur, L. Chen, and C. Shakher, “Measurement of focal length of lens using phase shifting Lau phase interferometry,” Optics Communications 248, 339–345 (2005).
[Crossref]

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

2000 (1)

Z. Zhang, “A flexible new technique for camera calibration,” Trans. Pat. Anal. Mach. Intel. 22, 1330–1334(2000).
[Crossref]

1994 (1)

F. Lei and L. Dang, “Measuring the focal length of optical systems by grating shearing interferometry,” Applied Optics 33, 6603–6608 (1994).
[Crossref] [PubMed]

1992 (1)

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

1988 (1)

E. Keren, K. Kreske, and O. Kafri, “Universal method for determining the focal length of optical systems by moiré deflectometry,” Applied Optics 27, 1383–1385 (1988).
[Crossref]

Chen, D.

D. Chen and G. Zhang, “A new sub-pixel detector for x-corners in camera calibration targets,” in “WSCG SHORT papers proceedings,” 97–100 (2005).

Chen, L.

C. Tay, M. Thakur, L. Chen, and C. Shakher, “Measurement of focal length of lens using phase shifting Lau phase interferometry,” Optics Communications 248, 339–345 (2005).
[Crossref]

Dang, L.

F. Lei and L. Dang, “Measuring the focal length of optical systems by grating shearing interferometry,” Applied Optics 33, 6603–6608 (1994).
[Crossref] [PubMed]

Dhanotia, J.

J. Dhanotia and S. Prakash, “Focal length and radius of curvature measurement using coherent gradient sensing and Fourier fringe analysis,” Optik - International Journal for Light and Electron Optics 124, 2115–2120 (2013).
[Crossref]

S. Trivedi, J. Dhanotia, and S. Prakash, “Measurement of focal length using phase shifted moiré deflectometry,” Optics and Lasers in Engineering 51, 776–782 (2013).
[Crossref]

Faridi, M. S.

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

Harris, C.

C. Harris and M. Stephens, “A combined corner and edge detector,” in “Alvey vision conference,” 10–5244 (1988).

Kafri, O.

E. Keren, K. Kreske, and O. Kafri, “Universal method for determining the focal length of optical systems by moiré deflectometry,” Applied Optics 27, 1383–1385 (1988).
[Crossref]

Karam, L. J.

N. D. Narvekar and L. J. Karam, “A no-reference image blur metric based on the cumulative probability of blur detection (CPBD),” IEEE Transactions on Image Processing 20, 2678–2683 (2011).
[Crossref]

Keren, E.

E. Keren, K. Kreske, and O. Kafri, “Universal method for determining the focal length of optical systems by moiré deflectometry,” Applied Optics 27, 1383–1385 (1988).
[Crossref]

Kingslake, R.

R. Kingslake, Applied Optics and Optical Engineering, vol. 1 (Elsevier, 2012).

Kothiyal, M. P.

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

Kreske, K.

E. Keren, K. Kreske, and O. Kafri, “Universal method for determining the focal length of optical systems by moiré deflectometry,” Applied Optics 27, 1383–1385 (1988).
[Crossref]

Lei, F.

F. Lei and L. Dang, “Measuring the focal length of optical systems by grating shearing interferometry,” Applied Optics 33, 6603–6608 (1994).
[Crossref] [PubMed]

Miks, A.

A. Miks and P. Pokorny, “Use of diffraction grating for measuring the focal length and distortion of optical systems,” Applied Optics 54, 10200–10206 (2015).
[Crossref]

A. Miks, J. Novak, and P. Novak, “Analysis of imaging for laser triangulation sensors under scheimpflug rule,” Optics Express 21, 18225–18235 (2013).
[Crossref]

A. Miks and J. Novak, “Estimation of accuracy of optical measuring systems with respect to object distance,” Optics Express 19, 14300–14314 (2011).
[Crossref]

Narvekar, N. D.

