Abstract

We present a measurement technique to determine the thickness of a transparent glass plate (GP) by using a lateral shearing cyclic path optical configuration (CPOC) setup and polarization phase shifting interferometry (PPSI). In the technique, the GP introduces a longitudinal shift in the focus of the beam and, as a result, a spherical wavefront emerges from the lens, which is otherwise set for producing a collimated beam. Using CPOC, two laterally sheared orthogonally polarized beams are generated from the incident spherical wavefront. By applying PPSI, the slope of the optical path difference variation between the laterally sheared interfering beams is evaluated, and the radius of the spherical wavefront and the longitudinal shift of the beam focus are calculated. The thickness of the GP is determined from the standard relation between the longitudinal shift of the focus introduced by the GP and the thickness of the GP. Results obtained for a GP of 9.810mm thickness are presented.

© 2010 Optical Society of America

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References

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  1. D. Malacara, Optical Shop Testing (Wiley, 2007).
    [CrossRef]
  2. D. S. Kumar, G. Gobi, and B. Renganathan, “Determination of the thickness of a transparent plate using a reflective fiber optic displacement sensor,” Opt. Laser Technol. 42, 911–917(2010).
    [CrossRef]
  3. S. Y. El-Zaiat, “Measuring the thickness and refractive index of a thick transparent plate by an unexpanded laser beam,” Opt. Laser Technol. 29, 63–65 (1997).
    [CrossRef]
  4. Y. K. Ryu, C. Oh, and J. S. Lim, “Development of a noncontact optical sensor for measuring the shape of a surface and thickness of transparent objects,” Opt. Eng. 40, 500–502 (2001).
    [CrossRef]
  5. C. H. Liu, S. C. Yeh, and H. L. Huang, “Thickness measurement system for transparent plates using dual digital versatile disc (DVD) pickups,” Appl. Opt. 49, 637–643 (2010).
    [CrossRef] [PubMed]
  6. J. C. Brasunas and G. M. Cushman, “Interfrometric but nonspectroscopic technique for measuring the thickness of a transparent plate,” Opt. Eng. 34, 2126–2130 (1995).
    [CrossRef]
  7. G. Coppola, P. Ferraro, M. Iodice, and S. De Nicola, “Method for measuring the refractive index and the thickness of transparent plates with a lateral-shear, wave length-scanning interferometer,” Appl. Opt. 42, 3882–3887 (2003).
    [CrossRef] [PubMed]
  8. Y. P. Kumar and S. Chatterjee, “Noncontact thickness measurement of plane-parallel transparent plates with a lateral shearing interferometer,” Opt. Eng. 46, 035602 (2007).
    [CrossRef]
  9. M. P. Kothiyal and C. Delisle, “Shearing interferometer for phase shifting interferometry with polarization phase shifter,” Appl. Opt. 24, 4439–4441 (1985).
    [CrossRef] [PubMed]
  10. W. J. Smith, “Prisms and mirrors,” in Modern Optical Engineering, 2nd ed. (McGraw-Hill, 1991), Chap. 4, pp. 96–97.
  11. M. W. Grindel, “Testing collimation using shearing interferometry,” Proc. SPIE 680, 44–47 (1986).
  12. M. P. Kothyial, R. S. Sirohi, and K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
    [CrossRef]
  13. S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase-shifting interferometer,” Opt. Laser Technol. 39, 268–274 (2007).
    [CrossRef]
  14. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2506 (1987).
    [CrossRef] [PubMed]
  15. K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1998), Vol. 26, pp. 349–393.
    [CrossRef]

2010 (2)

D. S. Kumar, G. Gobi, and B. Renganathan, “Determination of the thickness of a transparent plate using a reflective fiber optic displacement sensor,” Opt. Laser Technol. 42, 911–917(2010).
[CrossRef]

C. H. Liu, S. C. Yeh, and H. L. Huang, “Thickness measurement system for transparent plates using dual digital versatile disc (DVD) pickups,” Appl. Opt. 49, 637–643 (2010).
[CrossRef] [PubMed]

2007 (2)

