Abstract

The objective of this study was to present a high-speed, on-line means of measuring interior tilt and decentration in a singlet lens. We propose a noncontact method based on polarized optics, which provides inspection functions for the practical measurement of lenses. The proposed system was used to measure a tilted and decentered lens, and the results of which showed strong agreement with those obtained in theoretical predictions and CodeV simulations. The proposed method provides a wide field of inspection applicable to lenses with a diameter up to 70 mm. Measurement accuracy is of 0.14deg/pixel in tilt, and 33μm/pixel in decentration. Inspection time is only 0.78 s.

© 2013 Optical Society of America

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References

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  1. W. S. Beich, “Injection molded polymer optics in the 21st century,” Proc. SPIE 5865, 58650J (2005).
    [CrossRef]
  2. C. C. Chang, Y. L. Wu, and C. C. Lee, “Error compensation in reflection type centering error testing,” Opt. Rev. 16, 149–152 (2009).
    [CrossRef]
  3. P. Scott, “Recent developments in the measurement of aspheric surfaces by contact stylus instrumentation,” Proc. SPIE 4927, 199–207 (2002).
    [CrossRef]
  4. D. J. Whitehouse, “Surface metrology,” Meas. Sci. Technol. 8, 955–972 (1997).
    [CrossRef]
  5. M. F. Küchel, “Interferometric measurement of rotationally symmetric aspheric surfaces,” Proc. SPIE 7389, 738916–738934 (2009).
    [CrossRef]
  6. K. Yoshizumi, T. Murao, J. Masui, R. Imanaka, and Y. Okino, “Ultrahigh accuracy 3-D profilometer,” Appl. Opt. 26, 1647–1653 (1987).
    [CrossRef]
  7. M. Cherrier, I. Erichsen, A. Ruprecht, and S. Krey, “Ultra-fast wavefront analyser for high volume production of camera modules lenses,” Proc. SPIE 6995, 699512 (2008).
    [CrossRef]
  8. J. Heinisch, E. Dumitrescu, and S. Krey, “Novel technique for measurement of centration errors of complex completely mounted multi-element objective lenses,” Proc. SPIE 6288, 628810 (2006).
    [CrossRef]
  9. B. K. Pierscionek and D. D. Y. Chan, “Mathematical description of isogyre formation in refracting structures,” Ophthalmic Physiolog. Opt. 13, 212–215 (1993).
    [CrossRef]
  10. B. K. Pierscionek, “Explanation of isogyre formation by the eye lens,” Ophthalmic Physiolog. Opt. 13, 91–94 (1993).
    [CrossRef]
  11. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley-Interscience, 2007).
  12. E. Hecht, Optics, 4th ed. (Addison Wesley, 2001).
  13. J. Lekner, “Isogyre formation by isotropic refracting bodies,” Ophthalmic Physiolog. Opt. 15, 69–72 (1995).
    [CrossRef]
  14. P. Yeh, “Extended Jones matrix method,” J. Opt. Soc. Am. 72, 507–513 (1982).
    [CrossRef]
  15. P. L. Ruben, “Aberrations arising from decentrations and tilts,” J. Opt. Soc. Am. 54, 45–46 (1964).
    [CrossRef]
  16. R. K. Kimmel and R. E. Parks, ISO 10110 Optics and Optical Instruments: Preparation of Drawings for Optical Elements and Systems: A User’s Guide (Optical Society of America, 2002).
  17. K. Miyamoto, “Image evaluation by spot diagram using a computer,” Appl. Opt. 2, 1247–1250 (1963).
    [CrossRef]
  18. J. Turuwhenua, “A theoretical study of intraocular lens tilt and decentration on perceptual image quality,” Ophthalmic Physiolog. Opt. 25, 556–567 (2005).
    [CrossRef]
  19. P. D. Lin and C. Y. Tsai, “Skew ray tracing and sensitivity analysis of ellipsoidal optical boundary surfaces,” Appl. Math. Model. 32, 2526–2537 (2008).
    [CrossRef]

2009

C. C. Chang, Y. L. Wu, and C. C. Lee, “Error compensation in reflection type centering error testing,” Opt. Rev. 16, 149–152 (2009).
[CrossRef]

M. F. Küchel, “Interferometric measurement of rotationally symmetric aspheric surfaces,” Proc. SPIE 7389, 738916–738934 (2009).
[CrossRef]