N. D. Narvekar and L. J. Karam, “A no-reference image blur metric based on the cumulative probability of blur detection (CPBD),” IEEE Transactions on Image Processing 20, 2678–2683 (2011).
[Crossref]

Novak, J.

A. Miks, J. Novak, and P. Novak, “Analysis of imaging for laser triangulation sensors under scheimpflug rule,” Optics Express 21, 18225–18235 (2013).
[Crossref]

A. Miks and J. Novak, “Estimation of accuracy of optical measuring systems with respect to object distance,” Optics Express 19, 14300–14314 (2011).
[Crossref]

Novak, P.

A. Miks, J. Novak, and P. Novak, “Analysis of imaging for laser triangulation sensors under scheimpflug rule,” Optics Express 21, 18225–18235 (2013).
[Crossref]

Pedrotti, L.

L. Pedrotti, “Basic geometrical optics,” Society of Photo-Optical Instrumentation Engineers, 2017 (2008).

Pokorny, P.

A. Miks and P. Pokorny, “Use of diffraction grating for measuring the focal length and distortion of optical systems,” Applied Optics 54, 10200–10206 (2015).
[Crossref]

Prakash, S.

J. Dhanotia and S. Prakash, “Focal length and radius of curvature measurement using coherent gradient sensing and Fourier fringe analysis,” Optik - International Journal for Light and Electron Optics 124, 2115–2120 (2013).
[Crossref]

S. Trivedi, J. Dhanotia, and S. Prakash, “Measurement of focal length using phase shifted moiré deflectometry,” Optics and Lasers in Engineering 51, 776–782 (2013).
[Crossref]

Qiu, L.

J. Yang, L. Qiu, W. Zhao, and H. Wu, “Laser differential reflection-confocal focal-length measurement,” Optics Express 20, 26–27 (2012).
[Crossref]

Rajabi, Y.

S. Rasouli, Y. Rajabi, and H. Sarabi, “Microlenses focal length measurement using Z-scan and parallel moiré deflectometry,” Optics and Lasers in Engineering 51, 1321–1326 (2013).
[Crossref]

Rasouli, S.

S. Rasouli, Y. Rajabi, and H. Sarabi, “Microlenses focal length measurement using Z-scan and parallel moiré deflectometry,” Optics and Lasers in Engineering 51, 1321–1326 (2013).
[Crossref]

Sarabi, H.

S. Rasouli, Y. Rajabi, and H. Sarabi, “Microlenses focal length measurement using Z-scan and parallel moiré deflectometry,” Optics and Lasers in Engineering 51, 1321–1326 (2013).
[Crossref]

Shakher, C.

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

C. Tay, M. Thakur, L. Chen, and C. Shakher, “Measurement of focal length of lens using phase shifting Lau phase interferometry,” Optics Communications 248, 339–345 (2005).
[Crossref]

Singh, P.

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

Sirohi, R.

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

Sirohi, R. S.

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

Sriram, K. V.

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

Stephens, M.

C. Harris and M. Stephens, “A combined corner and edge detector,” in “Alvey vision conference,” 10–5244 (1988).

Tay, C.

C. Tay, M. Thakur, L. Chen, and C. Shakher, “Measurement of focal length of lens using phase shifting Lau phase interferometry,” Optics Communications 248, 339–345 (2005).
[Crossref]

Thakur, M.

C. Tay, M. Thakur, L. Chen, and C. Shakher, “Measurement of focal length of lens using phase shifting Lau phase interferometry,” Optics Communications 248, 339–345 (2005).
[Crossref]

Trivedi, S.

S. Trivedi, J. Dhanotia, and S. Prakash, “Measurement of focal length using phase shifted moiré deflectometry,” Optics and Lasers in Engineering 51, 776–782 (2013).
[Crossref]

Wu, H.

J. Yang, L. Qiu, W. Zhao, and H. Wu, “Laser differential reflection-confocal focal-length measurement,” Optics Express 20, 26–27 (2012).
[Crossref]

Yang, J.