Y. P. Kumar and S. Chatterjee, “Noncontact thickness measurement of plane-parallel transparent plates with a lateral shearing interferometer,” Opt. Eng. 46, 035602 (2007).
[CrossRef]

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase-shifting interferometer,” Opt. Laser Technol. 39, 268–274 (2007).
[CrossRef]

2003 (1)

2001 (1)

Y. K. Ryu, C. Oh, and J. S. Lim, “Development of a noncontact optical sensor for measuring the shape of a surface and thickness of transparent objects,” Opt. Eng. 40, 500–502 (2001).
[CrossRef]

1997 (1)

S. Y. El-Zaiat, “Measuring the thickness and refractive index of a thick transparent plate by an unexpanded laser beam,” Opt. Laser Technol. 29, 63–65 (1997).
[CrossRef]

1995 (1)

J. C. Brasunas and G. M. Cushman, “Interfrometric but nonspectroscopic technique for measuring the thickness of a transparent plate,” Opt. Eng. 34, 2126–2130 (1995).
[CrossRef]

1988 (1)

M. P. Kothyial, R. S. Sirohi, and K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[CrossRef]

1987 (1)

1986 (1)

M. W. Grindel, “Testing collimation using shearing interferometry,” Proc. SPIE 680, 44–47 (1986).

1985 (1)

Bhaduri, B.

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase-shifting interferometer,” Opt. Laser Technol. 39, 268–274 (2007).
[CrossRef]

Brasunas, J. C.

J. C. Brasunas and G. M. Cushman, “Interfrometric but nonspectroscopic technique for measuring the thickness of a transparent plate,” Opt. Eng. 34, 2126–2130 (1995).
[CrossRef]

Chatterjee, S.

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase-shifting interferometer,” Opt. Laser Technol. 39, 268–274 (2007).
[CrossRef]

Y. P. Kumar and S. Chatterjee, “Noncontact thickness measurement of plane-parallel transparent plates with a lateral shearing interferometer,” Opt. Eng. 46, 035602 (2007).
[CrossRef]

Coppola, G.

Creath, K.

K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1998), Vol. 26, pp. 349–393.
[CrossRef]

Cushman, G. M.

J. C. Brasunas and G. M. Cushman, “Interfrometric but nonspectroscopic technique for measuring the thickness of a transparent plate,” Opt. Eng. 34, 2126–2130 (1995).
[CrossRef]

De Nicola, S.

Delisle, C.

Eiju, T.

El-Zaiat, S. Y.

S. Y. El-Zaiat, “Measuring the thickness and refractive index of a thick transparent plate by an unexpanded laser beam,” Opt. Laser Technol. 29, 63–65 (1997).
[CrossRef]

Ferraro, P.

Gobi, G.

D. S. Kumar, G. Gobi, and B. Renganathan, “Determination of the thickness of a transparent plate using a reflective fiber optic displacement sensor,” Opt. Laser Technol. 42, 911–917(2010).
[CrossRef]

Grindel, M. W.

M. W. Grindel, “Testing collimation using shearing interferometry,” Proc. SPIE 680, 44–47 (1986).

Hariharan, P.

Huang, H. L.

Iodice, M.

Kothiyal, M. P.

Kothyial, M. P.

M. P. Kothyial, R. S. Sirohi, and K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[CrossRef]

Kumar, D. S.

D. S. Kumar, G. Gobi, and B. Renganathan, “Determination of the thickness of a transparent plate using a reflective fiber optic displacement sensor,” Opt. Laser Technol. 42, 911–917(2010).
[CrossRef]

Kumar, Y. P.

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase-shifting interferometer,” Opt. Laser Technol. 39, 268–274 (2007).
[CrossRef]

Y. P. Kumar and S. Chatterjee, “Noncontact thickness measurement of plane-parallel transparent plates with a lateral shearing interferometer,” Opt. Eng. 46, 035602 (2007).
[CrossRef]

Lim, J. S.

Y. K. Ryu, C. Oh, and J. S. Lim, “Development of a noncontact optical sensor for measuring the shape of a surface and thickness of transparent objects,” Opt. Eng. 40, 500–502 (2001).
[CrossRef]

Liu, C. H.

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, 2007).
[CrossRef]

Oh, C.