2008

M. Cherrier, I. Erichsen, A. Ruprecht, and S. Krey, “Ultra-fast wavefront analyser for high volume production of camera modules lenses,” Proc. SPIE 6995, 699512 (2008).
[CrossRef]

P. D. Lin and C. Y. Tsai, “Skew ray tracing and sensitivity analysis of ellipsoidal optical boundary surfaces,” Appl. Math. Model. 32, 2526–2537 (2008).
[CrossRef]

2006

J. Heinisch, E. Dumitrescu, and S. Krey, “Novel technique for measurement of centration errors of complex completely mounted multi-element objective lenses,” Proc. SPIE 6288, 628810 (2006).
[CrossRef]

2005

W. S. Beich, “Injection molded polymer optics in the 21st century,” Proc. SPIE 5865, 58650J (2005).
[CrossRef]

J. Turuwhenua, “A theoretical study of intraocular lens tilt and decentration on perceptual image quality,” Ophthalmic Physiolog. Opt. 25, 556–567 (2005).
[CrossRef]

2002

P. Scott, “Recent developments in the measurement of aspheric surfaces by contact stylus instrumentation,” Proc. SPIE 4927, 199–207 (2002).
[CrossRef]

1997

D. J. Whitehouse, “Surface metrology,” Meas. Sci. Technol. 8, 955–972 (1997).
[CrossRef]

1995

J. Lekner, “Isogyre formation by isotropic refracting bodies,” Ophthalmic Physiolog. Opt. 15, 69–72 (1995).
[CrossRef]

1993

B. K. Pierscionek and D. D. Y. Chan, “Mathematical description of isogyre formation in refracting structures,” Ophthalmic Physiolog. Opt. 13, 212–215 (1993).
[CrossRef]

B. K. Pierscionek, “Explanation of isogyre formation by the eye lens,” Ophthalmic Physiolog. Opt. 13, 91–94 (1993).
[CrossRef]

1987

K. Yoshizumi, T. Murao, J. Masui, R. Imanaka, and Y. Okino, “Ultrahigh accuracy 3-D profilometer,” Appl. Opt. 26, 1647–1653 (1987).
[CrossRef]

1982

P. Yeh, “Extended Jones matrix method,” J. Opt. Soc. Am. 72, 507–513 (1982).
[CrossRef]

1964

P. L. Ruben, “Aberrations arising from decentrations and tilts,” J. Opt. Soc. Am. 54, 45–46 (1964).
[CrossRef]

1963

K. Miyamoto, “Image evaluation by spot diagram using a computer,” Appl. Opt. 2, 1247–1250 (1963).
[CrossRef]

Beich, W. S.

W. S. Beich, “Injection molded polymer optics in the 21st century,” Proc. SPIE 5865, 58650J (2005).
[CrossRef]

Chan, D. D. Y.

B. K. Pierscionek and D. D. Y. Chan, “Mathematical description of isogyre formation in refracting structures,” Ophthalmic Physiolog. Opt. 13, 212–215 (1993).
[CrossRef]

Chang, C. C.

C. C. Chang, Y. L. Wu, and C. C. Lee, “Error compensation in reflection type centering error testing,” Opt. Rev. 16, 149–152 (2009).
[CrossRef]

Cherrier, M.

M. Cherrier, I. Erichsen, A. Ruprecht, and S. Krey, “Ultra-fast wavefront analyser for high volume production of camera modules lenses,” Proc. SPIE 6995, 699512 (2008).
[CrossRef]

Dumitrescu, E.

J. Heinisch, E. Dumitrescu, and S. Krey, “Novel technique for measurement of centration errors of complex completely mounted multi-element objective lenses,” Proc. SPIE 6288, 628810 (2006).
[CrossRef]

Erichsen, I.

M. Cherrier, I. Erichsen, A. Ruprecht, and S. Krey, “Ultra-fast wavefront analyser for high volume production of camera modules lenses,” Proc. SPIE 6995, 699512 (2008).
[CrossRef]

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison Wesley, 2001).

Heinisch, J.

J. Heinisch, E. Dumitrescu, and S. Krey, “Novel technique for measurement of centration errors of complex completely mounted multi-element objective lenses,” Proc. SPIE 6288, 628810 (2006).
[CrossRef]

Imanaka, R.

