Abstract

A new laser differential confocal lens refractive index measurement is proposed, which uses the absolute zero of the differential confocal axial intensity curve to precisely identify the positions of the objective when the measurement pencil is focused on the vertex of the test lens and the reflector with or without the test lens in the measurement light-path, and then uses aberration compensation and ray tracing facet iterative calculation to obtain the refractive index of the test lens, thereby achieving the high-precision noncontact measurement of lens refractive index. The theoretical analyses and preliminary experiments indicate that the accuracy of the approach can reach about 2.5×104.

© 2011 Optical Society of America

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References

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  1. R. Ulrich and R. Torge, “Measurement of thin film parameters with a prism coupler,” Appl. Opt. 12, 2901–2908(1973).
    [CrossRef] [PubMed]
  2. M. Debenham, G. D. Dew, and D. E. Putland, “An improved recording refractometer for optical glasses in the wavelength range 300 to 2600 nm,” Opt. Acta 26, 1487–1503(1979).
    [CrossRef]
  3. S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65, 167–180 (2002).
    [CrossRef]
  4. S. H. Lee, S. H. Kim, and K. H. Kim, “A novel method for measuring continuous dispersion spectrum of electro-optic coefficients of nonlinear materials,” Opt. Express 17, 9828–9833(2009).
    [CrossRef] [PubMed]
  5. P. H. Tomlins, P. Woolliams, C. Hart, A. Beaumont, and M. Tedaldi, “Optical coherence refractometry,” Opt. Lett. 33, 2272–2274 (2008).
    [CrossRef] [PubMed]
  6. L. Su, Y. Chen, A. Y. Yi, F. Klocke, and G. Pongs, “Refractive index variation in compression molding of precision glass optical components,” Appl. Opt. 47, 1662–1667 (2008).
    [CrossRef] [PubMed]
  7. G. Smith, “Liquid immersion method for the measurement of the refractive index of a simple lens,” Appl. Opt. 21, 755–757(1982).
    [CrossRef] [PubMed]
  8. R. S. Kasana, A. Goswami, and K. Soni, “Non-destructive multiple beam interferometric technique for measuring the refractive indices of lenses,” Opt. Commun. 236, 289–294 (2004).
    [CrossRef]
  9. K. Soni and R. S. Kasana, “The use of defocussed position of a Ronchi grating for evaluating the refractive index of lens,” Opt. Laser Technol. 39, 1334–1338 (2007).
    [CrossRef]
  10. K. Soni and R. S. Kasana, “The role of an acousto-optic grating in determining the refractive index of a lens,” Meas. Sci. Technol. 18, 1667–1671 (2007).
    [CrossRef]
  11. H. Suhara, “Interferometric measurement of the refractive-index distribution in plastic lenses by use of computed tomography,” Appl. Opt. 41, 5317–5325 (2002).
    [CrossRef] [PubMed]
  12. V. K. Chhaniwal, A. Anand, and C. S. Narayanamurthy, “Determination of refractive indices of biconvex lenses by use of a Michelson interferometer,” Appl. Opt. 45, 3985–3990 (2006).
    [CrossRef] [PubMed]
  13. A. Anand and V. K. Chhaniwal, “Measurement of parameters of simple lenses using digital holographic interferometry and a synthetic reference wave,” Appl. Opt. 46, 2022–2026 (2007).
    [CrossRef] [PubMed]
  14. W. Zhao, J. Tan, and L. Qiu, “Bipolar absolute differential confocal approach to higher spatial resolution,” Opt. Express 12, 5013–5021 (2004).
    [CrossRef] [PubMed]
  15. W. Zhao, R. Sun, L. Qiu, and D. Sha, “Laser differential confocal radius measurement,” Opt. Express 18, 2345–2360 (2010).
    [CrossRef] [PubMed]

2010 (1)

2009 (1)

2008 (2)

2007 (3)

A. Anand and V. K. Chhaniwal, “Measurement of parameters of simple lenses using digital holographic interferometry and a synthetic reference wave,” Appl. Opt. 46, 2022–2026 (2007).
[CrossRef] [PubMed]

K. Soni and R. S. Kasana, “The use of defocussed position of a Ronchi grating for evaluating the refractive index of lens,” Opt. Laser Technol. 39, 1334–1338 (2007).
[CrossRef]

K. Soni and R. S. Kasana, “The role of an acousto-optic grating in determining the refractive index of a lens,” Meas. Sci. Technol. 18, 1667–1671 (2007).
[CrossRef]

2006 (1)

2004 (2)

R. S. Kasana, A. Goswami, and K. Soni, “Non-destructive multiple beam interferometric technique for measuring the refractive indices of lenses,” Opt. Commun. 236, 289–294 (2004).
[CrossRef]

W. Zhao, J. Tan, and L. Qiu, “Bipolar absolute differential confocal approach to higher spatial resolution,” Opt. Express 12, 5013–5021 (2004).
[CrossRef] [PubMed]

2002 (2)

1982 (1)

1979 (1)

M. Debenham, G. D. Dew, and D. E. Putland, “An improved recording refractometer for optical glasses in the wavelength range 300 to 2600 nm,” Opt. Acta 26, 1487–1503(1979).
[CrossRef]

1973 (1)

Anand, A.