Y. K. Ryu, C. Oh, and J. S. Lim, “Development of a noncontact optical sensor for measuring the shape of a surface and thickness of transparent objects,” Opt. Eng. 40, 500–502 (2001).
[CrossRef]

Oreb, B. F.

Renganathan, B.

D. S. Kumar, G. Gobi, and B. Renganathan, “Determination of the thickness of a transparent plate using a reflective fiber optic displacement sensor,” Opt. Laser Technol. 42, 911–917(2010).
[CrossRef]

Rosenbruch, K. J.

M. P. Kothyial, R. S. Sirohi, and K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[CrossRef]

Ryu, Y. K.

Y. K. Ryu, C. Oh, and J. S. Lim, “Development of a noncontact optical sensor for measuring the shape of a surface and thickness of transparent objects,” Opt. Eng. 40, 500–502 (2001).
[CrossRef]

Sirohi, R. S.

M. P. Kothyial, R. S. Sirohi, and K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[CrossRef]

Smith, W. J.

W. J. Smith, “Prisms and mirrors,” in Modern Optical Engineering, 2nd ed. (McGraw-Hill, 1991), Chap. 4, pp. 96–97.

Yeh, S. C.

Appl. Opt. (4)

Opt. Eng. (3)

Y. K. Ryu, C. Oh, and J. S. Lim, “Development of a noncontact optical sensor for measuring the shape of a surface and thickness of transparent objects,” Opt. Eng. 40, 500–502 (2001).
[CrossRef]

J. C. Brasunas and G. M. Cushman, “Interfrometric but nonspectroscopic technique for measuring the thickness of a transparent plate,” Opt. Eng. 34, 2126–2130 (1995).
[CrossRef]

Y. P. Kumar and S. Chatterjee, “Noncontact thickness measurement of plane-parallel transparent plates with a lateral shearing interferometer,” Opt. Eng. 46, 035602 (2007).
[CrossRef]

Opt. Laser Technol. (4)

D. S. Kumar, G. Gobi, and B. Renganathan, “Determination of the thickness of a transparent plate using a reflective fiber optic displacement sensor,” Opt. Laser Technol. 42, 911–917(2010).
[CrossRef]

S. Y. El-Zaiat, “Measuring the thickness and refractive index of a thick transparent plate by an unexpanded laser beam,” Opt. Laser Technol. 29, 63–65 (1997).
[CrossRef]

M. P. Kothyial, R. S. Sirohi, and K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[CrossRef]

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase-shifting interferometer,” Opt. Laser Technol. 39, 268–274 (2007).
[CrossRef]

Proc. SPIE (1)

M. W. Grindel, “Testing collimation using shearing interferometry,” Proc. SPIE 680, 44–47 (1986).

Other (3)

D. Malacara, Optical Shop Testing (Wiley, 2007).
[CrossRef]

W. J. Smith, “Prisms and mirrors,” in Modern Optical Engineering, 2nd ed. (McGraw-Hill, 1991), Chap. 4, pp. 96–97.

K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1998), Vol. 26, pp. 349–393.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup.

Fig. 2
Fig. 2

Shear fringes formed on the RDS due to introduction of a GP between L and PM.

Fig. 3
Fig. 3

Least square fit to the OPD values.

Equations (12)

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

Δ f = ( 2 ( μ 1 ) μ ) t ,
R = S d λ D + K ,
R = S θ D + K ,
Δ f f 2 = 1 R .
t = μ f 2 2 ( μ 1 ) R .
α = π 2 2 γ ,
I ( x , y ) = I 0 ( x , y ) { 1 + V ( x , y ) cos [ Φ ( x , y ) + α i ] } ,
Φ = tan 1 [ 2 ( I 2 I 4 ) 2 I 3 I 1 I 5 ] .
OPD = ( λ 2 π ) Φ .
d t = ( t f ) 2 d f 2 + ( t R ) 2 d R 2 ,
d t = ( μ 2 ( μ 1 ) ) ( 2 f R ) 2 d f 2 + ( f 2 R 2 ) 2 d R 2
d R = ( 1 θ ) 2 d S 2 + ( S θ 2 ) 2 d θ 2 + d D 2 .

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