Abstract

The proposed total internal reflection (TIR)-based technique can be used for measuring the refractive index of lenses. Distribution of the phase difference between the $s$- and $p$-polarization states of the reflected light induced by TIR can be obtained by a polarization camera. The refractive index of the lens can be determined from the detected maximum phase difference, with the specific measurement equation. Only the maximum phase difference needs to be measured. Information about the incident angle, thickness of the lens, and the matching liquid is not needed. The experimental results demonstrate that the resolution of the system can reach ${4.8} \times {{1}}{{{0}}^{- 4}}\;{\rm{RIU}}$.

© 2021 Optical Society of America

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References

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  1. C. Y. Wang and P. J. Wang, “Analysis of optical properties in injection-molded and compression-molded optical lenses,” Appl. Opt. 53, 2523–2531 (2014).
    [Crossref]
  2. G. C. Firestone and A. Y. Yi, “Precision laboratory apparatus for high temperature compression molding of glass lenses,” Rev. Sci. Instrum. 76, 063101 (2005).
    [Crossref]
  3. A. Y. Yi and A. Jain, “Compression molding of aspherical glass lenses–a combined experimental and numerical analysis,” J. Am. Ceram. Soc. 88, 579–586 (2005).
    [Crossref]
  4. D. Tentori and J. R. Lerma, “Refractometry by minimum deviation: accuracy analysis,” Opt. Eng. 29, 160–168 (1990).
    [Crossref]
  5. G. Smith, “Liquid immersion method for the measurement of the refractive index of a simple lens,” Appl. Opt. 21, 755–757 (1982).
    [Crossref]
  6. 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]
  7. 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]
  8. 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]
  9. 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]
  10. 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]
  11. V. K. Chhaniwal, J. M. Kihiko, S. Dubey, G. Shearon, B. Javidi, and A. Anand, “Digital holographic testing of biconvex lenses,” Appl. Opt. 52, 8714–8722 (2013).
    [Crossref]
  12. V. K. Chhaniwal and A. Anand, “Determination of lens parameters with digital holography,” Proc. SPIE 6616, 66164H (2007).
    [Crossref]
  13. L. Chen, X. Guo, and J. Hao, “Lens refractive index measurement based on fiber point-diffraction longitudinal interferometry,” Opt. Express 21, 22389–22399 (2013).
    [Crossref]
  14. M. H. Chiu, W. C. Chen, and C. T. Tan, “Small displacement measurements based on an angular-deviation amplifier and interferometric phase detection,” Appl. Opt. 54, 2885–2890 (2015).
    [Crossref]
  15. J. Y. Lee, T. K. Chou, and H. C. Shih, “Polarization-interferometric surface-plasmon-resonance imaging system,” Opt. Lett. 33, 434–436 (2008).
    [Crossref]
  16. R. G. Driggers, Encyclopedia of Optical Engineering, 2nd ed. (Marcel Dekker, 2003).
  17. M. H. Chiu, J. Y. Lee, and D. C. Su, “Refractive-index measurement based on the effects of total internal reflection and the uses of heterodyne interferometry,” Appl. Opt. 36, 2936–2939 (1997).
    [Crossref]
  18. P. P. Herrmann, “Determination of thickness, refractive index, and dispersion of waveguiding thin films with an Abbe refractometer,” Appl. Opt. 19, 3261–3262 (1980).
    [Crossref]
  19. H. Li and S. Xie, “Measurement method of the refractive index of biotissue by total internal reflection,” Appl. Opt. 35, 1793–1795 (1996).
    [Crossref]
  20. Q. W. Song, C. Y. Ku, C. Zhang, R. B. Gross, R. R. Birge, and R. Michalak, “Modified critical angle method for measuring the refractive index of bio-optical materials and its application to bacteriorhodopsin,” J. Opt. Soc. Am. B 12, 797–803 (1995).
    [Crossref]
  21. R. M. A. Azzam, “Phase shifts that accompany total internal reflection at a dielectric–dielectric interface,” J. Opt. Soc. Am. A 21, 1559–1563 (2004).
    [Crossref]
  22. S. Patskovsky, M. Meunier, and A. V. Kabashin, “Phase-sensitive silicon-based total internal reflection sensor,” Opt. Express 15, 12523–12528 (2007).
    [Crossref]
  23. “Polarized color camera with 5.0 MP PHX050S-QC,” https://www.edmundoptics.com/p/lucid-vision-labs-phoenixtrade-phx050s-qc-sony-imx250myr-50-mp-polarized-color-camera/41797/ .
  24. K. H. Chen, Y. H. Wang, J. H. Chen, and C. H. Lin, “Full-field refractive index measurement using absolute-phase total internal reflection heterodyne interferometry,” Appl. Phys. B 126, 109 (2020).
    [Crossref]
  25. “Refractive indices of different materials,” https://refractiveindex.info/ .
  26. B. S. Lin, M. J. Su, P. H. Cheng, P. J. Tseng, and S. J. Chen, “Temporal and spatial denoising of depth maps,” Sensors 15, 18506–18525 (2015).
    [Crossref]
  27. M. Camplani, T. Mantecón, and L. Salgado, “Depth-color fusion strategy for 3-D scene modeling with Kinect,” IEEE Trans. Cybern. 43, 1560–1571 (2013).
    [Crossref]
  28. R. J. Moffat, “Describing the uncertainties in experimental results,” Exp. Therm. Fluid. Sci. 1, 3–17 (1988).
    [Crossref]
  29. H. L. Hsieh, J. Y. Lee, L. Y. Chen, and Y. Yang, “Development of an angular displacement measurement technique through birefringence heterodyne interferometry,” Opt. Express 24, 6802–6813 (2016).
    [Crossref]