Beaumont, A.

Chen, Y.

Chhaniwal, V. K.

Debenham, M.

M. Debenham, G. D. Dew, and D. E. Putland, “An improved recording refractometer for optical glasses in the wavelength range 300 to 2600 nm,” Opt. Acta 26, 1487–1503(1979).
[CrossRef]

Dew, G. D.

M. Debenham, G. D. Dew, and D. E. Putland, “An improved recording refractometer for optical glasses in the wavelength range 300 to 2600 nm,” Opt. Acta 26, 1487–1503(1979).
[CrossRef]

Goswami, A.

R. S. Kasana, A. Goswami, and K. Soni, “Non-destructive multiple beam interferometric technique for measuring the refractive indices of lenses,” Opt. Commun. 236, 289–294 (2004).
[CrossRef]

Hart, C.

Kasana, R. S.

K. Soni and R. S. Kasana, “The use of defocussed position of a Ronchi grating for evaluating the refractive index of lens,” Opt. Laser Technol. 39, 1334–1338 (2007).
[CrossRef]

K. Soni and R. S. Kasana, “The role of an acousto-optic grating in determining the refractive index of a lens,” Meas. Sci. Technol. 18, 1667–1671 (2007).
[CrossRef]

R. S. Kasana, A. Goswami, and K. Soni, “Non-destructive multiple beam interferometric technique for measuring the refractive indices of lenses,” Opt. Commun. 236, 289–294 (2004).
[CrossRef]

Kim, K. H.

Kim, S. H.

Klocke, F.

Lee, S. H.

Narayanamurthy, C. S.

Pongs, G.

Putland, D. E.

M. Debenham, G. D. Dew, and D. E. Putland, “An improved recording refractometer for optical glasses in the wavelength range 300 to 2600 nm,” Opt. Acta 26, 1487–1503(1979).
[CrossRef]

Qiu, L.

Sha, D.

Singh, S.

S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65, 167–180 (2002).
[CrossRef]

Smith, G.

Soni, K.

K. Soni and R. S. Kasana, “The use of defocussed position of a Ronchi grating for evaluating the refractive index of lens,” Opt. Laser Technol. 39, 1334–1338 (2007).
[CrossRef]

K. Soni and R. S. Kasana, “The role of an acousto-optic grating in determining the refractive index of a lens,” Meas. Sci. Technol. 18, 1667–1671 (2007).
[CrossRef]

R. S. Kasana, A. Goswami, and K. Soni, “Non-destructive multiple beam interferometric technique for measuring the refractive indices of lenses,” Opt. Commun. 236, 289–294 (2004).
[CrossRef]

Su, L.

Suhara, H.

Sun, R.

Tan, J.

Tedaldi, M.

Tomlins, P. H.

Torge, R.

Ulrich, R.

Woolliams, P.

Yi, A. Y.

Zhao, W.

Appl. Opt. (6)

Meas. Sci. Technol. (1)

K. Soni and R. S. Kasana, “The role of an acousto-optic grating in determining the refractive index of a lens,” Meas. Sci. Technol. 18, 1667–1671 (2007).
[CrossRef]

Opt. Acta (1)

M. Debenham, G. D. Dew, and D. E. Putland, “An improved recording refractometer for optical glasses in the wavelength range 300 to 2600 nm,” Opt. Acta 26, 1487–1503(1979).
[CrossRef]

Opt. Commun. (1)

R. S. Kasana, A. Goswami, and K. Soni, “Non-destructive multiple beam interferometric technique for measuring the refractive indices of lenses,” Opt. Commun. 236, 289–294 (2004).
[CrossRef]

Opt. Express (3)

Opt. Laser Technol. (1)

K. Soni and R. S. Kasana, “The use of defocussed position of a Ronchi grating for evaluating the refractive index of lens,” Opt. Laser Technol. 39, 1334–1338 (2007).
[CrossRef]

Opt. Lett. (1)

Phys. Scr. (1)

S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65, 167–180 (2002).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Refractive index measurement principle.

Fig. 2
Fig. 2

Schematic of ROC measurement principle.

Fig. 3
Fig. 3

Refractive index measurement principle.

Fig. 4
Fig. 4

Ray tracing used for refractive index calculation.