J. Yang, L. Qiu, W. Zhao, and H. Wu, “Laser differential reflection-confocal focal-length measurement,” Optics Express 20, 26–27 (2012).
[Crossref]

Zhang, G.

D. Chen and G. Zhang, “A new sub-pixel detector for x-corners in camera calibration targets,” in “WSCG SHORT papers proceedings,” 97–100 (2005).

Zhang, Z.

Z. Zhang, “A flexible new technique for camera calibration,” Trans. Pat. Anal. Mach. Intel. 22, 1330–1334(2000).
[Crossref]

Zhao, W.

J. Yang, L. Qiu, W. Zhao, and H. Wu, “Laser differential reflection-confocal focal-length measurement,” Optics Express 20, 26–27 (2012).
[Crossref]

Zimmer, H.-G.

H.-G. Zimmer, Geometrische Optik (Springer-Verlag, 2013).

Applied Optics (5)

E. Keren, K. Kreske, and O. Kafri, “Universal method for determining the focal length of optical systems by moiré deflectometry,” Applied Optics 27, 1383–1385 (1988).
[Crossref]

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

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

F. Lei and L. Dang, “Measuring the focal length of optical systems by grating shearing interferometry,” Applied Optics 33, 6603–6608 (1994).
[Crossref] [PubMed]

A. Miks and P. Pokorny, “Use of diffraction grating for measuring the focal length and distortion of optical systems,” Applied Optics 54, 10200–10206 (2015).
[Crossref]

IEEE Transactions on Image Processing (1)

N. D. Narvekar and L. J. Karam, “A no-reference image blur metric based on the cumulative probability of blur detection (CPBD),” IEEE Transactions on Image Processing 20, 2678–2683 (2011).
[Crossref]

Optics and Lasers in Engineering (2)

S. Rasouli, Y. Rajabi, and H. Sarabi, “Microlenses focal length measurement using Z-scan and parallel moiré deflectometry,” Optics and Lasers in Engineering 51, 1321–1326 (2013).
[Crossref]

S. Trivedi, J. Dhanotia, and S. Prakash, “Measurement of focal length using phase shifted moiré deflectometry,” Optics and Lasers in Engineering 51, 776–782 (2013).
[Crossref]

Optics Communications (1)

C. Tay, M. Thakur, L. Chen, and C. Shakher, “Measurement of focal length of lens using phase shifting Lau phase interferometry,” Optics Communications 248, 339–345 (2005).
[Crossref]

Optics Express (3)

J. Yang, L. Qiu, W. Zhao, and H. Wu, “Laser differential reflection-confocal focal-length measurement,” Optics Express 20, 26–27 (2012).
[Crossref]

A. Miks and J. Novak, “Estimation of accuracy of optical measuring systems with respect to object distance,” Optics Express 19, 14300–14314 (2011).
[Crossref]

A. Miks, J. Novak, and P. Novak, “Analysis of imaging for laser triangulation sensors under scheimpflug rule,” Optics Express 21, 18225–18235 (2013).
[Crossref]

Optik - International Journal for Light and Electron Optics (1)

J. Dhanotia and S. Prakash, “Focal length and radius of curvature measurement using coherent gradient sensing and Fourier fringe analysis,” Optik - International Journal for Light and Electron Optics 124, 2115–2120 (2013).
[Crossref]

Trans. Pat. Anal. Mach. Intel. (1)

Z. Zhang, “A flexible new technique for camera calibration,” Trans. Pat. Anal. Mach. Intel. 22, 1330–1334(2000).
[Crossref]

Other (5)

R. Kingslake, Applied Optics and Optical Engineering, vol. 1 (Elsevier, 2012).

C. Harris and M. Stephens, “A combined corner and edge detector,” in “Alvey vision conference,” 10–5244 (1988).

D. Chen and G. Zhang, “A new sub-pixel detector for x-corners in camera calibration targets,” in “WSCG SHORT papers proceedings,” 97–100 (2005).