2020 (1)

K. H. Chen, Y. H. Wang, J. H. Chen, and C. H. Lin, “Full-field refractive index measurement using absolute-phase total internal reflection heterodyne interferometry,” Appl. Phys. B 126, 109 (2020).
[Crossref]

2016 (1)

2015 (2)

B. S. Lin, M. J. Su, P. H. Cheng, P. J. Tseng, and S. J. Chen, “Temporal and spatial denoising of depth maps,” Sensors 15, 18506–18525 (2015).
[Crossref]

M. H. Chiu, W. C. Chen, and C. T. Tan, “Small displacement measurements based on an angular-deviation amplifier and interferometric phase detection,” Appl. Opt. 54, 2885–2890 (2015).
[Crossref]

2014 (1)

2013 (3)

2008 (1)

2007 (5)

V. K. Chhaniwal and A. Anand, “Determination of lens parameters with digital holography,” Proc. SPIE 6616, 66164H (2007).
[Crossref]

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]

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]

S. Patskovsky, M. Meunier, and A. V. Kabashin, “Phase-sensitive silicon-based total internal reflection sensor,” Opt. Express 15, 12523–12528 (2007).
[Crossref]

2006 (1)

2005 (2)

G. C. Firestone and A. Y. Yi, “Precision laboratory apparatus for high temperature compression molding of glass lenses,” Rev. Sci. Instrum. 76, 063101 (2005).
[Crossref]

A. Y. Yi and A. Jain, “Compression molding of aspherical glass lenses–a combined experimental and numerical analysis,” J. Am. Ceram. Soc. 88, 579–586 (2005).
[Crossref]

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]

R. M. A. Azzam, “Phase shifts that accompany total internal reflection at a dielectric–dielectric interface,” J. Opt. Soc. Am. A 21, 1559–1563 (2004).
[Crossref]

1997 (1)

1996 (1)

1995 (1)

1990 (1)

D. Tentori and J. R. Lerma, “Refractometry by minimum deviation: accuracy analysis,” Opt. Eng. 29, 160–168 (1990).
[Crossref]

1988 (1)

R. J. Moffat, “Describing the uncertainties in experimental results,” Exp. Therm. Fluid. Sci. 1, 3–17 (1988).
[Crossref]

1982 (1)

1980 (1)

Anand, A.