K. Yoshizumi, T. Murao, J. Masui, R. Imanaka, and Y. Okino, “Ultrahigh accuracy 3-D profilometer,” Appl. Opt. 26, 1647–1653 (1987).
[CrossRef]

Kimmel, R. K.

R. K. Kimmel and R. E. Parks, ISO 10110 Optics and Optical Instruments: Preparation of Drawings for Optical Elements and Systems: A User’s Guide (Optical Society of America, 2002).

Krey, S.

M. Cherrier, I. Erichsen, A. Ruprecht, and S. Krey, “Ultra-fast wavefront analyser for high volume production of camera modules lenses,” Proc. SPIE 6995, 699512 (2008).
[CrossRef]

J. Heinisch, E. Dumitrescu, and S. Krey, “Novel technique for measurement of centration errors of complex completely mounted multi-element objective lenses,” Proc. SPIE 6288, 628810 (2006).
[CrossRef]

Küchel, M. F.

M. F. Küchel, “Interferometric measurement of rotationally symmetric aspheric surfaces,” Proc. SPIE 7389, 738916–738934 (2009).
[CrossRef]

Lee, C. C.

C. C. Chang, Y. L. Wu, and C. C. Lee, “Error compensation in reflection type centering error testing,” Opt. Rev. 16, 149–152 (2009).
[CrossRef]

Lekner, J.

J. Lekner, “Isogyre formation by isotropic refracting bodies,” Ophthalmic Physiolog. Opt. 15, 69–72 (1995).
[CrossRef]

Lin, P. D.

P. D. Lin and C. Y. Tsai, “Skew ray tracing and sensitivity analysis of ellipsoidal optical boundary surfaces,” Appl. Math. Model. 32, 2526–2537 (2008).
[CrossRef]

Masui, J.

K. Yoshizumi, T. Murao, J. Masui, R. Imanaka, and Y. Okino, “Ultrahigh accuracy 3-D profilometer,” Appl. Opt. 26, 1647–1653 (1987).
[CrossRef]

Miyamoto, K.

K. Miyamoto, “Image evaluation by spot diagram using a computer,” Appl. Opt. 2, 1247–1250 (1963).
[CrossRef]

Murao, T.

K. Yoshizumi, T. Murao, J. Masui, R. Imanaka, and Y. Okino, “Ultrahigh accuracy 3-D profilometer,” Appl. Opt. 26, 1647–1653 (1987).
[CrossRef]

Okino, Y.

K. Yoshizumi, T. Murao, J. Masui, R. Imanaka, and Y. Okino, “Ultrahigh accuracy 3-D profilometer,” Appl. Opt. 26, 1647–1653 (1987).
[CrossRef]

Parks, R. E.

R. K. Kimmel and R. E. Parks, ISO 10110 Optics and Optical Instruments: Preparation of Drawings for Optical Elements and Systems: A User’s Guide (Optical Society of America, 2002).

Pierscionek, B. K.

B. K. Pierscionek and D. D. Y. Chan, “Mathematical description of isogyre formation in refracting structures,” Ophthalmic Physiolog. Opt. 13, 212–215 (1993).
[CrossRef]

B. K. Pierscionek, “Explanation of isogyre formation by the eye lens,” Ophthalmic Physiolog. Opt. 13, 91–94 (1993).
[CrossRef]

Ruben, P. L.

P. L. Ruben, “Aberrations arising from decentrations and tilts,” J. Opt. Soc. Am. 54, 45–46 (1964).
[CrossRef]

Ruprecht, A.

M. Cherrier, I. Erichsen, A. Ruprecht, and S. Krey, “Ultra-fast wavefront analyser for high volume production of camera modules lenses,” Proc. SPIE 6995, 699512 (2008).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley-Interscience, 2007).

Scott, P.

P. Scott, “Recent developments in the measurement of aspheric surfaces by contact stylus instrumentation,” Proc. SPIE 4927, 199–207 (2002).
[CrossRef]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley-Interscience, 2007).

Tsai, C. Y.

P. D. Lin and C. Y. Tsai, “Skew ray tracing and sensitivity analysis of ellipsoidal optical boundary surfaces,” Appl. Math. Model. 32, 2526–2537 (2008).
[CrossRef]

Turuwhenua, J.