L. Pedrotti, “Basic geometrical optics,” Society of Photo-Optical Instrumentation Engineers, 2017 (2008).

H.-G. Zimmer, Geometrische Optik (Springer-Verlag, 2013).

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Figures (7)

Fig. 1
Fig. 1 The thick-lens model.
Fig. 2
Fig. 2 Measurement principle schematic diagram.
Fig. 3
Fig. 3 Measurement procedures.
Fig. 4
Fig. 4 Experimental apparatus.
Fig. 5
Fig. 5 External parameters.
Fig. 6
Fig. 6 Image sharpness.
Fig. 7
Fig. 7 Experimental results.

Tables (1)

Tables Icon

Table 1 Results of Ri and the parameters of Ti

Equations (15)

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1 f + Z C , i + 1 f + z i = 1 f
f = l u , i l u , i + 1 Δ Z C l C , i + 1 l u , i l C , i l u , i + 1
l C , i = ( X C , i ( 1 ) X C , i ( 2 ) ) 2 + ( Y C , i ( 1 ) Y C , i ( 2 ) ) 2 l u , i = ( X u , i ( 1 ) X u , i ( 2 ) ) 2 + ( Y u , i ( 1 ) Y u , i ( 2 ) ) 2
Maximum incident angle = arctan ( D lens + D CCD 2 ( f + Z C , i ) )
[ X C , i Y C , i Z C , i ] = R i [ X W Y W Z W ] = [ r 11 i r 21 i r 31 i r 12 i r 22 i r 32 i r 13 i r 23 i r 33 i ] [ X W Y W Z W ]
[ X C , i Y C , i Z C , i ] = R i [ X W Y W Z W ] + T i = [ r 11 i r 21 i r 31 i r 12 i r 22 i r 32 i r 13 i r 23 i r 33 i ] [ X W Y W Z W ] + [ t x + k x d i t y + k y d i t z + k z d i ]
δ l u , d , i l u , d , i = | m m P + m 2 ( 1 2 m P 2 ) 8 ( m P m ) 2 F 0 2 |
l u , i = l u , d , i + sign ( δ l u , d , i ) δ l u , d , i
Δ f = f l u , i Δ l u , i + f l u , i + 1 Δ l u , i + 1 + f l C , i Δ l C , i + f l C , i + 1 Δ l C , i + 1 + f ( Δ Z C ) Δ ( Δ Z C )
f l u , i = l C , i l u , i + 1 2 Δ Z C ( l C , i + 1 l u , i l C , i l u , i + 1 ) 2 = f Z C , i l u , i Δ Z C
f l u , i + 1 = l C , i + 1 l u 2 Δ Z C ( l C , i + 1 l u , i l C , i l u , i + 1 ) 2 = ( Z C + Δ Z C ) 2 l C , i + 1 Δ Z C
f l C , i = l u , i l u , i + 1 2 Δ Z C ( l C , i + 1 l u , i l C , i l u , i + 1 ) 2 = f Z C , i l C , i Δ Z C
f l C , i + 1 = l u , i 2 l u , i + 1 Δ Z C ( l C , i + 1 l u , i l C , i l u , i + 1 ) 2 = f ( Z C , i + Δ Z C ) l C , i + 1 Δ Z C
f ( Δ Z C ) = l u , i l u , i + 1 l C , i + 1 l u , i l C , i l u , i + 1 = f Δ Z C
Δ f f = ( f l u , i Δ l u , i ) 2 + ( f l u , i + 1 Δ l u , i + 1 ) 2 + ( f l C , i Δ l C , i ) 2 + ( f l C , i + 1 Δ l C , i + 1 ) 2 + ( f ( Δ Z C ) Δ ( Δ Z C ) ) 2 = 9.2710 7 + 1 1000 f 2 f

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