Azzam, R. M. A.

Birge, R. R.

Camplani, M.

M. Camplani, T. Mantecón, and L. Salgado, “Depth-color fusion strategy for 3-D scene modeling with Kinect,” IEEE Trans. Cybern. 43, 1560–1571 (2013).
[Crossref]

Chen, J. H.

K. H. Chen, Y. H. Wang, J. H. Chen, and C. H. Lin, “Full-field refractive index measurement using absolute-phase total internal reflection heterodyne interferometry,” Appl. Phys. B 126, 109 (2020).
[Crossref]

Chen, K. H.

K. H. Chen, Y. H. Wang, J. H. Chen, and C. H. Lin, “Full-field refractive index measurement using absolute-phase total internal reflection heterodyne interferometry,” Appl. Phys. B 126, 109 (2020).
[Crossref]

Chen, L.

Chen, L. Y.

Chen, S. J.

B. S. Lin, M. J. Su, P. H. Cheng, P. J. Tseng, and S. J. Chen, “Temporal and spatial denoising of depth maps,” Sensors 15, 18506–18525 (2015).
[Crossref]

Chen, W. C.

Cheng, P. H.

B. S. Lin, M. J. Su, P. H. Cheng, P. J. Tseng, and S. J. Chen, “Temporal and spatial denoising of depth maps,” Sensors 15, 18506–18525 (2015).
[Crossref]

Chhaniwal, V. K.

Chiu, M. H.

Chou, T. K.

Driggers, R. G.

R. G. Driggers, Encyclopedia of Optical Engineering, 2nd ed. (Marcel Dekker, 2003).

Dubey, S.

Firestone, G. C.

G. C. Firestone and A. Y. Yi, “Precision laboratory apparatus for high temperature compression molding of glass lenses,” Rev. Sci. Instrum. 76, 063101 (2005).
[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]

Gross, R. B.

Guo, X.

Hao, J.

Herrmann, P. P.

Hsieh, H. L.

Jain, A.

A. Y. Yi and A. Jain, “Compression molding of aspherical glass lenses–a combined experimental and numerical analysis,” J. Am. Ceram. Soc. 88, 579–586 (2005).
[Crossref]

Javidi, B.

Kabashin, A. V.

Kasana, R. S.

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]

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]

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]

Kihiko, J. M.

Ku, C. Y.

Lee, J. Y.

Lerma, J. R.

D. Tentori and J. R. Lerma, “Refractometry by minimum deviation: accuracy analysis,” Opt. Eng. 29, 160–168 (1990).
[Crossref]

Li, H.

Lin, B. S.

B. S. Lin, M. J. Su, P. H. Cheng, P. J. Tseng, and S. J. Chen, “Temporal and spatial denoising of depth maps,” Sensors 15, 18506–18525 (2015).
[Crossref]

Lin, C. H.

K. H. Chen, Y. H. Wang, J. H. Chen, and C. H. Lin, “Full-field refractive index measurement using absolute-phase total internal reflection heterodyne interferometry,” Appl. Phys. B 126, 109 (2020).
[Crossref]

Mantecón, T.

M. Camplani, T. Mantecón, and L. Salgado, “Depth-color fusion strategy for 3-D scene modeling with Kinect,” IEEE Trans. Cybern. 43, 1560–1571 (2013).
[Crossref]

Meunier, M.

Michalak, R.

Moffat, R. J.

R. J. Moffat, “Describing the uncertainties in experimental results,” Exp. Therm. Fluid. Sci. 1, 3–17 (1988).
[Crossref]

Narayanamurthy, C. S.

Patskovsky, S.

Salgado, L.

M. Camplani, T. Mantecón, and L. Salgado, “Depth-color fusion strategy for 3-D scene modeling with Kinect,” IEEE Trans. Cybern. 43, 1560–1571 (2013).
[Crossref]

Shearon, G.

