Abstract

Thickness measurement of an opaque optics using a cyclic path optical configuration (CPOC) setup and polarization phase shifting interferometry (PPSI) is presented. The CPOC setup is used to simultaneously focus two orthogonally polarized counterpropagating converging beams at its hypotenuse arm. The opaque optics is placed at the hypotenuse arm of the CPOC setup such that one of its surfaces reflects back one of the counterpropagating focusing beams. Because of the thickness of the opaque optics, the other focusing beam suffers a longitudinal shift in the beam focus. Applying PPSI, the longitudinal shift in the beam focus which is twice the thickness of the opaque optics is determined. The results obtained for a silicon plate of thickness 0.660 mm with a measurement uncertainty of 0.013 mm are presented.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. 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]
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  10. K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, Vol. 26, E. Wolf, ed. (Elsevier, 1998), pp. 349–393.
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    [CrossRef]
  12. Y. Pavan Kumar and S. Chatterjee, “Technique for the focal-length measurement of positive lenses using Fizeau interferometry,” Appl. Opt. 48, 730–736 (2009).
    [CrossRef]
  13. R. S. Sirohi, “Interference of light,” in Wave Optics and Its Applications (Orient Longman, 2001), pp. 164–165.

2011

2009

E. N. Morel and J. R. Torga, “Dimensional characterization of opaque samples with a ring interferometer,” Opt. Lasers Eng. 47, 607–611 (2009).
[CrossRef]

Y. Pavan Kumar and S. Chatterjee, “Technique for the focal-length measurement of positive lenses using Fizeau interferometry,” Appl. Opt. 48, 730–736 (2009).
[CrossRef]

2008

2007

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

2003

S. H. Lu, C. I. Chiueh, and C. C. Lee, “Measuring thickness of opaque plane-parallel parts using external cavity diode laser and a double-ended interferometer,” Opt. Commun. 226, 7–13 (2003).
[CrossRef]

1988

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

1987

1986

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

Bhaduri, B.

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

Chatterjee, S.

Chiueh, C. I.

S. H. Lu, C. I. Chiueh, and C. C. Lee, “Measuring thickness of opaque plane-parallel parts using external cavity diode laser and a double-ended interferometer,” Opt. Commun. 226, 7–13 (2003).
[CrossRef]

Creath, K.

K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, Vol. 26, E. Wolf, ed. (Elsevier, 1998), pp. 349–393.

Eiju, T.

Grindel, M. W.

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

Hariharan, P.

Ilev, K.

Kang, J. U.

Kim, D. H.

Kothyial, M. P.

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

Kumar, Y. Pavan

Kumar, Y. Pawan

S. Chatterjee and Y. Pawan Kumar, “Simple technique for the generation of white light Young’s fringes with a cyclic path optical configuration,” Appl. Opt. 47, 2956–2960 (2008).
[CrossRef]

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

Lee, C. C.

S. H. Lu, C. I. Chiueh, and C. C. Lee, “Measuring thickness of opaque plane-parallel parts using external cavity diode laser and a double-ended interferometer,” Opt. Commun. 226, 7–13 (2003).
[CrossRef]

Lu, S. H.

S. H. Lu, C. I. Chiueh, and C. C. Lee, “Measuring thickness of opaque plane-parallel parts using external cavity diode laser and a double-ended interferometer,” Opt. Commun. 226, 7–13 (2003).
[CrossRef]

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, 2007).

Morel, E. N.

E. N. Morel and J. R. Torga, “Dimensional characterization of opaque samples with a ring interferometer,” Opt. Lasers Eng. 47, 607–611 (2009).
[CrossRef]

Oreb, B. F.

Rosenbruch, K. J.

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

Sirohi, R. S.

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

R. S. Sirohi, “Interference of light,” in Wave Optics and Its Applications (Orient Longman, 2001), pp. 164–165.

Song, C. G.

Torga, J. R.

E. N. Morel and J. R. Torga, “Dimensional characterization of opaque samples with a ring interferometer,” Opt. Lasers Eng. 47, 607–611 (2009).
[CrossRef]

Appl. Opt.

Opt. Commun.

S. H. Lu, C. I. Chiueh, and C. C. Lee, “Measuring thickness of opaque plane-parallel parts using external cavity diode laser and a double-ended interferometer,” Opt. Commun. 226, 7–13 (2003).
[CrossRef]

Opt. Lasers Eng.

E. N. Morel and J. R. Torga, “Dimensional characterization of opaque samples with a ring interferometer,” Opt. Lasers Eng. 47, 607–611 (2009).
[CrossRef]

Opt. Lasers Technol.

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

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

Proc. SPIE

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

Other

D. Malacara, Optical Shop Testing (Wiley, 2007).

K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, Vol. 26, E. Wolf, ed. (Elsevier, 1998), pp. 349–393.

R. S. Sirohi, “Interference of light,” in Wave Optics and Its Applications (Orient Longman, 2001), pp. 164–165.

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Figures (4)

Fig. 1.
Fig. 1.

Initial alignment of the experimental setup for simultaneous focusing of the orthogonally polarized counterpropagating beams at a common focus P.

Fig. 2.
Fig. 2.

Opaque optics of thickness t placed in the experimental setup.

Fig. 3.
Fig. 3.

Interferogram formed because of the interference of the collimated and spherical beams, WA and WB, respectively.

Fig. 4.
Fig. 4.

Least-squares circle fit to the OPD values evaluated along the central section of the interferogram.

Equations (6)

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Δf=2t.
Δf=f2R,
t=f22R.
OPD=(λ2π)Φ.
dt=(tf)2df2+(tR)2dR2,
dt=(fR)2df2+(f22R2)2dR2.

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