J. Turuwhenua, “A theoretical study of intraocular lens tilt and decentration on perceptual image quality,” Ophthalmic Physiolog. Opt. 25, 556–567 (2005).
[CrossRef]

Whitehouse, D. J.

D. J. Whitehouse, “Surface metrology,” Meas. Sci. Technol. 8, 955–972 (1997).
[CrossRef]

Wu, Y. L.

C. C. Chang, Y. L. Wu, and C. C. Lee, “Error compensation in reflection type centering error testing,” Opt. Rev. 16, 149–152 (2009).
[CrossRef]

Yeh, P.

P. Yeh, “Extended Jones matrix method,” J. Opt. Soc. Am. 72, 507–513 (1982).
[CrossRef]

Yoshizumi, K.

K. Yoshizumi, T. Murao, J. Masui, R. Imanaka, and Y. Okino, “Ultrahigh accuracy 3-D profilometer,” Appl. Opt. 26, 1647–1653 (1987).
[CrossRef]

Appl. Math. Model.

P. D. Lin and C. Y. Tsai, “Skew ray tracing and sensitivity analysis of ellipsoidal optical boundary surfaces,” Appl. Math. Model. 32, 2526–2537 (2008).
[CrossRef]

Appl. Opt.

K. Yoshizumi, T. Murao, J. Masui, R. Imanaka, and Y. Okino, “Ultrahigh accuracy 3-D profilometer,” Appl. Opt. 26, 1647–1653 (1987).
[CrossRef]

K. Miyamoto, “Image evaluation by spot diagram using a computer,” Appl. Opt. 2, 1247–1250 (1963).
[CrossRef]

J. Opt. Soc. Am.

P. Yeh, “Extended Jones matrix method,” J. Opt. Soc. Am. 72, 507–513 (1982).
[CrossRef]

P. L. Ruben, “Aberrations arising from decentrations and tilts,” J. Opt. Soc. Am. 54, 45–46 (1964).
[CrossRef]

Meas. Sci. Technol.

D. J. Whitehouse, “Surface metrology,” Meas. Sci. Technol. 8, 955–972 (1997).
[CrossRef]

Ophthalmic Physiolog. Opt.

B. K. Pierscionek and D. D. Y. Chan, “Mathematical description of isogyre formation in refracting structures,” Ophthalmic Physiolog. Opt. 13, 212–215 (1993).
[CrossRef]

B. K. Pierscionek, “Explanation of isogyre formation by the eye lens,” Ophthalmic Physiolog. Opt. 13, 91–94 (1993).
[CrossRef]

J. Turuwhenua, “A theoretical study of intraocular lens tilt and decentration on perceptual image quality,” Ophthalmic Physiolog. Opt. 25, 556–567 (2005).
[CrossRef]

J. Lekner, “Isogyre formation by isotropic refracting bodies,” Ophthalmic Physiolog. Opt. 15, 69–72 (1995).
[CrossRef]

Opt. Rev.

C. C. Chang, Y. L. Wu, and C. C. Lee, “Error compensation in reflection type centering error testing,” Opt. Rev. 16, 149–152 (2009).
[CrossRef]

Proc. SPIE

P. Scott, “Recent developments in the measurement of aspheric surfaces by contact stylus instrumentation,” Proc. SPIE 4927, 199–207 (2002).
[CrossRef]

M. F. Küchel, “Interferometric measurement of rotationally symmetric aspheric surfaces,” Proc. SPIE 7389, 738916–738934 (2009).
[CrossRef]

W. S. Beich, “Injection molded polymer optics in the 21st century,” Proc. SPIE 5865, 58650J (2005).
[CrossRef]

M. Cherrier, I. Erichsen, A. Ruprecht, and S. Krey, “Ultra-fast wavefront analyser for high volume production of camera modules lenses,” Proc. SPIE 6995, 699512 (2008).
[CrossRef]

J. Heinisch, E. Dumitrescu, and S. Krey, “Novel technique for measurement of centration errors of complex completely mounted multi-element objective lenses,” Proc. SPIE 6288, 628810 (2006).
[CrossRef]

Other

R. K. Kimmel and R. E. Parks, ISO 10110 Optics and Optical Instruments: Preparation of Drawings for Optical Elements and Systems: A User’s Guide (Optical Society of America, 2002).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley-Interscience, 2007).

E. Hecht, Optics, 4th ed. (Addison Wesley, 2001).

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Figures (16)

Fig. 1.
Fig. 1.