Fig. 5
Fig. 5

Annular beam.

Fig. 6
Fig. 6

Effect of spherical aberration A 040 ρ 4 on identification precision.

Fig. 7
Fig. 7

Effect of astigmatism A 022 ρ 2 cos 2 γ on identification precision.

Fig. 8
Fig. 8

Test samples.

Fig. 9
Fig. 9

The principle of the MDM.

Fig. 10
Fig. 10

DCRIM experiment setup.

Fig. 11
Fig. 11

Calibration of the numerical aperture NA.

Fig. 12
Fig. 12

Radius measurement curves.

Fig. 13
Fig. 13

Refractive index measurement curves.

Equations (34)

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I A ( v , u , u M ) = | 1 π 0 2 π 0 1 p C ( ρ , γ ) · p 1 ( ρ , γ ) · p 1 ( ρ , π + γ ) · p 2 ( ρ , π + γ ) · e j ρ 2 ( 2 u + u M ) / 2 · e j ρ v cos γ ρ d ρ d γ | 2 | 1 π 0 2 π 0 1 p C ( ρ , γ ) · p 1 ( ρ , γ ) · p 1 ( ρ , π + γ ) · p 2 ( ρ , π + γ ) · e j ρ 2 ( 2 u u M ) / 2 · e j ρ v cos γ ρ d ρ d γ | 2 ,
{ u = 2 π λ NA 2 · z v = π λ NA · r obj ,
I A ( 0 , u , u M ) = | 2 0 1 e j ρ 2 ( 2 u + u M ) / 2 ρ d ρ | 2 | 2 0 1 e j ρ 2 ( 2 u u M ) / 2 ρ d ρ | 2 .
I B ( v , u , u M ) = | 1 π 0 2 π 0 1 e j ρ 2 ( 2 u + u M ) / 2 · e j 2 k Φ ( ρ , γ ) · e j ρ v cos γ ρ d ρ d γ | 2 | 1 π 0 2 π 0 1 e j ρ 2 ( 2 u u M ) / 2 · e j 2 k Φ ( ρ , γ ) · e j ρ v cos γ ρ d ρ d γ | 2 ,
I B ( 0 , u , u M ) = | 1 π 0 2 π 0 1 e j ρ 2 ( 2 u + u M ) / 2 · e j 2 k Φ ( ρ , γ ) ρ d ρ d γ | 2 | 1 π 0 2 π 0 1 e j ρ 2 ( 2 u u M ) / 2 · e j 2 k Φ ( ρ , γ ) ρ d ρ d γ | 2 .
I ( v , u , u M , ε ) = | 1 π 0 2 π ε 1 e j ρ 2 ( 2 u + u M ) / 2 · e j 2 k ψ ( ρ , γ ) · e j ρ v cos γ ρ d ρ d γ | 2 | 1 π 0 2 π ε 1 e j ρ 2 ( 2 u u M ) / 2 · e j 2 k ψ ( ρ , γ ) · e j ρ v cos γ ρ d ρ d γ | 2 ,
I ( 0 , u , u M , ε ) = | 1 π 0 2 π ε 1 e j ρ 2 ( 2 u + u M ) / 2 · e j k ψ ( ρ , γ ) ρ d ρ d γ | 2 | 1 π 0 2 π ε 1 e j ρ 2 ( 2 u u M ) / 2 · e j k ψ ( ρ , γ ) ρ d ρ d γ | 2 ,
θ 1 = arctan ( ρ · NA 2 1 NA 2 ) .
t ( r 1 , d 1 , n , ρ , NA ) = r 1 + n 0 n · sin θ 1 · ( d 1 r 1 ) sin [ θ 1 + arcsin ( d 1 r 1 r 1 · sin θ 1 ) arcsin ( n 0 n · d 1 r 1 r 1 · sin θ 1 ) ] .
{ θ 1 = θ 1 + arcsin ( d 2 r 1 r 1 · sin θ 1 ) arcsin ( n 0 n · d 2 r 1 r 1 · sin θ 1 ) , l 1 = r 1 + n 0 n · sin θ 1 sin θ 1 · ( d 2 r 1 ) , θ 2 = θ 1 + arcsin ( l 1 t r 2 r 2 · sin θ 1 ) arcsin ( n n 0 · l 1 t r 2 r 2 · sin θ 1 ) , l 2 ( r 1 , r 2 , d 1 , d 2 , n , ρ , NA ) = r 2 + n n 0 · sin θ 1 sin θ 2 · ( l 1 t r 2 ) ,
d 3 = t + l 2 .
t = 2 ( 1 ε 2 ) ε 1 t ( r 1 , d 1 , n , ρ , NA ) · K ( ρ ) · ρ d ρ ,