Shih, H. C.

Smith, G.

Song, Q. W.

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, D. C.

Su, M. J.

B. S. Lin, M. J. Su, P. H. Cheng, P. J. Tseng, and S. J. Chen, “Temporal and spatial denoising of depth maps,” Sensors 15, 18506–18525 (2015).
[Crossref]

Tan, C. T.

Tentori, D.

D. Tentori and J. R. Lerma, “Refractometry by minimum deviation: accuracy analysis,” Opt. Eng. 29, 160–168 (1990).
[Crossref]

Tseng, P. J.

B. S. Lin, M. J. Su, P. H. Cheng, P. J. Tseng, and S. J. Chen, “Temporal and spatial denoising of depth maps,” Sensors 15, 18506–18525 (2015).
[Crossref]

Wang, C. Y.

Wang, P. J.

Wang, Y. H.

K. H. Chen, Y. H. Wang, J. H. Chen, and C. H. Lin, “Full-field refractive index measurement using absolute-phase total internal reflection heterodyne interferometry,” Appl. Phys. B 126, 109 (2020).
[Crossref]

Xie, S.

Yang, Y.

Yi, A. Y.

G. C. Firestone and A. Y. Yi, “Precision laboratory apparatus for high temperature compression molding of glass lenses,” Rev. Sci. Instrum. 76, 063101 (2005).
[Crossref]

A. Y. Yi and A. Jain, “Compression molding of aspherical glass lenses–a combined experimental and numerical analysis,” J. Am. Ceram. Soc. 88, 579–586 (2005).
[Crossref]

Zhang, C.

Appl. Opt. (9)

C. Y. Wang and P. J. Wang, “Analysis of optical properties in injection-molded and compression-molded optical lenses,” Appl. Opt. 53, 2523–2531 (2014).
[Crossref]

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]

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]

V. K. Chhaniwal, J. M. Kihiko, S. Dubey, G. Shearon, B. Javidi, and A. Anand, “Digital holographic testing of biconvex lenses,” Appl. Opt. 52, 8714–8722 (2013).
[Crossref]

G. Smith, “Liquid immersion method for the measurement of the refractive index of a simple lens,” Appl. Opt. 21, 755–757 (1982).
[Crossref]

M. H. Chiu, J. Y. Lee, and D. C. Su, “Refractive-index measurement based on the effects of total internal reflection and the uses of heterodyne interferometry,” Appl. Opt. 36, 2936–2939 (1997).
[Crossref]

P. P. Herrmann, “Determination of thickness, refractive index, and dispersion of waveguiding thin films with an Abbe refractometer,” Appl. Opt. 19, 3261–3262 (1980).
[Crossref]

H. Li and S. Xie, “Measurement method of the refractive index of biotissue by total internal reflection,” Appl. Opt. 35, 1793–1795 (1996).
[Crossref]

M. H. Chiu, W. C. Chen, and C. T. Tan, “Small displacement measurements based on an angular-deviation amplifier and interferometric phase detection,” Appl. Opt. 54, 2885–2890 (2015).
[Crossref]

Appl. Phys. B (1)

K. H. Chen, Y. H. Wang, J. H. Chen, and C. H. Lin, “Full-field refractive index measurement using absolute-phase total internal reflection heterodyne interferometry,” Appl. Phys. B 126, 109 (2020).
[Crossref]

Exp. Therm. Fluid. Sci. (1)

R. J. Moffat, “Describing the uncertainties in experimental results,” Exp. Therm. Fluid. Sci. 1, 3–17 (1988).
[Crossref]

IEEE Trans. Cybern. (1)

M. Camplani, T. Mantecón, and L. Salgado, “Depth-color fusion strategy for 3-D scene modeling with Kinect,” IEEE Trans. Cybern. 43, 1560–1571 (2013).
[Crossref]

J. Am. Ceram. Soc. (1)

A. Y. Yi and A. Jain, “Compression molding of aspherical glass lenses–a combined experimental and numerical analysis,” J. Am. Ceram. Soc. 88, 579–586 (2005).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