Optical setup of isogyre: definition and rotation of coordinate.

Fig. 2.
Fig. 2.

Intensity contour of isogyre effect: a plano–convex lens.

Fig. 3.
Fig. 3.

Definition and image quality of (a) standard lens, (b) tilted lens, and (c) decentered lens.

Fig. 4.
Fig. 4.

Isogyre contour: a plano–convex lens with (a) a standard profile and (b) a tilt imperfection.

Fig. 5.
Fig. 5.

Inspection functions for a tilted plano–convex lens in different surface curvature.

Fig. 6.
Fig. 6.

Inspection functions for a tilted plano–convex lens in different refractive index.

Fig. 7.
Fig. 7.

Inspection functions for a tilted concave–convex lens in different refractive index.

Fig. 8.
Fig. 8.

Inspection functions for a decentered concave–convex lens in different refractive index.

Fig. 9.
Fig. 9.

Inspection functions for a concave–convex lens.

Fig. 10.
Fig. 10.

Source code of Code Simulation: concave–convex singlet.

Fig. 11.
Fig. 11.

Source code of Code Simulation: isogyre simulation.

Fig. 12.
Fig. 12.

Optical system of the automatic optical inspection used in this study.

Fig. 13.
Fig. 13.

Experimental setup of automatic optical inspection.

Fig. 14.
Fig. 14.

Inspection instrument adopts the inspection method.

Fig. 15.
Fig. 15.

Control panel of the automatic inspection system.

Fig. 16.
Fig. 16.

Measured result of one of customized lens with 1 mm decentration.

Equations (26)

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E1=ε^sE0ejk1·r=(e^sE0cosϕ+e^pE0sinϕ)ejk1·r,
E2=(e^stsE0cosϕ+e^ptpE0sinϕ)ejk2·r.
ts=2n1cosθ1n1cosθ1+n2cosθ2,
tp=2n1cosθ1n1cosθ2+n2cosθ1,
k1·r=k2·r.
E2=[ε^s(tpsin2ϕ+tscos2ϕ)]E0+ε^psinϕcosϕ(tpts)E0]ejk2·r.
Eres=ε^psinϕcosϕ(tpts)E0ejk2·r.
Eres=ε^psinϕcosϕ[2n1cosθ1(n1n2)(cosθ1cosθ2)(n1cosθ1+n2cosθ2)(n1cosθ2+n2cosθ1)]E0ejk2·r,
[0Eres]=[0001]analyzer[cosϕsinϕsinϕcosϕ]inverse coordinate rotation[ts00tp]Fresnel eqs.[cosϕsinϕsinϕcosϕ]coordinate rotation[1000]polarizer[EεEψ]light source.
Ei+1=[ts00tp]iEi=[ts00tp]i[EsEp]i,
Ei+1=(2nicosθinicosθi+ni+1cosθi+1e^sEs(i)+2nicosθinicosθi+1+ni+1cosθie^pEp(i))ejki+1·r.
E3=(e^sts(2)ts(1)E0cosϕ+e^ptp(2)tp(1)E0sinϕ)ejk3·r.
E3=[tp(2)tp(1)sin2ϕ+ts(2)ts(1)cos2ϕsinϕcosϕ(tp(2)tp(1)ts(2)ts(1))]E0ejk3·r,
Eres=ε^psinϕcosϕ(tp(2)tp(1)ts(2)ts(1))E0ejk3·r.
x¯=1ni=1nxi,
y¯=1ni=1nyi.
σρ=02π0D/2ρ|Eres|2ρdρdϕ02π0D/2|Eres|2ρdρdϕ,
σ^ϕ=02π0D/2ϕ^|Eres|2ρdρdϕ02π0D/2|Eres|2ρdρdϕ.
f(σρ,σ^ϕ)=g(α,e^α,β,e^β;R1,R2,n1,n2,t,D),
f(σρ,σ^ϕ)=g(α,e^α,β,e^β,).
f1(σρ)=g1(α,β),
f2(σ^ϕ)=g2(e^α,e^β).
σρ=C1α+C2β+ερ,
σ^ϕ=C3e^α+C4e^β+C5ε^ϕ.
(R1,R2,n1,n2,t,D)=(268.92,54.638,1.00,1.52,5.00,70).
σres=Ires×C.

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