l 2 = 2 ( 1 ε 2 ) ε 1 l 2 ( r 1 , r 2 , d 1 , d 2 , n , ρ , NA ) · K ( ρ ) · ρ d ρ .
d 3 = 2 ( 1 ε 2 ) ε 1 [ t ( r 1 , d 1 , n , ρ , NA ) + l 2 ( r 1 , r 2 , d 1 , d 2 , n , ρ , NA ) ] · K ( ρ ) · ρ d ρ ,
σ n ri = | n r i σ ri | .
σ n di = | t d i σ di | .
σ L = | σ n air L deadpath 2 + d i 2 | ( L deadpath 2 + d i 2 ) 1 / 2 · [ ( 2.68 × 10 9 σ Pa ) 2 + ( 9.27 × 10 7 σ K ) 2 + ( 1 × 10 8 σ H ) 2 ] 1 / 2 ,
S ( 0 , 0 , u M , 0.7 ) = | I ( 0 , u , u M , 0.7 ) u | u = 0 | = | 2 · sinc ( 0.51 u M 4 ) · [ ( 0.51 u M 4 ) · cos ( 0.51 u M 4 ) sin ( 0.51 u M 4 ) ( 0.51 u M 4 ) 2 ] | .
σ z = | δ I ( 0 , 0 , u M , 0.7 ) 0.54 · 2 λ π · NA 2 / ( 1 NA 2 ) | = 3.70 · λ · ( 1 NA 2 ) π · SNR · NA 2 ,
I ( 0 , u , u M , ε , A 040 ρ 4 ) = | 2 ε 1 e 2 j A 040 ρ 4 · e j ρ 2 ( 2 u + u M ) / 2 ρ d ρ | 2 | 2 ε 1 e 2 j A 040 ρ 4 · e j ρ 2 ( 2 u u M ) / 2 ρ d ρ | 2 .
I ( 0 , u , u M , ε , A 022 ρ 2 cos 2 γ ) = 1 π 2 · | 0 2 π ε 1 e j ρ 2 ( 2 u + u M ) / 2 · e j 2 k A 022 ρ 2 cos 2 γ ρ d ρ d γ | 2 1 π 2 · | 0 2 π ε 1 e j ρ 2 ( 2 u u M ) / 2 · e j 2 k A 022 ρ 2 cos 2 γ ρ d ρ d γ | 2 .
σ di σ L 2 + 2 · σ Z 2 .
σ n NA = | n NA σ NA | .
σ n = ( σ n r 1 2 + σ n r 2 2 + σ n d 1 2 + σ n d 2 2 + σ n d 3 2 + σ n NA 2 ) 1 / 2 .
n = sin α sin β = sin [ ( δ + A ) / 2 ] sin ( A / 2 ) .
NA = 2 · [ n given 2 ( t given / d flat ) 2 ] 1 ( t given / d flat ) 2 .
σ NA = | 2 NA · ( d flat 2 t given 2 ) · [ ( n given 2 · d flat NA 2 · d flat ) · σ d flat + ( NA 2 · t given t given ) · σ t given + d flat 2 · n given · σ n given ] | .
{ a P 1 + b P 1 = 0.00008 mm a P 2 + b P 2 = 0.00020 mm .
16.7423 = 1 π · ( 1 0.7 2 ) 0.7 1 [ t ( , 3.3440 , n , ρ , 0.14894 ) + l 2 ( , 100.0968 , 3.3440 , 14.3483 , n , ρ , 0.14894 ) ] · 2 π ρ d ρ .
{ σ r 1 = 0 σ r 2 = r 2 × 4 × 10 6 0.0004 mm .
σ L d 1 σ L d 2 σ L d 3 0.000017 mm .
σ z = | 3.70 · λ · ( 1 NA 2 ) π · SNR · NA 2 | = | 3.70 × 632.8 × 10 6 × ( 1 0.14894 2 ) π × 200 × 0.14894 2 | mm 0.00016 mm .
σ NA = | 2 × ( 1.513601 2 0.14894 2 ) × 19.9583 × 0.0002 0.14894 × ( 19.9583 2 30.3042 2 ) + 2 × ( 0.14894 2 1 ) × 30.3042 × 0.0005 0.14894 × ( 19.9583 2 30.3042 2 ) + 2 × 19.9583 2 × 1.513601 × 3 × 10 6 0.14894 × ( 19.9583 2 30.3042 2 ) | 7.2 × 10 5 .
σ n analysis = [ 0 2 + ( 1.4 × 10 6 ) 2 + ( 1.7 × 10 5 ) 2 + ( 4.8 × 10 5 ) 2 + ( 4.2 × 10 5 ) 2 + ( 1.25 × 10 4 ) 2 ] 1 / 2 1.4 × 10 4 .

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