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. 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. Eng. (1)

D. Tentori and J. R. Lerma, “Refractometry by minimum deviation: accuracy analysis,” Opt. Eng. 29, 160–168 (1990).
[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)

Proc. SPIE (1)

V. K. Chhaniwal and A. Anand, “Determination of lens parameters with digital holography,” Proc. SPIE 6616, 66164H (2007).
[Crossref]

Rev. Sci. Instrum. (1)

G. C. Firestone and A. Y. Yi, “Precision laboratory apparatus for high temperature compression molding of glass lenses,” Rev. Sci. Instrum. 76, 063101 (2005).
[Crossref]

Sensors (1)

B. S. Lin, M. J. Su, P. H. Cheng, P. J. Tseng, and S. J. Chen, “Temporal and spatial denoising of depth maps,” Sensors 15, 18506–18525 (2015).
[Crossref]

Other (3)

“Refractive indices of different materials,” https://refractiveindex.info/ .

R. G. Driggers, Encyclopedia of Optical Engineering, 2nd ed. (Marcel Dekker, 2003).

“Polarized color camera with 5.0 MP PHX050S-QC,” https://www.edmundoptics.com/p/lucid-vision-labs-phoenixtrade-phx050s-qc-sony-imx250myr-50-mp-polarized-color-camera/41797/ .

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Figures (8)

Fig. 1.
Fig. 1. TIR introduced phase difference.
Fig. 2.
Fig. 2. Phase difference curves with different refractive index.
Fig. 3.
Fig. 3. Schematic diagram of the measurement system.
Fig. 4.
Fig. 4. Four phase quadrature intensities from the PLC.
Fig. 5.
Fig. 5. Phase difference distribution of cylindrical BK7 lens from the PLC.
Fig. 6.
Fig. 6. Schematic diagram for testing the minimum resolvable phase difference $\Delta {\delta _{\max }}$.
Fig. 7.
Fig. 7. Measured phase differences for each step.
Fig. 8.
Fig. 8. Simulated distributions of the phase difference distortion influenced by (a) the polarizers in the polarization camera and (b) the quarter-wave plate.

Tables (1)

Tables Icon

Table 1. Measurement of the Refractive Indices of Different Types of Lensesa

Equations (10)

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

δ = 2 tan 1 sin 2 θ i ( n 2 / n 1 ) 2 cos θ i sin θ i .
δ max = 2 tan 1 [ 1 2 ( n 1 n 2 n 2 n 1 ) ] .
n 1 = n 2 / [ sec ( δ max 2 ) tan ( δ max 2 ) ] .
E o ( α , δ ) = P ( α ) Q W P ( 45 ) T I R ( δ ) E i ( 45 ) = ( cos 2 α sin α cos α sin α cos α sin 2 α ) 1 2 ( 1 i i 1 ) ( e i δ / 2 0 0 e i δ / 2 ) 1 2 ( 1 1 ) = 1 2 ( i e i ( δ + 2 α ) / 2 + e i ( δ + 2 α ) / 2 ) ( cos α sin α ) ,
I ( α , δ ) = | E o | 2 = 1 2 [ 1 + sin ( δ + 2 α ) ] .
δ = tan 1 I ( 0 , δ ) I ( 90 , δ ) I ( 45 , δ ) I ( 45 , δ ) .
I ( α , δ ) = A [ 1 + V sin ( δ + 2 α ) ] ,
Δ n 1 = ( n 1 δ max Δ δ max _ t ) 2 + ( n 1 δ max Δ δ max _ s ) 2 = n 2 ( Δ δ max _ t ) 2 + ( Δ δ max _ s ) 2 2 [ 1 + sin ( δ max / 2 ) ] .
I = | E | 2 = | P ( α + Δ α , e ) Q ( 45 + Δ θ , 90 + Δ Γ ) T I R ( δ ) E ( 45 ) | 2 .
δ = δ + Δ δ .

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